CFD and PIV investigation of the flow inside the USP throat and in a replica of the human upper airways

Transcription

1 CFD and PIV investigation of the flow inside the USP throat and in a replica of the human upper airways Christian Gjellerup Sigurd Ove Frederiksen Department of Mechanical Engineering Fluid Mechanics Section Technical University of Denmark June 2007

2 Abstract An investigation of the velocity field in the mid plane of the USP throat and in an idealised replica of the human upper airways under steady inspiration was performed. The flow was studied experimentally using endoscopic Particle Image Velocimetry (PIV) technique. Measurements were carried out for flow rates between l/min, which corresponds to a large range of physiological conditions. Numerical calculations were also carried out using Reynolds Averaged Navier Stokes (RANS) Computational Fluid Dynamics (CFD) methods in conjunction with both the k ε and SST turbulence models. Good agreement between the CFD calculations and the PIV measurements was found when simulating the flow using the SST turbulence model which captured more of the complex flow phenomena seen in the PIV measurements.

3 Preface This project is conducted in cooperation with the Department of Mechanical Engineering Fluid Mechanics Section at DTU and Novo Nordisk A/S and is a result of a seven month master project. The scope of the project is to map the flow inside the current inhaler tester device known as an USP throat and a relatively newly proposed Alberta geometry. These models are of relevance when performing medical deposition analyses where they are used to mimic the upper airways of the respiratory system. The purpose of the project is to increase the knowledge of the flow inside the two throat models and gain information about the different flow structures that occur under steady inspiration. The project has been supervised by Knud Erik Meyer and Ulrik Ullum and Novo representative Dan Nørtoft Sørensen, which we thank for their help and guidance.

4 Table of Contents Nomenclature... 1 Introduction and Background... 3 Throat Models... 7 Turbulence Models Differencing Scheme and Grid convergence Boundary conditions and domain settings Experimental Method Models and Manufacturing Experimental Setup Air Flow Measurement Particle Generator PIV Equipment PIV Measurements and Analysis Particle Motion Discussion of Experimental Errors and Uncertainties in the Setup Results for USP Throat CFD Results for USP k ε Solution SST Solution PIV Results for USP Throat and Comparison with CFD Results for Alberta Geometry CFD Results PIV Results for Alberta Geometry and Comparison with CFD Summary of Results and Discussion Comparison Conclusion References... 80

5 Nomenclature English symbols A area [m 2 ] C μ, C ε 1, C ε 2 closure constants [ ] Co Courant number [ ] d diameter [m] De Dean Number [ ] D h hydraulic diameter [m] e relative error [%] F s safety factor [ ] g gravitational force [m/s 2 ] h element size [m] I turbulence intensity [ ] k turbulent kinetic energy [m 2 /s 2 ] n number of samples [ ] N number of elements [ ] P o order of numerical scheme p pressure [Pa] p c perimeter [m] P k produktion of k [m2/s 3 ] P time averaged pressure [Pa] Q flow rate [m 3 /s] r grid refinement factor [ ] R radius of curvature [m] Re Reynolds number [ ] S image scale factor [ ] Sf linear scale factor [ ] t time [s] t p time between pulses [s] u Cartesian velocity component [m/s] u g settling velocity [m/s] U time averaged Cartesian velocity component [m/s] V mean velocity V velocity y + dimensionless distance from wall [ ] x,y,z Cartesian coordinates Greek symbols δ ij Kroneckers delta [ ] ε dissipation [m 2 /s 3 ] κ von Karman constant 1

6 ω specific dissipation rate turbulence model variable [s 1 ] ρ density [kg/m 3 ] θ viewing angle [degrees] ν t eddy viscosity [m 2 /s] λ wave length [m] Subscripts coarse coarse mesh fine fine mesh I,j Einstein notation p particle Abbreviations CFD Computational Fluid Dynamics CCD Charged Coupled Device DEHS Di Ethyll Hexyl Sebacat GCI Grid Convergence Index LFE Laminar Flow Element PIV Particle Image Velocimetry RANS Reynolds Averaged Naviers Stokes RP Rapid Prototype SST Shear Stress Transport UDS Upwind Differencing Scheme USP United States Pharmacopeia 2

7 Introduction and Background The number of diabetes patients is increasing worldwide, with an estimated 246 million people being affected worldwide [38]. In Denmark, the estimated number of people affected is 150,000, with 25,000 of them receiving insulin, while the remaining patients are receiving other treatments. Furthermore, several hundred thousand people are estimated to be affected by diabetes that has not been diagnosed [41]. Diabetes patients are normally divided into two groups, those with insulin dependant diabetes mellitus, and those with non insulin dependent diabetes mellitus. The former group is also referred to as Type 1 Diabetes Mellitus (T1DM), the latter as Type 2 Diabetes Mellitus (T2DM). Insulin is a natural substance, which is produced in the β cells in the pancreas and allows glucose to be obtained from the bloodstream. Without the glucose the cells will starve and eventually be unable to function correctly, leading to a decline in body functions such as blurred vision and lack of energy. When the cells are unable to retrieve the glucose, the blood sugar level will increase, and glucose will eventually appear in the urine. Among the symptoms of high levels of glucose in the bloodstream are thirst and weight loss. T1DM patients lack the ability to produce natural insulin because their β cells have been destroyed by the body s own immune system. The cause of this is still unknown. Since this disease often appears in children and the young, it is also termed juvenile diabetes and is assumed to be inheritable. Because the patients are unable to produce insulin, they require the administration of additional insulin several times a day (3 6 times) in order to ensure the uptake of glucose by the cells and the maintenance of a normal level of blood sugar. As opposed to T1DM, no genetic factors have been shown to contribute to the development of T2DM. The main causes of the development of this disease are aging and overweight. Although T2DM patients still produce natural insulin, their cells are refractory to the insulin, so that they do not take up adequate amounts of glucose from the blood. The development of T2DM is a slow process and may take several years. In many cases, patient lifestyle intervention such as weight loss, exercise and diet will prevent the development of the disease. In other cases, however, insulin has to be administered several times a day. Insulin was first brought into clinical use in 1922, before which diabetes had been associated with a high mortality [25]. Typically, insulin is administered using a syringe to deposit the insulin in the subcutaneous tissue, from where it is slowly absorbed into the bloodstream. This delivery method ensures a controlled quantity of insulin, which is essential in order to avoid under or overmedication. Since the introduction of insulin, several alternative methods of insulin delivery have been investigated [25]. There are a lot of reasons why less invasive routes for insulin delivery should be developed. Patients often find the use of a syringe uncomfortable, and this method tends to lead to infections. Many T2DM patients, who are familiar with different treatments fear, the insulin injections and tend to look upon their need for insulin treatment as a failure. Administration by the pulmonary route has proved to be a most promising method of delivering insulin to the bloodstream. This method benefits from the advantage of a large surface area, a highly permeable membrane, a rich blood perfusion and the lack of mucociliary clearance [25]. Several different inhaler systems have been developed, such as pressurized meter dose inhalers (pmdi), dry powder inhalers (DPI), nebulizers and aqueous mist inhalers (AMI). Several devices are being developed, and some are already available. A DPI device, approved by the Food and Drugs Administration (FDA), called the Nektar/Exubera device from Pfizer Inc. is currently marketed. This device consists mainly of two chambers; an upper and a lower chamber, each measuring approx. 10 cm. Blisters with 3

8 insulin powder are inserted between the two reservoirs and are punctured when the patient pushes a button. The powder is dispersed into the upper chamber, from where the patient inhales it by taking a deep breath [20]. Although market analyses have shown diabetics to be interested in an insulin inhaler device, the Exubera has not yet proved successful [5]. Being too large to carry in your pocket (measuring 17 cm in the collapsed state), the device is inconvenient in use. Therefore, there is an urgent need for a more well designed device, and this is an area of priority in many pharmaceutical companies [20]. When new medical devices are being introduced, they are often tested to the standards of the United States Pharmacopeia (USP), which is recognized in more than 130 countries [42]. One such test of inhaler devices involves the use of a USP throat in conjunction with a cascade impactor. The USP throat is basically a 90 degrees bend metal pipe with uniform cross section, slight contractions at the inlet and a small diffuser at the outlet (see Figure 1). The cascade impactor consists mainly of plates arranged in vertical succeeding order. By the simultaneous application of suction to this system and release of particles into the air stream upstream to the USP throat, a deposition analysis can be performed. In the USP throat, large particles will deposit first because they are unable to follow the airflow around the bend of the USP. This discharge of particles is meant to resemble the airflow in the oropharynx. As the flow passes through the different stages of the cascade impactor, more particles are caught, ending up with very fine particle sizes. The different stages may be compared with the different areas of the respiratory system, the first stages mimicking the deposition in the trachea, while the following stages correspond to the lower levels of the system. Using this setup, the levels of deposition in the airway can be mapped, to provide an estimate of the amount of drug available to reach the lungs and eventually entering the bloodstream. The USP throat s ability to resemble the oropahrynx with regard to the deposition efficiency has been studied by Zang, Finlay and Matida [36], who found that the USP throat was inadequate in mimicking the deposition characteristics of the upper airway. This was mainly because the USP throat failed to simulate the acceleration, deceleration and rotation of the airflow, which are brought about by the existing variation in the cross sectional area of the mouth throat region. A comparison of the experimental deposition values in the USP throat with the in vivo results obtained by Stalhofen [30] showed the particle deposition in the USP throat to be unrealistically low. Zang et. al. [36] also analysed a highly idealised mouth throat model with non uniform cross area section with a bend contraction to simulate the oral cavity. They found the idealised throat geometry to follow the total deposition efficiency average curve obtained in vivo by Stalhofen et. al. [30], and suggested this to be used as a substitute for the inadequate USP throat. The flow and deposition patterns of the human upper airways have been studied in different papers [3], [10], [15], [30], [31] and [36]. All of these investigations concern only the flow and deposition in the airways during simulation of steady inhalation, thus not taking any effect of breath holding, exhalation and compliant mucous surfaces into account. Stapleton, Guentsch, Hokinson and Finlay [31] proposed a geometry that modelled the flow from the teeth to the trachea. Their model was based on available literature, supplemented by CT scans of ten patients at the University of Alberta Hospital and observations of five living subjects. From the data obtained, a model of the extrathoracic airway was drawn up using simple geometric shapes. This model was the forerunner of, and very similar to, the Alberta geometry used in this project, see Figure 2. Using this model, Stapleton et. al. [31] examined the experimentally measured deposition and made a comparison with Computational Fluid Dynamic (CFD) calculations for both laminar and turbulent flow rates using a k ε turbulent model in the latter case. 4

9 Good agreement was found for the deposition efficiency, η, for the laminar case when comparing experimental results (η=15.7 ± 0.3%) and CFD calculations (η=16%). The deposition efficiency, η, is the ratio of the mass of deposited particles to the total mass of the inserted particles in experiments. However, in the turbulent case, large inconsistencies were found between experimental data (η=25.6 ± 0.7%) and CFD calculations (η= 65%). These divergences were concluded to be due to the k ε turbulence model s inability to accurately predict the deposition in a flow characterised by complex flow phenomena such as curved streamlines and recirculation zones. Kleinstreuer and Zang [15] examined the deposition in a slightly less complex geometry of the upper airways using CFD with a Low Reynolds Number (LRN) k ω turbulence model employed. Using the k ω turbulence model as opposed to previously studied k ε turbulence model, more accurate predictions of deposition were made possible, thus emphasizing the importance of choice of turbulence model when using CFD to predict particle deposition. Empirical models based on experimental data for deposition in the upper airways have been suggested. Dehaan and Finlay [3] experimentally examined aerosol deposition using different inlets, particle sizes (3 8 μm), turbulence intensities, flow rates and inlet conditions. The geometry used was based on Stapleton s [31] research and modelled primarily in the upper part of the extrathoracic region. Deposition analyses were made for flow rates ranging from l/min, different inlets such as contraction nozzles, straight tubes, a turbulence generator and six commercially available DPI s. A predictive model was derived to predict the in vivo deposition from DPIs, which agreed well with published experimental data. In the present study, the flow in the USP throat and an Alberta geometry 1 model investigated. The flow analysis will be conducted experimentally by using endoscopic Particle Image Velocimetry (PIV) technique. CFD calculations are made solving the Reynolds Average Navier Stokes (RANS) equations and using linear eddy viscosity turbulence models. The main goal of the project is, for different flow rates (15 90 l/min), to map the flow inside the two geometries and compare the different flow characteristics. The models are shown in a cut through the mid plane also denoted the sagittal plane (see Figure 1 and Figure 2). Firstly an introduction of the USP throat and the Alberta geometry will be given. In chapter 2 the governing equations for the flow and the used turbulence model are presented along with the computational grid and applied boundary conditions. In chapter 3, 4 and 5 the experimental method, setup and PIV technique are discussed and presented. Chapter 6 and 7 present the results for the USP throat and Alberta geometry respectively follow by the overall discussion and conclusion. 1 Courtesy of Dr. Finlay's Aerosol Research Laboratory of Alberta at the University of Alberta. See also [3],[11],[12] and [31]. 5

10 Figure 1: USP Throat in sagittal cut [36] Figure 2: Alberta geometry in sagittal cut 6

11 Chapter 1 Throat Models Figure 1 shows a sagittal section of the USP throat. This consists basically of two steel pipes, cut at a 45 degree angle in one end and then soldered together to create the 90 degree bend. The inlet of the USP throat consists of two small contractions reducing the diameter of the throat from 31.5 to 19 mm. From here, the diameter of the USP throat is nearly uniform, until the diameter is expanded to 25.2mm by a diffuser near the outlet. After this, a sharp circular edge which enables a suction device to be directly connected to the USP can be seen. The overall dimensions for the height and width are 130 and 110 mm, respectively. Appendix C shows a detailed drawing based on internal measurements of an original USP throat. As opposed to the USP, which only offers very limited resemblance to human anatomy and only models the upper parts of the extrathoracic region, the Alberta geometry is a more complete model, which mimicks the complete extrathoracic area from the oral cavity to the trachea of an adult human. Its overall dimensions of height and width are and 85.6 mm, respectively. The Alberta geometry represents a mean of the dimensions of the airway, which will change during the breathing cycle and therefore, are not easily modelled. The Alberta geometry has many distinct features representing the actual physical parts of the extrathoracic region; while this complicates the model design it offers a more accurate description of the airways. Figure 3: Left to right, internal Alberta geometry, cross section area at a number of locations. Outer shell geometry with corresponding anatomical names [12] In Figure 3, the internal model geometry with matching cross sections and the outer shell of the Alberta geometry can be seen. The internal geometry is the flow domain and consists of several double curved faces. The cross sections reveal the complexity of the model 7

12 and the variability of the downstream cross section area, which causes complex flow phenomena. The sagittal section of the Alberta geometry shows the anatomical names of the different sections, which include the most important structures as far as air flow analyses are concerned. Both the USP throat and the Alberta geometry have smooth walls, thus disregarding the finer details of the walls found physically in the mouth throat region. By using smooth walls, this model also disregards the significance of mucous and saliva, which would contribute to the deposition of particles entering the models. Figure 4 (left) shows the area variation as a function of the distance from the inlet of the USP throat and the Alberta geometry. The distance from the inlet is measured along a line passing through the geometric centre of the downstream cross sections. From the figure the complexity of the Alberta geometry in comparison with the USP throat can clearly be seen Oral cavity USP throat Alberta geometry USP throat Alberta geometry 6 Trachea 3000 Trachea Area [cm 2 ] 5 4 Pharynx Re 2500 Oral cavity Pharynx Distance from Alberta/USP inlet [mm] Distance from Alberta/USP inlet [mm] Figure 4: Area variation (left) and Reynolds number (right) based on hydraulic diameter as a function of distance from inlet. Flow rate 30 l/min Figure 4 (right) shows the Reynolds number variation of the USP throat and the Alberta geometry based on the hydraulic diameter D h =4 A/P c, where A is the cross sectional area and P c is the perimeter. The variation of the USP throat can be seen to be relatively small. In the Alberta geometry the transition from the oral cavity to the pharynx where the local area expands and the Reynolds number decreases, is clearly seen by the sharp downward bend of the curve. The abrupt changes in the region of the pharynx demonstrate the complexity of this region of the model. Even though the Reynolds numbers in the figure are of such values that they could be associated with laminar flow pipe this is not expected to be the case because the shape of the geometries will most likely cause transition to turbulent flow even at small Reynolds numbers. It is noted that the lines passing through the geometric centre of the downstream cross sections are approximately equal in length for both geometries, even though the USP throat models only the upper part of the extrathoracic region while the Alberta geometry models the whole extrathoracic region. 8

13 Chapter 2 Numerical Calculations The flow inside the USP throat and Alberta geometry is investigated by solving the governing equations that are the Navier Stokes equation and mass conservation equations. The equations are solved using ANSYS CFX (version 10.0, Ansys Europe, UK). An explanation of the governing equations and applied turbulence models will be given in the following. Later the computational grid and applied boundary conditions will be explained. Governing Equations The governing equations are the continuity and Navier Stokes equations [24]. Assuming the air is incompressible the equations reduces to δui δ x i = 0, δui u 1 p u + uj = +. δt x x x 2 i i υ 2 j ρ i j Where u i is the velocity components in the x i direction. ρ is the fluid density and ν is the kinematic viscosity and p is the pressure. Ideally these equations should be solved directly using DNS (Direct Numerical Simulations) with no approximation to predict turbulence or LES (Large Eddy Simulation), where the equations are filtered to remove very fine time and length scales to predict turbulence. However since such calculations require very fine grids and small timesteps, large computer power is needed and these methods are often not practical for solving typical engineering problems. Instead the flow can be simulated using the RANS (Reynolds Average Navier Stokes) equations, which solve the flow for time averaged quantities. These equations are less demanding of computer power, as the small unsteady structures in the flow are expressed through the so called Reynolds stresses. Expressing the unsteady structures through the Reynolds stresses assumes that the scales of the vortices are small compared to the geometry and the time scales of the fluctuations are small compared to 9

14 the time scale of the mean unsteadiness of the flow. This is often fulfilled in many internal flows of engineering interest [1]. Decomposing the flow quantities into a time averaged and a fluctuating part and using the continuity equation the RANS equations can be obtained U i Ui 1 P Ui ' ' + Uj = + ν u ρ iu j. t x j xi xj xj U and P express the time averaged velocity and pressure. The time averaging of the quantities is done in a time interval that is large compared to the fluctuations of interest, making the time average of the fluctuations zero. The term U t expresses the variation in time of the time i averaged velocities on a large time scale compared to the turbulent fluctuations and is set to ' ' zero in the steady state calculations. The term uu is known as Reynolds or turbulent stresses, see Appendix A for details. The full Reynolds stress tensor is symmetrical and contains six new unknowns, which leads to an underdetermined system of equations also known as the closure ' ' problem. In order to close the system of equations the term uu, that accounts for the effects of turbulence, has to be modelled using a turbulence model. i j i j Turbulence Models For internal flow in a straight pipe the flow will normally be considered turbulent when exceeding a Reynolds number of For the low flow rates of 15 and 30 L/min the Reynolds number will be below this value in most parts of the models. A laminar flow solution was attempted for both models, but failed to converge, thus indicating as expected that the geometric shape of the models will cause turbulence, even at small Reynolds numbers or unsteady flow behaviour. Several models for simulating Reynolds stresses have been proposed. Among these are the main groups, linear eddy viscosity models, Reynolds stress models and non linear eddy viscosity models. Which model to implement depends on the flow characteristics and therefore no general model exists. One popular approach is to impose a linear relation of the Reynolds stresses to the average velocity gradients. Models based on this assumption of isotropic turbulence are also known as linear eddy viscosity models. Eddy Viscosity Models The eddy viscosity turbulence models are based on the concept that turbulence consists of small eddies continuously forming and dissipating. Applying the Boussinesq eddy viscosity assumption, a linear relation between the Reynolds stresses tensor and the average velocity gradients can be found ' ' U U i j 2 uu i j = ν t + kδ ij. xj xi 3 10

15 1 ' ' Where k is the turbulent kinetic energy defined as k uu, with dimension m 2 /s 2 and δ ij 2 i i denotes the Kronecker delta. ν t is the eddy viscosity and has the same dimension as ν [m 2 /s]. The eddy viscosity is not a fluid property but a function of the state of turbulence. Taking the divergence of the Reynolds stress tensor leads to ' ' uu i j Ui 2 = ν δ t k i xj xj xj xj 3 Inserting the above expression for the divergence of the Reynolds stresses in the RANS equations yields ( P ρk) j. 2 U + i Ui 1 + = 3 Ui Uj + ( ν + ν ) ρ t. t x j xi xj x j In the group of turbulence models called two equation models, the eddy viscosity is calculated from two transported variables. This allows the two equation model to account for history effects like convection and diffusion of turbulent energy. In the three two equation models considered here, the first transported variable is the turbulent kinetic energy k. The second depends on the model and can be either ε which is the dissipation of turbulent kinetic energy or ω which is the frequency of the large eddies and has the dimension s 1. The k variable determines the energy in the turbulence, whereas ε and ω can be thought as variables that determine the length or time scale of the turbulence. k-ε Model The standard k ε is a two equation turbulence model and is the most widely used model for most flows of engineering interest. k denotes the kinetic energy and ε denotes the rate at which turbulent energy dissipates into smaller eddies. The main reason for its popularity is that it has proven numerical robust while still achieving accurate flow predictions for flows without separation from smooth surfaces and strong swirls. All solutions, when using the k ε turbulence model, achieved convergence fast, normally within a 100 iterations. The eddy viscosity is defined as 2 k ν t = C μ. ε Where C μ is found empirically to A transport equation for the turbulent kinetic energy k, is derived by multiplying the Navier Stokes equations with ' u i and decomposing the quantities and taking time average. Applying the Boussinesq approximation the following equation for the turbulent kinetic energy can be found 11

16 k k τ U ν k ν t x x x x ij i t + U j = + + j ρ j j σk j ε. Where Ui U U i j τij ν = t + = Pk. x i xj x i P k is the production term of turbulent kinetic energy. The dissipation of turbulent kinetic energy ε, is defined as ε ν ' ' ui ui x x. The dissipation is always larger than zero, since it is a sum of the average of squared quantities. As ε is subtracted in the energy equation this will always cause a negative rate of change of kinetic turbulent energy thus the name dissipation. Physically the energy is dissipated because of the work done by the fluctuating viscous stresses in resisting deformation of the fluid material by the fluctuating strain rates. The transport equation for the dissipation ε is given by: j j ε ε ε τ ε + Uj = C + + C t x k x x x 2 ij Ui ν t ε ε1 ν ε2, j ρ j j σε j k The models constants used are C μ =0.09, σ k =1.0, σ ε =1.3, C ε1 =1.44, C ε2 =1.92. The standard k ε model is a high Reynolds number model and uses a logarithmic law of the wall to characterise the flow close to the wall, and is therefore not intended to resolve the fine details in the boundary layer. A k ε low Reynolds number formulation exists with damping functions to dampen the eddy viscosity in the near wall regions, but is not available in CFX Scaleable Wall Function CFX 10.0 uses scalable wall functions, which ensure that the resolution of the boundary layer is less crucial when applying the standard k ε model. The logarithmic relation for the near wall velocity outside the viscous sublayer is given by Where u + U t + u τ κ 1 ln ( y ) = = + C. 12

17 + ρδyu y = μ u τ τ w = ρ τ, 1 2. Where u + is the near wall velocity, U t is the velocity tangent to the wall at a distance Δy from the wall, κ is the von Karman constant y + is the dimensionless distance from the wall, C is a loglayer constant dependent on the wall roughness and τ w is the wall shear stress. When speaking about grid resolution, the term y + refers to the dimensionless distance from the wall to the first node. To avoid that the equation for the near wall velocity becomes singular as U t approaches zero CFX uses an alternative formulation for the velocity scale * u = C k μ where: U uτ = 1 ln κ τ = ρ, w * uuτ * ( y ) * ( ρu Δy) t, + C * y =. μ By defining a limit for the y * value used in the logarithmic formulation by a lower value of * * y = max ( y,11.06) the wall function only applies where the velocity profile is assumed to be logarithmic. Using the k ε formulation to calculate inside the viscous sublayer necessitates damping functions to balance the diffusion and dissipation in the vicinity of the walls which are not incorporated in the formulation used in CFX CFX 10.0 uses scalable wall functions and if refining the mesh in a manner that places nodes in the viscous sub layer these nodes will be automatically calculated as if they were located at the edge of the viscous sublayer. The use of logarithmic wall functions makes it computationally cheap, but as the flows in the models has relatively small Reynolds number up to 8000 in the Alberta geometry for the 60 L/min flow rate, resolving the complete boundary layer is not a problem regarding the computational power. Therefore is the best performance achieved by resolving the logarithmic layer by placing at least 5 to 10 nodes here starting at the outer edge of the sub layer, thus limiting the use of the wall functions and thereby resolving the boundary layer to widest extent possible. K-ω Model The k ω model by Wilcox solves the turbulent quantities k and ω, where ω can be seen as a frequency of the large eddies and has the dimension s 1. The model is a low Reynolds number turbulence model and can integrate the equations through the viscous sublayer. 13

18 The eddy viscosity is defined as: The transport equations for k and ω is k ν t =. ω k k τ ij Ui k * + U j = + ( ν + σk1νt) β ωk, t xj ρ xj xj xj ω ω γ1 Ui ω 2 + U j = τ ij + ( ν + σω1νt) βω 1. t xj ρν t xj xj xj where σ k1 σω 1, β 1, β*, γ 1, a 1 are model constants. The model is capable of calculating the boundary layer details on grids with very fine near wall resolution. However the model is very sensitive to freestream condition and depending of the value of ω specified at the inlet significantly different flows could be obtained see Menter [23]. SST Model The SST (Shear Stress Transport) k ω based turbulence model by Menter has proven effective when calculating the onset of flow separation under adverse pressure gradients. This is due to its improved performance for non equilibrium boundary layer regions, such as those found close to separation [2]. The eddy viscosity for the SST model is given as ak ν t = max ; 1 a1 F. 2 ( ω Ω ) Where F 2 is a blending function, which limits the eddy viscosity in the near wall regions. Ω is the mean strain rate and a 1 is a constant. The SST model uses the same transport equation for the turbulent kinetic energy as the k ω model and the transport equation for the specific dissipation frequency given below: ω ω γ1 Ui ω 1 k ω + U j = τij + ( ν + σω1νt) + 21 ( F1) σω2. t xj ρν t xj xj xj ω xj x j Where σ k1, σω 1, β 1, β*, γ 1, a 1 are all model constants not available in the CFX documentation [2]. Moving close to the wall the blending function F 1 goes towards one thus the last term in the equation goes towards zero. The SST model blends to a k ε like model away from the wall, when blending function F 1 goes towards zero. This is to avoid the downside of the standard k ω model, that can produce very different results for free shear flows due to the sensitivity of the 14

19 free stream value of ω. As the SST model is able to solve the fine details in the boundary layer, the model can catch the instabilities in the viscous sublayer, which lead to separation. This makes the model capable of predicting separation from smooth surfaces and the duration of separation more accurately than the k ε model. The k ε turbulence model tends to predict flow separation from smooth surfaces too late, and is also known to under predict the amount of separated flow later on [23]. When using the SST turbulence model the limitation of not being able to calculate a solution inside the viscous sub layer as found when using the standard k ε model can be overcome. As both the USP throat and the Alberta geometry involve complex flow phenomena such as flow separation from smooth surfaces, flow with adverse pressure gradients and reattachment zones the SST model is considered most suitable for mapping the flow in the throat models. However, as the SST model is able to capture more complex flow phenomena it can be more difficult to obtain a converged solution. Difficulties in achieving convergence arose in the USP throat, as the SST model captured more separation than the k ε model which led to additional free shear flow and unsteady flow behaviour. Automatic Near-Wall Treatment The SST model in CFX 10.0 uses automatic near wall treatment, which makes the near wall grid resolution somehow relaxed. If the grid is refined in such a manner that y + is below 1 then the SST model is able to calculate the flow very close to the wall and no wall function is imposed. If the grid is not refined a wall function will be used to simulate the flow close to the wall. To fully benefit from the SST model it is recommended to have a y + resolution of less than 2 and place at least 10 mesh points in the boundary layer [6]. The boundary layer thickness and thereby the y + values varies over the faces of the geometries in the computational domains, due to the changes in the wall shear stress. Therefore a compromise between max values of y + and mesh resolution was made. Mesh Generation The computational mesh defines the discrete locations, at which the values are to be calculated. The quality of the generated meshes plays a direct role in the quality of the obtained flow solution. Therefore it is of great importance that the generation of the meshes are done in accordance with the chosen turbulence model and flow type, to obtain a valid solution. Moreover the flow solver is more robust and efficient when using a well constructed mesh. CFX is a finite volume based code and uses vertex centred elements, where control volumes are constructed around the nodes in contrast to some CFD codes that use cell centred volumes, where the mesh elements are identical to the control volumes. The four element types that are often used in can be seen Figure 5. 15

20 Figure 5: Mesh element types Generating meshes with mainly hexahedral elements is not easy to automate and requires significant user time, especially for the Alberta geometry that has a complex shape. The solutions based on these meshes are often associated with high quality, as the hexahedral element, if generated with appropriate shape and orientation, has a low numerical diffusion. The mesh generation module built into CFX 10.0, generates an unstructured mesh employing prism, tetrahedral and pyramid elements. The mesh is basically unstructured, because of the unstructured way that the data are stored in the underlying matrix system. Furthermore the mesh often has an unstructured look because the arrangement of the elements has no discernible pattern. Generation of unstructured meshes with mainly tetrahedral elements, adapts easily to complex geometries and can be constructed fast, but may increase levels of numerical diffusion. This is especially the case in one directional flows, where structured mesh of prismatic elements aligned with the main flow direction, is more efficient than an unstructured tetrahedral mesh [2]. Longest et. al. [18] has compared the flow in the lower human airways using different meshes made of hexahedral and tetrahedral elements. The hexahedral elements was found to capture more secondary flow structures than the tetrahedral, such as vortices that can be seen in cross sectional slices. Using the grid convergence index (GCI) as suggested by Roach [28] based on 1000 velocity point, the hexahedral mesh achieved a better convergence rate than tetrahedral using less elements. Based on these considerations, a structured hexahedral element based mesh would probably obtain more accurate results compared to a tetrahedral based mesh using the same number of elements, when applied to the two throat models considered in this project. However, very fine computational grids are used to compensate for the lower efficiency of the tetrahedral elements. Inflation of prism cells and volume meshing In order to resolve the region close to solid boundaries where strong gradients are present many elements are required. Using tetrahedral elements in this region will result in flat tetrahedral elements, which are pressed towards the wall. As the element size typically will be larger in the direction parallel to the solid boundary than the orthogonal direction the elements will have a high aspect ratio. Using these highly stretched tetrahedral elements (high aspect ratio) to model the flow close to the wall is known to create problems in the approximation of the diffusive fluxes [6]. To overcome the problem of resolving the boundary layer with tetrahedral elements several layers of prismatic cells can be added in the region close to the walls. A thin layer of prismatic cells added to the walls will automatically be aligned with the flow direction in the inner part of the boundary layer. Using these stretched prismatic elements to solve the near wall region improves the grid quality and the solution [1]. The faces of the elements are initially created on the surface using Delaunay triangulation, and then a specified number of layers are inflated into the domain. The thickness of the inflated layers is mainly controlled by the height of the first prism and an 16

21 expansion factor. The height of the first prism is set in accordance with the requirements of the chosen turbulence model, and is evaluated after a solution has been obtained. The expansion factor is the rate, which the elements layers grow in thickness away from the wall, and is typically set between 1.0 and 1.1, depending on the thickness of the first layer. Figure 6 shows an inflated layer on the USP figure with 40 layers of prism cells used for the SST model. Figure 6: Inflation layer at inner corner of USP throat The inflation of prism layers is defined in the same way through out the surface of the model, and it is not possible to add more layers or decrease the thickness, in areas with high gradients near the walls. Making the inflated layer thicker, by adding more layers or increase the cell height, in an attempt to fill the model entirely with prismatic cells, results in poor mesh quality in the centre of the domain. The main purpose of the inflated layers is to get an improved solution in the boundary layer, and therefore no layers are added to the in and outlet faces. When using k ε turbulence model the y + values based on the distance to the first grid point should be approximately 11. Insuring a y + value of about 11 results in a thick first near wall element and thereby making the following elements too large to ensure at least 5 nodes in the boundary layer as recommended [2]. Therefore a compromise between obtaining y + values about 11 and using an appropriate amount of nodes in the boundary layer had to be made. The mesh density is mainly controlled by means of a point control or a line control. These control options make it possible to define volumes, in which the size of the elements can be regulated. A point control regulates the size of the elements within a sphere, while the line control option makes it possible to regulate the size of elements in a certain distance from a line placed in the domain. E.g. is it possible to let the elements vary linearly in size along the line. The size of the prismatic cells in the inflated layers is affected in size parallel to the wall, but not in the direction normal to the wall. Line and point controls are illustrated on the Alberta geometry in Figure 7. 17

22 Figure 7: Illustration element size controls used for mesh generation It should be noticed, that the size of the spheres is not related to the size of the generated volumes, but is an illustration of the volume in which the elements are regulated. Generally the mesh is created in an attempt to resolve areas with expected high velocity gradients using fine mesh and to coarsen the mesh in areas with low gradients to save computational power. In the USP throat model the mesh is relatively coarse at the inlet and then made gradually denser towards the section just before and after the bend of the pipe, where the densest mesh is located. A fine mesh for the USP model can be seen in Figure 8. Figure 8: Computational domain and mesh used on the USP throat 18

23 The large cylinder seen on the figure is added to the inlet of the USP throat to mimic a flow conditioner mounted on the inlet of the throat models in the experiments. On the outlet that is located in the bottom of the picture, an extension of 60 mm is added to mimic the first part of the hose connected to the throat model in the experiments. The extension also reduces backflow that can occur due to the expansion of the USP throat at the outlet. This backflow can create problems when specifying the outlet boundary condition. The Alberta model is fairly more complex and needs special treatment before a mesh with a good quality can be generated. This involves the creation of virtual surfaces and edge controls to avoid highly skewed elements in narrow places e.g. around the epiglottis. Figure 9 shows the mesh and computational domain used on the Alberta geometry. Similar to the USP throat a cylinder is added on the inlet to mimic the flow conditioner mounted on the model in the experiments. Figure 9: Mesh used on the Alberta geometry Figure 10 and Figure 11 shows the mesh in a sagittal cut in the Alberta geometry. The figures show the inflated mesh elements used on the walls on the geometry along with the mesh density of the volume mesh. 19

24 Figure 10: Mesh for SST model for Alberta geometry Figure 11: Mesh detail Differencing Scheme and Grid convergence All calculations are performed with the high resolution mode enabled which is recommended in the CFX manual [2]. By this CFX 10.0 uses a blended scheme, using both second order and first order differencing schemes. The second order scheme is used to the widest extent possible without violating boundedness principles. The first order UDS (Upwind Differencing Scheme) is used near discontinuities and in the free stream where the solution has little variation [2], [37]. The solution is thereby close to second order accurate while maintaining robustness and a bounded solution. The actual differencing schemes are not well documented in the CFX manual [2], but the high resolution is the recommended and most accurate scheme available with the used turbulence models in CFX When performing CFD calculations it should always be checked if the solution changes when refining the mesh. The solution should ideally be independent of the computational grid, but this is not always possible especially in three dimensional domains due to limited computational power. The grid convergence is investigated for the 30 L/min flow rate on both models. To determine the grid convergence and establish a nearly grid independent solution the Grid Convergence Index by Roache [28] is used. The GCI provides a conservative estimate of the error between the unknown exact solution of the governing equations and fine grid solution. The GCI is defined by GCI = F r s P o e 1. 20

25 Where F s is a safety factor which is set to a conservative value of F s = 3 as recommended by Roache. r is the grid refinement factor between two grids. P o is the order of the discretization scheme which is set to 2 and e is the relative error between two solutions and can be applied to any variable of interest. The total pressure loss p in the models is an integral quantity of the solution and is related to the internal flow. This means that any changes in the internal flow most likely would affect the pressure drop as the wall shear stress is closely connected to the velocity gradients near the walls. The calculation of the relative error, e is therefore based on the pressure loss, and is between a coarse and a fine mesh given as Δpcoarse Δpfine e = 100%. Δp fine The refinement factor of the meshes is based on the total number of elements and is for the three dimensional domain given by 1 3 r N, fine = Ncoarse where N fine and N coarse denotes the number of elements used in the meshes. Table 1, Table 2,Table 3 and Table 4 show the specifications for investigated meshes and for the meshes that have been used for calculations for the 30 l/min flow rate. The thickness of the first element was made larger on the coarse meshes and thereby not fulfilling the requirements of the y + values of the turbulence models. The coarse mesh for the SST turbulence model (mesh 1 in Table 4) had y + values up to 50. Meshes similar to the meshes marked with bold script are the meshes used to calculate the presented results in chapter 6 and 7. Table 1 shows the mesh specifications for the used meshes for the USP throat model used with calculations using the k ε turbulence model, along with the GCI. Four different meshes are investigated with the k ε turbulence model the coarsest having and the finest elements. It is noted that the GCI of 12.0 % from Mesh 2 to Mesh 3 is surprisingly high. k ε mesh for USP Mesh 1 Mesh 2 Mesh 3 Mesh 4 Elements Nodes Tetrahedral 36 x Prisms Pyramids Pressure loss [Pa] Refinement factor, r Relative error, e [%] GCI % Table 1: Mesh specifications for USP k ε meshes As a converged solution with the SST turbulence model could not be obtained for the USP throat, a relatively fine mesh was constructed to use for transient calculations with the SST 21

26 turbulence model where a detail of the inflated layers can be seen in Figure 6. The properties of the used SST mesh can be seen in Table 2. SST mesh for USP Elements Nodes Tetrahedral Prisms Pyramids Table 2: Mesh specifications for USP SST mesh Table 3 and Table 4 show the properties of the meshes used for thealberta geometry with the SST and the k ε model. k ε meshes for Alberta Mesh 1 Mesh 2 Mesh 3 Mesh 4 Elements Nodes Tetrahedral Prisms Pyramids Pressure loss [Pa] Refinement factor, r Relative error, e [%] GCI % Table 3: Mesh specifications for Alberta k ε meshes SST meshes for Alberta Mesh 1 Mesh 2 Mesh 3 Elements Nodes Tetrahedral Prisms Pyramids Pressure loss [Pa] Refinement factor, r Relative error, e [%] GCI % Table 4: Mesh specifications for Alberta SST meshes Y + values Figure 12 shows a plot of the Y + values based on the distance from the wall to the first node, for the Alberta geometry. 22

27 Figure 12: Y + values for the SST model at 30 L/min The values are seen to lie in the range of 0 to 7 [ ]. The low value occurs in oral cavity where the velocity is generally low. In the larynx the cross sectional area is small and the high speed here leads to the higher values of y +. The y + values rises in the domain when the flow rate is made higher. To obtain y + values in accordance with the k ε and SST model at the different flow rates (15 90 L/min) it was necessary to lower the thickness of the first element, when changing to a higher flow rates. In practice 3 meshes for each turbulence model was constructed, so the flow rates of 60 and 90 L/min shared the same mesh, making the Y + values slightly lower on the 60 L/min flow rate. The thickness of the first element was changed from 0.05 mm to 0.1 mm. The value of 0.01 to 0.1 mm was used for the high flow rates with the SST turbulence model while a firstlayer thickness of 0.5 to 1 mm was used on the low flow rates with the k ε model. Boundary conditions and domain settings The use of well posed boundary conditions in the calculations is critical to obtain correct solutions and should be chosen so they model the conditions in the experiments as close as possible. In the experiments air is sucked through the throat models by a hose mounted on the outlet. A flow conditioner is mounted on the inlet to minimise the influence from unknown air movements of the surrounding environment thus providing a more controlled inlet condition. This suction from free air was modelled by employing a plug flow inlet condition to a cylinder added on the computational domain and thereby modelled the flow conditioner, see e.g. Figure 10. The outlet was modelled to maintain an average static pressure of 0 Pa and the fluid was only allowed to flow out of the domain. During the solution process, a virtual wall was placed by the solver on the outlet of the USP throat model as the air tried to flow into the USP domain in some small areas across the outlet. An extension of 60 mm was therefore mounted on the domain ensuring a more unidirectional flow near the outlet and this solved the problem. An opening type of boundary condition that allows the flow to go both out and into the domain, could as well have been applied but the first approach was chosen as the 23

28 opening type is less robust than the chosen one way average static pressure outlet condition. The opening type was tried without the extension on the USP and showed no effect on the velocity contours when subtracting the solutions from each other. As the used inlet and outlet conditions can be seen as actually pushing the air through the domain, the opposite was tested by specifying an outgoing plug flow on the extension on the USP throat combined with an average static pressure of 0 Pa on the inlet. This was done to test the dependency of the solution due to changes in the boundary conditions but also as a part of the parameter changes carried out in an attempt to obtain a converged steady state solution with the SST turbulence model. These changes showed however no improvement on the convergence rate on the steady state SST calculations. The solutions for k ε turbulence model with the different boundary settings for 30 and 60 L/min flow rates were subtracted from each other and showed no visible effect on the main flow. The maximum deviations found was around 0.02 m/s inside the figures and not surprisingly larger in the artificial parts of the computational domain mimicking the flow conditioner and the extension on the outlet. All surfaces have the no slip condition applied and are assumed to be hydraulic smooth, and the calculations were carried out with air at 25 C assumed to be incompressible. Simulation type and timestep selection In general fluid flows are transient, and the found steady state solutions with zero timederivatives are only a special case of the transient solution. Both the steady state and transient solutions have been calculated for the two throat models using the k ε and the SST turbulence model. When solving for steady state solution it is necessary to specify a timestep as the solution is found by a transient development from the initial values to the final steady state solution. The timestep, or pseudo timestep, can be seen as a relaxation parameter that should be set to ensure that the solution does not change too much between each iteration. CFX uses a robust implicit solver that allows relatively large timesteps to be selected so a converged solution can be obtained as fast as possible. A too large timestep can cause convergence problems and may also converge naturally unsteady flow to steady flow [1]. The timestep for steady state solution is recommended to be set to 1/5 of retention time that is the average time that the fluid (or a particle releases in the flow) would take flow through the domain [2]. The k ε solutions were calculated using auto time scale together with a maximum timestep that was set to approximately 1/5 of the retention time. For the flowrate 30 L/min the retention time is about 0.1 s for both geometries. In order to achieve a converged SST solution for the Alberta geometry a small fixed timestep had to be used as the solution with the auto timescale option enable had problems converging. For calculations of 30 l/min the timestep was set to s. The residual is a measure of the imbalance of the conservation equations, and describes how close the iterative process is to the unknown exact solution of the problem. The residuals shown in CFX are normalized making the independent of cell size and initial values in the domain. The steady state solutions were said to be converged when the RMS residuals for momentum and mass balance had reached , which is a strict convergence criteria [2]. With the k ε model a converged solution could be obtained after approximately 5 hours. The SST calculations were started with a converged k ε result as initial values in the domain. The SST model converged much slower using from about 300 to 1000 iterations which took up to 50 hours CPU time on the Alberta geometry. Figure 13 shows the RMS residuals for a k ε 24

29 solution that converges nicely within 70 iterations. Figure 14 shows the convergence of the steady state SST solution started with a k ε solution as initial values in the domain. All calculation was carried out using double precision to avoid round off errors. Figure 13: Convergence of k ε solution Figure 14: Convergence of SST solution A converged steady state solution on the USP throat could not be obtained using the SST turbulence model. Several runs were conducted with different boundary conditions, varying the turbulence intensity (1, 5 and 10 %), switching to opening on outlet as well as opening on inlet and plug flow on the outlet. The timestep was changed as well, using auto timescale, auto timescale with max timescale, and physical timescale of to 0.5 second. Different meshes were also used with elements varying from up to with varying number of inflated layers of prism cells on the walls (2 40). Switching to lower order differential schemes were also tried. As no one of these attempts turned out successfully, and the residuals showed bouncy behaviour in some cases, transient calculations were conducted. In transient calculation mode the time is an additional variable in the solution process. The timestep for transient solutions is more critical as it affects the quality of the obtained solution heavily, and should generally be much smaller than the fluctuations of interest. The Courant number is the relation between the distance travelled by the fluid in a timestep to the size of the computational cells and can be defined as VΔt Co =, h V is the velocity of the fluid and h a measure of the size of the computational cells. The Courant number should generally be low 1 to achieve time correct behaviour in the solution. The timestep used for the transient solutions was found by defining a RMS Courant number (based on all elements) of 1 combined with the adaptive timestep option that kept the timestep sufficiently low to maintain this. It was found that a timestep of s for 30L/min made the solution converge to a RMS residual of within 5 8 inner loop iterations, keeping the residuals to The residual target 25

30 of is quite conservative in a transient solution [2], [37], but was chosen as the long calculation times made a systematic investigation difficult. The found timestep was the used as fixed timestep on later calculations, giving a better control over the solution transient results. With the mesh from Table 2, 0.5 seconds of real time calculation used approximate 72 hours using four parallel CPU s. On the USP it was found from the obtained solution that the flow showed a clear cyclic behaviour with a period of around 0.07 s (30 L/min). This gives a time resolution of 45 timesteps during a period which is discussed in chapter 6. A few transient calculations were carried out on the Alberta geometry with the SST model and on the USP throat using the k ε model. It was seen on both geometries that after few timestep ( 50) that the solution converged to a solution very similar too the solution for the steady state case. These transient cases were not examined further. All transient solutions were found with a converged steady state solution obtained with the k ε model as initial solution guess. 26

31 Chapter 3 Experimental Method Models and Manufacturing To experimentally map the flow inside the USP throat and the Alberta geometry, a series of two dimensional (2 D) PIV measurements was carried out. In the PIV technique small tracer particles that are assumed to follow the movements of the fluid are inserted in to the flow. A plane within the flow is illuminated by two laser pulses with a time given time interval. Light scattered by the tracer particles, are then captured in two frames by a digital camera mounted perpendicular to the light sheet. A computer program determines the distance travelled of the particles, using a correlation process that does not involve tracking of individual particles. The displaced distance of the particles and the time between the two frames, is then used to calculate the velocity. Hereby is it possible to obtain an instantaneously velocity vector field of the internal flow in a plane. The measurements were mainly performed in the sagittal plane, where the out of plane motion is small. Some PIV measurements were also performed with the illuminated plane 90 to the main flow direction, to investigate the secondary movement of the flow. Other techniques are available for measuring an internal flow, such as Laser Doppler Anemometry (LDA) and hotwire measurements. These point measurement methods are impractical as they would require thousands of measurement points to map the entire flow. The required access to the flow for imaging in the PIV technique can cause practical problems as the models are small and have a complex shape, but is made possible my means of an endoscope inserted through holes in the geometry. Endoscopic PIV is a well known technique and has been used successfully used in other investigations of the flow in idealized geometries of the human airways [11], [12]. The tree dimensional model of the USP throat used in the experiments was designed using ProEngineer (Wildfire 3.0, PTC, USA) software package. A CAD model of the outer shell of the Alberta geometry was provided by Novo Nordisk A/S and was then modified for use in the experiments. The USP model was based on the original USP throat which was measured internally by means of pin gauges, see appendix C for details. All constructed models was manufactured by a rapid prototyping (RP) system, which uses fused deposition modelling to built the models in ABS plastic. The models had a wall thickness of approximately 6 mm. The flow rates considered were mainly 15, 30 and 60 L/min. 15 L/min is light breathing, while 60 L/min corresponds to medium heavy breathing that might go up to 90 L/min. The USP was made in full scale and the Alberta geometry was scaled by a factor of approximately two. This is done because of the complexity of the model Alberta model, after initial PIV experiments on the USP model is carried out, is believed to give practical problems when laser sheets and optical access has to be established. The actual linear scale factor is sf=1.83 due to limitations in the RP equipment. In order to maintain the same Reynolds number the velocities was scaled linearly down with the scale factor sf. Thereby the flow rates were scaled up with the scale factor giving the flow rates seen Table 2. The used flow rates for the USP throat model can be seen in Table 5. 27

32 USP throat scale 1:1 Flow rate [L/min] Inlet Diameter [mm] U inlet [m/s] App. Re at inlet Table 5: Flow rates and Re at inlet for USP throat Alberta geometry original Alberta geometry scaled 1.83 : 1 Flow rate [L/min] Inlet diameter [mm] U inlet [m/s] App. Re at inlet Flow rate [L/min] Inlet Diameter [mm] U inlet [m/s] App. Re at inlet Table 6: Flow rates and Re at inlet for original and scaled Alberta geometry The models were designed in two halves with an offset from the sagittal plane of 3 and 6 mm to allow laser windows to be placed here. The laser sheet enters the model through 1 mm wide rectangular openings. 0.1 mm thick over head plastic film was initially used for the windows and is glued and sealed on to the models with black marine silicone (Casco, Kolbotn, Norway). Overhead film has good optical properties as it has a low reflecting surface and is sufficiently stiff to maintain shape after it has been positioned in the model. To each laser window an approximately 8 mm wide and 0.1 mm deep recess was made on the internal surface in to which the window pane was inserted. It was discovered that the over head plastic windows tended to spread the laser light through the material perpendicular to the laser sheet and reflect this light on the edges of the window recesses. As the reflected light lowered the quality of the near wall PIV pictures, the windows material was changed to an ultra clear tape (Crystal Clear, 3M), which is so thin that it solved the problem. In Figure 19 a picture of the laser windows in the USP throat can be seen. The surfaces where the windows are located are curved, but as the radii of the curvature is sufficiently large, an inclusion of a nearly flat windows caused only a negligible change in the local geometry. The assembly of the two halves was hold together by 5 and 6 mm bolts and made air tight with a packing inserted in an o ring slot. After manufacturing the models were first cleaned thoroughly with a 75 C warm solution of water and a detergent to remove a layer of wax that was a result of the RP manufacturing process. Afterwards they were wet grinded with fine grinding paper to make the internal surfaces smooth. Finally, the surfaces were painted with 2 layers of black matte spray paint (Motip Dupli, Wolvega, Netherland) to minimize laser reflections inside the models. In the first part of the project the funding for the purchase of an endoscope was not available. A model of the USP throat with large windows in one side made of over head film was constructed in an attempt to make 2 D PIV measurements with a standard camera lens through the side instead of an endoscope. A picture of this model showing the bend of the USP throat can be seen in Figure

33 Figure 15: Model of USP throat with large windows in the side In the picture the transparent windows that are glued onto small bridges that span across the pipe can be seen. The overhead film continues down on the inside of figure, and covers also the openings where the laser sheet enters the model. The process of gluing the windows into place without scratching the surface of the over head film and at the same time ensuring correct positioning and an air tight sealing, turned out to be difficult. As was not been possible to obtain PIV pictures of high quality through the transparent sides, this approach was skipped after an endoscope became available for the experiments. As seen on the picture hexagon recesses were made in the plastic with precisely the same size as the nuts used to bolt the two halves of the model together. These fixed nuts secured a precise alignment of the two halves when they were assembled, and all constructed models were aligned this way. Figure 16 shows a CAD model of one half of the USP used for the endoscopic PIV measurements. The model has two laser windows, o ring slot and a 60 mm extension on the outlet end to which a flexible hose with suction is connected. Figure 16: Model of the USP throat used for the PIV experiments 29

34 Figure 17: Model of the Alberta geometry used for the PIV experiments Figure 17 shows a CAD model of the large half part of the Alberta geometry with three laser windows and an o ring slot, used for the endoscopic PIV measurements. Air was sucked through the model by connecting it to a flexible hose in the bottom with an aluminium adaptor not shown on the picture. The endoscope was inserted through 8.1 mm holes that were drilled in the geometry by a pillar drill equipped with an X Y table. The positions of the holes were then read when they were drilled and then used as a reference frame when plotting obtained results later. After measurements had been conducted at one place, the hole was closed by modelling wax as seen on a section of the Alberta model, see Figure 18. The wax has a slightly rougher surface than the painted model, but the difference is small and considered to have no significant effect on the flow. To minimize any possible effect on the flow, measurements and drilling of the holes were started downstream near the outlet, gradually moving upstream towards the inlet. 30

35 Figure 18: Holes closes with modelling wax after measurements with endoscope, pharynx on Alberta geometry Figure 19: Laser window made of ultra clear tape in USP throat Pressure Loss Measurements The pressure loss in the USP throat was measured through 1 mm holes drilled through the walls at the in and outlet ends. Small brass fittings were fitted on the outside screwed into 2.5 mm deep holes with 5 mm thread tapped into the plastic. The pressure readings from the pressure outtakes was averaged by joining small silicone hoses, mounted on each fitting, to one hose leading to the pressure gauge, measuring the static pressure loss of the models. The pressure outtakes were drilled with a small offset of approximately 3 mm in the main flow direction. This was done to minimise any possible effect of local flow phenomenon s that could influence pressure readings. 31

36 Figure 20 shows two pressure fittings out of three in total on the outlet end of the USP throat. Figure 20: Pressure outtakes for pressure loss measurements on the USP throat 32

37 Chapter 4 Experimental Setup Figure 21 shows a schematic of the experimental setup. Figure 21: Experimental setup The throat models were mounted on a stand which allows them to be turned so that the laser, which is heavy and difficult to move around, could deliver the laser sheet through the windows at the required angles. A flow conditioner, were mounted on the inlet on both models, consisting of a acrylic pipe of 100 mm in diameter with three plastic mosquito net inserted across the flow direction with 20 mm distance. The purpose of the conditioner is to mix of seeding particles and air and to dampen large fluctuations in the air coming from supply hose, thereby ensuring more homogeneous inlet conditions in all experiments. Figure 22 shows the Alberta model with flow conditioner and inserted endoscope taking pictures in the frontal part of the oropharynx along with laser and air particle mixture supply hose at the top. The laser sheet entering the model in the frontal part of the oral cavity is shown on the right picture. 33

38 Figure 22: Alberta model with inserted endoscope and visible laser sheet (right picture) Particles were delivered from a particle generator constructed and manufactured for the experiments; see section Particle Generator later in this chapter. The particles were mixed in a pipe with compressed air, see Figure 23. The mixing pipe had an opening to let excess particles out in exhaust ventilation mounted above. The volume fraction of tracer particles supplied to the models is controlled by the ratio between the flow rates of compressed air lead into the mixing pipe to the flow rate of particles coming from the particle generator. The amount of air and particle mixture is controlled by a butterfly valve inserted in the flexible hose after the mixing pipe, see Figure 24. Figure 23: Mixing pipe Figure 24: Butterfly valve 34

39 Air Flow Measurement Two types of flow meters were used in the experiments, a laminar flow element (LFE) and a small venturi flow meter. The LFE was designed and fabricated to use in the experiments, and was used for the low and medium flow rates up to 90 L/min. A LFE determines the flow rate by measuring the differential pressure in an established laminar flow region, passing through a fixed area. As the flow rate in a laminar pipe flown is directly proportional to the pressure loss, this ensures a rather linear flow pressure characteristic of the system. The LFE was designed to have a pressure loss of 250 Pa 15 L/min to ensure a relatively high accuracy of reading at the low flow rates. This resulted in a design with 60 brass pipes with length of 30 cm. The brass pipes have an inner diameter of 1mm and were inserted in an acryl pipe with pressure outlets see Figure 25 and Figure 26. Figure 25: LFE with pressure reading outlets Figure 26: LFE seen from the end The second flow meter used in the experiments was a small venturi flow meter and was used for flow rates from L/min. Both flow meters were characterised, using a 120 L chaincompensated gasometer (Collins, Braintree, USA). A metered amount of air at atmospheric pressure enclosed in the gasometer were sucked through the flow meters at constant speed, meanwhile the time was recorded. This was repeated several times for different flow rates. The time and exact volume of air that was put trough the flow meter was then used to obtain a pressure difference flow rate diagram, which can be seen in Appendix B. When used in the experiments, the pressure difference on both the venturi and the laminar flow meter, was corrected for density changes in the air due to changes in static 35

40 pressure and temperature. The pressure loss in the LFE is mainly due to viscous shear stress in the small pipes. Therefore a correction was made that accounted for the increase in pressure loss in the LFE at a given flow rate when the temperature raised due to higher viscosity and vice versa. A variable speed centrifugal fan was used to suck the fluid through the models and thereby controlled the flow rates. Particle Generator A particle generator was built to provide small particles for the PIV measurements. The generator was constructed in accordance with Kähler, Sammler and Kompenhans [14] who has investigated different simple methods for generating monodisperse tracer particles for PIV measurements. The generator consists of a transparent acryl cylinder measuring 150 mm in diameter and 280 mm in height. The bottom is closed by a 25 mm acryl plate with a circular slot in which the cylinder is glued into place. On the top is the detachable lid placed which is sealed with an o ring. Four vertical tension rods hold the total assembly together. The cylinder is half filled with DEHS (Di Ethyll Hexyl Sebacat), which is liquid substance that resembles vegetable oil. A brass disc is placed on the top of the lid through which an 8 mm brass pipe is inserted 220 mm down in the cylinder and connected to pressurized air regulator. In case of accidental choking of the air and particle outlet, the generator is constructed to withstand the maximum pressure of the air supply system of 12 bars. The brass pipe is plugged at the lower end and a 1 mm horizontal hole is drilled approximately 40 mm from the bottom. Pressurized air is lead down the brass pipe, through the 1 mm hole where it forms a jet into the cylinder, see Figure 28. The jet produces submicron particles when the high velocity region in the jet interacts with the DEHS. The particles are embedded in bubbles and escape when they reach the surface [26]. Figure 27 shows the particle generator with the vertical brass pipe reaching down in the DEHS. The blue plastic hose is the pressurized air supply going through a pressure regulator connected to the large inlet pressure gauge on the top and the vertical brass pipe. The grey hose has an inner diameter of 13 mm and leads the generated particles to the mixing pipe. Figure 27: Particle generator Figure 28: Air jet entering DEHS 36

41 Particles from the seeding generator were characterized in a Spraytech 2000 laser diffraction particle characterizer (Malvern Instruments Ltd, UK) varying the inlet pressures from 0.4 to 1 bar. In the characterizer laser was directed into the DEHS particles flowing through the apparatus. The scattered light was measured by a series of photo detectors placed opposite of the laser at different angles. As small particles scatter the light at larger angles than the bigger particles, the obtained diffraction pattern, can be used to calculate the particle size distribution. Prior to each measurement the background scatter of a particle free system was found and subtracted from the final measurements. Figure 29 shows the particle characteristic for the particle generator, with an inlet pressure of 1 Bar. Figure 29: Particle size distribution for paticle generator The medium diameter is 2 μm as seen on the figure. The graph shows also a tail of large particles up to 30 μm, indicating that two different processes are involved in the particle generation. These large particles may be filtered out in particle supply systems of pipes and hoses as the have not been observed at any time in the PIV measurements. The medium particle size tends to rise as the supply pressure is lowered, and is 2.39 μm at 0.4 bar. The obtained results are not identical to the one found by Kähler et. al.[14]. Kähler found an average particle size of around 1 μm for at supply pressure of 1 bar, in a generator similar to the constructed, but with four 1 mm holes arranged in a cross wire pattern. Furthermore, the level of DEHS was only 40 mm over the 1 mm hole in the pipe in the experiments, compared to 80 mm used by Kähler et. al. [14]. The particles will therefore be embedded in the bubbles for a shorter time before they reach the surface as the surface is closer to the horizontal jet. This might lead to the generally larger particles as it is possible that fewer of the large particles will be caught by hitting the inner surfaces of the bubbles spending less time embedded in the air bubbles. The process of generating the particles is highly complicated and even small changes in the conditions can lead to changes in the size distribution of the particles as pointed out by Kähler [14]. A brass pipe with four vertical 1 mm holes were fabricated, but not tested to investigate the phenomenon. See appendix B for machine drawings of the generator and graphs for particle size distribution, for inlet pressures of 0.4 to 1 bar. 37

42 PIV Equipment A pair of ND:YAG lasers enclosed in one cabinet (MiniLase, New Wave Research, USA) provided an approximately 2 mm thick laser sheet for illumination of the particles. The particle images were recorded using a digital HiSense CCD (Charge Coupled Device) camera (Dantec Dynamics A/S, Skovlunde, Denmark) with a resolution of 1280x1024 pixels mounted on a work bench that allowed the camera to be adjusted in all directions. The camera was mounted with an endoscope (R.Wolf, Germany) 370 mm long, with a field of view of 78 and an outer diameter of 8 mm. Between the camera and the endoscope was inserted an adapter which also served to focus the endoscope. An optical correction of the fish eye distortion normally associated with endoscope images, were incorporated in the endoscope, thereby in practice making it distortion free. This distortion arises when the observed displacement at the particles at the edges at the camera image seen through a non distortion free endoscope, is reduced at the high projection angles present at the edges. The camera pictures were recorded with a FlowMap 1500 acquisition and control unit [Dantec Dynamics A/S, Skovlunde, Denmark] which also controlled the lasers. Using full resolution and a data buffer the system was able to capture approximately 4 5 image pair per second in shorter periods of time. Reducing the picture resolution to the half the system was able to capture approximately 12 pictures per second. 38

43 Chapter 5 PIV Measurements and Analysis Measurement is taken at 14 different locations on the USP and at 8 different locations on the Alberta model each representing essentially an independent experiment. At each location the image scale factor S which is the relation between the physical size of the image in the model and the image on the CCD in the camera. The image scale factor was experimentally determined by inserting a ruler in the middle of the light sheet as seen on Figure 30. Figure 30: A ruler inserted into the laser sheet to measure the image scale factor A picture was taken and a distance on a captured image is measured and S can calculated. The camera with mounted endoscope was then moved perpendicular to the light sheet to a series of equally spaced position, for which S was determined. Hereby a linear relation for S as a function of the camera distance to the image plane was obtained. This relation was then used to find S at the many different camera positions required to investigate the flow in the models. The captured images from the camera were divided into rectangular regions called interrogation areas. The interrogation areas from the first and second light pulse, is then correlated with an adaptive cross correlation incorporated in FlowManager, version Linear digital signal processing is used to find a spatial displacement of the particles, and the process is speeded up using Fast Fourier Transform (FFT). The adaptive correlation is an iterative process which offers a high dynamic range for the PIV measurements compared to standard cross correlation. From an initial interrogation area in the first frame a guess is made to place the next interrogation area in second frame. The obtained displacement vector is validated and used as estimate for the window offset in the second iteration in which the size of the interrogation area is made smaller. Initial interrogation areas of 128x128 pixels were used with two refinement steps giving a final interrogation area of 32x32 pixels resulting in approximately 5000 velocity vectors, as the interrogation area overlapping at the final pass. 39

44 During the experiments particle density was adjusted after visual inspection so that approximately particles were captured in each (final) interrogation area. The time between pulses was set between 30 and 150 μs giving an average particle displacement of 5 15 pixels. Spurious vectors were detected and replaced by comparing each vector to its neighbours with a moving average algorithm. The average diameter d CCD of the scattered light from the particles on the CCD can be calculated from [7]: dp 1 d CCD= f λ 2 S S Where d p is the particle diameter, λ is the wave length of the laser light of 532 nm and f is the effective f number of the camera with mounted endoscope that is approximately 12. The light scattered by the 2 μm DEHS particles covers approximately pixels on the CCD for the image scale factors used between S =1.5 to 3. Covering three pixels is just adequate to benefit from the sub pixel interpolation used in the correlation process, providing a resolution in the displacement down to 0.1 pixels [7]. As the scattered light has a diameter more than twice of the pixels on the CCD the Nyquist sampling theorem is also fulfilled. See Appendix E for calculations. Between 150 and 500 image pairs were taken at each location for each flow rate. A higher number of recordings would provide better statistical data, but due to various problems with the equipment, the number of image pairs was limited. The problem was mainly repeated loss of connection, between the PC and the PIV Flow Map unit, resulting in loss of captured images, while downloading from the data buffer. Particle Motion A basic assumption in PIV analysis is that the tracer particles follow the flow in the fluid in motion. When seeding particles with density ρ p are inserted to the air flow with density ρ air the gravitational force will induce a settling velocity U g. Assuming spherical particles in a viscous flow at very low Reynolds number, the particles will be subject to Stokes drag and the settling velocity U g yields [26]: ( ρp ρair) ug = d g. 18μ 2 p air Where g is the acceleration due to gravity, d p is the particle diameter and μ air the dynamic viscosity of the air. A DEHS seeding particle with a diameter of 2 μm has a settling velocity of approximately 0.1 mm/s. Comparing this velocity, to the time between the two laser pulses of 25 μs to 100 μs, it is clear that this effect easily can be neglected. As the gravity effect has a totally negligible effect on the particle motion, is it not necessary to take the orientation of the models in to account under measurements. When the density of the particles, is much greater than the fluid density, the step response of the particles can be said to follow an exponential law where τ s is the relaxation time given by [26]: ρ τ = 2 p s d p. 18μ air 40

45 If applying a velocity step function on the tracer particles, they will reach 99.9 % of the velocity after τ s seconds. The relaxation time for the 2 μm DEHS particles yields approximately s or ms, and grows with the particle diameter squared. The assumption of stokes drag does not apply at high flow velocities, and the equation of motion becomes complicated. τ s can however be used to estimate the used tracer particles ability to stay in velocity equilibrium with the fluid in motion. The fastest fluctuations in the flow can be estimated by the Kolmogorow time scale given as ν τ = ε Where ν is the kinematic viscosity of the air and ε is the dissipation. From the CFD calculations the highest values of ε is seen to be up to 600 m 2 /s 3 in the USP (60 L/min). The values are generally much lower and this high value occurs in a small region just after the bend. On the Alberta geometry the values low but does reach high values especially in the trachea region where it reaches values up to 1500 m 2 /s 3 in the mean flow regions. With a kinematic viscosity of air of m 2 /s this gives a timescale of to seconds. The estimate for the timescales of the particles ( s) is much smaller than the estimated time scale for the smallest fluctuations in the flow, indicating that the 2 μm DEHS particles are able to follow the small fluctuations in the observed flow. For the smaller flow rates, and in the main flow generally, the timescale for the fluctuations is much larger and the particles should be able to follow even the fine fluctuations of the flow faithfully Turbulence Intensity The PIV measurements give information about the fluctuations of the velocity components in the illuminated laser plane. The third fluctuation component can be estimated from w = u + v 2 2 ( ) assuming that the fluctuation in the out of plane direction is a mean value of the two known components. The turbulent kinetic energy can then be estimated from 3 k= u + v ( ) Normalising by a reference velocity squared the turbulence intensity is., I k = U 2 ref. As reference velocity the averaged velocity throughout the models is used, as this velocity is less influenced by the different shape of the two throat models that e.g. the inlet velocity. The averaged velocity in the model are found form the CFD calculations. 41

46 Discussion of Experimental Errors and Uncertainties in the Setup Three dimensionality The flows in the throat geometries are clearly three dimensional and the out of plane motion becomes a source of error in the two dimensional PIV measurements. This error will however be small in the sagittal plane where the out of plane motion is generally very small compared to the in plane motion. The error that arises from an out of plane motion is illustrated in Figure 31. Figure 31: Illustration of the out of plane motion in laser sheet The figure illustrates the perspective error caused by a pure out of plane motion, where ө is the viewing angle. x p is the apparent in plane motion of the particle on the CCD and is given by Xp=- z. S. tan(θ) [35a]. This error will be zero when the particles are located directly in the endoscope axis and be larger in the edges of the plane. As seen in the figure a thick laser sheet will also present a larger error when out of plane motion is present. A large out of plane motion in the sagittal plane would show up as a systematic error in the PIV velocity contour plot where they are overlapping. This is because a finite z component will bias the velocity components on two overlapping plots in roughly opposite direction, away from or towards the respective centres. A few measurements were carried out on the throat models to investigate the secondary flow with the main flow direction 90 to the light sheet. These measurements were heavily affected by the out of plane motion which can be seen on the vector plots shown in the results chapter. 42

47 Uncertainties and Errors in the Setup The average particle displacement of was around 5 15 pixels. Using the sub pixels interpolation providing an average displacement accuracy of 0.1 pixel, the uncertainty is up to 2% in velocity in areas with good picture quality, but larger in areas that are affected by wall glare or insufficient illumination. The determination of the image scale factor also contributes to the uncertainty of the velocity and was estimated for the USP throat to be 4% and 1.5% for the Alberta geometry. The difference in the uncertainties is due to the larger scale of the Alberta geometry which reduced the relative measure uncertainty. The uncertainty of the flow rates used in the experiments is two fold. First as the pressure loss vs. flow rate relationship was examined using a chain compensated gasometer and later during the reading of the pressure loss during the PIV experiments. In the gasometer test the uncertainty increased as the flow rates were increased (for large flow rates on LFE 6%). In the experiments the reading of the pressure loss remained within mm causing a larger uncertainty for the smaller flow rates. These two uncertainties combined were estimated to cause an overall uncertainty for the velocities of 5%. These uncorrelated uncertainties for the measured velocities the USP throat are estimated to 7 % and 5% for the Alberta geometry. An inaccurate alignment of camera, model and laser can lead to systematic errors. Therefore a set of systematic measurements was conducted at each location to ensure that the camera always was located perpendicular to the laser sheet, and that the laser sheet entered the sagittal plane of the models. The alignment is carried out by measuring several distances from the camera workbench to the throat stand and from the throat stand to the laser sheet, thereby ensuring the above mentioned issues. Any error in the alignment will most likely show up as deviations in the velocity contour plots in areas where the measurements overlap, and can therefore be used as a measure of the overall error present in the PIV setup. Inaccuracy in determining the positions of endoscope holes also affects the matching of the contours. As the Alberta geometry is scaled by a factor 1.83 the systematic errors will on this model be relatively smaller than on the USP throat. The effective accuracy after the alignment of the setup will therefore be approximately twice as large for the scaled Alberta geometry as it will be with the setup with the USP throat. The obtained contour plot show a better agreement for the Alberta model in the places where the endoscopic PIV pictures overlap than it was the case for the USP throat. In the overlapping regions the measurements generally agree within ±7% percent for the Alberta, while it in some areas can be up to ±10% for the USP. The higher deviation in the USP throat is also a consequence of a more precise alignment technique developed for the experiments for the Alberta Geometry, which was investigated after the USP throat. The found deviations of ±7% for the Alberta model and ±10 % for the USP on the velocities in the overlapping regions are used as an overall estimate for the maximum error present of the PIV velocity results. Improvements of the Experimental Setup More precise PIV measurements could be obtained by improving the experimental setup in a few ways. The x y z stand which mounts the camera should be bolted to the stand that holds the throat models. Furthermore, an x y z stand with a span large enough to let the camera reach all measurement holes in the figure should be used. Hereby would the movement of the stands during the experiments not be necessary. By doing this the image scale factor S, which is a large source of error, could be determined more precisely. This is especially when doing measurements on the 1:1 scale USP throat, where all errors are relatively large. 43

48 Based on the experience of the PIV experiments we would recommend fabricating the USP throat in double scale when carrying PIV analysis out in the future. This should be done to minimise the practical difficulties when gluing in the windows into place and to ensure a higher effective accuracy in the setup. 44

49 Chapter 6 Results The results are divided into three following chapters. In the first results chapter the USP throat results are presented and in chapter 7 the results for the Alberta geometry can be seen. Under each chapter results obtained using the two different turbulence models are shown as well as PIV results for the given model. These chapters are followed by a discussion and comparison of the flow in the two geometries. Generally all results are shown at the 30 l/min flow rate, which is the most interesting flow rate concerning the testing of inhaler devices. Also, the effect of increased Reynolds number is seen to have very limited effect regarding the structure of the flow in the two models. Chapter 6 Results The results are divided into the three following chapters. In the first result chapter the results for the USP throat are presented and in chapter 7 the results for the Alberta geometry can be seen. Under each chapter results obtained using the two different turbulence models are shown as well as PIV results for the given model. These chapters are followed by a discussion and a comparison of the flow in the two geometries. Generally all results are shown at the 30 l/min flow rate, which is the most interesting flow rate concerning the testing of inhaler devices. Also, the effect of increased Reynolds number is seen to have very limited effect regarding the structure of the flow in the two models. 45

50 Results for USP Throat CFD Results for USP Firstly the results obtained using the k ε model is presented followed by the transient SST results. k ε Solution Figure 32 shows a velocity contour plot of the USP throat obtained with the k ε model for a flow rate of 30 l/min and Figure 33 shows a corresponding 2 D streamline plot in the sagittal plane. The flow enters the throat model at the inlet located in the upper right part of the figure. At the 90 degree bend the flow accelerates and is pushed close to the outer wall, creating a zone with recirculation just downstream of the bend. As seen on the streamline plot the flow reattaches after approximately 2 cm. After the bend the flow reaches its highest speed of 2. 7 m/s which is 4 times faster than at the inlet velocity (0.64 m/s) y [m] y [m] x [m] Figure 32: Velocity contour 30 l/min [m/s] (k ε) x [m] Figure 33: 2 D streamline 30 l/min (k ε) Increasing the Reynolds number has barely any effect on the flow structure that can be seen by comparing velocity contour and streamlines plots for different flow rates see Appendix C. For all flow rates the flow pattern is seen to be almost identical to the ones presented here, also in regards to the reattachment length after the bend. No flow rates show any recirculation or separation in outer corner area. The streamlines are seen to have a direction slightly away from the wall in the area downstream of the recirculating zone. This is due to secondary motion that is a result of the strong curvature of the flow. In regions with strong curves in the geometry a secondary dean flow occurs which can be characterized by the dimensionless Dean number [12]. The Dean number expresses the ratio of viscous forces to the centrifugal forces acting on the fluid and can be given by 1 2 A Q De =. 2R ν A 46

51 A, refers to the area of the local cross section, Q is the flow rate and R is the radius of the curvature of the bend. At the sharp bend of the USP the Dean number has values of 300 and 1400 for the corresponding flow rates of 30 l/min and 60 l/min respectfully. The secondary motion of the flow is illustrated in Figure 34 where different cross sectional areas of the USP throat with tangential velocity vectors can be seen. In the top left corner a picture of the USP with numbered lines corresponding to the locations for the cross sectional cuts are viewed Figure 34: Cross sections of the USP throat with tangential velocity vectors (k ε) The orientation of the cross section cuts are made from following the air flow though the USP throat facing the inlet for at first cross section area and then turning towards the outlet for the four succeeding cross section cuts. The upper parts of the vector plots 2 5 are then located in the high speed region in the right side of the vertical part of the USP throat. From the first cross section area, just before the sharp bend of the USP throat, the flow begins its movement around the bend, which can clearly be seen from the downward tendency of the first vector plot. As the plane is placed parallel to the inlet and not perpendicular to the primary flow direction the majority of the vectors are representatives of the primary flow and limited secondary motion can be seen. In the second cross section plane, immediate after the sharp bend, the velocities become large towards the wall due to centrifugal forces. Here the vectors are a mixture of the primary and secondary flow and the onset of a counter rotating Dean vortex pair can be seen. In the succeeding cross sections the planes are perpendicular to the primary flow direction and the secondary motion i.e. flow rotation and development of a Dean vortex pair can be seen. The vortices are symmetrical about the sagittal plane, which is orientated vertically through the figure centres. SST Solution The transient SST solutions are very different from the k ε solutions in the USP throat. This is believed to be due to the SST models ability to integrate through the viscous sublayer and catch the instabilities here that lead to separation 47

52 The transient SST solution of the USP was investigated by making movies of the velocity contour in the sagittal plane along with three dimensional streamlines. These movies revealed a clear cyclic behaviour of the flow in the throat model, after the solution had changed from the k ε solution that was used as initial values in the domain. Figure 35 and Figure 36 show the velocity contour and the in plane velocity vectors of the two outer solutions in the cycle (30 l/min) A A y [m] 0.08 B 1.5 y [m] 0.08 B x [m] Figure 35: Transient SST [m/s] x [m] Figure 36: Transient SST half a period later [m/s] In Figure 35 the flow is seen to create a smoothly turning high speed flow that pushes the flow up against the outer vertical wall (x=0.04 m). The high speed flow creates a low speed region downstream of the bend, but shows no recirculation as seen in this area using k ε model. In the outer corner a large recirculating zone is observed which is not shown by the k ε solution. The recirculating flow pushes fluid against the main flow direction towards the inlet in a thin region close to the horizontal wall (1). This flow reaches up to a position opposite of the inner corner (x= 0.023) before the motion is stopped by the main flow. Figure 36 shows a solution half a period (0.034 s) later. This solution shows less separation in the corner region but much more three dimensional flow compared to the flow in Figure 35. Instead of being smoothly turned around the corner of the throat model, a large portion of the fluid is seen to continue towards the vertical wall (2) where the flow is forced out of the sagittal plane. As the flow approaches the vertical wall it is forced into a strong swirling motion due to the high momentum of the flow along with the geometry of the model. The flow is led either out of or into the plane (z+ or z ) in the corner region (2) where it continues downstream. The flow going into the plane in the corner region appears in the sagittal plane again in form of a concentrated jet like flow structure coming out of the plane which can be seen by the small region of high velocity (w 2 m/s) downstream of the bend (3). The flow going out of the plane in the corner region is seen going into the sagittal plane in a 48

53 small oblong area (w 1.5 m/s) left of the before mentioned high velocity area (x=0.11, y=0.7 to y=0.88). See Appendix C for w velocity contour plot. Both mentioned out of plane flows continue downstream where they are absorbed by the main flow in the left side of the vertical pipe section. The cyclic behaviour can be characterized by two types of flow: Figure 35, smooth flow pass the corner with a large recirculation in the outer corner area, and Figure 36, flow going straight towards the vertical wall that leads to massive three dimensional flow and little recirculation close to the corner. The cyclic behaviour of the flow is illustrated by taking the arithmic mean velocity along line A and line B in Figure 35 and Figure 36 for at series of transient results. In Figure 37 the relationship between the velocities and time can be seen Line A Line B Line A Line B Vel [m/s] Vel [m/s] Time [s] Figure 37: Frequency 14.7 Hz (30 l/min), timestep s Time [s] Figure 38: Frequency 14.3 Hz (30 l/min), timestep s The figure shows that when the flow recirculating in the corner as in Figure 35 the velocity is low in the corner region (low velocity at line A) and low in the region downstream of the bend (low velocity line B). When the flow is as shown in Figure 36 where it is forced out of the sagittal plane in the corner region (high velocity at line A) this leads to high velocity in a small region downstream of the bend (line B). The velocity from line B is phase shifted 0.01 s forward in time in the flow cycle downstream of the bend. This is due to distance between the two locations, so the 0.01 s corresponds to time it takes for the flow structure from line A to emerge downstream of the bend near line B. The marked points on the curves correspond only to the saved transient solution. The actual time resolution of the transient calculation at 30 l/min was s which gives approximately 45 timesteps in a period. Calculations were performed with different timesteps. In Figure 38 the frequency graph for the solution obtained using a timestep of can be seen. The marks on the graph display velocity values from every timestep. As seen on the graph, the large timestep converges the naturally unstable flow to a more steady solution which can be seen by the decreasing fluctuations. However, the frequency of the fluctuations is maintained. A smaller timescale of s did not change the period of the cycle. For the 60 l/min flow rate is the period s (29.5 Hz), see Appendix C. The time averaged (n=650) transient SST solution is shown in Figure 39. The figure shows the velocity contour and the in plane velocity vectors of 30 l/min. A similar vector and velocity contour plot of the k ε solution can be seen in Appendix C. 49

54 y [m] x [m] Figure 39: Average of transient solutions (n=650) [m/s] The averaged solution shows some basic differences compared to the k ε solution. In the region near the outer corner the flow is recirculating. In the region downstream of the bend (1) the flow shows a direction towards the outlet showing that none or very limited recirculation is present in this region. Further downstream (2) the flow has a velocity component pointing out in the domain towards the high speed region in the right side of the vertical pipe. The high velocity region in area (3) has a sharp bend compared to the structure of the k ε solution seen in Figure 32. These characteristics are important in the later comparison with the experimentally obtained data. The secondary flow in the SST solution also differs significantly from the k ε solution. Figure 40 and Figure 41 shows the secondary flow of the transient solutions presented in Figure 35 and Figure 36. The numbers refers to the position and orientation of the cross sectional planes shown in Figure 34. The secondary flow is not symmetrical about the sagittal plane as the k ε solution and develops faster as it is already present in cross section 2. The onset of a Dean vortex pair can be seen at both transient solutions in cross section 2 and 3, but are replaced further downstream by one counter clock wise rotating vortex which grows in size and fills the entire cross section further downstream in cross section 4 and 5. 50

55 Figure 40: secondary flow of transient solution shown in Figure Figure 41: secondary flow of transient solution shown in Figure 36 The secondary flow of the averaged transient SST solution can be seen in Appendix C, but does not differ significantly from the two transient solutions shown above. 51

56 PIV Results for USP Throat and Comparison with CFD The PIV results are obtained using the adaptive cross correlation method with final interrogation areas of 32x32 pixels with 50% overlap. Spurious vectors are removed with a moving average algorithm and the vectors and replaced with valid vectors. The numbers of vectors are reduced to get a better over view. Appendix D shows selected instantaneous and averaged vector maps as well as PIV pictures from selected locations of the models. Averaged Flow The flow in the USP throat was investigated with the endoscope inserted 14 different positions, as shown on Figure 42. (A photo of the model can be seen in Appendix B). Figure 42: Endoscope positions on USP throat The obtained velocity maps are plotted at the corresponding locations to get an overview of the flow pattern inside the throat model. Figure 43 shows overlapping vector plots from the 12 locations shown on Figure 42. The figures show several zero velocity areas that comes from the biasing of velocities towards zero where the picture quality is poor due to wall glare. This can be seen close to the inner corner and in the long region along the right part of the vertical part of the pipe which is heavily affected of wall glare. Figure 44 shows the average (n= ) velocity contour for the 30 l/min flow rate. Contour and vector plots for 15, 45 and 60 l/ min can be seen in appendix D. 52

57 y [m] y [m] x [m] x [m] Figure 43: Velocity vectors from PIV measurements (30l/min) Figure 44: Velocity contours form PIV measurements (30l/min) [m/s] The PIV measurements show that the flow in the USP throat has a few distinct characteristics that are also seen in the averaged SST solution (see Figure 39). In the outer corner (1) the flow has a recirculating zone that reaches half pipe diameter out from the corner both horizontally and vertically. In the area just downstream of the bend (2) the flow is moving in the mainstream direction towards the outlet indicating that only very limited or no recirculation is taking place in the sagittal plane in this region. Below this region the velocities are very low, mainly due to poor PIV picture quality because of wall glare. In the region further downstream of the bend (3) the flow has a small velocity component pointing towards the high speed region at the left pipe wall. This indicates that the secondary flow in this region might be similar to the one found by the SST solution. The high velocity region in (4) has a sharp bend that is different from the smooth shape in the k ε solution ( Figure 32) but resembles the shape of the SST averaged solution in Figure 39. These four characteristics that reveal the nature of the time averaged flow show that the averaged SST solution offers a much better correspondence with the PIV measurements than the k ε turbulence model in the USP throat. Generally the time resolution of the PIV equipment was too large (maximum 12 Hz) to capture the development of flow structures in the USP throat. However examining instantaneous vector plots can give some idea to the nature of the flow. 53

58 Instantaneous Flow Structures The instantaneous vector plot offers a unique opportunity to study the actual flow movements inside the geometries. Downstream of the inlet (location 1 and 2 see Figure 42), the flow is seen to be steady and time independent, flowing nicely into the USP throat parallel to the outer walls. Figure 45 (right) shows a PIV picture taken from hole position 3 that is located close to the outer corner of the of the USP throat. In the picture the laser window can be seen in the upper part along with the particles that scatters the laser light in the laser sheet. In the two upper corners of the picture two dark areas can be seen. These areas stems from the round field of view in the endoscope that is smaller than the rectangular CCD area in the camera. The particles close to the window scatters more light than the particles at the lower part of the picture. This is because the light intensity is gradually lowered as more particles scatters and absorbs the light when moving away from the window. Another factor is that the light sheet spreads out at a small angle perpendicular to the viewing plane making it slightly thicker at the bottom of the picture and thus less intensive. In the middle of the lower part of the picture light glare from inner corner of the USP can be seen. At a third of the picture width to the left two nearly vertical streaks with lower light intensity can be seen. These streaks come from dirt or tracer particles stocked on the laser windows, but does not seems to affect the vector plots y [m] x [m] Figure 45: Location of hole 3 and 9 (left). Corresponding PIV picture from hole 3 (right) Figure 46, Figure 47 and Figure 48 shows instantaneous vector plots obtained from hole position 3 from PIV pictures similar to the one shown in Figure 45. In the upper part of Figure 46 the flow is seen to follow the inner wall of the USP throat basically all the way through the picture. 54

59 y [m] x [m] Figure 46: Attached flow Instantaneous vector map from hole 3 In the lower part of the figure just left the zero velocity area that stems from the area with wall glare, the flow is seen to start its movement around the inner corner of the USP. In Figure 47 another situation shown is that occurs 0.22 seconds later. Here a large separated region is observed close to the wall in the upper left side of the figure. 55

60 y [m] x [m] Figure 47: Separation from wall Instantaneous vector map from hole 3 This separated region is due to fluid coming from the corner that is pushed opposite the main flow direction in the thin region close to the wall. The separation deflects the flow direction in the lower left part of the figure in a more downward facing direction compared to Figure 46. The two vector plots show a periodic phenomenon occurring at the outer wall of the USP just before the bend. Part of the time the flow is close to fully attached to the wall and flows towards the outer corner and is first separated close to here. Suddenly separation occurs and sends separated flow structures into the flow in the USP thereby affecting the flow downstream of the corner. Figure 48 shows the reattachment of the flow to the wall. In the upper right part of the picture a clockwise rotating eddy is seen close to the wall. Left of this eddy the flow reattaches to the wall, which can be seen by the main flow going behind the large separated flow structures thereby flowing parallel to the wall flowing in the main flow direction. The separated flow is most likely swept out in the main flow, contributing to the unsteady flow observed further downstream in the USP. 56

61 y [m] x [m] Figure 48: Reattachment to wall Instantaneous vector map from hole 3 The separation phenomenon has been studied in series of vector maps captured using low resolution on the camera obtaining a capturing rate of 12 frames per second. From this its is clear that the separation phenomenon has a timescale smaller than 0.1 second even at 15 l/min as no correlation hardly can bee seen in the obtained series of vector maps. These instantaneous vector plots of the alternating separation and reattachment situations of the flow along the wall close to the corner show that the flow in the corner region cannot be considered stationary. The alternating separation and reattachment bear resemblance to the cyclic behaviour of the transient SST solution, where the attached flow seen in Figure 46 resembles the SST solution seen in Figure 36. When the flow is separated as in Figure 35 this resembles the SST solution in shown in Figure 47. The flow after the bend is characterized by a high speed region in the left side of the vertical pipe and a highly turbulent zone in the right side. The vector field shown in Figure 49 is taken in hole 9 located downstream of bend in the as shown in Figure 45 The plot covers an area from the outer wall going approximately 14 mm into the model. The high speed flow that is created after the bend can be seen at the left side of the figure. In the right part of the figure a large unsteady flow structure can be seen. The unsteady zone varies in width and extends on outside the picture down to 4 5 mm and covers then up to three quarters of the pipe diameter. 57

62 y [m] x [m] Figure 49: Instantaneous vector plot of velocity after bend in USP throat (hole 9) Even though the high speed region on the left side of Figure 49 in the majority of time looks steady, large turbulent structures are transported in the fluid. This can be seen on Figure 50 where the average (n=200) vector field is subtracted from an instantaneous vector field. In the left part of the figure an eddy with diameter of approximately 5 mm y [m] x [m] Figure 50: Instantaneous vector subtracted averaged (n=200) mean velocity plot (hole 9) 58

63 The above instantaneous vector maps all show resembles to flow structures found in the transient results. To additionally gain experimental information about the flow structure PIV measurements were attempted in a cross sectional plane downstream of the sharp bend of the USP throat in order to achieve some information about the secondary motion. Secondary Flow A few PIV measurements were carried out to reveal the structure of the secondary flow. This was done by illuminating a plane perpendicular to the main flow direction inside the USP throat, thereby determining the flow in this plane. See Appendix B for a photo of the experimental setup. This setup makes the out of plane motion dominant which introduces a large error as discussed in Chapter 6. Figure 51 (right) shows the flow in a cross sectional plane located and orientated as plane 3 in Figure 34. In the experimental setup the main flow direction is going away from the camera lens. This setup biases the velocity vectors towards a direction pointing towards the optical axis, which is located as shown on the corresponding PIV picture in Figure 51 (left). This biasing of velocity vectors can be seen throughout the figure, especially in the perimeter of the pipe where all vectors are pointing towards the centre of the figure. This systematic error makes a direct comparison of the velocity sizes with the CFD results without meaning. Optical axis Figure 51: PIV picture (left). Averaged (n=900) PIV measurements of secondary flow in USP (right). At the 6 o clock position is what looks like a strong secondary flow structure going towards the centre of the pipe. As the velocity vectors are biased towards the optical axis, the downward going velocities in the right side close to the perimeter indicates a clock wise rotating flow following the right pipe wall. At the four o clock position a small vortex is seen, that is created by the downward going flow in the right side of the pipe and upward going flow at the sic o clock position. Even though that the experimental setup in this configuration introduces a systematic error, it is clear that secondary flow in the USP throat is very different from the secondary flow found by the k ε solution (see Figure 34) that was seen to be symmetrical in the sagittal plane. The secondary flow from the averaged SST solution is shown for comparison in Figure

64 A B 3 Figure 52: Secondary flow at 30 l/min. Averaged (n=650) SST solution In the third plot (3) the secondary flow for the SST model corresponding to the same location as the PIV measurements is seen. The secondary flow in 3 shows small resemblance to the motion found in the same plane for the PIV measurements see Figure 51. However better correspondence of the flow structure is seen upstream from plane 3. Cross section A and B show the secondary flow in two planes located between plane 2 and 3 (see Figure 34) where A is furthest upstream. These two figures show a flow structure that has some of the same characteristics that are seen from the PIV measurements. In figure A and B, a counter clock wise rotating vortex is starting to develop with strong flow motion from the four o clock position towards the centre of the pipe. This flow structure resembles the structure seen in PIV measurements. The main difference is that in the PIV measurements it seems like a clock wise rotating vortex is developing which is in the opposite direction of the CFD calculations. The above discussion indicates that the SST model is able to capture, to some extent, the complex secondary flow structure seen from the PIV measurements. However is seems like the structure in the CFD calculations develops faster as the best matches are located 5 and 10 mm upstream of plane 3. Turbulence Intensity The fluctuations of the flow are normalized with the average velocity in the model (1.46 m/s at 30 l/min) to display the turbulence intensity as described in Chapter 5. The turbulence intensity obtained from the PIV measurements are shown in Figure 53. Turbulence intensities are not surprisingly at their lowest in the horizontal part of the USP before the flow reaches the bend, except for small isolated regions which stem from wall glare or insufficient light that can lead to artificially high or low values. These non physical high or low turbulence intensities are present in several other places of the figure especially close to the edges of the contour plots from the individual endoscope hole positions. In the outer corner the intensity is very high which is in agreement with the seen fluctuating flow that was a result of the alternating separation and reattachment here. In the separated shear layer in the region downstream of the bend high turbulence intensities are seen as expected. The main flow in the high speed region in the left side of the vertical pipe shows low values. This agrees well with the earlier discussed behaviour of this region and the instantaneous vector map shown in Figure 49. The intensities (I=k/U 2 ref) from the CFD calculations are seen in Figure 54 (k ε) and Figure 55 (SST). The turbulence intensity values are very different for the two turbulence models where the k ε model predicts up to 20 times higher values. In the outer corner values form both models are very low. The outer corner shows relatively higher intensities for the PIV measurements compared to both CFD calculations. 60

65 y [m] y [m] x [m] Figure 53: Turbulence intensity from PIV measurements (30 l/min) x [m] Figure 54: Turbulence intensity k ε (30 l/min) y [m] y [m] x [m] Figure 55: Averaged (n=650) turbulence intensity SST (30 l/min) x [m] Figure 56: Turbulence intensity based on flow fluctuations from transient SST run at 30 l/min. (n=650) The intensity plot from the PIV measurements should ideally contain contributions from fluctuations reaching from very small timescales (down to s) up to large timescales seen in the alternating separation and reattachment in the outer corner (up to 0.1 s). It was estimated in Chapter 5 that the particles are able to follow these fluctuations reasonable. Despite this, it is possible that they do not contribute with full magnitude since the spatial resolution in the PIV measurements are limited to the size of the interrogation areas and the fluctuations with the smallest timescales might have length scales smaller than this. The CFD calculations solve the RANS equations using a turbulence model where k is incorporated as the kinetic energy of the small timescale fluctuations. As the flow is seen to be unsteady it can be discussed if the value of k expresses the true fluctuations of the turbulent flow seen in the PIV measurements. The turbulence intensity based on the STD values (n=650) 61

66 of the unsteady velocity field from the transient SST calculations is seen in Figure 56. The figure shows high intensity values up to around 0.3. It could be argued that these intensity values should actually be added to the intensity values seen in Figure 55, thereby giving a better correspondence with the experimentally obtained values. Due to the small number of samples ( ) in the PIV measurements and poor picture quality due to wall glare in some areas the intensities are not examined further. Pressure loss The pressure loss is measured experimentally in the USP throat by small pressure outlet mounted on the model. Figure 57 shows the pressure loss of the USP throat as a function of the flow rate plotted in a double logarithmic coordinate system Pressure Drop [Pa] Experiments CFD y=0.0025x Flow Rate l/min Figure 57: Pressure loss of the USP The pressure loss is seen to be proportional to the square of the flow rate. As seen on the figure the CFD results do agree well with the experimentally obtained pressure losses. However the experiments show a tendency of higher pressure loss at the higher flow rates than the calculated. 62

67 Chapter 7 Results for Alberta Geometry The presented CFD results for the Alberta geometry are all steady state solutions, as opposed to the USP throat where the solution using the SST turbulence model turned out to be unsteady with large time dependant variations in the flow. This was to some extent also seen in the PIV measurements where an alternating flow separation and reattachment was seen in the outer corner. On the Alberta geometry, no periodic or other variation on a large timescale have been observed in the PIV measurements. Running in transient mode using the SST turbulence model with a timestep of s showed no unsteady behaviour. CFD Results Generally all results like for the USP throat are shown at the 30 l/min flow rate as increased Reynolds number is seen to have very limited effect regarding the structure of the flow in the Alberta geometry. Figure 58 shows a velocity contour plot in the sagittal plane of the Alberta geometry obtained by the k ε turbulence model. Figure 59 shows a corresponding 2 D streamline plot for the same solution. In Figure 60 and Figure 61 the corresponding plots for the SST turbulence model are seen. 63

68 z [m] z [m] x [m] Figure 58: Velocity contour 30 l/min [m/s] (k ε) x [m] Figure 59: 2 D streamline 30 l/min (k ε) z [m] 0.08 z [m] x [m] Figure 60: Velocity contour 30 l/min [m/s] (SST) x [m] Figure 61: 2 D streamline 30 l/min (SST) The flow in the oral cavity is quite different for the two turbulence models. It is generally observed that the SST turbulence model shows much more secondary flow than the k ε model. The airflow enters the model in the front of the oral cavity and creates a large zone with recirculation due the expansion in cross sectional area from the inlet orifice of the oral cavity. For the k ε solution recirculating zone measures 2 cm in height and extends to around 6 cm back from the front of the cavity where the flow reattaches. The streamlines from the SST 64

69 solution (Figure 61) show that the flow in the upper frontal part of the oral cavity has a large downward facing velocity component at the sagittal plane. This is due to strong secondary motion that will be discussed later. The streamlines in the upper frontal part of the model that goes from the top of the oral cavity towards the inlet of the model show that the flow is recirculating. The size and shape of the recirculations are not seen to vary significantly in size or shape for different flow rates. The flow speeds up as it continuous further down the oral cavity due to the contracting cross sectional area where it is accelerated to nearly four times the inlet velocity. Hereafter the flow enters the pharynx where the cross sectional area is expanded due to the backward facing step that mimics the inlet from the nasopharynx. This expansion causes a recirculating zone just downstream of the backward facing step and both turbulence models show a reattachment length for the flow of about 2 cm. The short reattachment length compared to the height of the step (0.6 cm) is because the flow is pushed close to outer wall (x=0) before entering the trachea, along with the generally small cross sectional area of the pharynx. This acceleration in combination with the strong curvature of the geometry in the back of the oral cavity speeds up the secondary flow shown by the SST solution. This secondary flow bends clearly the streamlines in the pharynx towards the frontal vertical wall located above the epiglottis (x=0.015). This behaviour is also evident in the contour plot where high speed region reaches further down and is closer to the frontal wall of the pharynx than the solution for the k ε model. Entering the larynx the flow accelerates due to the small cross sectional area and reaches the highest velocity in the beginning of the trachea of approximately 5 times U inlet. This high speed flow is known as the laryngeal jet. The high speed jet pushes the flow against the vertical rear wall of the larynx (x=0.015) before it continues down towards the outlet, creating a large zone of separation at the backside of the larynx. Because of the high speed flow is unable to follow the strong curvature at the beginning of the larynx a small separation bubble is formed on the lower side of the epiglottis along with a smaller bubble on the upper part of larynx just right of the flat bottom of the pharynx. The flow enters the vertical larynx at high speed that is more than five times the inlet velocity (U inlet =1.13 [m/s]). The streamlines in Figure 59 and Figure 61 are seen to violate the 2 D continuity at several places e.g. on the top of the epiglottis and in front of the inlet to the larynx, which shows that the flow is three dimensional. This is also the in the top of the oral cavity for the SST solution. The secondary flow in the Alberta geometry is illustrated in Figure 62 and Figure 63. The figures show the in plane velocity vectors for the k ε and SST solutions in a series of cross sectional planes located perpendicular to the main flow direction. The orientation of the cross section cuts are made from following the air flow though the geometry facing the inlet for at first cross section area and then turning towards the outlet for the four succeeding cross section cuts. The secondary flow is seen to develop quickly after the inlet on both turbulence models. The secondary motion starts in the oral cavity where fluid starts flowing up along the outer walls of the cavity creating two counter rotating vortices. These vortices are generally more prominent for the SST solution and cause the characteristic downward direction of the streamlines in the oral cavity. From the back of the oral cavity to the inlet of the pharynx the two turbulent models develop the flow very differently. Using the SST model the secondary flow is speeded up and strong vortices are seen at (6). These vortices continue all the way down in the pharynx (7). Oppositely, the k ε model wipes out the vortices when the flow is accelerated and are nearly non existing at (5), (6) and (7). The speed up of the vortices seen by 65

70 the SST model is caused by the strong curvature of the geometry along with the contracting cross sectional area in the back of the oral cavity. Using a medium radius of the curvature in the back of the oral cavity, the flow reaches Dean numbers of 1200 and 4800 for flow rates of 30 and 60 l/min respectively Figure 62: Cross sections of the Alberta geometry with tangential velocity vectors (k ε) (30 l/min) 66

71 Figure 63: Cross sections of the Alberta geometry with tangential velocity vectors (SST) (30 l/min) Even though the CFD results show strong secondary motion, the flow is primarily symmetrical about the sagittal plane and therefore the out of plane motion in the sagittal plane is relatively small. This proposes good conditions for the PIV measurements as a small out of plane motion increases the signal to noise ratio in the correlation process. 67

72 PIV Results for Alberta Geometry and Comparison with CFD The Alberta geometry is investigated with the endoscope inserted at nine different positions, as shown on Figure 64. These locations were chosen to give an overall view of the flow structure in the geometry above trachea. Figure 65 shows the averaged (n= ) velocity contour from the Alberta geometry at the 30 l/min flow rate z [m] Figure 64: Endoscope positions on Albert geometry x [m] Figure 65: Velocity contour from PIV measurements [m/s] (30l/min) 0 There is a generally good agreement between the measurements and the calculations in respect to the magnitude of the velocity. A part of the velocity contour at the inlet is removed because of artificial high velocities as a result of poor picture quality. The location of the abrupt change in velocity magnitude seen in the area between position 1 and 2, are in good agreement with the CFD solutions. This is not surprising since the change stems from the height of the upper edge of the inlet orifice. The velocity contours further downstream seem to resemble that of the SST solution. This is mainly seen in the contours of position 3 and 8, which are investigated in the following. Figure 66 (left) shows the location of the vector maps obtained from hole position 3 and 8 along with the vector map from hole position 3 (right). In Figure 67 the corresponding k ε and SST solutions are seen respectively. 68

73 z [m] 0.08 z [m] x [m] x [m] Figure 66: Location of hole 3 and hole 8 (Left). Average PIV (n=350) measurements from hole 3 (Right) (30 l/min) z [m] z [m] x [m] x [m] Figure 67: k ε solution corresponding to hole 3 (Left). SST solution corresponding to hole 3 (Right) (30 l/min) In the PIV measurements the flow seems to come from two different directions, from the right side of the figure and top of the picture. The flow coming from the right is the main flow coming directly from the inlet of the geometry, while the flow, which comes from the top, must be due to secondary motion. The downward facing velocity component in the flow in the upper part of the picture has the same velocity magnitude as the primary flow in the lower right part, suggesting that significant secondary flow motion is present in the top of the oral cavity. Figure 67 (right) shows the solution for the same area using the k ε model. The majority of the velocity vectors in the top of the oral cavity have a direction following the mean line of the geometric curve indicating that limited secondary motion is present here. The SST solution (left) shows right away large resemblance to the measured data. The region separating the 69

74 down going velocity vectors from the velocity vectors coming from the right side, where low velocity is seen is a result of the vortices developing through the oral cavity. In Figure 68 the velocity profiles in the oral cavity for PIV measurements and corresponding CFD solutions are shown for the locations of line 1 and 2 in Figure 64. Good agreement between the SST solution and the PIV measurements is seen especially close to the inlet. The excellent in the velocity profile close to the inlet left shows that the chosen boundary condition in the computations are corresponding well to the actual physics of the experiments. As the PIV measurements close to the wall were affected by wall glare the steep slope close to the wall (x=0) is a results of zero velocity biasing rather than actual velocity measurement in the thin boundary layer. In the back of the oral cavity larger inconsistencies between the profiles are seen (2). The SST model captures the basic shape of the measured profile even though the match is less convincing. The profile from the PIV measurements is tacky near the upper part of the oral cavity (z=0.16) because of poor picture quality from wall glare caused by peeling of the mat wall paint k ε SST PIV 2 PIV k ε SST PIV u 0.5 (u 2 +w 2 ) 1/ z z Figure 68: Velocity profiles in the oral cavity at line 1(left) and line 2 (right) (30 l/min) The velocity profiles from the CFD calculation in the region close to the wall (x=0) are very different in both (1) and (2). This might be a result of too low y + values, which are around 3 for the k ε model in this region. The values in the grid points very close to the wall are then calculated as they were located outside the viscous sublayer, which might explain why it looks + like the k ε model calculates closer to the wall than the SST model. The y values for the SST model was around 1 in this region with a thickness of the first inflated prism cell of 0.08 mm. The tacky form of the SST velocity profile close to the wall is therefore not caused by poor grid resolution and represents the actual form of the calculated velocity profile. The density of the tracer particles and the picture quality inside the Alberta geometry just above the epiglottis at hole position 9 can be seen in Figure 69 along with the corresponding vector map. The flow enters the pharynx just above the figure and causes a large recirculating zone that extends down in the left side of the figure. In the top right corner a snare of the high speed flow region from the inlet jet to the pharynx can be seen by the slightly sloped vectors pointing towards the frontal wall (right side of the vector map). A detailed vector map from hole position 7 which reveals, to a higher extent the sloped vectors, can be seen in Appendix D. These sloped vectors in the upper part of the pharynx are most likely a result of a strong secondary motion, as described in the going through of the SST results. As the flow continues down the pharynx it reattaches to the outer wall (x=0) before entering the larynx. The reattachment length varies slightly for the PIV and CFD results where 70

75 it measures 2, 1.9 and 2.2 cm for PIV, k ε and SST respectively. See Appendix C corresponding vector plots for the k ε and SST solutions. for z [m] x [m] x 10 3 Figure 69: PIV picture from hole 9 (left) and corresponding average (n=250) vector map (right) (30 l/min) The velocity profiles across the pharynx along line 3 and 4 in Figure 64 are shown in Figure 70. From profile along line 3 the width of the recirculating zone can be seen as the crossing of the graphs at zero velocity. The SST solution predicts a wide zone of recirculation that is to some extent seen for the PIV measurements as well. Line 4 is located just above the epiglottis and coincides with the reattachment point predicted by the k ε model. 1 k ε SST PIV k ε SST PIV w x x 10 3 w x x 10 3 Figure 70: Velocity profiles in the pharynx along line 3 (left) and 4 (right) (30 l/min) In the right hand side of the graph the PIV measurements and SST solution show a large (3.5 m/s) downward going velocity close to the wall. This indicates that a large portion of the fluid is actually flowing around the epiglottis out of the sagittal plane before entering the larynx. Figure 71 shows an average velocity contour plot of 150 vector maps from PIV measurement in the oral cavity of the Alberta geometry taken in plane 3 see Figure 63. The laser sheet enters through the side of the model and is orientated 90 degrees to the main flow direction, see appendix C for photos of the setup. The figure is orientated so it represents the flow seen from the inlet of the figure. 71