Spray and Wall Film Modeling with Conjugate Heat Transfer in OpenFOAM

Transcription

1 Spray and Wall Film Modeling with Conjugate Heat Transfer in OpenFOAM Emil Sjölinder Applied Thermodynamics and Fluid Mechanics Degree in Master of Science with a major in Mechanical Engineering Linköping University Department of Management and Engineering LIU-IEI-TEK-A 12/01495 SE

2 Abstract This master thesis was provided by Scania AB. The objective of this thesis was to modify an application in the free Computational Fluid Dynamics software OpenFOAM to be able to handle spray and wall film modeling of a Urea Water Solution together with Conjugate Heat Transfer. The basic purpose is to widen the knowledge of the vaporization process of a Urea Water Solution in the exhaust gas after treatment system for a diesel engine by using OpenFOAM. First, urea has been modeled as a very viscous liquid at low temperature to mimic the solidification process of urea. Second, the development of the new application has been done. At last, test simulations of a simple test case are performed with the new application. The results are then compared with simplified hand calculations to verify a correct behavior of certain exposed source terms. The new application is working properly for the test case but to ensure the reliability, the results need to be compared with another Computational Fluid Dynamics software or more preferable, real experiments. For more advanced geometries, the continued development presented last in this thesis is highly recommended to follow. This document has been typeset using L A TEX and is preferably viewed in color.

3 Acknowledgements First of all I would like to thank my supervisor at Scania, Niklas Nordin, for guidance and help in the code-jungle of OpenFOAM. Niklas has also taught me about CFD, thermodynamics and of course, about shoes, as a great art, for which I m grateful. I m also very grateful to Raymond Reinmann, for he trusted his instincts and gave me this challenge despite the low odds of completing it. I would also like to thank everyone at the Fluid and Combustion simulation group for giving me useful insights to my work and appreciated morning greetings. Their smiles have lifted me up from the deepest holes of source code. Of course, I also want to thank my supervisor at Linköpings University, Jonas Lantz, for his humble and clear guidance of how to write this master thesis. Emil Sjölinder Vimmerby, August 2012

4 Contents 1 Introduction and Background Todays Diesel Engines Exhaust Gas After Treatment Systems Computational Fluid Dynamics Objective of the Thesis Structure of the Thesis Theory Urea and Water Solution Governing Equations Reynolds-avaraged Navier-Stokes equations Turbulence Models Spray Modeling Wall Film Modeling Conjugate Heat Transfer The Finite Volume Method Method Modeling Liquid Urea Development of chtmultiregionsprayfilmfoam The Wall Film Region The Buffer Layer Assumptions and Approximations Simulation Setup for the Test Case Computing Platform Simulation Domain and Boundary Conditions Mesh and Solution Criteria Results Urea Viscosity chtmultiregionsprayfilmfoam

5 5 Discussion Urea Viscosity chtmultiregionsprayfilmfoam General Comments Conclusion 39 A Modeling Liquid Urea 43 A.1 Implementation Parameters A.2 Matlab Code for Dynamic Viscosity of Urea B chtmultiregionsprayfilmfoam 46 B.1 Development of the Code B.2 Implementation of Kliq and deltamap B.3 Tutorial B.4 File Structure for the Tutorial C Settings for the Simulation 65 C.1 Solution Settings C.2 Numerical Schemes

6 List of Figures 1.1 European legislation for soot and NO x emission from Euro 1 to Euro The simplified test domain desired to calculate Velocity in turbulent flow A staggered grid for the FVM T µ curve for water and desirable T µ curve for urea Numerical grid of a fluid and a wall film Numerical grid of a fluid, a wall film, a buffer layer and a solid The simulation domain A visualization of the mesh Calculated T µ curve for urea The formation of the wall film with water or urea Comparison of wall film thickness for water and urea Surface temperature at the solid for all four cases Temperature drop at the surface for the solid Heat distribution in cross sections for the steel solid

7 List of Tables 2.1 Liquid properties for water and urea Fluid and solid properties for the test simulations Boundary conditions for the fluid region in the test simulations Boundary conditions for the wall film region in the test simulations Boundary conditions for the buffer layer in the test simulations Thermodynamic properties for the solid Spray properties for the test simulations Number of elements and size of elements for the test domain Tolerance criterias for the test simulations Change of conserved energy for the solid and the wall film after 1.5 s A.1 Parameters for T µ relationship for water and urea B.1 Region and boundary names for the tutorial guide C.1 Numerical schemes for the test simulations

8 Nomenclature Latin symbols u, U velocity vector [m/s] u, v, w U, V, W velocity [m/s] S M S i m external forces [N] external energy sources [J] mass [kg] p pressure [P a] p rgh pressure with buoyancy included [P a] T temperature [ C, K] k thermal conductivity [W/m 2 K] Q q i h C p C v R energy [J] specific energy [J/kg] specific internal energy [J/kg] enthalpy [J/kg] specific heat at constant pressure [J/kgK] specific heat at constant volume [J/kgK] specific gas constant [J/kgK] Greek symbols µ dynamic viscosity [kg/ms] ν kinematic viscosity [m 2 /s] ρ density [kg/m 3 ] γ δ surface tension [N/m] thickness [m]

9 Subscripts atm melt vap decompose gen f surrounding conditions atmospheric conditions melting point vaporization point decomposition point of molecular internal generation film conditions Chemical compositon H 2 O water CO(NH 2 ) 2 urea NO x nitrogen oxide H hydrogen N 2 O 2 CO 2 NH 3 HN CO nitrogen oxygen carbon dioxide ammonia isocyanic acid Abbreviations CFD Computational Fluid Dynamics CHT Conjugate Heat Transfer UWS HTC FVM SCR RANS Urea Water Solution Heat Transfer Coefficient Finite Volume Method Selective Catalytic Reduction Reynolds-avaraged Navier-Stokes

10 Chapter 1 Introduction and Background Scania is today a manufacturer of heavy trucks, buses and diesel engines with an annual turnover of approximately 88 billion SEK and a total of employees in 100 different countries. Approximately 3000 of these work with research and development in Södertälje. Scania s diesel engines are developed mainly for their own trucks and buses but also for other heavy duty vehicles, marine applications, industrial applications and power generation [1]. This thesis is carried out at the engine development department at Scania s research and development division in Södertälje. More specific at the Fluid and Combustion simulation group which are specialized in simulations of different internal flows in the diesel engine. 1.1 Todays Diesel Engines Twenty years ago the diesel engine was a very dirty engine with high emissions and the usage was concentrated to heavy duty vehicles or other applications where high power was needed. As the world realized that we need to take care of our environment in terms of reducing fuel consumption and harmful emissions, a lot of diesel engine manufacturers started to develop more fuel efficient engines together with after treatment systems to reduce emission of particulate matter (soot) and nitrogen oxide (NO x ). Today the development has come so far that the diesel engine is a powerful challenger to other engines developed with the aim to be environmental friendly e.g. engines that runs on renewable fuels. The development of the engines is mainly driven by legislations of how much harmful emissions are allowed to be released into the air. In Europe the first regulation for diesel engines in heavy duty vehicles came This legislation was called Euro 1 and today the engine manufacturers are heading for the Euro 6 and Euro 7 legislation [2]. 1

11 As mentioned before the main focus is to reduce soot and NO x emission. Unfortunately, it is very hard to achieve fuel-efficient combustion in the engine with both low soot and NO x emission because when the combustion is optimized for low NO x, the soot emissions will be high and vice versa. This is also known as the Diesel Dilemma and can be visualized as the curved black line in Fig One way to reduce both soot and NO x is to optimize the combustion to low soot and high NO x, and then use an after treatment system to reduce NO x before the emissions goes into the air, see the colored dots in Fig Figure 1.1: European legislation for soot (PM) and NO x emission from Euro 1 to Euro 6 [3]. The black curved line shows the ratio between soot and NO x emission which is possible to achieve from the combustion process. The green dot shows the emission when the combustion is optimized for low soot and the blue dot shows the emission after a NO x reducing after treatment system Exhaust Gas After Treatment Systems The basic principle for an exhaust gas after treatment system developed to reduce NO x, is to transform the NO x into other less harmful emissions. One method for this is developed from the basic idea to let the NO x interact with a large amount of hydrogen (H), and then simplified it will transform into air (N 2 ), water (H 2 O) and a by-product 2

12 of carbon dioxide (CO 2 ) [4]. Today, Scania among other manufacturers are using Selective Catalytic Reduction (SCR) together with the Urea Water Solution (UWS) AdBlue as a hydrogen carrier to achieve this interaction. In practice the UWS will vaporize in the exhaust system and then by using the SCR application the reaction between the NO x and the vaporized UWS will start. The vaporization of UWS is a technical challenge due to the different thermodynamic properties for urea and water. In atmospheric pressure water vaporizes at 100 C and urea starts to melt and decompose at 133 C, therefore in the temperature range of 100 C 133 C the water in the UWS will vaporize leaving urea alone in a solid form [4]. If this process continues, more and more urea will get stuck in the exhaust system and prevent exhaust gases to come out from the engine, which will give pressure losses and higher fuel consumption. Therefore, it is imperative that the temperature in the exhaust system is above the decomposition and vaporization temperature of urea around 133 C 192 C [5] to make the after treatment work correctly. 1.2 Computational Fluid Dynamics The basic purpose of Computational Fluid Dynamics (CFD) is to predict the physics of real flow phenomena with the help of computers. These flow phenomena could be e. g. how the air moves inside a room or how the air moves along the wing of an airplane. In some cases there are other fluids then air involved e. g. in a water boiler where water vaporizes into the air and raises the humidity. When CFD first was developed it was a tool to complement expensive hardware testings in the industry. These hardware testings could also be hard to analyze due to its difficulty to measure complex flow phenomena inside a hardware, e.g. an engine. CFD is therefore commonly used to predict flow-patterns in or outside hardwares, where it is hard to do measurements. As mentioned before, CFD is a tool to predict the flow and therefore the user should always be critical to the accuracy of the results from a CFD simulation with respect to a real flow-pattern. Technically described, CFD is an analyzing method from the basic idea of computing equations in a numerical grid. These equations describe a three-dimensional flow, due to change in velocity and pressure, around or inside a given geometry and in some cases heat transfer is also included. The accuracy in the CFD analysis depends on several factors such as the resolution of the grid and also which equations are used to describe the flow. A high resolution grid and complex equations, demand a lot of computer power. Therefore it is always a tradeoff between the time it takes to do the computation and the accuracy wanted in the results. 3

13 There are different ways to solve the motion of the flow in the CFD applications used today. One common way is to use Reynolds-averaged Navier-Stokes (RANS) equations together with the energy equation to describe the flow and heat transfer in a given fluid domain. To be able to close the mathematical system of above equations a turbulence model is used with the basic idea to predict the turbulence in the flow. In some analysis it is desired to know how the heat transfer proceeds inside a solid, located nearby a fluid with high temperature gradients. Conjugate Heat Transfer (CHT) is commonly used together with CFD to analyze a three-dimensional heat transfer in a solid and the heat transfer between a solid and a fluid. In the NO x reducing after treatment system mentioned above, there are high temperature gradients between different places at the wall. This is because of the large energy transfer from the wall to the UWS in order to vaporize the UWS. In this case the coupled CFD and CHT computing method is a good way to predict the flow and heat transfer during the vaporization of UWS. The most common CFD softwares used today are commercial and expensive. Open- FOAM however, is a free CFD software that has begun to challenge the commercial softwares. OpenFOAM [6] is a CFD solver without a Graphical User Interface (GUI) i.e. every parameter that need to be set for a particular application, are set in a text file. Pre-processing can be done in the same way but with complex geometries it is preferable to use a software with a GUI. Post-processing is preferably done in another software such as ParaView which is a free scientific visualization software with a GUI. OpenFOAM is a software with open source which makes it possible to develop new code or modify existing code. It is made by the concept to be object oriented in the programming language C++, i.e. each application consists of several classes. In this way it is easy to change an existing code to fit a particular purpose by modifying an application to handle different classes. 1.3 Objective of the Thesis The basic objective is to modify an application in OpenFOAM to handle spray and wall film modeling of a Urea Water Solution together with Conjugate Heat Transfer in the exhaust gas after treatment system for a diesel engine. Because the geometry in the exhaust system is very complex, the simplified test domain in Fig. 1.2 will be used to allow more time for developing and testing the code. The workflow during this degree project can be divided into three different parts: Implement the viscosity for urea into OpenFOAM s library of liquid properties and verify that it behaves in the expected way for different temperatures. 4

14 Develop the new application chtmultiregionsprayfilmfoam where the classes spraycloud and surfacefilm will be implemented into the original application chtmultiregionfoam. Test the developed application chtmultiregionsprayfilmfoam with the simplified test domain in Fig. 1.2 and verify the heat transfer with basic hand calculations of heat transfer and thermodynamic. Figure 1.2: The simplified test domain, containing a fluid and a solid region. The spray creates a wall film which cools the upper surface of the solid and enable a heat transfer from the solid to the wall film. 1.4 Structure of the Thesis Chapter 2 deals with the theory of the substance urea and the SCR process in the exhaust gas after treatment system. The Chapter continues with a theory part about those elements in the field of CFD which are concerned in this thesis. Chapter 3 describes how the viscosity of urea will be determined and the approach to develop the original application chtmultiregionfoam to fit this particular purpose. This Chapter ends with a description of how the test case simulations were set up. Chapter 4 presents results from the test case simulations and Chapter 5 is a discussion of the results from the developed application chtmultiregionsprayfilmfoam and the test case simulations. The last Chapter contains general conclusions about this thesis and also some suggestions for future work in the field of exhaust gas after treatment systems together with Open- FOAM. For a more intuitive explanation through the code development, the application names in this thesis are denoted with blue color and the class names are denoted with green color. 5

15 Chapter 2 Theory In this chapter the basic theory of the vaporization of a Urea Water Solution (UWS) will be presented together with some CFD theory which correlates to the given problem formulation. This includes the governing equations for the flow, the wall film and the spray in the fluid region and also the governing equations for the heat transfer in the solid region. The temperature unit used in this thesis is Kelvin (K) and K is approximately equal to 0 C and there is no difference in the scale. 2.1 Urea and Water Solution AdBlue is a registered trademark of a UWS which contains 32.5 wt % urea and the rest is water. For the basic chemical and thermodynamic properties for water and urea see Table 2.1. The vaporization of urea is a complicated process because the chemical decomposition of urea is approximately in the same temperature range as for the vaporization of urea. This leads to the formation of different by-products, with other vaporization properties than pure urea. There is also studies of chemical decomposition of urea slightly above the melting temperature of urea [7]. The desired chemical decomposition and vaporization of a UWS for the Selective Catalytic Reduction (SCR) process is as follows: The water (H 2 O) in the UWS will first vaporize, leaving solid urea (CO(NH 2 ) 2 ) behind, CO(NH 2 ) 2 (l) + H 2 O(l) CO(NH 2 ) 2 (s) + H 2 O(g) (2.1) The solid urea will then vaporize to ammonia (NH 3 ), which will act as the hydrogen carrier, and isocyanic acid (HN CO), CO(NH 2 ) 2 (s) NH 3 (g) + HNCO(g) (2.2) 6

16 The icocyanic acid will then transform to ammonia leaving a by-product of carbon dioxide (CO 2 ), HNCO(g) + H 2 O(g) NH 3 (g) + CO 2 (g) (2.3) At last, ammonia will interact with nitrogen oxide (NO x ) in the exhaust gases and oxygen (O 2 ) leaving nitrogen (N 2 ) and water behind, 4NH 3 (g) + 4NO(g) + O 2 (g) 4N 2 (g) + 6H 2 O(g) (2.4) For a more detailed explanation of the chemical decomposition of a UWS, with all byproducts formations see [4], and for the SCR technique with urea see [8]. In OpenFOAM the dynamic viscosity for urea is modeled to be the same as for water. This is because of the almost non-existing knowledge of the behavior of pure urea in liquid form. Therefore it is imperative to first determine a better approximation of the real dynamic viscosity for urea to be able to more accurately simulate the given simulation domain. Water Urea Chemical composition H 2 O CO(NH 2 ) 2 Properties at 300K Density ρ 996 kg/m kg/m 3 * Specific heat capacity C p 4177 J/kgK 2006 J/kgK* Dynamic viscosity µ kg/ms Surface tension γ N/m 1 N/m* Vapor pressure p vap 3565 kp a 0 kp a* Thermal conductivity k 0.61 W/mK Properties at p atm T melt 273 K 406 K T vap 373 K 466 K* T decompose > 423 K Heat of vaporization H vap 40.7 kj/mol kj/mol Table 2.1: Liquid properties for water and urea from [4] and [9]. Dynamic viscosity and thermal conductivity for urea is modeled to be the same as for water in OpenFOAM and the values with a * are from the liquid properties library in OpenFOAM [5]. 7

17 2.2 Governing Equations The text in the following section is based on the book An Introduction to Computational Fluid Dynamics, The Finite Volume Method by H. K. Versteeg and W. Malalasekera [10]. As mostly everything in the field of mechanics the behavior of a flow could be described by Newton s second law which states: The rate of change of momentum for a fluid particle = The sum of all forces acting on the fluid particle In other words there is a way to describe the flow when all forces are known. But when it comes to fluid dynamics one surface force, the viscous stress τ ij is really hard to determine. The viscous stress force acts in three dimensions at each of the three different planes in a three dimensional coordinate system. This implies that six unique viscous stress terms (due to symmetry) need to be determined to be able to describe the movement for a fluid particle. The continuity equation together with the momentum equation in three dimensions are used to describe the movement for a fluid particle according to this viscous stress tensor plus a sum of all other active forces (see [10] for the derivation of the momentum equations). This implies six unknown viscous stress variables in four equations and therefore it is not a mathematically closed system. The Navier-Stokes equations are derived from the momentum equations in three dimensions with the statement that the viscous stress is proportional to the deformation rate of a fluid particle. This statement applies only for a Newtonian fluid which means that the viscous stress change linearly with respect to the strain rate. Due to the given problem formulation, this thesis only regards compressible flows for Newtonian fluids. The Navier-Stokes equations reads, (ρu) t (ρv) t + div(ρuu) = p x + div(µ grad u) + S Mx (2.5) + div(ρvu) = p y + div(µ grad v) + S My (2.6) (ρw) + div(ρwu) = p t z + div(µ grad w) + S Mz (2.7) and the continuity equation, ρ + div(ρu) = 0 (2.8) t 8

18 together with the equation of state after which a more explicit form of the behavior of the flow is obtained, p = p(ρ, T ) and i = i(ρ, T ) (2.9) e.g. perfect gas p = ρrt and i = C v T where ρ is the density for the fluid, p is pressure and µ is dynamic viscosity. The variables u, v and w define the flow velocity in the x-, y- and z-direction as well the velocity vector u contain all these velocity components. The variable S M contains the external forces acting on the fluid particle. For the equation of state the variable i define the internal energy for the fluid particle, R the specific gas constant, T the temperature and C v the specific heat capacity at constant volume. With the Navier-Stokes equations , the continuity equation 2.8, the equation of state 2.9 and the energy equation, it is possible to get a mathematically closed system with seven unknowns and seven equations. The energy equation reads, ρ i t + div(ρiu) = p div u + div(k grad T ) + Φ + S i (2.10) where k is the thermal conductivity for the fluid, Φ the dissipation function describing the effects due to viscous stresses and S i is the internal energy of the fluid particle except the kinetic energy Reynolds-avaraged Navier-Stokes equations The Reynolds number (Re) measure the intensity of the flow within certain places with respect to inertia forces and viscous forces. For Reynolds numbers above Re critical, the behavior of the flow will be random and chaotic, i.e. turbulent flow. Within a certain point in a turbulent flow the velocity will fluctuate randomly over time, see Fig Figure 2.1: Measuring of velocity in an arbitrary point located in a turbulent flow. 9

19 This velocity is decomposed into u(t) = U + u (t) where U is the mean velocity vector and u (t) is the fluctuating components according to the turbulent behavior of the flow. This is called the Reynolds decomposition and is the start of modeling turbulence. By introducing the flow property φ, which represents the necessary flow terms such as velocity, pressure, temperature etc, the flow can be declared in a more overall definition as, φ = Φ + φ (2.11) Reynolds averaging is also known as time averaging (or ensemble averaging when the boundary conditions for the flow are time-dependent) of φ in equation 2.11 as, φ = Φ + φ (2.12) where, Φ = Φ (2.13) T φ 1 = lim T T 0 φ (t)dt = 0 (2.14) T: averaging interval To continue, all the time averaged flow terms from equation 2.12 are substituted into the Navier-Stokes equations and the continuity equation 2.8. Thus, the Reynoldsaveraged Navier-Stokes equations (RANS) for compressible flows are obtained (see [10] for the derivation of the RANS equations), ( ρũ) t +div( ρũũ) = P [ ] +div(µ grad Ũ)+ ( ρu 2 ) ( ρu v ) ( ρu w ) +S Mx x x y z [ ] (2.15) ( ρṽ ) P +div( ρṽ Ũ) = +div(µ grad Ṽ )+ ( ρu v ) ( ρv 2 ) ( ρv w ) +S My t y x y z (2.16) ( ρ W [ ] ) P +div( ρ W Ũ) = t z +div(µ grad W )+ ( ρu w ) ( ρv w ) ( ρw 2 ) +S Mz x y z (2.17) and the continuity equation, ρ + div( ρũ) = 0 (2.18) t where ρ is the mean density for the fluid and P is the mean pressure. The variables Ũ, Ṽ and W is the density-weighted or Favre-averaged velocity components in the x, y and z-direction as well the velocity vector Ũ contain all these velocity components. The terms located inside the brackets are the turbulent stresses, also known as the Reynolds stresses. 10

20 2.2.2 Turbulence Models To be able to solve the RANS equations, the Reynolds stresses need to be modeled which often refers to turbulence modeling. Over the past years, several turbulence models have been developed such as Spalart-Allmaras, k ɛ, k ω, SST k ω, Reynolds stress model etc. These turbulence models contain different amount of equations to calculate the turbulence in the flow, e.g. Spalart-Allmaras uses one equation and the Reynolds stress model evaluates all Reynolds stresses independently with seven equations. The k ɛ model is a two equation turbulence model which have been proven accurate in flows with flat boundary layer and in flows near smooth geometries. It is widely used because of its stability and fast convergence in a lot of different industrial cases [10]. Therefore, the k ɛ turbulence model is used in this thesis where the geometry is simple and fast convergence is desirable for testing and verifying the developed code. The k ɛ turbulence model is built up by the transport equation of turbulent kinetic energy k, [ ] (ρk) µt + div(ρku) = div grad k + 2µ t S ij S ij ρɛ (2.19) t σ k and the transport equation for the dissipation of turbulent kinetic energy ɛ, [ ] (ρɛ) µt ɛ + div(ρɛu) = div grad ɛ + C 1ɛ t σ ɛ k 2µ ts ij S ij C 2ɛ ρ ɛ2 k (2.20) where the S ij tensor is the mean deformation rate of a fluid particle and the term µ t is the eddy viscosity defined as, k 2 µ t = ρc µ (2.21) ɛ The five constants in equation are set to default values according to [10] as, C µ = 0.09 σ k = 1.00 σ ɛ = 1.30 C 1ɛ = 1.44 C 2ɛ = 1.92 (2.22) 2.3 Spray Modeling A spray is tricky to model in CFD softwares firstly due to the random velocity direction for all the droplets coming out of the spray. Every droplet also has a random size and mass which makes it even harder to make an accurate prediction of a spray. In OpenFOAM the spray is modeled to be a given amount of parcels coming out of the spray where this amount is set in the pre-processing part. The total mass injected in the system through the spray is also set in the pre-processing part and together it is possible to determine the mass given to each parcel. Each parcel is also given one random number from a stochastic variable at the outlet, which declares the radius for the droplets in that specific parcel. Thus, the mass (or volume) given to each parcel rarely match the volume for the droplets in that parcel due to the different radius for the 11

21 droplets. This gives that the amount of droplets in each parcel is a statistical number which most certain vary from a fraction of a droplet to thousands of droplets, e.g. a parcel can contain number of droplets [11]. In aspect of the flow in the simulation domain, the parcels or droplets will impact on the fluid particles according to Newton s second law. This extra force is included in the external force S M in the Navier-Stokes equations Unlike the Eulerian representation of the flow, the spray is modeled with a Lagrangian representation, i.e. all parcels from the spray are tracked separately inside the fixed numerical grid which is used by the flow equations. This will remove the necessity for resolving the nozzle and will therefore need less computational power [11]. 2.4 Wall Film Modeling Wall film modeling in CFD softwares is a challenge because of the complex formation of the liquid film at the wall and also the multiphase treatment required to handle both gas and liquid. The formation of the liquid film at the wall is especially hard to predict due to the many external factors that will affect the formation, such as gas flow, gravity, wall properties and wall roughness. The properties of the liquid will also affect the formation such as viscosity, which will be discussed later in this thesis, but also surface tension and surface shear which are a subject that will not be discussed in this thesis. In OpenFOAM the wall film is modeled to be in an own external mesh region extruded from the fluid region. This mesh region is one layer thick and the flow perpendicular to the surface is neglected which imply a two-dimensional flow along the wall. The flow is modeled with a continuous Eulerian phase with the momentum, continuity and the energy equation. The thickness of the liquid film is derived from the momentum and continuity equation [12]. The class surfacefilm in OpenFOAM (which is used to solve the movement of the liquid film) can only handle one chemical component and not a multi component mixture. First of all, this implies that the liquid for the wall film is the only component which can be defined in the wall film region and the gas in the fluid region is not included in the wall film region. In reality, if the velocity of the gas flow is relatively high, the gas flow located in the frontline of the liquid film (while it is being formed) most likely will experience some adverse pressure gradients near the wall. These adverse pressure gradients can create vortices or turbulence which can interfere with the formation of the liquid film. However, if the liquid film is relatively thin and the velocity of the gas flow is low, these effects will most likely be negligible. Secondly, because of the non multi component mixture of the liquid in the wall film region, the liquid film can only be defined to handle urea or water, not a UWS as for 12

22 the after treatment system case. Since the objective of this thesis is formulated by the usage of a UWS, the results will be different than expected and the liquid film will only be urea or water independently. 2.5 Conjugate Heat Transfer Heat transfer inside a solid can be described according to the law of heat-conduction or Fourier s law in one-dimension as reads, q x = ka T x (2.23) where q x is the heat transfer rate, k is the thermal conductivity, A is the area of the surface perpendicluar to the direction of the heat flow and T/ x is the temperature gradient in the direction of the heat flow. With equation 2.23 it is possible to derive a three-dimensional heat-conduction equation as reads, x (k T x x ) + y (k T y y ) + z (k T z z ) + q T gen = ρc p t (2.24) where q gen is the heat generation inside the solid, ρ is the density of the material and C p is the specific heat at constant pressure [13]. Heat transfer from a fluid to a solid is mainly caused by convection but a small part also comes from radiation which in this thesis is neglected to give more time for code development. The convection part is normally natural driven when the density for a fluid changes nearby a hot or cold solid, causing the fluid to move due to the density gradient. If external forces makes the fluid to move around at the surface of the solid, e.g. when a fan blows on a hot radiator, it is called forced convection. The convection heat transfer can simplified be described by Newton s law of cooling as reads, q = h(t wall T ) (2.25) where q is the heat transfer rate, h is the Heat Transfer Coefficient (HTC), T wall is the temperature at the wall and T is the surrounding temperature [13]. In CFD softwares, heat transfer between a solid and a fluid is called Conjugate Heat Transfer (CHT). This involve variations of temperature within a solid and a fluid because of the thermal interaction between the solid and the fluid, i.e. the three-dimensional heat-conduction equation 2.24 in the solid is coupled with the energy equation 2.10 in the fluid. 13

23 2.6 The Finite Volume Method The Finite Volume Method (FVM), or the control volume method, is a numerical method developed to handle the transport process of diffusion and convection (advection) for the governing equations. The basic idea of the FVM is to divide the domain into discrete control volumes where each side has the specified length i. Inside each control volume and in each corner of the control volumes, certain nodal points are located. The control volumes together with the nodal points construct a so-called staggered grid which is visualized in Fig. 2.2 for a two-dimensional case. Figure 2.2: A two-dimensional staggered grid for the FVM where P is referring to the current point where the flow properties will be calculated and the N, S, W and E letters refers to the north, south, west and east point. The grey cells refer to the staggered cells with central point n, s, w and e, which characterize the staggered grid in the FVM. The next step is the integration of the governing equations over the grid to yield discretized equations at the arbitrary node point P. To solve these discretized equations in point P, the flow properties in the neighbor nodes need to be known. In the middle of the simulation domain these flow properties will be unknown, but if nodal point P is located at the beginning of the domain, the boundary conditions will define the flow properties for the first node. This process will then proceed through the domain over and over until the flow properties between two iterations are less than a certain tolerance criterion set by the user. In a three-dimensional case as in this thesis, the approach is similar but with one more dimension (see [10] for a more detailed description of the FVM). The three-dimensional FVM is used in OpenFOAM for solving the flow equations in the fluid and also for the heat distribution inside solids. This implies a natural connection between the fluid and the solid in the simulations with CHT. 14

24 Chapter 3 Method This chapter starts with presenting how urea is modeled to fit this particular application. It continues with a description of the workflow during the spray and wall film implementation and also the approach to use a buffer layer region with the developed application chtmultiregionsprayfilmfoam. At last, there is a presentation of how the CFD simulations for the test case are set up with all necessary parameters and approximations. 3.1 Modeling Liquid Urea The natural state of urea at atmospheric conditions is to be a solid. But it is difficult to simulate a phase change from solid to liquid. This is mainly because of the numerical instability when calculating the flow equations, i.e. when the fluid instantly goes to a solid. In other words the flow equations need to be active in the fluid region but not in the solid region. To handle a case when ice melts to water, the solver need to be capable to solve the partially melted regions in the ice and also the huge energy transfer to the ice during the melting process. To make such a case the solver and the numerical grid need to be complex which in the end requires more computational power. Vaporization of a Urea Water Solution (UWS) in the after treatment system is a technical challenge because of the vaporization of water before urea. To do an accurate CFD simulation for this scenario, urea needs to be modeled as a liquid below T UreaMelt but still behave as a solid. A way to achieve this is to model urea as a liquid with a viscosity that will go very high when the temperature drops below T UreaMelt (i.e. urea will be like a very viscous syrup). The correct viscosity of melted urea above T UreaMelt is hard to determine due to the complex decomposition of urea, i.e. the liquid substance of melted urea will most likely be a chemical compound of different substances. Thus, the correct behavior of pure urea in terms of viscosity is not investigated in this thesis and is not desirable either, due to the infrequent presence of pure melted urea in the after treatment system. In other words, the modeling of liquid urea in this thesis is only a way to predict where it is possible for this chemical compound to grow stiff in the after 15

25 treatment system. In OpenFOAM the liquid properties for fluids are modeled with the functions from the National Standard Reference Data System (NSRDS) [14]. To model dynamic viscosity OpenFOAM is using the NSRDS function no. 1 which reads, µ(t ) = e A+ B T +ClogT +DT E (3.1) The dynamic viscosity for mostly all the fluids in OpenFOAM is described by setting different values for the parameters A to E in function 3.1. Water e.g. have the parameters A to E set in a way which gives the T µ curve shown in Fig. 3.1 (please see appendix A.1 for the values of each parameter A to E). One way to achieve a desirable behavior for the dynamic viscosity of urea is to use the T µ curve for water and basically shift the curve to the right, as can be shown in Fig. 3.1, giving that the viscosity will grow very high at T UreaMelt instead of at T W atermelt as for water. Thus, the desirable dynamic viscosity for urea needs to be described with the function 3.1 by setting parameters A to E to certain values. A method for this is to use the Matlab function lsqcurvefit with the desirable T µ curve for urea as an input value. Figure 3.1: T µ curve for water and a desirable T µ curve for urea. 16

26 3.2 Development of chtmultiregionsprayfilmfoam The original application chtmultiregionfoam in OpenFOAM v2.1.0 is developed to handle transient compressible flow and heat transfer calculations in an arbitrary numbers of fluid and solid regions. The three-dimensional heat transfer in the solid is handled by heatconductionfoam and the conjugate heat transfer between the solid and the fluid regions is handled by buoyantfoam, see the User Guide [15]. To calculate heat transfer and vaporization of liquid urea in the after treatment system case, the application chtmultiregionfoam needs to be able to handle spray and wall film calculations in each fluid region. For the spray calculations, the class spraycloud is implemented in the solver for chtmultiregionfoam. In the same way the class surfacefilm is implemented in the solver and the new application is called chtmultiregionsprayfilmfoam. To handle the extra thermodynamic which comes with the liquid spray and the liquid wall film in the gas flow, some other classes also need to be implemented. For a more detailed overview of the implementation, see appendix B.1. The implementation is done with help from the Programmer s Guide [16]. A tutorial for the developed application chtmultiregionsprayfilmfoam is presented in appendix B The Wall Film Region Solving the spray with spraycloud is carried out in the ordinary fluid region, but solving the wall film with surfacefilm is carried out in an own mesh region as described in Section 2.4. This mesh region is extruded from the ordinary fluid mesh region with the application extrudetoregionmesh, see Fig The input parameters for this application are basically which wall to be extruded, number of cell layers in the new extruded mesh (surfacefilm is only compatible with one cell layer) and thickness for the new extruded mesh. Figure 3.2: A visualization of the numerical grid of a fluid and the wall film extrusion of a single cell layer mesh from the fluid region mesh. 17

27 Thus, in the test domain shown in Fig. 1.2, the mesh for each region is split before the mesh for the wall film is created. This implies that the mesh for the wall film region will be extruded into the mesh for the solid region. In visualization purpose this could be confusing but for the solver this is not a problem because the different meshes are calculated separately and the connection between the boundaries for each region are not affected by the position of the boundaries. Due to the two-dimensional flow and the separate wall film thickness variable derived from the momentum and continuity equation, as presented in Section 2.4, the thickness of the mesh is irrelevant for the formation of the liquid film The Buffer Layer In reality, the heat transfer will go instantly from the solid to those places at the surface in which a liquid film is formed. In the other places where there is gas, the heat transfer will be described by a Heat Transfer Coefficient (HTC). In the wall film region in OpenFOAM, it is not possible to calculate a HTC due to the lack of thermodynamic properties for the gas. This is because the wall film region only contains one chemical component, i.e. the liquid film. The connection between a fluid region and a wall film region is carried out via the settings for the boundary and is handled automatically with the application extrudetoregionmesh. In chtmultiregionfoam, the connection between a solid and a fluid region is carried out automatically when using the application splitmeshregions. However, when connecting a wall film region to a solid region, there will be a direct temperature coupling from the wall-film-to-solid boundary to the solid-to-wall-film boundary and not a heat transfer depending on a HTC. A way to circumvent this is to introduce a buffer layer between the wall film and the solid, please see Fig The buffer layer is a way to solve the problem with the HTC because the buffer layer is an ordinary fluid region where the desirable thermodynamic properties for the gas will be available. The buffer layer will basically be a thin fluid region with the same fluid properties as for the big fluid region. This implies a heat transfer from the solid to the buffer layer, with a correct calculated HTC. The connection between the buffer layer and the wall film will be an ordinary fluid-to-wall-film connection, enabling a correct heat transfer from the buffer layer to the liquid film. However, due to the very low thermal conductivity for air, the buffer layer will act as an insulating layer between the liquid film and the solid. In order to have a direct heat transfer from the solid to the liquid film and a heat transfer depending on a HTC from the solid to the gas, two new scalar fields need to be created in the chtmultiregionsprayfilmfoam code. The first scalar field will contain the new thermal conductivity variable Kliq which will be used in the buffer layer. This variable will have the same thermal conductivity as the original conductivity for the gas in the fluid region, except at those faces where a liquid film is formed. In these faces, Kliq 18

28 shall be set to the same thermal conductivity as the liquid film. Figure 3.3: A visualization of the position for each region and the connection between. To know where the liquid film is formed, the other scalar field will contain a new variable called deltamap, which will be mapped from the wall film thickness deltaf located in the wall film region. Thus, with the variable deltamap it is possible to know in which cells the liquid film is formed and by that, which cells should have greater thermal conductivity by changing the variable Kliq (see appendix B.2 for the implementation of Kliq and deltamap). The value for the new thermal conductivity is set by the user through the parameter KValue in the file constant/bufferlayer/surfacefilmproperties and shall be set to the same thermal conductivity as the liquid film. The mesh for the buffer layer is copied to be the exact same mesh as for the wall film region. This makes the pre-processing when setting up a buffer layer much faster. If the buffer layer is thin, the flow calculations will have some numerical instability, i.e. for a good convergence, the buffer layer needs to be relatively thick. The mesh for the buffer layer shall be one cell layer thick for the new approach with the Kliq and deltamap variable to work. 19

29 3.2.3 Assumptions and Approximations Heat transfer from radiation is assumed to be negligible. This is because the heat transfer via radiation is normally much less than the heat transfer via convection, in cases similar to the after treatment system case. In other words, the effect of adding radiation for the after treatment system case in this thesis, will be negligible changes in the result and a lot of more time will be spent on developing the code. The thermal conductivity variable Kliq is activated in the cells where the wall film thickness is > 10 6 m. This is because a wall film thickness less than 10 6 m is assumed to have negligible effect on the heat transfer between the wall film and the solid. The thermal conductivity variable Kliq is set to a constant value by the user in the pre-processing part. Since the temperatures within the wall film do not have high temperature gradients, and because the temperature for a liquid is often related to the thermal conductivity, the change of thermal conductivity between different places within the wall film is most likely negligible. 20

30 3.3 Simulation Setup for the Test Case Six different transient simulations are made with two different liquids for the spray and two different materials for the solid according to Table 3.1. Air is used as fluid in the fluid region instead of exhaust gases which implies that no chemical reactions are taking place, i.e. chemical reactions are deactivated in all simulations. Case Fluid Solid Spray Time Vaporization 1 Air Copper 100 g Urea 1.2 s No 2 Air Copper 100 g Water 1.2 s No 3 Air Copper 10 g Water 2.5 s Yes 4 Air Copper 10 g Urea 2.5 s Yes 5 Air Steel, 1% C 10 g Water 2.5 s Yes 6 Air Steel, 1% C 10 g Urea 2.5 s Yes Table 3.1: Fluid and solid properties for the test simulations made with the chtmultiregionsprayfilmfoam application Computing Platform The CFD simulations are made on a local workstation with six CPU cores of 2.93 GHz each and 24 GB RAM. Operating system is Linux Red Hat distribution v and the code development is made from OpenFOAM v Simulation Domain and Boundary Conditions The simulation domain with dimensions is located in Fig Figure 3.4: A sketch of the simulation domain with dimensions. The thickness of the solid is 0.01 m and the direction of the spray is in the same direction as for the gravity, i.e negative y-direction. The spray creates a wall film which cools the upper surface of the solid and enable a heat transfer from the solid to the wall film. 21

31 The Fluid The air in the fluid region is a mixture of 23.4% oxygen (O 2 ) and 76.6% nitrogen (N 2 ). The boundary conditions are set according to Table 3.2. The boundary to wall film is set to slip condition because the non-existing gas in the wall film region assumed to flow with the same velocity as the fluid region. The buoyantpressure condition for the outlet calculates the normal gradient from the local density gradient. The initial conditions for velocity and temperature are set to be the same as for the inlet and the initial pressure is P a. Inlet Outlet p calculated calculated p rgh zerogradient buoyantpressure T fixedvalue zerogradient - value 300K - U fixedvalue inletoutlet - value 0.5 m/s 0.5 m/s (inletvalue = 0 m/s) Walls Boundary to wall film p calculated calculated p rgh zerogradient zerogradient T zerogradient mapped - value - - U fixedvalue slip - value 0 m/s - Table 3.2: Boundary conditions for the fluid region. The Wall Film The surface film model is defined to be the OpenFOAM specific thermosinglelayer with the surface shear coefficient set to 0.9. The liquid in the wall film is defined to contain either water or urea. The boundary conditions are set according to Table 3.3. Vaporization is activated with the phase change model standardphasechange. Walls Boundary to fluid Boundary to buffer layer T f zerogradient zerogradient zerogradient - value U f fixedvalue mapped fixedvalue - value 0 m/s - 0 m/s Table 3.3: Boundary conditions for the wall film region. 22

32 The Buffer Layer Air is used as fluid in the buffer layer with the same composition as the air in the fluid region. The boundary conditions are set according to Table 3.4. The initial conditions for velocity and temperature are set to be the same as for the inlet and the initial pressure is P a. The thermal conductivity Kliq in the buffer layer is set to water according to Table 2.1 in all cases. Inlet Outlet Walls p zerogradient zerogradient zerogradient p rgh zerogradient zerogradient zerogradient T fixedvalue zerogradient zerogradient - value 300K - - U fixedvalue inletoutlet fixedvalue - value 0.01 m/s 0.01 m/s (inletvalue = 0 m/s) 0 m/s Boundary to wall film Boundary to solid p zerogradient zerogradient p rgh zerogradient zerogradient T mapped turbulenttemperaturecoupledbafflemixed - value - - U mapped fixedvalue - value - 0 m/s Table 3.4: Boundary conditions for the buffer layer. 23

33 The Solid The simulations are made with two different types of material for the solid, copper and steel with 1% carbon. The thermodynamic properties for these materials are shown in Table 3.5. The initial temperature in the solid is set to 300K and the only energy transfer is between the buffer layer and the solid. The other walls are adiabatic with the OpenFOAM specific zerogradient boundary. The surface coupled to the buffer layer are set with the OpenFOAM specific conjugate heat transfer boundary, turbulenttemperaturecoupledbafflemixed. Copper (Cu) ρ 8954 kg/m 3 C p 384 J/kgK k 398 W/mK Steel with 1% C ρ 7800 kg/m 3 C p 473 J/kgK k 43 W/mK Table 3.5: Thermodynamic properties for the materials representing the solid in the simulations [9]. The Spray The external forces which are affecting the spray are gravity and drag. The heat transfer model for the interaction between the parcels and the fluid is RanzMarshall and vaporization is activated with the phase change model liquidevaporationboil. The properties for the spray are presented in Table 3.6. For liquid properties of water and urea see Table 2.1. Nozzle type t start t end D spraynozzle θ spraycone U spray T spray m total conenozzleinjection 0 s 1 s 2 mm 5 1 m/s 293K 10 g / 100 g N r. of parcels D parcels (uniform distribution) 1 mm Table 3.6: Spray properties for the water and urea spray. 24

34 3.3.3 Mesh and Solution Criteria The mesh is structured and the total number of elements and element size for each region are shown in Table 3.7. A visualization of the mesh is shown in Fig An analysis of a results independent mesh has not been done since this thesis only regard spray and wall film modeling with CHT in OpenFOAM. Tolerance criterias for the most common flow properties are listed in Table 3.8. Fluid elements size 1.6 mm 3.3 mm Solid elements size 1 mm 3.3 mm Elements in wall film and buffer layer size 2.2 mm 3.3 mm Table 3.7: Number of elements and size of elements. The wall film and the buffer layer have a thickness of 10 mm for a single cell layer beyond the listed element size in the table. Figure 3.5: A visualization of the mesh. The blue region is the fluid region and the grey region is the solid region. The mesh for the wall film region and the buffer layer is not shown because these are inside the solid region. 25

35 Fluid Region Wall Film Buffer Layer U p rgh ρ h s Table 3.8: Tolerance criterias for all test case simulations for the most common flow properties where p rgh is the pressure with the buoyancy from the air and h s is the sensible enthalpy. The tolerance criteria for the temperature in the solid region is For a more detailed overview of all tolerance criterias and the relaxation factors for the buffer layer (the only region that use relaxation factors), see the solution setting files in appendix C.1. The files with all numerical schemes used in the test simulations are located in appendix C.2 and a description for each scheme is found in Table C.1. The turbulence model used is the k ɛ model with default values for all modeling constants. The initial time step is set to s and the maximum time step is manually adjusted between s s where the shorter time step is set during the spray injection. 26

36 Chapter 4 Results This chapter starts by presenting the new viscosity for urea in OpenFOAM and the results from the behavior of liquid urea with respect to water. The results from the test case simulations with the developed application chtmultiregionsprayfilmfoam are then presented with a brief description of the most interesting parts. 4.1 Urea Viscosity After several iterations with lsqcurvefit the parameters A to E are set in a way which enables the function 3.1 to fit the desirable T µ curve for urea shown in Fig. 4.1 (please see appendix A.2 for the Matlab code and appendix A.1 for the calculated values of each parameter A to E). Figure 4.1: The desirable T µ curve for urea together with the T µ curve for urea calculated from function

37 Two simulations are done according to case 1-2 in Table 3.1. The simulations are done with water respectively urea as the spray liquid to verify the new dynamic viscosity for urea. The total injected spray mass is 100 g in both cases and vaporization is not active. The temperature for the spray is 293K and the rest of the domain has a surrounding temperature of 300K. The dynamic viscosity for water at 300K is kg/ms and for urea kg/ms which implies that urea appear as a liquid, approximately 100 times more viscous than water in these test simulations. A comparison for the wall film thickness of water and urea is shown in Fig. 4.3 and the formation of the wall film can be seen in Fig Figure 4.2: The formation of the wall film with water or urea at the upper surface of the solid (the xz-plane in Fig. 3.4). The left picture couple show wall film thickness deltaf [m] after t = 0.2 s and the right show after t = 0.8 s. The lines show the extraction points which are used in Fig. 4.3 and the spray is located at z = 0.03 m. 28

38 In Fig. 4.2 at t = 0.8 s the wall film for the water case is formed to the end of the domain and in the case with urea it is only formed to approximately 80% of the length of the domain. From the results of wall film thickness in Fig. 4.3 it is found that the formed wall film at the location of the spray impact at t = 0.2 s, is more extended in the case with the water spray than in the case with the urea spray. Figure 4.3: Comparision of wall film thickness deltaf [m] for water and urea. The left figure show wall film thickness at the location for the spray impact after t = 0.2 s and the right show in the middle of the test domain after t = 0.8 s. The extraction lines are visualized in Fig chtmultiregionsprayfilmfoam Four simulations are done according to case 3-6 in Table 3.1. The total injected spray mass is 10 g in all cases and vaporization is active in all regions. Fig. 4.4 show the surface temperature at the solid for all four cases and when compared to the formation of the wall film in Fig. 4.2, it is possible to verify the heat transfer from the solid to the wall film (through the buffer layer) since the heat distribution at the solid is similar to the wall film formation. With Table 3.5 and the dimension for the solid from Fig. 3.4, it is calculated that the copper solid has an energy conservation of 1375 J/K and the steel solid has 1476 J/K. Simplified, this implies in a steady state condition that a water spray with the total mass of 10 g and with the temperature of 293K, will cool the total temperature for the copper solid 0.21K and the steel solid 0.20K, if there only occur heat transfer from the solid to the wall film. In the same way a urea spray will cool both the copper and the steel solid 0.10K. 29

39 Figure 4.4: Surface temperature T [K] at the upper surface of the solid (the xz-plane in Fig. 3.4) after t = 1.5 s. The left picture couple show surface temperature with a water spray and the right with a urea spray. The lines show the extraction points which are used in Fig. 4.5 and the spray is located at z = 0.03 m. Since there is heat transfer from the air region to the spray, from the air region to the wall film and since the fluid in the buffer layer also will be cooled by the wall film, the temperature drop for the solid will be much less than K and 0.10K. Table 4.1 show the total temperature and change of conserved energy for the solid and the wall film after 1.5 s. 30

40 Case T total,solid [K] Q solid [J] T total,film [K] Q film [J] Urea, Cu Urea, Steel Water, Cu Water, Steel Table 4.1: Total temperature and change of conserved energy (with respect to initial temperature, 300K for the solid and 293K for the spray) for the solid and the wall film after 1.5 s. Figure 4.5: Temperature drop in different places at the surface of the solid for t = 1.5 s. The temperature is normalized with 0.10K and the black line refer to the initial temperature (300K). The extraction lines are visualized in Fig The temperature in Fig. 4.5 is normalized with the total temperature drop of 0.10K for the solid if a urea spray cools the solid, as presented in the beginning of this section. This implies that the normalized temperature at the surface of the solid in the case with 31

41 a urea spray in Fig. 4.5, should be 1 if there is an adiabatic process and steady state condition has been reached (if it is 0 it means that there is no heat transfer at all). The thermal conductivity for copper is almost 10 times higher than it is for steel (see Table 3.5). It is found from Fig. 4.5 that the surface temperature at the solid differ the most between the cases with a copper solid and a steel solid which most likely are because of the difference in thermal conductivity. The wall film cools the solid more widely in the case with water than urea, e.g. see cross section z = 0.03 m for 1.5 s and z = 0.06 m for 2.5 s in Fig In the same figure at z = 0.20 m for 2.5 s it is possible to see the effect of re-heating the solid from the fluid region (i.e. buffer layer) when the wall film has flowed past the z = 0.20 m location. Figure 4.6: Cross section of the solid at four different locations. The comparison are only for the steel solid where the top picture group show for t = 1.5 s and the bottom group for t = 2.5 s. The location for all cross sections are visualized in Fig. 4.4 and the cross section at z=0.03 is the spray location. The energy loss via the outlet for the buffer layer is most uncertain in these results but can be approximated in a simplified way. If it is assumed that all the air that goes out through the outlet, have been instant cooled from the inital temperature of the buffer layer (300K) to the mean temperature of the wall film after 1.5 s (295K, see Table 4.1), it is found that during 1.5 s there is a total energy loss of 0.09 J. This is calculated 32