Numerical Modelling of the flow and settling in a Trailing Suction Hopper Dredge
|
|
- Ethan Adrian Douglas
- 6 years ago
- Views:
Transcription
1 Numerical Modelling of the flow and settling in a Trailing Suction Hopper Dredge C. van Rhee Faculty of Mechanical Engineering and Marine Technology, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands. ABSTRACT A Trailing Suction Hopper Dredge (TSHD) is loaded by pumping a sand-water mixture in the cargo hold, the so-called hopper. Sand settles in the hopper and the excess water flows overboard. During the loading stage a part of the volume of sand pumped in the hopper will not settle but is lost with the overflow. In this paper a two-dimensional numerical model to simulate the flow and settling in a hopper will be presented. The model is based on the Reynolds Averaged Navier Stokes equations with a k-epsilon turbulence model. The model includes the influence of the overflow level of the hopper (moving water surface) and a moving sand bed due to the filling of the hopper. The influence of the particle size distribution (PSD) is included in the sediment transport equations. The computational results will be compared with experiments and prototype measurements. 1 INTRODUCTION A Trailing Suction Hopper Dredge (TSHD) (figure 1) is a sea-going vessel that is equipped with one or two suction pipes, which are lowered to the bottom during dredging. From the bottom a sand-water mixture is sucked up and discharged in the cargo hold, the so-called hopper. Sand settles and when the hopper is filled the ship sails to the locating where the load is being dumped or pumped ashore. When relative fine sand is loaded a part of the incoming sand will not settle, but will be lost overboard with the overflow. For production, sand quality and environmental reasons it is important to develop a method to predict these so-called overflow losses. For this reason a research program was initiated and financed by the Dutch dredging industry to improve knowledge and to develop a model that included the influencing factors. The research program consisted of three parts: Laboratory tests. Numerical modelling using one-dimensional (1DV) and two-dimensional approaches. Prototype verification of the numerical models. In this paper the developed two-dimensional numerical model is described. The model results are compared with laboratory and prototype tests.
2 Figure 1. Trailing Suction Hopper Dredge HAM PROCESS DESCRIPTION The research programme started with model hopper sedimentation tests (8). During these large-scale model tests a flow pattern was observed that could be schematised as indicated in figure 2. The inflow is located at the left side and the overflow at the right side of the hopper. The hopper area can be divided into 5 different sections: Inflow section, settled sand, density current over settled bed, horizontal flow at surface towards the overflow and the suspension in the remaining area. Figure 2. Schematised flow field inside hopper In the inflow section the incoming mixture flows towards the bottom owing to the high density. An erosion crater is formed below the inflow area. Over the sandbed a density current flows from which sand will settle. Depending on the operational parameters a part of the incoming sediment will not settle and will move upward into suspension. At the water surface a relative strong horizontal flow of low concentrated mixture towards the overflow is present.
3 2.1 Existing hopper sedimentation models Based on Camp s theory In the past a number of models to describe the hopper sedimentation process are published. These models were all based on the ideal settlement basin theory of Camp (1946) and Dobbins (1944). In this theory the hopper is divided in three areas: the inflow, outflow and settling sec-tion. It is assumed that the mixture flows horizontally from the inflow to the overflow section. Both the flowfield as the diffusion coefficient are based on a velocity distribution (uniform or logarithmic) over the total depth. Vlasblom and Miedema (1995) extended this theory with the influence of hindered settling and the influence of the rising sand bed. Due to the rising sand bed, horizontal velocity increases during loading which leads to increased scour. The effect on the overflow losses is however limited since the assumed velocity distribution leads to a low bottom shear stress apart from the very last moment of the loading stage The one-dimensional vertical hopper sedimentation model The laboratory test revealed that in a large part of the hopper the flow was in fact in vertical direction instead of the horizontal (figure 2). This motivated the development of a onedimensional model in vertical direction (8,9). The 1DV model supplies sand from the bottom equally distributed over the bottom (fed by the density current) and the overflow is located at the top. The model includes the important effect of the vertical velocity component and the mutual interaction of the different grain sizes of the particle size distribution in a relative simple way. The latter effect is totally absent in the Camp model; every fraction is calculated independently. The 1DV model was capable to simulate the laboratory hopper sedimentation tests quite well. 3 TWO DIMENSIONAL HOPPER SEDIMENTATION MODEL 3.1 Introduction This chapter presents the 2D model that has been developed to simulate the sedimentation process in a hopper. One might question why a two-dimensional model should be developed when the results of the above mentioned one-dimensional model already showed a good agreement with the experiments. The motivation is that although the 1D model predicts the experiments quite well, it is unsure whether the comparison on prototype scale would be as favourable. This is caused by the absence of horizontal transport in the 1D model. The horizontal transport is accompanied with a horizontal velocity near the bottom which can reduce sedimentation (7). This phenomenon did not play a major role during the experiments due to scale effects. 3.2 Summary of the process conditions to be included in the model In chapter 2 a very brief phenomenological description of the sedimentation process was given. Hereafter the most important issues influencing the process and therefore to be included in the numerical model will be summarised. Non-stationary process Due to the relative high sedimentation velocity the filling time will be of the same order of magnitude as the adaptation time of the process. So in most cases the hopper is fully loaded before a stationary situation is established. This discerns the loading process from the sedimentation process in clarifiers used in sewage and water treatment where the settled
4 sediment is scraped to a central location resulting in a constant water depth. This enables a stationary situation (as long as the inflow conditions remain constant obviously). Non-Hydrostatic pressure distribution The length and depth scales are of the same magnitude in a hopper. This implies that a correct representation of the flow in corners is important. A hydrostatic pressure distribution (commonly used for estuarine models) is therefore not permitted since this will lead to a very unrealistic flowfield in the corners. The hydrodynamic pressure must be taken into account. Moving Bed Since it is the intention to fully load the hopper with sediment, the interface between the settled sand and the mixture above must be movable, hence a morphological model is needed. The variation in flow depth is large, from maximum depth upto almost zero. Moving water surface The location of the water surface must be variable due to variation of the overflow level or filling of the hopper during the first phase of the loading when the water level is situated below the overflow level. The water level influences the sedimentation process in several ways. The most important influence is the entrainment in the inflow section. When the water level increases the jet in the inflow section must travel over a longer distance before the bottom is reached. This will lead to lower concentration near the bottom. Influence of sediment characteristics The results of the 1DV model have shown the importance of the shape of the particle size distribution (9). For the 2D model the same influence is expected and must hence be included in the model. Erosion / sedimentation boundary condition The sedimentation velocity depends on concentration, grain size and the local flow velocity expressed as turbulent energy or bottom shear stress. A correct description of this boundary condition is vital for the proper functioning of the model. Influence of discharge system A big advantage of the 2D model compared with the one-dimensional model is the possibility to include the influence of the inflow system in the model. The following variations are possible: Number of loading points, location of the inflow point(s), inflow velocity and turbulence intensity. Influence of overflow system The 2D model enables as well the influence of the overflow system on the process. The location, height and the number of overflows can be varied. 3.3 Motivation of the mixture model The equations used for the 2D model will be presented below. An Eulerian approach is followed. Since the model deals with a mixture of sand and water a multiphase flow approach looks obvious. In such a simulation the continuity and momentum equation are solved for every phase. In this case every fraction must be considered as a single phase. To represent a Particle Size Distribution accurately this would lead to order of ten different phases. Problem is the difficult (and often unknown) interaction between the different phases, which needs to be modelled. Despite of the increased computing power, in industrial applications multiphase
5 simulations are still often abandoned because of the long computing times, especially in the case of several dispersed phases. Complete multiphase simulations are also often numerically unstable and simplified forms of the inter-phase forces are often needed (14). Various approximations have been developed in order to avoid full multiphase simulations. In Civil Engineering circumstances dispersed concentration is often low and emphasis is given to modelling of the water flow. When the flow field is solved the transportation of solids is computed using a transport equation for the sediment. Often this involves a one-way coupling: the density variations are not used in the momentum equations. The sediment is in fact regarded as neutrally buoyant solvent. In a hopper sand concentrations are too large to ignore density variations. On the other hand, a complex numerical model for hopper sedimentation only has added value when relative fine sand is loaded. In case of coarse sands everything settles and even the simplest model will predict that outcome. For fine sands the Stokes number is low, which means that the sand grains are following the mean flow. In this case the mixture model can be applied. The mixture model (or algebraic slip model) preserves the essential multiphase character of the flow, although it is an approximation of the full Eulerian model. It is based on the assumption of a local equilibrium between the continuous and dispersed phases, i.e. the particles are assumed to move always with the terminal slip velocity relative to the liquid phase (14) The mathematical model The horizontal momentum equation in conservative form reads: t Ω ρu dω + The vertical momentum equation: S r r ρu v n ds = S r τ i xj j r nds S r p i x r nds ( 1 ) t Ω r r r r r r ρw dω+ ρw v n ds = τ i nds p i nds ρg dω zj j z S S S Ω ( 2 ) In the left-hand side of the equation the total derivative is split in the unsteady and advection term. In the right hand side the shear stress term is still generic, the relation with the flow field is not yet defined. Beside the momentum equation the continuity equation is needed to solve the system. For an incompressible fluid in conservative notation this equation reads: v r ¼ n r ds = 0 ( 3 ) S To solve this system of equations a relation between the shear stresses and velocities must be known. Let us investigate the shear stress on the top side (north side) of a control volume. For a Newtonian fluid a linear relation exists between the shear stress and the velocity gradient. t u xz = rn z ( 4 ) In this relation is ν the kinematic viscosity of the fluid. The product ρν is called the dynamic viscosity. The shear stresses on the other surfaces of the control volume can be written
6 likewise. All stresses can now be expressed in term of velocity gradients leading to a system of three equations. The horizontal and vertical momentum equations and continuity equation with three unknowns (in case the density is constant): velocity components u, w and pressure p. With the appropriate boundary conditions a solution can be found in principle. For laminar flow (low Reynolds number) this is indeed the case. For higher Reynolds numbers however the flowfield becomes unstable (turbulent). Eddies are developing and the flow can only be described correctly if the smallest eddies are simulated in the calculation. The only way to solve the equations is numerically so this will lead to a very small grid size and hence huge computer memory demands and computational effort. This is the reason that this so-called Direct Numerical Simulation (DNS) approach will not be feasible for practical problems with large dimensions in the near future (5). The time scale at which the turbulent fluctuations take place are however very often much smaller that the time scale of the boundary conditions. Velocities can therefor be averaged over a period relative small to the changes in flow conditions (11). The relevant quantities can in that case be written as the sum of a time averaged value and a turbulent fluctuation. The substitution in the Navier-Stokes (NS) equations and time averaging and application of the eddy-viscosity concept leads to the following expressions fore the shear stress in the fluid. (Here only written for one component) τ ρν u u xz uw e z ρ ρ = = z ν + ν ( ) ( 5 ) The correlated velocity fluctuations are replaced with the product of the eddy viscosity n e and a velocity gradient. The NS equation after time averaging is called the Reynolds Averaged Navier-Stokes equation (RANS). 3.5 Turbulent closure The RANS-equations can be solved when a relation can be found between the flow field and the eddy-viscosity. The k ε model has been used for very different flow problems in the past with success. The eddy viscosity is computed using ( c m is a model constant): 2 k ν e = c µ ( 6 ) ε In order to compute the eddy-viscosity the problem is shifted towards determination of the values of the k (turbulent energy) and e (dissipation rate of turbulent energy). Both quantities are obtained from transport equations. The continuity and momentum equations together with these two transport equations form a strongly coupled system of equations. To solve the momentum equations the eddy viscosity must be known as function of time and space. To compute the eddy-viscosity, k and ε must be known and these values are dependent on the velocity distribution. 3.6 Sediment Transport In the Navier-Stokes equations the density of the mixture is present. The other important reason to know this density is that the sedimentation and hence filling of the hopper is directly related to the bottom concentration.
7 The grain size distribution is approximated with a finite number N of different grain diameters. The concentration of a certain fraction with grain diameter d j is c j. The mixture density follows from the total concentration:. ( 1 ) ρ cρ c ρ c c s w j j= 1 N = + = ( 7 ) For every fraction the distribution of the concentration is calculated with the transport equation for that fraction. This equation is used in conservative or integral form, which forms the basis of the Finite Volume Method. t W ( ) r v v c dw+ c v ¼ n ds = Ggrad c ¼n ds j j z, j j S S ( 8 ) The first term gives the rate of change of the concentration of a fraction, the second term represents the transport of that fraction due to advection. In the right-hand side the diffusive transport (caused by turbulence) is given. The diffusion coefficient Γ is related to the eddy viscosity with the Schmidt-Prandtl number: n G= e ( 9 ) s Generally this number is regarded as constant throughout the computational domain (11). Uittenbogaard (15) showed that in free turbulence, even in highly stratified conditions, σ = 0.6 can be used Coupling of the sediment fractions In horizontal direction it is assumed that the grain velocity is equal to the mixture velocity. In vertical direction a slip velocity between the fluid velocity and grain velocity is assumed. In (9) is shown that the relation between the vertical particle velocity, mixture velocity and slip velocity for a multi-sized mixture can be written as: N v = w+ c v v ( 10 ) z, j k s, k s, j k = 1 The mixture velocity w follows from the solution of the NS equations. Provided the concentration is known the slip velocity for every fraction can be calculated and consequently the grain velocities, which are used in the sediment transport equations can be computed. For the slip velocity the approach of Mirza & Richardson (4) is followed: s, j 0, j 1 ( ) n j 1 v = w c ( 11 ) In which w 0 is the fall velocity of a single grain and n j the hindered settling exponent for that grain size.
8 3.7 Overview of the model Now the three different parts of the model have been described the mutual relations can be shown in figure 3. The different modules contain transport equations for momentum, sediment and turbulent quantities. Figure 3. Model overview In the 2D RANS module the flowfield is solved using the spatial distribution of the eddyviscosity and the density. The sediment transport and turbulence module supply these quantities respectively. The Sediment transport and turbulence model both need the flowfield solved by the 2D RANS module. The turbulence and the sediment transport module exchange the eddy-viscosity and the density. The eddy-viscosity supplies the diffusion coefficient needed to compute the diffusive transport of sediment (equation ( 9 )). The density gradient is used in the turbulence model to take the extra dissipation (or production in case of unstable stratification) of turbulent energy into account. 3.8 Boundary conditions The hopper is schematised as a rectangular domain. Boundary condition must be applied at the bottom (interface between settled sand and mixture above), water surface, vertical walls, inflow section and outflow section Boundary conditions at walls, bottom and water surface The normal component of the mixture velocity at the vertical walls and bottom is equal to zero. For the bottom and vertical walls a wall-function approach is used for the velocity components parallel to the wall (11,12). At the water surface a rigid-lid assumption is used since surface wave phenomena are not important for the subject situation. A rigid-lid can be regarded as a smooth horizontal plate covering the water surface in the hopper. Depending on the total volume balance inside the hopper this plate will be moved up and down. The vertical velocity of the surface w follows from: H w H q q L in out = ( 12 ) In this simple equation is in q and out q the specific in- and outflowing discharge and L the length of the water surface. At the water surface the values of k and the normal gradient of ε
9 are put equal to zero. For the vertical walls and bottom the value of these quantities must be consistent with the wall function approach (11). u u k = = ( 13 ) 2 3 * * ε c µ κy With Y as the normal distance from the first grid point to the wall and u * as the friction velocity. For the sediment transport equations the fluxes through vertical walls and water surface is equal to zero since no sediment enters or leaves the domain at these boundaries. At the bottom for every fraction the sedimentation flux S i is prescribed. The influence of the bottom shear stress on the sedimentation is modelled using a reduction factor R. S R = Rcw i i z, i θ 1 θ < θ0 θ = 0 > 0 θ θ 0 ( 14 ) This simple relation between the reduction factor and Shields parameter θ is based on flume tests (7,15). The critical value for the Shields parameter proved to be independent of the grain size for the sands tested (d 50 < 300 µ m). It will be clear that this approach can only be used when over all sedimentation (like in a hopper of a TSHD) will take place. When the Shields value exceeds the critical value erosion will occur in reality and this effect is not (yet) modelled Boundary condition at inflow and outflow section Usually the inflow is in vertical direction through the water surface in the hopper. The vertical velocity will therefore be prescribed over the width of the entering jet at the surface. The turbulent quantities have be prescribed at this location as well. For the turbulent energy it is common to prescribe (2,11,17) ( v in is the inflow velocity). k = αv = 1.5I v ( 15 ) in T in The value of the turbulence intensity I T can vary strongly on the situation. For the dissipation rate the following boundary condition is normally used (2): 3/4 3/2 cµ k ε = ( 16 ) l The mixing length l m is related to the width of the inflow section or inflowing jet. The following relation between the mixing length and inflow geometry is used (2): m l = c 0.5d ( 17 ) m For the sediment transport equations the influx of every fraction is prescribed at the inflow. µ in
10 The outflow boundary is only active when overflow is present, so when the mixture level in the hopper exceeds the overflow level. In that case the outflow velocity is prescribed, and follows simply from the ratio of the overflow discharge and the difference between the hopper and overflow level. For the other quantities the normal gradients are equal to zero (Neumann condition). 3.9 Numerical Approach The momentum and sediment transport equations are solved using the Finite Volume Method to ensure conservation. The transport equations for the turbulent quantities k and ε are solved using the Finite Difference method. A Finite Difference Method is allays implemented on a rectangular (cartesian) grid. Although a Finite Volume Method can be applied on any grid it is advantageous to use a cartesian approach for this method as well especially when a staggered arrangement of variables is used. In general the flow domain is however not rectangular. The water surface can be considered horizontal on the length scale considered, but a sloping bottom will not coincide with the gridlines. Different approaches are possible. The first method is to use a cartesian grid and to adjust the bottom cells (cut-cell method). Another method is to fit the grid at the bottom. In that case a boundary fitted non-orthogonal grid can be used. A third method is using grid transformation. By choosing an appropriate transformation the equations are solved on a cartesian domain in transformed co-ordinates. Although this transformation allows for a good representation of a curved topography the method has the disadvantage that due to truncation errors in the horizontal momentum equation artificial flows will develop when a steep bottom encounters density gradients. These unrealistic flows can be partly suppressed when the diffusion terms are locally discretized in a cartesian grid. (12,13). Since however in a hopper both large density gradients as steep bottom geometry can be present it was decided to develop the model in cartesian co-ordinates. Figure 4. Staggered grid arrangement near bottom In figure 4 a possible situation at the sand bed is shown. The location of the bed is indicated with the dotted line. The heights of the cells that intersect with the bed are adjusted. In the figure the staggered arrangement of variables is shown as well (star: horizontal velocity, rectangle: vertical velocity; dot: concentration, pressure). An overview of the model was shown in figure 3. The computational procedure can only be outlined here very roughly. The flow is not stationary hence the system is evaluated in time. The following steps are repeated during time:
11 Update the velocity field to time t n+1 by solving the NS-equations together with the continuity equation using a pressure correction method (SIMPLE-method (6)) using the density and eddy viscosity of the old time step t n. Update the turbulent quantities k and ε to time t n+1 using the velocity field of t n+1. Compute the eddy-viscosity for the new time. Use the flowfield of t n+1 to compute the grain velocities for the next time and update the concentrations for all fractions and hence the mixture density to time t n+1. Compute the new location for the bed level and mixture surface in the hopper. 4 APPLICATION OF THE MODEL 4.1 Introduction Because the code for the model was not based on available commercial CFD software the first step was to validate the results with known flow problems like the backward facing step, plane buoyant and non-buoyant jets, density currents on a slope and sediment transport in a canal. The code proved to be capable to simulate these types of flow. 4.2 Simulation of Laboratory Experiments In the framework of the research programme model laboratory tests were carried out at WL Delft hydraulics. A description of the experimental set up and test programme was given in (8). The model will be compared with the result of test 6. The operation parameters are summarised in the table below (average during the test): Discharge m3/s Bed level at start 0.18 m Density 1420 kg/m3 Length of hopper 12.0 m Overflow level 2.25 m Width of hopper 3.08 m Water level at start 1.25 m The measured inflow concentration and discharge as function of time was used as input for the model. Some variation of the particle size diameter in the inflow was observed, but during the calculations the PSD was kept constant. Figure 5. Computed concentration profiles during time
12 During the calculations the PSD is represented with 8 fractions, hence for the cumulative distribution 9 points were needed. Figure 5 shows the computed concentration profiles at four different positions for 9 different times. The inflow is located at the upper left side, the outflow at the right side. The overflow level was kept constant during the test at 2.25 m. The location of the sand bed is shown with the hatched lines. The erosion crater at the left side is clearly visible. The first profile in time was taken before the overflow level was reached. The other profiles were taken at the overflow phase. A strong similarity is present between the computed and measured concentration profiles as is shown in figure 6 where the measured and computed concentration profiles are compared for one location (x = 6 m). A sharp interface between the suspension and sand bed is present. The profiles are almost vertical over a large distance After some time (about 1000 s) the value of the concentration in suspension remains at a constant value. The measured value of the concentration is however larger than calculated, which can be partly explained by the larger computed vertical diffusion. In figure 7 the calculated velocity profiles at different times are plotted at 4 locations. It is clear that due to the density effect the flow is concentrated close to the bottom. Above this density current a return flow, caused by entrainment in the inflow section, is present. During time the magnitude of the horizontal velocity decreases, as can be seen from the maximum values of the profiles. (the same tendency was observed during the laboratory tests) Figure 6. Computed and measured concentration at x=6 m A very important quantity during the calculations is the overflow loss, in fact one of the major goals of the research program. The computed concentration in the overflow is compared with the measured value in figure 7. The agreement between theory and experiments is satisfactory. The maximum outflow concentration is somewhat smaller and the losses during the first part of the overflow phase are higher. The latter being caused by the larger diffusion during that time as already discussed above.
13 . Figure 7. Computed velocity profile in the hopper Figure 8. Measured and computed overflow concentration 4.3 Simulation of Prototype Measurements To test the model in a prototype situation, measurements were carried out onboard the Trailing Suction Hopper Dredge Cornelia owned by Royal Boskalis Westminster. The dredging area is near IJmuiden (Dutch Coast). The dimensions of the hopper are: Length = 52 m, Width = 11.5 m, Hopper Volume= 5000 m 3. The hopper has the typical silo shape. Since the model is based on a rectangular shape, the hopper area is simplified to a rectangular basin with a depth op 5000/(52*11.5) = 8.36 m. Typical operation parameters during loading (with two suction pipes) are. Discharge Q = 6 m3/s, Mixture Density = 1260 kg/m3, Water density = 1021 kg/m3 and Porosity (settled sand) n = Samples were taken from the seabed to determine the particle size distribution. d 50 = 235 micron. For the calculation 10 fractions were used. In figure 9 the cumulative overflow loss defined as the ratio between the total volume of sand lost overboard and the total volume of sand pumped into the hopper is plotted versus time. The measured overflow loss was based on the measured tonnage of the ship (from the
14 draught), the measured hopper volume and the total measured influx of sand. This method has the disadvantage that at the beginning of the loading process the outcome is very sensitive on the draught and hopper volume and therefore unreliable. The results improve however during time. This is phenomenon is visible in the results of the procedure. Before t=1500 s the (indirectly) measured overflow loss varies strongly Figure 9. Discharge and cumulative overflow loss The upper figure shows the measured discharge into the hopper and the calculated overflow discharge (dotted line). The agreement between the measurements and model is encouraging, especially taking into account that no calibration of the numerical model (like k - e equations) was undertaken. 5 CONCLUSIONS The two-dimensional model based on the Reynolds Averaged Navier-Stokes for mixture flow simulates the sedimentation process quite well. The model includes all important phenomena of the hopper sedimentation process. The numerical model has been compared with laboratory experiments and a limited number of prototype measurements. Differences between measured and computed overflow losses are small. The concentration and velocity profile in the model hopper differ from the simulated values. These differences are all caused by the behaviour of the model in the inflow zone where the velocity of the mixture is over predicted. This phenomenon is most probably caused by a deficiency of the turbulence model in strong buoyant situations. The higher flow velocity in the jet over predicts entrainment and hence dilution of the inflowing mixture which results in a lower suspension concentration. Owing to the larger entrainment the circulation in the hopper is slightly exaggerated which enlarges the mixing in the hopper. ACKNOWLEDGEMENT The financial support of the VBKO (Vereniging van Waterbouwers in Bagger-, Kust en Oeverwerken) is gratefully acknowledged. I want to thank Dr. F. van Kats for the preparation,
15 execution and processing of the prototype measurements and Royal Boskalis Westminster for making available the results. REFERENCES 1. Camp, T.R.,1946, Sedimentation and the Design of Settling Tanks, Trans. ASCE, 111(2285), pp Celik, I., Rodi, W., Stamou, A. I, Prediction of hydrodynamic characteristics of rectangular settling tanks. Turbulence measurements and flow modelling. ASCE, New York, N.Y 3. Dobbins, W.E., 1944, Effect Of Turbulence On Sedimentation. ASCE Trans., Vol 109, no. 2218, pp Mirza, S., and Richardson, J. F., 1979, Sedimentation of suspensions of particles of two or more sizes, Chem. Eng. Sci., 34, Nieuwstadt, F.T.M, 1992, Turbulentie; inleiding in de theorie en toepassingen van turbulente stromingen., Utrecht Epsilon. 6. Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York. 7. Rhee, C. van, Talmon, A.M., 2000, Entrainment of sediment (or reduction of sedimentation) at high concentration, 10th Int. Symposium on Transport and Sedimentation of Solid Particles, Wroclaw, Poland. 8. Rhee, C. van, 2001, Numerical Simulation of the Sedimentation Process in a Trailing Suction Hopper Dredge, 16th World Dredging Congress and Exhibition (WODCON), Kuala Lumpur. 9. Rhee, C. van, 2001c, Modelling the sedimentation process in a trailing suction hopper dredge, 4th Int. Conference on Multiphase Flows, New Orleans. 10. Rhee, C. van, 2002, The influence of the bottom shear stress on the sedimentation of sand, 11 th Int. Symposium on Transport and Sedimentation of Solid Particles, Gent, (to be published) 11. Rodi, W., 1993, Turbulence Models and their Application in Hydraulics, A state of the art review, IAHR, Third Edition. 12. Stansby, P.K., 1997, Semi-Implicit Finite Volume Shallow-Water Flow and Solute Transport Solver with k-epsilon Turbulence Model, Int. Journal for Numerical Methods in Fluids, Vol. 25, pp Stelling, G. S., Kester, J. A. Th. M. van, 1994, On the approximation of Horizontal Gradients in Sigma Co-ordinates for Bathymetry with steep bottom slopes,, Int. Journal for Numerical Methods in Fluids, Vol. 18, pp Taivassalo, V., Manninen, M., 2001, Formulation and Validation of the Mixture Model for Multiphase Flows, 4th Int. Conference on Multiphase Flows, New Orleans. 15. Uittenboogaard, R.E., 1995, The importance of Internal Waves for Mixing in a Stratified Estuarine Tidal Flow, PhD-Thesis, Delft University of Technology 16. Vlasblom, W.J.,Miedema, S.A., 1995, A theory for determining sedimentation and overflow losses in hoppers, Proc. of the 14th World Dredging Congress, Amsterdam. 17. Zijlema, M., 1994, Finite volume computation of 2D incompressible turbulent flows in general co-ordinates on staggered grids, Technical University Delft
Modelling the Sedimentation Process in a Trailing Suction Hopper Dredger
Terra et Aqua Number 86 March 2002 Cees van Rhee Modelling the Sedimentation Process in a Trailing Suction Hopper Dredger Cees van Rhee Since 1985 Cees van Rhee has been engaged with research for the dredging
Literature Study Hopper Loading OE44140 Multidisciplinary Project
Literature Study Hopper Loading OE44140 Multidisciplinary Project Delft University of Technology B.F. Sloof - 4158768 Contents 1 Introduction 1 2 Hopper modelling 2 2.1 Processes in the hopper...................................
Dredging Processes. The Loading Process of a Trailing Suction Hopper Dredge. Dr.ir. Sape A. Miedema
Dredging Processes The Loading Process of a Trailing Suction Hopper Dredge Dr.ir. Sape A. Miedema Copyright Dr.ir. S.A. Miedema Page 2 of 146 Dredging Processes The Loading of Trailing Suction Hopper
Erosion of sand under high flow velocities
Delft University of Technology Faculty of Mechanical, Maritime and Materials Engineering Department of Offshore Engineering Erosion of sand under high flow velocities Author: Juneed Sethi MSc Thesis Thesis
Geomorphological Modelling in Coastal Waters
Abstract Geomorphological Modelling in Coastal Waters Morteza Kolahdoozan 1, Roger A. Falconer 2 (Fellow), Yiping Chen 3 Details are given herein of the development and application of a three dimensional
A two-fluid model of turbulent two-phase flow for simulating turbulent stratified flows
Ocean Engineering 30 (2003) 153 161 www.elsevier.com/locate/oceaneng A two-fluid model of turbulent two-phase flow for simulating turbulent stratified flows Y.M. Shen a,, C.-O. Ng b, A.T. Chwang b a State
FLOW VELOCITIES IN AN AXI-SYMMETRICAL ROTATING CUTTER SUCTION HEAD
18th International Conference on TRANSPORT AND SEDIMENTATION OF SOLID PARTICLES 11-15 September 2017, Prague, Czech Republic ISSN 0867-7964 ISBN 978-83-7717-269-8 FLOW VELOCITIES IN AN AXI-SYMMETRICAL
WATER INJECTION DREDGING by L.C. van Rijn
WATER INJECTION DREDGING by L.C. van Rijn (info@leovanrijn-sediment.com) Description of method Almost all harbour basins suffer from the problem of siltation of sediments. Usually, the deposited materials
Fluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
Calculation of Sand Losses During Hopper Loading Process in Trailers
C. Paris and I. Martinez Calculation of Sand Losses During Hopper Loading Process in Trailers Abstract During the actual dredging process, the instrumentation on board a trailing suction hopper dredger
Turbulence Modeling I!
Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!
NONLINEAR FEATURES IN EXPLICIT ALGEBRAIC MODELS FOR TURBULENT FLOWS WITH ACTIVE SCALARS
June - July, 5 Melbourne, Australia 9 7B- NONLINEAR FEATURES IN EXPLICIT ALGEBRAIC MODELS FOR TURBULENT FLOWS WITH ACTIVE SCALARS Werner M.J. Lazeroms () Linné FLOW Centre, Department of Mechanics SE-44
CHAPTER 199 ARTIFICIAL SAND FILLS IN WATER
CHAPTER 199 ARTIFICIAL SAND FILLS IN WATER J. van 't Hoff 1, M.B. de Groot 2, J.C. Winterwerp 3 H. Verwoert 4 and W.T. Bakker 5 l Introduction Experience has been obtained on the construction of sand fills
Turbulent Boundary Layers & Turbulence Models. Lecture 09
Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects
15. Physics of Sediment Transport William Wilcock
15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) OCEAN/ESS 410 Lecture/Lab Learning Goals Know how sediments are characteried (sie and shape) Know the definitions
meters, we can re-arrange this expression to give
Turbulence When the Reynolds number becomes sufficiently large, the non-linear term (u ) u in the momentum equation inevitably becomes comparable to other important terms and the flow becomes more complicated.
Numerical Methods in Aerodynamics. Turbulence Modeling. Lecture 5: Turbulence modeling
Turbulence Modeling Niels N. Sørensen Professor MSO, Ph.D. Department of Civil Engineering, Alborg University & Wind Energy Department, Risø National Laboratory Technical University of Denmark 1 Outline
A LARGE-SCALE EXPERIMENTAL STUDY OF HIGH DENSITY SLURRIES DEPOSITION ON BEACHES
ISBN 978-83-927084-8-3 ISSN 0867-7964 A LARGE-SCALE EXPERIMENTAL STUDY OF HIGH DENSITY SLURRIES DEPOSITION ON BEACHES Walther van Kesteren 1 ; Tom van de Ree 2 ; Arno Talmon 3 ; Miguel de Lucas Pardo 4
Securing Manoeuverability of a Deep Draft Ship in a Sediment loaded Tidal River Berth
Securing Manoeuverability of a Deep Draft Ship in a Sediment loaded Tidal River Berth O. Stoschek 1, A. Matheja 1 & C. Zimmermann 1 1 Franzius-Institute for Hydraulic, Waterways and Coastal Engineering,
Conclusion Evaluating Methods for 3D CFD Models in Sediment Transport Computations
Conclusion Evaluating Methods for 3D CFD Models in Sediment Transport Computations Hamid Reza Madihi* 1, Bagher Keshtgar 2, Sina Hosseini Fard 3 1, 2, 3 M.Sc. Coastal Environmental Engineering, Graduate
Evaluating methods for 3D CFD Models in sediment transport computations
American Journal of Civil Engineering 2015; 3(2-2): 33-37 Published online February 10, 2015 (http://www.sciencepublishinggroup.com/j/ajce) doi: 10.11648/j.ajce.s.2015030202.17 ISSN: 2330-8729 (Print);
Investigation of Flow Profile in Open Channels using CFD
Investigation of Flow Profile in Open Channels using CFD B. K. Gandhi 1, H.K. Verma 2 and Boby Abraham 3 Abstract Accuracy of the efficiency measurement of a hydro-electric generating unit depends on the
Modelling of dispersed, multicomponent, multiphase flows in resource industries. Section 3: Examples of analyses conducted for Newtonian fluids
Modelling of dispersed, multicomponent, multiphase flows in resource industries Section 3: Examples of analyses conducted for Newtonian fluids Globex Julmester 017 Lecture # 04 July 017 Agenda Lecture
The mean shear stress has both viscous and turbulent parts. In simple shear (i.e. U / y the only non-zero mean gradient):
8. TURBULENCE MODELLING 1 SPRING 2019 8.1 Eddy-viscosity models 8.2 Advanced turbulence models 8.3 Wall boundary conditions Summary References Appendix: Derivation of the turbulent kinetic energy equation
Towards the prediction of free-forming meander formation using 3D computational fluid dynamics
Wasserbaukolloquium 2006: Strömungssimulation im Wasserbau 31 Dresdner Wasserbauliche Mitteilungen Heft 32 Towards the prediction of free-forming meander formation using 3D computational fluid dynamics
Dynamics of the Ems Estuary
Dynamics of the Ems Estuary Physics of coastal systems Jerker Menninga 0439738 Utrecht University Institute for Marine and Atmospheric research Utrecht Lecturer: Prof. dr. H.E. de Swart Abstract During
Modeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!
http://www.nd.edu/~gtryggva/cfd-course/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady Navier-Stokes equations
2.3 The Turbulent Flat Plate Boundary Layer
Canonical Turbulent Flows 19 2.3 The Turbulent Flat Plate Boundary Layer The turbulent flat plate boundary layer (BL) is a particular case of the general class of flows known as boundary layer flows. The
B-1. Attachment B-1. Evaluation of AdH Model Simplifications in Conowingo Reservoir Sediment Transport Modeling
Attachment B-1 Evaluation of AdH Model Simplifications in Conowingo Reservoir Sediment Transport Modeling 1 October 2012 Lower Susquehanna River Watershed Assessment Evaluation of AdH Model Simplifications
Sand Ripple Dynamics on the Inner Shelf
Sand Ripple Dynamics on the Inner Shelf Donald N. Slinn Department of Civil and Coastal Engineering, University of Florida Gainesville, FL 32611-6590, Phone: (352) 392-9537 x 1431 Fax: (352) 392-3466 E-mail:
Colloquium FLUID DYNAMICS 2012 Institute of Thermomechanics AS CR, v.v.i., Prague, October 24-26, 2012 p.
Colloquium FLUID DYNAMICS 212 Institute of Thermomechanics AS CR, v.v.i., Prague, October 24-26, 212 p. ON A COMPARISON OF NUMERICAL SIMULATIONS OF ATMOSPHERIC FLOW OVER COMPLEX TERRAIN T. Bodnár, L. Beneš
Figure 34: Coordinate system for the flow in open channels.
OE466 redging Processes 5. SCOUR 5.. Steady uniform flow in open channels This chapter is written with a view to bottom scour. The main outcome is the scour velocity as a function of the particle diameter.
Thomas Pierro, Donald Slinn, Kraig Winters
Thomas Pierro, Donald Slinn, Kraig Winters Department of Ocean Engineering, Florida Atlantic University, Boca Raton, Florida Applied Physics Laboratory, University of Washington, Seattle, Washington Supported
EXAMPLES (SEDIMENT TRANSPORT) AUTUMN 2018
EXAMPLES (SEDIMENT TRANSPORT) AUTUMN 2018 Q1. Using Cheng s formula estimate the settling velocity of a sand particle of diameter 1 mm in: (a) air; (b) water. Q2. Find the critical Shields parameter diameter
15. GRIT CHAMBER 15.1 Horizontal Velocity in Flow Though Grit Chamber
15. GRIT CHAMBER Grit chamber is the second unit operation used in primary treatment of wastewater and it is intended to remove suspended inorganic particles such as sandy and gritty matter from the wastewater.
WQMAP (Water Quality Mapping and Analysis Program) is a proprietary. modeling system developed by Applied Science Associates, Inc.
Appendix A. ASA s WQMAP WQMAP (Water Quality Mapping and Analysis Program) is a proprietary modeling system developed by Applied Science Associates, Inc. and the University of Rhode Island for water quality
THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL
Tenth International Water Technology Conference, IWTC10 2006, Alexandria, Egypt 281 THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL Karima Attia 1 and Gamal El Saied 2 1
Eddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr):
AdOc 4060/5060 Spring 2013 Chris Jenkins Eddy viscosity Turbulence (video 1hr): http://cosee.umaine.edu/programs/webinars/turbulence/?cfid=8452711&cftoken=36780601 Part B Surface wind stress Wind stress
CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE
CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral
NUMERICAL SIMULATION OF SUSPENDED SEDIMENT TRANSPORT AND DISPERSAL FROM EVROS RIVER INTO THE NORTH AEGEAN SEA, BY THE MECHANISM OF TURBIDITY CURRENTS
NUMERICAL SIMULATION OF SUSPENDED SEDIMENT TRANSPORT AND DISPERSAL FROM EVROS RIVER INTO THE NORTH AEGEAN SEA, BY THE MECHANISM OF TURBIDITY CURRENTS GEORGOULAS A. 1, TZANAKIS T. 1, ANGELIDIS P. 1, PANAGIOTIDIS
7. Basics of Turbulent Flow Figure 1.
1 7. Basics of Turbulent Flow Whether a flow is laminar or turbulent depends of the relative importance of fluid friction (viscosity) and flow inertia. The ratio of inertial to viscous forces is the Reynolds
Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing.
Turbulence is a ubiquitous phenomenon in environmental fluid mechanics that dramatically affects flow structure and mixing. Thus, it is very important to form both a conceptual understanding and a quantitative
Donald Slinn, Murray D. Levine
2 Donald Slinn, Murray D. Levine 2 Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis,
On the validation study devoted to stratified atmospheric flow over an isolated hill
On the validation study devoted to stratified atmospheric flow over an isolated hill Sládek I. 2/, Kozel K. 1/, Jaňour Z. 2/ 1/ U1211, Faculty of Mechanical Engineering, Czech Technical University in Prague.
Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles
Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction &
Computational Fluid Dynamics Modelling of Natural Convection in Copper Electrorefining
16 th Australasian Fluid Mechanics Conference Crown Plaza, Gold Coast, Australia 2-7 December 2007 Abstract Computational Fluid Dynamics Modelling of Natural Convection in Copper Electrorefining A computational
On the Turbulence Modelling for an Air Cavity Interface
1 Introduction On the Turbulence Modelling for an Air Cavity Interface Gem Rotte, Maarten Kerkvliet, and Tom van Terwisga TU Delft, Delft/The Netherlands MARIN, Wageningen/The Netherlands G.M.Rotte@tudelft.nl
Masters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,
Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =
ADAPTATION OF THE REYNOLDS STRESS TURBULENCE MODEL FOR ATMOSPHERIC SIMULATIONS
ADAPTATION OF THE REYNOLDS STRESS TURBULENCE MODEL FOR ATMOSPHERIC SIMULATIONS Radi Sadek 1, Lionel Soulhac 1, Fabien Brocheton 2 and Emmanuel Buisson 2 1 Laboratoire de Mécanique des Fluides et d Acoustique,
Numerical Computation of Inception Point Location for Flat-sloped Stepped Spillway
International Journal of Hydraulic Engineering 2013, 2(3): 47-52 DOI: 10.5923/j.ijhe.20130203.03 Numerical Computation of Inception Point Location for Flat-sloped Stepped Spillway Bentalha Chakib Department
J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and
J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883
2. Governing Equations
1. Introduction Submarine pipeline, unlike any other hydraulic structures that are vertically erected, are laid horizontally on the bed of oceans and rivers. Hence, the design of submarine pipelines associated
C C C C 2 C 2 C 2 C + u + v + (w + w P ) = D t x y z X. (1a) y 2 + D Z. z 2
This chapter provides an introduction to the transport of particles that are either more dense (e.g. mineral sediment) or less dense (e.g. bubbles) than the fluid. A method of estimating the settling velocity
Boundary-Layer Theory
Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
Figure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m
1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)
THE BREACHING OF SAND INVESTIGATED IN LARGE-SCALE MODEL TESTS. Cees van Rhee* and Adam Bezuijen"
THE BREACHING OF SAND INVESTIGATED IN LARGE-SCALE MODEL TESTS Cees van Rhee* and Adam Bezuijen" Abstract The physical principles, which govern the breaching process, are analysed. It will be shown that
CFD ANALYSIS OF TURBULENCE EFFECT ON REACTION IN STIRRED TANK REACTORS
CFD ANALYSIS OF TURBULENCE EFFECT ON REACTION IN STIRRED TANK REACTORS Udaya Bhaskar Reddy R*, Gopalakrishnan S, Ramasamy E Department of Chemical Engineering, Coimbatore Institute of Technology, Coimbatore-
Fluid Mechanics. Chapter 9 Surface Resistance. Dr. Amer Khalil Ababneh
Fluid Mechanics Chapter 9 Surface Resistance Dr. Amer Khalil Ababneh Wind tunnel used for testing flow over models. Introduction Resistances exerted by surfaces are a result of viscous stresses which create
Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity
Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity Tobias Knopp D 23. November 28 Reynolds averaged Navier-Stokes equations Consider the RANS equations with
Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition
Sādhanā Vol. 40, Part 2, April 2015, pp. 467 485. c Indian Academy of Sciences Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition RAMBIR BHADOURIYA,
ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS
ROLE OF THE VERTICAL PRESSURE GRADIENT IN WAVE BOUNDARY LAYERS Karsten Lindegård Jensen 1, B. Mutlu Sumer 1, Giovanna Vittori 2 and Paolo Blondeaux 2 The pressure field in an oscillatory boundary layer
Minimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes
Computational Methods in Multiphase Flow V 227 Minimum fluidization velocity, bubble behaviour and pressure drop in fluidized beds with a range of particle sizes B. M. Halvorsen 1,2 & B. Arvoh 1 1 Institute
THREE-DIMENSIONAL NUMERICAL ANALYSIS OF SEDIMENT TRANSPORT AROUND ABUTMENTS IN CHANNEL BEND
THREE-DIMENSIONAL NUMERICAL ANALYSIS OF SEDIMENT TRANSPORT AROUND ABUTMENTS IN CHANNEL BEND Han Sang Kim 1 and Hamn-Ching Chen 1 In this paper, the results for sediment transport simulation around bridge
Post-trenching with a Trailing Suction Hopper Dredger
Post-trenching with a Trailing Suction Hopper Dredger Master thesis Hydraulic Engineering Kevin Van de Leur - 1170279 This thesis may not be released before 13-12-2012 Post-trenching with a Trailing Suction
Module 15 : Grit Chamber. Lecture 19 : Grit Chamber
1 P age Module 15 : Grit Chamber Lecture 19 : Grit Chamber 2 P age Grit chamber is the second unit operation used in primary treatment of wastewater and it is intended to remove suspended inorganic particles
Sedimentation Scour Model Gengsheng Wei, James Brethour, Markus Grünzner and Jeff Burnham August 2014; Revised October 2014
Flow Science Report 03-14 Sedimentation Scour Model Gengsheng Wei, James Brethour, Markus Grünzner and Jeff Burnham August 2014; Revised October 2014 1. Introduction The three-dimensional sediment scour
Computational Fluid Dynamics 2
Seite 1 Introduction Computational Fluid Dynamics 11.07.2016 Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016 Seite 2
Principles of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
Before we consider two canonical turbulent flows we need a general description of turbulence.
Chapter 2 Canonical Turbulent Flows Before we consider two canonical turbulent flows we need a general description of turbulence. 2.1 A Brief Introduction to Turbulence One way of looking at turbulent
THE INFLUENCE OF LOCAL HINDERED SETTLING ON THE CONCENTRATION DISTRIBUTION IN SLURRY TRANSPORT. Sape Andries Miedema 1
18th International Conference on TRANSPORT AND SEDIMENTATION OF SOLID PARTICLES 11-15 September 2017, Prague, Czech Republic ISSN 0867-7964 ISBN 978-83-7717-269-8 THE INFLUENCE OF LOCAL HINDERED SETTLING
International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May ISSN
International Journal of Scientific & Engineering Research, Volume 6, Issue 5, May-2015 28 CFD BASED HEAT TRANSFER ANALYSIS OF SOLAR AIR HEATER DUCT PROVIDED WITH ARTIFICIAL ROUGHNESS Vivek Rao, Dr. Ajay
Fundamentals of Fluid Dynamics: Elementary Viscous Flow
Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research
D.R. Rector, M.L. Stewart and A.P. Poloski Pacific Northwest National Laboratory P.O. Box 999, Richland, WA
Modeling of Sediment Bed Behavior for Critical Velocity in Horizontal Piping 9263 D.R. Rector, M.L. Stewart and A.P. Poloski Pacific Northwest National Laboratory P.O. Box 999, Richland, WA ABSTRACT A
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
This document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore. Title Modified logarithmic law for velocity distribution subjected to upward seepage. Author(s) Cheng, Nian-Sheng;
CFD ANALYSIS OF TURBULENT THERMAL MIXING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT
ISTP-6, 005, PRAGUE 6 TH INTERNATIONAL SYMPOSIUM ON TRANSPORT PHENOMENA CFD ANALYSIS OF TURBULENT THERMAL MIING OF HOT AND COLD AIR IN AUTOMOBILE HVAC UNIT Hideo Asano ((, Kazuhiko Suga (3, Masafumi Hirota
U.S. Army Corps of Engineers Detroit District. Sediment Trap Assessment Saginaw River, Michigan
U.S. Army Corps of Engineers Detroit District December 2001 December 2001 This report has been prepared for USACE, Detroit District by: W.F. BAIRD & ASSOCIATES LTD. 2981 YARMOUTH GREENWAY MADISON, WISCONSIN
Modeling and simulation of bedload transport with viscous effects
Introduction Modeling and simulation of bedload transport with viscous effects E. Audusse, L. Boittin, M. Parisot, J. Sainte-Marie Project-team ANGE, Inria; CEREMA; LJLL, UPMC Université Paris VI; UMR
A Computational Investigation of a Turbulent Flow Over a Backward Facing Step with OpenFOAM
206 9th International Conference on Developments in esystems Engineering A Computational Investigation of a Turbulent Flow Over a Backward Facing Step with OpenFOAM Hayder Al-Jelawy, Stefan Kaczmarczyk
BOUNDARY LAYER FLOWS HINCHEY
BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,
dynamics of f luids in porous media
dynamics of f luids in porous media Jacob Bear Department of Civil Engineering Technion Israel Institute of Technology, Haifa DOVER PUBLICATIONS, INC. New York Contents Preface xvii CHAPTER 1 Introduction
Numerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
Modelling of flow and sediment transport in rivers and freshwater deltas Peggy Zinke
1 Modelling of flow and sediment transport in rivers and freshwater deltas Peggy Zinke with contributions from Norwegian and international project partners 2 Outline 1. Introduction 2. Basic ideas of flow
CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel
CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey
CFD Analysis for Thermal Behavior of Turbulent Channel Flow of Different Geometry of Bottom Plate
International Journal Of Engineering Research And Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 13, Issue 9 (September 2017), PP.12-19 CFD Analysis for Thermal Behavior of Turbulent
The Shallow Water Equations
The Shallow Water Equations Clint Dawson and Christopher M. Mirabito Institute for Computational Engineering and Sciences University of Texas at Austin clint@ices.utexas.edu September 29, 2008 The Shallow
Chapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
Available online at ScienceDirect. Procedia Engineering 90 (2014 )
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 9 (214 ) 599 64 1th International Conference on Mechanical Engineering, ICME 213 Validation criteria for DNS of turbulent heat
General Curvilinear Ocean Model (GCOM): Enabling Thermodynamics
General Curvilinear Ocean Model (GCOM): Enabling Thermodynamics M. Abouali, C. Torres, R. Walls, G. Larrazabal, M. Stramska, D. Decchis, and J.E. Castillo AP0901 09 General Curvilinear Ocean Model (GCOM):
DEVELOPMENT OF A NUMERICAL APPROACH FOR SIMULATION OF SAND BLOWING AND CORE FORMATION
TMS (The Minerals, Metals & Materials Society), DEVELOPMENT OF A NUMERICAL APPROACH FOR SIMULATION OF SAND BLOWING AND CORE FORMATION G.F. Yao, C. W. Hirt, and
Computational fluid dynamics study of flow depth in an open Venturi channel for Newtonian fluid
Computational fluid dynamics study of flow depth in an open Venturi channel for Newtonian fluid Prasanna Welahettige 1, Bernt Lie 1, Knut Vaagsaether 1 1 Department of Process, Energy and Environmental
A combined application of the integral wall model and the rough wall rescaling-recycling method
AIAA 25-299 A combined application of the integral wall model and the rough wall rescaling-recycling method X.I.A. Yang J. Sadique R. Mittal C. Meneveau Johns Hopkins University, Baltimore, MD, 228, USA
Detailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces
Detailed 3D modelling of mass transfer processes in two phase flows with dynamic interfaces D. Darmana, N.G. Deen, J.A.M. Kuipers Fundamentals of Chemical Reaction Engineering, Faculty of Science and Technology,
An Overview of Impellers, Velocity Profile and Reactor Design
An Overview of s, Velocity Profile and Reactor Design Praveen Patel 1, Pranay Vaidya 1, Gurmeet Singh 2 1 Indian Institute of Technology Bombay, India 1 Indian Oil Corporation Limited, R&D Centre Faridabad
Homework 4 in 5C1212; Part A: Incompressible Navier- Stokes, Finite Volume Methods
Homework 4 in 5C11; Part A: Incompressible Navier- Stokes, Finite Volume Methods Consider the incompressible Navier Stokes in two dimensions u x + v y = 0 u t + (u ) x + (uv) y + p x = 1 Re u + f (1) v
Chapter 9: Differential Analysis
9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control
Numerical studies on natural ventilation flow in an enclosure with both buoyancy and wind effects
Numerical studies on natural ventilation flow in an enclosure with both buoyancy and wind effects Ji, Y Title Authors Type URL Numerical studies on natural ventilation flow in an enclosure with both buoyancy
The most common methods to identify velocity of flow are pathlines, streaklines and streamlines.
4 FLUID FLOW 4.1 Introduction Many civil engineering problems in fluid mechanics are concerned with fluids in motion. The distribution of potable water, the collection of domestic sewage and storm water,
Turbulence: Basic Physics and Engineering Modeling
DEPARTMENT OF ENERGETICS Turbulence: Basic Physics and Engineering Modeling Numerical Heat Transfer Pietro Asinari, PhD Spring 2007, TOP UIC Program: The Master of Science Degree of the University of Illinois
Explicit algebraic Reynolds stress models for internal flows
5. Double Circular Arc (DCA) cascade blade flow, problem statement The second test case deals with a DCA compressor cascade, which is considered a severe challenge for the CFD codes, due to the presence
Convective Mass Transfer
Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface