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Numerical Simulation of Flow Near Stagnation Regions |
| Researcher: |
Anders Jönson lada@chalmers.se |
| Supervisor: |
Lars Davidson lada@chalmers.se |
| Cooperation: | Volvo Data |
| Sponsors: | NUTEK |
| Publications: | [1] |
| Start of project: | autumn 1994 |
| End of project: | spring 1998 |
THE PROJECT With the computer resources of today, it is possible to use CFD as a tool in designing cars and trucks. This has been done at Volvo Data for several years. One important parameter in car design is the drag of the vehicle since it is closely related to the fuel consumption. The drag is the sum of pressure and friction forces acting on the car. The pressure forces are largest, hence it is important to predict the pressure distribution correctly. The drag of a car is mainly built up by the difference between a high pressure area in the front region of the car and a low pressure area in the back region. Since the front of the car, the stagnation region, has a large projected vertical area, small errors in the pressure field will produce large errors in the predicted drag coefficient CD. This makes accurate predictions of the stagnation pressure distribution very important. To gain further insight in numerical simulation of flow near stagnation regions, a collaboration project between Volvo Data, AEA Technology, and Chalmers University of Technology was started 1996. In this work the commercial CFD-code, CFX, was used as a platform for development and research. AEA Technology has developed the CFD-code CFX and are selling it through out the world. There are several important decisions that has to be made before a numerical simulation can be performed. Choice of mesh density, mesh distribution, discretization scheme and turbulence model are all important factors for the accuracy of the result. Unfortunately, high mesh density demands large computer resources, and high-order numerical schemes and complex turbulence models can cause numerical instability problems. In this work, both mesh-related questions and choice of turbulence model has been addressed. NUMERICAL ACCURACY A first study compared the velocity predictions in the stagnation region using three different discretization schemes. Since Volvo already had ruled out any first-order accurate scheme for the momentum equations, only higher order schemes were used. The tested schemes were HUW which is second order accurate and unbounded, QUICK, third order accurate and unbounded and CCCT, a bounded version of QUICK. The configuration used in this study was an axisymmetric impinging jet, where detailed velocity measurements are available. For this study, a Low-Reynolds number k-eps model was used. Two different mesh sizes where used (108x80 and 152x150). On the fine mesh, all schemes predicted very similar velocity profiles while QUICK was slightly better then HUW on the coarse mesh. This was expected since QUICK is a third order accurate scheme. The pressure distribution in the stagnation region has also been studied. The influence of mesh density, resolution of the stagnation line and extrapolation to the true stagnation point on three different mesh sizes was investigated. From a fine mesh, 264x200 cells, two consecutive coarser meshes was created by halving the number of cells in each direction. The total pressure along the stagnation line was found to be sensitive for mesh density. A too coarse mesh gives a large dip in the total pressure as the stagnation point is approached. This results in an underprediction of the stagnation pressure. It was also shown that a fine enough mesh can predict the stagnation pressure correctly. A short parametric study on mesh distortion has also been made. From a smooth mesh, different types of distortions, such as sudden biasing and non-orthogonal cells were introduced. These types of distortions are common in complex geometries. The results were compared with the undistorted mesh. It was shown that the total pressure coefficient Cp along the stagnation line were locally distorted, but recovered very fast. Thus if the distortion are not in the immediate vicinity of the stagnation point, no effect on the stagnation point pressure was observed. TURBULENCE MODELLING For industrial purpose, the most common computational approach to turbulence is the Eddy Viscosity Model (EVM) or a Second Moment Closure. Both these approaches are based on the time-averaged Navier-Stokes equations, but differ in the modelling of the unknown Reynolds stresses. Eddy viscosity models assumes a functional relation between the stress and the strain field, coupled with the eddy viscosity concept. Models based on the eddy viscosity such as the k-eps two-equation model have been shown to give accurate predictions in many flow fields. However, conventional linear EVM's are known to have severe defects in predicting stagnation, swirl, separation, recirculation, streamline curvature effects etc. These problems problems are mainly due to the crude assumption of a linear stress-strain relation. A second-moment closure solves a full set of transport equations for the unknown Reynolds stresses. These models are also called Reynolds Stress Models (RSM). These transport equations are based on an exact set of equations and thus has in principle the potential to mimic any complex strain field. Unfortunately, second-moment closures are often computationally too expensive in industrial cases. This is often due to numerical problems such as convergence and stability problems. As a consequence, linear eddy viscosity models are still used for routine work in the industry because of its numerical stability and less demands on computer resources, compared with more elaborate models. This makes the route towards Non-Linear Eddy Viscosity Models (NLEVM) and Explicit Algebraic Reynolds Stress Models (EARSM) interesting. As stated above, linear EVM's perform poorly in stagnation regions, producing too a high stagnation pressure. This is because a linear EVM overpredicts the production term in the k equation, Pk. This produces too high values of the turbulent viscosity which gives an overprediction of the modeled diffusion term in the momentum equation. Since the diffusion term is mainly balanced by the pressure gradient, this results in too a high stagnation pressure. This anomaly can be removed by switching to a second-moment closure model, because then the production term is exact and need not to be modeled. However, these models have been found too unstable for industrial purposes. The idea was then to replace the simple linear stress-strain relation with a more complex expression. Hopefully, such a model would retain the stable behavior of a linear EVM, but better model different physical flow phenomena. In order to investigate such models a team was formed at Volvo. This had several advantages, Chalmers got access to fast computers and complex three dimensional test cases and Volvo gained from Chalmers experience in turbulence modelling. A general stress-strain expression was implemented, allowing all non-linear eddy viscosity model or explicit algebraic Reynolds stress model to be tested. The Volvo Environmental Concept Car (ECC) has been used as a basis for this investigation. These models were shown to be superior to a linear EVM in predicting the stagnation pressure. They also seems to be slightly less sensitive for mesh resolution along the stagnation line. Still, the computational cost was only slightly higher than the standard linear EVM. As a spinoff, the accuracy of the overall flow field predictions was increased with these models. It was shown that the separation in the back of the car and the wake structure behind the car were more correctly predicted. In this study, the effect of mesh resolution was also shown to be important, a fine mesh producing a better base pressure. This is mainly for its ability to predict stagnation pressure and separation more correctly then a coarse mesh. 
REFERENCES
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