FLOW OVER A AHMED BODY
Aim
The aim of the project is to perform grid dependency test on the Ahmed body and also to determine the appropriate Y+ value to capture the near wall flow field.
Ahmed body
The Ahmed body represents a simplified bluff ground vehicle. Accurate flow simulations can be derived from this body due to its simple design and various practical features of a real time automobiles, which are tested using this model. This model is used specially for turbulent flow field determination around a car body. It is a general reference body where it is used to test different typr of flows which we find in cars. It is good computational model where we can test the changes before going on to the actual geomentry where lengthy and costly wind-tunnel testing and computational cost are involved. The geomentry of the model is described below.
Figure1: Geomentry of the Ahmed body
Y + Siginificance
In turbulence modelling the near wall mesh size determination is very important in solving the turbulent models. But how small should the mesh to be to obtain the exact turbulent modelling. This is where the Y+ value comes into play where it determine the first cell hight from the wall. The Y+ plus value is dimensionless and is define as the distance from the wall to the first cell. To understand the Y+ value, lets first discuss boundary layer theory.
Figure 2: Boundary Layer
From the figure 2 we could see that in the log-layer the flow is fully turbulent i.e) the velocity is very high leading to higher reynolds number. In these area the interia forces dominate the viscous forces. As we move closer to the wall where y value tends to zero the viscous forces dominate as we know that near wall the flow velocity is zero. This region is called the Viscous sublayer. In the transition layer where the laminar flow transition to the turbulent flow neither of the law holds. In terms of y+value we can say that
In viscous sublayer it is 1 <Y+<5
In the transition layer it is 5<y+<30
In the log layer it is 30<y+<500
From the above discussion we can say that placing the first cell in the mesh region is very vital to determine the turbulent model and as well as to compensate on the computational mesh and time.
Figure 3: First cell definition
From the Y+ value either wall function approach or two layer zonal model approach is determined. The Wall function function approach is carried out in the k-epsilon, RSM and LES models which used for modelling turbulent flows where the first cell is somewhat far from walls. The k-omega and the spalart-Allmaras are used throughtout the boundary layer.
Determination of the Y+ Value
Source:simscale
Geomentry set up
The geomentry is a half body Ahmed body to reduce the computational time. The geomentry is split using spaceclaim and the final Model is shown below
Figure 4: Geomentry of the Symmentry Model
Simulation set up
The simulation is carried out in with three different mesh size with a appropriate Y+ value and the results are discussed based on the computational outcome.
Case 1 (Coarse mesh)
A coarse mesh size was taken to run a basline simulation to understand the flow geomentry.
A body sizing of 50mm and a face sizing of 80mm with Y+ value of 1 where all the cells were the cells are in the viscous sublayer and the log region. The pre processing was carried out with a turbulence model of K-Omega SST model with pressure-based solver since the mach number is less than 0.3.Standard initialization was carried out and turbulence model was selected since the reynold obtained was 1740000, which is a turbulent flow. The inlet velocity is taken as 25m/s.
Mesh parameters
Element size = 100mm
Body sizing = 50mm
Total Thickness = 0.0294877 mm (y+ = 1)
Total elements = 249004
Figure 5: Coarse mesh with 30 layers
Results for case 1
Figure 6: Convergence of the Residuals for the coarse mesh
Figure 7: The velocity and the Presuure plots for the coarse mesh
Figure 8: Vector and Streamline plots for the coarse mesh
Case 2 (medium mesh)
Mesh Parameters
Element size = 100mm
Body sizing = 40mm
Total Thickness = 0.0294877 mm (y+ = 1)
Total elements = 341433
Results for case 2
Figure 9: Convergence of the Residuals for the medium mesh
Figure 10: The velocity and the Presuure plots for the medium mesh
Figure 11: Vector and Streamline plots for the medium mesh
Case 3 (Fine mesh)
Mesh Parameters
Element size = 100mm
Body sizing = 35mm
Total Thickness = 0.0294877 mm (y+ = 1)
Total elements = 430355
Results for case 3
Figure 12: Convergence of the Residuals for the fine mesh
Figure 13: The drag and lift plot for the fine mesh
Figure 14: The velocity and the Presuure plots for the fine mesh
Figure 15: Vector and Streamline plots for the fine mesh
Discussion on the results
Mesh Independency test
From the results we could see that the drag values are more refined when we have a refine mesh compared to the coarse and the medium mesh. The appropriate drag value can be obtained by refining the mesh more. The Drag values drag and lift values are shown in the tabl 1 below.Due the limit of the elements in the student version further refinement is not done. Also, the results of the finer mesh shows the presence of the bubbbles at the rear end more defined comparing the coarse and the medium mesh. The convergence of the models are confirmed from the residual convergences which are presented in the figure 6,9 and 12.
|
Mesh Size |
Coarse mesh |
Medium mesh |
Fine mesh |
|
Drag Co-efficient (Cd) |
0.39431285 |
0.3772995 |
0.355710504 |
|
Lift Co-efficient (Cl) |
0.22831765 |
0.22877345 |
0.245183281 |
Table 1: Cd and Cl values for different mesh size
Point of seperation and Negative pressure
To understand Point of seperation and negative pressure let us see what is boundary layer seperation. Boundary layer seperation is phenomena where when the flow gets detached from the boundary surafce and moves into wake. When a fluid comes into contact with a surface a boundary layer segment is formed. When the interial forces are higher than the viscous force an adverse pressure gradient flow is developed where the flow is against the increasing pressure. when the flow travels far enough in the adverse pressure gradient region the flow gets seperated forming eddies and vortices which is called as the wake region. In the wake region due to the recirculations there is a decrease in pressure making it negative. When this wake region continues to an extent, the flow becomes stall and the lift force is lost in the case of an aerfoil. In interal flow this can create vibrations leading to several mechanical losses. In flows over automobile, this wake region increases the pressure drag reducing the speed of the vehicle. This pressure drag acts in the direction perpendicular to the direction of the vehicle increasing the friction of the vehicle, leading to loss in speed.
Point of seperation is the point where the wake region starts and when the point of seperation is too early the seperation leads to several losses. In modern day industrial designs, the developments are made to delay the point of seperation to overcome the losses.
Since the finer mesh produced more defined results, lets take the velocity and pressure plot of the refined mesh. We couls see that when that air hits the front end of the car the velocity becomes zero and reaches the stagnation point. As the flow travels over the curved structure of the front end it losses its velocity since it has to travel over a longer surface region leading to seperation. Since the flow is seperated the velocity moves into the free stream region which increases its velocity and the at the same time the region between the surface and the flow becomes negative pressure which can be seen in the pressure and velocity plots in figure 14. The flow then gets attached to the surface due to its uniformity and again gets dettached at the slant region leading to same effects. This flow continue at the rear end forming vortices or eddy bubbles in the wake region producing pressure drag which can be seen in figure 15. Due to this wake region there is negative pressure in the rear end of the vehicle.
Total layer thickness
In meshing process, total layer thickness is taken instaed of the first layer thicknes since applying first layer thickness give ununiform distribution of the layers which is shown in the figure 16.
Figure 16: Ununiform distribution of the layers