Modeling and Simulation of flow around an Ahmed Body

Objectives

To simulate and analyse flow over an ahmed body

To calculate Lift and Drag force coefficients

Problem Description

The geometrical shape of the Ahmed body investigated is depicted in Figure 1 for inlet bulk velocity of 40 m/s. The body represents the basic aerodynamic properties of a vehicle, especially in the rear part. The slant angle ϕ has a strong influence on the aerodynamic drag and lift at the back. Both the drag and lift coefficients change abruptly at the angle ϕ=30°. Therefore, this angle is called the critical slant angle.

In this simulation the slant angle of 35° is considered and the simulation data at different locations is validated from the available experimental data from recent experiments.

The experimental setup is such that 400 mm in front of the body there should be a boundary layer of 30 mm thickness.

Geometry

Figure 1 : Geometry

WindTunnel size

Height - 2 m (should be atlest twice the length of body)

Bredth -2 m (should be atlest twice the length of body)

Calculation of length

The boundary layer thickness in 30 mm at 400 mm front of body

Data @300 K taken from https://www.engineeringtoolbox.com/dry-air-properties-d_973.html

So the total distance from start of the boundary layer is 3.444 m

Before the start of boundary layer we have to develop free stream of 40 m/s to develop athe free stream we have considered 3 m of slip wall boundary condition.

From front of the wall to the exit atmospheric pressure the length is 10 m (It should be around 8-10 m so that the exit pressure should not affect the flow which is required to analyse the simulation)

Length of tunnel = 3+3.444+10

Length of tunnel = 16.444 m

Initial Conditions

Fluid flow at 40 m/s at 101325 Pa pressure at 300K.

(We can give inlet flow value anything it won't affect the final result but by setting up 40 m/s can drastically reduce the time taken to reach steady state)

Boundary Condition

1. Inlet velocity at 40 m/s @ 300 K
2. Exit total pressure at 101325 Pa @300 K
3. Front, back and top wall are symmetry boundary condition
4. For bottom wall first 3 m is slip boundary condition and remaining part is no - slip boundary condition so we can get 30 mm boundary layer at 400 mm front of body both at 300 K.
5. Law of wall boundary condition for Ahmed body and legs of body at 300 K. (The ahmed body represents the basic aerodynamic properties of vehicle so law of wall boundary is best suited for wall of ahmed body.

Simulation Parameters for Course Simulation

Solver - Transient Solver (More stable and accurate than steady state solver)

Simulation mode - Fully Hydrodynamic

Gas Flow Solver - Compressible

Start time - 0 s.

End Time - 0.7 s (It should be atleast 1.5 - 2 times the time taken by the flow to pass through the tunnel)

Time Interval for 3D output file - 0.01 s (Total 71 frames)

Time Interval for Text output file - 1e-7 s

Initial time-step - 1e-7 s

Minimum time-step - 1e -7 s

Maximum time step - 1 s

Turbulence model - standard k-ω (2006)

standard k-ω is used for wall bounded boundary layer and for adverse pressure gradient and seperation of flow.

We are interested in validation of flow over the body as well as flow in the wake region developed

and there is an adverse pressure gradient There we have selected standard k-ω model.

Fixed Embedding -

Permanent Boundary embedding over ahmed body of scale 4 upto 2 layers.

Permanent Box embedding 1 over ahmed body of scale 2.

Center point of the embedded box (x,y,z)- 1.3 m, 0.0 m, 0.5 m

The half-size of the box (x,y,z)- 2.5 m, 0.6 m, 0.6 m

Permanent Box embedding 2 over ahmed body of scale 2.

Center point of the embedded box (x,y,z)- 0.75 m, 0.0 m, 0.0 m

The half-size of the box (x,y,z)- 4.25 m, 1 m, 0.05 m

The box embeding 2 was applied by considering the no slip boundary condition. The size of the cells should be very less to calculate the correct boundary layer simulation.

Base Grid Size (course simulation)

x=0.2 m y = 0.2 m z = 0.2 m

A course simulation was run for about 0.78 million cells but it was observed that it has not simulated the seperation region over the slant surface correctly So, we have applied another permanent box embedding of scale 4

Permanent Box embedding 3 over ahmed body of scale 4

Center point of the embedded box (x,y,z)- 1.044 m, 0.0 m, 0.4 m

The half-size of the box (x,y,z)- 0.4 m, 0.4 m, 0.4 m

Result and Analysis (Course Simulation)

1)Mesh

Figure 2: Mesh

Figure 3 : Mesh (zoomed upto box embedding)

Figure 4: Mesh (zoomed upto boundary embedding)

Figure 5: Velocity Contours

Figure 6: Pressure Contours

Figure 7: Velocity Glyph vector

Figure 8 : Drag on front wall (in terms of Pressure resolved over normals)

Figure 9: Drag on rear wall (in terms of Pressure resolved over normals)

Figure 10: lift on top wall (in terms of Pressure resolved over normals)

Figure 10 : lift force on bottom wall (in terms of Pressure resolved over normals)

Plot 1: Average Velocity over wall vs time

Plot 2 : average Y+ over wall vs time

Simulation

Velocity contours at mid plane

Pressure Contours at mid cut plane

Calculation of drag and lift forces

Plot over line data compairison with the experimental value

Simulation Parameters for Final Simulation

The final simulation was performed over half cut section.

The wind tunnel size

Length - 10 m

Bredth - 1 m

Height - 2 m

Solver - Transient Solver (More stable and accurate than steady state solver)

Simulation mode - Fully Hydrodynamic

Gas Flow Solver - Compressible

Start time - 0 s.

End Time - 0.32 s (from course simulation it was reached steady state at 0.2 s )

Time Interval for 3D output file - 0.001 s (Total 320 frames)

Time Interval for Text output file - 1e-7 s

Initial time-step - 1e-7 s

Minimum time-step - 1e -7 s

Maximum time step - 1 s

Turbulence model - standard k-ω (2006)

Permanent Boundary embedding over ahmed body of scale 3 upto 11 layers.

Permanent Box embedding 1 over ahmed body of scale 2

Base Grid Size (course simulation)

x=0.02 m y = 0.02 m z = 0.02 m

Grid size over the ahmed body = 0.02/2^3=0.0025 m

In previous case of course simulation the Y+ value was around 780 and grid size over ahemed body was 0.0125 m. considering Y+ is linearly related to grid size to get Y+ of around 30-50 the grid size should be around 0.0006 m but as we are low on the computational resources the Y+ for above grid size will be around 120 -150 m.

Result and Analysis of Final Simulation

1)Mesh

Figure 11: Mesh

Figure 12: Mesh (zoomed upto box embeding)

Figure 13 : Mesh (zoomed upto boundary embedding)

Figure 14: Velocity Contours

Figure 15: Pressure Contours

Figure 16:Drag on front surface (in terms of Pressure resolved over normals)

Figure 17: Drag on rear surface (in terms of Pressure resolved over normals)

Figure 18 :Lift on top surface (in terms of Pressure resolved over normals)

Figure 19: Lift on bottom surface (in terms of Pressure resolved over normals)

Plot 5 : Average velocity over wall vs time

Plot 6: Average Y+ over wall vs time

Calculation

Plot over line data compairison with the experimental value

Inference

1. The simulation achieved steady state at 0.15 seconds
2. Average Y+ value over ahmed body wall is around 110.
3. Average velocity value over wall 27 m/s
4. Total cell count for course simulation is 1024411 cells
5. Total cell count for Final simulation is 17405534 cells
6. The drag force coefficient is 0.219 by method 1 and around 0.192 by method 2
7. The downforce (lift) coefficient is 0.692 by method 1 and 0.70 by method 2
8. The lift coefficient results from course simulation and final simulation are quite similar but the drag coefficient for courser simulation is higher this is due to the fact that the area over which downforce (lift) acts is quite planar compaired to the area where the drag force acts Therefore, we require a finer mesh for calculation of drag force.
9. Though the Y+ is higher than the recommended values (30- 100 ) the results are compairable with the experimental within 10%.
10. There is a wake region formation behind the body of around 300 mm
11. The fluid seperation takes place over slant angle of 35° which is valid as the critical angle of seperation for air at 40 m/s at 300 K temperature is 30°.
12. We need a grid size of around 0.006-0.008 m to get results within 5% of experimental value.
13. Velocity profiles over the wall (from x=-13 mm to x= -113 mm) denotes the flow seperation taking place Therefore, there is slight negative dip in the plot.
14. Velocity profiles over the wall (from x=37 to x= 187) have wake region formed There fore the velocity is decreased over from z =50 mm to z = 250 mm
15. Velocity profile over x=263 mm denotes simple fluid flow over wall phenomenon.