External Flow Simulation over an Ahmed body to study its Aerodynamic Properties

STEADY STATE EXTERNAL FLOW SIMULATION OVER AN AHMED BODY TO STUDY ITS AERODYNAMIC PROPERTIES USING ANSYS FLUENT

1. AIM

Our aim is to simulate a steady state external flow over an Ahmed body to study the properties of lift and drag using ANSYS FLUENT and perform grid independent study.

2. THEORY/EQUATIONS/FORMULAE USED

ANSYS FLUENT academic version CFD package is used to carry out the simulation. It is a user friendly interface which provides high productivity and easy-to-use workflows. Workbench contains all workflow needed for solving a problem such as pre-processing, solving and post-processing.

Structure of ANSYS FLUENT simulations

The basic steps for a simulation are as follows,

1. Pre-processing – It includes geometry creation, discretization, providing named selection for using as boundary conditions. The packages used in pre-processing step are SpaceClaim, Ansys Mesher.
2. Solving – It includes applying initial and boundary conditions, adding material properties, applying suitable turbulence model as per the problem and running the iteration till convergence. The package used in post-processing step is Fluent.
3. Post-processing – It includes analyzing the results by plotting the results as charts, contour, and exporting the data, also validating the results both qualitatively and quantitatively. The package used in post-processing step is CFD-Post.

Ahmed Body

Ahmed body is a representation of a standard passenger car. Actually a passenger car has complex design in reality but the Ahmed body is a simplified design which has car like features. The flow over Ahmed body helps us capturing the essential features such as lift, drag and its coefficients, flow behavior such as velocity profiles around the wall. So it is majorly used to validate the CFD codes and understand the behavior of flow and start improvising. It was first defined and characterized in the experimental work of S.R. Ahmed in 1984, as the name suggests Ahmed Body.

Fig: Dimensions of Ahmed Body

Concept of Wall Function

Wall function is an important defining criterion that tells the solver about the approach to solve near the boundary wall as it’s different for every case.

The boundary wall may be laminar or turbulent as well.

1. For laminar boundary, wall will be in no-slip condition.
2. For turbulent boundary, the laminar region near the wall is very small.

There are three regions in the turbulent boundary layer.

1. Turbulent Layer [ 30 < Y+ < 300 ]
2. Buffer Layer [ 5 < Y+ < 30 ]
3. Viscous-sub Layer [ Y+ < 5]

As our problem requires the study of essential features such as lift, drag, drag coefficient on the Ahmed Body wall, so wall treatment is required. Also it’s a turbulent flow, so we need to choose a turbulence model, and each model will have a wall function.

K-epsilon is best suited for flow away from the walls and K-omega is best suited for flow near the walls, high Reynolds number. Our interest lies in the average values over the wall such as lift, drag where the choice between the above mentioned turbulence model does not make a difference.

Y+ value

Y+ value is used to determine the first cell height based on whether to use wall function or not. Wall functions are required as the gradients of velocity, temperature, etc. close to the wall are large.

Y⁺ = y * U_t

ν

where y is Cell height, U_t is frictional velocity, and ν is Kinematic Viscosity of the fluid.

There are two approaches for solving i.e,

1. Piecewise linear [Near Wall Approach] – where fine grids are required to accurately resolve the gradient near the wall.
2. Non-linear [Wall Function Approach] – where the first grid height is more and the viscosity affected area is skipped.

Problem – Flow over a Cylinder

• The challenge includes 2 parts.

1. Steady state external flow simulation over an Ahmed body and to determine the Lift, Drag, and Drag Coefficient for a flow velocity of 25 m/s.
2. Perform Grid Independent study to check the results.

Calculation

Reference values - Ahmed Body

Length = 1.044 m, Breadth = 0.389 m, Height = 0.288 m

Projected Area = Breadth x Height = 0.065 m²

• Part 1 - Steady State External Flow Simulation

Fluid chosen for the problem – Air

Density of Air = 1.225 kg/m3, Dynamic viscosity = 1.7894e-5 kg/ms, Velocity of fluid = 25 m/s, Characteristic length = 1.044 m

So, Reynolds Number, Re = 1.78e^-6

Calculation of first cell height with an assumption of Y⁺ = 50 (As K-Epsilon Turbulence Model is used)

Skin Friction Coefficient, C_f

C_f = 0.058 * Re^(-0.2) [External Flow]

C_f = 0.079 * Re^(-0.25) [Internal Flow]

So, C_f = 0.00323 [using External Flow Eq.]

Wall Shear Stress, τ_w

τ_w = 0.5C_f ρu²

τ_w = 1.236 N/m²

Frictional Velocity, U_t

U_t = (τ_w / ρ)^(1/2)

U_t = 1 m/s

Cell Height, y

y = Y⁺ * ν

U_t

Where y = 0.73 mm

• Part 2 - Grid Independent Study

Lift, Drag and Coefficient of drag needs to be calculated for different mesh, so the size of elements in body sizing, face sizing differs for each setting.

3. PROCEDURE

Part 1

• In the process, firstly the geometry with flow domain is created in SpaceClaim. As the body is symmetric, the complete domain is split into half in order to save the number of cells and to get the results faster.
• Then the meshing is done in order to study the flow near the walls clearly and named the boundaries. Also made sure that mesh is good enough to carry out the current simulation.
• In fluent, the material, solver type, the initial and boundary condition, suitable turbulence model are defined as per the problem.
• Monitor plane is created in order to monitor the velocity and pressure during run time.
• Coefficient of Drag, Drag, and Lift plot is also initiated in order to validate the essential features with the experimental data. Finally the animation is also added to study the overall behavior after the simulation is converged.

Part 2

• The same procedure is followed for each simulation with different element size in order to perform grid independent study.

4. NUMERICAL ANALYSIS (Software used – ANSYS 2018 R1)

• Geometric Model

The 3D geometry of Ahmed Body with flow domain is created in SpaceClaim as per the figure given below. In order to study the external flow behavior, the domain width of 0.5m is created. Also a space of 2m before the Ahmed body and more importantly 5m after the Ahmed body is created to capture the flow.

3D Geometry with the flow domain – Ahmed Body

• Mesh
• 

Fig: Edge Sizing on the wall

Fig: Inflation Layers

Fig: Final Mesh for the complete domain

• Boundaries
• 

Fig: Boundaries for the complete domain

• Solver Set-up

1. The mesh file is imported into the FLUENT software for the analysis of the modeled surface.
2. Once the mesh file is loaded and displayed, it is checked for the units, scale, and mesh.
3. There are two types of numerical solver methods pressure –based and density-based solver. The pressure based solver was used rather than the density based solver as the simulation is for lower Mach number. Absolute velocity formulation, steady state was used for the analysis.

4. Energy equation was switched off for the analysis process as we are not interested in temperature of the system.

5. K-epsilon turbulence model was used for the analysis as the Reynolds number used for simulation is in the range of 1780000.

6. The fluid material chosen is air.

7. Plane named as cut-plane is created at -0.1 m in z-plane from the centre of the geometry as shown in the below figure to observe the velocity and pressure contours in the domain.

8. Report definitions of forces on the cut-plane are set up as we are interested in the physical quantity such as Lift, Drag and Coefficient of drag.

9. Convergence Criteria are checked as it might take some more time and we want to run the complete number of iterations or time step set for the simulation in order to witness the physics behind of the problem.

10. Solution methods – SIMPLE Scheme used for Pressure-Velocity coupling and the methods for Spatial Discretization are as per the below image.

11. Hybrid initialization is done and numbers of iterations are set for running the steady simulation and time step size and number of time step for transient simulation.

12. Velocity and pressure contours are set in order to monitor the fluctuations during run time and also animations are added.

Initial Setup and Boundary Condition

Zone	Type	Boundary Condition	Additional conditions (if any)
Inlet	Velocity - Inlet	Velocity – 25 m/s,	Steady State, Transient State, Pressure Based, Absolute Switched OFF Energy equation Turbulence Model – k-epsilon & k-omega
Outlet	Pressure - Outlet	Gauge pressure of 0Pa
Symmetry	Symmetry	Symmetry
Wall	Wall	Stationary wall without slip

5. RESULTS

• Convergence Plot

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-omega

• Lift plot at Wall

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Drag plot at Wall

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Drag Coefficient plot at Wall

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Velocity contour of flow over a Ahmed Body

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Pressure contour of flow over a Ahmed Body

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Velocity Vector Plot of flow over a Ahmed Body

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

• Velocity Profile along the Lines at the Wake regions of the Ahmed Body

Fig: Baseline Mesh

Fig: Case 1 Fig: Case 2

Fig: Case 3 k-e Fig: Case 3 k-w

• Pressure on the Wall (Ahmed Body)

Fig: Baseline Mesh Fig: Case 1

Fig: Case 2 Fig: Case 3 k-e

Fig: Case 3 k-w

Grid Independent Study

6. CONCLUSION

1. The steady state external flow simulation of flow past the Ahmed body is done for flow velocity of 25 m/s in ANSYS FLUENT, from the convergence plot we can see that the solution got converged around 1000 iterations in all cases.
2. From the above grid independent study table, we can see and compare the values of lift, drag, drag coefficient, Pressure range on the car wall surface, and velocity dip in wake region for different cases with different element sizes.
3. Firstly, it can be easily noticed that the values for baselines mesh is different from all other cases. As the mesh is very coarse which makes it difficult to capture these essential characteristics, hence the results are not accurate.
4. It can be concluded that the drag on the car wall is comparatively more than the lift. The pressure on the car wall for all the cases are more or less equal that ranges from around +390 to -1230 Pascal’s except the baseline mesh case. We can clearly see that there is a negative pressure region which is called as wake region.
5. Flow over a blunt Ahmed body creates a wake region. It starts forming in the rear end as the momentum of the flow doesn’t allow the flow to surround the object or wrap the contour. It is due to the separation of flow from the body which can be seen due to the adverse pressure gradient as it leaves a low pressure at the back compared to the front. The low pressure at the back of the object sucks the flow backwards. This pressure difference forms the pressure drag.
6. This point of separation is very important as it directly impacts the pressure drag. We need to always try to delay the boundary layer separation in order to reduce the pressure drag but in turns there will be skin-friction drag and then look to have a better trade-off.
7. Velocity dip basically means the lowest velocity values taken across three different lines spaced at a small interval in the wake region. Line 1 and 2 values are negative which tells us about the recirculation in the region, flow in the opposite direction.
8. In the validation perspective the experimental value of drag coefficient across ahmed body lies around 0.28 to 0.33 in different publications and the drag coefficient value from the numerical simulation also lies in the same range (0.29-0.30). Hence the results are in good agreement and the underlying physics is visible clearly.
9. Grid independent study is done by changing the number of cells and observed that the lift, drag, dra coeffiecient, velocity, pressure in the flow across the ahmed body is almost same in all the cases except the baseline mesh case. Hence we can consider it as grid independent.

7. REFERENCES

1. https://www.simscale.com/forum/t/ahmed-body/64235
2. https://www.cfd-online.com/Wiki/Ahmed_body
3. https://www.youtube.com/watch?v=fJDYtEGMgzs&ab_channel=FluidMechanics101
4. https://www.computationalfluiddynamics.com.au/y-plus_part3_understanding-impact-of-y-and-number-of-prism-layers-on-flow-resolution/
5. https://www.researchgate.net/post/Do_we_need_to_check_the_y_values_for_SST_K_W_turbulence_model_during_post_processing_and_if_yes_should_the_y_value_be_1_everywhere_on_the_wall