Ahmed Body Challenge

JORGE LOZANO

Advanced CFD using ANSYS Fluent

Ahmed Body Challenge

Objective

Run the simulation for the velocity of 25 m/sec with the default air properties in fluent.

For this challenge, you will have to provide answers to the following questions:

Q1. Describe Ahmed's body and its importance.

Q2. Explain the reason for the negative pressure in the wake region.

Q3. Explain the significance of the point of separation.

Expected Results:

1. Velocity and pressure contours.
2. The drag coefficient plot for a refined case. (For velocity of 25m/sec, the drag coefficient should be around 0.33).
3. The vector plot clearly showing the wake region.
4. Perform the grid independency test and provide the values of drag and lift with each case.

Important of Ahmed body

An Ahmed body represents a simplified like vehicle volume which helps understand the fundamental physics defining by the engineers the lift and drag forces and coefficients at certain characteristically velocities, pressure differences, and seeing and analyzing the vortices, turbulence and Reynolds number obtained. ANSYS is a general purpose FEA and CFD simulation software. It gives numerical prediction of the behavior of a system.

These numerical predictions need to be validated by experimental data. People working in vehicle aerodynamics use Ahmed body to validate their numerical model because the experimental data from wind tunnel testing is available for Ahmed body. Once the numerical model in validated, it is used to design new models of the car.

Its shape is simple enough to allow for accurate flow simulation but retains some important practical features relevant to automobile bodies. This model describes how to calculate the turbulent flow field around a simple car-like geometry using the Turbulent Flow, k-epsilon and k-omega interface. Later, either experimentally or computationally it can be recreated all the same but with a desired geometry, new to come up to the market or a research.

The Ahmed body was described originally by S. R. Ahmed in 1984 [1]. Three main features were seen in the wake:

1. The A recirculation region that is formed as the flow separates at the top of the vertical back surface of the model
2. The B recirculation region that is formed due to the separation at the base of the model.
3. The c-pillar vortices that form as the vorticity in the side boundary layers roll up over the slant edges.

The wake was shown to be highly dependent on slant angle. For slant angles less than 12°, the flow remains attached over the slant. The flow is essentially two-dimensional and has low drag. Between 12° and 30° the flow becomes much more three-dimensional as the c-pillar vortices form. These reach maximum strength at 30°. The drag increases significantly as the low-pressure cores act on the rear surfaces. Past 30° the flow separates fully off the slant. This results in a sudden decrease in drag and weaker c-pillar vortices.

The negative pressure is due to the velocity difference applied at a certain Reynold number and the rear angle, which at a low Reynolds number when this difference in pressure happens the wake obtained increases the drag due to the pressure drop behind the Ahmed body, which at a high Reynolds number due to the vortices generated it produces small amounts of pressure thrusting the body.

According to the point of separation defined by the Ahmed body and the flow, the alpha angle depending on which value is at it causes change in flow direction, forces required, lift on the body, induced drag due to “tip vortex”, at a critical value flow in slant stalls and reduced lift-reducing as well drag, all depending on the value of alfa and the Reynolds number.

The Reynolds number

The Navier-Stokes equation is a rather complicated-looking nonlinear partial differential equation. In order to make some progress in understanding the possible solutions, it is useful to do some dimensional analysis and to make some estimates. For this purpose, we want to compare the inertial terms on the left-hand side to the viscous terms on the right-hand side. Let's assume that the flow is steady, so that

Let U be a characteristic speed of the flow (usually taken to be the free-stream speed far from the object), and let L be some characteristic dimension of the flow (the typical size of an object in the fluid, say). Then for the inertial term,

Let U be a characteristic speed of the flow (usually taken to be the free-stream speed far from the object), and let L be some characteristic dimension of the flow (the typical size of an object in the fluid, say). Then for the inertial term;

For the viscous term;

Both quantities have the same dimension, so we can define a dimensionless number, the Reynolds number Re, by taking the ratio:

with n = h/r the kinematic viscosity.

To get an idea of the magnitude of the Reynolds number, considering a car moving at a certain speed and an appropriate value of L would be the typical width of the car, it’s fairly a typical--large Reynolds number flow tends to be the rule in most situations

The law of the wall – y+ according to Fluent turbulence models

The flow demands solving viscous sublayer

-This situation includes those cases where the wall bounded effects are very important. Common examples are heat transfer, aerodynamic drag, pressure drop, flows with adverse pressure gradients…

-To solve viscous sublayer, the mesh must have a y+<1

The flow does not demand solving the viscous sublayer

-These are cases where the wall-bounded effects are secondary, or worth flow undergoes geometry-induced separation. A typical example is the flow surrounding a Bluff body.

-To solve this case is the first cell closed the wall should have a y+ value within 30 to 300.

F.1 RANS turbulence model usage characteristics

SIMULATION SET-UP

To perform simulations using Ansys/Fluent it’s desirable to have knowledge in the type of fluid model to adjust the condition of turbulent or laminar models according to the Reynolds number, the naiver-stokes equations, mesh characteristics, and the data postprocessing. For this case several simulations will be performed variating in the mesh, and solving algorithm methods having as follows parametric results, duplicating several simulations and modifying the unique variables, as in F.2.

F.2 Project schematic

The geometry in F.3, consists of an Ahmed body which according to its symmetry it will be possible to use the split command in order to obtain half the geometry being able to refine the mesh even more, and still obtaining a desired symmetry results convergence.

F.3 Original geometry and ready for physics calculation

Before to even start generating any kind of mesh, we must perform an analytical calculation the F.4 shows an automatic solution to obtain the Y+ value and the total boundary thickness according to the Reynolds number, showing the formulas and images representing the expected result, which is used to adjust an optimal mesh as the result, the selection for tetrahedrons is due to the turbulence expected which generally obtains a better visualization and data entry in this selection.

F.4 Y+ calculator and boundary layer total thickness calculation

F.5 Shows the methods selected to perform the first, most refined mesh, with 511,947 elements, performing a layered mesh according to the analyzed boundary thickness layer, and generating a local refined mesh in the inner volume as well as in the car wall.

F.5 1-Mesh layered and locally refined according to analytical calculation

F.6 Shows the methods selected to perform the second, most refined mesh, with 487,756 elements, not performing a layered mesh, and only generating a local refined mesh in the inner volume as well as in the car wall.

F.6 2-Mesh locally refined according to analytical calculation

F.7 Shows no methods selected to perform the third, most refined mesh, with 504,753 elements, not performing a layered mesh, nor a local volume mesh and only generating a global refined mesh.

F.7 3-Mesh generated with global refinement

Due to the input values such as the velocity, Reynolds number, air properties and geometry, the model is turbulent, which to obtain a turbulence model dependency as the mesh, both models K-epsilon and k-omega will be performed applying the SIMPLE scheme with the second order upwind for the turbulent and momentum pressure-velocity coupling convergence method, as seen in F.8. The material will be air according to the fluent database.

F.8 Models and methods calculated

RESULTS

Several simulations were performed as follows:

Mesh 1	1	K-omega method	2	K-epsilon method
Mesh 2	3	K-omega method	4	K-epsilon method
Mesh 3	5	K-omega method	6	K-epsilon method

Whereas every simulation performed will have post-processed the residuals to convergence, the drag and lift coefficient according to the surface transverse area of contact, as well as an output parameter to plot the relationship within each of the simulations, several vectors obtaining the velocity around the wake region, velocity and contour plots , and y+ contour for the geometry analyzed and its histogram plot and the surface floor contour and histogram plot.

• Mesh 1, K-omega method

F.9 K-omega mesh 1 steady state residuals

F.10 K-omega mesh 1, Drag & lift coefficient vs iterations plot

F.11 K-omega mesh 1 Velocity vectors graph and wake region analysis

F.12 K-omega mesh 1 Pressure and velocity contour, and streamline velocity pattern

F.13 K-omega mesh 1 y+ contour and histogram verification car wall

F.14 K-omega mesh 1 y+ contour and histogram verification surface

In F.13 and F.14 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 50 for the car-wall surface and 100 for the floor surface.

• Mesh 1, K-epsilon method

F.15 K-epsilon mesh 1 steady state residuals

F.16 K-epsilon mesh 1, Drag & lift coefficient vs iterations plot

F.17 K-epsilon mesh 1 Velocity vectors graph and wake region analysis

F.18 K-epsilon mesh 1 Pressure and velocity contour, and streamline velocity pattern

F.19 K-epsilon mesh 1 y+ contour and histogram verification car wall

F.20 K-epsilon mesh 1 y+ contour and histogram verification surface

In F.19 and F.20 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 52 for the car-wall surface and 100 for the floor surface.

• Mesh 2, K-omega method

F.21 K-omega mesh 2 steady state residuals

F.22 K-omega mesh 2, Drag & lift coefficient vs iterations plot

F.23 K-omega mesh 2 Velocity vectors graph and wake region analysis

F.24 K-omega mesh 2 Pressure and velocity contour, and streamline velocity pattern

F.25 K-omega mesh 2 y+ contour and histogram verification car wall

F.26 K-omega mesh 2 y+ contour and histogram verification surface

In F.25 and F.26 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 140 for the car-wall surface and 300 for the floor surface.

• Mesh 2, K-epsilon method

F.27 K-epsilon mesh 2 steady state residuals

F.28 K-epsilon mesh 2, Drag & lift coefficient vs iterations plot

F.29 K-epsilon mesh 2 Velocity vectors graph and wake region analysis

F.30 K-epsilon mesh 2 Pressure and velocity contour, and streamline velocity pattern

F.31 K-epsilon mesh 2 y+ contour and histogram verification car wall

F.32 K-epsilon mesh 2 y+ contour and histogram verification surface

In F.31 and F.32 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 150 for the car-wall surface and 400 for the floor surface.

• Mesh 3, K-omega method

F.33 K-omega mesh 3 steady state residuals

F.34 K-omega mesh 3, Drag & lift coefficient vs iterations plot

F.35 K-omega mesh 3 Pressure and velocity contour, and streamline velocity pattern

F.36 K-omega mesh 3 Velocity vectors graph and wake region analysis

F.37 K-omega mesh 3 y+ contour and histogram verification car wall

F.38 K-omega mesh 3 y+ contour and histogram verification surface

In F.37 and F.38 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 150 for the car-wall surface and 475 for the floor surface.

6- Mesh 3, K-epsilon method

F.39 K-epsilon mesh 3 steady state residuals

F.40 K-epsilon mesh 3, Drag & lift coefficient vs iterations plot

F.41 K-epsilon mesh 3 Velocity vectors graph and wake region analysis

F.42 K-epsilon mesh 3 Pressure and velocity contour, and streamline velocity pattern

F.43 K-epsilon mesh 3 y+ contour and histogram verification car wall

F.44 K-epsilon mesh 3 y+ contour and histogram verification surface

In F.43 and F.44 even though the contour y+ values shows all values where it needs the refinement in the inflation (boundary layers) methods, the histogram shows the average quantity for each specific range groups, which for this cases is 125 for the car-wall surface and 475 for the floor surface.

CONCLUSION

By having simulated several steady state simulations, performing a mesh dependency with three cases and two turbulence models on a Ahmed geometry, obtaining for each one of them their own significant convergence according to the velocity, drag and lift coefficients to a quasi-steady results, the final (average) drag and lift coefficients were calculated for all of them. Contours and plots were post-processed in order to facilitate the selection and determine the variations within the independent variables.

The following animations show the results for the most precise simulation case which is the K-omega turbulence model, refined mesh case with the SIMPLE scheme, having the lowest error percentage according to an early analysis in an article.

ANIMATION VELOCITY

ANIMATION STATIC PRESSURE

ANIMATION DYNAMIC PRESSURE

ANIMATION VORTICITY

ANIMATION PATHLINE CAR WALL VELOCITY

ANIMATION PATHLINE ISOMETRIC VIEW VELOCITY

F.45 and F.46 show the mesh dependency velocity vectors, variation within their own turbulence models, seeing the effect within each other and the computational time required to perform, or obtain the results.

F.45 K -omega turbulence model dependency mesh comparison velocity results.

F.46 K -epsilon turbulence model dependency mesh comparison velocity results.

Finally F.47 and F.48 show the drag and lift coefficient error percentage and a plot with all values, being possible to visually see the effect of the mesh, turbulence model, scheme, and any other variable available to take decisions or make presentations.

F.47 Drag coefficient percentage error plot

F.48 Drag and lift coefficient values plot, according to the simulations

Due to the simulation size file, the following link will contain the simulation setup and outputs:https://drive.google.com/file/d/1Jwx36PwBhZiLUgD-uvWB7RfAVTP5HRiN/view?usp=sharing

References & Links

1. R. Ahmed, G. Ramm, Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984
2. http://galileo.phys.virginia.edu/classes/311/notes/fluids2/node4.html
3. https://www.cfd-online.com/Wiki/Ahmed_body
4. https://www.comsol.com/blogs/studying-the-airflow-over-a-car-using-an-ahmed-body/
5. A Zonal SST-DES Formulation, F. Menter, M. Kuntz, Ansys CFX Germany, St. Petersburg,2003.
6. Article Effects of Rear Angle on the Turbulent Wake Flow between Two in-Line Ahmed Bodies, Ebenezer Essel, Subhadip Das and Ram Balachandar, 28 March 2020.