Ahmed Body Challenge

1. PROBLEM STATEMENT AND AIM:

For this project, we need to provide answers to the following questions using analysis of obtained results through the simulations performed on an Ahmed’s body (a simplified car model)

• Describe Ahmed body and its importance
• Explanation for the reason of negative pressure in the wake region
• Explanation for the significance of the point of separation

1.1 AIM:

The results in support to the above aim will be shown in the project with the help of:

• Velocity and pressure contours to support the required solution for the problem statement
• The drag coefficient plot for a refined case keeping the velocity 25m/sec
• The value of drag coefficient has to be around 0.33 as provided by previous research papers
• Vector plots clearly showing the wake region
• Performing the grid independency test and providing the values drag and lift for each case

2. INTRODUCTION:

2.1 Ahmed’s body and its importance:

Ahmed’s body is a basic simplified car model which has a curved part in the front usually referred to as the nose. The rear vertical part as it back body of the car. The slant part as ‘slope’ which can be varied in the angle if one needs to compare the flow simulations for the different slope angle cases. The roof of the car is perfectly horizontal and the whole car body all over is least streamlined in nature. Although the body is symmetric about the axis along its length and centre of mass.

The test was 1^st performed by Ahmed in 1980s to study the nature of the Cd (drag coefficient) for flow over the car body. The wake study in the rear region of the body can be studied better with this experiment at a simplified level. Researchers have already worked on the experiments and numerical modelling of the flow over the Ahmed body. Ahmed studied the wake structure and drag of the Ahmed body, while Lienhart and his colleagues conducted the experiments for two rear slant angles (25°, 35°) for the rear slope region.

For this particular project we are only going to verify the results for the Cd drag coefficient and see the behaviour of the plots and the explanation for negative pressure and wake region in the contours obtained and the plots achieved for various parameters. Although we are not going to verify the solution for different slopes and nor are we going to compare the different turbulence models and their results. Thus we are only going to perform only the K-epsilon model and see the results for the specific Y+ value which will be kept in range that will further give the Cd value much nearer to what is required.

3. GIVEN PRAMETERS AND CONDITIONS:

One of the important input boundary parameters given is the velocity which has to be 25m/sec through the inlet. The specific sides and regions of the body has be named parameterised in a specific way for the Fluent to understand the boundary conditions and give the correct results.

The use of ‘body split’ command in the Space claim can also be too handy as per the mesh independency test is performed. The actual enclosure within which the flow has to be analysed is spilt here into two equal parts symmetrically so that the more refined mesh can be performed on the rest half part which definitely gives the better precise results and also reduces the time of calculations. Also the double the amount of refined mesh can be dealt with without any effect on the nature of results obtained. Thus this is the best practice where you can save on the number of cells and get the results faster as well.

4. GEOMETRY, CAD MODEL AND MESHING:

Below CAD model shows the Ahmed body with its dimensions in required views to get the full understanding of the model and where splitting the body is required and how much in dimensions should the enclosure be.

Fig: Side view of geometry with the dimensions

The fig below shows the half split part of the enclosure and the actual model inside it (suppressed physics) on which the analysis has to be performed is only the outer enclosure and the inner enclosure.

Fig: Front view dimensions of the car body and the enclosures

Fig: side view of the enclosures

4.1 NAMED PARAMETERS:

The below fig show the all named parameters on which further the boundary conditions will be set upon for a preferred turbulence model. The list of the parameters from A to E has its name defined in the list in the left side.

Fig: Named parameters

4.2 MESHING (REFINED CASE):

Fig: The refined mesh

The below fig shows the proportion of tetra, hex, wedge and pyramid type of mesh incorporated under the multizone meshing type. This plot shows that we are okay to go with the minimum mesh metric criterion which is 0.38.

Fig: The mesh metric plot for the refined mesh case

4.2.1 MESHING DATA:

Fig: Data for the mesh quality and element size

4.3 INFLATION LAYERS:

The below fig shows the inflation layers chosen as per the model which we want to go with for the solution. The turbulence model here we will go with is the K-epsilon model which will require the value of Y+ in the range of 30 < Y+ <300 so as to get the desired result for the Cd value and other contours. As per this analysis the value of Y+ chosen is 200 for which the minimum value of thickness in the inflation layer is around 5.739 e-04 m or 0.0005739 m. This value here is the 1^st layer thickness which has been given the growth rate of 1.17 and total 5 layers has been incorporated in total for the inflation layers. The above value of ΔY here is calculated by the formula:

Y+= (ƿ*Y*V)/ µ

Considering the Y+ as 200 and considering the materialistic properties of the fluid as default what has been set in the fluent as:

Ƿ= 1.225 kg/m^3, V= 25m/sec and µ= 1.78*10^5 kg/m-sec

We get the value of minimum layers thickness as 0.0005739 m on which the further solution and calculation will be performed.

Fig: Inflation layers set at the car wall portion

Fig: inflation layers data

5. SOLVER, DISCRETIZATION, PHYSICS AND MODEL:

The Solver here is Pressure-Based with absolute velocity formulation and transient state. The model used here is the turbulence model of K-epsilon of standard wall function type. The preferred reason for the selection of k-epsilon standard turbulence model here is because k-epsilon is much more preferred in the conditions where we want the analysis much precise both near and away from wall so as to get the more accurate streamlines and also rear wake regions and other contours analysis like near wall pressure and velocity analysis at certain regions of inflations and around it. Solution method used here are:

• Pressure: Velocity coupling (coupled scheme)
• Gradient: least square cell based
• 2^nd order Pressure
• 2^nd order Momentum upwind
• 1^st order Turbulent KE upwind
• 1^st order turbulent dissipation rate
• 1^st order implicit Transient Formulation

6. FLUID FLOW MEDIUM AND AHMED BODY MATERIAL:

Material	Density(kg/m^3)	Specific heat(J/kg-K)	Thermal Conductivity(W/m-K)	Viscosity(kg/m-s)
Fluid (AIR)	1.225	1006.43	0.0242	1.7894e-05
Ahmed’s body (Aluminium)	2719	871	202.4	---

6.1 REFERENCE VALUES & BOUNDARY CONDITIONS FOR FLUENT:

The area stated in the reference values here is the area projected by the Ahmed body when interacting with the fluid medium here. The length stated in the below fig is the length of the Ahmed body.

The velocity for the inlet is given as 25m/sec and temperature been considered at room temperature other properties of the fluid has been considered as default as per the Fluent database

Fig: The reference values in fluent.

7. RESULTS AND DISCUSSION FOR THE MESH INDEPENDENCY TEST:

7.1 QUALITY ON WHICH PRECISENESS OF RESULTS FOR THE COARSER MESH WILL DEPEND:

The below fig states the quality of mesh which incorporates different kind of meshes which includes the tetra, hex, pyramid and other types.

Fig: Mesh metric for the coarser mesh

The below fig states the stats of the mesh before we see the results depending on it. It’s important to know the comparative study of the mesh data

Fig: Mesh data and stats

Below fig shows the inflation data to be followed as per the chosen turbulence model. The inflation data has been kept same for both the refined and coarse cases and just mesh, body and face sizing is what have been changed which has resulted into the total elements around 1.2 lack

Fig: Mesh quality data and inflation data

Fig: coefficient of drag

The coefficient of drag value for the coarser mesh case comes out to be 0.31987 ≈0.32 which is much considerable as our aim was to get the value around 0.33. Similarly the coefficient of lift value comes out to be 0.241852

Fig: coefficient of lift value.

Fig: velocity plot with the mesh lines

Fig: velocity contours

Fig: Pressure contours

The below fig shows the pressure contours in the front fluid interacting region of the body. The pressure in the front most and 1^st interacting region of the nose shows the highest pressure region in nose area. Also to be noted from the geometry that this part of highest pressure region is the flat surface and around it is the curved portion which here seems to be guiding the fluid smoothly through it. The region doesn’t shows negative pressure of high magnitude, although negative pressure of lower order can be seen.

Fig: Pressure contours on the nose of the car body

Fig: velocity streamlines

Below fig shows the proper wake regions in the rear of the Ahmed body. Which shows the circularity in the fluid flow pattern and its path lines. The better vector path lines diagram will give much clearer representation

Fig: Rear wake regions depicted by the velocity streamlines functions

7.2 THE CONCEPT BEHIND WAKE GENERATION & NEGATIVE PRESSURE IN WAKE REGION:

7.2.1 DISCUSSIONS ON THE CIRCULARITY GENERATION IN THE REAR REGION:

• The path lines showing the exact circular motion or vorticity generation just at the rear end of the car. The separation takes two regions of distribution. One at the upper part of the rear and the other at the lower part of the rear end.
• The path lines shows about the nature of the fluid interaction with the rear end of the Ahmed body which here shows that the fluid just after leaving the contact from the slope still possess the momentum in it and the fluid particles near to the surface almost shows the no slip region which means very least possible velocity of the fluid particles is in contact with the slope and base of the rear part. Thus the fluid particles away from the rear region having the higher pressure beside the wake region tries to approach from the higher pressure region to the lower pressure region thus creating a circularity exactly in the wake region created.

7.2.2 DISCUSSIONS ON WAKE GENERATIONS:

The body penetrating the fluid creates a region of emptiness just beside its end due to the nature of the geometry of the body here which can be seen least in case of a perfectly streamlined shaped body. This emptiness created is a low pressure region towards which the fluid column exactly behind the wake region which of atmospheric pressure tries to fill the space thus dragging the fluid column with it thus creating the region of vorticity. This also results in the huge pressure gradient in the region exactly rear of the body creating the –ve pressure at end. Also this is the layman’s reason why there is negative gauge pressure in the wake region.

Fig: Path lines for velocity vector

NOTE: THE REGION OF SEPERATION WILL BE DISCUSSED CLEARLY WITH THE PLOTS LATER

The below fig shows the velocity vortex core region of the fluid interacting with the Ahmed body wall.

Fig: vortex core generation for fluid at the surface of the car body

7.3 ON PLOTS COMPARISION OF PARAMETERS FOR DIFFERENT REGIONS OF THE CAR WALL

Fig: The nomenclature of all the lines along which the parameters are to be plotted.

7.3.1 VELOCITY & PRESSURE PLOT COMPARISION:

Fig: Velocity plot comparisons of different car wall features

Fig: pressure plot comparisons

7.3.2 PRESSURE VARIATION PLOT ALONG X-axis IN THE WAKE REGION:

• The most negative pressure can be seen in the wake 1 region as shown in the plot which goes on increasing as per the count as we move more farther behind the car rear body. This explains much better why the circularity prevails in the fluid flow just behind the car body.
• The region of fluid from the high to low pressure region is this obvious here. In this case from rear 3 region towards the rear 1 region. The magnitude of pressure goes on increasing as we move further away from the wake region.
• The point after some time where the count shows around 450-500 is the region where the fluid column from the roof and the base part meets again.

Fig: pressure plots for the wake region

7.3.3 EDDY VISCOSITY RATIO SIGNIFICANCE AND PLOTS TO SUPPORT IT:

• Eddy viscosity ratio is the term we generally use where there is not much high of a turbulence or generally where there is low turbulence. The conditions where a moderate turbulence can be felt like the flow of fluid around a body, other aerodynamic conditions where eddies formed contributes in the turbulent transfer of energy in the form of small eddies.
• Eddy viscosity ratio basically defines the ratio of turbulent viscosity to the laminar viscosity.

• The rear wake 1 region is the region in the below shown plot which shows the least area under the eddy viscosity plot and also has the lowest peak which shows that the turbulent viscosity is the least in the rear 1 region as compared to its further region like rear 2 and rear 3 region.
• The last statement clearly means that there is a huge difference in the magnitude of turbulence viscosity among this 3 rear regions. This could possibly the reason for why the boundary layers separations get caused which later again meets with the continuous fluid flow further away from the region as body keeps on moving.

Fig: Eddy viscosity ratio in the rear region

7.2 THE RESULTS FOR THE FINE MESH & ITS COMPARATIVE PRECISENESS FROM COARSER MESH

Fig: The time dependent K-epsilon and other residual convergence plot

The plot below shows the coefficient of drag convergence plot which shows the value of Cd = 0.2941 which is clearly slightly lesser as compared to the coarser mesh (=0.32) case given that rest other conditions for the calculations and operations were same. This has also been verified with the research paper “cfd prediction of seperation flow over a simplified car model modelling and simulation (ahmed body)” which showed through simulations that when the mesh is much finer there is a slight more preciseness and slight change compared to coarser mesh case as a result thus 0.2941 value could be trusted with around 8% of change with previous obtained Cd value

The coefficient of lift value comes out to be around Cl=0.25 for the refined case.

Fig: Cd plot

Fig: Cl plot

7.2.1 VELOCITY & PRESSURE CONTOURS WITH PLOTS TO SUPPORT THE RESULTS:

The below plot is much different from the previous coarse mesh contour as per the preciseness of the wake region is concerned. The wake region seems to be much more distributed here in this contour and much distinct and extended as compared to the previous case. The next figure with contour lines will be much able to define the difference of precision as compared to the coarse mesh velocity case.

Fig: velocity contours in a plane with mesh lines

Fig: Velocity contours with contour lines

The velocity streamlines contours here clearly shows that difference in the preciseness as compared to the coarser mesh condition. The Vorticity generation at the wake region can be seen much more distinct and detailed as compared to the coarser mesh case.

Fig: Velocity streamlines Contours

Fig: Velocity streamlines in the nose region of the car

Fig: streamlines of velocity in the rear Wake region

Fig: velocity vector with direction vector represented on its streamlined path.

Fig: Pressure contours

7.2.2. THE SIGNIFICANCE OF THE FLUID SEPERATION REGION:

The fluid separation point can be defined as a point where the dv/dy i.e. gradient of velocity goes zero along with the dp/dx = 0, for the specific point. In more simplified term we can say that the point where the velocity gradient goes zero and the pressure gradient along the x- direction goes zero the point of separations starts occurring or the negative pressure gradient starts forming after that point. The point of separation cannot be understood just by single contour in hard and fast way. It can be supportively studied with the help of the dp/dx plots or velocity plots w.r.t the Y direction and other such plots in which we can see the nature of such physical properties like dp/dx=0, and dv/dy=0 experiencing in a particular region of fluid and body interaction

Fig: dp/dx plot for all car wall regions

• We have already seen through the velocity contours about the region where there is no change in velocity w.r.t the Y direction but as per the pressure plot is concerned we have almost every car wall regions which is in contact with the fluid continuously and with the help of plot here we can distinguish the regions which interacts with the zero line of the Y axis value.
• The functions of dp/dx value above for the sloe region only intersects once in the initial stage but not till the count goes up to 500. Thus the separation zone was prevalent on the initial zone of slope region.
• Secondly the function of the rear wake region intersects more than 5 times then after continues t0 be =0 which suggests that there are many regions of separation in this region and almost negligible linearity in the flow is to be found here.
• The region of roof and base goes almost same as per its behaviour of the function it follows up in the graph i.e. they follow an immediate separation region at the point where the body fluid interaction at its start and end of it prevails. A small region also prevails in exactly middle of the roof and base where through both plots & contours we can see the point of separation region

7.2.3 PLOTS OF VELOCITY AND PRESSURE AND OTHER PHYSICAL QUANTITIES:

Fig: velocity plot comparisons

Fig: pressure plot comparisons

• Below graph shows the pressure coefficient logarithmic values Vs chart count where we can see a drastic difference in the magnitude of the pressure coefficient as per the change of slight distance in the wake region of the fluid flow simulation.

• The rear 3 part is where the coefficient of pressure is very high which signifies that this region contains relatively very high pressure region as compared to the other rear 2 and rear 3 regions.

• Relative pressure of rear 2 region is still slightly greater that the rear 3 region which is very obvious as seen from the pressure contours too which explained the reason for the circularity in the wake region and the direction of fluid flow in the wake region.

Fig: Logarithmic Pressure coefficient plot

Fig: Wake region velocity comparisons

Fig: Wake region eddy viscosity ratio plot for refined case

Fig: Turbulence KE in wake region

Fig: Turbulence KE contours (refined case)

As per the vortex core region around the car body surface is analysed the refined mesh case gives a better detailed view and precise plot for the velocity plot for vortex core region as compared to the coarser mesh case.

This can be better understood if we compare the rear trailing part in case of the refined plot of vortex core and the coarse case vortex core plot. The longer and finer trailing part here can be seen here in this rear part. Although the separation zone above the wake region can be clearly seen here too where the layers of green vortex core region overlaps above the blue wake region.

Fig: Vortex core region for the refined mesh case.

CONCLUSION:

The importance and explanation about the Ahmed’s body with its initial experimentation has been clearly studied in the introduction section of the report.

The negative pressure in the wake region which depends on the pressure gradient and the vortex shedding in the rear part of the Ahmed body has been discussed with the help of different pressure contours plots and graphs which did satisfied the theoretical explanation. The previous discussions about the –ve pressure suggest sin a nutshell that the viscosity and the pressure gradient all together play a major role in the generation of negative pressure in the rear part or the wake region.

As per the separation point significance is concerned:

• We have seen through the velocity contours for the region where there is no change in velocity w.r.t the Y direction but as per the pressure plot is concerned we have almost every car wall regions which is in contact with the fluid continuously and with the help of plot here we can distinguish the regions which interacts with the zero line of the Y axis value.
• The separation zone was prevalent on the initial zone of slope region (roof interacting zone)
• Secondly the function of the rear wake region intersects more than 5 times then after continues t0 be =0 which suggests that there are many regions of separation in this region and almost negligible linearity in the flow is to be found here.
• The region of roof and base goes almost same as per its behaviour of the function it follows up in the graph i.e. they follow an immediate separation region at the point where the body fluid interaction at its start and end of it prevails.

The Cd value in the refined case was observed to be around approx. =0.3 (0.2941) and that of the coarse case to be around 0.32 which as per the problem statement was expected to be around 0.33 which is acceptable within the limits as per the referred research papers are concerned.

Also as observed from one of the research papers attached below which too says that the value of Cd does vary slightly when we go from the coarser mesh to the refined mesh case.

“cfd prediction of seperation flow over a simplified car model modelling and simulation (ahmed body)”

The velocity and pressure contours along with its plots in the required region has been discussed along with its significance in the report.

Thus the values as obtained from the grid independency test shows below in the table:

TABLE: 1

CASES	Cd	Cl
COARSE MESH CASE	0.31987	0.241852
REFINED MESH CASE	0.2941	0.25

The vortex core regions for the velocity has also been discussed for both the cases and the distinct plots difference can also be observed for both the cases.