Numerical investigation and validation of flow through ahmed body with variation in slant angle.

AIM

Numerical investigation of flow through ahmed body with variation in slant angle.

INTRODUCTION

Ahmed body is developed to validate various the turbulence model to encounter the aerodynamics . ahmed body is a similar form of car such that external aerodynamics simulation can be performed on similar body to validate the turbulence model. Validating the turbulence model depends on the experimental results validation. These experiments are performed generally in the wind tunnel.

Drag force experienced by the car always resist the body hence decreasing the speed of car therefore main aim is to see for flow behaviour and calculate the drag force or drag coefficient, location where the flow separates is seen to get the better idea is wake region formed behind the model.

Dimensions given below are used to create the geometry and to perform simulation.

FIGURE(1)

For this simulation k-`omega` SST model and k - `epsilon` realizable model is used as it is very suitable for complex flows with adverse pressure gradient. y+ value is used according to the turbulence model and assuming y+ value as 50 as in STAR - CCM+ both models are provided with all Y+ wall treatment and calculating first height thickness according to the reynolds number contributing to the velocity of 40 m/s for air.

WORK FLOW OF THE PROJECT

• Open STAR-CCM+ create a new 3D-CAD model by going to geometry`rarr`3D-CAD Models`rarr`new
• In 3D-CAD model XY plane is selected to make the first sketch by right clicking XY plane and selecting create sketch. Slant angle is made as design parameter. Sketch is made given below.

FIGURE(1)

• Above sketch is extruded with proper dimensions in two way symmetric, Fillet is added in the front face with 100 mm radius, Ahmed leg is created in the YZ - plane with its revolution with respect to construction line and linear pattern is created to have 4 legs at appropriate locations.Wind tunnel is created with proper dimension in XZ - plane and then extruded upwards, Inlet face is extended to have no slip road before the slip road. snippet given below.

(a) Extrusion

(b) Legs creation

(c) fillet creation

(c) Wind tunnel sketch

(d) Extended surface

FIGURE(2)

• After creating the geometry. 3D-CAD model is closed and this geometry is transferred to parts by right clicking created geometry and selecting "new geometry part". which transfer geomtery to part in the form of surface, necessary names are changed, Also to replicate external flow blocks are created around the geometry by assuming the respective dimensions. Figure given below.

FIGURE(3)

• Surface errors checked once to see whether the geometry have any surface errors. After giving appropriate names all parts are assigned to regions to give boundary conditions to them. To have no interection between legs and the road boolen operation is performed.

FIGURE(4)

• After this volume mesh is created by going to geometry`rarr`operations`rarr`new`rarr`mesh`rarr`automated mesh. As the simulation to be performed is external aerodynamics therefore trimmed meshing is used as volume mesh with this surface remesher, automated surface repair and prism layer mesher is selected.

FIGURE(5)

• After selecting the mesher base size is given as 25 cm of geometry dimension, number of prism layer is set to 10 layers, maximum cell size is given as 1000% relative to the base. surface control is given to the aerofoil to accurately capture the properties near wall region by giving reating a small block around the ahmed body, isometric size is given appropriately as 50% of base size and faster default and surface growth rate.
• Prism layer total thickness is obtained with respect to the Y+ value of 50, according to the characteristic length of geometry and velocity of the flow based on the reynolds number of 2780000. Velocity of 40 m/s according to the reynolds number and pressure at atmosphere.hence, Total thickness came as 13.48 mm.
• Before executing the automated mesh proper boundary conditions are given to the boundaries in regions. Inlet`rArr`velocity inlet, Outlet`rArr`pressure outlet, Symmetry wall`rArr`symmetry plane, geometry`rArr`wall, Road`rArr`wall, slip road`rArr`slip wall. hence prism layer is only created near the wall which is the geometry. boundary conditions in appropriate surface is given by going to Regions`rarr`region`rarr`boundraies. At last automated mesh is executed to obtain volume mesh.

(a) Mesh in plane section

(b) prism layer near the slip wall and ahmed body

FIGURE(6)

• After the creation of Volume mesh appropriate models can be applied to the geometry by going to Continua`rarr`physics`rarr`models. Appropriate models are selected to simulate the flow through the pipe. snippets given below.

FIGURE(7) assign models

• 3D space model is selected as model is 3D, Steady time model is selected to look for final result and neglect temporal terms, Material is selected as gas because in external flow air act as fluid, Segregated flow is selected as the flow is incompressible.
• As the mach number is very small ( Ma<0.3) hence constant density model is selected as equation of state.
• Reynolds number comes under turbulent region as flow above reynolds number of 5e5 is turbulent.
• K - epsilon realizable turbulent model with two layer all Y+ near wall treatment model and k - omega model with all Y+ near wall treatment is choosen to obtain better results and compare between two models. Y+ value of 50 is assumed.
• After selecting the appropriate model properties can be given to the boundaries by going to Regions`rarr`region`rarr`boundraies`rarr`Created boundary`rarr`Physics Values. Constant velocity magnitude is given to inlet and Constant guage pressure of 'zero' pascal is given to the outlet to have atmospheric condition because the reference pressure present in continua`rarr`physics`rarr`reference values`rarr`reference pressure is atmospheric pressure.
• Mesh quality and mesh validity is checked by clicking the mesh diagnostics having representation of volume mesh and report type as compact. It is observed that the mesh obtained is good.
• Report is created to observe the drag and lift of the geomtery by right clicking the report and selecting the force coefficient. For drag coefficient direction is given in the direction of the flow with ref. density, ref. velocity and ref. area, For lift coefficent the direction is given normal to the direction of the flow with ref. density, ref. velocity and ref. area. Reference area is the projected area of the geometry experienced by the flow normal to it. Frontal or projected area can be obtained by giving normal as the plane of projected surface and view up as the normal vector for the plane from which the projection is calculated.
• Also velocity profile is checked near the ahmed body by creating line probes according to the given experimental locations. Figure given below.

FIGURE(8) Probe creation

BODY OF THE CONTENT

• Convergence

(a) 25 degree slant angle

(b) 35 degree slant angle

FIGURE(1) Residual Plots

(a) 25 degree slant angle

(b) 35 degree slant angle

FIGURE(2) Drag coefficient Plots

(a) 25 degree slant angle

(b) 35 degree slant angle

FIGURE(3) Lift coefficient Plots

From Figure(1,2,3) it can be seen that convergence has reached as residuals for all simulations are less than 1e-4 and Plots of drag and lift coefficient become stable generally after 200 iterations.

• Validation

For validation of Simulation the results obtained from simulation are validated from two sources which gives the validation with experimental drag coefficient and Velocity profile at different probes which is shown below with the help of plot and table.

Slant Angle	Turbulence model	Drag coefficient ( Experimental)	Drag coefficient ( Simulation)	Error(%)	Lift coefficient
25	K – ε	0.299	0.32	7	0.43
	K – ω	0.299	0.303	1.337	0.42
35	K – ε	0.279	0.31	11.11	0.24
	K - ω	0.279	0.288	3.225	0.08

TABLE(1)

From Table -1 It can be clearly seen that both approaches give good results when compared with experimental results where K - `omega` turbulence model gave better results than K - `epsilon`.

(a)

(b)

FIGURE(4) - Comparison between Drag coefficient obtained in simulation and experimental

With above comparison to further validate the results the line probes used in different location are validated with experimental results. Plot are given below

(a) 25 degree slant angle

(b) 35 degree slant angle

FIGURE(5) - velocity profile plots at different x - positions

Line Probe are created in -362mm, -262mm,-212mm,88mm,238mm and 538 mm both in positive are negative side of the origin.From above plots it can be seen that both K - `omega` and K - `epsilon` are giving good results with some variation in wake region which is expectable. regions after zero represents the wake region presnt after the slant height and regions before zero represents before the slant height region. Large flow separation is clearly evident after the slant height which hints towards the presence of wake region after slant height which can be clearly seen in the contours.

• Contours

(a) K - Epsilon

(b) K - omega

FIGURE(6) Velocity plot for 25 degree slant angle

From figure(6) it can be seen that for both turbulence model wake region and stagnation zones seems to be the same. there is no major difference between both models results. wake region formation is seen behind the ahmed body which extends to a distance. Maximum velocity can be seen in the curvature which is due to low pressure zone creation in the curvature due to flow separation because of curvature.

(a) K - Epsilon

(b) K - omega

FIGURE(8) Pressue plot for 25 degree slant angle

From above plot it can be seen tha pressure is maximum at the front face as it is normal to the flow. and minimum pressure regions are present at the curvature of the ahmed body where flow experiences the separation in the flow. hence sudden increase in velocity in that region. Both turbulent models gave same result with negligible variation in the results, hence both models are good to simulate flow through ahmed body.

(a) K - Epsilon

(b) K - Omega

FIGURE(9) Velocity plot for 35 degree slant angle

From Figure 9 it can be observed that with increase in slant angle there is increase in wake region which is wide and larger in lenght. Also, wake region in k - omega is larger than wake region of k - epsilon and from table 1 and figure 5 it can be said that k - omega turbulence model give far more accurate results compared to k - epsilon model in both cases.

(a) K - Epsilon

(b) K - Omega

FIGURE(9) Pressure plot for 35 degree slant angle

From above plot it can be seen tha pressure is maximum at the front face as it is normal to the flow. and minimum pressure regions are present at the curvature of the ahmed body where flow experiences the separation in the flow. hence sudden increase in velocity in that region.

More clarity can be given with the help of streamline plots given below for both slant angles

(a) Streamline for 25 degree slant angle

(b) Streamline for 35 degree slant angle

FIGURE(10)

Increase in wake region is clearly evident as both counter rotating circulation zone are present in both 25 and 35 degree slant angle but there is increase in upper recirculation zone due to larger flow separation. therefore increasing the overall lenght of wake region. For more clear observation Animation can be observed which shows the seperation in opposite direction and formation of two opposite rotating vortices in YZ- plane which began to separate as we go downstream.

Streamline animation for 25 degree ahmed body

Streamline animation for 35 degree ahmed body

CONCLUSION

• Simulation result hold good agreement with experimental results for both turbulent models.
• k - omega turbulent model give more accurate results as compared to k - epsilon turbulent model hence it is suggested for large adverse pressure gradient and large separation flows k - omega turbulent model is well suited.
• There is decrease in drag and lift due to formation of large wake in upper region which decreases the lift coefficient of the ahmed body when we increase the slant angle from 25 to 35 degree.

REFERENCES

• Experiments and numerical simulations on the aerodynamics of the Ahmed body - Walter Meile et al 2011