Modeling and Simulation of flow around an Ahmed Body
AIM : To design a model of Ahmed body and to simulate the flow over the designed Ahmed body.
SIMULATION-SETUP :
- MODEL DESIGN : CATIA V5
- Case setup : CONVERGE CFD STUDIO
- Commanad editor : Cygwin
- Post-processor : Paraview
OBJECTIVES:
- To create a cad model of the Ahmed Body according to the given 2D drawing.
- To setup a coarse CFD simulation.
- Design of virtual wind tunnel
- Applying the right boundary conditions and solver settings.
- Using a coarse mesh to show that the setup runs successfully.
- Post processing the coarse mesh results and extracting the x component of velocity along a line.
- To measure Lift and Drag forces generated.
THEORY :
Air has a tendency to curl downwards around the ends of a car, travelling upwards from the high-pressure region under the car to the low-pressure region on top, at the rear end of the automobile and subsequently collides with moving low-pressure air. The kinetic energy of these turbulent air spirals acts in a direction that is negative relative to the direction of travel intended. Thus, the car engine must compensate for the losses created by this drag. Vortices are released during flow separation and trail downstream to form structured or unstructured wake patterns. A wake is the region of re-circulating flow immediately behind a moving or stationary solid body, caused by the flow of surrounding fluid around the body. The local disturbances in the flow pattern behind the vehicle causes a momentum loss thus causing form drag which extends far behind the bodyworks of a vehicle.
AHMED BODY :
What Is an Ahmed Body?
Ahmed Body is an approximate shape of automotive vehicles (specifically a generic car model) used to capture the essential flow features like lift, drag, wake regions and all, around the body when it is moving through a fluid (air).
The simple geometrical shape has a length of 1.044 meters, height of 0.288 meters, and a width of 0.389 meters. It also has 0.3-meter cylindrical legs attached to the bottom of the body and the rear surface has a slant that falls off at 35 degrees (slant angle).
Why Study the Drag Coefficient in Cars?
The drag-coefficient quantifies the resistance of an object in a fluid environment. It is not an absolute constant for a body’s shape because it varies with the speed and direction of flow, object shape and size, and the density and viscosity of the fluid. The lower the drag coefficient of an object, the less aerodynamic or hydrodynamic drag occurs. In terms of a car, the lower the drag coefficient, the more efficient the car is. As well as affecting the top speed of a vehicle, the drag coefficient also affects the handling. Cars with a low drag coefficient are sought after, but decreasing the drag drastically can reduce the down force and lead to loss in road traction and a higher chance of car accidents.
MODELLING OF THE AHMED BODY :
The entire model was designed in a cad package “ CATIA V5” according to the 2D drawings given.
The designed model according to the above 2D drawings is shown below.
The designed model was imported to converge solver as an .stl file and surface clean up was done and all the surface errors were resolved.
CREATING A VIRTUAL WIND TUNNEL :
A wind tunnel is an aerodynamic facility to visualize the flow over an external surface. Designing the wind tunnel for any model is a crucial point in any CFD analysis and if the design parameters go wrong, we’ll end up in a wrong simulated answers. Hence setting up a good wind tunnel is a crucial point in any CFD analysis.
The above model shows the dimensions for creating a virtual wind tunnel. From CFD point of view, the length in the front of the body should be at least 2 to 3 times that of the body ie,, nothing but the inlet length form where the body is placed and the outflow length should be 5 to 10 times that of the body, for a good and better results.
JUSTIFICATION FOR ABOVE MENTIONED PARAMETERS :
A question arises, why should some-one give the above mentioned dimensions only?? Well the answer is quite simply, initially the flow at the inlet will have a uniform velocity profile, once the flow starts or starts accelerating there will be a development of boundary layer due to the wall in the wind-tunnel.
Well, why does the boundary layer develops??
It is due to the effect called “ coanda effect ”. It says that the fluid jet has a tendency to remain attached to the surface (convex) of the body. So when there is a small region of fluid flow, there will be a development of viscosity. Viscosity is the resistance offered by the fluid for it’s flow, the reason for development of viscosity and viscous forces is ‘shear stresses’.
Hence boundary layer is a region of small fluid flow where viscous forces are dominant, hence to capture theses effects the length should be logically acceptable and that’s the reason for inflow length.
When we come to the outflow side , as discussed above the flow has a tendency to curl according to the geometry of the body, so when the flow encounter any curvatures or complex shaped, the behavior of flow is entirely different. When the flow separates from the body , it leads to formation of vortices. Vortices are then released downstream of the body leading to the formation of structured or unstructured ‘wake patterns’.
Wake is a region of re-circulation where the flow re-circulates and it is the zone of low-pressure. All this happenes because of the drop in the static pressure.
In the region of re-circulation ie,, wake, we don’t know what is the velocity of the flow there and hence to captures all this things, we need to position the body from the outlet at sufficient length, so that the flow can straighten out and come back to the free-stream conditions, where we can then get to know the velocity of the flow in the wake region accurately.
Above figures shows the modeling of virtual wind tunnel in converge. The Ahmed Body has a length (L) of 1.044m and a height of 0.288m and width of 0.389m. The slant angle is chosen to be 35º and has a face fillet radius if 0.1m.
As discussed above the length in front of the body is chosen to be 3 times the length of the body ie,,,
3 * 1.044 = 3.132 m.
And the length from rear end of the body is six times the length of the body ie,,,
6 * 1.044 = 6.262 m.
Therefore the entire length of the wind tunnel is
Total length = 3.132 + 6.262 = 9.324 m.
CALUCLATING THE DISTANCE FOR GROWTH OF BOUNDARY LAYER:
The condition statement given is that, the boundary layer should be 30mm thick at 400mm in front of the body. An approximation of boundary layer thickness over a flat plate is given by,
where is the boundary layer thickness (m), which is 30mm.
‘ x ’ is the length of the plate (m)
is the Reynolds number at location ‘x’
Here the unknown is
w.k.t Reynolds number,
Re=ρVL/µwhere is the density of fluid flow (air) which is 1.225 kg/m^3
is the velocity of the flow, which is 40 m/s
is the kinematic viscosity of air, which is
but here instead of ‘L’ we have ‘x’ which is the length of the plate.
Hence,
Rex = ρVx/µSubstituting in the above boundary layer equation, we get
calculating for ‘x’ we get,
(x) ≈ 1.66 m.This means that at 1.66 m in front of the body there will be a boundary layer which is of thickness 30mm.
Hence to know the actual growth of boundary layer 400mm is to be added in front of the Ahmed body ie,,,
1.66 + 0.4 = 2.04 m.
Since we want a uniform velocity profile at the inlet where there should be no growth of boundary layer, let’s provide a boundary condition of ‘slip’ where the fluid motion is not zero and hence there will be no growth of boundary layer.
The slip distance is taken as one times the length of the body, ie,,,
1*1.044 = 1.044 m (slip distance)
Hence the inflow length from inlet to the front part of the body is 3.132 m ( ie,, 3*L).
Remaining distance is ‘Law of wall’ including Ahmed Body ( 6.264 m).
BOUNDARY FLAGGING AND BOUNDARY CONDITIONS :
The designed geometry was flagged into different boundaries.
BOUNDARY CONDITIONS :
- INLET – Inlet is an inflow type boundary condition assigned, since we know the velocity, the velocity condition will be a Dirchlet boundary condition (DI) , with velocity being 40 m/s and pressure being a Nueman boundary condition (NE)
- OUTLET – Outlet is an outflow type boundary condition assigned, with pressure being specified as Dirchlet boundary condition (DI) of 3k Pa and since we don’t know the exit velocity, the condition assigned for velocity is a Nueman boundary condition (NE).
- FRONT_BACK_TOP SURFACES – All these surfaces were assigned to a symmetry boundary conditions, since we want the flow properties to be same on both the sides and also for a 2D simulation front and back are just walls.
- SLIP BOUNDARY – At a distance of 1.044 m from inlet, as we don’t want a growth of boundary layer and we want a uniform profile of velocity, for this distance the boundary (1.044m) was assigned a ‘ slip ’ type boundary condition.
- LAW OF WALL – Remaining length of the wind tunnel was assigned to be ‘ Wall ’ and boundary condition being ‘law of wall’ where the formation of boundary layer was required.
- AHMED BODY : Since the main aim of doing the simulation is over this body, ‘law of wall boundary’ condition was selected as formation of boundary layer was required in this region.
WRITING TIME INTERVALS AND TURBULENCE MODELLING :
The entire length of the wind tunnel created is 9.324 m. Say that the flow of 40 m/s , starts from inlet and reaches the exit of the wind tunnel, so the time taken by the flow to reach the exit of the tunnel is,
t = dx/v
t = 9.324/40 = 0.2331 sec.
Let us simulate the flow for about 3 to 4 times, therefore total time or end time of the simulation is
0.2331 * 4 = 0.9324 sec
≈ 1 sec.Therefore the simulation starts at 0 sec and ends at 1sec.
Initial time step for the simulation is 1e-5 sec and the minimum time step is also 1e-5 sec and maximum time step of the simulation being 1sec, although the simulation doesn’t reach the maximum time step of 1sec.
Density-based solver is used as it is suitable for both compressible and incompressible flows.
TURBULENCE MODEL :
The turbulence model used here is ‘ k−ωSST ’
- This turbulence model is the combination of RNGk−ε and Standard k−ω And hence it near the wall ‘k−ωSST ’ works as a Standard k−ω model and away from the wall it works RNGk−ε model.
- Hence it gives an accurate prediction near the wall and away from the wall, as we are interested in capturing boundary layer growth.
Also k−ωSST model is well known for it’s automatic wall-treatment, which captures boundary layer accurately.
GRID CONTROL (BASE GRID AND FIXED EMBEDDING)
A base grid of dx = dy = dz = 0.1m was assigned , where converge predicted around 38,113 cells analytically. Since we are doing an aerodynamic simulation it is necessary to capture the data accurately around the body that has to be visualized.
Hence fixed embedding of box – type was added to capture the data more accurately and to improve the mesh refinement around the body.
SIMULATION RESULTS :
MESHING :
The designed model was discretized into finite number of elements. Initially converge analytically predicted around 38,000 cells without fixed embedding. Since in any aerodynamic simulation it is important to capture the data accurately, box-type fixed embedding was added around the Ahmed Body and at the end of the simulation there were around 1,50,000 cells or elements created.
CELL-COUNT :
The entire geometry was discretized into finite number of cells or elements. Above plot shows the number of cells or elements created (0.15 million cells). The total cell-count is constant throughout the simulation.
CALCULATING LIFT AND DRAG CO-EFFICIENTS :
DRAG :
Above plot shows the drag force generated on a body when the body moves through a fluid at 40 m/s ( although the science of body moving over a stationary fluid or fluid moving over a stationary body remains the same).
At the end of the simulation the drag force generated on the body converges to be 52.2 N.
Therefore we have,
D is the drag force in Newton (N)
is the density of the fluid or continuum
V is the free-stream or relative stream velocity
S is the surface area
Here ‘S’ can be calculated to be frontal cross-sectional area ie,, we have length as 288mm and breadth as 389mm so the area of the body turns out to be
= 0.288*0.389
= 0.112 m^2
We know density of air at 300K, which is 1.225 kg/m^3
We also have velocity, V = 40m/s.
Therefore,
LIFT :
Above plot shows the lift force generated on a body when the body moves through a fluid at 40 m/s (here in our case vertical direction is ‘Z’ axis).
At the end of the simulation the lift force generated on the body converges to be 30.5 N.
Therefore we have,
‘L’ is the drag force in Newton (N)
is the density of the fluid or continuum
V is the free-stream or relative stream velocity
S is the surface area
Hence,
Y – PLUS
Above plot shows the plot of Y-plus v/s time for the simulation. The value of y+ converges to be quite higher one ie,,, around 1500 which is quite high.
The reason for this is the computational accuracy , system constraints and time involved. To get a accurate values of Y-plus super computers are to be used, hence here the simulation is an accurate one.
VELOCITY :
Above plot shows the variation of velocity with time. Initially the flow has a velocity of 40 m/s and once the flow encounters the Ahmed Body the velocity decreases in the front portion of the body. The flow accelerates in the bottom portion of the body and reaches a maximum velocity of 60 m/s. Once the simulation reaches the steady state, velocity achieved is 25 m/s.
VELOCITY CONTOURS :
ANIMATION LINK :
PRESSURE :
Above plot shows the variation of pressure with time. The pressure over the body is increasing at some points on it and after some time it is decreasing over the body. To understand it better, there are some of the contours of pressure distribution over the body, shown below.
PRESSURE CONTOURS :
ANIMATION LINK :
DEPICTION OF FLOW BEHAVIOUR USING STREAM TRACER :
Above stream tracers clearly depicts the beahviour of flow throughout the body. The thickness of these streamlines is determined by turbulent kinetic energy.
GLYPH PLOTS :
In the above vector plots, the flow is diverting in the front portion of the ahmed body and at the rear end the flow is recirculating ie,, the region of low pressure or in other words 'wake' region.
COMPARITIVE STUDY WITH EXPERIMENTAL ANALYSIS :
In order to analysis the obtained data with experimental results we need to plot the line probes for different locations in the body w.r.t the velocity of the flow around it. This helps us to know the velocity at different locations on or above the body.
At x = -13mm and y = 0 mm at x = 37mm and y= 0 mm
x = -63 mm and y = 0mm x = 87mm and y = 0mm
x = -113mm and y = 0mm x = 137mm and y = 0mm
x = 187mm and y = 0mm at x = -263mm and y = 0mm
RESULTS AND INFERENCE :
The total drag coefficient of the Ahmed body is the key measurement for this simulation. It is made up of measurements for the pressure coefficients in the front, slant, and base of the body as well as the body’s skin friction. In the results of our simulation, the total drag is very well predicted but the individual measurements deviate from the experimental results in varying amounts. For a slant angle of 35-degree the value of drag and lift coefficients are found to be 0.4783 and 0.2778
Hence, from the simulation
Cd = 0.4783
Cl = 0.2778
When the body is moving at 40 m/s (although the science of air moving around stationary body or body moving around the stationary air is same) it encounters a resistive foroce of 52.5 N ie,, the drag force.