Week 3 - External flow simulation over an Ahmed body.
AIM: To model and simulate a flow around an ahmed body and analyze various factors affecting the flow.
THEORY:
Ahmed body and its importance: The Ahmed body is a simplified car body used in the automotive field to study the impact of the flow pattern on the drag. The external flow around the vehicle is characterized by high turbulent and three-dimensional flow separations as well as there is a growing need for more insight into the physical features of these dynamical flows. Ahmed body is made up of a round front part, a moveable z slant plane in the rear of the body to study the detachment phenomena at different angles, and a rectangular box which link the front part and the rear slant plane. The principal objective to study such a simplified car body is to tackle the flow processes involved in drag production. Through perceiving the mechanisms involved in creating drag one can be able to design a car to minimize drag and therefore reducing fuel consumption and maximize vehicle performance. The geometry of ahmed body is shown below:
An Ahmed body represents a simplified vehicle volume which helps understand the fundamental physics, lift and drag forces and coefficients at certain velocities, pressure differences and analyzing the vortices, turbulence, and Reynolds number. Ahmed body cfd simulations can be used to validate numerical models with the available experimental data. Once the numerical model is 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.
Wake region - The region of recirculating flow or disturbed flow behind a moving or stationary blunt body, caused by viscosity, which may be accompanied by flow separation and turbulence. 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.
Reason for negative pressure in the wake 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 show 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 show the no-slip region which means the 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 try to approach from the higher pressure region to the lower pressure region thus creating a circularity exactly in the wake region created.
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 where atmospheric pressure tries to fill the space, thus dragging the fluid column with it. which creates the region of vorticity. This also results in the huge pressure gradient in the region exactly rear of the body creating the negative pressure at the end. This is the layman’s reason why there is negative gauge pressure in the wake region.
Significance of the point of separation:
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.
MODEL SETUP AND SIMULATION:
The geometry and the dimensions of the ahmed body is shown below:
For the fluid domain, the Ahmed body was enclosed in a rectangular enclosure which is 2 m to the left, 5 m to the right, 1 m above and 0.5 m on both the sides body. To capture flow characteristics near the Ahmed body efficiently local mesh refinement with a smaller element size has to be created. A smaller enclosure around the ahmed body is created for this purpose. The enclosure is 1 m downstream, 0.5 m in upstream and above and 0.2 m at the sides of the Ahmed body. The domain and the geometry is shown below:
Since the body is symmetric along the domain, only half of the domain is considered for meshing and simulation in order to save time and attain more accurate results. The model after cut along the XY plane is shown below:
The simulation is run with three different mesh cases, from basic to refined case.
The fluid domains are divided into 2 regions, The outer region is rectangular which is made of hex elements which give the hightest accuracy and efficiency in computation. The inner enclosure is meshed with tria elements with 6 inflation layers on the surface of the Ahmed body to capture the drag coefficient and flow separation perfectly.
CASE 1: The outer region has an element sizing of 100mm and the inner region has 50 mm element size.
The inflation layers are captured as shown with a total thickness of around 12.5 mm and growth rate of 1.2.
Case Setup
The steady-state solver is used with K - omega turbulence model. the k-ω model predicts well near the wall better.
Inlet Velocity - 25m/s, Oulet Preesure - 0Pa (gauage preesure)
Default Air is selected as the working fluid.
The pressure contours are shown below:
Flow Separation occurred due to the adverse change in the pressure gradient. Front of the body has the positive pressure but at the rear end of the body has negative pressure.
The velocity stream lines are shown. Notice that the flow separates from the surface creating a highly turbulent region behind the cylinder called the wake region.
The drag coefficient plot is obtained as follows:
The lift coefficient plot is shown:
Case 2: More refined mesh:
Element Size
Inner region - 30mm
Outer region - 80mm
The pressure contours are shown below:
The velocity contours are shown below:
The drag coefficient is shown:
The lift coefficient is shown:
Case 3:
Element Size: Inner region - 30mm and Outer region - 60mm. The meshed region is shown below:
The plots of different variables are shown below:
Notice that the drag coefficient is approximately 0.32 for the refined case.
Since the analytical value for the drag coefficient is 0.33, the drag coefficient for the refined case approximately equals to the analytical value.
Comparision of results for different cases:
| number of cells | `C_d` | `C_L` | |
| case 1 | 99722 | 0.36 | 0.235 |
| case 2 | 332245 | 0.340 | 0.238 |
| case 3 | 1040730 | 0.322 | 0.2384 |
CONCLUSIONS:
High pressure is formed at the frontal area of the Ahmed body due to the loss of kinetic energy of the air. The adverse pressure gradient is created near the wake regions because of the flow separation which occurs because of the geometry of the model. As a result flow separation alters the pressure gradient which in turn affects the drag and lift coefficient. In order to reduce the size of the wake region, detachment of the fluid should be farther away from the body which can be achieved by an increase in the slant angle. Since the eddies formed cannot convert rotational kinetic energy into pressure head, some of the regions have negative pressure.