The document summarizes a CFD analysis of fluid flow around a classic Rolls-Royce vehicle. The initial model showed recirculating and reversed flow behind the vehicle. To improve the design, the author modeled an airfoil-shaped rear end. Simulation results for the original and modified designs showed that the modified design with smooth edges eliminated wake and low pressure regions behind the vehicle, indicating an efficient design. The author recommends preventing circulating velocity fields and low pressure spaces behind vehicles in CFD design work.

1.
The
University
of
Birmingham
CFD
Assignment
Ali
Tayebisadrabadi

2. Introduction
From the fluid mechanics point of view, we should always avoid the recirculated and
reversed flow. As shown in Fig.1, when the pressure gradient becomes positive, we have
backflow near to the wall [1]. One of the most critical design parameter for avoiding such
disturbance in fluid mechanical problems is geometry of the body, which is exposed to a
fluid flow. Therefore, we can easily improve our design by considering this factor.
Fig 1: Effect of pressure gradient on boundary-layer profiles (left) and Vortex shedding (right) [1]
Today we can easily model the CFD of almost each fluid mechanical problem, and
improve our design before making them real. CFD is a numerical method that solves the
Navier-Stokes equations for each element. As a result we can solve very complicated
models through this method, and a lot of software programs are designed for this purpose
such as ANSYS, FLUENT, ADINA, and so on. In this assignment we use ANSYS CFX
to solve the fluid domain considering boundary conditions.
Modeling
In this assignment, we want to improve the preliminary design of a classic Rolls-Royce.
As previously mentioned, we need a model to improve vortexes and reversed flow. If we
assume an airfoil, it has the best configuration to avoid such vortex in the rear end. So it

3. seems that we know what we want to do! Simulate an airfoil to our vehicle. At first we
select a classic Rolls-Royce as shown in the Figure 2.
Fig 2: A typical classic Rolls-Royce automobile in different view
We use a modeling software (SolidWorks), to model the fluid domain of this typical
classic Rolls-Royce to import it in ANSYS CFX software. The created model is shown in
Figure 3.
Fig 3: The fluid and solid domains of our model
Numerical Modeling
To solve our model, each CFD analysis combines two fundamental equations and solves
them simultaneously, which are known as Navier-Stokes equations [1]:
continuity:
𝜕𝜌
𝜕𝑡
+ 𝜌𝑢! ,!
= 0

4. Navier − Stokes momemtom conservation : 𝜌
!!!
!"
+ 𝑢! 𝑢!,! = 𝜎!",! + 𝜌𝑓!
The flow that we considered for our simulations in this study was air at 20°C with
properties of ρ = 1.205 kg/m3
and µ = 1.5 ×10-5
Pa.s [2]. And the boundary conditions are
defined as following:
Inlet boundary: uniform flow considering a velocity of 108 km/h
Outlet boundary: two sides of fluid field considering a static pressure of 1 atm
Symmetry boundary: this boundary condition is needed for each 2D CFD problem and I
tis applied to two front and back surfaces
Wall boundary: sides of our vehicle with no slip condition
Results and Discussion
We used total number of 121639 and 132532 nodes for the primary and improved design,
respectively; they included: pyramid, tetrahedral, and prisms shapes.
The extracted results are categorised to three parts: pressure magnitude (to demonstrate
the low pressure regions), velocity field (to show the magnitude and direction of velocity
in each point), and streamlines (to show the path of each particle at all the time). Figures
4 and 5 demonstrates our findings and results based on these three important outputs.
The velocity field is so circulated behind the vehicle (left and middle figures of Fig. 4
top) and we should avoid such disturbances in our design. Also, wake regions are
generated in the low pressure places. It can be seen from Figure. 4 (top) that there is a
low pressure region behind the vehicle and it confirms our guess about the wake and flow
separation.

5.
Fig 4: Comparing pressure, velocity, and streamlines in the fluid surrounded by the vehicle in the
classic Rolls-Royce (top) and the modified one (behind)
To overcome the above disturbance, we considered a new model with very smooth edges
at the rear end of our vehicle (unlike those sharp ones). As we see from Fig. 4 and Figure
5 , there is almost no wake at the back of the vehicle and also the pressure magnitude is
not low at that place. This shows that we had a great and efficient design.

6. Fig 5: Vector velocity behind the vehicle in a typical classic Rolls-Royce (top) compare to the
modified one (Design Recommendations: bottom)
Design Recommendations:
1. According to top-left and top-right parts of Fig 4. , we should prevent from
circulating of the velocity field behind the vehicle in our design.
2. Efficient design has low pressure spaces behind the vehicle which leads to
generation of wake region and consequently results in flow separation (figure 4).
3. According to figure 5 the streamlines need to have their path for each particle;
secondary flows generates when there are no direct path for the particles.

7. Reference
[1] Frank M. White, University of Rhode Island 1991, Fluid Mechanics, WCB McGraw-
Hill
[2] http://www.engineeringtoolbox.com/air-properties-d_156.html