Part 1: Flow Around Obstacles: Key Parameters in Aerodynamics

1. Introduction

The flow around an obstacle is a well-known problem in fluid mechanics that has numerous engineering applications. It refers to the behavior of fluid dynamics that occurs when a fluid flows around an obstacle, which can take various shapes such as a cylinder, square, triangle, NACA, or angle member.

One of the most significant applications of understanding flow around an obstacle is in aerodynamics. For instance, in automotive applications, engineers can optimize designs to reduce drag, increase lift, and improve overall efficiency by studying the flow patterns. Such studies can be performed in wind tunnels by varying the operating conditions, which is feasible. However, evaluating the design of the structure each time can result in high costs. This is where CFD comes into play as a powerful tool for studying the impact of operating conditions on efficiency by analyzing the flow around an obstacle. Hereafter are the main parameters evaluated in aerodynamic flows.

2. Main dimensionless numbers involved in aerodynamic flows

• Reynolds number

The flow around an obstacle is governed by the Reynolds number, which characterizes whether the flow is turbulent or laminar. Re is defined as:

Re = U*D/ν        

where U is the free-stream velocity, D is the length of the angle member, and ν is the kinematic viscosity of the fluid.

• Drag coefficient

The drag coefficient is a dimensionless quantity, used to quantify the drag or resistance of an object to move in a fluid. A lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag.

CD = FD/(0.5*A*ρ*U^2) // drag coefficient        

where FD is the drag force applied on the obstacle, A is the reference area, and \rho is the fluid density. The drag coefficient varies with Reynolds number, hereafter is an illustration of a cylinder obstacle.

• Lift coefficient

The lift coefficient is a dimensionless quantity, used to describe the amount of lift generated by an object.

CL = FL/(0.5*ρ*U^2) // lift coefficient        

where FL is the lift force applied on the obstacle. When the obstacle is symmetrical the lift coefficient is equal to 0.

• Strouhal number

When a cylinder is immersed in a moving fluid, it is observed that, for certain regimes, the velocity of the fluid in the vicinity of the walls of this body can undergo strong disturbances, which can lead to the formation of alternating rotating vortices downstream of the flow, creating pressure differentials. The position of the point of formation of these vortical detachments is unstable in time and space. However, as a first approximation, it can be considered that the vortices created at the rear of the body detach periodically on each side of it. This is then referred to as a Karman vortex street.

By studying this phenomenon, the physicist Vincent Strouhal observed that the frequency f of the vortex shedding was related to the velocity U of the flow and a characteristic length D of the obstacle.

St = f*D/U        

3. Evaluation of the drag and lift coefficients in OpenFOAM

To simulate the flow around a cylinder using OpenFOAM, you may find this video tutorial helpful.

To calculate the drag and lift coefficients in OpenFOAM, a function object called forcesCoeffs is available in OpenFOAM.

functions
{
?? ?forcesCoeff
?? ?{
?? ???? type??????????? forceCoeffs;
?? ???? libs??????????? ("libforces.so");
?? ???? writeControl??? timeStep;
?? ???? writeInterval?? 1;

?? ???? patches???????? ("cylinder");
?? ???? pName?????????? p;
?? ???? UName?????????? U;
?? ???? rho???????????? rhoInf;????? // Indicates incompressible
?? ???? log???????????? true;

?? ???? liftDir???????? (0 1 0); // lift direction
?? ???? dragDir???????? (1 0 0); // drag direction
?? ???? CofR??????????? (0 0 0);? // Axle midpoint on ground
????????pitchAxis?????? (0 0 1);
?? ??? ?
?? ???? magUInf???????? 5.0; // fluid velocity
????????rhoInf????????? 1.0;?
?? ???? lRef??????????? 2.0;?// reference length (ex. projected length)
?? ???? Aref??????????? 2.0; // reference area (ex. projected area)
?? ?}
}        

In Python, the Fast Fourier Transform (FFT) function can be used to calculate the frequency of the lift coefficient, which is an indicator of vortex shedding. Once the frequency is obtained, it can be multiplied by D/U to compute the Strouhal number.

4. Conclusion

The flow around an obstacle has numerous applications, especially in the field of aerodynamics. This article outlines the key parameters that are involved in this flow and explains how to calculate them using CFD. This article serves as an excellent starting point for beginners who wish to explore this phenomenon further and investigate more complex configurations.

5. Useful References