Calculating drag and pressure forces from numerical simulations

[Janko1]

Homework Statement

I am simulating flow around a square and have obtained pressure and velocity in whole domain. I have to calculate the drag and pressure forces, but have trouble with choosing where to take the velocities and pressures.

Relevant Equations

$$F_d = 1/2 c_p A \rho u^2$$, $$F = \dfrac{\rho A u_2 \delta t u_2 - \rho A u_1 \delta t u_1}{\delta t}$$

So as stated, I am calculating the pressure and drag forces on an obstacle, but have trouble with which velocities to take. This is my geometry: http://shrani.si/f/3l/13P/2Tihb3iM/projekt2.png . I am guessing that I have to take pressure just before the obstacle and just after the obstacle and the velocities above the obstacle at the beginning and at the end. Is this the right thinking?

Can anyone please help?

 

[Chestermiller]

Can you please use LaTex to provide the equation for the drag force. In its current form, it is unreadable.

You need to integrate the pressure over the area of the leading and trailing faces of your object to get the pressure force.

The drag shear stress on the upper face is given by $\eta\frac{dv_x}{dy}$

 

[Janko1]

Yeah, sorry.
$$F_d = 1/2 c_p A \rho u^2 $$ is the drag force, and $$F = \dfrac{\rho A u_2 \delta t u_2 - \rho A u_1 \delta t u_1}{\delta t} $$ is the conservation of momentum.

So I should just take this shear stress at the upper obstacle boundary or am I missing anything else? I believe that every other force is symmetrical and cancels out?

 

[Chestermiller]

I can see what you are doing with your 2nd equation above. You are using a macroscopic momentum balance (with a control volume) to get the force exerted by the object on the fluid, which is minus the force exerted by the fluid on the object. For the upstream end of the control volume, it is OK to just multiply by the overall area because the velocity is uniform, but, for the downstream end, you need to integrate over the area. (And, of course, cancel out those delta t's). I'm not sure how accurate an answer you will get using this approach, because I would expect lots of roundoff in the calculation.

For the pressure component of the overall force Fp, you would integrate the pressure over the upstream and downstream faces of the object, and take the difference. The frictional drag force could then be determined from the difference between F and Fp. But, like I said, I don't know how accurate it will be to get the overall force from the macroscopic momentum balance. Therefore, I would also integrate the shear stress over the upper and lower faces of the object to get the frictional drag by a second independent means.

 

[Janko1]

Thank you very much for all the help, the things are clearer now and I think I will be able to properly solve the problem.