Drag and lift forces
 

Can anyone help me with the formulations for drag and lift force computation in generalized curvilinear coordinates using structured grids please!

Well, what exactly do you need help with?
You willprobably have a pressure (and surface tension if viscous) field over your geometry, so what you need to do is to find a description of your geometry (its normals), and integrate the pressure times the surface area along the geometry....

please post back if you have further questions!

Thank your for your reply. I am studying a numerical analysis of 3D flow past an hydrofoil under single-phase conditions. The flow is assumed to be viscous incompressible.
At every timestep I have pressure p , u,v, and w velocity components. What I need is to calculate the total forces acting on the hydrofoil surface. The hydro foil surafce is defined by (i,j,k) grid points (say i=100-200, j=1, k=1-5).

Can you help me with the formulations for the calculations of total forces in generalized curvilinear coordinates please?

Thank you in advance!

Ok, I will try to walk you through it:
in viscous flow, you have two forces acting on the hydrofoil: the pressure forces and the viscous forces. Your computation already gives you the pressure forces, so you will only have to compute the viscous shear stress. You might want to look up how this is done, in general, the viscous stress is determined by the velocity gradient at the surface (which you will get from your velocity field by some interpolation) and the coefficient of viscosity. With that, you get two stresses: pressure and the viscous stress. Note that both have units of force per square unit of area.
So to determine the actual force, you need to consider the area your force is acting upon.....that totally depends on how your grid is defined, where your velocities and pressure are located....

The usual way to determine the surface area is by the normal vectors at each gridpoint which are the crossproduct of the two vectors on the surface that span the surface element.... so you would have to figure out how your surface is defined, how you find the surface area.....

Note that the pressure acts normally onto the surface, and the viscous stress tangential to it. wiht the direction of the normal, that will give you a way of defining the contributions to the global force vector.

Hope this helps, if not, please keep asking!

That was a part of my jobs three years ago. I wrote down these formulations for your reference (see the images attached)

For the lift and drag calculations, you should use the fine grids to reduce numerical error in the calculation of surface area.

Thank you for your great help, cfdnewbie and congtuha. That is exactly what I want, congtuha. I have spent a lot of time trying to get these formulations but I failed.

:):)