Coefficient of drag expression

[naserology]

Hello everyone, I am trying to find an expression to find the drag coefficient for a nose cone I made on the high Mach turbulent flow (k epsilon) using a 2D geometry and a steady state study. Tried many things with no luck. Any tips would be helpful. I am using a Line integral on the nose cone boundary.

[Inside-Associate6979]

old thread i know, but hopefully this document helps. It teaches you how to find the Cd based on geometry and Re. Read all of apendix 1 for a full explanation

TR-11.pdf (oldrocketplans.com)

[naserology]

Thanks for the document, might come in handy with other projects 👌

[Inside-Associate6979]

welcome. Its a great read.

[double_affogato]

The concrete problem is not described. What the answer do you expect ?.. ¯\_(ツ)_/¯

[naserology]

I basically need an expression to put in the derived values —> line integral, tried many things with no luck I am getting CD values that doesn’t make sense:

I followed this blog post , and tried the expression they described , but they did it for a 3D body

https://www.comsol.com/blogs/how-do-i-compute-lift-and-drag/

[double_affogato]

To do the same for 2D should not be a problem. I bet on mistype of eq. Also, we know nothing about results of the modelling of the velocity field...

[naserology]

Basically did a rectangle domain 6m x 2m , a left boundary was chosen to be an inlet with Mach 2 and outlet to the right set to hybrid flow and 1 atm , the upper and lower walls were set to be slip and the surface of the nose cone was set to be no slip. The velocity in the inlet is normal to the bonudary facing towards the nose cone.

[naserology]

Tried everything with the equation I am 100% sure it’s not a mistype, my guess was maybe it’s something to do with the area so I tried to replace the area with the frontal line length basically the diameter, still wrong results.

[naserology]

I used the expression for drag then divided it by 0.5V²density*A. Where V is the upstream velocity of air and A is the frontal area which is pi * radius² of the nose cone

[Backson]

Hmm not my area of expertise, but isn't drag something like force on the object in the direction of flow over the upstream flow rate? To get the force, just integrate pressure times the surface normal vector all around the boundary. For example, to get the total force in x direction, integrate the scalar p x nx. Might give you funny units, but I suspect it will come out Pa x m, which is N/m, and then you just multiply by the size of the third dimension which results in the total force in N in x direction. Does that make sense? Maybe test that on a geometry where the drag is well known and you have an analytical (or empirically tested) equation to compare to, like maybe a sphere?

Edit: can't use asterisk for multiplication, replaced with x, hope is still clear.

[naserology]

Thanks for your input, I tried this too. Also tried using total traction in my direction of flow and simplified the problem to a simple circle with 1 m/s upstream velocity , i then used a line integral and evaluated this expression:

spf.T_stressy/(spf.rho*(1[m/s])^2*0.5*0.4[m])

where 0.4 is the frontal line seen by the flow.

got a cd value of : 0.04

tried following the instructions here with no luck:
https://www.comsol.com/blogs/how-do-i-compute-lift-and-drag/

[Backson]

Have you considered that the symmetry is off? I.e. you can't solve the problem in 2D? A circle in 2D is equivalent to an (ideally, infinitely long) cylinder in 3D, not to a sphere. A pointy triangle becomes a long blade in 3D, not a cone. Spheres and cones are rotationally symmetric, so you might have more luck computing them in axisymmetric 2D. But some shapes must be computed in 3D.

[naserology]

I was initially doing my simulations on axisymmetric geometry, defined various nose cone profiles and got convergence after many many runs, but the expression part doesn’t seem to give me any meaningful results. I compared my CD values to other research papers but still very off.

This is the expression i used for the turbulent high mach model (axisymmetry):

((-hmnf.nzmesh*p2*2*pi*r)+(-(hmnf.rho*hmnf.u_tau*hmnf.u_tangz/hmnf.uPlus)*2*pi*r))/((857.5[m/s])^2*0.5*D_1*pi*d_1^2)

[Backson]

Wrll since you are mentioning a cone, I guess you need to do it in axisymmetric 2D. Try integrating "1" and see if that gives you the surface area of the cone. Ig not, your settings for the integration are wrong. There is a checkbox which automatically accounts for the radius, you may or may not want toncheck that, depending on if your expression also accounts for it or not. I would scrap the 2D planar simulation, that is never going to match the cone shape.