[CFD-Lover]

Hi All,

I am working on a problem where I would hope that there is a solution or a general formula for it. I am trying to find a polynomial represents a C-D nozzle as in the following picture. The polynomial must except the length of the C-D nozzle, nozzle radius, diffuser radius, throat radius, as well as the number of points that lay on the polynomial.

Is there any formula for this shape like that for an airfoil shape or do I need to create it from scratch ? The polynomial must always fit by either change R1, R2, R, and L or by changing one variable?

Many thanks in advance,

[jbreunig]

How do you know where along the horizontal axis the entrance and exits would be? Given the variables, it looks like you could slide the entrance/exit side to side, and not effect any of the variables (under-constrained/not well posed).

If you want to solve it, I think you need to define one more variable. How far is R1 or R2 from the throat (parabola minimum)? I did some quick math to show what I mean.

https://flic.kr/p/Vytp4s

Solving this is simple with the additional variable defined. I don't work with nozzles like this much, so there may be something I'm missing. Just looking at the math alone, it looks like you need one more variable defined. Just substitute the variables into the parabola equation, and solve the system of equations.

[CFD-Lover]

Hi Jim,

Many thanks for the reply. I have found this formula, and it seems very handy but the issue is that it is only for R1=R2, which I thought that I could manipulate it for R1 not equal to R2.

clear all;clc;close all
Xi = -0.096414761;%0.08568;
L = 0.22543;
t = 0.002;
x0 = Xi+L/2;
R1 = 0.559467; % Nozzel diameter
f0 = 0.08;%0.509515; % Throat diameter
nPoints = 23;
for ii = 1:nPoints
    x(ii) = Xi + L*ii/(nPoints+1);
    y(ii) = R1*(1-f0/2*(1+cos(2*pi*(x(ii)-x0)/L)));
end
figure(1)
plot(x,y,'r--')

Which gives the following ;

untitled.jpg

[jbreunig]

No problem.

You can still get an equation if you need one. You just need to know how far R1 or R2 is from the center of the parabola. You can also do it if you know the distance from center to R1 as a percentage of L.

More than one way to skin a cat! Thanks for the fun problem.

[CFD-Lover]

You are welcomed Jim. Thanks for the help.

Best,