Generating the contraction section of a CD Nozzle

Dear all,

I want to generate the contraction section of a CD Nozzle based on this paper "Contour Design Techniques for Super/Hypersonic Wind Tunnel Nozzles". This paper describes the use of a cylindrical-quartic-conical-quartic contraction design. I have tried to work out the code but the result is not what I want. I have attached relevant screenshots from the paper as well as my code. I believe the CQCQ does not work for shor contraction lengths.

Any help is appreciated!

%% CQCQ

clearvars;clc;close all;

%% Define the design parameters

clearvars;clc;

% all are normalized wrt throat radius

Ri = 1.6870; % inlet convergent section height

Rstar = 8.0; % Downstream radius of curvature

rstar = 1.0; % throat radius

Rstar_rstar = 8.0; % ratio of downstream radius of curvature to throat radius

theta = 25; % max angle

a = 2.5; % length of the cylindrical section

L = 10 ;%5.82249226683321/3.3422; % total length of the convergent section

%% Model Equations

d = 3.0/2.0 * Rstar*tand(theta);

xplus = L-d;

rplus = (5.0*d^2) / (12.0*Rstar) +rstar;

b = 2.0*(xplus + (rplus-Ri)/tand(theta)-a );

e = (Ri - rstar)/tand(theta);

c = e- b/2.0 - (5.0/8.0) *d;

%% Cylindrical region

x_cylindrical = linspace(0,a,100);

r_cylindrical = Ri * ones(size(x_cylindrical));

plot(x_cylindrical,r_cylindrical,'.b')

hold on

%% Upstream Quartic

x_upstream_q = linspace(a, a + b, 100);

r_upstream_q = Ri - (b*tand(theta))/2.0*((x_upstream_q-a)./b).^3.*(2-(x_upstream_q-a)./b);

plot(x_upstream_q,r_upstream_q,'.k')

hold on

%% Conical Region

x_conical = linspace(a+b,a+b+c,100);

r_conical = Ri + ((a+b)/2.0)*tand(theta) -x_conical.*tand(theta);

plot(x_conical,r_conical,'.r')

%% Downstream quartic

x_downstream_q = linspace(a+b+c,L,100);

r_downstream_q = ((L-x_downstream_q).^2)./(12.0*Rstar).*(6.0-((L-x_downstream_q)./d).^2) + rstar;

plot(x_downstream_q,r_downstream_q,'.g')

%%

% Combine the x and r values for plotting

x_combined = [x_cylindrical, x_upstream_q, x_conical, x_downstream_q];

r_combined = [r_cylindrical, r_upstream_q, r_conical, r_downstream_q];

% Plot the curve

figure;

plot(x_combined, r_combined, 'LineWidth', 2);

xlabel('x');

ylabel('r(x)');

title('CQ-CQ Nozzle Curve');

grid on;

axis equal;

Answer 1

[Vinay]

Hi @Bamelari Jovani,

The issue arises because of the negative value of 'c' causing the downstream and upstream quartic sections to overlap with the conical region. The parameter ‘c’ represents the length of the conical section, and having a negative value would not be physically meaningful. Additionally, there was an error in the equation for `r_conical`, which can be corrected as

r_conical = Ri + (a+b/2.0)*tand(theta) -x_conical.*tand(theta);

If you could provide the entire research paper used to construct the CQ-CQ curve, it would be very helpful.

I hope this helps!