Issue during for loop.

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Shawn Alcorn 2022-9-8

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编辑： Cris LaPierre 2022-9-9

The issue occurs during the for loop using j. When I calculate deltaTheta it should be pretty constant at the start but eventually decrease in value, problem is my deltaTheta continues to grow by a constant value. The next issue is my M array. The initial value is correct but the while loop is suppose to compare the values until the error is met but my M is decreasing at a constant rate when it should be increasing until a final value of about 2.4. I have verified that all values up to this point are accurate.

%% AEM 624 Hypersonic Flow HW 2

clear all

close all

clc

M1 = 3; %Upstream Mach Number

gamma = 1.4;

P1 = 101325; %Pa

T1 = 298.15;%K

i = 1;

V = M1*343;

q = (gamma/2)*P1*(M1^2);

CpMax = (2/(gamma*(M1^2)))*((((((gamma+1)^2)*(M1^2))/((4*gamma*(M1^2))-(2*(gamma-1))))^(gamma/(gamma-1)))*((1-gamma+(2*gamma*(M1^2)))/(gamma+1))-1);%Modified Newtonian

for x = .01370207:.001:3.291

x_save(i) = x;

y = -0.008333 + (0.609425*x) - (0.092593*(x^2));

dy = 0.609425 - .185186*x;

y_save(i) = y;

theta = atan(dy);

theta_save(i) = theta;

thetaTan = tan(theta);

thetaTan_save(i) = thetaTan;

betaIterDeg = 1;

betaIterRad = betaIterDeg*(pi/180);

thetaTanIter = 2*cot(betaIterRad)*(((M1^2)*(sin(betaIterRad)^2)-1)/(((M1^2)*(gamma+cos(2*betaIterRad)))+2));

while abs(thetaTan - thetaTanIter) > .001

betaIterDeg = betaIterDeg + .001;

betaIterRad = betaIterDeg * (pi/180);

thetaTanIter = 2*cot(betaIterRad)*(((M1^2)*(sin(betaIterRad)^2)-1)/(((M1^2)*(gamma+cos(2*betaIterRad)))+2));

end

beta(i) = betaIterRad;

CpTanWedge = (4/(gamma+1))*((sin(betaIterRad)^2)-(1/(M1^2)));% Tangent Wedge

Cp = 2*((sin(theta))^2); %Newtonian

CpModNewt = CpMax*(sin(theta)^2);% Modified Newtonian

p = (q*Cp)+P1;% Newtonian

pModNewt = (q*CpModNewt)+P1;% Modified Newtonian

pTanWedge = (q*CpTanWedge)+P1;% Tangent Wedge

pnorm(i) = p./P1;% Newtonian

pModNewtNorm(i) = pModNewt/P1;% Modified Newtonian

pTanWedgeNorm(i) = pTanWedge/P1;% Tangent Wedge

i = i + 1;

end

for j = 1:3277

M(1) = (1/sin(beta(1)-theta_save(1)))*sqrt((1+((gamma-1)/2)*(M1^2)*(sin(beta(1))^2))/((gamma*(M1^2)*(sin(beta(1))^2))-((gamma-1)/2)));

PrandtlM(j) = sqrt((gamma+1)/(gamma-1))*(atan(sqrt(((gamma-1)/(gamma+1))*((M(j)^2)-1))))-atan(sqrt((M(j)^2)-1));

deltaTheta(j) = abs(theta_save(j) - theta_save(j+1));

deltaTheta_save(j) =deltaTheta(j);

PrandtlM(j+1) = PrandtlM(j) + deltaTheta(j);

MIter = 1;

PrandtlIter = (sqrt((gamma+1)/(gamma-1))*(atan(sqrt(((gamma-1)/(gamma+1))*((MIter^2)-1)))))-atan(sqrt((MIter^2)-1));

while abs(PrandtlM(j+1)-PrandtlIter) > .001

MIter = MIter + .001;

PrandtlIter = sqrt((gamma+1)/(gamma-1))*(atan(sqrt(((gamma-1)/(gamma+1))*((MIter^2)-1))))- atan(sqrt((MIter^2)-1));

end

j = j + 1;

M(j) = MIter;

end

for k = 1:3277

pipn = ((2*gamma)/(gamma+1))*((M(k)^2)*(sin(beta(k))^2)-1);

CpExpansion = (2/(gamma*(M(1)^2)))*(pipn-1);

pExpansion = (CpExpansion*q)+P1;

pExpansionNorm(k) = pExpansion./P1;

k = k + 1;

end

plot(x_save,y_save)

hold on

plot(x_save,(-1)*y_save)

figure

plot(x_save,pnorm)

hold on

plot(x_save,pModNewtNorm)

hold on

plot(x_save,pTanWedgeNorm)

hold on

plot(x_save(2:3278),pExpansionNorm)

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Rik 2022-9-9

You have extremely long expressions. I never trust myself to get all the braces correct. How did you verify that you did?

And did you use the debugger to see step by step what happens to your variables? Did you intend to overwrite M(1) every iteration of j?

Shawn Alcorn 2022-9-9

I verified by using the expressions from a previous working code that I used last week. The main problem is my deltaTheta keeps increasing, the values should be almost constant for a while and then begin to approach 0.

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Answer 1

Cris LaPierre 2022-9-9

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1800595-issue-during-for-loop#answer_1049750

编辑：Cris LaPierre 2022-9-9

在 MATLAB Online 中打开

We are not familiar with the problem you are trying to solve, so can't comment on what the code 'should' be doing. We can only comment on what it is doing.

Follow your calculation steps to understand why deltaTheta is behaving the way it is. Working backwards

deltaTheta(j) = abs(theta_save(j) - theta_save(j+1));
theta_save(i) = theta;
theta = atan(dy);
dy = 0.609425 - .185186*x;
x = .01370207:.001:3.291

So you create an evenly spaced vector, x, and then the equation of a line to calculate dy. You then take atan to get theta.

x = .01370207:.001:3.291;

dy = 0.609425 - .185186*x;

theta = atan(dy);

plot(theta)

I notice you treat your angles as degrees elsewhere in your code, converting them to radians before using trigonometric functions on them (the ones you use expect radians). Should dy also be converted to radians before calculating atan?

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Shawn Alcorn 2022-9-9

dy is not an angle, so it can't be converted to radians. I have already verified that my theta is correct. dy is the derivative of the initial parabolic function which becomes a linear function. By definition dy is equivalent to the rise over run at each point along the parabolic function, then by using the inverse of tangent you get the angle at that specific x location. Looking into the theta_save variable, the theta follows the curve and approaches 0 radians as it should.

Cris LaPierre 2022-9-9

编辑：Cris LaPierre 2022-9-9

Good point on atan.

Sounds like your code is working as designed then.

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Issue during for loop.

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