Prandtl-Meyer Function Iteration

[nanvinnie]

hi.. I'm trying to write a MATLAB code that will iterate the mach value given a certain value for nu.

nu = sqrt((gamma +1)/(gamma -1))*atan(sqrt((gamma - 1)/(gamma +1)*(M^2-1)))-atan(sqrt(M^2-1))

this is the equation for the prandtl-meyer function, but how do i write it in MATLAB so that i can extract the value of nu for a given M value? sort of like the goal seak function in excel...

i would appreciate anyone's help!

 

[KLoux]

I don't know of any built-in MATLAB function that does this for you (without any additional toolboxes, that is), but that doesn't mean there isn't one...

I would look into something like the Newton-Raphson's method (but there are many others). The wikipedia article on Newton's Method is pretty good, and at the bottom is a list of similar algorithms. It's not difficult to write some algorithm like this for MATLAB.

-Kerry

 

[oswaler]

The Prandtl-Meyer function is an important tool in the field of fluid mechanics, specifically in the study of compressible flows. It relates the Mach number (M) and the deflection angle (nu) of a flow over a solid surface. The equation you have provided is the inverse of the Prandtl-Meyer function, which calculates the value of nu for a given Mach number.

To write this equation in MATLAB, you can use the "fzero" function to find the root of the equation. This function takes in an initial guess for the root and an anonymous function representing the equation. For example, you can write the following code to find the value of nu for a given Mach number (M=2 in this case):

nu = fzero(@(nu) sqrt((gamma +1)/(gamma -1))*atan(sqrt((gamma - 1)/(gamma +1)*(2^2-1)))-atan(sqrt(2^2-1)), 1);

This will give you the value of nu for M=2. You can change the value of M as per your requirement.

I would also recommend looking into the "fsolve" function, which is similar to "fzero" but can handle more complex equations with multiple variables. You can use it to solve for nu in terms of M.

I hope this helps in writing your MATLAB code. Good luck!