Compressible flow calculator #

About this calculator #

Compressible flow equations are used in orbit re-entry vehicles to supersonic jets. Traditionally we used printed tables to get the values of unknown. This calculator is a replacement for printed tables. This calculator solves compressible flow equations with accuracy up to 9 digits which is far more accurate than printed tables and more reliable than any other compressible flow calculator in the market.

Developed using: Android Studio, Java and processing java library. #

Get it on Google play store #

Please click the below link to visit the playstore page or search Gas Table and Compressible flo in play store.

Play store: Gas Table and Compressible flow calculator

Pre-requisite #

It would be better if you know the basics of the following,

• Gas-dynamics
• Numerical Methods
• Any programming language

Objective #

When I was studying gas dynamics I came across the "Gas Table" which is a set of inputs variables and output variables of an equation. Without computers, we cannot solve these equations easily. So, I decided to make a calculator on my own to solve these equations. Though there are two calculators in the market doing the same, I wanted to test my skills.

Implementation #

The equation to be solved looks like the below,

where we know A/A* and γ, we need to solve for M. You might realize that this equation cannot be solved for M easily by hand. I used two methods to solve this equation but, I'm going to explain the easiest method to keep this post interesting. I call this easy method as BRUTE FORCE method.

for example consider an equation,

x^2 + 2x = 3,

So,

x^2 + 2x - 3 = 0

We will substitute values of x from -10 to 10 at a step of +1,

I'm using JavaScript here,

for(let i = -10; i < 11; i++){
    x = i;
    console.log( x*x - 2*x - 3);
} 

Output we got is,

117
96
77
60
45
32
21
12
5
0
-3
-4
-3
0
5
12
21
32
45
60
77

at x = -1 and x = 3, We got the solution. Within -10 to 10 we got two solutions. There can be multiple solutions if the range is more.

Implementing what we learned #

Similarly, We will substitute multiple values to M and we will find the solution. The value to start and end will be given by PHYSICS. The solution doesn't always need to be a whole number. In those cases we will reduce the step size around 1e-5 and we will try to take near zero value like +0.00005 or -0.00005 for accuracy of 4 digit.

Second method [ Newtons method ] #

This method is very fast compared to the above method. It is more than 1000 times faster. Since, computers solve simple equations in micro seconds the difference is negligible for simple equations. The explanation of this method is not in this scope of post. Click here to know more about this method.