Calculate compressible aerodynamic properties and visualize T-S diagrams
Welcome to Tesseract Software's Real Gas Calculator. We created this tool to enable code-free compressible aerodynamic calculations for real gases in a web browser. A multitude of tools exist to for such calcualtaions with perfect gases (such as this one, which inspired this tool) but no such tool exists for real gases due to the lack of closed form relations. Whilst our tool is simple, it has nonetheless been useful for us when working with compressible aerodynamics for real gases. The real strength of this tool is being able to quickly identifiy the flow regime (based on the Isentropic Mach Number) for a given pressure ratio. This helped use immensly during our Organic Rankine Cycle turbine design projects.
Our calculator uses CoolProp for the thermodynamic calculations. To this end we would like to thank the developers of CoolProp for their work, espeically the JavaScript WASM module! For more information on the theory behind the calculations, please see the Equations of Compressible Aerodynamics section.
If you are interested in this tool have any feedback/suggestions, or which to discuss the development of similar tools, then please get in touch with us at support@tesseractsoftware.co.uk.
To use the tool, simply select a fluid from the dropdown menu, set the initial conditions and set a final pressure. The tool will then calculate the thermodynamic properties and plot the T-s diagram. For valid results you must ensure that the start and end points for the fluid are in the vapour phase.
For the calcualtions undertaken in this tool we assume that the expansion process is isentropic, i.e. the entropy of the fluid is constant through the expansion. The process of calculating an isentropc expansion of a real gas is the same as for a perfect gas. Unlike the case for a perfect gas, a closed form solution does present itself for a real gas.
In practice most equations of state work with density and temperature as state variables, however CoolProp's API is sufficiently flexible such that is allows any two variables to be used. For the sake of the explanation below we will use density and temperature as the state variables.
Consider the intial point, denoted with a subscript 0, of a generic fluid. The end point of the expansion is denoted with a subscript 1. The total enthalpy (denoted with superscript total) of the fluid at the initial point is given equal to the static enthalpy as the initial velocity is zero:
For an isentropic expansion the entropy of the fluid is constant, therefore:
Using CoolProp we can calculate the static enthalpy at the end point of the expansion as a function of entropy and pressure ( as behind the scenes CoolProp uses density and temperature as the state variables):
As total enthalpy is conserved through an isentropic expansion, the velocity of the fluid at the of the expansion is given by:
Solving for the velocity at the final state we get:
At the final state the speed of sound be can calculated as a function of pressure and entropy:
Leading to the final calculation of the isentropic Mach number: