Isentropic Relations for Real Gas in Converging-Diverging nozzle

In summary, the problem being discussed is the calculation of the maximum flow rate through a converging-diverging nozzle for an unusual gas that does not follow the ideal gas law. The suggested method is to use the isentropic assumption and iterate the temperature to achieve the same stagnation enthalpy as the inlet conditions. However, this method relies on having an equation of state for the real gas or approximating it with a polynomial. The alternative is to use computational methods.
  • #1
Jonny6001
20
0
Hello,

I am looking at a problem concerning flow through a converging-diverging nozzle. The governing equations are relatively straight-forward for gasses that closely follow the ideal gas law. However I am looking at an unusual gas which is certainly not represented by the ideal gas assumption.

I am curious how you would go about calculating the maximum flow rate through the nozzle when the flow is choked at the throat, I do not want to use CFD initially.
My first thoughts would be to use the isentropic assumption that the stagnation enthalpy is constant throughout the nozzle. From having access to thermodynamic properties of the gas via 'refprop' it should be possible to iterate the temperature in the nozzle to achieve the same stagnation enthalpy as the inlet conditions. But the enthalpy is also dependent on the pressure so I thought I could use the isentropic pressure-temperature relation to couple the pressure to the temperature so that everything at the throat would be defined from knowing the temperature. But it using the isentropic law P0/P1=(T0/T1)^(gamma-1/gamma) assuming that the gas behaves according to the ideal gas law?

Thank you
 
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  • #2
Yes, the typical isentropic relations - [itex]p/p_0 = (\rho_\rho_0)^{\gamma} = (T/T_0)^{\gamma/(\gamma-1)}[/itex] - directly follow from the equation of state for an ideal gas. If you had an equation of state for your real gas you could likely come up with an equivalent set of isentropic relations for your real gas. Otherwise, you may be able to approximate it with a polynomial. The only other option beyond that would be to do it computationally.
 

1. What is the purpose of using isentropic relations for real gas in converging-diverging nozzles?

The purpose of using isentropic relations in these types of nozzles is to analyze the behavior of a compressible fluid as it passes through a converging and diverging section. This allows for the determination of important parameters such as pressure, temperature, velocity, and density, which are crucial in the design and optimization of these nozzles for different applications such as rocket engines and supersonic aircraft.

2. How does the use of isentropic relations differ for real gases compared to ideal gases in converging-diverging nozzles?

In ideal gas isentropic relations, the gas is assumed to have no intermolecular forces and the specific heat ratio is constant. However, in real gas isentropic relations, the effects of intermolecular forces and variable specific heat ratio must be taken into account. This leads to more complex equations to accurately describe the behavior of real gases in these nozzles.

3. What are the main assumptions made when using isentropic relations for real gas in converging-diverging nozzles?

The main assumptions made include: the gas is in a steady flow, the flow is one-dimensional, the gas is continuously compressible, the nozzle is adiabatic, and there is no friction or heat transfer between the gas and the nozzle walls.

4. How does the Mach number affect the use of isentropic relations in converging-diverging nozzles?

The Mach number, which is the ratio of the flow velocity to the speed of sound, has a significant impact on the behavior of gases in converging-diverging nozzles. As the Mach number increases, the gas becomes more compressible and the effects of variable specific heat ratio become more pronounced. Therefore, the use of isentropic relations becomes more important for accurately predicting the behavior of the gas.

5. What are some practical applications of isentropic relations for real gas in converging-diverging nozzles?

Isentropic relations for real gas in converging-diverging nozzles are used in various engineering applications, such as designing and optimizing rocket engines, supersonic aircraft, and steam turbines. They are also used in the analysis of gas flow in pipelines, turbochargers, and compressors. In addition, these relations are crucial in understanding the behavior of gases in high-speed flows, such as in hypersonic vehicles and space exploration missions.

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