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Gas effect with the presence of the thermal and calorific imperfections on the Prandtl Meyer function

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Abstract

The authors of this paper develop a computational program to determine the effects of gaseous imperfections on calculations of the Prandtl Meyer function. Which is often applied to minimum length nozzle (MLN) design. The aim is to improve the design parameters of supersonic nozzles when using a gas propellant for cold propulsion or heated thruster systems under a high pressure and temperature. We considered H2, O2, Cl2, N2, CO, NO, and air to this end. The Prandtl–Meyer function depends on the stagnation temperature, pressure, Mach number, and the gas used as non-flammable fuel. As values of the parameters of stagnation of the gases increased, their specific heats as well and ratio began to vary, and the ideal gas began behaving as a real gas. This can be explained by Berthelot’s correction of the terms of the equation of state related to a perfect gas, because the co-volume and intermolecular forces of attraction of the gas influenced system. We calculated differences in values of the Prandtl–Meyer function for different gases and air. The results showed that the use of H2, N2, and CO led to a significant reduction in the weight, length, and volume of the MLN, and it yielded better performance in terms of the manufacture of aerospace propulsion systems that can attain the maximum thrust than when air was used. The performance of the system when the above gases were used was 16% better than when air was used.

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Abbreviations

a :

Constant of intermolecular forces

b :

Constant of molecular size

v :

Specific volume

M :

Mach number

P :

Pressure

R :

Gas constant

T :

Temperature

V :

Velocity

C P :

Specific heat at constant pressure

C V :

Specific heat at constant volume

C T :

Constant determined at constant temperature

C S :

Sound velocity

γ :

Specific heat ratio

ρ :

Density

β :

Flow deviation angle

θ :

Molecular vibrational energy constant

υ :

Prandtl Meyer function

PG:

Perfect gas

HT:

High temperature

RG:

Real gas

PMF:

Prandtl Meyer function

MLN:

Minimum length nozzles

0:

Stagnation conditions

1:

Conditions at state 1

2:

Conditions at state 2

*:

Critical condition

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Authors and Affiliations

  1. Mechanical Engineering Department, Fundamental and Applied Physics Laboratory, Blida 1 University, Soumaa Road, P. O. Box 09000, Blida, Algeria

    N Bengherbia, M Salhi & M Roudane

Authors
  1. N Bengherbia
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  2. M Salhi
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  3. M Roudane
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Correspondence to N Bengherbia.

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Bengherbia, N., Salhi, M. & Roudane, M. Gas effect with the presence of the thermal and calorific imperfections on the Prandtl Meyer function. Indian J Phys 98, 2461–2473 (2024). https://doi.org/10.1007/s12648-023-03004-3

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