Abstract
Propellants or combustion products can reach high pressures and temperatures in advanced or conventional propulsion systems. Variations in flow properties and the effects of real gases along a nozzle can become significant and influence the calculation of propulsion and thermodynamic parameters used in performance analysis and design of rockets. This work derives new analytical solutions for propulsion parameters, considering gases obeying the van der Waals equation of state with specific heats varying with pressure and temperature. Steady isentropic one-dimensional flows through a nozzle are assumed for the determination of specific impulse, characteristic velocity, thrust coefficient, critical flow constant, and exit and throat flow properties of He, H2, N2, H2O, and CO2 gases. Errors of ideal gas solutions for calorically perfect and thermally perfect gases are determined with respect to van der Waals gases, for chamber temperatures varying from 1000 to 4000 K and chamber pressures from 5 to 35 MPa. The effects of covolumes and intermolecular attraction forces on flow and propulsion parameters are analyzed.
Highlights
The classical equations for the calculation of rocket propulsion parameters are based on one-dimensional flows of ideal gases with constant properties [1]
The percent errors of propulsion parameters ∅ = Isp, Γ, etc. of calorically perfect (CP) and thermally perfect (TP) ideal gases (IG) in relation to van der Waals (VDW) gases were calculated from ε∅
Similar tendencies have been observed in the present results for the critical flow constants, for both calorically and thermally perfect ideal gases compared to VDW gases
Summary
The classical equations for the calculation of rocket propulsion parameters are based on one-dimensional flows of ideal gases with constant properties [1]. The characteristic velocity is a measure of propellant performance and motor design quality, whereas the thrust coefficient indicates nozzle design efficiency Another important parameter, mainly used for a nozzle design, is the critical flow constant which determines the mass flow rate from chamber stagnation conditions [1]. The AGARD-AR-321 report [16] presented real gas discharge coefficients, based on experimental and numerical data from Masure and Johnson, in order to correct the mass flow rate and thrust in air nozzles for stagnation temperatures up to 344 K and stagnation pressures up to 100 bar, and the results were compared to calorically perfect ideal gas solutions. The present work extends previous studies and derives new analytical solutions for rocket propulsion parameters and nozzle flow thermodynamic parameters of real gases obeying the van der Waals equation of state and provides data for a broad range of stagnation pressures and temperatures. Lower temperatures (1000-2500 K) are usually reached in electrothermal and catalytic augmented thrusters while higher temperatures (2500-4000 K) can be attained in chemical and nuclear rockets
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