Sonic Condition Prediction for Non-Isentropic Real-Gas Nozzle Flows for Fuel Injection Applications

Date of Award

5-1-2025

Degree Name

M.S. in Aerospace Engineering

Department

Department of Mechanical And Aerospace Engineering

Advisor/Chair

C. Taber Wanstall

Abstract

This work presents a methodology for predicting the sonic condition (∆P) in non-isentropic real-gas nozzle flows for arbitrary boundary conditions. In order to develop an agnostic boundary condition solver, the methodology will be developed for 3 cases. Case 1’s methodology is relevant to fuel injector applications with ill-posed boundary conditions, meaning a single boundary condition is known at the inlet and exit of the nozzle. The basis for case 1 is developed around knowing the inlet temperature and exit pressure, which is applicable to rotating detonation engines. The other two boundary condition scenarios include knowing both inlet boundary conditions or both exit boundary conditions. The main focus of this work is case 1, which is applicable to rotating detonation engines. This ill-posed thermodynamic state problem (one boundary condition at the inlet and one at the exit) is solved iteratively by first computing the isentropic process and then adjusting the exit state through a modified energy equation that incorporates a nozzle discharge coefficient. A similar procedure is developed for the other two cases. Results are presented for a range of inlet and exit conditions spanning both the ideal gas and real-gas regime. In order to span both the ideal gas and non-ideal gas operating conditions, the inlet temperature is fixed at the critical temperature while the inlet and exit pressures are swept across a thermodynamic range promoting both ideal gas exit conditions and non-ideal gas exit conditions relative to air breathing and rocket applications. Ethane is selected for theoretical development and hexane, decane, and carbon dioxide are included in the analysis as parametric fluids. The results analyze the choking pressures calculated for a range of exit pressures and discharge coefficients that include both ideal and non-ideal gas effects for all 4 fluids. The fuels were selected because they span the alkane range from light to heavy, with ethane being the light fuel, hexane as being the moderately heavy fuel, and decane as the heavy fuel. Decane and hexane serve as a more realistic example of jet fuels being liquid for a broader range of conditions. Carbon dioxide is selected due to its ubiquitous use and applications as a supercritical fluid. An experiment was conducted using carbon dioxide as the fluid to validate the choking pressure predicted by the methodology. Additionally, the theory was also compared with previous findings in the literature.

Keywords

Aerospace Engineering

Rights Statement

Copyright 2025, author.

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