This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/ nitrogen and oxygen/ hydrogen mixing layers at supercritical pressures. These layers consist of two counter- flowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemicalspecies masses. In these equations, the expressions for heat fluxes and chemicalspecies mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the error-function profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles.
This work was done by Nora Okong’o and Josette Bellan of Caltech for NASA’s Jet Propulsion Laboratory.
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Real-Gas Effects on Binary Mixing Layers
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Overview
The document presents a technical report on a computational study conducted by researchers Nora Okong’o and Josette Bellan at NASA’s Jet Propulsion Laboratory, focusing on the real-gas effects on the mean flow and temporal stability of binary mixing layers. The study specifically examines heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures, which are relevant to applications in liquid rocket engines, gas turbine engines, and diesel engines that operate under high-pressure conditions.
The research utilizes the Navier-Stokes equations of compressible flow, along with equations for the conservation of total energy and chemical species masses, to model the behavior of these mixing layers. The expressions for heat fluxes and chemical species mass fluxes are derived from fluctuation-dissipation theory, incorporating Soret and Dufour effects, which are critical for understanding the interactions in non-ideal gas mixtures.
A key aspect of the study is the derivation of similarity equations for streamwise velocity, temperature, and mass fractions, which serve as approximations to the governing equations. The results indicate that the similarity profiles exhibit significant real-gas, non-ideal mixture effects, particularly in temperature behavior, which deviates from the expected error-function profile typical of incompressible flow. This deviation is attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers.
The researchers also conducted temporal linear inviscid stability analyses using both similarity and error-function profiles as mean flow representations. The findings reveal that the growth rates of instabilities are larger for the similarity profiles compared to the error-function profiles, with shorter wavelengths of highest instability. Additionally, the range of unstable wavelengths is broader for the similarity profiles, highlighting the complexities introduced by real-gas effects.
This study is significant as it provides insights into the stability and behavior of mixing layers under conditions that closely resemble those found in practical high-pressure applications. The work contributes to a deeper understanding of fluid dynamics in real-gas scenarios, which is essential for the design and optimization of various propulsion systems. The research was submitted to the AIAA Journal in February 2003 and represents a novel exploration of mixing layer stability at high pressures, a topic that had not been extensively studied before.
