Unsteady interaction mechanism of transverse stage separation in hypersonic flow for a two-stage-to-orbit vehicle

The interactions between oblique and bow shock waves are significant problems related to the aerodynamic force and thermal performance of hypersonic vehicles, but few studies have considered the dynamic effect of the body's motion on the phenomena. In this work, a numerical study on the oblique and bow shock waves ahead of an elliptic cylinder rotating with a forced-oscillation approach was conducted at Mach 5 by solving the unsteady, two-dimensional Navier–Stokes equations in a non-inertial coordinate system. The hysteresis loops of aerodynamic coefficients were analyzed first, and it was found that the moment is sensitive to rotation. Then, two different hysteresis forms were found at positive and negative angles of rotation (AOR), corresponding to cases with the interference point above or below the wall, respectively. When AOR is positive, the rate-dependent transition hysteresis among various shock interaction types causes the movement of strong flow structures (reflected shock wave, Mach stem, and jet) to always lag behind the body's motion. When AOR is negative, besides the evolution hysteresis of flow structures, two unusual patterns between Edney Types III and VI were observed on different transition paths, which led to very different peak pressures. Also discussed are the driving mechanisms associated with the effect of the subsonic region and the downstream boundary of the interaction zone, as well as the modulating action of the formed virtual Laval flow channel. Additional simulations were performed to study the effect of rotation speed on the transition boundary and the transition structures between Types III and VI.

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Effects of bulk viscosity, heat capacity ratio, and Prandtl number on the dispersion relationship of compressible flows

Bhaumik,

Deepak

2023

Physics of Fluids

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Here, we present the variation of the dispersion characteristics of the three-dimensional (3D) linearized compressible Navier–Stokes equation (NSE) to bulk viscosity ratio, specific heat ratio (γ), and Prandtl number (Pr). The 3D compressible NSE supports five types of waves, two vortical, one entropic, and two acoustic modes. While the vortical and entropic modes are non-dispersive, the acoustic modes are dispersive only up to a specific bifurcation wavenumber. We illustrate the characteristics and variation of relative (with respect to the vortical mode) diffusion coefficient for entropic and acoustic modes and a specially designed dispersion function for acoustic modes with depressed wavenumber η=KM/Re, the bulk viscosity ratio, γ, and Prandtl number Pr of the flow. Here, K, M, and Re denote the absolute wavenumber of disturbances, Mach number, and Reynolds number of the flow, respectively. At lower wavenumber components, the deviation of the dispersion function from the inviscid and adiabatic case is proportional to η2 at the leading order, and the relative diffusion coefficients increase linearly with bulk viscosity ratio and γ while varying inversely with Pr. With the increase in the bulk viscosity ratio, the shape and extent of the dispersion function alter significantly, and the change is more substantial for higher wavenumber components. The relative diffusion coefficient for entropic and acoustic modes shows contrasting variation with wavenumber depending upon bulk viscosity ratio, γ, and Pr. We also show by solving linearized compressible NSE that relatively significant evolution and radiation of acoustic and entropic disturbances occur when the bulk viscosity ratio is close to the corresponding critical value of maximum bifurcation wavenumber. Based on this criterion, we have presented an empirical relation for estimating bulk viscosity ratio depending upon γ and Pr, giving the corresponding range for obtaining relatively significant disturbance evolution.

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Unsteady interaction mechanism of transverse stage separation in hypersonic flow for a two-stage-to-orbit vehicle

Cited by 5 publications

References 34 publications

The Numerical and Experimental Research on Supersonic Parallel Separation

The Numerical and Experimental Research on Supersonic Parallel Separation

Numerical investigation of unsteady aerodynamic characteristics induced by the interaction of oblique/bow shock waves during rotation

Effects of bulk viscosity, heat capacity ratio, and Prandtl number on the dispersion relationship of compressible flows

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