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Register a new userPrediction of shock wave configurations in compression ramp flows
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Here, we provide a theoretical framework revealing that a steady compression ramp flow must have the minimal dissipation of kinetic energy, and can be demonstrated using the least action principle. For a given inflow Mach number $M_{0}$ and ramp angle $alpha$, the separation angle $theta_{s}$ manifesting flow system states can be determined based on this theory. Thus, both the shapes of shock wave configurations and pressure peak $p_{peak}$ behind reattachment shock waves are predictable. These theoretical predictions agree excellently with both experimental data and numerical simulations, covering a wide range of $M_{0}$ and $alpha$. In addition, for a large separation, the theory indicates that $theta_{s}$ only depends on $M_{0}$ and $alpha$, but is independent of the Reynolds number $Re$ and wall temperature $T_{w}$. These facts suggest that the proposed theoretical framework can be applied to other flow systems dominated by shock waves, which are ubiquitous in aerospace engineering.
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The bistable states and separation hysteresis in curved compression ramp (CCR) flows, and the corresponding aerothermal characteristics (including wall friction, pressure and heat flux), are studied numerically and theoretically. Direct numerical simulations of separation hysteresis induced by variation of turning angle, as well as the influence of inflow Mach number and wall temperature on hysteresis loops, are carried out. Distributions of wall friction, pressure and heat flux are analyzed. Further, emergence of wall frictions first and second minima in the separation bubble is interpreted, revealing it is dominated by the adverse pressure gradient induced by separation and reattachment shocks. The present results and analysis indicate that the reversed-flow singularity of Smith (Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1988, 420: 21-52) is less likely to occur in CCR flows. The prediction of peak pressure of separation states confirms the model based on the minimum viscous dissipation theorem (Physics of Fluids, 2020, 32(10):101702). While the pressure overshoot can be analyzed by shock-polars with pressure match of compression and expansion process. The correlation between peak heat flux and peak pressure rise of both separation and attachment states is also discussed in terms of the classical power relations.
A new spatial-related mechanism is proposed to understand separation hysteresis processes in curved compression ramp (CCR) flows discovered recently (Hu et al. Phy. Fluid, 32(11): 113601, 2020). Two separation hystereses, induced by variations of Mach number and wall temperature, are investigated numerically. The two hystereses indicate that there must exist parameter intervals of Mach number and wall temperature, wherein both attachment and separation states can be established stably. The relationships between the aerodynamic characteristics (including wall friction, pressure and heat flux) and the shock wave configurations in this two hystereses are analyzed. Further, the adverse pressure gradient (APG) Isb(x) induced by the upstream separation process and APG Icw(x) induced by the downstream isentropic compression process are estimated by classic theories. The trend of boundary layer APG resistence Ib(x) is evaluated from the spatial distributions of the physical quantities such as the shape factor and the height of the sound velocity line. With the stable conditions of separation and attachment, a self-consistent mechanism is obtained when Isb, Icw and Ib have appropriate spatial distributions.
We report the mechanism of the hysteresis in the transition between Regular and Mach reflections. A new discovery is that, the hysteresis loop is in fact the projection of a higher dimensional path, i.e. the valley lines in the surface of dissipation, of which minimal values correspond to stable reflection configurations. Since the saddle-nodes bifurcate the valleies of the surface, they are actually the transition points of the two reflections. Furthermore, the predicted reflection configurations agree well with the experimental and numerical results, which is a validation of this theory.
We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired.
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the reduced dynamical equations only wave modes are retained, and vortices and horizontally uniform vertical shears are excluded. Despite the simplifications, our simulations reproduce some key features of oceanic internal-wave spectra: accumulation of energy at near-inertial waves and realistic frequency and horizontal wavenumber dependencies. Furthermore, we provide evidence that formation of the energy spectra in the inertial subrange is dominated by scale-separated interactions with the near-inertial waves. These findings support oceanographers intuition that spectral energy density of internal waves is the result of predominantly wave-wave interactions.
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