Ballistic Range Testing Data Analysis of Tianwen-1 Mars Entry Capsule

A typical blunt body such as Tianwen-1 Mars entry capsule suffers dynamic instability in supersonic regime. To investigate the unstable Mach range of flight and to confirm the design of aerodynamic shape and mass properties, a ballistic range test was carried out aiming at capturing supersonic dynamic characteristics of Tianwen-1. Aerodynamic coefficients of free-flight scaled models were derived by modified linear regression method based on position and attitude data, while the dynamic coefficients were established under the assumption of small angle linearization. The static moment coefficients and dynamic derivatives were identified thereafter. Results show that models in untrimmed configuration are dynamically unstable at certain Mach numbers, whereas models in trimmed configuration are dynamically stable at other Mach numbers tested. Both trimmed and untrimmed configurations are statically stable in all testing cases.

Pressure fluctuations due to ‘trapped waves’ in the initial region of compressible jets

An experimental study is conducted on unsteady pressure fluctuations occurring near the nozzle exit and just outside the shear layer of compressible jets. These fluctuations are related to ‘trapped waves’ within the jet's potential core, as investigated and reported recently by other researchers. Round nozzles of three different diameters and rectangular nozzles of various aspect ratios are studied. The fluctuations manifest as a series of peaks in the spectra of the fluctuating pressure. Usually the first peak at the lowest frequency (fundamental) has the highest amplitude and the amplitude decreases progressively for successive peaks at higher frequencies. These ‘trapped wave spectral peaks’ are found to occur with all jets at high subsonic conditions and persist into the supersonic regime. Their characteristics and variations with axial and radial distances, jet Mach number and aspect ratio of the nozzle are documented. For round nozzles, the frequency of the fundamental is found to be independent of the jet's exit boundary layer characteristics and scales with the nozzle diameter. On a Strouhal number (based on diameter) versus jet Mach number plot it is represented by a unique curve. Relative to the fundamental the frequencies of the successive peaks are found to bear the ratios of 5/3, 7/3, 9/3 and so on, at a given Mach number. For rectangular nozzles, the number of peaks observed on the major axis is found to be greater than that observed on the minor axis by a factor approximately equal to the nozzle's aspect ratio; the fundamental is the same on either edge. For all nozzles the onset of screech tones appears as a continuation of the evolution of these peaks; it is as if one of these peaks abruptly increases in amplitude and turns into a screech tone as the jet Mach number is increased.

Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria

A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on a numerical equilibrium that has been extensively used by discrete velocity methods since the late 1990s. Here, it is extended to reproduce an arbitrary number of moments of the Maxwell–Boltzmann distribution. These extensions to the standard 5-constraint (mass, momentum and energy) approach lead to the correct simulation of thermal, compressible flows with only 39 discrete velocities in 3D. The stability of this BGK-LBM is reinforced by relying on Knudsen-number-dependent relaxation times that are computed analytically. Hence, high Reynolds-number, supersonic flows can be simulated in an efficient and elegant manner. While the 1D Riemann problem shows the ability of the proposed approach to handle discontinuities in the zero-viscosity limit, the simulation of the supersonic flow past a NACA0012 aerofoil confirms the excellent behaviour of this model in a low-viscosity and supersonic regime. The flow past a sphere is further simulated to investigate the 3D behaviour of our model in the low-viscosity supersonic regime. The proposed model is shown to be substantially more efficient than the previous 5-moment D3Q343 DDF-LBM for both CPU and GPU architectures. It then opens up a whole new world of compressible flow applications that can be realistically tackled with a purely LB approach. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

A new and simple prescription for planet orbital migration and eccentricity damping by planet–disc interactions based on dynamical friction

ABSTRACT During planet formation, gravitational interaction between a planetary embryo and the protoplanetary gas disc causes orbital migration of the planetary embryo, which plays an important role in shaping the final planetary system. While migration sometimes occurs in the supersonic regime, wherein the relative velocity between the planetary embryo and the gas is higher than the sound speed, migration prescriptions proposed thus far describing the planet–disc interaction force and the time-scales of orbital change in the supersonic regime are inconsistent with one another. Here we discuss the details of existing prescriptions in the literature and derive a new simple and intuitive formulation for planet–disc interactions based on dynamical friction, which can be applied in both supersonic and subsonic cases. While the existing prescriptions assume particular disc models, ours include the explicit dependence on the disc parameters; hence, it can be applied to discs with any radial surface density and temperature dependence (except for the local variations with radial scales less than the disc scale height). Our prescription will reduce the uncertainty originating from different literature formulations of planet migration and will be an important tool to study planet accretion processes, especially when studying the formation of close-in low-mass planets that are commonly found in exoplanetary systems.

Shock Reduction through Opposing Jets—Aerodynamic Performance and Flight Stability Perspectives

In this research paper, investigations of counter flow (opposing) jet on the aerodynamic performance, and flight stability characteristics of an airfoil with blunt leading-edge in supersonic regime are performed. Unsteady Reynolds-Averaged Navier-Stokes ( U R A N S ) based solver is used to model the flow field. The effect of angle of attack ( α ), free-stream Mach number ( M ∞ ), and pressure ratio ( P R ) on aerodynamic performance of airfoil with and without jet are compared. The results indicate that the opposing jet reduces drag from 30 % to 70 % , improves the maximum lift-to-drag ratio from 2.5 to 4.0, and increases shock stand-off distance from 15 % to 35 % depending on flow conditions. The effect of opposing jet on longitudinal flight stability characteristics, studied for the first time, indicate improvement in dynamic stability coefficients ( C m q + C m α ˙ ) at low angles of attack. It is concluded that the opposing jet can help mitigate flight disturbances in supersonic regime.

Design of converging-diverging nozzles with constant-radius centerbody

Several flow phenomena, such as recirculating wake flows or noise generation, occur in aerodynamic configurations with backward facing steps. In this context, subsonic nozzles with constant-radius centerbodies exist, which enable fundamental research of these phenomena for $$M < 1$$M<1. For the supersonic regime, however, the existing database and knowledge are limited. Therefore, this work presents a design approach for a converging-diverging nozzle with constant-radius centerbody. For the nozzle throat, Sauer’s method is modified to include a centerbody. The method of characteristics is used for the subsequent supersonic portion. Comparing the analytical calculations to numerical simulations results in very good agreement and therefore underlines the feasibility of the chosen approach. Viscosity reduced the Mach number on the exit plane by 1.0–1.2% and therefore had little influence.

Dynamical friction in slab geometries and accretion discs

ABSTRACT The evolution of planets, stars, and even galaxies is driven, to a large extent, by dynamical friction of gravitational origin. There is now a good understanding of the friction produced by extended media, either collisionless or fluid-like. However, the physics of accretion or protoplanetary discs, for instance, is described by slab-like geometries instead, compact in one spatial direction. Here, we find, for the first time, the gravitational wake due to a massive perturber moving through a slab-like medium, describing e.g. accretion discs with sharp transitions. We show that dynamical friction in such environments can be substantially reduced relatively to spatially extended profiles. Finally, we provide simple and accurate expressions for the gravitational drag force felt by the perturber, in both the subsonic and supersonic regime.