Shock Standoff Research Articles

Nozzle Flow Characterization of the SNU Hypersonic Shock Tunnel

AbstractThis paper presents the operational capabilities and the characteristics of the nozzle flow of the Seoul National University Hypersonic Shock Tunnel (SHyST), a recently added impulse facility designed to produce high-enthalpy flows reaching up to 5 MJ/kg through hypersonic contoured nozzles. Within this investigation, emphasis is placed on the design and utilization of a pitot rake, serving as an essential instrument for quantifying pitot pressure and Mach number distributions throughout the test section. The experimental results confirm the presence of axis-symmetric behavior and spatial–temporal uniformity of the freestream Mach number at the nozzle outlet and along the test section. In addition, the study demonstrates a good agreement with the predictions of numerical simulation. Mach number validation is further supported by the measurement of shock standoff distance through schlieren visualization.

Effect of multi-temperature models on heat transfer and electron behavior in hypersonic flows

In hypersonic computational fluid dynamics, the two-temperature (2-T) model is widely used to simulate thermochemical nonequilibrium. The 2-T model incorporates translational-rotational and electron-electronic-vibrational energies, assuming that the integrated energies have the equivalent temperature. In this study, multi-T models are constructed to accurately predict the effects on heat flux and free electrons due to the separation of energy modes under hypersonic environments. The three-temperature (3-T) model separates the electron-electronic energy from the electron-electronic-vibrational energy of the 2-T model. The 3-T model can accurately predict the distribution and temperature of free electrons by separating the energy of free electrons, which has different characteristics from heavy particles. The four-temperature model treats rotational energy as a nonequilibrium energy mode, distinct from translational-rotational energy. While the rotational temperature reaches equilibrium rapidly at low temperatures, at high-temperature regime rotational temperature shows a relaxation time similar to that of vibrational temperature, which cannot be ignored. To develop multi-T models, electron-vibrational relaxation and translational-rotational relaxation, which are omitted in the 2-T model, are considered. Various flight test and ground facility conditions are analyzed to verify the effects of electron and heat flux under circumstances that include shock, expansion, and shock wave boundary layer interaction. The results of the multi-T models show significant differences in electron temperature and distribution caused by electron-electronic nonequilibrium. Additionally, rotational nonequilibrium increases the shock standoff distance and alters the electron distribution at high altitudes. The heat flux difference across multi-T models is found to be negligible, except in the high degree of ionization condition.

Unsteady Standoff Shock Behaviour Associated With Supersonic Impinging Jets

It was observed in an earlier study [Lim, H. D., New, T. H., Mariani, R., & Cui, Y. D. (2019). Effects of bevelled nozzles on standoff shocks in supersonic impinging jets. Aerospace Science and Technology, 94, 105371.] that standoff shocks in M=1.45 supersonic impinging jets produced by non-bevelled and bevelled nozzles under small separation distances may undergo large and abrupt fluctuations in their positions above the impingement points. This occurs when the separation distance is h/d=1.5 and for nozzle-pressure-ratio (NPR) between NPR=4 and 5, where h is the distance between the nozzle exit and flat-wall and d is the jet diameter. It has to be highlighted that the observed behaviour is unlike the more minor positional fluctuations typically associated with supersonic impinging jets. To reveal further details on the unsteadiness of the standoff shock, color schlieren results will be presented here to shed more light on the flow phenomenon, while initial modelling efforts to reproduce these standoff shock behaviour will be elaborated. Present results reinforce the notion that the large standoff shock fluctuations are due to the standoff shock trying to achieve pressure equilibrium through abrupt displacements when variation in the NPR changes the location of the shock reflection point. Considering the small separation distance used, small NPR changes are able to trigger abrupt standoff shock unsteadiness.

Large-Eddy Simulations of a Supersonic Impinging Jet Using OpenFOAM

Supersonic impinging jets are a versatile configuration that can model the compressible flows of cold-spray manufacturing and vertical take-off-and landing strategy. In this work, rhoCentralFoam, solver of the OpenFOAM framework, and a large-eddy simulation formulation were used to simulate an underexpanded supersonic jet of Mach 1.45 and nozzle pressure ratio of 4, impinging on a flat wall situated at 1.5 nozzle diameters away from the jet outlet. Care was taken in the mesh construction to properly capture the characteristic standoff shock and vortical structures. The grid convergence index was evaluated with three meshes of increasing spatial resolution. All meshes can generally be considered as sufficient in terms of results focused on time-averaged values and mean physical properties such as centerline Mach number profile. However, the highest resolution mesh was found to capture fine shear vortical structures and behaviors that are absent in the coarser cases. Therefore, the notion of adequate grid convergence may differ between analyses of time-averaged and transient information, and so should be determined by the user’s intention for conducting the simulations. To guide the selection of mesh resolution, scaling analyses were performed, for which the current rhoCentralFoam solver displays a good weak scaling performance and maintains a linear strong scaling up to 4096 cores (32 nodes) for an approximately 40 million-cell mesh. Due to the internode communication bottlenecks of OpenFOAM and improvements in central processing units, this work recommends, for future scaling analyses, adopting a “cells-per-node” basis over the conventional “cells-per-core” basis, with particular attention to the interconnect speed and architecture used.

Deep learning-based prediction of CME-driven shock standoff distances in metric type II radio emissions

Deep learning-based prediction of CME-driven shock standoff distances in metric type II radio emissions

Experimental studies on the Hartmann tube

Abstract The effect of tube depth, the separation distance between the tube and nozzle exit, and the nozzle pressure ratio on the characteristics of the flow coming out of the Hartmann tube was studied experimentally. The configuration used in this work consists of an underexpanded sonic jet emanating from a convergent nozzle directed into a closed-ended cylindrical tube of the same diameter (D) as the nozzle exit. The nozzle was operated at two levels of underexpansion corresponding to nozzle pressure ratio (NPR) 3 and 5. The distance (S) from nozzle exit and tube inlet was varied from 0.4D to 4D. Discrete high-amplitude tones (the jet regurgitant, JRG) were produced, only at certain (periodic) intervals (near the shock-cell terminations) of spacing for NPR 3, while for NPR 5 the JRG tones are produced at all points beyond the first shock-cell. For locations other than these, high-frequency tones (screech mode) were observed. The connection between the jet structure and operating modes revealed that the location of standoff shock ahead of the tube with respect to the jet structure plays a dominant role in the observed ‘modes’ rather than the nozzle tube separation. The results reveal that the frequency response of longer tubes in JRG mode approaches their quarter wave frequencies. The high-frequency oscillations observed in the screech mode showed independency with cavity (pipe) depth, contrary to the available literature, the transition between ‘different modes’ oscillation is a function of cavity depth.

In situ plasma and neutral gas observation time windows during a comet flyby: Application to the Comet Interceptor mission

A comet flyby, like the one planned for ESA’s Comet Interceptor mission, places stringent requirements on spacecraft resources. To plan the time line of in situ plasma and neutral gas observations during the flyby, the size of the comet magnetosphere and neutral coma must be estimated well. For given solar irradiance and solar wind conditions, comet composition, and neutral gas expansion speed, the size of gas coma and magnetosphere during the flyby can be estimated from the gas production rate and the flyby geometry. Combined with flyby velocity, the time spent in these regions can be inferred and a data acquisition plan can be elaborated for each instrument, compatible with the limited data storage capacity. The sizes of magnetosphere and gas coma are found from a statistical analysis based on the probability distributions of gas production rate, flyby velocity, and solar wind conditions. The size of the magnetosphere as measured by bow shock standoff distance is 105–106km near 1au in the unlikely case of a Halley-type target comet, down to a nonexistent bow shock for targets with low activity. This translates into durations up to 103–104 seconds. These estimates can be narrowed down when a target is identified far from the Sun, and even more so as its activity can be predicted more reliably closer to the Sun. Plasma and neutral gas instruments on the Comet Interceptor main spacecraft can monitor the entire flyby by using an adaptive data acquisition strategy in the context of a record-and-playback scenario. For probes released from the main spacecraft, the inter-satellite communication link limits the data return. For a slow flyby of an active comet, the probes may not yet be released during the inbound bow shock crossing.

Influence of magnetohydrodynamics configuration on aerothermodynamics during Martian reentry

This paper investigates the role of magnetohydrodynamics (MHD) on the aerothermodynamics (ATD) of a representative entry vehicle while flying into the Martian atmosphere. By strategically placing a flight-ready superconducting magnet at varied positions in the Schiaparelli reentry capsule of the ExoMars mission, we discern its impact on essential flow properties. The primary consequence of MHD during atmospheric entry is the generation of the Lorentz force, which increases the shock standoff distance resulting in a reduction of the heat flux on the spacecraft by pushing high-energy plasma particles away. Through different magnet configurations, three distinct cases are formed to comprehensively understand the effects and implications of each setup. The study is performed using the COOLFluiD MHD for EnTries, an in-house ATD solver. For case 1, the magnet's placement behind the ExoMars forebody at the stagnation point reduces the heat flux. In case 2, the magnet's relocation to the shoulder region explores its potential to mitigate communication blackouts by influencing the wake region's flow. However, this positioning also induces shock bending, leading to variations in post-shock species mass fractions and heat flux spikes in the post-shock region. Case 3, involving an additional magnet where the shock bends in case 1, showcases a consistent increase in shock standoff distance across the forebody, providing a longer relaxation zone for species equilibration. Our findings highlight that while the strength of the applied magnetic field is crucial, the magnet's size is equally pivotal in determining ATD behavior. Case 3 emerges as the most promising configuration, consistently reducing heat flux across the forebody and maintaining it in the afterbody. This study underscores the potential of multi-magnet configurations as next-generation MHD heat shields for Martian atmospheric entry, emphasizing the criticality of magnet placement and configuration in enabling future MHD-enhanced deep space exploration missions.

Mercury’s Bow Shock and Magnetopause Variations According to MESSENGER Data

Using data from the MESSENGER spacecraft magnetometer that describes the magnetopause and the bow shock crossing points of the Mercury’s magnetosphere, we have calculated the parameters of the paraboloids of revolution approximating the obtained points. For each spacecraft orbit, the subsolar magnetopause and bow shock standoff distances were obtained, based on the paraboloid parameters for each crossing point. The dependences of the magnetopause and bow shock subsolar standoff distances on the Mercury’s position relative to the Sun have been obtained. These profiles agree with decreases of the solar wind plasma dynamic pressure and the interplanetary magnetic field strength with heliocentric distance. The variations of the interplanetary and magnetosheath magnetic field were investigated. The average subsolar magnetosheath thickness and the value of the magnetic field jump at the bow shock during the transition from the upstream interplanetary magnetic field region to the magnetosheath were obtained.

A Spectral/hp-Based Stabilized Solver with Emphasis on the Euler Equations

The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries.

Hypersonic flow study in a pneumatically operated academic shock tunnel.

A hypersonic shock tunnel is a primary tool used for basic experimental research and may be used in engineering and university courses to study compressible flows involving shock waves. In the present study, a pneumatically operated shock tunnel is demonstrated for hypersonic flow studies. The high-pressure nitrogen gas is used to drive a pneumatic cylinder, which is used to burst the thin metal diaphragms. Tunnel-free stream conditions are quantified using the measured pressure values and by applying shock tube relations. The free-stream Mach number of 5.5-7.2 is achieved by varying the bursting pressure and test gas pressure from 2.1 to 4.5 bars and 0.2 to 0.5bar, respectively. The simulation is performed and the shock standoff distance quantified, and the stagnation pressures measured. The results demonstrate that the pneumatically operated tunnel enhanced operation capacity compared to the manually operated tunnel and well suits the academic hypersonic research and developmental activities.

Heat transfer investigation on under-expanded supersonic impinging jets

In this study, wall-resolved large-eddy simulations are performed to investigate the underpinning physics of impingement heat transfer in under-expanded supersonic impinging jets. The jet is generated with an infinite-lipped nozzle of diameter D, has a nozzle-to-wall distance of 5D, a nozzle pressure ratio (NPR) of 3.4 and a Reynolds number of 6×104 based on the ideally-expanded jet velocity. Two thermal boundary conditions of a heated isothermal wall and an adiabatic wall for the impingement plate are considered.Both impinging jets in the current study feature a strong stand-off shock, which oscillates periodically in front of the impingement plate at two dominant frequencies. These oscillations result in two local peaks of the mean heat transfer coefficients with the first peak located in the stagnation region but shifted away from the stagnation point (i.e. jet axis), whilst the second peak is located in the wall jet region. The instantaneous fields of pressure, vorticity and Nusselt number are first discussed to study qualitatively the connection between these two peaks of the mean heat transfer coefficient and the near-wall flow structures. The characteristics of these two peaks are then analysed using the near-wall statistics and spectra of the pressure, axial velocity and Nusselt number distribution.It is found that the first peak of the Nusselt number forms as a consequence of the jet impingement of the non-periodic turbulent structures, whilst the second peak is linked to the reattachment of the recirculation bubble in the wall jet. It is shown that the unsteady separation and reattachment processes are strongly related to the oscillatory motion of the stand-off shock at the dominant frequencies. Last but not the least, the first local minimum close to the stagnation point is also found to be associated with the strong oscillatory behaviour of the stand-off shock.

A quasi-one-dimensional model for the stagnation streamline in hypersonic magnetohydrodynamic flows

The flow near the stagnation streamline of a blunt body is often attracted and analyzed by using the approximation of local similarity, which reduces the equations of motion to a system of ordinary differential equations. To efficiently calculate the stagnation-streamline parameters in hypersonic magnetohydrodynamic (MHD) flows, an improved quasi-one-dimensional model for MHD flows is developed in the present paper. The Lorentz force is first incorporated into the original dimensionally reduced Navier–Stokes equations to compensate for its effect. Detailed comparisons about the shock standoff distance and the stagnation point heat flux are conducted with the two-dimensional Navier–Stokes calculations for flows around the orbital reentry experiment model, including gas flows in thermochemical nonequilibrium under different magnetic field strengths. Results show that the shock curvature should be considered in the quasi-one-dimensional model to prevent accuracy reduction due to the deviation from the local similarity assumption, particularly for hypersonic MHD flows, where the shock standoff distance will increase with larger magnetic strength. Then, the shock curvature parameter is introduced to compensate for the shock curvature effect. A good agreement between the improved quasi-one-dimensional and the two-dimensional full-field simulations is achieved, indicating that the proposed model enables an efficient and reliable evaluation of stagnation-streamline quantities under hypersonic MHD flows.

Numerical study of flow over blunt bodies moving at supersonic speed

In the present study, shock waves produced over different blunt bodies moving at Mach 2.0 at zero angle of attack have been captured and analysed using computational investigations. Forebodies of distinct bluntness (hemisphere, ellipse, and ogive) are adopted, and the effect of the forebody geometry on the flow parameters is investigated. The flow parameters such as shock stand-off distance and shock strength have been captured over various forebody geometries and correlated with the forebody drag coefficient. With the reduction in the forebody bluntness, the shock stand-off distance and the shock strength are found to be decreasing, resulting in a decrease in the forebody drag coefficient values. The effect of the free-stream supersonic Mach number over a typical blunt body (hemisphere) was also investigated. With increasing freestream Mach number, the shock wave generated ahead the blunt hemisphere moved closer to the forebody and an increase in the forebody drag was observed.

Stagnation heat flux estimation in spherically blunt axisymmetric hypersonic models

Hypersonic flows have high heat transfer rates, and their management is essential to avoid detrimental effects. Since accurate prediction and measurement of heat flux in hypersonic test facilities are complicated, heat flux at the stagnation point is mostly estimated using Fay and Riddell formulation with Newtonian tangential velocity gradient approximation. Although it is relatively accurate and reliable, some errors creep in due to incompetent modelling of the tangential velocity gradient. This article studies the applicability of Olivier's tangential velocity gradient formulation for a sphere in the estimation of stagnation heat flux for spherically blunt axisymmetric hypersonic models. Oliver’s estimation accurately models the tangential velocity gradient of spherically blunt axisymmetric hypersonic models as the heat flux estimates deviated only by approx. 2%–4% from the measured heat flux. A simplified model for tangential velocity gradient using Shock Standoff Distance and density ratio is also derived and tested for accuracy.

Magnetospheric responses to solar wind Pc5 density fluctuations: Results from 2D hybrid Vlasov simulation

Ultra-low frequency (ULF) waves are routinely observed in Earth’s dayside magnetosphere. Here we investigate the influence of externally-driven density variations in the near-Earth space in the ULF regime using global 2D simulations performed with the hybrid-Vlasov model Vlasiator. With the new time-varying boundary setup, we introduce a monochromatic Pc5 range periodic density variation in the solar wind. A breathing motion of the magnetopause and changes in the bow shock standoff position are caused by the density variation, the time lag between which is found to be consistent with propagation at fast magnetohydrodynamic speed. The oscillations also create large-scale stripes of variations in the magnetosheath and modulate the mirror and electromagnetic ion cyclotron modes. We characterize the spatial-temporal properties of ULF waves at different phases of the variation. Less prominent EMIC and mirror mode wave activities near the center of magnetosheath are observed with decreasing upstream Mach number. The EMIC wave occurrence is strongly related to pressure anisotropy and β‖, both vary as a function of the upstream conditions, whereas the mirror mode occurrence is highly influenced by fast waves generated from upstream density variations.

Simulation of high-Mach-number inviscid flows using a third-order Runge-Kutta and fifth-order WENO-based finite-difference lattice Boltzmann method

A discrete-velocity Boltzmann equation(DVBE) with Bhatnagar-Gross-Krook (BGK) approximation is discretized in time and space using a third-order Runge-Kutta (RK3) and fifth-order weighted essentially nonoscillatory (WENO) finite-difference scheme to simulate benchmark inviscid compressible flows. The implementation of the WENO ensures that solutions behave with minimal or no oscillations, narrowing the gap between the exact and the numerical results. Discrete-velocity sets given by Kataoka and Tsutahara [Phys. Rev. E 69, 056702 (2004)10.1103/PhysRevE.69.056702] are used. The additional dissipation terms as well as artificial viscosity are incorporated in the formulation to solve the compressible flows at high Mach number. Further, the flows which are subjected initially to a high density ratio are effectively simulated. In this article, one-dimensional benchmarks are simulated at initial Mach number up to 30 and density ratio up to 1000, whereas, the benchmarks in two dimensions are simulated with a Mach number up to 10. The algorithm is assessed by simulating numerous benchmarks, namely, (i) one-dimensional Riemann problem for various shock waves combinations [namely (a) shock-shock waves in the case of different Mach numbers, (b) rarefaction-shock waves for various density ratios, (c) sudden contact shock discontinuity, and (d) shock-rarefaction waves for density ratio 5], (ii) isentropic vortex convection test, (iii) regular shock reflection (RR) for Mach numbers 2.9 and 10, (iv) double Mach reflection (DMR) for inflow Mach numbers as 6 and 10, and (v) forward-facing step for inflow Mach numbers 2 to 5. Further, the effect of change in Mach numbers and wedge angles on the flow structures in the case of DMR are detailed. In the case of a forward-facing step, the variations of flow structure (e.g., the Mach stem height, triple points location, and shock standoff distance) are detailed with respect to Mach number, step height, and specific-heat ratios. Finally, the numerical stability of the proposed formulation is carried out to assess the behavior of the free parameters.

Experimental Investigation of Flow Interaction Dynamics in Supersonic Retropropulsion

Supersonic retropropulsion experiments were performed using a 12.7-cm-diameter 70 deg sphere–cone body with a single jet in the center of the model with a 4:1-area-ratio Laval nozzle directed into a Mach 4 freestream. Data were acquired using high-speed schlieren imaging and direct axial force measurements. Spectral analyses of the total axial force, jet total pressure, and bow shock standoff distance were performed, resulting in the observation of three characteristic modes. For all tests, a dominant frequency in the axial force, independent of the jet and tunnel flow, of 1.9 kHz was observed, which was determined to be a structural vibration mode. A mode at 4.2 kHz in the axial force is observed to correspond to the motion of flow structures, suggesting a coupling between the jet flow and the freestream. A dependency on the presence of the jet and the selection of jet gas is shown for a 13.7 kHz mode, indicating it is acoustic in nature. Proper orthogonal decomposition on the schlieren image data is used to show that the flowfield structures in which dominant modes manifest are dependent on the thrust coefficient.

Magnetohydrodynamic Experiments of Total Heat Flux Mitigation for Superorbital Earth Reentry

A set of experiments was conducted with the aim of evaluating total heat flux mitigation using magnetohydrodynamic flow control over ionized shock layers surrounding planetary entry vehicles. The University of Queensland’s X2 expansion tube was used to generate a flow condition representative of a Mars return trajectory. Spherical permanent magnets were fitted into a scaled test model based on NASA’s Stardust capsule. Thermocouples located at the stagnation point and shoulder of the test model, as well as thin-film heat transfer gauges located in the aft section, measured total heat flux for both magnetic and nonmagnetic experiments. High-speed imaging of the shock layer showed a significant increase in shock standoff when using the magnet, and polynomial fits were derived, describing standoff distance along the model’s forebody. Despite significant noise affecting the heat flux gauges signals for the magnetic experiments, a simple methodology allowed to compare heat flux during the useful test time. It was found that the applied magnetic field significantly reduces total heat flux at the stagnation point and shoulder of the test model, although heat flux to the aft section was found to significantly increase. Reasonable agreement with the numerical predictions was found for the aft section of the test model, but discrepancies were observed at the other locations.

Computational Fluid Dynamics Analysis and Design of Payload Shroud of Satellite Launch Vehicle

The main focus of the present paper is to computational fluid dynamics analysis and design of payload fairing of satellite launch vehicle at freestream Mach number range of 0.6 - 3.0. Initially, time-dependent compressible three-dimensional Euler equations are solved employing a finite volume discretization method with a multi-stage Runge-Kutta time-stepping scheme to compute surface pressure and aerodynamic coefficients at various payload fairing and at angle of attack up to 5o with an increment of 1o. Payload fairing dimensions are selected that satisfies permissible structure load on satellite launch vehicle. Detailed flowfield simulation is carried out on the selected payload fairing employing axisymmetric compressible Reynolds-average Navier-Stokes equations to assess unsteady flowfield characteristics. The numerical simulations are used to locate terminal shock on the payload fairing at transonic Mach number. Unsteady flow characteristics are used to compute acoustic load. Shock standoff distances at supersonic speeds are tabulated and compared with the analytical solution. Schlieren images and oil flow pictures are compared with experimental results and in good agreement. Aerodynamic shape optimization of satellite launch vehicle payload fairing shape has been performed to satisfy structural load at maximum drag and dynamic pressure.