Large Mach Numbers Research Articles

Inverse and direct impedance eduction of liners in the MAINE Flow facility

The assessment of acoustic liners typically involves conducting experiments with airflow in a duct under various incident sound pressure levels and flow velocities. Impedance, as the most intrinsic parameter characterizing an acoustic wall (due to its independence from the duct section), is often the primary focus. Experimental techniques for its determination can be categorized into two classes: direct and inverse eduction methods. This paper contrasts these two methodological classes within the context of the MAINE Flow facility-a 150mm x 280mm rectangular duct capable of generating flow Mach numbers up to 0.63 and multimodal sound fields of Sound Pressure Levels up to 150 dB. Direct impedance determination necessitates a substantial degree of attenuation along the liner. However, in the current implementation, inverse impedance determination is constrained by the uniform flow hypothesis, which is invalid for large Mach numbers in such facilities. The findings illustrate that both methods can yield valuable impedance data, enabling the examination of the effects of flow and incident modal content on the measured impedance.

Classification and wall heat transfer of non-ideal CO2 isothermal laminar boundary layers

The heat transfer properties of non-ideal fluids are crucial in engineering applications. In order to investigate the wall heat transfer characteristics, the self-similar method has been employed to solve supercritical carbon dioxide (SCO2) isothermal laminar boundary layers. The temperature profile regimes are classified into 14 different categories based on their monotonicity and position relative to the pseudo-critical temperature, Tpc. For no trans-Tpc, the boundary layer exhibits subcritical liquid or supercritical vapor, being liquid-like or gas-like region. When free-stream temperature and wall temperature are both lower than Tpc at a large Mach number (Ma), the temperature profile intersects the Tpc twice. In this scenario, the boundary layer is composed of liquid layer, supercritical vapor layer and liquid layer adjacent to the wall, and the wall heat transfer is determined by the thickness of the two bottom layers. At once trans-Tpc, it is seen that the formation of supercritical vapor or liquid film due to pseudo-boiling/condensation plays a key role in the heat transfer deterioration or enhancement. Mainly related to the film thickness and the pseudo-boiling/condensation intensity, the influence of wall temperature and free-stream pressure on the wall heat transfer has been explored by introducing a new dimensionless number Nu*.

A priori tests of turbulence models for compressible flows

PurposeThe purpose of the paper is to analyse the performances of closures and compressibility corrections classically used in turbulence models when applied to highly-compressible turbulent boundary layers (TBLs) over flat plates.Design/methodology/approachA direct numerical simulation (DNS) database of TBLs, covering a wide range of thermodynamic conditions, is presented and exploited to perform a priori analyses of classical and recent closures for turbulent models. The results are systematically compared to the “exact” terms computed from DNS.FindingsThe few compressibility corrections available in the literature are not found to capture DNS data much better than the uncorrected original models, especially at the highest Mach numbers. Turbulent mass and heat fluxes are shown not to follow the classical gradient diffusion model, which was shown instead to provide acceptable results for modelling the vibrational turbulent heat flux.Originality/valueThe main originality of the present paper resides in the DNS database on which the a priori tests are conducted. The database contains some high-enthalpy simulations at large Mach numbers, allowing to test the performances of the turbulence models in the presence of both chemical dissociation and vibrational relaxation processes.

Accelerating the Solution of the Boltzmann Equation by Controlling Contributions to the Collision Integral

A method of reducing the number of arithmetic operations needed to evaluate the Boltzmann collision integral by the conservative projection method is proposed. This is achieved by eliminating the contributions that are less than a certain threshold. An estimate of the maximum magnitude of this threshold is given. For four such thresholds that differ by an order of magnitude from each other, calculations of the flows of rarefied gas at Mach numbers in the range from 0.5 to 10 are carried out, and the results are compared with those obtained using the basic method. In all cases, there is a slight (within a few percent) difference for the highest threshold and almost complete coincidence for the other thresholds. A multiple acceleration of the solution of the Boltzmann equation was obtained, which is most significant for large Mach numbers.

Riemann’s wave and an exact solution of the main turbulence problem

ABSTRACT The paper presents a review of the results that allowed us to find an exact analytical solution to the main problem of the turbulence theory consisting in a closed description of any moments and spectra of all random fields that are described by the Euler hydrodynamic equations for a compressible medium. This solution is based on an exact and explicit analytical solution to n-dimensional Euler equations in the limit of large Mach numbers (S. G. Chefranov, 1991). Based on the Dirac delta function theory, this solution gives an n-dimensional generalization of the well-known implicit Riemann (1860) solution to the one-dimensional Euler equations. In the one-dimensional case, the resulting solution exactly coincides with the explicit form of the Riemann solution for an arbitrary Mach numbers. We have obtained for the first time the exact value of the universal scaling exponent -2/3 for a spectrum of the turbulence energy dissipation rate corresponds to the exact analytical solution to fourth-order two-point moments of the velocity field gradient. We have noted a good agreement between this value and the observational data of turbulence intermittency in the surface atmosphere layer (M. Z. Kholmyansky, 1972) and with the findings of the well-known turbulence intermittency model by Novikov-Stewart (1964).

Ion acoustic solitons at the acoustic speed in a warm negative ion plasma with superthermal electrons

Using the Sagdeev pseudopotential method, the existence of Korteweg–de Vries (KdV) and non-KdV solitons is investigated in a negative ion plasma comprising adiabatic positive and negative ions and kappa distributed electrons. For some plasma parameter values, the plasma model supports the coexistence of solitons of both polarities. Positive KdV solitons coexist with negative non-KdV solitons at low values of negative to positive ion density ratio, and positive non-KdV solitons coexist with negative KdV solitons at higher values. There is therefore a switch in polarity between positive KdV and negative KdV solitons at a critical value of negative to positive ion density ratio and a switch in polarity between negative non-KdV and positive non-KdV solitons at the same point. At the critical point, there is no soliton at the acoustic speed, although there is coexistence at larger Mach numbers. This confirms that the existence of a soliton at acoustic speed is not a necessary condition for the coexistence of solitons of both polarities. When electrons are strongly non-thermal and the ion temperatures are important, the coexistence region vanishes and the non-KdV solitons disappear with it. It was also found that there is a forbidden region in terms of negative (positive) ion temperatures when the negative (positive) ion temperature increases with the other plasma parameters held fixed.

Characteristics of Detonation Propagating in Silane-Nitrous Oxide-Nitrogen Mixtures

ABSTRACT The present study investigated for the first time the characteristic length scale and chemical dynamics of steady and quasi-steady detonation waves propagating in silane-nitrous oxide-nitrogen mixtures, which are widely used in the semi-conductor industry and can be a promising additive for propulsion application. The conditions investigated cover the following ranges: equivalence ratio = 0.5–5; initial pressure = 10–1000 kPa; nitrogen mole fraction = 0–0.8; initial temperature = 300 K. The energy released by the formation of SiO(s) and SiO2(s) was taken into account whereas the phase change from gas to liquid/solid was neglected. It was found that detonation in these silane-based mixtures is characterized by unusually large Mach numbers which result in up to 128.5 times pressure jump across the leading shock, and few micrometer-long induction zone length. For steady planar waves, the shortest induction distances were identified in the range = 2–4, while for curved detonations, the most resilient wave to curvature-induced losses was identified at around 1.5 for undiluted mixtures. Such phenomena are the results of the enhanced formation of SiO(s) under fuel-rich conditions, which also contributes to stabilizing the detonation wave, though the mixture should still be classified as unstable, according to traditional stability parameters. Detailed thermo-chemical analyses were performed to investigate the chemical dynamics. The study of the heat release per reaction shows the dominant contributions of R65: H+N2O=N2+OH, R207: SiH4(+M)=H2+SiH2(+M), R377: N2O+SiH2=H2SiO+N2, R379: N2O+Si=N2+SiO, and R400: 2SiO = 2SiO(s). The dominant reactions for heat release are not modified by the curvature-induced loss according to sensitivity analyses.

Local geometry of a weak normal shock wave interacting with turbulence

The shock surface geometry is investigated with direct numerical simulations of a weak normal shock wave propagating in turbulence. The geometry is quantified with the principal curvatures of the surface. A large part of the surface has an approximately flat saddle shape, while elliptic concave and convex shapes with a large curvature intermittently appear on the shock surface. The pressure–dilatation correlation in the governing equation of pressure is investigated at the shock wave with the decomposition into three terms associated with the velocity gradients in the two directions of the principal curvatures and the normal direction of the shock wave. Fluid expansion in the tangential direction occurs at the shock wave with a convex shape in the direction of the shock propagation, resulting in a smaller pressure jump across the shock wave. For a concave shape, compression in the tangential direction can amplify the pressure jump. Consistently, small and large shock Mach numbers are observed for convex and concave shapes, respectively. The geometric influences are the most significant for elliptic concave and convex shapes with approximately equal curvatures in the two principal directions because the compression or expansion occurs in all tangential directions. These relations between the shock surface geometry and shock Mach number observed in turbulence are consistent with the theory of deformed shock waves, suggesting that the three-dimensional geometrical features of the shock surface are important in the modulation of shock waves due to turbulence.

Planetary Impacts: Scaling of Crater Depth From Subsonic to Supersonic Conditions

AbstractPlanetary impacts have shaped the surfaces and interiors of planets. They were particularly critical in the last stage of planetary accretion, as they have eventually formed terrestrial planets. During these large supersonic collisions, shock waves melted the impactor and the target, and formed silicate magma oceans. Because the propagation of shock waves and the melting is faster than the excavation of an impact crater, the cratering stage can be considered as a purely hydrodynamic process. Here, we use both laboratory impact experiments in water and numerical simulations to investigate the crater dimensions resulting from the impact of a liquid impactor onto a liquid target. We show that our numerical models reproduce the laboratory experiments at subsonic impact velocities. We then explore the effect of both the Froude number, which is the ratio of the impactor kinetic energy to gravity, and the Mach number, which is the ratio of the impact speed to the sound speed. We vary these two parameters independently in impact simulations, going from subsonic to supersonic conditions. We obtain a new scaling law for the crater dimensions that describes the transition from subsonic to supersonic impacts. Our results indicate that the transition between these two regimes results from a change in the partitioning of the impactor kinetic energy into potential energy in the crater and internal energy. Finally, our scaling suggests that, in the limit of large Mach numbers, the crater depth depends only on the sound velocity and gravity, and is independent of the impact speed.

Kelvin–Helmholtz instability at the interface of H ii region and molecular cloud under the influence of ambipolar diffusion: a discontinuous model of the interface

ABSTRACT For typical flow velocities in the interstellar medium (ISM), the Kelvin–Helmholtz instability (KHI) may result in the development of structures in molecular clouds near the interface between the clouds and H ii regions flowing past them (Berné et al. 2010). Ambipolar diffusion (AD) is one of the significant mechanisms considered frequently in the dynamics of molecular clouds. It may play a relevant role in the development of the KHI in the interface of the H ii region and the molecular clouds. Here, we examine the role of AD in the evolution of the KHI, using linear perturbation analysis. We model the interaction of two regions as a planar discontinuity separating two fluids in relative motion. Linear analysis, for a certain range of magnetosonic Mach number of flow ($\mathcal {M}_{sA1}\lt 1$), shows that AD has a destabilizing effect on the KHI and consequently decreases the e-fold time-scale of instability. The results indicate that AD is more effective on the KHI for large magnetosonic Mach numbers than for low magnetosonic Mach numbers. This may give rise to the development of larger numbers of KH structures in high-velocity flows. The results also indicate that AD is more effective for perturbation wavelengths $\lambda _{\rm KH} \ \lt \ 1\rm pc$ than for $\lambda _{\rm KH}\gt 1\rm pc$. This nominates a length-scale ($L=1 \rm \, pc$) above which AD is not important for the formation of KH structures. Conforming to the results, AD is proposed as a triggering factor in the development of the small-scale KH structures in the regions of high-velocity streams in ISM.

Gas Injection and Suction Effect on the Instability of a Supersonic Boundary Layer

We present the results of an investigation of the boundary layer stability on a flat plate having a region of gas injection/suction normal to the wall at a large supersonic freestream Mach number. The laminar flow past a flat plate having a region of distributed injection/suction of fixed intensity is modeled numerically using the integration of Navier—Stokes equations. The unstable disturbances in the boundary layer distorted by injection/suction are analyzed within the framework of the linear stability theory and the eN{{e}^{N}} method for compressible flows. High-frequency disturbances belonging to the plane second mode of the boundary layer, which are the most unstable at high velocities, are considered. It is shown that gas injection/suction leads to a nonmonotonic variation of disturbance growth rates with the appearance of stabilization/destabilization regions, as compared with the case in which injection/suction is absent.

IC 5146 Dark Streamer: The First Reliable Candidate of Edge Collapse, Hub-filament Systems, and Intertwined Sub-filaments

The paper presents an analysis of multiwavelength data of a nearby star-forming site, the IC 5146 dark streamer (d ∼ 600 pc), which has been treated as a single and long filament, fl. Two hub-filament systems (HFSs) are known to exist toward the eastern and the western ends of fl. Earlier published results favor simultaneous evidence of HFSs and end-dominated collapse (EDC) in fl. A Herschel column density map (resolution ∼13.″5) reveals two intertwined sub-filaments (i.e., fl-A and fl-B) toward fl, displaying a nearly double helix-like structure. This picture is also supported by the C18O(3–2) emission. The fray and fragment scenario may explain the origin of intertwined sub-filaments. In the direction of fl, two cloud components around 2 and 4 km s−1 are depicted using 13CO(1–0) and C18O(1–0) emission and are connected in velocity space. The HFSs are spatially found at the overlapping areas of these cloud components and can be explained by the cloud–cloud collision scenario. Nonthermal gas motion in fl with a larger Mach number is found. The magnetic field position angle measured from the filament’s long axis shows a linear trend along the filament. This signature is confirmed in the other nearby EDC filaments, presenting a more quantitative confirmation of the EDC scenario. Based on our observational outcomes, we witness multiple processes operational in the IC 5146 streamer. Overall, the streamer can be recognized as the first reliable candidate for edge collapse, HFSs, and intertwined sub-filaments.

Nonuniform Clearance Effects on Pressure Distribution and Leakage Flow in the Straight-through Labyrinth Seals

Straight-through labyrinth seal is a simple and reliable noncontact seal structure widely used in aeroengines. During the actual operation of aeroengines, the labyrinth seal clearance might experience a nonuniform variation in the flow direction due to asymmetric structure and uneven temperature. In order to characterize the degree of nonuniformity, the nonuniformity coefficient is defined in current paper. The effect of nonuniform causes (rotor deformation or stator deformation), nonuniform type (convergent clearance or divergent clearance), and nonuniformity coefficient (nonuniformity degree) is carefully studied by numerical simulation. Comparative analysis has shown that there is no obvious difference in flow coefficient (less than 0.8% in current studies) between two nonuniform causes. As for nonuniform type, the nonuniformity impact of divergent type on the flow coefficient is more significant than that of convergent type, as a result of stronger axial inertia. Pressure distributions of teeth cavities indicate that the total pressure drop of the divergent type is more obvious than that of the convergent type when the pressure ratio is the same. With the same dimensionless minimum tip clearance, clearance nonuniformity would result in the increase of leakage flow of the straight-through labyrinth, particularly for the condition with small pressure ratio, large circumferential Mach number, and small dimensionless minimum tip clearance. When the nonuniformity coefficient is within the range of -0.1 to 0.1, the variation curves of nonuniformity impact factor versus the nonuniformity coefficient almost coincide (the maximum deviation is no more than 1.2%) under different operation conditions (Reynolds number, pressure ratio, circumferential Mach number, and dimensionless minimum tip clearance). Current work proves it that the effect of seal clearance nonuniformity on the leakage flow requires special attention for the refined design of aeroengines.

Compressible modification of boundary-layer momentum thickness localized method in transition model

In current transition models, Menter’s correlation between the maximum vorticity Reynolds number Revmax in the boundary layer and momentum thickness Reynolds number Reθ has been widely used in the localization of the boundary layer length scale. However, the existing correlations have problems in correctly reflecting compressibility effects and only relying on local variables. In this paper, the similarity solutions of laminar compressible boundary layer equations are adopted to study the relation between Revmax and Reθ. Through extracting the local Mach number Malocal and the ratio of wall temperature to the local temperature Tw/Tlocal right at the position where Revmax happens, the influences of the Mach number effect and wall heat transfer effect are characterized, meanwhile a new correlation only relying on local variables between Revmax and Reθ is proposed. For plat-plate boundary layers, the relative error is tiny within a large Mach number and wall-to-adiabatic temperature ratio range and the error caused by the streamwise pressure gradient is not of great concern for general pressure gradients. Furthermore, numerical results over common geometries, including wedges, sharp cones and blunt cones, demonstrate that the proposed correlation could give much better predictions of the relation between Revmax and Reθ than previous correlations. At last, the present correlation is applied to the γ-Reθ transition model as an application presentation.

Wind‐Enhanced Hydrogen Escape on Mars

AbstractHydrogen escape is a metric of water loss on Mars, which controls the long‐term evolution of the planet. While the Jeans formulism has been traditionally used to evaluate hydrogen escape on Mars, here we propose that this escape could be significantly enhanced by horizontal winds near the exobase. The enhancement reaches 20% for H and 100% for H2, and presents solar cycle, seasonal, and diurnal variations well correlated with the variations of the horizontal wind velocity. Physically, the enhancement is driven by the departure of the particle velocity distribution from ideal Maxwellian and is critically controlled by the Mach number as the ratio of the horizontal wind velocity to the thermal velocity. A larger Mach number (due to a larger wind velocity, a lower temperature, a larger particle mass, or any combination of the three) implies a stronger degree of departure and consequently more enhanced escape over the Jeans case.

Mathematical model and method of solving the generalized Dirichle problem of heat exchange of a cut count

The choice of thermal protection of the rocket fairing is approached with special care, because the fairing must protect against aerodynamic heating, radiation, temperature changes. Currents with large Mach numbers are accompanied by gas-dynamic and physicochemical effects. When flowing around the blunt body, a shock wave is formed, which departs from the body, remaining in the vicinity of the frontal point almost equidistant to its surface. Physico-chemical effects are due to rising temperatures caused by the inhibition of gas by the shock wave. At the same time there is a transition of kinetic energy of a stream rushing in thermal, fluctuating degrees of freedoms of gas molecules are excited, its dissociation and even ionization begins. Therefore, among the problems of great theoretical and practical interest is the problem of studying the temperature fields arising in the fairings for missiles in the form of a truncated cone, which rotate around its axis, given the finiteness of the rate of heat propagation. In the article the mathematical model of calculation of temperature fields for a truncated cone is constructed for the first time which approximately models distribution of temperature fields which arise in fairings for rockets, with taking into account the angular velocity and the final speed heat distribution in the form of a boundary value problem of mathematical physics for hyperbolic equation of thermal conduc-tivity with boundary conditions Dirichlet. A new integral transformation for a two-dimensional finite space is constructed, in the application of which the temperature field in the form of a convergent series is found. The solution found can be used to predict the possible value of thermomechanical stresses, to promote the correct choice of technological parameters, objective control, allows to identify ways to improve the thermal protection of fairings for missiles.

Analytic Solution to the Dynamical Friction Acting on Circularly Moving Perturbers

Abstract We present an analytic approach to the dynamical friction (DF) acting on a circularly moving point mass perturber in a gaseous medium. We demonstrate that, when the perturber is turned on at t = 0, steady state (infinite time perturbation) is achieved after exactly one sound-crossing time. At low Mach numbers  ≪ 1 , the circular-motion steady-state DF converges to the linear-motion, finite time perturbation expression. The analytic results describe both the radial and tangential forces on the perturbers caused by the backreaction of the wake propagating in the medium. The radial force is directed inward, toward the motion center, and is dominant at large Mach numbers. For subsonic motion, this component is negligible. For moderate and low Mach numbers, the tangential force is stronger and opposes the motion of the perturber. The analytic solution to the circular-orbit DF suffers from a logarithmic divergence in the supersonic regime. This divergence appears at short distances from the perturber solely (unlike the linear-motion result, which is also divergent at large distances) and can be encoded in a maximum multipole. This is helpful to assess the resolution dependence of numerical simulations implementing DF at the level of Liénard–Wiechert potentials. We also show how our approach can be generalized to calculate the DF acting on a compact circular binary.

A new many-objective aerodynamic optimization method for symmetrical elliptic airfoils by PSO and direct-manipulation-based parametric mesh deformation

A new many-objective aerodynamic optimization method is proposed to design the distinctive symmetrical elliptic airfoil applied on the canard rotor wing aircraft with special requirements on both low drag in different Mach numbers and large drag divergence Mach number. A parameterized direct manipulation of free form deformation (DFFD) method is proposed to realize the one-step process on geometry parameterization and mesh deformation. Then an efficient multi and many-objective particle swarm optimization algorithm (LMPSO) is built to optimize the symmetrical elliptic airfoil to comprehensively improve its aerodynamics. The biobjective optimization of drag reductions at hover stage and at cruise flight shows that the new method can significantly reduce the drag of the elliptic airfoil but at the cost of drag increases at high angles of attack. The four-objective optimization results indicate that the consideration of the high angle of attack flight conditions can improve the aerodynamic performance of the airfoil over a large lift range, which is more practical in engineering application. The five-objective optimization presents that the maximization of the drag divergence Mach number of the elliptic airfoil can be significantly promoted when adding three more design conditions at high Mach number. In general, the optimization results demonstrate that the developed new method can effectively improve the aerodynamic performance of symmetrical elliptic airfoils and provide support on the development of the canard rotor wing aircraft.

Active control behavior on the flow pattern in a circular duct

The current analysis aims to review the effectiveness of the flow regulations at Mach 1.87, a considerably large Mach number. The duct radius is11 mm, and the diameter ratio concerning the exit of the nozzle is 2.2. Tests were done at different expansion levels for eight different duct sizes. Here we are pondering in a situation where there is a considerable variation of pressure is noticed. The flow control was located at a PCD of 13 mm from the axis. The control jets of 0.001 m diameter producing a Mach unity jet, used as energetic flow control. For shorter tube sections at smaller NPRs, the pressure undertakes a minimal value. Soon After, with an increase of the tube size and expansion levels, a continuing fall in pressure owing to the decline in the level of adverse pressure and shock waves intensity. Flow fluctuations are witnessed for various duct sizes. The duct size represents a vital part while ascertaining the flow advancement in the duct. Relatively high pressure is seen for duct length L = 132 mm and L = 220 mm for nozzle pressure ratios three and five. The pressure becomes modest due to the effect of duct size. For NPR = 7, an increase in pressure is restricted by the separated zone, and atmospheric restrictions are almost accomplished. For the 10D duct, the realization of the ambient condition is additionally enhanced near the upstream.

Shock Properties and Associated Characteristics of Solar Energetic Particles in the 2017 September 10 Ground-level Enhancement Event

Abstract The solar eruption on 2017 September 10 was accompanied by a fast coronal mass ejection (∼3000 km s−1) and produced a ground-level enhancement (GLE) event at Earth. Multiple-viewpoint remote sensing observations are used to find the three-dimensional (3D) structure of the shock. We determine the shock parameters by combining the 3D shock kinematics and the solar wind properties obtained from a global magnetohydrodynamic (MHD) simulation, in order to compare them with the characteristics of the solar energetic particles (SEPs). We extract the magnetic connectivities of the observers from the MHD simulation and find that L1 was magnetically connected to the shock flank (rather than the nose). Further analysis shows that this shock flank propagates through the heliospheric current sheet (HCS). The weak magnetic field and relatively dense plasma around the HCS result in a large Mach number of the shock, which leads to efficient particle acceleration even at the shock flank. We conclude that the interaction between the shock and HCS provides a potential mechanism for production of the GLE event. The comparison between the shock properties and the characteristics of SEPs suggests an efficient particle acceleration in a wide spatial range by the shock propagating through the highly inhomogeneous coronal medium.