Mach Number Dependence Research Articles

Morphology and Mach Number Dependence of Subsonic Bondi–Hoyle Accretion

Abstract We carry out three-dimensional computations of the accretion rate onto an object (of size R sink and mass m) as it moves through a uniform medium at a subsonic speed v ∞. The object is treated as a fully absorbing boundary (e.g., a black hole). In contrast to early conjectures, we show that for an accretor with R sink ≪ R A = 2 Gm / v ∞ 2 in a gaseous medium with adiabatic index γ = 5/3, the accretion rate is independent of Mach number and is determined only by m and the gas entropy. Our numerical simulations are conducted using two different numerical schemes via the Athena++ and Arepo hydrodynamics solvers, which reach nearly identical steady-state solutions. We find that pressure gradients generated by the isentropic compression of the flow near the accretor are sufficient to suspend much of the surrounding gas in a near-hydrostatic equilibrium, just as predicted from the spherical Bondi–Hoyle calculation. Indeed, the accretion rates for steady flow match the Bondi–Hoyle rate, and are indicative of isentropic flow for subsonic motion where no shocks occur. We also find that the accretion drag may be predicted using the Safronov number, Θ = R A /R sink, and is much less than the dynamical friction for sufficiently small accretors (R sink ≪ R A ).

Gas Dynamical Friction on Accreting Objects

The drag force experienced by astronomical objects moving through gaseous media (gas dynamical friction) plays a crucial role in their orbital evolution. Ostriker derived a formula for gas dynamical friction by linear analysis, and its validity has been confirmed through subsequent numerical simulations. However, the effect of gas accretion onto the objects on the dynamical friction is yet to be understood. In this study, we investigate the Mach number dependence of dynamical friction considering gas accretion through three-dimensional nested-grid simulations. We find that the net frictional force, determined by the sum of the gravitational force exerted by surrounding gas and momentum flux transferred by accreting gas, is independent of the resolution of simulations. Only the gas outside the Bondi–Hoyle–Lyttleton radius contributes to dynamical friction, because the gas inside this radius is eventually absorbed by the central object and returns the momentum obtained through the gravitational interaction with it. In the subsonic case, the front–back asymmetry induced by gas accretion leads to larger dynamical friction than predicted by the linear theory. Conversely, in the slightly supersonic case with a Mach number between 1 and 1.5, the nonlinear effect leads to a modification of the density distribution in a way that reduces the dynamical friction, compared with the linear theory. At a higher Mach number, the modification becomes insignificant and the dynamical friction can be estimated with the linear theory. We also provide a fitting formula for dynamical friction based on our simulations, which can be used in a variety of applications.

Hybrid large eddy simulation and Lagrangian simulation of a compressible turbulent planar jet with a chemical reaction

AbstractLarge eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is applied to investigate high‐speed turbulent reacting flows. Here, LES solves a velocity field while LPS solves scalar transport equations with notional particles. Although LPS does not require sub‐grid scale models for chemical source terms, molecular diffusion has to be modeled by a so‐called mixing model, for which a mixing volume model (MVM), that is originally proposed for an inert scalar in incompressible flow, is extended to reactive scalars in compressible flows. The extended model is based on a relaxation process toward the average of nearby notional particles and assumes a common mixing timescale for all species. LES/LPS with the MVM is applied to a temporally‐evolving compressible turbulent planar jet with an isothermal reaction and is tested by comparing the results with direct numerical simulation (DNS). The results show that LES/LPS well predicts the statistics of mass fractions. As the jet Mach number increases, the reaction progress delays due to the delayed jet development. This Mach number dependence is also well reproduced in LES/LPS. The mean molecular diffusion term of the product calculated as a function of its mass fraction also agrees well between LES/LPS and DNS. An important parameter for the MVM is the distance among particles, for which the requirement for accurate prediction is presented for the present test case. LES/LPS with the MVM is expected to be a promising method for investigating compressible turbulent reactive flows at a moderate computational cost.

Ideal and non-ideal planar compressible fluid flows in radial equilibrium

Two-dimensional compressible flows in radial equilibrium are investigated in the ideal dilute-gas regime and the non-ideal single-phase regime close to the liquid–vapour saturation curve and the critical point. Radial equilibrium flows along constant-curvature streamlines are considered. All properties are therefore independent of the tangential streamwise coordinate. A differential relation for the Mach number dependency on the radius is derived for both ideal and non-ideal conditions. For ideal flows, the differential relation is integrated analytically. Assuming a constant specific heat ratio $\gamma$ , the Mach number is a monotonically decreasing function of the radius of curvature for ideal flows, with $\gamma$ being the only fluid-dependent parameter. In non-ideal conditions, the Mach number profile also depends on the total thermodynamic conditions of the fluid. For high molecular complexity fluids, such as toluene or hexamethyldisiloxane, a non-monotone Mach number profile is admissible in single-phase supersonic conditions. For Bethe–Zel'dovich–Thompson fluids, non-monotone behaviour is observed in subsonic conditions. Numerical simulations of subsonic and supersonic turning flows are carried out using the streamline curvature method and the computational fluid dynamics software SU2, respectively, both confirming the flow evolution from uniform flow conditions to the radial equilibrium profile predicted by the theory.

Aeroacoustic testing on a full aircraft model at high Reynolds numbers in the European Transonic Windtunnel

This paper presents an end-to-end approach for the assessment of pressurized and cryogenic wind tunnel measurements of an EMBRAER scaled full model close to real-world Reynolds numbers. The choice of microphones, measurement parameters, the design of the array, and the selection of flow parameters are discussed. Different wind tunnel conditions are proposed which allow separating the influence of the Reynolds number from the Mach number, as well as the influence of slotted and closed test sections. The paper provides three-dimensional beamforming results with CLEAN-SC deconvolution, the selection of regions of interest, and the corresponding source spectra. The results suggest that slotted test sections have little influence on the beamforming results compared to closed test sections and that the Reynolds number has a profound, non-linear impact on the aeroacoustic emission that lessens with increasing Reynolds number. Further, sources show a non-linear Mach number dependency at constant Reynolds number but are self-similar in the observed Mach number range. The findings suggest that it is possible to study real-world phenomena on small-scale full models at real-world Reynolds numbers, which enable further investigations in the future such as the directivity of sources.

Mach Number Dependence of Tone Generation by Impinging Round Jets

The Mach number dependence of tone generation by jets impinging on a plate is investigated using large-eddy simulations, for seven jets at Mach numbers between 0.6 and 1.3 and a nozzle-to-plate distance of 8 nozzle radii. For , the upstream sound radiation is broadband, whereas for , tones emerge in the near-nozzle spectra, highlighting the establishment of feedback loops. The tone frequencies are consistent with those for aeroacoustic feedback loops between the nozzle and the plate, and exhibit a staging behavior with the Mach number, staying inside or close to the ranges of the upstream-traveling free-stream guided jet waves predicted by a vortex-sheet model. The azimuthal and radial structures of the pressure fields at the tone frequencies agree with those of these waves closing the loops. The selection of the dominant tone and the staging behavior are discussed by evaluating the power gains of the shear-layer instability waves between the nozzle and the plate using linear stability. In most cases, the dominant tones emerge at the possible tone frequencies with the highest gain. For , the gain of the instability waves at the frequency of the guided jet waves most likely to close feedback mechanisms is lower than the gain peak values, possibly contributing to the absence of resonance.

Mach and Reynolds number dependency of the unsteady shock-induced drag force on a sphere

Shock–particle interaction is an important phenomenon in a wide range of technological applications and natural phenomena, and the development of accurate models for this interaction is therefore of interest. This study investigates the transient forces during shock–particle interaction at particle Reynolds numbers between 100 and 1000, and incident shock wave Mach numbers between 1.22 and 2.51. This is achieved with the aid of particle-resolved large-eddy simulations. The simulation results show that shock–particle interaction differs qualitatively for subcritical and supercritical incident flow conditions. By decomposing the total force, the inviscid and viscous unsteady forces are estimated. The inviscid unsteady component is significantly larger than the viscous contribution, but the magnitude of the viscous component is comparable to steady-state drag. The predictions of current state of the art force models are compared to the computed particle forces. For subcritical flows, the models are quite successful in predicting the drag. For these conditions, the magnitudes of both the inviscid and viscous unsteady force models agree well with the simulation results, but the transient nature of the viscous unsteady force history is not well captured. For supercritical flows, the inviscid unsteady force model is not able to capture the force dynamics. This highlights the need for the development of unsteady force models for supercritical flow conditions.

The Motion of Strong Plane Shock Wave in Highly Viscous Medium

Neglecting the effect of overtaking disturbances, the motion of strong plane shock wave in highly viscous medium has been investigated by Chester-Chisnell- Whitham method. The analytical expressions for shock strength decreases as shock advances for low viscous region of a medium to the high viscous region. The dependence of mach number on propagation distance, Pressure and Particle velocity as well as on adiabatic index has also been analyzed for the cases. The results obtained here are also compared Yadav et al. (2008) for a freely propagating shock. The obtained expansions are computed and discussed through table.

Survival and mass growth of cold gas in a turbulent, multiphase medium

ABSTRACT Astrophysical gases are commonly multiphase and highly turbulent. In this work, we investigate the survival and growth of cold gas in such a turbulent, multiphase medium using three-dimensional hydrodynamical simulations. Similar to previous work simulating coherent flow (winds), we find that cold gas survives if the cooling time of the mixed gas is shorter than the Kelvin–Helmholtz time of the cold gas clump (with some weak additional Mach number dependence). However, there are important differences. Near the survival threshold, the long-term evolution is highly stochastic, and subject to the existence of sufficiently large clumps. In a turbulent flow, the cold gas continuously fragments, enhancing its surface area. This leads to exponential mass growth, with a growth time given by the geometric mean of the cooling and the mixing time. The fragmentation process leads to a large number of small droplets which follow a scale-free dN/dm ∝ m−2 mass distribution, and dominate the area covering fraction. Thus, whilst survival depends on the presence of large ‘clouds’, these in turn produce a ‘fog’ of smaller droplets tightly coupled to the hot phase which are probed by absorption line spectroscopy. We show with the aid of Monte Carlo simulations that the simulated mass distribution emerges naturally due to the proportional mass growth and the coagulation of droplets. We discuss the implications of our results for convergence criteria of larger scale simulations and observations of the circumgalactic medium.

An experimental validation of a nonlinear acoustic resistance model for an acoustically compact area contraction with steady mean flow.

In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.

Ion Acceleration Efficiency at the Earth’s Bow Shock: Observations and Simulation Results

Abstract Collisionless shocks are some of the most efficient particle accelerators in heliospheric and astrophysical plasmas. Here we study and quantify ion acceleration at Earth’s bow shock with observations from NASA’s Magnetospheric Multiscale (MMS) satellites and in a global hybrid-Vlasov simulation. From the MMS observations, we find that quasiparallel shocks are more efficient at accelerating ions. There, up to 15% of the available energy goes into accelerating ions above 10 times their initial energy. Above a shock-normal angle of ∼50°, essentially no energetic ions are observed downstream of the shock. We find that ion acceleration efficiency is significantly lower when the shock has a low Mach number (M A < 6) while there is little Mach number dependence for higher values. We also find that ion acceleration is lower on the flanks of the bow shock than at the subsolar point regardless of the Mach number. The observations show that a higher connection time of an upstream field line leads to somewhat higher acceleration efficiency. To complement the observations, we perform a global hybrid-Vlasov simulation with realistic solar-wind parameters with the shape and size of the bow shock. We find that the ion acceleration efficiency in the simulation shows good quantitative agreement with the MMS observations. With the combined approach of direct spacecraft observations, we quantify ion acceleration in a wide range of shock angles and Mach numbers.

Mach number dependence of the transition structure during jet diffusion in a supersonic jet

Mach number dependence of the transition structure during jet diffusion in a supersonic jet

Implicit large eddy simulation of passive scalar transfer in compressible planar jet

AbstractImplicit large eddy simulation (ILES) of passive scalar transfer in compressible turbulence is evaluated for subsonic and supersonic turbulent planar jets. The ILES used in this study relies on fully explicit numerical schemes for spatial and temporal discretization and low‐pass and shock‐capturing filters used as an implicit subgrid‐scale (SGS) model. The ILES results are compared with the direct numerical simulation (DNS) database of the same flows. The ILES results exhibit good agreements with the DNS for first‐ and second‐order statistics of velocity and passive scalar. The scalar transport by turbulent velocity fluctuations is well captured by the ILES. The temporal evolution of the jet strongly depends on the jet Mach number, where a higher Mach number results in the delay of jet development. The Mach number dependence of velocity and passive scalar fields is consistent between the ILES and DNS. The low‐pass filters used as the implicit SGS model contribute to the dissipation of turbulent kinetic energy and scalar variance. Under the present numerical conditions, the filters account for about 50% of the dissipation in a fully developed turbulent jet. The dissipation rate in the ILES, which is the sum of the grid‐scale and SGS dissipation rates, is very close to the dissipation rate in the DNS, and the amount of the SGS dissipation is well controlled by the low‐pass filters. The filters also dump numerical oscillations in the velocity field caused by strong pressure waves outside the supersonic jet at the high Mach number.

Direct numerical simulation of decaying homogeneous isotropic turbulence — numerical experiments on stability, consistency and accuracy of distinct lattice Boltzmann methods

Stability, consistency and accuracy of various lattice Boltzmann schemes are investigated by means of numerical experiments on decaying homogeneous isotropic turbulence (DHIT). Therefore, the Bhatnagar–Gross–Krook (BGK), the entropic lattice Boltzmann (ELB), the two-relaxation-time (TRT), the regularized lattice Boltzann (RLB) and the multiple-relaxation-time (MRT) collision schemes are applied to the three-dimensional Taylor–Green vortex, which represents a benchmark case for DHIT. The obtained turbulent kinetic energy, the energy dissipation rate and the energy spectrum are compared to reference data. Acoustic and diffusive scaling is taken into account to determine the impact of the lattice Mach number. Furthermore, three different Reynolds numbers [Formula: see text], [Formula: see text] and [Formula: see text] are considered. BGK shows instabilities, when the mesh is highly underresolved. The diverging simulations for MRT are ascribed to a strong lattice Mach number dependency. Despite the fact that the ELB modifies the bulk viscosity, it does not mimic a turbulence model. Therefore, no significant increase of stability in comparison to BGK is observed. The TRT “magic parameter” for DHIT at moderate Reynolds numbers is estimated with respect to the energy contribution. Stability and accuracy of the TRT scheme is found to be similar to BGK. For small lattice Mach numbers, the RLB scheme exhibits lowered energy contribution in the dissipation range compared to an analytical model spectrum. Overall, to enhance stability and accuracy, the lattice Mach number should be chosen with respect to the applied collision scheme.

Effects of Turbulence Driving and Sonic Mach Number on the Davis–Chandrasekhar–Fermi Method

Abstract The Davis–Chandrasekhar–Fermi (DCF) method is a tool that is widely used to obtain the strength of the mean magnetic field projected on the plane of the sky. However, it may overestimate the strength of the magnetic field when there are many independent structures (or, eddies) along the line of sight. Recently, Cho & Yoo proposed a modified DCF method that corrects such an effect. In this paper, we compare the conventional DCF method and the modified DCF method for various sonic Mach numbers and driving schemes. We find that, when we apply the conventional DCF method to turbulence generated by solenoidal and compressive driving schemes, the results are notably different. In particular, when there are many independent eddies along the line of sight, the estimates of the plane-of-sky mean magnetic field for compressive driving show strong dependence on the sonic Mach number, while those for solenoidal driving exhibit a very weak dependence on it. We find that intermittency of magnetic and density structures is responsible for the sonic Mach number dependence of the conventional DCF method. On the other hand, the modified DCF does not show strong dependence on the sonic Mach number or the driving scheme.

Supersonic plasma turbulence in the laboratory

The properties of supersonic, compressible plasma turbulence determine the behavior of many terrestrial and astrophysical systems. In the interstellar medium and molecular clouds, compressible turbulence plays a vital role in star formation and the evolution of our galaxy. Observations of the density and velocity power spectra in the Orion B and Perseus molecular clouds show large deviations from those predicted for incompressible turbulence. Hydrodynamic simulations attribute this to the high Mach number in the interstellar medium (ISM), although the exact details of this dependence are not well understood. Here we investigate experimentally the statistical behavior of boundary-free supersonic turbulence created by the collision of two laser-driven high-velocity turbulent plasma jets. The Mach number dependence of the slopes of the density and velocity power spectra agree with astrophysical observations, and supports the notion that the turbulence transitions from being Kolmogorov-like at low Mach number to being more Burgers-like at higher Mach numbers.

The role of waves on mixing in shallow waters

The role of waves on mixing is examined in a transverse shear flow in shallow waters for sub-critical, trans-critical, and super-critical flow over a range of convective Froude numbers. At low convective Froude numbers, the rollup of the vortex sheet to form an eddy defines the mixing. The mixing at higher convective Froude numbers, on the other hand, is affected by the shock waves and the radiation of the wave energy from an elongated vorticity element. Significant structural changes of the shear flow occur as the shock waves become discernible in the trans-critical and super-critical range of the convective Froude number. The shear layer growth is restrained while the momentum-thickness to vorticity-thickness ratio increases by a factor greater than 3. The fractional growth rate of the mixing layer in shallow waters and its dependence on the convective Froude number follows analogously the observed Mach-number dependence in gas dynamics.

The Maximum Amplitude of Dust-Acoustic Waves in Dusty Plasma with Vortex-Like Ions

Theoretical investigations are carried out for the properties of small amplitude dust-acoustic solitary waves in plasmas consisting of extremely massive, high negatively charged inertial dust grains, Boltzmann distributed electrons and trapped ions, for one-dimensional case and three-dimensional case. An energy integral equation involving the Sagdeev potential is derived. The dependence of the critical Mach number corresponding to maximum amplitude on other parameters is obtained. It is observed that the magnitude of the external magnetic field has no effect on the amplitude of the solitary waves.

Turbulent Flame Speeds of Premixed Supersonic Flame Kernels

It is unclear whether turbulent flame speed scalings established in low speed regimes are applicable to supersonic flames. To investigate this question, the canonical flame kernel is investigated in a scramjet-like channel having a one degree wall divergence. The growth, shape and internal kernel dynamics are investigated. Results are presented for three Mach numbers, four equivalence ratios, and three turbulence generators. Schlieren photography provides flame images for growth rate statistics and particle image velocimetry (PIV) provides turbulence statistics and investigation of internal kernel dynamics. Supersonic flame kernels are self-propagating and respond to the equivalence ratio in a fashion that is similar to low speed flames. However, supersonic flame kernels have features that are not present in subsonic flame kernels. Baroclinicity, resulting from pressure-density misalignment, creates a reacting vortex ring structure. Further, the mean kernel shape has a Mach number dependence and the vortex ring enhances the turbulent flame speed through entrainment of reactants and augmented flame surface growth. Hence, the previously established (low speed) flame speed scalings are inappropriate for supersonic flame kernels. Drawing motivation from vortex ring literature, the ring propagation velocity is used as the characteristic velocity and a new flame speed scaling is proposed.

Stability of plasma cylinder with current in a helical plasma flow

Stability of a plasma cylinder with a current wrapped by a helical plasma flow is studied. Unstable surface modes of magnetohydrodynamic (MHD) oscillations develop at the boundary of the cylinder enwrapped by the plasma flow. Unstable eigenmodes can also develop for which the plasma cylinder is a waveguide. The growth rate of the surface modes is much higher than that for the eigenmodes. It is shown that the asymmetric MHD modes in the plasma cylinder are stable if the velocity of the plasma flow is below a certain threshold. Such a plasma flow velocity threshold is absent for the symmetric modes. They are unstable in any arbitrarily slow plasma flows. For all surface modes there is an upper threshold for the flow velocity above which they are stable. The helicity index of the flow around the plasma cylinder significantly affects both the Mach number dependence of the surface wave growth rate and the velocity threshold values. The higher the index, the lower the upper threshold of the velocity jump above which the surface waves become stable. Calculations have been carried out for the growth rates of unstable oscillations in an equilibrium plasma cylinder with current serving as a model of the low-latitude boundary layer (LLBL) of the Earth’s magnetic tail. A tangential discontinuity model is used to simulate the geomagnetic tail boundary. It is shown that the magnetopause in the geotail LLBL is unstable to a surface wave (having the highest growth rate) in low- and medium-speed solar wind flows, but becomes stable to this wave in high-speed flows. However, it can remain weakly unstable to the radiative modes of MHD oscillations.