本研究旨在更完整地理解高亚声速 Mach 数湍流射流中发生的共振机制，如 Towne 等人（J. Fluid Mech., vol. 825, 2017, pp. 1113-1152）所示。该研究提出共振存在于向上游和向下游传播的导波之间。研究假设了五种可能的共振机制，每种机制涉及不同的导波族，这些导波在喷嘴出口平面以及若干下游转折点处发生反射。然而，该研究并未确定这五种共振机制中哪一种支撑了观测到的谱峰。在本研究中，通过将大涡模拟数据双正交投影到由局部平行线性稳定性分析提供的特征基上，识别了支撑共振的波。由此确认，Towne 等人假设的五种情况中有两种存在于该湍流射流中。此外，还确定了喷嘴出口和转折点平面的反射系数。这些信息可作为简化共振建模策略的输入，例如 Jordan 等人（J. Fluid Mech., vol. 853, 2018, pp. 333-358）针对射流边缘共振以及 Mancinelli 等人（Exp. Fluids, vol. 60, 2019, pp. 1-9）针对超声速尖啸所开发的策略。
英文摘要：
This work aims to provide a more complete understanding of the resonance mechanisms that occur in turbulent jets at high subsonic Mach number, as shown by Towne et al. (J. Fluid Mech., vol. 825, 2017, pp. 1113-1152). Resonance was suggested by that study to exist between upstream- and downstream-travelling guided waves. Five possible resonance mechanisms were postulated, each involving different families of guided waves that reflect in the nozzle exit plane and at a number of downstream turning points. However, that study did not identify which of the five resonance mechanisms underpin the observed spectral peaks. In this work, the waves underpinning resonance are identified via a biorthogonal projection of Large Eddy Simulation data on eigenbases provided by a locally parallel linear stability analysis. Two of the five scenarios postulated by Towne et al. are thus confirmed to exist in the turbulent jet. The reflection-coefficients in the nozzle exit and turning-point planes are, furthermore, identified. Such information is required as input for simplified resonance-modelling strategies such as developed in Jordan et al. (J. Fluid Mech., vol. 853, 2018, pp. 333-358) for jet-edge resonance, and in Mancinelli et al. (Exp. Fluids, vol. 60, 2019, pp. 1-9) for supersonic screech.
The Variable Density and Speed of Sound Vessel (VDSSV) produces subsonic turbulent flows that are both compressible and observable at all scales with existing instrumentation including hot wires and particle tracking. We realize this objective by looking at the flow of a heavy gas (sulfur hexafluoride $SF_6$), with a speed of sound almost three times lower than for air. By switching between air and $SF_6$, we isolate the influence of the turbulent Mach number (up to $M_t$ = 0.17) on turbulence statistics from the influences of changes in the Reynolds number (up to $R_λ$ = 1600), and boundary c…
The subgrid-scale modelling of a low Mach number strongly anisothermal turbulent flow is investigated using direct numerical simulations. The study is based on the filtering of the low Mach number equations, suited to low Mach number flows with highly variable fluid properties. The results are relevant to formulations of the filtered low Mach number equations established with the classical filter or the Favre filter. The two most significant subgrid terms of the filtered low Mach number equations are considered. They are associated with the momentum convection and the density-velocity correlat…
A combined analytical and numerical study is conducted to investigate the asymmetric cap-shock non-uniform Mach Reflection (csMR) phenomenon outside of an over-expanded supersonic jet. Prior analytical works have only considered the wedge-induced steady symmetric and asymmetric Mach reflection (MR) configurations, as well as symmetric MR in an open jet. However, there is another structure occurring in nozzle flow fields known as a non-uniformity induced cap-shock pattern. We derive a new analytical model to predict the wave structure of the asymmetric csMR in the absence of internal shocks by …
Shock reflection experiments are performed to study the large-scale convective mixing created by the forward jetting phenomenon. Experiments are performed at a wedge angle of $θ_{\mathrm{w}} = 30^{\circ}$ in nitrogen, propane-oxygen, and hexane with incident shock Mach numbers up to $M = 4$. Experiments are complimented by shock-resolved viscous simulations of triple point reflection in hexane for $M = 2.5$ to $6$. Inviscid simulations are performed over a wider range of parameters. Reynolds numbers up to $Re \lesssim 10^3$ are covered by simulations and Reynolds numbers of $Re \sim 10^5$ are …
The present study addresses the self-similar problem of unsteady shock reflection on an inclined wedge. The start-up conditions are studied by modifying the wedge corner and allowing for a finite radius of curvature. It is found that the type of shock reflection observed far from the corner, namely regular or Mach reflection, depends intimately on the start-up condition, as the flow "remembers" how it was started. Substantial differences were found. For example, the type of shock reflection for an incident shock Mach number $M=6.6$ and an isentropic exponent $γ=1.2$ changes from regular to Mac…
The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier-Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition, when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet wa…
Even in the absence of externally applied temperature gradients, spontaneously generated temperature fluctuations arise in turbulent flows. We experimentally study these fluctuations in a closed von Karman swirling flow of air at Mach number of order $10^{-3}$, whose boundaries are maintained at a constant temperature. We observe intermittent peaks of low temperature correlated with pressure drops within the flow and show that they are caused by vorticity filaments. The measured ratio of temperature to pressure fluctuation agrees with the prediction based on adiabatic cooling within vortex cor…
The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach Reflection (MR) and Regular Reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the $x$-direction with a velocity, $V(t)$ at a free-stream Mach number of $3$. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. Further, the Arbitrary Lagrangian-Eulerian (ALE) technique is appli…
We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is non-local both in space and time, i.e. the closure terms are parametrized in terms of the spatial neighborhood of the resolved quantities but also their history. The data-driven scheme is complemented with a physical constrain expressing the energy conservation property of the nonlinear advection terms. We show that the adoption of this physical constrain not only increases the accuracy of the closure scheme but also impr…
Previous work (S. Davidovits and N. J. Fisch, "Sudden viscous dissipation of compressing turbulence," Phys. Rev. Lett., 116(105004), 2016) demonstrated that the compression of a turbulent field can lead to a sudden viscous dissipation of turbulent kinetic energy (TKE), and suggested this mechanism could potentially be used to design new fast-ignition schemes for inertial confinement fusion. We expand on previous work by accounting for finite Mach numbers, rather than relying on a zero-Mach-limit assumption as previously done. The finite-Mach-number formulation is necessary to capture a self-co…
University of Notre Dame（圣母大学）；Missouri University of Science and Technology（密苏里科技大学）；Virginia Tech（弗吉尼亚理工大学）
Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonical incompressible flows. However, its performance on high-Mach-number flows is still not clear. In this work we use the PIML approach to predict the discrepancies in RANS modeled Reynolds stresses in high-Mach-number flat-plate turbulent boundary lay…
The transition between the Regular Reflection (RR) and Mach Reflection (MR) phenomenon impacts the design of the supersonic and hypersonic air-breathing vehicles. The aim of this paper is to numerically investigate the dynamic transition from RR to MR of unsteady supersonic flow over a two-dimensional wedge, whose trailing edge moves along the $x$-direction upstream with a velocity, $V(t)$ at a free-stream Mach number of $M_{\infty}=3$. The simulation is conducted using the unsteady compressible inviscid flow solver, which is implemented in OpenFOAM\textsuperscript{\textregistered}, the open-s…
In the current study, the influence of turbulent mixing and local reaction rates on deflagration to detonation transition (DDT) was investigated using a state-of-the-art large eddy simulation (LES) strategy. Specifically, detonation attenuation by a porous medium, and the subsequent re-initiation for methane-oxygen, a moderately unstable mixture, was considered. The purpose of the investigation was to validate the numerical strategy with previous experimental observations, and to determine what specific roles turbulent mixing and shock compression have on flame acceleration during the final st…
The present paper seeks to determine the mechanism of flame acceleration and transition to detonation when a turbulent flame preceded by a shock interacts with a single obstruction in its path, taken as a cylindrical obstacle or a wall in the present study. The problem is addressed experimentally in a mixture of propane-oxygen at sub-atmospheric conditions. The turbulent flame was generated by passing a detonation wave through a perforated plate, yielding flames with turbulent burning velocities 10 to 20 larger than the laminar values and incident shock Mach numbers ranging between 2 and 2.5. …
A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is employed in the two homogeneous spatial directions and a number of discretizations can be used in the inhomogeneous direction. The momentum is decomposed into divergence- and curl-free portions which allows the momentum equations to be rewritten, removing the need to solve for the pressure. The temporal discretization is based on an explicit, segregated Runge-Kut…
In this paper, we study the Mach reflection phenomenon in inviscid flows using a higher order discontinuous Galerkin method and overset grids. We use the shock capturing procedure proposed in Siva Prasad Kochi et al. using overset grids to capture the discontinuities occurring in the supersonic flow over a wedge accurately. In this procedure, we obtain a coarse grid solution first and using the troubled cell data, we construct an overset grid which is approximately aligned to all the discontinuities. We rerun the solver with the coarse grid solution as the initial condition while using the tro…
We report the mechanism of the hysteresis in the transition between Regular and Mach reflections. A new discovery is that, the hysteresis loop is in fact the projection of a higher dimensional path, i.e. the valley lines in the surface of dissipation, of which minimal values correspond to stable reflection configurations. Since the saddle-nodes bifurcate the valleies of the surface, they are actually the transition points of the two reflections. Furthermore, the predicted reflection configurations agree well with the experimental and numerical results, which is a validation of this theory.
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main features, both new and old, as the discovery of bi-directional cascades or the role of helical vortices in the enhancement of large-scale magnetic fields in the dynamo problem. The dynamical contribution in magnetohydrodynamic (MHD) of the cross-correlation between velocity and induction is discussed as well. We consider next how turbulent transport is affected b…
We present the first study on the amplification of magnetic fields by the turbulent dynamo in the highly subsonic regime, with Mach numbers ranging from $10^{-3}$ to $0.4$. We find that for the lower Mach numbers the saturation efficiency of the dynamo, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$, increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes, $(E_{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$ $\gtrsim 10^{-2}$ at a Mach number of $10^{-3}$. We apply our results to magnetic field amplification in the ea…
A hybrid lattice Boltzmann/finite-difference solver for low Mach thermo-compressible flows developed in earlier works is extended to more realistic and challenging configurations involving turbulence and complex geometries in the present article. The major novelty here as compared to previous contributions is the application of a more robust collision operator, considerably extending the stability of the original single relaxation time model and facilitating larger Reynolds number flow simulations. Additionally, a subgrid model and the thickened flame approach have also been added allowing for…
In this paper the propagation of acoustic plane waves in turbulent, fully developed flow is studied by means of an experimental investigation carried out in a straight, smooth-walled duct.The presence of a coherent perturbation, such as an acoustic wave in a turbulent confined flow, generates the oscillation of the wall shear stress. In this circumstance a shear wave is excited and superimposed on the sound wave. The turbulent shear stress is modulated by the shear wave and the wall shear stress is strongly affected by the turbulence. From the experimental point of view, it results in a measur…
Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $δ\mathbf{B}$ and large-scale, $\mathbf{B}_0$ fields, $\left< (δ\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}_{\mathcal{V}}$. By considering th…
