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Faccanoni, Gloria, Bérénice Grec, and Yohan Penel. "A homogeneous relaxation low mach number model." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 4 (2021): 1569–98. http://dx.doi.org/10.1051/m2an/2021032.
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In the present paper, we investigate a new homogeneous relaxation model describing the behaviour of a two-phase fluid flow in a low Mach number regime, which can be obtained as a low Mach number approximation of the well-known HRM. For this specific model, we derive an equation of state to describe the thermodynamics of the two-phase fluid. We prove some theoretical properties satisfied by the solutions of the model, and provide a well-balanced scheme. To go further, we investigate the instantaneous relaxation regime, and prove the formal convergence of this model towards the low Mach number approximation of the well-known HEM. An asymptotic-preserving scheme is introduced to allow numerical simulations of the coupling between spatial regions with different relaxation characteristic times.
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Jardine, M., and E. R. Priest. "Energetics of compressible models of fast steady-state magnetic reconnection." Journal of Plasma Physics 43, no. 1 (1990): 141–50. http://dx.doi.org/10.1017/s0022377800014677.
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An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1–6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics.
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Ji, Zifei, Huiqiang Zhang, and Bing Wang. "Thrust control strategy based on the minimum combustor inlet Mach number to enhance the overall performance of a scramjet engine." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 13 (2019): 4810–24. http://dx.doi.org/10.1177/0954410019830816.
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A lower combustor inlet Mach number is desirable in order to design a compact, lightweight combustor and boost the overall performance of the scramjet engine. In this study, a thrust control strategy is proposed for a hydrogen-fueled scramjet taking into account the operating limitations, which is called the minimum combustor inlet Mach number rule since the combustor inlet Mach number is used as the control variable. By scheduling the fuel supply and modifying the intake geometry, the combustor inlet Mach number can be minimized while ensuring a certain thrust output within the operation constraints. In this manner, the scramjet engine can be operated with high specific thrust and low fuel consumption throughout the flight envelope. The thrust control strategy is further applied to a hydrogen-fueled scramjet in the hypersonic flight regime. Because the combustor inlet Mach number varies with flight conditions, the thrust strategy can be applied in practice by monitoring the following aerothermodynamic parameters in different flight regimes instead: (1) combustor outlet Mach number, (2) combustor inlet static temperature, and (3) combustor outlet static temperature. Furthermore, the effects of the thrust output on the division of flight regime are investigated, and the overall performance of the hydrogen-fueled scramjet engine obtained from applying the thrust control strategy is discussed in detail.
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Baus, Franziska, Axel Klar, Nicole Marheineke, and Raimund Wegener. "Low-Mach-number and slenderness limit for elastic Cosserat rods and its numerical investigation." Asymptotic Analysis 120, no. 1-2 (2020): 103–21. http://dx.doi.org/10.3233/asy-191581.
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This paper deals with the relation of the dynamic elastic Cosserat rod model and the Kirchhoff beam equations. We show that the Kirchhoff beam without angular inertia is the asymptotic limit of the Cosserat rod, as the slenderness parameter (ratio between rod diameter and length) and the Mach number (ratio between rod velocity and typical speed of sound) approach zero, i.e., low-Mach-number–slenderness limit. The asymptotic framework is exact up to fourth order in the small parameter and reveals a mathematical structure that allows a uniform handling of the transition regime between the models. To investigate this regime numerically, we apply a scheme that is based on a Gauss–Legendre collocation in space and an α-method in time.
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Shajii, A., and J. P. Freidberg. "Theory of low Mach number compressible flow in a channel." Journal of Fluid Mechanics 313 (April 25, 1996): 131–45. http://dx.doi.org/10.1017/s0022112096002157.
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The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.
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Turner, Stephen E., Lok C. Lam, Mohammad Faghri, and Otto J. Gregory. "Experimental Investigation of Gas Flow in Microchannels." Journal of Heat Transfer 126, no. 5 (2004): 753–63. http://dx.doi.org/10.1115/1.1797036.
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This paper presents an experimental investigation of laminar gas flow through microchannels. The independent variables: relative surface roughness, Knudsen number and Mach number were systematically varied to determine their influence on the friction factor. The microchannels were etched into silicon wafers, capped with glass, and have hydraulic diameters between 5 and 96 μm. The pressure was measured at seven locations along the channel length to determine local values of Knudsen number, Mach number and friction factor. All measurements were made in the laminar flow regime with Reynolds numbers ranging from 0.1 to 1000. The results show close agreement for the friction factor in the limiting case of low Ma and low Kn with the incompressible continuum flow theory. The effect of compressibility is observed to have a mild (8 percent) increase in the friction factor as the Mach number approaches 0.35. A 50 percent decrease in the friction factor was seen as the Knudsen number was increased to 0.15. Finally, the influence of surface roughness on the friction factor was shown to be insignificant for both continuum and slip flow regimes.
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Tomasini, M., N. Dolez, and J. Léorat. "Instability of a rotating shear layer in the transonic regime." Journal of Fluid Mechanics 306 (January 10, 1996): 59–82. http://dx.doi.org/10.1017/s0022112096001231.
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We have studied numerically the stability of a two-dimensional Couette flow in a polytropic fluid subjected to a localized shear, using a pseudo-spectral method (Fourier-Chebyshev). The polytropic index has been chosen equal to 2 and a radial force (pseudo-gravity) is introduced in order to perform comparisons with the shallow water experimental results. When the Reynolds number is not too low, the initial flow which is purely azimuthal becomes unstable and a stable rotating pattern is formed, with a number of azimuthal modes which decreases when the Mach number increases. A qualitative agreement is found with the experimental results, although the spatial resolution constraint strongly limits the numerical Reynolds and Mach numbers. From the variation of the linear growth rate of the unstable modes with the Mach number, we are able to show the transition between a flow subjected to Kelvin-Helmholtz instability towards one essentially driven by a centrifugal instability, which is efficient for rotating supersonic flows if the angular momentum decreases outwards. The latter situation may occur for some flows in astrophysical disks.
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Beccantini, A., E. Studer, S. Gounand, et al. "Numerical simulations of a transient injection flow at low Mach number regime." International Journal for Numerical Methods in Engineering 76, no. 5 (2008): 662–96. http://dx.doi.org/10.1002/nme.2331.
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Pröbsting, S., Y. Yang, H. Zhang, P. Li, Y. Liu, and Y. Li. "Effect of Mach number on the aeroacoustic feedback loop generating airfoil tonal noise." Physics of Fluids 34, no. 9 (2022): 094115. http://dx.doi.org/10.1063/5.0107181.
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Airfoil tonal noise emission at low-to-moderate Reynolds number and flow conditions featuring a laminar separation bubble close to the trailing edge is often related to an aeroacoustic feedback mechanism and, therefore, the Mach number is a primary parameter for the flow field and noise generation. This study experimentally explores the effect of the Mach number on airfoil tonal noise generation in the nominally incompressible flow regime. Using airfoil profiles of different chord lengths, the Mach number is varied for a constant Reynolds number. Acoustic and flow field measurements for a range of combinations of Reynolds and Mach numbers were conducted. At zero incidence, the tonal noise regime in the Reynolds number domain is found to be sensitive to the Mach number. At non-zero angle of attack (2°), the noise generation is found to be dominated by vortex shedding over a separation bubble on the pressure side. The details of the separation bubble and shedding process depend on the Mach number. The frequencies of the dominant tones and the frequency intervals between tones increase with the Mach number. Moreover, the measured frequency interval can be collapsed using a relation based on the aeroacoustic feedback loop model. The relation is rewritten to separate the effects of the Reynolds and Mach numbers. As a result, the dependence on the Mach number is identified and tested. In contrast, the tonal noise level shows a more complex dependence on details of the laminar separation bubble and the vortex shedding process.
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Degond, Pierre, and Min Tang. "All Speed Scheme for the Low Mach Number Limit of the Isentropic Euler Equations." Communications in Computational Physics 10, no. 1 (2011): 1–31. http://dx.doi.org/10.4208/cicp.210709.210610a.
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AbstractAn all speed scheme for the Isentropic Euler equations is presented in this paper. When the Mach number tends to zero, the compressible Euler equations converge to their incompressible counterpart, in which the density becomes a constant. Increasing approximation errors and severe stability constraints are the main difficulty in the low Mach regime. The key idea of our all speed scheme is the special semi-implicit time discretization, in which the low Mach number stiff term is divided into two parts, one being treated explicitly and the other one implicitly. Moreover, the flux of the density equation is also treated implicitly and an elliptic type equation is derived to obtain the density. In this way, the correct limit can be captured without requesting the mesh size and time step to be smaller than the Mach number. Compared with previous semi-implicit methods, firstly, nonphysical oscillations can be suppressed by choosing proper parameter, besides, only a linear elliptic equation needs to be solved implicitly which reduces much computational cost. We develop this semi-implicit time discretization in the framework of a first order Local Lax-Friedrichs (or Rusanov) scheme and numerical tests are displayed to demonstrate its performances.
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Auddy, Sayantan, Shantanu Basu, and Takahiro Kudoh. "The Magnetic Field versus Density Relation in Star-forming Molecular Clouds." Astrophysical Journal Letters 928, no. 1 (2022): L2. http://dx.doi.org/10.3847/2041-8213/ac5a5a.
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Abstract We study the magnetic field to density (B–ρ) relation in turbulent molecular clouds with dynamically important magnetic fields using nonideal three-dimensional magnetohydrodynamic simulations. Our simulations show that there is a distinguishable break density ρ T between the relatively flat low-density regime and a power-law regime at higher densities. We present an analytic theory for ρ T based on the interplay of the magnetic field, turbulence, and gravity. The break density ρ T scales with the strength of the initial Alfvén Mach number A 0 for sub-Alfvénic ( A 0 < 1 ) and trans-Alfvénic ( A 0 ∼ 1 ) clouds. We fit the variation of ρ T for model clouds as a function of A 0 , set by different values of initial sonic Mach number 0 and the initial ratio of gas pressure to magnetic pressure β 0. This implies that ρ T, which denotes the transition in mass-to-flux ratio from the subcritical to the supercritical regime, is set by the initial turbulent compression of the molecular cloud.
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Radhakrishnan P, Ramanan G, Chandan Gowda H R, Meghana C K, and Chaithra A N. "Aerodynamic Performance Analysis of a Variable Sweep Wing for Commercial Aircraft Applications." ACS Journal for Science and Engineering 1, no. 1 (2021): 31–37. http://dx.doi.org/10.34293/acsjse.v1i1.5.
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This study presents a detailed study on wing and its configurations and the morphing techniques for the wing. The morphing methods of the wing such as variable chord, variable span variable cambers have been studied in detail. In this study in detail about the effects of morphable sweep wing, the commercial aircraft wing has been designed and it‘s been modelled using the solid works software. To study the aerodynamic performance the wing, the wing has been analysed in ANSYS Fluent software and the results are interpreted in detail to analyze the effect of wing and its shapes. From the results it‘s been clear that at low speed (Mach=0.8) straight wing has high L/D ratio and at the sonic speed (Mach=1) sweep wing has higher L/D ratio and in Supersonic Speed (Mach=1.2) delta wing tends to have higher L/D ratio. Based on these results the wing can be morphed to the configurations to obtain a better performance in each flight regime. Based on these morphing, aircraft performance can be improved in all flight regimes.
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Wang, L., Y. Zhao, and S. Fu. "Computational study of drag increase due to wall roughness for hypersonic flight." Aeronautical Journal 121, no. 1237 (2017): 395–415. http://dx.doi.org/10.1017/aer.2017.9.
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ABSTRACTIn this study, a series of numerical experiments are performed on supersonic/hypersonic flows over an adiabatic flat plate with transitionally and fully rough surfaces. The Mach numbers simulated are 4, 5, 6, and 7; the flight heights considered are 20, 24, 28, 32, and 36 km. First, a modified roughness correction is proposed and validated with the measured data for low-speed flat-plate cases. It is verified that for the equivalent sand grain heights in the intermediate and fully rough regimes, there is a good agreement with the semi-empirical formula available in the open literature. Then, this roughness correction is applied to high-speed flow regime to investigate the effects of flight heights and Mach numbers on drag for rough-wall flat-plate cases. It is found that within the roughness measured in real flight, the roughness height change has little effect on drag compared to the variations of both flight heights and Mach numbers. The drag coefficient derivation between rough-wall and smooth-wall conditions, achieves the maximum value of 0.79% for the 60 cases selected.
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Chalons, Christophe, Mathieu Girardin, and Samuel Kokh. "An All-Regime Lagrange-Projection Like Scheme for the Gas Dynamics Equations on Unstructured Meshes." Communications in Computational Physics 20, no. 1 (2016): 188–233. http://dx.doi.org/10.4208/cicp.260614.061115a.
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AbstractWe propose an all regime Lagrange-Projection like numerical scheme for the gas dynamics equations. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization with respect to the Mach number M, i.e. such that the ratio between the Mach number M and the mesh size or the time step is small with respect to 1. The key idea is to decouple acoustic and transport phenomenon and then alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in term of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and the internal energy. A discrete entropy inequality under a condition on the modification is obtained thanks to a reinterpretation of the modified scheme in the Harten Lax and van Leer formalism. A natural extension to multi-dimensional problems discretized over unstructured mesh is proposed. Then a simple and efficient semi implicit scheme is also proposed. The resulting scheme is stable under a CFL condition driven by the (slow) material waves and not by the (fast) acoustic waves and so verifies the all regime property. Numerical evidences are proposed and show the ability of the scheme to deal with tests where the flow regime may vary from low to high Mach values.
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Meng, Jianping, Yonghao Zhang, Nicolas G. Hadjiconstantinou, Gregg A. Radtke, and Xiaowen Shan. "Lattice ellipsoidal statistical BGK model for thermal non-equilibrium flows." Journal of Fluid Mechanics 718 (February 8, 2013): 347–70. http://dx.doi.org/10.1017/jfm.2012.616.
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AbstractA thermal lattice Boltzmann model is constructed on the basis of the ellipsoidal statistical Bhatnagar–Gross–Krook (ES-BGK) collision operator via the Hermite moment representation. The resulting lattice ES-BGK model uses a single distribution function and features an adjustable Prandtl number. Numerical simulations show that using a moderate discrete velocity set, this model can accurately recover steady and transient solutions of the ES-BGK equation in the slip-flow and early transition regimes in the small-Mach-number limit that is typical of microscale problems of practical interest. In the transition regime in particular, comparisons with numerical solutions of the ES-BGK model, direct and low-variance deviational Monte Carlo simulations show good accuracy for values of the Knudsen number up to approximately $0. 5$. On the other hand, highly non-equilibrium phenomena characterized by high Mach numbers, such as viscous heating and force-driven Poiseuille flow for large values of the driving force, are more difficult to capture quantitatively in the transition regime using discretizations chosen with computational efficiency in mind such as the one used here, although improved accuracy is observed as the number of discrete velocities is increased.
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Galié, Thomas, Jonathan Jung, Ibtissem Lannabi, and Vincent Perrier. "Extension of an all-Mach Roe scheme able to deal with low Mach acoustics to full Euler system." ESAIM: Proceedings and Surveys 76 (2024): 35–51. http://dx.doi.org/10.1051/proc/202476035.
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We propose to extend the fix of Roe’s approximate Riemann solver developed for the Barotropic Euler equations in [2] to the full Euler equations. This scheme is built mainly to handle low Mach acousticwaves. Moreover, compared to pressure-centered type schemes, this numerical fix has the advantage of improving the numerical solution in the sense that the oscillating modes are reduced. The theoretical study is based on a two-time scales asymptotic analysis. It is proved that the Euler system equipped with a general equation of state is consistent with a first-order wave system in a low Mach number regime. Similar analysis is performed at the discrete level on the Roe scheme to derive the new fix. Numerical tests confirm the results obtained for the Barotropic case about the ability of this fix to deal with both steady and low Mach acoustic computations also in the case of full Euler equations.
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Wang, Meng, Yi Liu, and Kan Wang. "Wall-pressure fluctuations in weakly compressible turbulent channel flow." Journal of the Acoustical Society of America 154, no. 4_supplement (2023): A282. http://dx.doi.org/10.1121/10.0023529.
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Wall-pressure fluctuations in turbulent wall-bounded flows are detrimental in many applications because they can cause structural vibrations and acoustic radiation. Their spectral behavior at subconvective wavenumbers are to date poorly understood and predicted, particularly in low-Mach-number flows. In this study, compressible direct numerical simulation is employed to elucidate the low-wavenumber behavior of wall-pressure fluctuations in turbulent channel flow and the effect of flow Mach number in the nearly incompressible regime. Simulations are conducted at bulk Mach numbers of 0.4, 0.2, and 0.1, and friction Reynolds number of 180. In addition to the convective ridge that is virtually Mach-number independent, acoustic ridges representing longitudinal and oblique waves are clearly identified in the two-dimensional wavenumber-frequency spectrum. The acoustic peaks are orders of magnitude weaker than the convective peak and decay with flow Mach number, but remain distinctly identifiable even at Mach 0.1. The acoustic energy in the supersonic wavenumber range is significantly enhanced by the onset of the first oblique mode but not much affected by the higher modes. The effect of a small, two-dimensional surface hump is also considered, which is shown to elevate the spectral level of the fluctuating wall pressure in the subconvective wavenumber range by several decades due to acoustic diffraction by the hump. [Work supported by the U.S. Office of Naval Research.]
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Rubin, T., E. J. Kolmes, I. E. Ochs, M. E. Mlodik, and N. J. Fisch. "Fueling limits in a cylindrical viscosity-limited reactor." Physics of Plasmas 29, no. 8 (2022): 082302. http://dx.doi.org/10.1063/5.0101271.
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Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. The threshold for this effect occurs at [Formula: see text]. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number [Formula: see text] is investigated. The limitation is found to be at moderate Mach numbers.
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Barsukow, Wasilij, Philipp V. F. Edelmann, Christian Klingenberg, Fabian Miczek, and Friedrich K. Röpke. "A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics." Journal of Scientific Computing 72, no. 2 (2017): 623–46. http://dx.doi.org/10.1007/s10915-017-0372-4.
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Zou, Ziqiang, Edouard Audit, Nicolas Grenier, and Christian Tenaud. "An Accurate Sharp Interface Method for Two-Phase Compressible Flows at Low-Mach Regime." Flow, Turbulence and Combustion 105, no. 4 (2020): 1413–44. http://dx.doi.org/10.1007/s10494-020-00125-1.
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Alam, Mahbub, and Paul L. Voss. "Graphene quantum interference photodetector." Beilstein Journal of Nanotechnology 6 (March 12, 2015): 726–35. http://dx.doi.org/10.3762/bjnano.6.74.
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In this work, a graphene quantum interference (QI) photodetector was simulated in two regimes of operation. The structure consists of a graphene nanoribbon, Mach–Zehnder interferometer (MZI), which exhibits a strongly resonant transmission of electrons of specific energies. In the first regime of operation (that of a linear photodetector), low intensity light couples two resonant energy levels, resulting in scattering and differential transmission of current with an external quantum efficiency of up to 5.2%. In the second regime of operation, full current switching is caused by the phase decoherence of the current due to a strong photon flux in one or both of the interferometer arms in the same MZI structure. Graphene QI photodetectors have several distinct advantages: they are of very small size, they do not require p- and n-doped regions, and they exhibit a high external quantum efficiency.
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van Marle, Allard Jan. "On the influence of supra-thermal particle acceleration on the morphology of low-Mach, high-β shocks". Monthly Notices of the Royal Astronomical Society 496, № 3 (2020): 3198–208. http://dx.doi.org/10.1093/mnras/staa1771.
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ABSTRACT When two galaxy clusters encounter each other, the interaction results in a collisionless shock that is characterized by a low (1–4) sonic Mach number, and a high-Alfvénic Mach number. Our goal is to determine if, and to what extent, such shocks can accelerate particles to sufficient velocities that they can contribute to the cosmic ray spectrum. We combine two different computational methods, magnetohydrodynamics (MHD) and particle-in-cell (PIC) into a single code that allows us to take advantage of the high computational efficiency of MHD while maintaining the ability to model the behaviour of individual non-thermal particles. Using this method, we perform a series of simulations covering the expected parameter space of galaxy cluster collision shocks. Our results show that for shocks with a sonic Mach number below 2.25 no diffusive shock acceleration can take place because of a lack of instabilities in the magnetic field, whereas for shocks with a sonic Mach number $\ge \, 3$ the acceleration is efficient and can accelerate particles to relativistic speeds. In the regime between these two extremes, diffusive shock acceleration can occur but is relatively inefficient because of the time- and space-dependent nature of the instabilities. For those shocks that show efficient acceleration, the instabilities in the upstream gas increase to the point where they change the nature of the shock, which, in turn, will influence the particle injection process.
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Li, Xiang-Yu, and Lars Mattsson. "Coagulation of inertial particles in supersonic turbulence." Astronomy & Astrophysics 648 (April 2021): A52. http://dx.doi.org/10.1051/0004-6361/202040068.
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Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). We find that the average coagulation kernel ⟨Cij⟩ scales linearly with the average Mach number ℳrms multiplied by the combined size of the colliding particles, that is, 〈Cij〉∼〈(ai+aj)3〉 ℳrmsτη−1, which is qualitatively consistent with expectations from analytical estimates. A quantitative correction 〈Cij〉∼〈(ai+aj)3〉(vp,rms/cs)τη−1 is proposed and can serve as a benchmark for future studies. We argue that the coagulation rate ⟨Rc⟩ is also enhanced by compressibility-induced compaction of particles.
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Eiximeno, Benet, Carlos Tur-Mongé, Oriol Lehmkuhl, and Ivette Rodríguez. "Hybrid Computation of the Aerodynamic Noise Radiated by the Wake of a Subsonic Cylinder." Fluids 8, no. 8 (2023): 236. http://dx.doi.org/10.3390/fluids8080236.
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The noise radiated by the flow around a cylinder in the subcritical regime at ReD=1×104 and at a subsonic Mach number of M=0.5 is here studied. The aerodynamic sound radiated by a cylinder has been studied with a wide range of Reynolds numbers, but there are no studies about how the Mach number affects the acoustic field in the subsonic regime. The flow field is resolved by means of large-eddy simulations of the compressible Navier–Stokes equations. For the study of the noise propagation, formulation 1C of the Ffowcs Williams–Hawkings analogy is used. The fluid flow results show good agreement when comparing the surface pressure coefficient, the recirculation length, the vortex shedding frequency and the force coefficients against other studies performed under similar conditions. The dynamic mode decomposition of the pressure fluctuations is used to relate them with the far-field noise. It is shown that, in contrast to what happens for low Mach numbers, quadrupoles have a significant impact mainly in the observers located in the streamwise direction. This effect leads to a global monopole directivity pattern as the shear fluctuations compensate for the lower value of the aeolian tone away from the cross-stream direction.
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Gat, Ilana, Georgios Matheou, Daniel Chung, and Paul E. Dimotakis. "Incompressible variable-density turbulence in an external acceleration field." Journal of Fluid Mechanics 827 (August 24, 2017): 506–35. http://dx.doi.org/10.1017/jfm.2017.490.
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Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.
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Huet, Maxime, and Alexis Giauque. "A nonlinear model for indirect combustion noise through a compact nozzle." Journal of Fluid Mechanics 733 (September 23, 2013): 268–301. http://dx.doi.org/10.1017/jfm.2013.442.
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AbstractThe present paper deals with the generation of sound by the passage of acoustic or entropy perturbations through a nozzle in the nonlinear regime and in the low-frequency limit. The analytical model of Marble and Candel for compact nozzles (J. Sound Vib., vol. 55, 1977, pp. 225–243), initially developed for excitations in the linear regime, is rederived and extended to the nonlinear domain. Full nonlinear and second-order models are written for both subcritical and supercritical nozzles in the absence of shock and a detailed methodology is provided for the resolution of the second-order system. The accuracy of the second-order model is assessed for entropy forcings. It is shown to be accurate for all waves, with the exception of the upstream generated wave for subcritical diverging geometries where higher-order nonlinear contributions cannot be neglected. In the context of indirect combustion noise, the phenomenon of regime change of the nozzle due to an incoming entropy fluctuation is also addressed. Regime change is related to a Mach number modification induced by temperature and velocity fluctuations. In the present study, it translates into a limitation of the maximum amplitude of the incoming entropy forcing. Such limitations are to be considered for subcritical nozzles with significant inlet or outlet Mach numbers, where the flow transition is observed even for very low-amplitude entropy excitations. With the constraint of those limitations, the analytical extended nozzle describing functions representing the full nonlinear response for indirect combustion noise are validated through detailed comparisons with numerical simulations.
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Doshi, Parshwanath S., Rajesh Ranjan, and Datta V. Gaitonde. "Global and local modal characteristics of supersonic open cavity flows." Physics of Fluids 34, no. 3 (2022): 034104. http://dx.doi.org/10.1063/5.0082808.
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Flows past cavities at high-speeds have become increasingly important in applications such as flame-holding and propulsion unstart control. Recently maturated linear techniques have helped discern the underlying mechanisms in the subsonic and low supersonic speed regime ([Formula: see text]). Here, we combine these linear methods with fully non-linear two- and three-dimensional simulations to assimilate the significant changes observed when the Mach number is increased further to the [Formula: see text] range. The resolvent method is first employed to analyze cavity-shear layer coupled oscillations and modal characteristics, which are found to differ in key respects from those reported at lower Mach numbers. At higher speeds, more 2D coupled modes are obtained with the dominant modes containing secondary waves displaying elaborate patterns. The role of the shear layer on the cavity dynamics is then examined with local spatial stability analyses. In addition to the well-known Kelvin–Helmholtz instability encountered in the subsonic and transonic regimes, forward-propagating ( k+) supersonic shear layer instabilities are detected at higher speeds. These are associated with Mach wave reflections between the shear layer and the cavity floor and may introduce higher order coupled modes. Furthermore, 3D modal analysis indicates a shift toward the dominance of 3D modes compared to 2D modes; although consistent with compressible free shear layer observations, 2D cavity modes remain significant to higher convective Mach number. When the Reynolds number is increased, resolvent-based mode shapes and frequencies continue to compare favorably with Dynamic Mode Decomposition of large-eddy simulations because of inviscid instability dominance.
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CHANG, KEH-CHIN, and WEN-CHUNG WU. "A STUDY ON FLOW REGIME NEAR CRITICAL RAYLEIGH NUMBER FOR BUOYANCY-DRIVEN CAVITY FLOW." Modern Physics Letters B 19, no. 28n29 (2005): 1635–38. http://dx.doi.org/10.1142/s0217984905010098.
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A benchmark problem with air medium in a square cavity heated by a vertical side is studied in a Ra range near its critical value without using the usual model approximations, such as Boussinesq or low-Mach-number approximation. Two analysis methods of power spectrum and phase trajectory are adopted to distinguish the flow pattern in the cavity. It demonstrates how the flow evolves from transition to turbulent regimes with increasing Ra values.
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Tabrizi, Amir Bashirzadeh, and Binxin Wu. "The role of compressibility in computing noise generated at a cavitating orifice." International Journal of Aeroacoustics 18, no. 1 (2018): 73–91. http://dx.doi.org/10.1177/1475472x18812801.
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The computational fluid dynamics calculation can be accomplished by solving either compressible or incompressible Navier–Stokes equations to determine the flow-field variables of the noise source. The proper assumption depends on both the physical situation and the Mach number. Although in cavitating devices usually we are dealing with low Mach number flow, cavitation is an acoustic phenomenon that can be affected by compressibility. Cavitation behaves acoustically as a monopole and it is mentioned by some researchers that incompressible solution is sufficient to study the dipole sources. However, in order to study the monopole (and quadrupole) sources a compressible solution may be required. In this study, the role of compressibility in computing noise generated at a cavitating single-hole orifice was investigated using large eddy simulation and Ffowcs Williams–Hawkings formulation. The fluid zone downstream of the orifice where the cavitation occurs was evaluated as the acoustic source which generates sound. Time-accurate solutions of the flow-field variables on source surfaces were obtained from both compressible and incompressible flow simulations. Three cases of cavitation were studied and the sound pressure signals far downstream of the orifice were computed by the Ffowcs Williams–Hawkings formulation. For a developed cavitation regime at low frequencies, there is a big discrepancy between the computed values of sound pressure level from compressible and incompressible simulations, and at higher frequencies greater than 6 kHz, both simulation methods provide almost the same values for sound pressure levels. For a super cavitation regime, both compressible and incompressible simulations provide similar values for sound pressure levels at frequencies greater than 2 kHz. The results of this work demonstrate that the compressibility has a significant role in terms of computing noise generated at a cavitating orifice and cannot be ignored, especially when the noise generated by developed cavitation regimes at low frequencies is investigated.
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Vera, M., H. P. Hodson, and R. Vazquez. "The Effects of a Trip Wire and Unsteadiness on a High-Speed Highly Loaded Low-Pressure Turbine Blade." Journal of Turbomachinery 127, no. 4 (2004): 747–54. http://dx.doi.org/10.1115/1.1934446.
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This paper presents the effect of a single spanwise two-dimensional wire upon the downstream position of boundary layer transition under steady and unsteady inflow conditions. The study is carried out on a high turning, high-speed, low pressure turbine (LPT) profile designed to take account of the unsteady flow conditions. The experiments were carried out in a transonic cascade wind tunnel to which a rotating bar system had been added. The range of Reynolds and Mach numbers studied includes realistic LPT engine conditions and extends up to the transonic regime. Losses are measured to quantify the influence of the roughness with and without wake passing. Time resolved measurements such as hot wire boundary layer surveys and surface unsteady pressure are used to explain the state of the boundary layer. The results suggest that the effect of roughness on boundary layer transition is a stability governed phenomena, even at high Mach numbers. The combination of the effect of the roughness elements with the inviscid Kelvin–Helmholtz instability responsible for the rolling up of the separated shear layer (Stieger, R. D., 2002, Ph.D. thesis, Cambridge University) is also examined. Wake traverses using pneumatic probes downstream of the cascade reveal that the use of roughness elements reduces the profile losses up to exit Mach numbers of 0.8. This occurs with both steady and unsteady inflow conditions.
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Proença, A. R., O. De almeida, and R. H. Self. "AERODYNAMICS AND AEROACOUSTICS SURVEY FOR A LOW SPEED SUBSONIC JET OPERATING AT MACH 0.25." Revista de Engenharia Térmica 13, no. 2 (2014): 33. http://dx.doi.org/10.5380/reterm.v13i2.62092.
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The purpose of this work is to study and characterize, in laboratory, the aerodynamics of a free jet operating at subsonic regime and identify its acoustic signature. This study aims to analyze the fundamental role of turbulent flow structures in the total noise produced at different Mach numbers. This work is focused at low speed subsonic jets operating at Mach number 0.25. The research is done by analyzing the data obtained in experiments using Pitot tube, hot-wire anemometer and acoustic measurements. This work also describes the experimental procedures for each step of analysis, as well as the characteristics of jet noise facility. The data from measurements with Pitot tube is used to study the mean velocity profiles. The average properties are also analyzed with anemometry system, likewise used to study the turbulent intensity of eleven axial lines, ranging from the center line to the edge of the nozzle (lipline). These results are compared with the literature and is verified the accuracy of hot-wire anemometers for turbulent intensities lower than 15%. A database with the sound pressure level as a function of frequency is constructed from experiments serving as data for further numerical analysis to solve this problem.
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Gouasmi, Ayoub, Scott M. Murman, and Karthik Duraisamy. "Entropy-stable schemes in the low-Mach-number regime: Flux-preconditioning, entropy breakdowns, and entropy transfers." Journal of Computational Physics 456 (May 2022): 111036. http://dx.doi.org/10.1016/j.jcp.2022.111036.
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Tahani, Mojtaba, Mohammad Hojaji, and Seyed Vahid Mahmoodi Jezeh. "Turbulent jet in crossflow analysis with LES approach." Aircraft Engineering and Aerospace Technology 88, no. 6 (2016): 717–28. http://dx.doi.org/10.1108/aeat-10-2014-0167.
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Purpose This study aims to investigate effects of sonic jet injection into supersonic cross-flow (JISC) numerically in different dynamic pressure ratio values and free stream Mach numbers. Design/methodology/approach Large Eddy simulation (LES) with dynamic Smagorinsky model is used as the turbulence approach. The numerical results are compared with the experimental data, and the comparison shows acceptable validation. Findings According to the results, the dynamic pressure ratio has critical effects on the zone related to barrel shock. Despite free stream Mach number, increasing dynamic pressure ratio leads to expansion of barrel shock zone. Consequently, expanded barrel shock zone would bring about more obstruction effect. In addition, the height of counter-rotating vortex pair increases, and the high-pressure area before jet and low-pressure area after jet will rise. The results show that the position of barrel shock is deviated by increasing free stream Mach number, and the Bow shock zone becomes stronger and close to barrel shock. Moreover, high pressure zone, which is located before the jet, decreases by high free stream Mach number. Practical implications In this study, LES with a dynamic Smagorinsky model is used as the turbulence approach. Effects of sonic JISC are investigated numerically in different dynamic pressure ratio values and free stream Mach numbers. Originality/value As summary, the following are the contribution of this paper in the field of JISC subjects: several case studies of jet condition have been performed. In all the cases, the flow at the nozzle exit is sonic, and the free stream static pressure is constant. To generate proper grid, a cut cell method is used for domain modelling. Boundary condition effect on the wall pressure distribution around the jet and velocity profiles, especially S shape profiles, is investigated. The results show that the relation between representing the location of Mach disk centre and at transonic regime is a function of second-order polynomial, whereas at supersonic regime, the relationship is modelled as a first-order polynomial. In addition, the numerical results are compared with the experimental data demonstrating acceptable validation.
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Kalita, B. C., та N. Devi. "Kinetic Alfvén solitons in a low-β plasma under the influence of electron drift motion". Journal of Plasma Physics 56, № 1 (1996): 35–44. http://dx.doi.org/10.1017/s0022377800019073.
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Fully nonlinear kinetic Alfvén solitary waves are investigated, taking account of the drifting effect of electrons in the direction of the external magnetic field in a low-β plasma (where β = 8πn0T/c2B02 is the ratio of the kinetic pressure to the magnetic pressure). Both compressive and rarefactive Alfvén solitons are found to exist in different ranges of kz (direction of wave propagation), depending on the values of M (the Mach number) and ve (the drift velocity, occurring implicitly in an effective parameter A). The existence domain of kinetic Alfvén solitons is found to be concentrated in the upper regime of β (≪ 1) and lower regime ofM ( < 1), but the values of M in the case of rarefactive solitons are observed to be higher than those of compressive solitons. The range of existence of kinetic Alfvén solitons is substantially narrowed when the initial drift velocity v′e of the electrons is taken into account.
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Deng, S., B. W. van Oudheusden, T. Xiao, and H. Bijl. "A Computational Study on the Aerodynamic Influence of a Propeller on an MAV by Unstructured Overset Grid Technique and Low Mach Number Preconditioning." Open Aerospace Engineering Journal 5, no. 1 (2012): 11–21. http://dx.doi.org/10.2174/1874146001205010011.
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The influence of a propeller on the aerodynamic performance of an MAV is investigated using an unstructured overset grid technique. The flow regime of a fixed-wing MAV powered by a propeller contains both incompressible regions due to the low flight speed, as well as compressible flow areas near the propeller-tip region. In order to simulate all speed flow efficiently, a dual-time preconditioning method is employed in the present study. The methodology in this paper is verified as providing a reliable numerical simulation tool for all flow regimes, in the additional presence of moving boundaries, which is treated with an overset grid approach.
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Khayat, Roger E., and Byung Chan Eu. "Generalized hydrodynamics and linear stability analysis of cylindrical Couette flow of a dilute Lennard–Jones fluid." Canadian Journal of Physics 71, no. 11-12 (1993): 518–36. http://dx.doi.org/10.1139/p93-081.
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Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible fluids and also for incompressible fluids. In the low Reynolds or Mach number regime, if the Knudsen number is sufficiently low, the marginal stability curves calculated by the generalized hydrodynamic theory coincide, within numerical errors, with those based on the Navier–Stokes theory. But there are considerable deviations between them in the regimes beyond those mentioned earlier, since nonlinear effects manifest themselves in the laminar mean flow through the nonlinear dissipation term and normal stresses. There are three marginal stability curves obtained in contrast to the Navier–Stokes theory, which yields only two. The previously observed phase-transition-like behavior in fluid variables and the slip phenomenon are found to occur beyond the hydrodynamic stability point. The disturbance entropy production associated with the Taylor–Couette vortices is calculated to first order in disturbances in flow variables and is found to decrease as the number of vortices increases and thereby the dynamic structure is progressively more organized.
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Desjacques, Vincent, Adi Nusser, and Robin Bühler. "Analytic Solution to the Dynamical Friction Acting on Circularly Moving Perturbers." Astrophysical Journal 928, no. 1 (2022): 64. http://dx.doi.org/10.3847/1538-4357/ac5519.
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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.
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Vilquin, Alexandre, Hamid Kellay, and Jean-François Boudet. "Shock waves induced by a planar obstacle in a vibrated granular gas." Journal of Fluid Mechanics 842 (March 7, 2018): 163–87. http://dx.doi.org/10.1017/jfm.2018.128.
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The low value of the speed of sound in dilute granular media permits the study of the properties of supersonic flows for a wide range of Mach numbers. In this paper, we report the experimental observation of a subsonic–supersonic transition in a vibrated granular gas. The shock fronts studied are obtained by simply pushing a rectangular obstacle into the granular gas for different obstacle velocities. The supersonic regime is characterized by the formation of normal shock waves whose width increases when the Mach number decreases to values close to 1. The bimodal model proposed by Mott-Smith in the 1950s provides a good description for the velocity distributions as well as the macroscopic quantities for shock waves in molecular gases but remains inadequate for dissipative media like granular gases and plasmas. Here by examining the shock front structure for a wide range of Mach numbers, we adapt the Mott-Smith bimodal description to a dissipative medium. By using balance equations from granular kinetic theory and taking into account different dissipation sources, the proposed model allows us to understand how this dissipation modifies temperature, mean velocity and volume fraction profiles through the shock front.
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Dimarco, Giacomo, Raphaël Loubère, Victor Michel-Dansac, and Marie-Hélène Vignal. "Second-order implicit-explicit total variation diminishing schemes for the Euler system in the low Mach regime." Journal of Computational Physics 372 (November 2018): 178–201. http://dx.doi.org/10.1016/j.jcp.2018.06.022.
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Rieper, Felix, and Georg Bader. "The influence of cell geometry on the accuracy of upwind schemes in the low mach number regime." Journal of Computational Physics 228, no. 8 (2009): 2918–33. http://dx.doi.org/10.1016/j.jcp.2009.01.002.
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Wu, J. S., S. Y. Chou, U. M. Lee, Y. L. Shao, and Y. Y. Lian. "Parallel DSMC Simulation of a Single Under-Expanded Free Orifice Jet From Transition to Near-Continuum Regime." Journal of Fluids Engineering 127, no. 6 (2005): 1161–70. http://dx.doi.org/10.1115/1.2062807.
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This paper describes the numerical analysis of the flow structure of a single underexpanded argon free jet issuing into a lower-pressure or vacuum environment using the parallel three-dimensional direct simulation Monte Carlo (DSMC) method employing dynamic domain decomposition. Unstructured and tetrahedral solution-based refined mesh depending on the local mean free path is used to improve the resolution of solution. Simulated Knudsen numbers of the stagnation conditions based on orifice diameter, Reynolds numbers based on the conditions at the orifice exit, and stagnation-to-background pressure ratios are in the range of 0.0005–0.1, 7–1472, and 5-∞, respectively, where “∞” represents vacuum condition in the background environment. Results show that centerline density decays in a rate proportional to the inverse of the square of the axial distance (z−2) from the orifice for all ranges of flow in the current study. The more rarefied the background condition is, the longer the z−2-regime is. In addition, a distinct flow structure, including barrel shock, Mach disk and jet boundary, is clearly identified as the Knudsen number reaches as low as 0.001. Predicted location and size of Mach disk in the near-continuum limit (Kn=0.001,0.0005) are found to be in reasonable agreement with experimental results in the continuum regime.
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Yamouni, Sami, Denis Sipp, and Laurent Jacquin. "Interaction between feedback aeroacoustic and acoustic resonance mechanisms in a cavity flow: a global stability analysis." Journal of Fluid Mechanics 717 (February 1, 2013): 134–65. http://dx.doi.org/10.1017/jfm.2012.563.
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AbstractWe perform a global stability analysis of a flow over an open cavity, characterized by a Reynolds number, based on the upstream velocity and the cavity length, of $7500$. We compute base flows and unstable global modes of the flow for different Mach numbers ranging from $0$ to $0. 9$. In the incompressible regime ($M= 0$), we show that the flow is subject to global instabilities due to Kelvin–Helmholtz instabilities in the shear layer, which become strengthened by a hydrodynamic pressure feedback. The influence of the boundary-layer thickness and of the length-to-depth ratio of the cavity on these shear-layer modes has been investigated. In the compressible regime ($M\gt 0$), we have shown that all unstable global modes are continuously connected to the incompressible shear-layer modes as $M\rightarrow 0$. These shear-layer modes correspond to the beginning of branches of global modes, whose frequencies evolve (as a function of the Mach number), in accordance with the feedback aeroacoustic mechanism (Rossiter, Tech. Rep. Aero. Res. Counc. R. & M., 1964). We have also identified branches of global modes behaving in agreement with acoustic resonance mechanisms (East, J. Sound Vib., vol. 3, 1966, pp. 277–287; Tam, J. Sound Vib., vol. 49, 1976, pp. 353–364; Koch, AIAA J., vol. 43, 2005, pp. 2342–2349). At the intersections between both types of branches, the growth rate of the global modes is seen to display a local maximum. Along the aeroacoustic feedback branches, the number of vortical structures in the shear layer is kept constant, while the pressure pattern inside the cavity is conserved along the acoustic resonance branches. We show that both the feedback aeroacoustic and acoustic resonance mechanisms are at play over the entire subsonic regime, from $M= 0$ to $M= 0. 9$. At low Mach numbers, we suggest that it is still the feedback aeroacoustic mechanism that selects the frequency, even though the fundamental acoustic resonance mode is also important due to enhancing the response. At higher Mach numbers, we observe that the pressure pattern of the acoustic resonance modes (fundamental acoustic modes, first longitudinal acoustic modes, first longitudinal-depth acoustic modes) inside the cavity determines the directivity of the radiated noise. Links with experimental results are finally discussed.
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GILL, TARSEM SINGH, HARVINDER KAUR, and NARESHPAL SINGH SAINI. "Dust-acoustic solitary waves in a finite temperature dusty plasma with variable dust charge and two temperature ions." Journal of Plasma Physics 70, no. 4 (2004): 481–95. http://dx.doi.org/10.1017/s0022377803002733.
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In this paper, the characteristics of dust-acoustic solitary waves in dusty plasma are studied. Dust charge and temperature are treated as variables. The authors have used the pseudopotential method to investigate the possibility of compressive as well as rarefactive solitons. An expression for the pseudopotential has been derived. The pseudopotential is a function of the Mach number, the relative temperature of low and high ion components, the relative ion concentration of dust charge and the temperature. Numerical computation shows that for the chosen set of parameters, only compressive solitons exist and their amplitudes increase with increasing Mach number. An increase in the dust temperature results in the disappearance of the compressive soliton. It is the only small parameter regime where compressive as well rarefactive solitons coexist. The effect of the relative ion temperature on solitons is also investigated. In the small amplitude limit, an increase in the dust temperature leads to a transition from compressive to rarefactive solitons.
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Yan, Chian, Hong Hui Teng, Xiao Cheng Mi, and Hoi Dick Ng. "The Effect of Chemical Reactivity on the Formation of Gaseous Oblique Detonation Waves." Aerospace 6, no. 6 (2019): 62. http://dx.doi.org/10.3390/aerospace6060062.
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High-fidelity numerical simulations using a Graphics Processing Unit (GPU)-based solver are performed to investigate oblique detonations induced by a two-dimensional, semi-infinite wedge using an idealized model with the reactive Euler equations coupled with one-step Arrhenius or two-step induction-reaction kinetics. The novelty of this work lies in the analysis of chemical reaction sensitivity (characterized by the activation energy Ea and heat release rate constant kR) on the two types of oblique detonation formation, namely, the abrupt onset with a multi-wave point and a smooth transition with a curved shock. Scenarios with various inflow Mach number regimes M0 and wedge angles θ are considered. The conditions for these two formation types are described quantitatively by the obtained boundary curves in M0–Ea and M0–kR spaces. At a low M0, the critical Ea,cr and kR,cr for the transition are essentially independent of the wedge angle. At a high flow Mach number regime with M0 above approximately 9.0, the boundary curves for the three wedge angles deviate substantially from each other. The overdrive effect induced by the wedge becomes the dominant factor on the transition type. In the limit of large Ea, the flow in the vicinity of the initiation region exhibits more complex features. The effects of the features on the unstable oblique detonation surface are discussed.
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Collé, Anthony, Jérôme Limido, and Jean-Paul Vila. "An Accurate SPH Scheme for Dynamic Fragmentation modelling." EPJ Web of Conferences 183 (2018): 01030. http://dx.doi.org/10.1051/epjconf/201818301030.
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We focus on the use of a meshless numerical method called Smooth Particle Hydrodynamics (SPH), to solve fragmentation issues as Hyper Velocity Impact (HVI) cases. Firstly applied to fluid flow simulations, this method can be extended to the solid dynamics framework. However it suffers from a lack of accuracy when evaluating state variables as the pressure field. And such inaccuracy generally generates non-physical processes (as numerical fragmentation). In the hydrodynamic context, SPH-ALE methods based on Riemann solvers significantly improve this evaluation, but increase the scheme complexity and low-Mach issues are difficult to prevent. We propose an alternative scheme called γ-SPH-ALE, firstly implemented to solve multi-regime barotropic flows, and secondly extended to solid dynamic cases. It relies on the combination of the SPH-ALE formalism and a finite volume stabilizing low-Mach scheme. Its characteristics are detailed and evaluated through a nonlinear stability analysis, highlighting CFL-like conditions on the scheme parameters. Finally, its implementation on several test cases reveals that the proposed scheme actually increases both stability and accuracy, in reduced computation time, with respect to classical solvers.
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Feireisl, Eduard, Mária Lukáčová-Medviďová, Šárka Nečasová, Antonín Novotný, and Bangwei She. "Asymptotic Preserving Error Estimates for Numerical Solutions of Compressible Navier--Stokes Equations in the Low Mach Number Regime." Multiscale Modeling & Simulation 16, no. 1 (2018): 150–83. http://dx.doi.org/10.1137/16m1094233.
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MAYER, CHRISTIAN S. J., DOMINIC A. VON TERZI, and HERMANN F. FASEL. "Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3." Journal of Fluid Mechanics 674 (January 13, 2011): 5–42. http://dx.doi.org/10.1017/s0022112010005094.
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A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer at Mach 3. Its downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using linear-stability theory, parabolized stability equations and direct numerical simulations (DNS). In the present paper, the linear regime is studied first in great detail. The focus of the second part is the early and late nonlinear regimes. It is shown how the disturbance wave spectrum is filled up by nonlinear interactions and which flow structures arise and how these structures locally break down to small scales. Finally, the study answers the question whether a fully developed turbulent boundary layer can be reached by oblique breakdown. It is shown that the skin friction develops such as is typical of transitional and turbulent boundary layers. Initially, the skin friction coefficient increases in the streamwise direction in the transitional region and finally decays when the early turbulent state is reached. Downstream of the maximum in the skin friction, the flow loses its periodicity in time and possesses characteristic mean-flow and spectral properties of a turbulent boundary layer. The DNS data clearly demonstrate that oblique breakdown can lead to a fully developed turbulent boundary layer and therefore it is a relevant mechanism for transition in two-dimensional supersonic boundary layers.
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Theofanous, T. G., G. J. Li, and T. N. Dinh. "Aerobreakup in Rarefied Supersonic Gas Flows." Journal of Fluids Engineering 126, no. 4 (2004): 516–27. http://dx.doi.org/10.1115/1.1777234.
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We present new experimental results on the interfacial instabilities and breakup of Newtonian liquid drops suddenly exposed to rarefied, high-speed (Mach 3) air flows. The experimental approach allows for the first time detailed observation of interfacial phenomena and mixing throughout the breakup cycle over a wide range of Weber numbers. Key findings are that Rayleigh-Taylor instability alone is the active mechanism for freestream Weber numbers as low as 28 for low viscosity liquids and that stripping rather than piercing is the asymptotic regime as We→∞. This and other detailed visual evidence over 26<We<2,600 are uniquely suitable for testing Computational Fluid Dynamics (CFD) simulations on the way to basic understanding of aerobreakup over a broad range of conditions.
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Zou, Ziqiang, Nicolas Grenier, Samuel Kokh, Christian Tenaud, and Edouard Audit. "Compressible solver for two-phase flows with sharp interface and capillary effects preserving accuracy in the low Mach regime." Journal of Computational Physics 448 (January 2022): 110735. http://dx.doi.org/10.1016/j.jcp.2021.110735.
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Rieper, Felix. "On the dissipation mechanism of upwind-schemes in the low Mach number regime: A comparison between Roe and HLL." Journal of Computational Physics 229, no. 2 (2010): 221–32. http://dx.doi.org/10.1016/j.jcp.2009.09.043.
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