Showing papers on "Mach number published in 2018"

Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

Abstract: To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of 1 x 10^6. The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97 % of the total acoustic energy at these angles and more than 65 % (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin–Helmholtz mode in the near-nozzle region.

Direct Numerical Simulation Database for Supersonic and Hypersonic Turbulent Boundary Layers

Abstract: In this paper, we present a direct numerical simulation database of high-speed zero-pressure-gradient turbulent boundary layers developing spatially over a flat plate with nominal freestream Mach number ranging from 2.5 to 14 and wall-to-recovery temperature ranging from 0.18 to 1.0. The flow conditions of the DNS are representative of the operational conditions of the Purdue Mach 6 quiet tunnel, the Sandia Hypersonic Wind Tunnel at Mach 8, and the AEDC Hypervelocity Tunnel No. 9 at Mach 14. The DNS database is used to gauge the performance of compressibility transformations, including the classical Morkovin's scaling and strong Reynolds analogy as well as the newly proposed mean velocity and temperature scalings that explicitly account for wall heat flux. Several insights into the effect of direct compressibility are gained by inspecting the thermodynamic fluctuations and the Reynolds stress budget terms. Precomputed flow statistics, including Reynolds stresses and their budgets, will be available at the website of the NASA Langley Turbulence Modeling Resource, allowing other investigators to query any property of interest.

Aerodynamic heating in transitional hypersonic boundary layers: Role of second-mode instability

Abstract: The evolution of second-mode instabilities in hypersonic boundary layers and its effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using fast-response pressure sensors, fluorescent temperature-sensitive paint, and particle image velocimetry. Calculations based on parabolic stability equations and direct numerical simulations are also performed. It is found that second-mode waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As the second-mode waves decay downstream, the dilatation-induced aerodynamic heating decreases while its shear-induced counterpart keeps growing. The latter brings about a second growth of the surface temperature when transition is completed.

Kinetic energy transfer in compressible isotropic turbulence

Abstract: Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales.

Jet-flap interaction tones

Abstract: Motivated by the problem of jet–flap interaction noise, we study the tonal dynamics that occurs when an isothermal turbulent jet grazes a sharp edge. We perform hydrodynamic and acoustic pressure measurements to characterise the tones as a function of Mach number and streamwise edge position. The observed distribution of spectral peaks cannot be explained using the usual edge-tone model, in which resonance is underpinned by coupling between downstream-travelling Kelvin–Helmholtz wavepackets and upstream-travelling sound waves. We show, rather, that the strongest tones are due to coupling between Kelvin–Helmholtz wavepackets and a family of trapped, upstream-travelling acoustic modes in the potential core, recently studied by Towne et al. (J. Fluid Mech. vol. 825, 2017) and Schmidt et al. (J. Fluid Mech. vol. 825, 2017). We also study the band-limited nature of the resonance, showing the high-frequency cutoff to be due to the frequency dependence of the upstream-travelling waves. Specifically, at high Mach number, these modes become evanescent above a certain frequency, whereas at low Mach number they become progressively trapped with increasing frequency, which inhibits their reflection in the nozzle plane.

Numerical simulation and analysis of condensation shocks in cavitating flow

Abstract: We analyse unsteady cavity dynamics, cavitation patterns and instability mechanisms governing partial cavitation in the flow past a sharp convergent–divergent wedge. Reproducing a recent reference experiment by numerical simulation, the investigated flow regime is characterised by large-scale cloud cavitation. In agreement with the experiments, we find that cloud shedding is dominated by the periodic occurrence of condensation shocks, propagating through the two-phase medium. The physical model is based on the homogeneous mixture approach, the assumption of thermodynamic equilibrium, and a closed-form barotropic equation of state. Compressibility of water and water vapour is taken into account. We deliberately suppress effects of molecular viscosity, in order to demonstrate that inertial effects dominate the flow evolution. We qualify the flow predictions, and validate the numerical approach by comparison with experiments. In agreement with the experiments, the vapour volume fraction within the partial cavity reaches values for its spanwise average. Very good agreement is further obtained for the shedding Strouhal number, the cavity growth and collapse velocities, and for typical coherent flow structures. In accordance with the experiments, the simulations reproduce a condensation shock forming at the trailing part of the partial cavity. It is demonstrated that it satisfies locally Rankine–Hugoniot jump relations. Estimation of the shock propagation Mach number shows that the flow is supersonic. With a magnitude of only a few kPa, the pressure rise across the shock is much lower than for typical cavity collapse events. It is thus far too weak to cause cavitation erosion directly. However, by affecting the dynamics of the cavity, the flow aggressiveness can be significantly altered. Our results indicate that, in addition to classically observed re-entrant jets, condensation shocks feed an intrinsic instability mechanism of partial cavitation.

Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances

Abstract: A random forcing approach was implemented into a high-order accurate finite-difference code in order to investigate ‘natural’ laminar–turbulent transition in hypersonic boundary layers. In hypersonic transition wind-tunnel experiments, transition is caused ‘naturally’, by free-stream disturbances even when so-called quiet tunnels are employed such as the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The nature and composition of the free-stream disturbance environment in high-speed transition experiments is difficult to assess and therefore largely unknown. Consequently, in the direct numerical simulations (DNS) presented here, the free-stream disturbance environment is simply modelled by random pressure (acoustic) disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers. Results of a high-resolution DNS for a flared cone at Mach 6, using the random forcing approach, are presented and compared to a fundamental breakdown simulation using a ‘controlled’ disturbance input (with a specified frequency and azimuthal wavenumber). The DNS results with random forcing clearly exhibit the ‘primary’ and ‘secondary’ streak pattern, which has previously been observed in our ‘controlled’ breakdown simulations and the experiments in the BAM6QT. In particular, the spanwise spacing of the ‘primary’ streaks for the random forcing case is identical to the spacing obtained from the ‘controlled’ fundamental breakdown simulation. A comparison of the wall pressure disturbance signals between the random forcing DNS and experimental data shows remarkable agreement. The random forcing approach seems to be a promising strategy to investigate nonlinear breakdown in hypersonic boundary layers without introducing any bias towards a distinct nonlinear breakdown mechanism and/or the selection of specific frequencies or wavenumbers that is required in the ‘controlled’ breakdown simulations.

Wall-Modeled Large-Eddy Simulation of Transonic Airfoil Buffet at High Reynolds Number

Abstract: In this study, wall-modeled large-eddy simulation of transonic buffet phenomena over the OAT15A supercritical airfoil at two different Mach number conditions (nonbuffet M∞=0.715 and buffet M∞=0.73 ...

Vertical-axis wind turbine experiments at full dynamic similarity

Abstract: Laboratory experiments were performed on a geometrically scaled vertical-axis wind turbine model over an unprecedented range of Reynolds numbers, including and exceeding those of the full-scale turbine. The study was performed in the high-pressure environment of the Princeton High Reynolds number Test Facility (HRTF). Utilizing highly compressed air as the working fluid enabled extremely high Reynolds numbers while still maintaining dynamic similarity by matching the tip speed ratio (defined as the ratio of tip velocity to free stream, λ = ωR/U) and Mach number (defined at the turbine tip, Ma = ωR/a). Preliminary comparisons are made with measurements from the full-scale field turbine. Peak power for both the field data and experiments resides around λ = 1. In addition, a systematic investigation of trends with Reynolds number was performed in the laboratory, which revealed details about the asymptotic behaviour. It was shown that the parameter that characterizes invariance in the power coefficient was the Reynolds number based on blade chord conditions (Re_c). The power coefficient reaches its asymptotic value when Re_c > 1.5 x 10^6, which is higher than what the field turbine experiences. The asymptotic power curve is found, which is invariant to further increases in Reynolds number.

All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics

Abstract: This paper presents an asymptotic preserving (AP) all Mach number finite volume shock capturing method for the numerical solution of compressible Euler equations of gas dynamics Both isentropic and full Euler equations are considered The equations are discretized on a staggered grid This simplifies flux computation and guarantees a natural central discretization in the low Mach limit, thus dramatically reducing the excessive numerical diffusion of upwind discretizations Furthermore, second order accuracy in space is automatically guaranteed For the time discretization we adopt an Semi-IMplicit/EXplicit (S-IMEX) discretization getting an elliptic equation for the pressure in the isentropic case and for the energy in the full Euler case Such equations can be solved linearly so that we do not need any iterative solver thus reducing computational cost Second order in time is obtained by a suitable S-IMEX strategy taken from Boscarino et al (J Sci Comput 68:975–1001, 2016) Moreover, the CFL stability condition is independent of the Mach number and depends essentially on the fluid velocity Numerical tests are displayed in one and two dimensions to demonstrate performance of our scheme in both compressible and incompressible regimes

Shock-wave structure for a polyatomic gas with large bulk viscosity

Abstract: Numerical simulation and theoretical analysis based on a model Boltzmann equation show that a plane shock wave in a polyatomic gas with large bulk viscosity exhibits three different types of structure, depending on the upstream Mach number.

Newly identified principle for aerodynamic heating in hypersonic flows

Abstract: Instability evolution in a transitional hypersonic boundary layer and its effects on aerodynamic heating are investigated over a 260 mm long flared cone. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP) and particle image velocimetry (PIV). Calculations are also performed based on both the parabolized stability equations (PSE) and direct numerical simulations (DNS). Four unit Reynolds numbers are studied, 5.4, 7.6, 9.7 and . As the second-mode waves decay downstream, the low-frequency waves continue to grow, with the consequent shear-induced heating increasing. The latter brings about a second, weaker growth of surface-temperature HT. A theoretical analysis is provided to interpret the temperature distribution resulting from the aerodynamic heating.

Experimental analysis of transonic buffet on a 3D swept wing using fast-response pressure-sensitive paint

Abstract: Transonic buffeting phenomena on a three-dimensional swept wing were experimentally analyzed using a fast-response pressure-sensitive paint (PSP). The experiment was conducted using an 80%-scaled NASA Common Research Model in the Japan Aerospace Exploration Agency (JAXA) 2 m × 2 m Transonic Wind Tunnel at a Mach number of 0.85 and a chord Reynolds number of 1.54 × 106. The angle of attack was varied between 2.82° and 6.52°. The calculation of root-mean-square (RMS) pressure fluctuations and spectral analysis were performed on measured unsteady PSP images to analyze the phenomena under off-design buffet conditions. We found that two types of shock behavior exist. The first is a shock oscillation characterized by the presence of “buffet cells” formed at a bump Strouhal number St of 0.3–0.5, which is observed under all off-design conditions. This phenomenon arises at the mid-span wing and is propagated spanwise from inboard to outboard. The other is a large spatial amplitude shock oscillation characterized by low-frequency broadband components at St < 0.1, which appears at higher angles of attack (α ≥ 6.0°) and behaves more like two-dimensional buffet. The transition between these two shock behaviors correlates well with the rapid increase of the wing-root strain fluctuation RMS.

Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach

Abstract: Shock-dominated hypersonic laminar flows over a double cone are investigated using time accurate direct simulation Monte Carlo combined with the residuals algorithm for unit Reynolds numbers gradually increasing from 9.35 × 104 to 3.74 × 105 m−1 at a Mach number of about 16. The main flow features, such as the strong bow-shock, location of the separation shock, the triple point, and the entire laminar separated region, show a time-dependent behavior. Although the separation shock angle is found to be similar for all Re numbers, the effects of Reynolds number on the structure and extent of the separation region are profound. As the Reynolds number is increased, larger pressure values in the under-expanded jet region due to strong shock interactions form more prominent λ-shocklets in the supersonic region between two contact surfaces. Likewise, the surface parameters, especially on the second cone surface, show a strong dependence on the Reynolds number, with skin friction, pressure, and surface heating rates increasing and velocity slip and temperature jump values decreasing for increasing Re number. A Kelvin-Helmholtz instability arising at the shear layer results in an unsteady flow for the highest Reynolds number. These findings suggest that consideration of experimental measurement times is important when it comes to determining the steady state surface parameters even for a relatively simple double cone geometry at moderately large Reynolds numbers.

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules.

Abstract: Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002)JSTPBS0022-471510.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

Simulation and stability analysis of oblique shock wave/boundary layer interactions at Mach 5.92

Abstract: Above a critical angle, an oblique shock impinging on a Mach 5.92 boundary layer causes the resulting separated flow to become unstable. Direct numerical simulation and global stability analysis reveal the physical mechanism that drives this three-dimensional instability.

DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality

Abstract: A direct-numerical-simulation study of spatially evolving compressible zero-pressure-gradient turbulent boundary layers is presented for a fine-meshed range of Mach numbers from 0.3 to 2.5. The use of an identical set-up for all subsonic and supersonic cases warrants proper comparability and allows a highly reliable quantitative evaluation of compressible mean-flow scaling laws and the settlement on a commonly accepted compressible mean-flow velocity profile in the considered Mach and Reynolds number range. All data are compared to the literature data-base where significant data scattering can be observed. The skin-friction distribution was found in excellent agreement with the prediction by the van Driest-II transformation. Contrary to the prevailing appraisal, the wake region of the mean-velocity profile is observed to scale much better with the momentum-thickness Reynolds number calculated with the far-field-viscosity than with the wall-viscosity. The time-averaged velocity fluctuations, density-scaled according to Morkovin’s hypothesis, are found to be noticeably influenced by compressibility effects in the inner layer as well as in the wake region. Allowing wall-temperature fluctuations affects neither the density nor velocity fluctuations.

Propagation of a Strong Shock Over a Random Bed of Spherical Particles

Abstract: Propagation of a strong incident shock through a bed of particles results in complex wave dynamics such as a reflected shock, a transmitted shock, and highly unsteady flow inside the particle bed. In this paper we present three-dimensional numerical simulations of shock propagation in air over a random bed of particles. We assume the flow is inviscid and governed by the Euler equations of gas dynamics. Simulations are carried out by varying the volume fraction of the particle bed at a fixed shock Mach number. We compute the unsteady inviscid streamwise and transverse drag coefficients as a function of time for each particle in the random bed for different volume fractions. We show that (i) there are significant variations in the peak drag for the particles in the bed, (ii) the mean peak drag as a function of streamwise distance through the bed decreases with a slope that increases as the volume fraction increases, and (iii) the deviation from the mean peak drag does not correlate with local volume fraction. We also present the local Mach number and pressure contours for the different volume fractions to explain the various observed complex physical mechanisms occurring during the shock–particle interactions. Since the shock interaction with the random bed of particles leads to transmitted and reflected waves, we compute the average flow properties to characterize the strength of the transmitted and reflected shock waves and quantify the energy dissipation inside the particle bed. Finally, to better understand the complex wave dynamics in a random bed, we consider a simpler approximation of a planar shock propagating in a duct with a sudden area change. We obtain Riemann solutions to this problem, which are used to compare with fully resolved numerical simulations.

Numerical investigation of nanosecond pulsed plasma actuators for control of shock-wave/boundary-layer separation

Abstract: This study numerically explores the flow physics associated with nanosecond pulsed plasma actuators that are designed to control shock-wave induced boundary-layer separation in a Mach 2.8 supersonic flow. By using two dielectric barrier surface discharge actuator configurations, parallel and canted with respect to the flow velocity vector, a previous experiment suggested that the actuator worked in two ways to influence the interaction: boundary layer heating and vorticity production. The heating effect was enhanced with the parallel electrode and made the boundary-layer separation stronger, while the canted electrode produced vorticity and suppressed the boundary-layer separation due to the momentum transfer from the core flow. Because the detailed physical processes are still unclear, in this paper a numerical investigation is undertaken with a large eddy simulation and an energy deposition model for the plasma actuation, in which the dielectric barrier discharge produced plasma is approximated as a high temperature region. The flow characteristics without the plasma actuation correspond to the experimental observation, indicating that the numerical method successfully resolves the shock-wave/boundary-layer interaction. With the plasma actuation, complete agreement between the experiment and calculation has not been obtained in the size of the shock-wave/boundary-layer interaction region. Nevertheless, as with the experiment, the calculation successfully demonstrates definite difference between the parallel and canted electrodes: the parallel electrode causes excess heating and increases the strength of the interaction, while the canted electrode leads to a reduction of the interaction strength, with a corresponding thinning of the boundary layer due to the momentum transfer. The counter flow created by the canted actuator plays an important role in the vortex generation, transferring momentum to the boundary layer and, consequently, mitigating the shock induced boundary layer separation.

Experimental study of the mean structure and quasi-conical scaling of a swept-compression-ramp interaction at Mach 2

Abstract: This study investigates the mean flow structure of two shock-wave boundary-layer interactions generated by moderately swept compression ramps in a Mach 2 flow. The ramps have a compression angle of either or and a sweep angle of . The primary diagnostic methods used for this study are surface-streakline flow visualization and particle image velocimetry. The shock-wave boundary-layer interactions are shown to be quasi-conical, with the intermittent region, separation line and reattachment line all scaling in a self-similar manner outside of the inception region. This is one of the first studies to investigate the flow field of a swept ramp using particle image velocimetry, allowing more sensitive measurements of the velocity flow field than previously possible. It is observed that the streamwise velocity component outside of the separated flow reaches the quasi-conical state at the same time as the bulk surface flow features. However, the streamwise and cross-stream components within the separated flow take longer to recover to the quasi-conical state, which indicates that the inception region for these low-magnitude velocity components is actually larger than was previously assumed. Specific scaling laws reported previously in the literature are also investigated and the results of this study are shown to scale similarly to these related interactions. Certain limiting cases of the scaling laws are explored that have potential implications for the interpretation of cylindrical and quasi-conical scaling.

Grid sensitivity of flow field and noise of high-Reynolds-number jets computed by large-eddy simulation:

Abstract: Three isothermal round jets at a Mach number of 0.9 and a diameter-based Reynolds number of 105 are computed by large-eddy simulation using four different meshes in order to investigate the grid se...