Showing papers on "Mach number published in 1991"

Motion of particles with inertia in a compressible free shear layer

Abstract: The effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion are studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by tau, the ratio of particle response time to the flow time scales (Stokes' number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like tau up to tau = 1 and taper off at higher tau. For tau = 0.2 the error is about 2 percent. In the flow visualizations based on Mie scattering, particles with tau more than 0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.

Self-similar jets

Abstract: General arguments and numerical calculations are used to show that the flow caused by a supersonic gas jet is self-similar under certain conditions. If we assume that the jet has a high initial Mach number and is generated in a region small compared to its length, then the type of similarity solution depends on the density distribution of the gas through which the jet propagates. If this density decreases faster than 1/R 2 , where R is the distance from the source, then the length of the jet increases linearly with time and it may evolve into a classical double if it subsequently encounters a region of higher density.

Experimental study of compressible turbulent mixing layers

Abstract: Compressible, turbulent mixing layers have been investigated experimentally using pressure mesurements, Schlieren photographs, and velocity measurements with a two-component laser Doppler velocimeter system. Seven mixing-layer cases were examined, with relative Mach numbers ranging from 0.40 to 1.97 which spans the region of significant compressibility effects. Both the spatial development and similarty of the mixing layers were considered.

Noise produced by a sawtooth trailing edge

Abstract: An analysis is made of the noise produced by low Mach number turbulent flow over the serrated edge of a flat plate airfoil at zero angle of attack. The serrations are of sawtooth profile of wavelength λ and root‐to‐tip distance 2h. At frequencies ω satisfying ωh/U≫1 (where U is the velocity of the main stream) it is predicted that the intensity of the radiation is reduced relative to that produced by the same flow over an unserrated edge by at least 10×log[1+(4h/λ)2] dB. Predictions are contrasted with analogous results derived [M. S. Howe, J. Fluids Struct. 5, 33–45 (1991)] for smoothly varying serrations of sinusoidal profile, for which it was concluded that attenuations of order 10×log(6h/λ) dB are possible.

Unsteady wave structure near separation in a Mach 5 compression rampinteraction

Abstract: Fluctuating wall-pressure measurements have been made under the unsteady separation shock and the separated shear layer in a Mach 5 compression ramp-induced turbulent interaction. The freestream unit Reynolds number was 49.6x10 6 m -1 and the turbulent boundary layer developed on the tunnel floor under approximately adiabatic wall-temperature conditions. Conditional sampling and «variable-window» ensemble-averaging techniques have been used to determine ensemble-averaged pressure distributions for different separation shock-wave positions.

Structure of the compressible turbulent shear layer

Abstract: The large-scale structure of the turbulent compressible shear layer is investigated in a two-stream supersonic wind tunnel. Double-exposure schlieren photography reveals that the two convective Mach numbers, corresponding to each side of the shear layer, are very different: one is sonic or supersonic and the other is low subsonic. This contradicts the current isentropic large-scale-structure model, which predicts the convective Mach numbers to be equal or very close. It is speculated that effects of shock waves are responsible for these asymmetries.

Compressible stability of growing boundary layers using parabolized stability equations

Abstract: The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

Real gas effects on hypersonic boundary-layer stability

Abstract: High‐temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high‐temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as ‘‘real gas model.’’ In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.

Linear and nonlinear stability of boundary layers with streamwise varying properties

Abstract: We present a new technique for the study of transition in convectively unsta­ ble flows that employs nonlinear partial diflerential equations of parabolic type based on the slow change of the betsic-flow and the disturbance velocity profiles, wavelength, and growth rate in the streamwise direction. Solutions comparable in accuracy to direct Navier-Stokes simulations can be obtained with a marching procedure utilizing a small fraction of the computationed cost. The development of Tollmien-Schlichting waves in the Blasius boundary layer is investigated. The results are compared with previous work and the effects of nonparaJlelism and nonlinearity are clarified. The effect of nonparallelism on two-dimensional waves is confirmed to be weak and consequently not responsible for the discrepancies between measurements and theoretical results for parallel flow. Possible reasons for the discrepancy are discussed. The effect of basic-flow nonparallelism becomes stronger on oblique waves. While nonlinear effects are small near branch I of the neutral curve, they are significant near branch II and delay or even prevent the decay of the wave. The linearized FSE equations are extended to compressible flow. Results up to a Mach number of 1.6 indicate that compressibility does not alter significantly

An investigation of a contoured wall injector for hypervelocity mixing augmentation

Abstract: An experimental and computational investigation of a contoured wall fuel injector is presented. The injector was aimed at enabling shock-enhanced mixing for the supersonic combustion ramjet engines currently envisioned for applications on hypersonic vehicles. Three-dimensional flow field surveys, and temporally resolved planar Rayleigh scattering measurements are presented for Mach 1.7 helium injection into Mach 6 air. These experimental data are compared directly with a three-dimensional Navier-Stokes simulation of the flow about the injector array. Two dominant axial vorticity sources are identified and characterized. The axial vorticity produced strong convective mixing of the injectant with the freestream. Shock-impingement was particularly effective as it assured seeding of baroclinic vorticity directly on the helium/air interface. The vorticity coalesced into a counter-rotating vortex pair of a sense which produced migration of the helium away from the wall. The influences of spatial averaging on the representation of the flow field as well as the importance of the fluctuating component of the flow in producing molecularly-mixed fluid are addressed.

Proxy studies of energy transfer to the magnetosphere

Abstract: The transfer of energy into the magnetosphere is studied using as proxy the Am geomagnetic index and multilinear regressions and correlations with solar wind data. In particular, the response of Am to the reconnection mechanism is examined in relation to the orientation of the interplanetary magnetic field as well as the upstream plasma parameters. A functional dependence of Am on clock angle, the orientation of the IMF in the plane perpendicular to the flow, is derived after first correcting the index for nonreconnection effects due to dynamic pressure and velocity. An examination of the effect of upstream magnetosonic Mach number shows the reconnection mechanism to become less efficient at high Mach numbers. The reconnection mechanism is shown to be slightly enhanced by higher dynamic pressures.

The equations of nearly incompressible fluids. I. Hydrodynamics, turbulence, and waves

Abstract: A unified analysis delineating the conditions under which the equations of classical incompressible and compressible hydrodynamics are related in the absence of large‐scale thermal, gravitational, and field gradients is presented. By means of singular expansion techniques, a method is developed to derive modified systems of fluid equations in which the effects of compressibility are admitted only weakly in terms of the incompressible hydrodynamic solutions (hence ‘‘nearly incompressible hydrodynamics’’). Besides including molecular viscosity self‐consistently, the role of thermal conduction in an ideal fluid is also considered. With the inclusion of heat conduction, it is found that two distinct routes to incompressibility are possible, distinguished according to the relative magnitudes of the temperature, density, and pressure fluctuations. This leads to two distinct models for thermally conducting, nearly incompressible hydrodynamics—heat‐fluctuation‐dominated hydrodynamics (HFDH’s) and heat‐fluctuation‐modified hydrodynamics (HFMD’s). For the HFD case, the well‐known classical passive scalar equation for temperature is derived as one of the nearly incompressible fluid equations and temperature and density fluctuations are predicted to be anticorrelated. For HFM fluids, a new thermal transport equation, in which compressible acoustic effects are present, is obtained together with a more‐complicated ‘‘correlation’’ between temperature, density, and pressure fluctuations. Although the equations of nearly incompressible hydrodynamics are envisaged principally as being applicable to homogeneous turbulence and wave propagation in low Mach number flow, it is anticipated that their applicability is likely to be far greater.

Parametric study of thermal and chemical nonequilibrium nozzle flow

Abstract: A numerical analysis of a thermochemical nonequilibrium inviscid nozzle flow was made for two types of wind tunnels. The first one was a French project of an arc jet wind tunnel. The second one was a generic wind tunnel, similar to a future European facility, with higher stagnation conditions than in the first wind tunnel. In the analysis, an equilibrium airflow is assumed up to the throat of the nozzles. Downstream, the calculation is carried out with a quasi-one-dimensional method, taking into account nonequilibrium thermochemistry, with possible vibration-dissociation coupling. There, the airflow is expanded quickly, and departure from equilibrium and then freezing are observed. Different models of chemical, electronic, and vibrational kinetics and different coupling models are studied. Their global influences are analyzed for one test condition for each wind tunnel. Futhermore, for the first nozzle, the computed frozen Mach number compares well with experimental results.

Correlation of separation shock motion with pressure fluctuations inthe incoming boundary layer

Abstract: Fluctuating wall pressures have been measured simultaneously in the incoming undisturbed turbulent boundary layer and under the unsteady separation shock in a Mach 5 compression ramp interaction Conditional sampling algorithms, a variable-window ensemble averaging technique, and the variable interval time averaging technique have been used to investigate the possibility of a correlation between pressure fluctuations in the incoming flow and the separation shock wave motion

On the structure of high-Reynolds-number supersonic turbulent boundary layers

Abstract: Experimental results are presented that reveal key features of the large-scale organized structures in a supersonic, turbulent boundary layer. Measurements were obtained in a Mach 3 zero-pressure-gradient boundary layer using a crossed-wire probe and arrays of normal hot wires with vertical, spanwise, and streamwise separations ranging from 0.1 to 0.6δ. Space–time correlation results indicate the existence of large-scale structures of a size comparable to δ, with a spanwise extent only slightly less than the vertical scale. The convection velocity of the large-scale motions is nearly constant across 80% of the boundary layer and is equal to approximately 0.9U∞.It is shown that positive events detected with the VITA conditional sampling technique correspond to steep gradients in the streamwise mass flux which extend across most of the boundary layer. These sharp gradients appear to be the upstream interfaces of large-scale turbulent ‘bulges’, similar to those seen in incompressible boundary layers. In a reference frame moving with the convection speed of the sharp gradients, low-momentum fluid is observed rotating on a large-scale, while high-momentum fluid forms a saddle point on the upstream edge of the large-scale motion. These motions are associated with elevated levels of the shear product, emphasizing their role in the dynamics of the boundary layer.

Evolution of the orszag-tang vortex system in a compressible medium. ii, supersonic flow

Abstract: The numerical investigation of Orszag–Tang vortex system in compressible magnetofluids continues, this time using initial conditions with embedded supersonic regions. The simulations have initial average Mach numbers M=1.0 and 1.5 and β=10/3 with Lundquist numbers S=50, 100, or 200. Depending on the particular set of parameters, the numerical grid contains 2562 or 5122 collocation points. The behavior of the system differs significantly from that found previously for the incompressible and subsonic analogs. Shocks form at the downstream boundaries of the embedded supersonic regions outside the central magnetic X point and produce strong local current sheets that dissipate appreciable magnetic energy. Reconnection at the central X point, which dominates the incompressible and subsonic systems, peaks later and has a smaller impact as M increases from 0.6 to 1.5. Reconnection becomes significant only after shocks reach the central region, compressing the weak current sheet there. Similarly, the correlation between the momentum and magnetic field begins significant growth later than in subsonic and incompressible flows. The shocks bound large compression regions, which dominate the wave‐number spectra of autocorrelations in mass density, velocity, and magnetic field. The normalized spectral amplitude of the cross helicity is almost zero over the middle and upper portions of the wave‐number domain, unlike the incompressible and subsonic flows. The thermal and magnetic pressures are anticorrelated over a wide wave‐number range during the earlier portion of the calculations, consistent with the presence of quasistationary structures bounded by shocks.

Time evolution of the shear layer of a supersonic axisymmetric jet

Abstract: We used a two-laser two-detector experiment to investigate the temporal evolution of the mixing layer of a pressure matched supersonic jet at an exit Mach number of 1.5. discharging into still air, resulting in a convective Mach number of O.7. The convective speed of the structures present in the flow was measured and compared with previous findings. Additional views of the mixing layer provided information on the three dimensionality of the mixing layer.

Computation of shock wave diffraction at a ninety degrees convex edge

Abstract: This paper presents a numerical study of shock wave diffraction at a sharp ninety degrees edge, using an explicit second-order Godunov-type Euler scheme based upon the solution of a generalized Riemann problem (GRP). The Euler computations produce flow separation very close to the diffraction edge, leading to a realistic development of the separated shear layer and subsequent vortex roll-up. The diffracted shock wave, and the secondary shock wave, are both reproduced well. In addition a pair of vortex shocks are shown to form, extending well into the vortex core.

Structure of medium Mach number quasi-parallel shocks: Upstream and downstream waves

Abstract: The transition from steady low-Mach-number to unsteady high-Mach-number quasi-parallel shocks was investigated by performing large-scale 1D hybrid code simulations at increasing Mach numbers. It was found that only at very low Mach number shocks the steepening is limited by upstream phase-standing whistlers, as predicted by the classical theory (Tidman and Northrop, 1968). In the intermediate region of Mach numbers between 1.5 and 3.5, a very diverse behavior is observed. Backstreaming ions generate fast magnetosonic waves which dominate the upstream, with wavelengths longer than phase-standing whistlers. At increasing Mach numbers, the phase and group velocities of the dominant waves are reduced until they point back toward the shock; when there is sufficient energy flux in these waves, they lead to unsteady shock behavior and eventually to shock reformation.

Nonclassical Dynamics of Classical Gases

Abstract: In the present article we examine the dynamics of single-phase, equilibrium, i.e., classical, fluids in the dense gas regime. The behavior of fluids of moderately large molecular weight is seen to differ significantly from that of air and water under normal conditions. New phenomena include the formation and propagation of expansion shocks, sonic shocks, double sonic shocks, and shock-splitting. The more complicated existence conditions for shock waves are described and related to the dissipative structure. We also give a brief description of transonic flows and show that the critical Mach number for conventional blade shapes can be increased by a factor of 30–50% for these fluids.

The free compressible viscous vortex

Abstract: The present study investigates the effects of compressibility on free (unsteady) viscous heat-conducting vortices. Analytical solutions are found in the limit of large but finite Reynolds number and small but finite Mach number. It is shown that the spreading of the vortex causes a radial flow. This flow is given by the solution of an ordinary differential equation, which gives the dependence of the radial velocity on the tangential velocity, density, and temperature profiles of the vortex. Estimates of the radial velocity found by solving this equation are found to be in good agreement with numerical solutions of the full equations. The equations for the viscous evolution are expanded in powers of Mach number to obtain detailed analytical solutions. It is shown that swirling axisymmetric compressible flows generate negative radial velocities far from the vortex core owing to viscous effects, regardless of the initial distributions of vorticity, density, and entropy.

Surface pressures and sound produced by turbulent flow over smooth and rough walls

Abstract: This paper is a summary account of empirical models of the turbulent boundary layer wall‐pressure spectrum and radiated sound. Terminology, definitions, and formulas are reviewed to enable the reader to gain access to the current literature. Empirical representations are given for the wall‐pressure wave number‐frequency spectrum and the acoustic pressure frequency spectrum for both smooth and rough walls at low mean flow Mach numbers, and for the wall point‐pressure spectrum at arbitrary Mach number.

Electron Acceleration in a Nonlinear Shock Model with Applications to Supernova Remnants

Abstract: We present Monte Carlo calculations of ion and electron spectra produced by Fermi acceleration in a steady state, plane, parallel, modified shock for Mach numbers of 170 and 43. The simulation assumes isotropic, elastic scattering in the local fluid frame, consistent with results from plasma simulations. The shock structure is calculated taking into account the back pressure of accelerated ions, and includes self-consistent pickup and acceleration of thermal ions.

Aerodynamic Preliminary Analysis System II: Part II---User''s Manual

Abstract: An aerodynamic analysis system based on linear potential theory at subsonic/supersonic speed and newtonian impact type finite element solutions at hypersonic conditions is described. Three dimensional configurations having multiple non-planar surfaces of arbitrary planform and bodies of non-circular contour may be analyzed. Static, rotary and control longitudinal and lateral directional characteristics may be generated. The analysis has been implemented on a time sharing system in conjunction with an input tablet digitizer and an interactive graphics input/output display and editing terminal to maximize its responsiveness to the preliminary analysis problem. CDC 175 computational time of 45 CPU seconds/Mach number at subsonic-supersonic speeds and 1 cpu second/Mach number/altitude at hypersonic conditions for a typical simulation indicates that the program provides an efficient analysis tool for systematically performing various aerodynamic configuration tradeoff and evaluation studies.

On the stability of compressible flow past axisymmetric bodies

Abstract: Compressible linear stability theory for axisymmetric flows is presented. The theory is applied to flow past a cylinder and a sharp cone at a Mach number of 5 with adiabatic wall conditions. The effect of transverse curvature and body divergence is studied. It is found that transverse curvature has a stabilizing influence on axisymmetric (first and second mode) disturbances while it has a destabilizing influence on the asymmetric (oblique first mode) disturbances. The body divergence effects are stabilizing for both symmetric and asymmetric disturbances. Comparisons made with the results of planar stability theory show that, for a cylinder, curvature effects become more pronounced with increasing distance along the cylinder. For a sharp cone, these effects become less significant further away from the cone tip since the body radius increases faster than the growth of the boundary layer. The effect of cone angle on stability is also studied.

Enhanced mixing of supersonic jets

Abstract: An experimental study of supersonic mixer nozzles in a coflowing stream has been conducted in the United Technologies Research Center open jet acoustic wind tunnel. Enhanced supersonic jet mixing is important in a number of applications including jet exhaust noise reduction and improved flow distribution within engine combustors. Recently discovered novel concepts promoting enhanced mixing via the introduction of axial vorticity into the exhaust have resulted in studies of the mixing process for nozzles operating at low, subsonic Mach number conditions and low temperatures. The goal of the present experimental study was to evaluate these approaches to jet mixing in the high-temperature, supersonic primary flow regime typical of turbofan/turbojet engine operation. Jet total temperature, total pressure, static pressure, and velocity distributions were measured to characterize the mixing process for baseline slot and circular nozzles, and for several mixer nozzles. The measurements were made at a jet exit Mach number of 1.5, a wind-tunnel forward flight Mach number of 0.5, and a jet total temperature of 1000°F. A principal conclusion of this study is that the axial vorticity mixing mechanism previously shown to be responsible for rapid mixing in low-speed, subsonic flows is also effective in a supersonic flow environment. Reductions in nozzle potential core length of approximately a factor of two relative to the slot nozzle configuration were observed for one of the mixer nozzles studied.

Numerical solutions of forward-flight rotor flow using an upwind method

Abstract: A finite-volume upwind algorithm for solving the three-dimensional Euler equations with a moving grid has been developed for computing helicopter forward-flight rotor flows. The computed pressure distributions and shock positions of high-speed rotor flow are compared with various experimental data as well as with other numerical results, and the agreement is encouraging