Showing papers on "Mach wave published in 1987"

Experimental cavity pressure distributions at supersonic speeds

Abstract: An investigation was conducted to define pressure distributions for rectangular cavities over a range of free-stream Mach numbers and cavity dimensions. These pressure distributions together with schlieren photographs are used to define the critical values of cavity length-to-depth ratio that separate open type cavity flows from closed type cavity flows. For closed type cavity flow, the shear layer expands over the cavity leading edge and impinges on the cavity floor, whereas for open type cavity flow, the shear layer bridges the cavity. The tests were conducted by using a flat-plate model permitting the cavity length to be remotely varied from 0.5 to 12 in. Cavity depths and widths were varied from 0.5 to 2.5 in. The flat-plate boundary layer approaching the cavity was turbulent and had a thickness of approximately 0.2 in. at the cavity front face for the range of test Mach numbers from 1.5 to 2.86. Presented are a discussion of the results and a complete tabulation of the experimental data.

Experimental study of shock wave interference heating on a cylindrical leading edge at Mach 6 and 8

Abstract: This paper presents the details of an experimental study of shock wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet. The study was conducted at Mach numbers of 6.3, 6.5 and 8.0. This study has provided the first (1) detailed pressure and heat transfer rate distributions for a two-dimensional shock wave interference on a cylinder and (2) insight into the effects of temperature dependent specific heats on the phenomena. The peak pressure and heat transfer rates were 10 times the undisturbed flow stagnation point levels. The peak levels and their gradients increased with Mach number. Variation in specific heats and hence the ratio of specific heats with temperature manifest in slightly lower loads and amplification factors than for corresponding perfect gas conditions.

Stability of axisymmetric boundary layers on sharp cones at hypersonic Mach numbers

Abstract: The stability of sharp-cone boundary layers at zero angle of attack is investigated. Standard linear stability theory is used to perform a numerical study at an edge Mach number M(e) of 6.8 of normal-mode stability characteristics on an adiabatic-wall cone with special reference to the conditions of the stability experiment of Stetson et al. (1983). Comparisons of the calculations with experimental measurements bring out major areas of disagreement which remain to be resolved even in this simple case. Finally, a series of calculations of both cone and flat-plate N factors at M(e) of 4.5, 5.8, and 6.8 is used to study the relation between transition on a cone and flat plate based on stability theory.

Computation of shock wave reflection by circular cylinders

Abstract: The nonstationary shock wave diffraction patterns generated by a blast wave impinging on a circular cylinder are numerically simulated using a second-order hybrid upwind method for solving the two-dimensional inviscid compressible Euler equations of gasdynamics. The diffraction was followed through about 6 radii of travel of the incident shock past the cylinder. A broad range of incident shock Mach numbers are covered. The complete diffraction patterns, including the transition from regular to Mach reflection, trajectory of the Mach triple point, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the cylinder are reported in detail. Pressure-time history and various contour plots are also included. Comparison between the work of Bryson and Gross, which included both experimental schlieren pictures and theoretical calculations using Whitham's ray/shock theory, and results of the present finite-difference computation indicate good agreement in every aspect except for some nonideal gas and viscous effects that are not accounted for by the Euler equations.

Computation of low-speed flow with heat addition

Abstract: A perturbation expansion is used to obtain a system of conservation laws for compressible flows that is valid at arbitrarily low Mach numbers. These equations are rendered hyperbolic by adding an artificial time derivative to the energy equation, thus introducing pseudoacoustic waves with a speed the same order as the particle velocity. Traditional time-iterative schemes are shown to be effective in solving this system numerically. Stability calculations of the complete vector system indicate unconditional stability at all Mach numbers in the absence of gravity, but the source term introduced by buoyancy becomes destabilizing at Froude numbers below about 1. This instability is amplified by approximate factorization thus precluding solutions with gravity below this Mach number level. Computations of strong heat addition in low-Mach-number flow both with and without gravity confirm the stability predictions. Convergent solutions are maintained and are used to show the effect of gravity on such flowfields.

Transition on swept leading edges at Mach 3.5

Abstract: Data and correlations for transition from laminar to turbulent flow on 45and 60-deg swept cylinders are presented. The data were obtained at Mach 3.5 in the Pilot Low-Disturbance Wind Tunnel at NASA Langley. Freestream noise levels were varied during the test program from extremely low values that were essentially in the instrument noise range to much higher values approaching those in conventional wind tunnels. The results show that end plates or large trips near the upstream end of the cylinders cause turbulent flow along the entire attachment line of the models over the freestream test Reynolds number range (based on cylinder diameter) of approximately 1.0 X10

Experimental investigation of heterogeneous compressible shear layers

Abstract: The compressible, two-dimensional shear layer is investigated experimentally in a novel facility. In this facility, it is possible to flow similar or, dissimilar gases of different densities and to select different Mach numbers for each stream over a wide range of Reynolds numbers. In the current experiments, ten combinations of gases and Mach numbers are studied in which the freestream Mach numbers range from 0.2 to 4, the density ratio varies from 0.2 to 9.2, and the velocity ratio varies from 0.13 to 1. The growth of the turbulent region of the layer is measured by means of pitot pressure profiles obtained at several streamwise locations. The resulting growth rate is estimated to be about 80% of the visual growth rate. The transition from laminar to turbulent flow, as well as the structure of the turbulent layer, are observed with Schlieren photographs of 20 nanosecond duration. Streamwise pressure distribution and total pressures are measured by means of a Scanivalve-pressure transducer system. An underlying objective of this investigation was the definition of a compressibility-effect parameter that correlates and consolidates the experimental results, especially the turbulent growth rates. A brief analytical investigation of the vortex sheet suggests that such a parameter is the Mach number in a frame of reference moving with the phase speed of the disturbance, called here the convective Mach number. In a similar manner, the convective Mach number of a turbulent shear layer is defined as the one seen by an observer moving with the convective velocity of the dominant waves and structures. It happens to have about the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases gradually with increasing convective Mach number, reaching an asymptotic value of about 0.25 for supersonic convective Mach numbers. The above behavior is in qualitative agreement with results of linear stability theory as well as with those of previous, one-stream experiments. Large-scale structures, resembling those observed in subsonic shear layers, are evident in the Schlieren photographs. It is estimated that the mean structure spacing, normalized by the local thickness, is reduced to about half its incompressible value as the convective Mach number becomes supersonic. An estimate of the transition Reynolds number has been obtained from the photographs of two shear layers having quite different convective Mach numbers, one low subsonic and the other sonic. In both cases, it is about 2 x 105, based on distance to transition and properties of the high unit Reynolds number stream, thus suggesting that, in this experiment, transition is dominated by instabilities of the wake, rather than of the shear layer.

Mach number effects on conical surface features of swept shock-wave/boundary-layer interactions

Abstract: A joint experimental and computational study is made of the shock-wave turbulent boundary-layer interaction generated by sharp fins, with emphasis on Mach-number effects. The Mach number range is from 2 to 4 and the unit Reynolds number is from 50 to 80 million per meter. Fin angles are varied from 4 to 22 deg. Surface-flow patterns are obtained using a color surface-flow-visualization technique. The results show that the upstream-influence response in the conical far-field region is a function of the freestream Mach number and the shock strength. A new interpretation of the behavior of the upstream influence with changes of the inviscid shock angle is given. Agreement between the experimental and the computed upstream-influence lines becomes poorer for stronger interactions, with the computations underpredicting the upstream-influence line.

Critical Mach numbers in classical magnetohydrodynamics

Abstract: Stationary point analysis is used to compute generalized critical Mach numbers for finite-amplitude fast and slow shocks in classical MHD fluids. Particular attention is paid to the case where the resistive and thermal conduction dissipation scale lengths are comparable and much larger than the viscous scale lengths. With both resistivity and thermal conduction, the critical Mach number at which viscosity must be invoked is determined by the condition that the downstream flow speed equals the isothermal sound speed. It is also shown that resistivity and thermal conduction can provide convergent stationary point solutions for nearly all slow shocks, except perhaps switch-off-shocks.

A reconsideration of the three-shock theory for a pseudo-steady Mach reflection

Abstract: The analytical solution of a pseudo-steady Mach reflection was considered. It was found that the solution of the well-known perfect-gas conservation equations of a pseudo-steady Mach reflection - the three-shock theory - failed to accurately predict the angles between the incident, reflected and Mach stem shock waves. The disagreement between theory and experiments was not settled even when real-gas effects were accounted for. However, the inclusion of real-gas effects did improve the analytical predictions. In order to improve the analytical model, the boundary layers developing on both sides of the slipstream were integrated into the analysis. Using these boundary layers, the displacement thickness as a function of distance along the slipstream from the triple point was calculated. The displacement thickness was then related to the angular displacement of the slipstream, as a function of that distance. Finally it was shown that the displacement, taken at a distance equivalent to the incident-shock-wave thickness, could be used to obtain computed results which agree with experimentally measured data.

The interaction of a conducting object with a supersonic plasma flow: ion deflection near a negatively charged obstacle

Abstract: An experimental study of the interaction of a conducting object with a flowing plasma is described. Particular attention is given to the deflection of ions in the sheath of a negatively charged body. The experiments were conducted in a double plasma device in which a relatively weak longitudinal magnetic field may also be present. For the particular conditions used in these experiments, it was found that ion deflection occurs primarily near the edge of the body. A simple physical model is discussed which accounts for the observed dependences of the convergence of ion streams on the body potential and ion beam velocity. A density rarefaction wave is also observed in the wake region, which propagates into the ambient plasma at roughly the ion acoustic Mach angle. Finally, some preliminary observations of the spatial distribution of plasma noise in the wake region are presented.

A perturbation solution for compressible viscous channel flows

Abstract: The two-dimensional compressible Navier-Stokes equations are solved by a perturbation expansion in the parameter (Mach number)2/Reynolds number. A fortieth-order solution is generated by a computer algorithm. These series are then summed as convergent series of diagonal Pade approximants. Effectively-exact solutions have been found for Reynolds numbers between zero and 1000 and a range of subsonic Mach numbers in the case of fully-developed isothermal flow between parallel side walls. Choking of the flow is shown to occur for a moderate value of channel Reynolds number. The two-dimensional velocity and pressure fields are obtained. The engineering assumption that friction factor is sensibly independent of Mach number may lead to significant underprediction of head loss in the laminar flow regime.

Supersonic turbulent flow past a 3-D swept compression corner at Mach 3

Abstract: Experimental and theoretical studies are presented on the three-dimensional shock wave-turbulent boundary layer interaction generated by a swept compression corner at Mach 3 for compression angle of 24 deg, sweep angle of 60 deg, and Reynolds numbers from 140,000 to 900,000. Two theoretical approaches were used, both of which utilize the full mass-averaged compressible three-dimensional Navier-Stokes equations but differ in the choice of turbulence model (the Baldwin-Lomax, 1978, and the Jones-Launder, 1972, model, respectively). The features of the computed mean flow structure were found to be qualitatively the same for both the Baldwin-Lomax and Jones-Launder models.

Shock structure measured in a transonic fan using laser anemometry

Abstract: Shock structure measurements acquired in a low aspect ratio transonic fan rotor are presented and analyzed. The rotor aspect ratio is 1.56 and the design tip relative Mach number is 1.38. The rotor flowfield was surveyed at near maximum efficiency and near stall operating conditions. Intra-blade velocity measurements acquired with a laser fringe anemometer on blade-to-blade planes in the supersonic region from 10 to 60 percent span are presented. The three-dimensional shock surface determined from the velocity measurments is used to determine the shock surface normal Mach number in order to properly calculate the ideal shock jump conditions. The ideal jump conditions are calculated based upon the Mach numbers measured on a surface of revolution and based upon the normal Mach number to indicate the importance of accounting for shock three dimensionality in turbomachinery design. Comparison of the shock locations with those predicted by a 3-D Euler code showed very good agreement and indicated the usefulness of integrating computational and experimental work to enhance the understanding of the flow physics occurring in transonic turbomachinery passages.

Driving Mechanism of Unsteady Separation Shock Motion in Hypersonic Interactive Flow

Abstract: Wall pressure fluctuations were measured under the steady separation shock waves in Mach 5 turbulent interactions induced by unswept circular cylinders on a flat plate. The wall temperature was adiabatic. A conditional sampling algorithm was developed to examine the statistics of the shock wave motion. The same algorithm was used to examine data taken in earlier studies in the Princeton University Mach 3 blowdown tunnel. In these earlier studies, hemicylindrically blunted fins of different leading-edge diameters were tested in boundary layers which developed on the tunnel floor and on a flat plate. A description of the algorithm, the reasons why it was developed and the sensitivity of the results to the threshold settings, are discussed. The results from the algorithm, together with cross correlations and power spectral density estimates suggests that the shock motion is driven by the low-frequency unsteadiness of the downstream separated, vortical flow.

Method and apparatus for nonintrusively determining mach number

Abstract: The Mach number M o of flow in the intake nozzle or bypass duct of a gas turbine aircraft engine is determined from the acoustic impedance of a Helmholtz resonator to an engine fan-stator sound source. Pressure measurements P 1 (t) and P 2 (t), made nonintrusively at the duct wall surface and resonator cavity bottom are subjected to Fourier analysis to give P 1 (f) and P 2 (f), and acoustic impedance for the flow is determined from a complex transfer function H 12 . Flow Mach number is then established using known acoustic impedance/Mach number correlation relationships or a stored look-up table. An alternative embodiment, utilizes a sound source mounted in the Helmholtz resonator bottom and determines Mach number by pressure measurements made at spaced locations on the resonator chamber wall.

Criteria for regular spacing of reacting Mach stems.

Abstract: Nonlinear geometric optics is developed to construct translating self-similar high-frequency nonlinear wave patterns as perturbed solutions behind reacting shock waves. The geometric conditions involving these wave patterns that yield the maximum acoustic amplification lead to criteria for both the formation and regular spacing dimension for Mach stems in reacting gases.

Study of multibody aerodynamic interference at transonic Mach numbers

Abstract: A wind tunnel experiment involving single, double, and triple combinations of mutually interfering generic, unfinned aircraft stores has been conducted. Each combination of stores was tested at Mach numbers from 0.60 to 1.20 and at angles of attack from 0 to 25 deg for the single store and from 0 to 6 deg for the double and triple store configurations. Extensive axial and circumferential pressure and flow visualization data at each store location were obtained. Euler solutions for each configuration at 0 deg incidence have been generated and compared with experimental data. This comparison indicates an Euler flow solver can yield accurate predictions of the location and magnitude of multibody interference provided an appropriate grid is used and the viscous effects associated with these configurations remain small. The data indicate multibody interference in the transonic region increases as the freestream Mach number approaches 1 from either direction, and subsides as the Mach number moves away from sonic conditions. This interference is characterized by a large, localized reduction in pressure on the inboard surfaces of the bodies which results in forces that draw the configuration closer together.

Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5

Abstract: A brief outline of the experimental and theoretical investigation of boundary layer instability mechanisms on a swept leading edge at Mach 3.5 is presented. Transition is affected by wind tunnel noise only when roughness is present. Local bar-R sub * Reynolds number and k/eta sub * are useful correlation parameters for a wide range of free stream Mach numbers. Stability theory is in good agreement with the experimental cross flow vortex wavelength. These conclusions are briefly discussed.

The structure of detonation waves

Abstract: Multidimensional time-dependent numerical simulations have been used to study the initiation, propagation, and extinction of detonations in gases and liquids. The simulations, which calculate the detailed behavior of the interacting shock waves and reaction zones forming the detonation wave, are used to study the evolution of the instability that leads to the cellular structure of detonations. The simulations consist of two-dimensional time-dependent solutions of the convection of mass density, momentum density and energy coupled to models for chemical energy release. The convective transport equations are solved by the Flux-Corrected Transport algorithm. The chemical reactions and energy release are usually modelled by the two-step induction parameter model. We conclude that the behavior of the multidimensional structure of a detonation depends on the differences of the thermodynamic properties in the inductiori zones behind the Mach stem and the incident shock. The formation of unreacted pockets behind the detonation front depends on the inclination of the transverse waves and the curvature of the shock fronts. Highly curved fronts may result in large pockets. The temperature dependence of the induction time is a major factor in the regularity of detonation structure. Detonation structure is affected by the energy release parameters. Instantaneous energy release leads to one-dimensional structures. Fast energy release results in less regular structures. Very slow energy release results in large pockets, highly curved fronts, and the detonation may die out. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987406

Boundary-layer instability mechanisms on a swept-leading edge at Mach 3.5

Abstract: Correlations have been made in NASA Langley's Mach 35 Pilot Quiet Tunnel for the transitions occurring from laminar to turbulent flow, in the cases of 45-deg and 60-deg swept cylinders While freestream noise variations had no effect on boundary layer transition, the addition of boundary layer trips to the leading edges led to transition at lower Re numbers, depending on both trip height and wind tunnel noise level Also presented are the results of compressible linear stability calculations for the boundary layer of an infinite swept cylinder; Tollmien-Schlichting waves are found to be amplified in the attachment line boundary layer

Mach number limit of electron holes in bounded beam-plasma system

Abstract: The upper limit of the electron hole Mach number under the presence of an electron beam is discussed theoretically by solving the Poisson equation When the beam component exists in plasmas, a new hole solution appears owing to shielding effects of the beam electrons The hole speed can greatly exceed the critical Mach number M0 equivalent to 13 For the beam component ratio above approximately 022 the upper limit of the Mach number intrinsically vanishes when the beam temperature is equal to that of the bulk The transverse effect due to a finite radial wave number K strongly modifies the parameter regimes for the hole solution

A study of the effects of Reynolds number and Mach number on constant pressure coefficient jump for shock-induced trailing-edge separation

Abstract: The influence of Mach and Reynolds numbers as well as airfoil and planform geometry on the phenomenon of constant shock jump pressure coefficient for conditions of shock induced trailing edge separation (SITES) was studied It was demonstrated that the phenomenon does exist for a wide variety of two and three dimensional flow cases and that the influence of free stream Mach number was not significant The influence of Reynolds number was found to be important but was not strong Airfoil and planform geometric characteristics were found to be very important where the pressure coefficient jump was shown to vary with the sum of: (1) airfoil curvature at the upper surface crest, and (2) camber surface slope at the trailing edge It was also determined that the onset of SITES could be defined as a function of airfoil geometric parameters and Mach number normal to the leading edge This onset prediction was shown to predict the angle of onset to within + or - 1 deg accuracy or better for about 90% of the cases studied

Interaction of a gasdynamic shock with small disturbances

Abstract: The stability of shock wave based on the definition of Landau and Lifschitz[1] is treated in this paper. This is tantamount to solving the problem of interaction of small disturbances with a shock wave. Small disturbances are introduced on both sides of a steady, non-dissipative, plane shock wave. Landau et al.[1] obtained the stability criterionM1>1,M2 1,M2<1 are fulfilled. Then several experiments are proposed, and the problem of ways to define the incident wave and diverging wave is discussed. The meaning of this problem is illustrated.

Chapter xiii – flow past finite bodies

Abstract: Publisher Summary This chapter discusses the formation of shock waves when the supersonic flow passes an arbitrary body. The disturbances in the supersonic flow caused by the presence of the body are propagated only downstream. Therefore, a uniform supersonic stream incident on the body would be unperturbed as far as the leading end of the body. The normal component of the gas velocity would then be nonzero at the surface there, in contradiction to the necessary boundary condition. The resolution of this difficulty can only be the occurrence of a shock wave because of which the gas flow between it and the leading end of the body becomes subsonic. Thus a shock wave is formed in front of the body when the incident flow is supersonic, and this shock does not touch the body; it is often called the bow wave. In front of the shock wave, the flow is uniform; behind it, the flow is modified and bends round the body. The surface of the shock wave extends to infinity. At great distances from the body, where the shock is weak, the surface intersects the incident streamlines at an angle approaching the Mach angle.