Showing papers on "Mach number published in 1993"

Boundary conditions for direct computation of aerodynamic sound generation

Abstract: A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

Nearly incompressible fluids. II - Magnetohydrodynamics, turbulence, and waves

Abstract: The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). On the basis of a singular expansion technique, modified systems of fluid equations are derived for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions (thus ‘‘nearly incompressible MHD’’). NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. The theory developed here does not hold in the presence of very large thermal, gravitational, or field gradients. It is found that there exist three distinct NI descriptions corresponding to each of the three possible plasma beta (β ≡ the ratio of thermal to magnetic pressure) regimes (β≪1, β∼1, β≫1). In the β≫1 regime, the compressible MHD description converges in the low Mach number limit to the equations of classical incompressible three‐dimensional (3‐D) MHD. However, for the remaining plasma beta regimes, the imposition of a large dc magnetic field forces the equations of fully compressible 3‐D MHD to converge to the equations of 2‐D incompressible MHD in the low Mach number limit. The ‘‘collapse in dimensionality’’ corresponding to the different plasma beta regimes clarifies the distinction between the 3‐D and 2‐D incompressible MHD descriptions (and also that of 21/2‐D incompressible MHD). The collapse in dimensionality that occurs as a result of a decreased plasma beta can carry over to the weakly compressible corrections. For a β∼1 plasma, Alfven waves propagate parallel to the applied magnetic field (reminiscent of reduced MHD), while for a β≪1 magnetofluid, quasi‐1‐D long‐wavelength acoustic modes propagate parallel to the applied magnetic field. The detailed theory of weakly compressible corrections to the various incompressible MHD descriptions is presented and the implications for the solar wind emphasized.

Supersonic Base Flow Experiments in the Near Wake of a Cylindrical Afterbody

Abstract: The near wake of a circular cylinder aligned with a uniform Mach 2.5 flow has been experimentally investigated in a wind tunnel designed solely for this purpose. Mean static pressure measurements were used to assess the radial dependence of the base pressure and the mean pressure field approaching separation. In addition, two-component laser Doppler velocimeter (LDV) measurements were obtained throughout the near wake including the large separated region downstream of the base. The primary objective of the research was to gain a better understanding of the complex fluid dynamic processes found in supersonic base flowfields including separation, shear layer development, reattachment along the axis of symmetry, and subsequent development of the wake

Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method

Abstract: A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

Toward a hydrodynamic theory of sonoluminescence

Abstract: For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Wing flutter boundary prediction using unsteady Euler aerodynamic method

Abstract: Modifications to an existing three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1) for the aeroelastic analysis of wings are described. These modifications, which were previously added to CFL3D Version 1.0, include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time-integration with the government flow equations. The paper gives a brief description of these modifications and presents unsteady calculations which check the modifications to the code. Euler flutter results for an isolated 45 degree swept-back wing are compared with experimental data for seven freestream Mach numbers which define the flutter boundary over a range of Mach number from 0.499 to 1.14. These comparisons show good agreement in flutter characteristics for freestream Mach numbers below unity. For freestream Mach numbers above unity, the computed aeroelastic results predict a premature rise in the flutter boundary as compared with the experimental boundary. Steady and unsteady contours of surface Mach number and pressure are included to illustrate the basic flow characteristics of the time-marching flutter calculations and to aid in identifying possible causes for the premature rise in the computational flutter boundary.

Visual observations of supersonic transverse jets

Abstract: We present experimental results on penetration of round sonic and supersonic jets normal to a supersonic cross flow. It is found that penetration is strongly dependent on momentum ratio, weakly dependent on free-stream Mach number, and practically independent of jet Mach number, pressure ratio, and density ratio. The overall scaling of penetration is not very different from that established for subsonic jets. The flow is very unsteady, with propagating pressure waves seen emanating from the orifice of helium jets.

Performance of compressible flow codes at low Mach numbers

Abstract: The accuracy and the performance of three two-dimensional compressible flow codes at freestream Mach numbers as low as 0.001 are examined. Two of the codes employ a finite volume discretization scheme along with a multistage time-stepping algorithm to solve the Euler equations. The two codes differ in their respective use of cell-centered and node-centered differencing schemes. The third code uses an implicit finite difference procedure to solve the unsteady Navier-Stokes equations. Computational test cases are the inviscid steady flow over a circular cylinder and the impulsively started viscous flow over a cylinder

Demonstration of mode transition in a scramjet combustor

Abstract: Direct-connect combustor hardware has been assembled at the Avery Propulsion Research Laboratory (APRL) of the Johns Hopkins University Applied Physics Laboratory (JHU/APL) to investigate a hydrogen-fueled scramjet combustor. The test hardware was designed to perform tests at simulated Mach 5 to Mach 8 flight conditions. This is done using a combustion heater with H2 fuel and makeup O2. The air, H2 and O2 flow rates are all supplied through computer-controlled digital valves. This system allows rapid changes in conditions and very steady flow rates can be maintained throughout the test. Recently, tests were performed in which the flow rates were systematically varied during the test to simulate an acceleration from M = 5.9 to 6.2. During this acceleration the fuel-air equivalence ratio was held constant and the combustor transitioned from a dual mode ramjet with a precombustion shock system creating subsonic flow at the injection plane, to a scramjet with no precombustion shock system. The results of these tests are presented along with descriptions of the hardware and control systems.

Turbulence amplification by a shock wave and rapid distortion theory

Abstract: Amplification of turbulent kinetic energy in an axial compression is examined in the frame of homogeneous rapid distortion theory (RDT) by using the Craya–Herring formalism. By separating the turbulent field into solenoidal and dilatational modes (Helmholtz decomposition), one can show the dilatational mode is mediated by the parameter Δm0=D0/a0k0, which corresponds to the initial ratio between the acoustic time scale (a0k0)−1 and the compression time scale D0−1, with D0 the compression rate. It is shown here that amplification of total kinetic energy is then limited by two analytical solutions obtained for Δm0=0 (purely solenoidal‐acoustical regime) and for Δm0≫1 (‘‘pressure released’’ regime), respectively. The results of the theory are first compared to results of direct numerical simulations (DNS) on homogeneous axial compression. The applicability of this homogeneous approach to the shock wave turbulence interaction, is then discussed. Considering a shock‐induced compression at given Mach number, it ...

Magnetic structure of the low beta, quasi‐perpendicular shock

Abstract: The structure of the low-beta quasi-perpendicular shock is examined in view of ISEE 1 and 2 magnetic field measurements. An analysis of shock overshoots indicates that the strength of the overshoots of low-beta, quasi-perpendicular shocks increases as the ratio of the Mach number to the first critical Mach number increases. Wave analysis indicates that the power of the downstream waves also increases as a function of this ratio of criticality. The thickness of the shock is a factor of 1-2 times greater than a precursor wavelength, countering the conjecture that the shock is the last amplified cycle of the precursor wave.

Transonic shock oscillations calculated with a new interactive boundary layer coupling method

Abstract: A new viscous-inviscid interactive coupling method is described with the aim of allowing time-accurate computation of unsteady transonic flows involving separation and reattachment. A lag-entrainment integral boundary layer method is used in conjunction with a transonic small disturbance potential code. The solutions are coupled with a novel variable gain, integral control method for the boundary layer displacement thickness. Efficient and robust computations of steady and unsteady separated flows, including steady separation bubbles and self-excited shock-induced oscillations, are presented. The buffet onset boundary for the NACA 0012 airfoil is accurately predicted and shown computationally to be a Hopf bifurcation. Shock-induced oscillations are also presented for the 18 percent thick circular arc airfoil. The oscillation onset boundaries and frequencies are accurately predicted, as is the experimentally observed hysteresis of the oscillations with Mach number; this latter stability boundary is identified as a jump phenomenon.

Multi-zone behavior of transverse liquid jet in high-speed flow

Abstract: The behavior of a liquid-fuel spray transversely injected into a uniform high-speed crossflow has been characterized using a laser-sheet imaging technique. The dependence of jet penetration upon jet-to-crossflow momentum ratio was studied by varying the ratio from 3 to 45. The static pressure inside the test section was varied from 14.7 to 30 psia, while the freestream Mach number was held constant at 0.4. A detailed comparison of the jet trajectories (penetration profiles) measured in this study with those predicted by currently available correlation functions revealed gross discrepancies. These discrepancies were attributed to the fact that the spray plume consists of several zones, i.e., a liquid column adjacent to the injector and ligament and droplet regions, exhibiting different characteristics which cannot be adequately described by empirical functions. A composite functional form which takes into account the behavior of these fundamcntally different spray regions has been formulated to provide a more accurate description of the penetration profile of the spray plume. The proposed empirical formula also describes the maximum (asymptotic) penetration of the spray plume in the far field. The dependence of asymptotic penetration hcight upon momentum ratio was analyzed to yield a general formula for predicting the spray trajectory over a wide range of momentum ratios. d’

Three-dimensional velocity field in a compressible mixing layer

Abstract: A turbulent, compressible mixing layer with a relative Mach number of 159 has been investigated experimentally using a two-component laser Doppler velocimeter system Two sets of profiles were obtained at each streamwise measurement location to compile the streamwise, transverse, and spanwise turbulence statistics Results from the fully developed region of the mixing layer showed similar peak values of streamwise and spanwise turbulence intensities along with reduced peak values of transverse turbulence intensity, normalized primary Reynolds shear stress, and normalized turbulent kinetic energy in comparison to the respective quantities from incompressible shear layers

The impact of a shock wave on porous compressible foams

Abstract: A phenomenological study of the processes occurring when a shock wave interacts with porous polyester and polyether foams has been undertaken. Plane shock waves generated in a shock tube were reflected off a slab of foam mounted against the back wall of the tube. Tests were conducted with an initial shock wave Mach number of 1.4 and a 70 mm thick slab of foam. The reduction in reflected shock wave strength and substantial increase in the back wall pressure over that for rigid wall reflection, found by other workers, were confirmed. Piezoelectric pressure transducers were used to record the pressure before, alongside and behind the foam specimen. Schlieren photographs of the flow were made and showed some features not previously reported. In particular it is shown that there is a flow of gas across the face of the foam at some point of the process. Previous investigations of this interaction process have assumed that the face of the foam is a contact surface. Short duration photographs of the distortion of the foam were taken, enabling the wave propagation in the foam material itself to be studied. It is established that the front of this compaction wave in the foam material moves at considerably lower velocity (- 90 m/s) than the gas wave as detected by the pressure transducers (- 200 m/s). This result contrasts with the assumption made in previous work that the two-phase medium behaves essentially as a homogeneous substance. A simple physical model based on a zone of compacted material in the foam acting as a high-resistance flow barrier, is proposed to explain the observed phenomena.

An Investigation of Factors Influencing the Calibration of Five-Hole Probes for Three-Dimensional Flow Measurements

Abstract: The effects of Reynolds number, Mach number, and turbulence on the calibrations of commonly used types of five-hole probe are discussed. The majority of the probes were calibrated at the exit from a transonic nozzle over a range of Reynolds numbers (7 × 10 3 < RE < 80 × 10 3 based on probe tip diameter) at subsonic and transonic Mach numbers. Additional information relating to the flow structure were obtained from a large-scale, low-speed wind tunnel. The results confirmed the existence of two distinct Reynolds number effects. Flow separation around the probe head affects the calibrations at relatively low Reynolds numbers while changes in the detailed structure of the flow around the sensing holes affects the calibrations even when the probe is nulled

Engineering approach to the prediction of shock patterns in bounded high-speed flows

Abstract: A two-dimensional symmetric wedge configuration representative of a single high-speed intake in steady flow was investigated. The analysis presented here is intended as an engineering approach for estimating certain features of the internal shock system. The primary interest here is the prediction of the size and location of the almost-normal shock wave that develops when the leading-edge shocks intersect at angles above a certain critical value that is less than the wedge detachment angle. The almost-normal shock wave is frequently referred to as the 'Mach stem', Parametric studies enabled the sensitivity of the Mach stem height to various flowfield parameters to be examined, thus indicating how accurately these parameters must be measured in a given experiment. Results of these predictions were compared with those of a steady-flow experiment performed at nominal freestream Mach numbers from 2.8 to 5. The predicted stem heights were consistently lower than the mean experimental values, attributable both to experimental uncertainties and to certain simplifying assumptions used in the analysis. Modification of these assumptions to better represent the test environment improved the analytical results.

Effects of Sweepback on Unsteady Separation in Mach 5 Compression Ramp Interactions

Abstract: Fluctuating wall pressure measurements have been made upstream of the corner line in Mach 5 compression ramp interactions generated by unswept and 10-, 20-, 25-, 30-, 40-, and 50-deg swept models. The streamwise ramp angle was 28 deg in all cases. The results show the following: 1) In highly swept interactions the rms distributions of pressure fluctuations as well as the mean distributions are essentially quasiconically symmetric. The rms levels decrease globally with increasing sweep as does the maximum rms generated by the translating separation shock. 2) The length of the intermittent region, over which the separation shock foot translates, decreases with increasing sweep. In a given interaction, the length of the intermittent region grows spanwise. 3) Dominant separation shock frequencies increase from about 0.3-0.5 kHz in unswept flows to about 2-7 kHz in highly swept flows. In a given interaction, shock frequencies decrease spanwise. 4) The higher frequencies are shown to be a direct result of the decrease in the length scale of the separation shock motion.

On solving the compressible Navier-Stokes equations for unsteady flows at very low Mach numbers

Abstract: The properties of a preconditioned, coupled, strongly implicit finite difference scheme for solving the compressible Navier-Stokes equations in primitive variables are investigated for two unsteady flows at low speeds, namely the impulsively started driven cavity and the startup of pipe flow. For the shear-driven cavity flow, the computational effort was observed to be nearly independent of Mach number, especially at the low end of the range considered. This Mach number independence was also observed for steady pipe flow calculations; however, rather different conclusions were drawn for the unsteady calculations. In the pressure-driven pipe startup problem, the compressibility of the fluid began to significantly influence the physics of the flow development at quite low Mach numbers. The present scheme was observed to produce the expected characteristics of completely incompressible flow when the Mach number was set at very low values. Good agreement with incompressible results available in the literature was observed.

Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number

Abstract: The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes – the nearly solenoidal and the ‘pressure-released’ – are defined by a single parameter involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows. In contrast to the well-documented observation that ‘compressibility’ (measured, for example, by the turbulent Mach number) is often associated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amplification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure–dilation correlation increases, in absolute terms, but its relative importance decreases compared to the magnitude of the kinetic energy production.

Mach wave emission from a high-temperature supersonic jet

Abstract: The paper considers the compressible Rayleigh equation as a model for the Mach wave emission mechanism associated with high temperature supersonic jets. Solutions to the compressible Rayleigh equation reveal the existence of several families of supersonically convecting instability waves. These waves directly radiate noise to the jet far field. The predicted noise characteristics are compared to previously acquired experimental data for an axisymmetric Mach 2 fully pressure balanced jet operating over a range of jet operating total temperatures from ambient to 1370 K. The results of this comparison show that the first order supersonic instability wave and the Kelvin-Helmholtz first, second, and third order modes have directional radiation characteristics that are in agreement with observed data. The assumption of equal initial amplitudes for all of the waves leads to the conclusion that the flapping mode of instability dominates the noise radiation process of supersonic jets. At a jet temperature of 1370 K, supersonic instability waves are predicted to dominate the noise radiated at high frequency at narrow angles to the jet axis.

Flip-Flop Jet Nozzle Extended to Supersonic Flows

Abstract: An experiment studying a fluidically oscillated rectangular jet flow was conducted. The Mach number was varied over a range from low subsonic to supersonic. Unsteady velocity and pressure measurements were made using hot wires, piezoresistive pressure transducers, and pitot probes. In addition, smoke flow visualization using high-speed photography was used to document the oscillation of the jet. For the subsonic flip-flop jet, it was found that the apparent time-mean widening of the jet was not accompanied by an increase in the mass flux. Fluidically oscillated jets up to a Mach number of about 0.5 have been reported before, but to our knowledge there is no information on fluidically oscillated supersonic jets. It was found that it is possible to extend the operation of these devices to supersonic flows. The streamwise velocity perturbation levels produced by this device were much higher than the perturbation levels that could be produced using conventional excitation sources such as acoustic drivers. In view of this ability to produce high amplitudes, the potential for using a small-scale fluidically oscillated jet as an unsteady excitation source for the control of shear flows in full-scale practical applications seems promising.

Hypersonic flow past open cavities

Abstract: The hypersonic flow over a cavity is investigated. The time-dependent compressible Navier-Stokes equations, in terms of mass averaged variables, are numerically solved. An implicit algorithm, with a subiteration procedure to recover time-accuracy, is used to perform the time-accurate computations. The objective of the study is to investigate the effects of Reynolds number and cavity dimensions. The comparison of the computations with available experimental data, in terms of time mean static pressure, heat transfer, and Mach number show good agreement. In the computations large vortex structures, which adversely affect the cavity flow characteristics, are observed at the rear of the cavity. A self-sustained oscillatory motion occurs within the cavity over a range of Reynolds number and cavity dimensions. The frequency spectra of the oscillations show good agreement with a modified semi-empirical relation.

Hypersonic Crossing Shock-Wave/Turbulent- Boundary-Layer Interactions

Abstract: Experimental data for two three-dimensional intersecting shock-wave/turbulent-boundary-layer interaction flows at Mach 8.3 are presented. The test bodies, composed of two sharp fins fastened to a flat plate test bed, were designed to generate flows with varying degrees of pressure gradient, boundary-layer separation, and turning angle. The data include surface pressure and heat transfer distributions as well as mean flowfield surveys both in the undisturbed and interaction regimes. The persistence of an extensive low-pressure region throughout the flowfield demonstrates that a sidewall compression inlet is not an efficient pressure increasing device. The data have been obtained in sufficient detail to validate existing or future computational models of these hypersonic flows.

On streamwise vortices in high Reynolds number supersonic axisymmetric jets

Abstract: Pitot pressure measurements and flow visualizations were used to investigate streamwise vortices previously observed in underexpanded jets. A simple model was developed, which gives reasonable agreement with the pressure measurements. A converging nozzle and converging–diverging nozzle of design Mach number 1.5 were used to generate jet flows of equivalent Mach numbers up to 2.5 (stagnation to ambient pressure ratios up to 17.1). By operating the nozzles fully expanded, overexpanded, and underexpanded, insight was gained into both the occurrence and cause for formation of the vortices. Spatially stationary streamwise vortices were found to exist in the near‐field region around the circumference of underexpanded jets in the vicinity of the jet boundary. Short exposure visualizations show the vortices persist much farther downstream with a loss of spatial organization. Visualizations suggest adjacent vortices have streamwise vorticity of opposite sign, so the action of adjacent vortices is to either pump jet fluid radially outward or entrain ambient fluid radially inward toward the jet. The downstream extent, strength, and number of vortices around the jet circumference increase with degree of underexpansion. A large number of vortices is found near the nozzle exit. Fewer vortices of larger scale are found farther downstream, indicative of a merging process. The absence of the vortices in fully expanded and overexpanded jets suggests the vortices are a consequence of a Taylor–Goertler‐type instability.

Characterization of cavity flow fields using pressure data obtained in the Langley 0.3-Meter Transonic Cryogenic Tunnel

Abstract: Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows.