Variation Of Mach Number Research Articles

Interstellar clouds in high-speed, supersonic flows: Two-dimensional simulations

We present a series of gasdynamical simulations of the interaction of a dense, cool interstellar cloud with a high-speed, supersonic wind that confines and accelerates the embedded cloud. Our goal is to attempt to determine if such clouds can survive various potentially disruptive instabilities, that occur at their peripheries, long enough to be accelerated to speeds which are comparable to the wind velocity. These simulations are performed using two-dimensional, Eulerian gas dynamics on both an axisymmetric (about the cloud axis) and 'slab' geometric grid. The spatial and temporal resolutions of the simulations are varied over a wide range to investigate the effects of small-scale instabilities on the overall acceleration of clouds and the development of large-scale, disruptive instabilities. Also, we study the effects of wind/cloud Mach number variations by changing the wind speed constant at about 12 km/s (which corresponds to a cloud temperature of 10,000 K). The current simulations track the evolution of clouds as they are accelerated to speeds approximately 4-5 times greater than their internal sound speeds. Furthermore, the models with the highest resolution were extended far beyond quasi-linear Rayleigh-Taylor growth times reaching 6-7 Rayleigh-Taylor growth times for the largest scale instabilities before being terminated because of the accumulation of errors at the rear grid boundary.

Numerical Calculation of Underexpanded Axisymmetric Supersonic Jet. Effects of Nozzle Divergence Angle and Mach Number on Shock Cell Length.

A numerical study of underexpanded axisymmetric supersonic jets is presented. The TVD finite-difference scheme is employed for the numerical calculation of Euler's equations. The numerical results are compared both with results from the theoretical shock cell spacing formula suggested by Tam and with previous experimental results. For nozzles having no divergence angle at the nozzle exit, a good agreement is obtained among the theoretical, experimental and numerical results for pressure ratios across the nozzle until the occurrence of a Mach disk in the jet. For nozzles having a divergence angle at the nozzle exit, the effects of the divergence angle, the nozzle design Mach number and the pressure ratio across the nozzle on the shock cell length are discussed and clarified.

Numerical simulation of incidence and sweep effects on delta wing vortex breakdown

The structure of the vortical flowfield over delta wings at high angles of attack was investigated. Three-dimensional Navier-Stokes numerical simulations were carried out to predict the complex leeward-side flowfield characteristics, including leading-edge separation, secondary separation, and vortex breakdown. Flows over a 75- and a 63-deg sweep delta wing with sharp leading edges were investigated and compared with available experimental data. The effect of variation of circumferential grid resolution grid resolution in the vicinity of the wing leading edge on the accuracy of the solutions was addressed. Furthermore, the effect of turbulence modeling on the solutions was investigated. The effects of variation of angle of attack on the computed vortical flow structure for the 75-deg sweep delta wing were examined. At moderate angles of attack no vortex breakdown was observed. When a critical angle of attack was reached, bubble-type vortex breakdown was found. With further increase in angle of attack, a change from bubble-type breakdown to spiral-type vortex breakdown was predicted by the numerical solution. The effects of variation of sweep angle and freestream Mach number were addressed with the solutions on a 63-deg sweep delta wing.

Numerical solution of Euler equations for aerofoils in arbitrary unsteady motion

AbstractThis paper is part of a DLR research programme to develop a three-dimensional Euler code for the calculation of unsteady flow fields around helicopter rotors in forward flight. The present research provides a code for the solution of Euler equations around aerofoils in arbitrary unsteady motion. The aerofoil is considered rigid in motion, and an O-grid system fixed to the moving aerofoil is generated once for all flow cases. Jameson's finite volume method using Runge-Kutta time stepping schemes to solve Euler equations for steady flow is extended to unsteady flow. The essential steps of this paper are the determination of inviscid governing equations in integral form for the control volume varying with time in general, and its application to the case in which the control volume is rigid with motion. The implementation of an implicit residual averaging with variable coefficients allows the CFL number to be increased to about 60. The general description of the code, which includes the discussions of grid system, grid fineness, farfield distance, artificial dissipation, and CFL number, is given. Code validation is investigated by comparing results with those of other numerical methods, as well as with experimental results of an Onera two-bladed rotor in non-lifting flight. Some numerical examples other than periodic motion, such as angle-of-attack variation, Mach number variation, and development of pitching oscillation from steady state, are given in this paper.

Physics of Coanda jet detachment at high-pressure ratio

Experimental measurements of surface pressure for an underexpanded two-dimensional supersonic Coanda flow with static conditions exterior to the jet flow was obtained for a fixed slot height to a radius ratio of 0.04. The data demonstrate that an oblique shock forms near the jet exit plane which vectors the jet flow from the curved surface at a pressure ratio of 7.6. The jet detachment occurs at a pressure ratio which is a function of the ratio of slot height to cylinder radius. An increase in the pressure ratio to 11.5 before jet detachment has been demonstrated by the translation of the upper wall providing for a converging-diverging geometry. The physics of the Coanda expansion and the jet detachment are qualitatively described using an optical schlieren system. A compressible in viscid model was derived analytically to demonstrate the variation in Mach number and surface pressure as a function of the geometric parameters with increasing pressure ratio.

Multielement airfoil performance due to Reynolds and Mach number variations

Experimental studies have been conducted to assess Reynolds and Mach number effects on a supercritical multielement airfoil. The airfoil is representative of the stall-critical station of an advanced transport wing design. The experimental work was conducted as part of a cooperative program between the Douglas Aircraft Company and the NASA Langley Research Center to improve current knowledge of high-lift flows and to develop a validation data base with practical geometries/conditions for emerging computational methods. This article describes results obtained for both landing and takeoff multielement airfoils (four- and three-element configurations) for a variety of Mach/Reynolds number combinations up to flight conditions. Effects on maximum lift are considered for the landing configurations, and effects on both lift and drag are reported for the takeoff geometry. The present test results revealed considerable maximum lift effects on the three-element landing configuration for Reynolds number variations, and significant Mach number effects on the four-element airfoil.

Low-frequency combustion oscillations in a model afterburner

Low-frequency combustion oscillations, involing the interaction between longitudinal acoustic waves and unsteady combustion, are investigated for a model afterburner. An experimental rig, in which a confined flame is stabilized in the wake of a conical gutter, is run with inlet conditions representative of an engine afterburner. Results are presented for inlet Mach numbers in the range of 0.15–0.27, with inlet temperatures up to 630 K. Comparison is made between theory and experiment. Although the theory was developed from low Mach number data, it is found to apply equally well at these faster flow rates. The theory is able to predict the frequency of the instability and the mode shape, accurately reproducing the changes due to variations in the inlet Mach number and temperature. The effect of altering the downstream boundary condition by replacing the open end by a choked nozzle is also investigated. Such a change is found to be highly destabilizing, both experimentally and theoretically. Again, predictions from the theory are in good agreement with the observations.

Study of ion-acoustic rarefactive soliton in a two-electron temperature plasma

The propagation characteristics of ion-acoustic rarefactive soliton (IARS) in a two-electron temperature plasma with two cold ion species are investigated considering the nonisothermal distributions of electrons using a kinetic model and fluid model for both ion species. Using the Sagdeev potential formalism the nonlinear dispersion relation and expression for width are derived for IARS. The variation of Mach number and width of the IARS with the amplitude is studied numerically and compared with earlier theoretical results as well as experimental observations. It is found that the results are improved qualitatively as well as quantitatively with the consideration of the presence of a suitable negative ion-impurity.

Buffet response of a hammerhead launch vehicle wind-tunnel model

A wind-tunnel test of a l/10th-scale Atlas-Centaur I launch vehicle model was conducted in the NASA Langley Transonic Dynamics Tunnel. The model was aeroelastically scaled to simulate flight bending modes using a partial mode technique. Several payload fairing configurations were tested at various angles of attack. No aeroelastic instabilities were found, and each configuration was generally more sensitive to Mach number variations than changes in angle of attack. Small length-to-diameter fairing ratios produced changes in buffet response in the second bending mode configuration. Additional testing was performed with vertical rods attached to the sting support to reduce the effects of mechanical vibration induced through the facility. The first flight of the Atlas-Centaur I vehicle successfully occurred on July 25, 1990, and the flight response was found to be well within the 3a level of the wind-tunnel data.

Three-Dimensional Rotational Flow in Transonic Turbomachines: Part II—Full Three-Dimensional Flow in CAS Rotor Obtained by Using a Number of S1 and S2 Stream Filaments

The general theory for three-dimensional flow in subsonic and supersonic turbo-machines has recently been extended to transonic turbomachines. In this paper, which is Part II of the study, quasi- and full three-dimensional solutions of the transonic flow in the CAS rotor are presented. The solutions are obtained by iterative calculation between a number of S1 stream filaments and, respectively, a central S2m Stream filament and a number of S2 stream filaments. Relatively simple methods developed recently for solving the transonic flow along S1 and S2 stream filaments are used in the calculation. The three-dimensional flow fields in the CAS rotor obtained by the present method are presented in detail with special emphasis on the converging process for the configuration of the S1 and S2 stream filaments. The three-dimensional flow fields obtained in the quasi- and full three-dimensional solutions are quite similar, but the former gives a lower peak Mack number and a smaller circumferential variation in Mach number than the latter. A comparison between the theoretical solution and the Laser-2-Focus measurement shows that the character of the transonic flow including the three-dimensional shock structure is in good agreement, but the measured velocity is slightly higher than the calculated one over most of the flow field.

High-resolution aerodynamic spectrometry of submicron particles: sheathed variable-cut impactors vs other devices

Aerosol size spectrometers based on single-jet variable-cut inertial impactors are shown to be capable of having fairly high resolution. The maximum size resolving power and the lowest particle size discernible with several well-known aerodynamic spectrometers are discussed first, to put the problem into perspective. Advantages and drawbacks of impactors as well as prior attempts at using them as continuous size spectrometers are reviewed before considering the theoretical limits on their resolving power, which we show may be higher than that of differential mobility analyzers (DMAs) even when the aerosol jet is surrounded with only 50% of combined inner and outer sheaths of clean air. The effect of adding an outer sheath of air of up to 67% to a core aerosol is studied experimentally with a thin-plate orifice nozzle in an impactor running at variable Mach number and fixed Reynolds number Re. At Re = 100, the best resolution observed is comparable to that of the DMA used as a monodisperse aerosol generator, and considerably higher than that of all the other aerodynamic size spectrometers considered. Substantial improvements in resolution over that of unsheathed jets are observed at Re = 50. The ability of the present scheme to yield differential spectra at similarly high resolutions is also demonstrated using two impactors in tandem with closely matched cuts. It is concluded that impactors have indeed a remarkable potential for high-resolution sizing of very fine particles, but substantial work will be needed to achieve it fully.

Linear panel flutter of an elliptic cylindrical shell

Panal flutter of an elliptic cylindrical shell exposed to an external supersonic air stream is investigated. Shallow cylindrical shell deformation theory and aerodynamic piston theory are used. The displacement function is expressed in two variants. A comparison between the results obtained by both versions is made. Numerical results for shells with different geometric parameters are shown. Hereby, the shell is considered as a system with two and with four degrees of freedom. The purpose of the investigation is to determine the variation of critical flutter Mach number with shell parameters.

An investigation of supersonic oscillatory cavity flows driven by thick shear layers

Abstract Flows around two-dimensional rectangular cavities driven by thick shear layers are investigated experimentally at two supersonic Mach numbers (Me = 1.5 and 2.5) to show the effects of variations in Mach number and length to depth ratio of the cavity. Flow oscillation is observed in the cavity. The characteristics of the oscillatory behaviour are determined by Mach number and the length of depth ratio of the cavity, as well as the shear layer spanning the cavity. Two oscillatory mechanisms can be identified: one in which a strong trailing-edge vortex and vortices which are shed from the leading-edge interact, the other in which a transverse oscillation of a single vortex occurs within the cavity. Changes in the time-dependent and the time-mean flow characteristics at different flow conditions are discussed.The time-dependent experimental results are compared with existing theoretical analyses of the frequencies. For one of these characteristic types of oscillation, the longitudinal oscillation, an existing theoretical description is improved with a modified phase relation.

Electron kinetic effects on an ion-acoustic rarefactive soliton in a two-electron temperature plasma

The propagation characteristics of an ion-acoustic rarefactive soliton (IARS) in a two-electron temperature plasma with cold ions are investigated including the effects of reflected electrons using a kinetic model. Following the Sagdeev potential formalism the nonlinear dispersion relation is derived for the IARS. It is found that the kinetic effects associated with the reflected electrons modify the results appreciably and the Mach number increases nonlinearly with the amplitude of the soliton. The results show that the present model is a distinct improvement over the usual KdV solution. The variation of Mach number and width of the IARS with amplitude is studied numerically. It is found that the variation of Mach number with amplitude matches fairly well with the experimental observations with selected values of the parameters of the distributions of cold and hot electrons.

Mach number effects on transonic aeroelastic forces and flutter characteristics

Transonic aeroelastic stability analysis and flutter calculations are presented for a generic transport-type wing based on the use of the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) finite-difference code. The CAP-TSD code was recently developed for transonic unsteady aerodynamic and aeroelastic analysis of complete aircraft configurations. A binary aeroelastic system consisting of simple bending and torsion modes was used to study aeroelastic behavior at transonic speeds. Generalized aerodynamic forces are presented for a wide range of Mach number and reduced frequency. Aeroelastic characteristics are presented for variations in freestream Mach number, mass ratio, and bending-torsion frequency ratio. Flutter boundaries are presented which have two transonic dips in flutter speed. The first dip is the usual transonic dip involving a bending-dominated flutter mode. The second dip is characterized by a single degree-of-freedom torsion oscillation. These aeroelastic results are physically interpreted and shown to be related to the steady state shock location and changes in generalized aerodynamic forces due to freestream Mach number.

Intercomparison among plasma wake models for plasmaspheric and ionospheric conditions

Intercomparisons are made among the angular distributions of ions in the wake of a body moving through a space plasma as computed from three different expressions (models). Both subsonic and supersonic relative flows are considered in order to examine the wake current depletion ratios under conditions realistic for the topside ionosphere and plasmasphere. Results of these comparisons demonstrate the importance of including the thermal flux at low Mach numbers and of taking into account the angular acceptance of ion detectors in making theory-experiment comparisons. Gradients in the angular variations of the fluxes are found to be steeper near the wake-ambient interface than closer to the maximum rarefaction region of all models, although quantitatively there is considerable variation among the models. From examining the variations of the wake depletion ratio parametrically with Mach number and normalized potential over ranges characteristic of the plasmasphere and topside ionosphere, we find considerable variation with both parameters, with sensitivity to normalized potential increasing dramatically with Mach number. Overall, however, the Mach number variation appears to be the more significant over this range of parameters.

Numerical modeling of complex viscous fluid vortical flows

The influence of the turbulence model, numerical diffusion, and methods of formulating the boundary conditions on a solid wall on computation results is analyzed in an example of a finite-difference simulation of viscous fluid vortical flows in a broad range of Mach and Reynolds number variation.

Structure of weak shocks in fluids having embedded regions of negative nonlinearity

The dissipative structure of weak shock waves in fluids in which the fundamental derivative is negative for a finite range of pressures and temperatures has been examined. Conditions under which the shock thickness increases with strength rather than decreases are delineated. Nonclassical features of the entropy distribution and variation of local Mach number are also described.

Comment on "Study of an Asymmetric Flap Nozzle as a Thrust-Vectoring Device"

A article by Wu and Chow prompted me to draw attention to the following points. 1) For convergent nozzles, validation of computation codes by pressure measurements along the walls is not sufficient. In actual fact, in the forward end of the convergent (Mach 0,7) the static pressure is not affected much by small variations of test Mach number. In the aft end, the pressure gradients along the abscissa are too high to allow a fair evaluation of differences. 2) When validating a method of the same type (1972) for convergent conical nozzles (axisymmetrical flow), we have tried to validate our methods by experimental overall (flow and thrust coefficients) and local (sonic line) cross-checks.' Apart from these above comments, we agree that this method is suitable for straight wall nozzles. SNECMA has developed a similar method for thrust vectoring nozzles. In addition, the straightforward coupling of the holograph method with the method of characteristics yields a mixed method of providing for rapid calculation of supersonic convergent-divergent nozzles.

Extension of equivalent angle-of-attack method for nonlinear flowfields

Recent experimental results show that the control effectiveness of a missile fin in supersonic flow at moderate to high angles of attack is a strong nonlinear function of freestream Mach number, body incidence angle, fin bank angle, and fin deflection angle. Analysis of the experimental results using an Euler finite-difference computer code with flow separation, together with the equivalent angle-of-attack concept, indicates that the observed nonlinearities are due to the variation of local dynamic pressure and local Mach number around the missile body alone. The nonlinearities are shown to be a strong source of control cross-coupling for high Mach number, high angle-ofattack combinations. The analysis suggests a relatively simple yet comprehensive approach for accurately accounting for these nonlinear effects. The impact of the results on missile aeroprediction methods is discussed.