Showing papers on "Mach number published in 1982"

The structure of perpendicular bow shocks

Abstract: A hybrid simulation model with kinetic ions, massless fluid electrons, and phenomenological resistivity is used to investigate the perpendicular configuration of the bow shocks of the earth and other planets. The range of parameters investigated includes the upstream Mach number, electron and ion beta (ratios of thermal to magnetic pressure), and resistivity. It is found that electron beta and resistivity have little effect on the overall shock structure. Quasi-stationary structures are obtained at moderately high ion beta, whereas the shock is found to become more dynamic in the low ion beta, large Mach number regime. The simulation results are shown to agree well with a number of observational features of quasi-perpendicular bow shocks, including the morphology of the reflected ion stream, the magnetic field profile throughout the shock, and the Mach number dependence of the magnetic field overshoot.

Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet

Abstract: Flow and acoustic properties of a jet at Reynolds number of 70,000 were studied at Mach 2.1. Measurements in a free jet test facility were made with pitot tubes and hot-wire anemometry. Center-line Mach number distributions for natural and excited jets were obtained. A slow initial growth rate was in the potential core region of the jet, indicating a transition from laminar to turbulent flow in moderate Reynolds number jets. The transition occurred within the first 2-3 diameters. Spectral components were calculated for the fluctuating flowfield, and sound pressure levels were measured for the overall near-field noise. The centroid of noise was located about 8 nozzle diameters downstream. The growth rates of instabilities were determined to be in agreement with linear stability theory predictions over a broad frequency range.

Observations of gyrating ions in the foot of the nearly perpendicular bow shock

Abstract: A beam of secondary ions which gyrate about the magnetic field have been detected by ISEE-1 satellite measurements of ion velocity distributions during a high Mach number bow shock crossing under nearly perpendicular conditions. The ions are encountered as the satellite enters the region ahead of the foot of the shock, and their behavior is that of solar wind ions reflected off the shock and then returned to it under the combined influence of magnetic field deflection and interplanetary electric field acceleration. Beam densities increase from 0.2 to 30% of the total plasma density as the main shock is approached, and the ion beam is not degraded through interaction with the counterstreaming solar wind upstream of the ramp. The gyrating ions provide strong dispersion in velocity space, and therefore constitute the first step in the process by which solar wind streaming energy is converted into the thermal energy of the ions at the bow shock.

Transition from regular to Mach reflection of shock waves Part 2. The steady-flow criterion

Abstract: It is shown experimentally that, in steady flow, transition to Mach reflection occurs at the von Neumann condition in the strong shock range (Mach numbers from 2.8 to 5). This criterion applies with both increasing and decreasing shock angle, so that the hysteresis effect predicted by Hornung, Oertel & Sandeman (1979) could not be observed. However, evidence of the effect is shown to be displayed in an unsteady experiment of Henderson & Lozzi (1979).

An experimental study of the interaction between a glancing shock wave and a turbulent boundary layer

Abstract: The glancing interaction between an oblique shock wave and a turbulent boundary layer has been studied experimentally using a variable-incidence wedge mounted from the side wall of a supersonic wind tunnel. The Mach number was 2·3 and the Reynolds number 5 × 104, based on the 99·5 % thickness of the boundary layer just upstream of the interaction region. The study includes oil flow pictures, vapour and smoke-screen photographs, wall-pressure distributions and local heat-transfer measurements. The results suggest that the complicated interaction region involves two viscous layers: an induced layer formed from fluid initially in the boundary layer growing along the wedge surface near the root, and the thick turbulent layer on the tunnel side wall. The mutual interference between these layers is described, separation is defined and a discussion of incipient separation is included.

Blunt fin-induced shock wave/turbulent boundary-layer interaction

Abstract: This paper presents results from an experimental study of blunt fin-induced shock wave/turbulent boundarylayer interaction Semi-infinite fin models with hemicylindrical, unswept leading edges were tested in Mach 3, high Reynolds number, turbulent boundary layers All tests were made under approximately adiabatic wall conditions The program had two fundamental objectives The first was to examine the spanwise development of the disturbed flowfield and to determine its dependence on the configuration geometry and incoming flow conditions To achieve this, streamwise surface pressure distributions were measured in the region extending from the centerline to 110 fin diameters outboard The second objective was to determine the vertical extent of the interaction on the fin This was carried out using a fin model whose leading edge and side face were instrumented with pressure taps The results show that, on the test surface near the fin and on the fin itself, the leading-edge diameter plays a dominant role in determining the interaction's scale and characteristics

Acoustic radiation from a semi-infinite annular duct in a uniform subsonic mean flow

Abstract: Using a Wiener-Hopf approach, ain analytical description is derived of the scattered field of a harmonic sound wave coming out of an open ended annular duct (a semi-infinite cylinder inside of which, coaxially, a doubly infinite hub), submerged in a subsonic, coaxial, uniform mean flow. The possibility of vortex shedding from the pipe exit edge is included.Explicit expressions are given of the acoustic power inside the pipe, in the acoustic far field, and, in the presence of vortex shedding, in the hydrodynamic far field and of the power absorbed by the vortex sheet. The formulae are evaluated with the aid of asymptotic expansions, and a method utilizing complex contour deformation, more convenient than those usually employed for this type of diffraction problems. The equality of power appeared to be an important check on the calculations. A numerical survey is made of the behaviour of the acoustic power loss, due to vortex shedding from the trailing edge, at frequencies near cut-off, as a function of Mach number, mode number of the incident wave, and hub radius. The power loss appears to increase with increasing Mach number, increasing hub radius and with decreasing frequency. Only in case of the plane wave (where k-K)) the ratio of radiated and transmitted power becomes zero, for the other modes (at their cutoff frequencies) this ratio tends to a finite value. Somewhat surprising is that, in comparison with the jet, the power loss in a uniform flow is much higher. As a typical example for higher frequencies, the far field radiation pattern of a k=50, m=U wave is considered as a function of Kutta condition and hub radius.

Nonlinear transonic flutter analysis

Abstract: A numerical procedure is presented for predicting the static and dynamic aeroelastic characteristics of thin, clean swept wings in transonic flow. The method is based upon the simultaneous time integration of the equations governing the coupled nonlinear fluid dynamic and structural aeroelastic system. Governing equations for the system are developed and the numerical algorithm, including the coupling procedure for their solution, is discussed. As a computational example, the flutter of a simple rectangular wing is considered. Solutions are presented for a range of Mach numbers and dynamic pressures and compared to other existing flutter analysis methods including doublet lattice, modified strip theory, and time linearization. Unlike other procedures, the method presented here is capable of predicting the nonlinear interaction between unsteady shock wave motions and the dynamic response of an elastic wing. Computed results indicate the existence of the "transonic bucket."

Overshoots in planetary bow shocks

Abstract: The parametric variation with solar wind conditions in the overshoot in magnetic field strength observed in planetary bow shocks and believed to be associated with the ion reflection process is examined based on both terrestrial and planetary bow shock data. The combined data from Venus, earth, Jupiter and Saturn cover a wider range of solar wind densities, magnetic field strength, electron and proton temperatures, Mach numbers, beta, spiral angle, and scale lengths than observable from earth alone. The bow shock structure, particularly the magnitude of the post-shock field strength overshoot, is found to depend principally on plasma beta and the magnetosonic Mach number with a continuously increasing overshoot strength associated with increasing beta and Mach number.

Multiple solutions of the transonic potential flow equation

Abstract: The two-dimensional transonic potential flow equation, when solved in discrete form for steady flow over an airfoil, has been found to yield more than one solution in certain bands of angle of attack and Mach number. The most striking ex- ample of this is the appearance of nonsymmetric solutions with large positive or negative lift, for symmetric airfoils at zero angle of attack. The behavior of these "anomalous" solutions is exam- ined as grid size is varied by large factors and found to be not qualitatively different from that of %ormalrf solutions (outside the nonuniqueness band). Thus it appears that the effect is not due to discretization error, and that the basic tran- sonic potential flow partial differential equation admits nonunique solutions for certain values of angle of attack and Mach number.

ISEE‐1 and ‐2 observations of laminar bow shocks: Velocity and thickness

Abstract: Thirteen bow shock crossings observed by ISEE-1 and -2 have been used to determine the thickness and velocity of the quasi-perpendicular laminar bow shock, i.e., those for which the Mach number and beta are low and the magnetic field is at large angles to the shock normal. The shock velocity ranges from a few kilometers per second to over 100 km/sec for these events. The shock thickness is found to be close to an ion inertial length, about 100 km for the conditions studied herein. In contrast to supercritical shocks, there is approximate equipartition of thermal energy between ions and electrons behind these shocks. Finally, there is a weak correlation between shock thickness and the angle between the interplanetary magnetic field and the shock normal, with more perpendicular shocks being thinner.

On a dusty-gas shock tube

Abstract: Analytical and numerical methods were used to investigate the flow in­duced by a shock wave in a shock-tube channel containing air laden with suspended small solid particles. Exact results are given for the frozen and equilibrium shock-wave properties as a function of diaphragm-pressure ratio and shock-wave Mach numbers. The driver contained air at high pressure. A modified random-choice method together with an operator-splitting technique show clearly both the decay of a discontinuous frozen shock wave and a contact discontinuity, and the formation of a stationary shock structure and an effective contact front of finite thickness. The effects of particle diameter, particle-number density and diaphragm- pressure ratio on the transitional behaviour of the flow are investigated in detail. The alteration of the flow properties owing to the presence of particles is discussed thoroughly and compared with classical shock-tube flows.

ISEE-1 and -2 observations of magnetic field strength overshoots in quasi-perpendicular bow shocks

Abstract: An examination of quasi-perpendicular shocks (42.7° ≲ θBn ≲ 88.3°) using ISEE-1 and -2 fluxgate magnetometer data has shown that the magnitude of the magnetic field behind the shock front often overshoots, i.e., rises to significantly larger values than observed some distance downstream from the shock. Usually the overshoot is followed by an undershoot of comparable or longer duration and comparable magnitude before the normal magnetosheath values are reached. 110 shock crossings are examined. Only shocks with ratios of fast Mach number to critical Mach number, M/Mc, greater than 1 exhibited the overshoot. This suggests that the structure is associated only with supercritical shocks. The amplitude of the overshoot increased with M/Mc and, to a lesser degree, with solar wind ion β. No dependence of overshoot amplitude on θBn was apparent. The thickness of the overshoot was found to be a few ion gyroradii based on the solar wind velocity and magnetic field strength upstream of the shock.

Solution of the two-dimensional Euler equations with generalized coordinate transformation using flux vector splitting

Abstract: An implicit finite difference code using flux vector splitting has been developed for solving the two-dimensional inviscid gas dynamics equations. The method is spatially second-order acurate, fully conservative, and uses body-conforming generalized coordinates for treating complex geometries. Numerical results have been obtained for transonic flow over a circular cylinder and airfoils. Steady results for a half cylinder (top and bottom symmetry-imposed) range from critical flow to a strong shock case with rotationally induced flow separation. Full cylinder solutions at freestream Mach number values of 0.5, however, show unsteady oscillation. A perturbation form of the method has also been developed and used to compute both fore and aft inviscid flow separation about a cylinder for a nonuniform incoming stream.

Mach 6 Experiments of Transition on a Cone at Angle of Attack

Abstract: Transition movement and patterns on the frustum of a cone at small angles of attack have been investigated at a Mach number of 5.9, using an 8-deg half-angle cone with both sharp and blunt nosetips. Small angles of attack produced large asymmetries in the frustum transition pattern for both sharp and blunt tipped configurations. For the configurations with nosetip bluntness most of the frustum transition asymmetry occurred between meridian angles of 60 and 120 deg. Data obtained with simulated laminar ablated nosetips were generally representative of what would be expected with a larger spherically blunt nosetip.

Comparison Between Experiment and Prediction for a Transonic Turbulent Separated Flow

Abstract: Solutions of the time-dependent, mass-averaged Navier-Stokes equations are compared In detail with experimental results obtained on an axisymmetric "bump" model at a transonic Mach number that produced an extensive separated now region. In addition, an inverse boundary method is evaluated for this type of flow. The Cebeci-Smith algebraic and the Wilcox-Rubesin two-equation turbulence models used in the Navier-Stokes calculations both predict the maximum boundary-layer displacement thickness generated by the interaction reasonably well, with the details of the now best described with the two-equation formulation. However, both models predict a shock location substantially farther aft on the bump than observed experimentally. This error in shock location was slightly less with the two-equation model (0.12 chord compared with 0.16 chord). In the vicinity of the shock, the calculations predict a more rapid increase in turbulent shear stress than observed in the experimental results; this more rapid increase is believed to be the cause or the poor predictions in shock position.

A Reattaching Free Shear Layer in Compressible Turbulent Flow

Abstract: A numerical simulation of the time-dependent, Reynolds-averaged, Navier-Stokes equations for the entire flowfield, employing a two-equation eddy viscosity turbulence model, is presented for free turbulent shear layer reattachment on inclined surfaces at high Mach number. The results are compared to the results of an investigation of a two-dimensional, free turbulent shear layer reattaching on an inclined surface at Mach 2.92 and at a high Reynolds number. The test geometry is specifically designed to isolate the reattachment process of a high-speed separated flow. Detailed comparisons of prediction and experiment are made in the free shear layer, at reattachment, and in the developing boundary layer downstream. These comparisons include mean surface quantities as well as mean and fluctuating flowfield quantities. Although the overall features of this complex flowfield are predicted, there are several deficiencies in the numerical solution, particularly in the region downstream of reattachment. Modifications of the turbulence model to correct these difficiencies are discussed.

Low-frequency sound radiation and generation due to the interaction of unsteady flow with a jet pipe

Abstract: In this paper we examine the low-frequency sound radiated when various types of unsteady flow interact with a jet pipe. In each case we solve the problem exactly by the Wiener-Hopf technique, producing results valid for arbitrary internal and ex- ternal Mach numbers and temperatures, discuss the importance of a Kutta condition at the duct exit, and provide an interpretation, in elementary terms, of the radiated sound field using the Lighthill acoustic analogy. A central feature is that the solutions are always obtained subject to a causality requirement, regardless of whether or not a Kutta condition is imposed at the pipe lip. When low-frequency sound propagates down the jet pipe, little of it reaches the far field, and the major disturbance outside the pipe is that associated with the jet instability waves. At subsonic jet speeds and low-enough Strouhal number these waves transport kinetic energy at a rate precisely balancing the loss of acoustic energy from the pipe, resulting in a net attenuation of the sound power. For supersonic jet condi- tions a further wave motion, the unsteady-flow counterpart of the steady wave struc- ture of an imperfectly expanded jet, is present in addition to the instability wave. We use the Lighthill acoustic analogy to show that, for high-enough jet Mach number and temperature, the sound radiation is caused largely by quadrupole sources arising from the jet instability waves. An alternative interpretation uses the acoustic analogy incorporating a mean flow due to Dowling, Ffowcs Williams and Goldstein, and expresses the far-field sound as the sum of contributions from monopoles and dipoles distributed over the duct exit. The directivity and power of the calculated far-field sound are in good agreement with experiments. We also calculate the sound scattered by the jet pipe when there is an incident external sound field, and show a previously published result to be in error. In general, the flbw phenomena produced by internal and external incident sound fields are similar. Finally, we discuss the effects of nozzle contraction. We find that the radiated sound field is little changed in character, but that the reflection properties of the nozzle may be drastically altered.

Steady-State Solution of the Euler Equations for Transonic Flow

Abstract: Publisher Summary The most important requirement for aeronautical applications of computational methods in fluid dynamics is the capability to predict the steady flow past a proposed configuration, so that key performance parameters such as the lift to drag ratio can be estimated. Thus, the aerodynamic design is based on analysis of steady flow. It is important to be able to calculate steady solutions of aerodynamic flows in the transonic range, where the formation of shock waves leads to the onset of drag rise, and a drastic deterioration of the lift to drag ratio as the speed of the airplane approaches the speed of sound. As the Mach number is increased and the shock waves become strong enough to produce appreciable amounts of entropy and vorticity, the assumption of potential flow becomes progressively less acceptable. The chapter also discusses time stepping schemes. The objective of the time-stepping procedure is to advance the solution to a steady state as rapidly as possible for a given amount of computational effort. The use of an implicit scheme permits a larger time step but requires more effort per time step.

Three-Dimensional Supersonic Viscous Flow over a Cone at Incidence

Abstract: : The viscous supersonic flow over a sharp cone at incidence is examined numerically with a coupled strongly implicit algorithm for the properties in the plane normal to the cone axis. The Navier-Stokes equations are considered in a boundary layer-like or parabolized manner and global relaxation is considered for the pressure interaction. It is shown that departure effects can be effectively eliminated by forward differencing for the axial pressure gradient. Moreover, this approximation retains the implicit free pressure interaction required for geometries where axial flow separation is possible. (Author)

Flow Oscillations of Spike-Tipped Bodies

Abstract: The oscillating flow field around a spike-tipped body has been simulated by the numerical solution of the 3-D compressible Navier-Stokes equations at a Mach number of 3.0 and a nominal Reynolds number of 7.87 x 10 to the 6th/m. Computations were performed using a vectorized 3-D Navier-Stokes program on the STAR 100 computer. Numerical solutions confirmed the experimental result that the self-sustained oscillation occurs within a limited range of the protruded spike length to shoulder height ratio. The numerical result predicted correctly the discrete frequency range as well as the rms pressure intensity. The detailed flow structure is also presented and discussed.

Transition from regular to Mach reflection of shock waves Part 1. The effect of viscosity in the pseudosteady case

Abstract: It is demonstrated experimentally that the influence of viscosity on the transition condition in pseudosteady flow is very significant. A mechanism is proposed for this effect, which explains the features of the observed behaviour. In particular, an experimental method of finding the inviscid transition condition, by extrapolation to infinite Reynolds number, gives excellent agreement with the calcwlatcd inviscid sonic criterion. It is thought that this provides the explanation for the usual persistence of regular reflection beyond the sonic: condition.

Self-generation of organized waves in an impinging turbulent jet at low Mach number

Abstract: Self-generation of highly organized waves in a nominally turbulent jet at very low Mach number can arise from its impingement upon the downstream orifice of an axisymmetric cavity, having an impingement length much shorter than the corresponding acoustic wavelength. The oscillation frequencies are compatible with the resonant modes of a long pipe located upstream of the cavity and with jet-instability frequencies based on the column mode (0·3 [siml ] SD [siml ] 0·6), as well as the near-field shear layer mode (0·016 [siml ] Sθ0 [siml ] 0·03). Moreover, the frequency of the organized wave is constant from separation to impingement; consequently vortex pairing does not occur.Within the cavity, the pressure amplitude associated with the organized wave is directly related to the phase difference between the organized velocity fluctuations at separation and impingement. Maximum pressure amplitude occurs when this phase difference, measured along the cavity (i.e. jet) centre-line, is 2nπ. Streamwise amplitude and phase distributions of the organized wave cannot be explained from purely hydrodynamic considerations; however, they can be effectively modelled by superposing contributions from hydrodynamic and acoustic waves. This aspect has important consequences for externally excited jets as well.

Evaluation of wind tunnel performance testings of an advanced 45 deg swept 8-bladed propeller at Mach numbers from 0.45 to 0.85

Abstract: The increased emphasis of fuel conservation in the world and the rapid increase in the cost of jet fuel has stimulated a series of studies of both conventional and unconventional propulsion systems for commercial aircraft. The results of these studies indicate that a fuel saving of 15 to 30 percent may be realized by the use of an advanced high-speed turboprop (Prop-Fan) compared to aircraft equipped with high bypass turbofan engines of equivalent technology. The Prop-Fan propulsion system is being investigated as part of the NASA Aircraft Energy Efficient Program. This effort includes the wind tunnel testing of a series of 8 and 10-blade Prop-Fan models incorporate swept blades. Test results indicate efficiency levels near the goal of 80 percent at Mach 0.8 cruise and an altitude of 10.67 km (35,000 ft). Each successive swept model has shown improved efficiency relative to the straight blade model. The fourth model, with 45 deg swept blades reported herein, shows a net efficiency of 78.2 at the design point with a power loading of 301 kW/sq meter and a tip speed of 243.8 m/sec (800 ft/sec.).

Fundamentals of Compressible Flow

Abstract: COURSE OUTLINE : “Gas Dynamics” is a topic of fundamental interest to Mechanical and Aerospace engineers that provides a link between core subjects i.e. “Fluid Mechanics and Thermodynamics”. It pertains the basic theory of compressible flow, formation of shock waves and expansion waves, nozzle flows. The treatment of the syllabus becomes the backbone of aerodynamic engineers towards research in the design of high-speed vehicles. The contents of the course starts with fluid and thermodynamic fundamentals followed by governing theories of compressible flow phenomena. Many aerodynamic high-speed facilities and their measurement diagnostics governed by these theories, are also covered in this course.

An experimental investigation of the unsteady behavior of blunt fin-induced shock wave turbulent boundary layer interactions

Abstract: : An experimental study has been made of blunt fin-induced shock wave turbulent boundary layer interactions. This type of interaction is known to be highly unsteady. The objective of this experiment was to determine the characteristics of the fluctuating surface pressure distribution and the parameters controlling it. Tests have been made using fins of different diameter, D, with incoming turbulent boundary layers varying in thickness, Delta, in the ratio of about 5:1. Measurements have been made on the fin centerline and up to four diameters outboard of it. All tests were made at a Mach number of 2.95 and a unit Reynolds number of 6.3 billion/m, and under approximately adiabatic wall conditions. The measurements show that very high intensity r.m.s. pressure levels occur--up to almost two orders of magnitude above that of the incoming boundary layer. The highest intensities occur on centerline ahead of the fin. Here, the r.m.s. pressure distribution is characterized by three distinct peaks which decrease at different rates with distance outboard. Even four diameters off centerline, the maximum r.m.s. value in the distribution is still an order of magnitude larger than that of the incoming boundary layer. Outboard of the centerline, the r.m.s. pressure level downstream of the freestream shock wave steadily decreases. Within a distance of six to eight diameters it is close to the undisturbed value. With different diameter fins and different boundary layers, the qualitative characteristics are the same. The quantitative results depend on the ratio D/Delta. (Author)

Comparison of gas dynamic model with steady solar wind flow around Venus

Abstract: A gas dynamic model for solar wind flow around Venus has been compared with Pioneer Venus orbiter plasma analyzer measurements from times when the solar wind flow seemed steadiest. The comparisons were made near the terminator. When the observed and model bow shock locations are matched, the model agrees fairly well with the observed parameters: the components of the flow velocity and magnetic field, and the proton number density and isotropic temperature. However, the Mach numbers required to fit the observed bow shock locations are less than 2/3 those estimated from the measured parameters of the free-stream flow, because the bow shock locations (near the terminator) are farther from Venus than expected. Sometimes the measured flow speeds appear to be retarded near the ionopause.