Constant Mach Number Research Articles

On shock waves in a confined reflector

The main objective of the present work is to carry out experimental studies concerning generation of polygonal-shaped shock waves in a procedure introduced by Apazidis and Lesser [N. Apazidis, M.B. Lesser, On generation and convergence of polygonal-shaped shock waves, J. Fluid Mech. 309 (1996) 301–309]. In this procedure an expanding circular cylindrical shock wave with constant Mach number distribution is generated at the center of a confined air-filled chamber. The chamber boundary has the form of a slightly perturbed circle. The shock reflects off the boundary and converges in the inner of the chamber into a polygonal shape. For this experimental study, an air-filled chamber was designed and manufactured. Shocks were generated by means of an electric discharge. A schlieren system with camera and delayed flash device, was used in order to visualize the process. Equipment for time control and measuring was also used. The experimental results of the current investigation confirmed the theoretical predictions obtained in earlier studies of similar problems. The major new result showed that it is possible to generate polygonal-shaped shocks with sharp corners and plane sides by means of reflection from a smooth boundary. The shock strength was estimated to M=1.1 and the observed shock form confirmed the earlier theoretical predictions. The proposed experimental procedure showed to be a simple, stable, repeatable and reliable method to produce highly symmetrical polygonal-shaped converging shocks.

SECONDARY POWER SYSTEM EVALUATIONS FOR ADVANCED AIRCRAFT

A computerized analytical program is being developed to help investigate the impact of power system requirements on aircraft performance. The program has an user interface that operates in MS-EXCEL, linking several subsystems analysis programs for execution and data transfer in the power systems analysis. The program presently includes an encoded propulsion engine cycle code, which allows the inspection of power extraction effects on engine performance. To validate the results of the encoded engine program, a study was conducted to investigate the separate effects of shaft power extraction and pneumatic bleed. The selected engine cycle was that for a standard tactical fighter, with a flight condition of varied altitude (sea level to 40,000 ft) and constant Mach Number (0.9). As expected the resultant data showed that the engine performance was more sensitive to pneumatic bleed than to shaft power extraction. The paper’s efficiency comparisons between shaft power and bleed air power helps indicate the higher efficiency for the power system of a more-electric type aircraft. Present efforts on the analytical interface are to incorporate a fuel thermal management analysis capability.

Experiments characterizing nonlinear shear layer dynamics in a supersonic rectangular jet undergoing screech

Jet screech is the result of a resonant aeroacoustic feedback loop. In modern high-performance aircraft jet screech has given rise to in-flight sonic fatigue failure of nozzle components. For this reason, jet screech has been the focus of numerous investigations. However, the prediction of screech amplitude has been a very elusive goal. A primary objective of the work to be reported is to experimentally characterize the nonlinear instability wave development in the shear layer of a rectangular supersonic jet undergoing screech. Hot-film probes are used to measure the instability wave development in the jet shear layers along a constant Mach number ray. Higher-order polyspectral techniques are employed to determine resonant nonlinear phase locking between multiple instability modes. A detailed comparison of the “inner loop” hot-film measurements with “outer loop” acoustic measurements is made. Such a comparison reveals the importance of incorporating nonlinear effects into a jet screech amplitude prediction method.

Response of a Two-Dimensional Cascade

Time-accurate Euler simulations of the ow through two-dimensional cascades were used to provide data on the response of the ow entering a compressor to an upstream disturbance. These data were then used to evaluate several compressor face boundary condition hypotheses intended for supersonic inlet stability simulations. An accurate out ow boundary condition for time-accurate Euler/Navier± Stokes simulations of inlet ows is needed to determine the stability margin of an inlet that encounters an atmospheric disturbance. The boundary condition must provide an approximation of the response from the compressor when a disturbance from upstream passes through the inlet and into the compressor face. In the cascade analysis, the blade stagger angle, solidity, shape, and loading; axial Mach number; and disturbance strength were each varied through a representative range. It was found that the response of a cascade to an acoustic disturbance is almost nonre ective for blade geometry parameters characteristic of the compressor hub region and almost at a constant velocity condition for blade geometry parameters characteristic of the blade tip region. A convective (temperature) disturbance was also examined and was found to pass through a cascade without generating an upstream disturbance. Screen, constant Mach number, and constant velocity out ow boundary conditions were evaluated as possible compressor face boundary conditions. It is concluded that the constant velocity boundary condition is preferable to either the screen or the constant Mach number boundary conditions for inlet stability simulations.

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.

COMPARISON OF ACCURACY AND PERFORMANCE FOR LATTICE BOLTZMANN AND FINITE DIFFERENCE SIMULATIONS OF STEADY VISCOUS FLOW

The lattice Boltzmann method (LBM) is used to simulate flow in an infinite periodic array of octagonal cylinders. Results are compared with those obtained by a finite difference (FD) simulation solved in terms of streamfunction and vorticity using an alternating direction implicit scheme. Computed velocity profiles are compared along lines common to both the lattice Boltzmann and finite difference grids. Along all such slices, both streamwise and transverse velocity predictions agree to within 0ċ5% of the average streamwise velocity. The local shear on the surface of the cylinders also compares well, with the only deviations occurring in the vicinity of the corners of the cylinders, where the slope of the shear is discontinuous. When a constant dimensionless relaxation time is maintained, LBM exhibits the same convergence behaviour as the FD algorithm, with the time step increasing as the square of the grid size. By adjusting the relaxation time such that a constant Mach number is achieved, the time step of LBM varies linearly with the grid size. The efficiency of LBM on the CM-5 parallel computer at the National Center for Supercomputing Applications (NCSA) is evaluated by examining each part of the algorithm. Overall, a speed of 13ċ9 GFLOPS is obtained using 512 processors for a domain size of 2176×2176.

Quenching of reaction in gas-sampling probes to measure scramjet engine performance

The problem of chemical quenching in gas-sampling probes was studied as a reactive, Rayleigh, and Fanno flow. The typical lengths of friction, convective heat transfer, and reactions in the probes are evalnated under the testing conditions of ramjet and scramjet engines. A reduced chemical kinetic scheme was adopted, and the reaction times were evaluated from the ignition times derived by reflected shock wave experiments. Thereby, criteria for quenching in probes were obtained analytically. The critical Damköhler number ( Da ) for quenching in an H 2 -air reaction was found to be 23 (1500 K) to 10.5 (3000 K). A 2.6-fold greater Da was derived for CH 4 -air mixtures. Because reactions in CH 4 -air mixtures can be quenched even above 2200 K, combustion performance in a CH 4 -fueled ramjet combustor was measured from gas analysis. However, quenching of H 2 unburned gas in more difficult than quenching of CH 4 , Cooling with supersonic expansion is essential to freeze reactions in H 2 -air mixtures in scramjets tested under a total temperature higher than 2000 K. A constant Mach number expansion is recommended downstream of the sampling orifice. The contour of the expansion region and the decay of total pressure were determined taking into account friction and cooling effects. Reactions with unburned H 2 can be quenched if the sampling probe works as a supersonic diffuser operating in the supercritical mode.

Hypersonic model testing in a shock tunnel

A shock tunnel is used to perform tests at hypersonic flow conditions including weak real gas effects. Pressure and heat flux distributions are measured around typical re-entry configurations. From these data cp values and Stanton numbers are deduced. For constant Mach and Reynolds number the experimental results achieved indicate a strong influence of the total temperature on the Stanton number distribution. For the results presented this behavior is mainly based on entropy layer and viscous interaction effects. A correlation function which takes into account these effects correlates the Stanton numbers achieved for different flow conditions and in different wind tunnels fairly well.

Non-equilibrium MHD channel theory and numerical simulation

The internal plasma processes and performance parameters of a non-equilibrium MHD channel are presented and analyzed. The one-dimensional model assumes uniform properties over the channel cross-sectional area and allows for variations of gas velocity, pressure, temperature, density, electric field, current density, electrical conductivity and electron temperature in the direction of the flow. The plasma composition is determined by particle balance equations which include collisional, radiative, diffusion and flow processes. The model provides a comprehensive description of the plasma processes, since it accounts for two-step ionization with the formation of excited state atoms, includes the particle convection and turbulent diffusion processes in both particle and electron energy balance equations and allows for radiative and thermal non-equilibrium. The electron energy balance equation is used for calculation of the electron temperature and its variation inside the channel and includes the energy input due to the applied electromagnetic field, balanced by the energy losses due to convection and elastic and inelastic collisions of the electrons with neutrals and excited state atoms in the plasma. The set of equations pertinent to the constant Mach number and cross-sectional area are also presented, and a sample calculation is performed for the segmented electrode generator operating in the Faraday mode with a gaseous mixture of helium seeded with a few percent cesium.

Control strategies for space boosters using air collection systems

A simple and efficient performance analysis method is developed for evaluating vehicle pitch and engine throttle controls to minimize booster fuel required to fill second-stage liquid oxygen (LOX) tanks and deliver the vehicle to the staging point. An optimization methodology finds a throttle schedule that controls both the air-breathing engine and the LOX collection rate. The altitude-velocity profile is derived from a variational calculus/energy management contouring method. Automatic adaptive-gain pitch-rate and throttle controls are developed. Results from a parametric study show that collecting on the run for an optimum schedule results in a 17% fuel savings over collection at a constant Mach number.

An Experimental Study on the Subsonic Diffuser with a Shock Wave at the Inlet.

A series of subsonic diffusers with a shock wave at the inlet was tested to establish a design technology in the development of a supersonic airintake. The effects of diffuser geometry and pressure gradient on the diffuser performance were investigated. The diffuser geometry with a constant Mach number gradient in the streamwise direction provides less total pressure loss than a straight diffuser. The bleed system employed upstream of the inlet is effective for the suppression of the total pressure loss. The diffuser performance depends strongly on the Mach number gradient, since it is sensitive to the flow separation due to large Mach number gradient.

One-dimensional theory of a thermal equilibrium MHD channel

The processes and variation of parameters inside an equilibrium MHD channel used as a generator or propulsion device are presented and examined. The performance and internal processes can be described by a set of equations comprising a two-level particle model for the seeding substance, coupled with the transport equations for the carrier gas. The one-dimensional model assumes uniform properties over the channel cross-sectional area and allows for variations of velocity, pressure, temperature, density, electric field, current density and electrical conductivity in the direction of the flow. The plasma composition is determined by particle balance equations which include collisional, radiative, diffusion and flow processes. This comprehensive model should aid and result in an accurate description of the processes inside a MHD channel and allow for a better interpretation of experimental results. An example of a linear constant Mach number segmented electrode generator operating in the Faraday mode with a helium, seeded with a few percent caesium, gaseous mixture is presented in this study. The calculations for typical MHD generator values of pressure, temperature, velocity, magnetic field, seed fraction and electrical efficiency show large deviations on predicted performance between the particle balance and Saha-Boltzmann models. The generator performance is also sensitive to the seed radiation and convection processes.

Comment on 'In-flight measurement of static pressures'

R 1 includes some very interesting in-flight measurements of the steady and fluctuating trailing-edge pressures on an A310-200 aircraft at high speeds. However, Ref. 1 includes two remarks which could mislead some readers. When discussing the measured pressure spectra (Ref. 1, Fig. 11) it is noted that harmonics of torsion can be detected up to eighth order. Such indicates strong buffet motion. It is true that the peaks in the spectra indicate motion (better response or buffeting as defined in Ref. 2). The peaks cannot represent excitation (buffet) at those frequencies. The separations concerned are incipient and of very small scale. Hence, these are unlikely to be modifying the excitation. These motion-induced pressures should be related directly to the aerodynamic damping. It would be interesting to reanalyze the data to see if there are any changes in the phase of the trailing-edge pressures with respect to the wing motions as Q increases at constant Mach number. Later in the article there is a curious reference to buffet frequencies of 45-70 for aerofoils and Ref. 3 is cited. Such discrete (buffet) is determined by a frequency parameter based on the aerofoil chord (only 0.25 m in Ref. 3). With respect to a local chord of about 3.8 m at 71% semispan on the aircraft, the frequency parameter of Ref. 3 would imply frequencies of about 3-5 for flight at sea level. Therefore, the reference to /* = 25 Hz at M = 0.73 is unhelpful. Attribution of the lower frequencies observed to three-dimensional flow at flight conditions is wrong. It is well known that the on aerofoils and high-aspect-ratio swept wings is, in fact, similar in character (e.g., Ref. 4).

An experimental analysis of oblique shock reflection over a two-dimensional multi-guttered wedge

The oblique shock reflection over a multi-guttered model wedge is investigated at constant Mach number. The experimental parameters were the reflecting wedge angle and the depth of the gutter. It is found that, unlike the case of a smooth surface, the wave structure is not self-similar but similar with respect to the coordinate system made dimensionless by the depth when the wedges are geometrically similar (regardless of Reynolds number based on the depth). Again, unlike the smooth surface, the wave structure is essentially unsteady, and the entire body of waves reflected from the bottom of the gutters play a key role in the configuration of a precursory reflected wave as well as in the behavior of the triple point. The slope of the triple point trajectory suggests that it approaches asymptotically that for a smooth surface.

Holographic techniques for whole-field thermal and fluid measurements

SummaryMeasurement methods using holography are non-invasive, whole-field and can be applied in real-time. They are particularly appropriate for experimental validation of current CFD (computational fluid dynamics) codes which have 3-dimensional, transient, irregular geometry capabilities.In holographic interferometry, the fringes formed by refractive index changes represent lines of constant Mach number in isentropic compressible flows and isotherms in convection. Examples are given of two-dimensional inter-ferograms in these areas, and their quantitative interpretation.Automatic fringe and data processing is a necessity, and the method is extendable to three dimensions using tomographical reconstruction. These issues are discussed, together with the general question of comparison with flow predictions.Fluid fields may also be treated on a three-dimensional time-dependent basis, using HCV (holocinematographic velocimetry), a holographic extension of PIV (particle image velocimetry). It is proposeds to run an experiment to measure both fluid and thermal fields, and surface temperatures simultaneously, using HCV or PIV, holographic interferometry and liquid crystal methods respectively.

Diabatic supersonic flows of dense gases

By adopting the van der Waals gas model the behavior of n-octane with addition or removal of heat in inviscid, steady, one-dimensional, supersonic flow is investigated. First, the given heat distribution is added in a constant area flow. Second, the effects in variable cross-sectional flows (nozzles) are shown for the additional condition of constant values of the Mach number or the static pressure, and for a given heat addition. As known from the isentropic flow of real gases, several gas-dynamic effects are inverted depending on the fundamental derivative Γ. Heat addition in a constant area duct at conditions near the thermodynamical critical point may cause an increase of the Mach number in transonic/supersonic flow, or a decrease in subsonic flow, which is the opposite behavior of a perfect gas. For heat addition at M=const a singularity is possible for Γ<0 in transonic/supersonic flow and for Γ≲1 in subsonic flow. Considering constant Mach number flows, the static pressure goes up for high values of Γ. Isobaric heat addition increases the Mach number for densities below the thermodynamical critical point. Perfect gas flow exhibits the opposite reaction in both cases without any singularity. Compared with the flow of a perfect gas (γ=1.4), in the dense gas the influence of the same rate of heat addition becomes much stronger.

Inertial impaction of fine particles at moderate reynolds numbers and in the transonic regime with a thin-plate orifice nozzle

Because the smallest size of very fine particles that can be separated in an impactor is proportional to the ratio Re/M 2, there is an interest in studying these instruments at moderate Reynolds numbers, Re, and at Mach numbers, M, up to sonic conditions. Here an inertial impactor of fixed geometry is tested at Reynolds numbers between 40 and 840, and in the transonic flow regime, at downstream to upstream pressure ratios between 0.42 and 0.79. Earlier theoretical and experimental work has shown that conventional impactors, with nozzles having relatively large length-to-diameter ratios, loose their resolution at Re smaller than several hundreds due to boundary layer growth at the nozzle walls. This effect is minimized here by means of nozzles having rapidly converging walls down to their exit, embodied by a thin-plate orifice with thickness to diameter ratio of 0.014. The nozzle to plate distance is equal to the orifice diameter. Test dioctyl sebacate (DOS) aerosols, with diameters ranging from 0.05 to 0.24 μm, were generated using a Differential Mobility Analyzer (DMA). Collection efficiencies were measured on-line at constant Reynolds and variable Mach numbers using two electrometers; one to monitor the current of charged particles impacting on the collecting plate, the other for the current of uncollected particles. A new method based on sweeping over the Mach number for a given test aerosol, rather than on varying the aerosol size at a fixed Mach number, provides an inversion technique which eliminates completely the effects of multiply charged particles from the DMA. Measurements show excellent resolution even at Re = 100, as well as through the transonic region, so that neither compressibility nor viscous phenomena limit the size of the smallest particle that can be inertially separated with high resolution. The limiting factor is Brownian diffusion. Its negative effects on particle collection efficiency curves are measured here for the first time using NaCl particles with diameters between 0.008 and 0.016 μm.

Parameters Affecting the Postshock Wave Relaxation Zone in an Oxygen Carbon Particle Suspension

A parametric study was conducted regarding the effects of the initial carbon concentration, the initial carbon particle diameter, the shock wave Mach number and the preshock suspension pressure on the suspension behavior in the relaxation zone. The suspension was composed of oxygen gas seeded with small carbon particles. It was found that changing either the initial carbon concentration or the shock wave Mach number has a marked effect on the suspension behavior in the relaxation zone and on the eventually reached postshock equilibrium state. Changes in the initial carbon particle diameter (at a constant shock wave Mach number and carbon concentration) has no effect on the postshock equilibrium state, but it does affect the way in which the suspension reaches this equilibrium state. Changes in the preshock suspension pressure has only minor effects on the suspension behavior in the relaxation zone.

Mass-loaded astronomical flows – I. General principles and their application to RCW 58

We discuss the general principles of mass addition to astrophysical flows via hydrodynamic mixing. We argue that in the absence of strong radiative cooling, a sustained one-dimensional mass-loaded flow will statistically mimic a steady flow of constant adiabatic Mach number about equal to unity. This proposition receives powerful support from observational data for the Wolf–Rayet wind-blown nebula RCW 58.

Mach number control of Ludwieg tubes

Ludwieg tubes offer a convenient and inexpensive way to provide high Reynolds number test flows; their primary defect is the very short run time available for flow measurement. Even during this period, the test section Mach number is liable to be affected by the boundary-layer growth along charge tube walls and shows gradual increase. In order to decrease this Mach number creep, a Ludwieg tube equipped with a quick-moving choker flap is developed. Through use of the flap the effective area ratio of the test section to the sonic throat is kept essentially constant for some period during the nominal run time. An appreciable time lag is observed between the tunnel start and the establishment of the constant Mach number flow. The finite inertia of the flap and the flap drive mechanism as well as the finite pressure signal propagation speed are the main causes of the delay and several means to eliminate the lag are discussed.