Showing papers on "Mach wave published in 2003"

Aero-optical characteristics of compressible, subsonic turbulent boundary layers

Abstract: An extensive experimental study of optical aberrations due to propagation through fully-developed turbulent boundary layers at high subsonic Mach numbers was performed. Time-resolved, high- bandwidth, direct optical measurements of the dynamic aberrations were made using a Malley probe. The probe was used to obtain the convective speeds of the optically-significant turbulence structures and to measure the optical path differences. Measurements were made over a range of boundary layer thicknesses and Mach numbers. Optical distortions were found to scale linearly with boundary layer thickness and freestream density, and to go as the square of the freestream Mach number.

Shock waves at microscales

Abstract: We present a model for the effects of scale, via molecular diffusion phenomena, on the generation and propagation of shock waves. A simple parametrization of the shear stresses and heat flux at the wall leads to the determination of new jump conditions, which show that, for a given wave Mach number at small scales, the resulting particle velocities are lower but the pressures are higher. Also, the model predicts that the flow at small scale is isothermal and that the minimum wave velocity can be subsonic. Experiments with a miniature shock tube using low pressures to simulate the effects of small scale have shown qualitative agreement with the proposed model. In fact, the effects of scale appear even more important than what has been incorporated in the model.

Compressibility effects on turbulence structures of axisymmetric mixing layers

Abstract: A real-time flow visualization system that produces 17 images over a time span of 150 μs is used to visualize the mixing layers of Mach 1.3 (Mc=0.59) and Mach 2.0 (Mc=0.87) ideally expanded high Reynolds number axisymmetric jets. These image sequences reveal details about the influence of compressibility on the dynamics of turbulence structures. In general, the behavior observed in axisymmetric jets is similar to that observed in planar shear layers at similar convective Mach numbers. In addition, large streamwise vortices are apparent in cross-stream images of the flow. Large-scale structures become more three-dimensional and less organized with increasing compressibility and more difficult to identify and track. Planar space–time correlations are used to track structures as they convect downstream. The histogram of the convective velocity for the Mach 1.3 jet revealed a broad distribution of convective velocities with an ensemble average of 266 m/s, which is much higher than the theoretical prediction of 206 m/s. The Mach 2.0 jet, however, exhibited a bimodal convective velocity distribution with an ensemble average of 402 m/s for the “fast” and 190 m/s for the “slow” mode. These modes are equally spaced from the theoretical convective velocity of 303 m/s. Approximately 2/3 of the measured velocities were in the slow mode.

Sound radiation in turbulent channel flows

Abstract: Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit.

First- and second-order theory of supersonic flow past bodies of revolution

Abstract: Methods are studied for improving the existing perturbation theories of supersonic flow past bodies of revolution. Applicability of the theory at high Mach Numbers is emphasized. For axial flow, a second-order solution isfound which represents a considerable improvement over the first-order result. For inclined flow, a second-order solution is not feasible except for a cone. Comparison with the exact solutions for cones shows that the slender-body series expansion causes large inaccuracies in both axial and inclined flow. The conclusion that first-order theory predicts the flow no better than slender-body theory is shown to be erroneous. When first-order theory is properly used,making no unnecessaryapproximations, greatly improved agreement is found with exact solutions and with experiment. The order estimates used to justify the approximations are shown to be invalid in most practical cases. A "hybrid" theory, combining first-order cross flow and second-order axial flow, gives further improvement. A physical explanation is advanced for the marked superiority of first-order theory over the true "linearized" theory. Nonlinearity in lift is shown to result primarily from viscous separation of the cross flow along the after portions of a long body. The magnitude of the resulting normal force can be estimated with reasonable accuracy using two-dimensional viscous sweep-back theory.

The wall-jetting effect in Mach reflection: theoretical consideration and numerical investigation

Abstract: The jetting effect often appears in the Mach reflection of a shock and in more complicated irregular shock reflections. It also occurs in some natural phenomena, and industrially important processes. It is studied numerically using a W-modification of the second-order Godunov scheme, to integrate the system of Euler equations. It is shown that there is no correspondence between the shock reflection patterns and the occurrence of jetting. Furthermore, there are two kinds of jetting: strong which occurs when there is a branch point on the ramp surface where the streamlines divide into an upstream moving jet and a downstream moving slug; and weak which has no branch point and may occur at small and large values of the ramp angle θw .T he width of the jet for Mach and other reflections is determined by the angle of the Mach stem at the triple point (also called the Mach node or three-shock node). Strong jetting is unstable and the primary instability is in the jet itself. The contact discontinuity is also unstable, but its instability is secondary with respect to the jet instability. Two types of irregular reflection are identified in the dual-solution-domain. They are at wo-node system comprising a Mach node followed by a four-shock (overtake) node; and another which seems to be intermediate between the previous system and at hree-node reflection, which was first hypothesized by Ben-Dor & Glass (1979). An approximate criterion for the jetting ↔ no-jetting transition is presented. It is derived by an analysis of the system of Euler equations for a self-similar flow, and has a simple geometrical interpretation.

Experiments on shock wave reflection transition and hysteresis in low-noise wind tunnel

Abstract: Experiments on the transition between steady regular and Mach reflections of shock waves have been performed in a low-noise wind tunnel. Owing to a very low level of free-stream disturbances inherent in this facility, the hysteresis phenomenon has been observed in close agreement with theoretical predictions and results of the previous numerical simulations. When increasing the incident shock wave angle, regular reflection persists in most of the dual solution domain. Thus, the detachment criterion can be considered as a true one for the transition from regular to Mach reflection, and an earlier transition observed in many wind tunnel experiments is certainly caused by free-stream disturbances, which were present in those facilities.

Numerical and Experimental Investigations on the Mach 2 Pseudo-Shock Wave in a Square Duct

Abstract: This paper describes numerical and experimental investigations for the multiple shock wave/turbulent boundary layer interaction in a Mach 2 supersonic square duct. The numerical simulation is carried out with the Harten-Yee second-order accuracy TVD scheme and the Baldwin-Lomax turbulence model. The flow conditions are a free-stream Mach number of M_∞ ≅ 2.0 and a Reynolds number of Re_∞ = 2.5 × 10^7 and the flow confinements are δ_∞/h = 0.15 (case A) and δ_∞/h = 0.25 (case B), respectively. The computational results for both cases show good agreement with the experimental results. Based on these agreements, the flow quantities, which are very difficult to obtain experimentally, are analyzed by numerical simulation. Moreover, the effect of flow confinement on the pseudo-shock wave characteristics is also presented.

Self-induced oscillations in the shock wave flow pattern formed in a stationary supersonic flow over a double wedge

Abstract: Numerical simulations of a two-dimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range 5⩽M⩽9, revealed the existence of self-induced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters.

Effect of energy addition on MR → RR transition

Abstract: A combined computational and experimental study was performed to investigate the effect of a single laser energy pulse on the transition from a Mach Reflection (MR) to a Regular Reflection (RR) in the Dual Solution Domain (DSD). The freestream Mach number is 3.45 and two oblique shock waves are formed by two symmetric $22^\circ$ wedges. These conditions correspond to a point midway within the DSD wherein either an MR or an RR is possible. A steady MR was first obtained experimentally and numerically, then a single laser pulse was deposited above the horizontal center plane. In the experiment, the laser beam was focused resulting in a deposition volume of approximately 3 mm3, while in the simulation, the laser pulse was modeled as an initial variation of the temperature and pressure using Gaussian profile. A grid refinement study was conducted to assess the accuracy of the numerical simulations. For the steady MR, the simulation showed the variation of Mach stem height along the span due to side effects. The predicted spanwise averaged Mach stem height was 1.96 mm within 2% of the experimental value of 2 mm. The experiment showed that the Mach stem height decreased to 30% of its original height due to the interaction with the thermal spot generated by the laser pulse and then returned to its original height by $300\;\mu$ s. That the Mach stem returned to its original height was most likely due to freestream turbulence in the wind tunnel. The numerical simulation successfully predicted the reverse transition from a stable MR to a stable RR and the stable RR persisted across the span. This study showed the capability of a laser energy pulse to control the reverse transition of MR $\rightarrow$ RR within the Dual Solution Domain.

Mach 4 Performance of a Fixed-Geometry Hypersonic Inlet with Rectangular-to-Elliptical Shape Transition

Abstract: Wind-tunnel testing of a hypersonic inlet with rectangular-to-elliptical shape transition has been conducted at Mach 4.0. These tests were performed to investigate the starting and back-pressure limits of this fixed-geometry inlet at conditions well below the Mach 5.7 design point. Results showed that the inlet required side spillage holes in order to self-start at Mach 4.0. Once started, the inlet generated a compression ratio of 12.6, captured almost 80% of available air and withstood a back-pressure ratio of 30.3 relative to tunnel static pressure. The spillage penalty for self-starting was estimated to be 4% of available air. These experimental results, along with previous experimental results at Mach 6.2 indicate that fixed-geometry inlets with rectangular-to-elliptical shape transition are a viable configuration for airframe- integrated scramjets that operate over a significant Mach number range.

Influence of Mach Number on Tornado Corner Flow Dynamics

Abstract: Since maximum Mach numbers in an F5 tornado are expected to, at least, reach ∼0.4, a study was undertaken to determine the major potential compressibility effects in such flows. Results from compressible large-eddy simulations of tornado corner flow dynamics are summarized. Comparison with previous incompressible simulations indicates that Mach number effects tend to be modest and may be estimated by an isentropic approximation. As the average maximum Mach number M within the tornado increases above one-half, the largest changes occur for “low-swirl” corner flows, those exhibiting a central vertical jet off the surface capped by a vortex breakdown, with the vortex breakdown found to occur at significantly greater heights as M increases. It also appears that the highest Mach numbers are most likely to occur during rapid transients in near-surface intensification that can sometimes occur during a tornado's evolution.

Characteristics of the mach disk in the underexpanded jet in which the back pressure continuously changes with time

Abstract: When the high-pressure gas is exhausted to the vacuum chamber from the nozzle, the underexpanded supersonic jet contained with the Mach disk is generally formed. The eventual purpose of this study is to clarify the unsteady phenomenon of the underexpanded free jet when the back pressure continuously changes with time. The characteristic of the Mach disk has been clarified in consideration of the diameter and position of it by the numerical analysis in this paper. The sonic jet of the exit Mach number Me=1 is assumed and the axisymmetric conservational equation is solved by the TVD method in the numerical calculation. The diameter and position of the Mach disk differs with the results of a steady jet and the influence on the continuously changing of the back pressure is evidenced from the comparison with the case of steady supersonic jet.

Experimental determination of the free-stream disturbance field in a short-duration supersonic wind tunnel

Abstract: The free-stream disturbance field in a short-duration supersonic wind tunnel is investigated at a nominal Mach number of Ma=2.54. A specially designed constant-temperature anemometer is used to be able to draw a complete fluctuation diagram within one wind tunnel run (testing time: 120 ms). It is shown that the disturbance field is dominated by acoustic waves radiated from the turbulent boundary layer on the nozzle and the sidewalls, like in conventional supersonic wind tunnels. The acoustic field appears to be composed of highly localized shivering Mach waves superimposed on a background of eddy Mach waves.

An Experimental Study of the Cavity Flow for Closed-Loop Flow Control

Abstract: We present the results of an experimental investigation conducted as part of a multidisciplinary effort intended to address systematically the problem of closed-loop flow control by assembling expertise from numerical and experimental flow analysis, flow modeling, and control design disciplines. Experiments were conducted using a shallow-cavity flow in a small-scale wind tunnel that can operate continuously in the subsonic regime. We restricted our attention to cavity flow in the Mach number range 0.25-0.5. The flow exhibits the characteristic staging behavior predicted by the semi-empirical Rossiter formula with multiple modes in the Mach number range 0.32-0.38 and a single strong mode in the other flow conditions. A preliminary survey of the velocity at the exit of the compression-driver actuator used for control reveals that this actuator has a non-linear behavior and was little influenced by the local effect of Mach 0.3 main flow. Forcing the Mach 0.3 flow with the actuator indicates that this has good authority over a large range of frequencies, with elimination of the resonant peak observed at some frequencies. We took advantage of this phenomenon to develop a preliminary, logic-based controller that searches the frequency space and maintains the optimal forcing frequency for peak reduction at each Mach number. Optimal frequencies and the corresponding reduced resonance have been obtained for all the flow conditions explored.

Alfvén-wave transmission and test-particle acceleration in parallel relativistic shocks

Abstract: Alfven-wave transmission through super-Alfvenic parallel relativistic shock waves is studied. We calculate the wave transmission coecients for given shock properties. We show (i) that the Alfven waves downstream the shock wave are propa- gating predominantly anti-parallel to the flow direction for low-Mach-number shocks, as in the case of non-relativistic shocks; and (ii) that for high-Mach-number ultra-relativistic shocks the forward and backward downstream waves are in equipartition. For low Alfvenic Mach numbers, the scattering center compression ratio of the shock, thus, becomes large and the spectral index of accelerated test particles approaches the limit ! 1 at shock waves approaching the critical value of the quasi-Newtonian Alfvenic Mach number (i.e., the ratio of upstream fluid and Alfven proper speeds), which depends on the shock properties, and equals the square root of the compression ratio at the test-wave limit. Although the inclusion of the wave electromagnetic and velocity fields to the shock jump conditions is likely to decrease the scattering-center compression ratio for shocks with critical Mach numbers, values significantly above the gas compression ratio can be expected for such shocks. Particle acceleration in weak relativistic shocks propagating in magnetized astrophysical jets may, therefore, be substantially more ecient than predicted by models neglecting turbulent electric fields.

Computational Aerodynamic Analysis of the Flow Field about a Hypervelocity Test Sled

Abstract: : The flow field about the nose section of a hypervelocity test sled is computed using computational fluid dynamics. The numerical model of the test sled corresponds to the Nike O/U narrow gage sled used in the upgrade program at the High Speed Test Track facility, Holloman Air Force Base, New Mexico. The high temperatures and pressures resulting from the aerodynamic heating and loading affect the sled structure and the performance of the vehicle. The sled transitions from an air environment to a helium environment at a speed of approximately 3,300 feet per second (Mach 3 in air, Mach 1.02 in helium) to reduce the effects of high Mach number flows. Steady, three-dimensional, inviscid flow solutions are computed for Mach numbers of 2 and 3 in air (2,200 and 3,300 feet per second), and for Mach numbers of 1.02, 2.5 and 3.1 in helium (3,300, 8,076 and 10,000 feet per second). Mesh adaptation is used to obtain a mesh-independent solution. Second-order solutions are obtained for the Mach 3 in air and Mach 1.02 in helium cases. The unsteady transition from air to helium at 3,300 feet per second is also modeled. Mach 3 in air computations are compared with analytical results.

Analogy between soap film and gas dynamics. II. Experiments on one-dimensional motion of shock waves in soap films

Abstract: This paper presents an experimental investigation of one-dimensional moving shock waves in vertical soap films. The shock waves were generated by bursting the films with a perforating spark. Images of propagating shock waves and small disturbances were recorded using a fast line scan CCD camera. An aureole and a shock wave preceding the rim of the expanding hole were clearly observed. These images are similar to the x-t diagrams in gas dynamics and give the velocities of shock and sound waves. The moving shock waves cause jumps in thickness. The variations of the induced Mach number, M2 and the ratio of film thickness across the shock wave, δ 2/δ 1, are plotted versus the shock Mach number, M s. Both results suggest that soap films are analogous to compressible gases with a specific heat ratio of γ≅1.0.

Low Mach number flows in time-dependent domains

Abstract: We perform a multiple time scale, single space scale analysis of a compressible fluid in a time-dependent domain, when the time variations of the boundary are small with respect to the acoustic velocity. We introduce an average operator with respect to the fast time. The averaged leading order variables satisfy modified incompressible equations, which are coupled to linear acoustic equations with respect to the fast time. We discuss possible initial-boundary data for the asymptotic equations inherited from the initial-boundary data for the compressible equations.

Three-dimensional propagation of the transmitted shock wave in a square cross-sectional chamber

Abstract: An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.