Dependence of Steady Mach Reflections on the Reflecting-Wedge Trailing-Edge Angle

Ben‐Dor, G.; Elperin, T.; Li, H.; Vasiliev, E.; Chpoun, A.; Zeitoun, D.

doi:10.2514/2.28

Cited by 9 publications

(3 citation statements)

References 7 publications

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“…As a result the throat of the converging nozzle formed by the slipstream and the plane of symmetry line is fixed at point E, and the Mach stem height is independent of the trailing-edge angle, θ e . This fact was recently verified by Ben-Dor et al (1997b) both numerically and experimentally.…”

Section: 2supporting

confidence: 57%

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

Ben‐Dor

Elperin

et al. 1999

J. Fluid Mech.

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The effect of the downstream pressure (defined here as the wake pressure behind the tail of the reflecting wedge) on shock wave reflection in steady flows is investigated both numerically and analytically. The dependence of the shock wave configurations on the downstream pressure is studied. In addition to the incident-shock-waveangle-induced hysteresis, which was discovered a few years ago, a new downstreampressure-induced hysteresis has been found to exist. The numerical study reveals that when the downstream pressure is sufficiently high, an inverse-Mach reflection wave configuration, which has so far been observed only in unsteady flows, can be also established in steady flows. Very good agreement between the analytical predictions and the numerical results is found.

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Section: 2supporting

confidence: 57%

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

Ben‐Dor

Elperin

et al. 1999

J. Fluid Mech.

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“…A brief comparison of the theoretical work by Azevedo, Li, and Ben-Dor and the current paper is presented in Table 1. The works by Li et al [6] and Schotz et al [7] consider downstream influences on the Mach stem height; however, the theoretical work of Ben-Dor et al [8] and the experimental work of Chpoun and Leclerc [9] show that the Mach stem height does not vary with downstream conditions. This is as expected, because the flow in the expansion region and downstream of the sonic throat is supersonic and therefore these influences cannot affect the Mach stem height.…”

mentioning

confidence: 97%

Mach Stem Height and Growth Rate Predictions

Mouton

Hornung

2007

AIAA Journal

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A new, more accurate prediction of Mach stem height in steady flow is presented. In addition, starting with a regular reflection in the dual-solution domain, the growth rate of the Mach stem from the time it is first formed till it reaches its steady-state height is presented. Comparisons between theory, experiments, and computations are presented for the Mach stem height. The theory for the Mach stem growth rate in both two and three dimensions is compared to computational results. The Mach stem growth theory provides an explanation for why, once formed, a Mach stem is relatively persistent. Nomenclature g = spacing between wedge and axis of symmetry M = Mach number P = pressure s = Mach stem height U = speed w = wedge length = leading shock angle with respect to the freestream = ratio of specific heats = triple-point slip-line angle = wedge angle with respect to the freestream = Mach angle = density = triple-point reflected shock angle Subscripts a = conditions directly behind Mach stem Ms = Mach stem properties tp = triple-point properties 1 = region 1 condition 2 = region 2 condition 3 = conditions between Mach stem and sonic throat ? = sonic throat condition 1 = freestream condition Superscripts tp = triple-point reference frame = nondimensional quantity

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“…14 The comparison of the numerical transition angles for twowedge 5 -8 (Á D 0 deg) and channel 15 (Á D 90 deg) geometries shows that they are independent of Á. Though the analytical models 16; 17 give contradictorypredictionsconcerningthe dependenceof the MS size on Á, there is numerical 18 and experimental 19 evidence that its size does not depend on the base angle either.…”

Section: Background: Rr and Mrmentioning

confidence: 93%

Numerical Analysis of Shock Wave Reflection Transition in Steady Flows

et al. 1998

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Different aspects of the transition between regular and Mach re ections of strong shock waves in steady ows are numerically studied. Two approaches-kinetic (the direct simulation Monte Carlo method) and continuum (Euler equations)-are used to investigate the hysteresis phenomenon in the ow about two symmetrical wedges in two-and three-dimensional statements. The dependence of the nal shock wave con guration on initial conditions, the transition from regular to Mach re ection by means of ow perturbations, and three-dimensional effects are examined. The three-dimensionality of the ow is shown to increase the angles of transition from regular to Mach re ection and back and to decrease the Mach stem height. IntroductionT HE hypothesis that a hysteresis phenomenon may exist in the transition between regular re ections (RR) and Mach re ections (MR) of strong shock waves in steady ows was rst put forward by Hornung et al. 1 They assumed that, when the angle of incidence ® changes smoothly, the transition from RR to MR and the reverse transition occur at different ® values. An attempt to assess this hypothesis was performed experimentally by Hornung and Robinson 2 and gave a negative result: No hysteresis was observed. They concluded that a possible reason might be the disturbances present in wind-tunnel ow. 2 Recently, though, the hysteresis was obtained experimentally by Chpoun et al. 3; 4 and numerically by Ivanov et al. 5 using the direct simulation Monte Carlo (DSMC) method. In later papers by Ivanov et al. 6 -9 the hysteresis phenomenon was examined carefully using two numerical approaches: kinetic and continuum. These numerical studies proved the existence of the hysteresis in accordance with the prediction of Hornung et al. 1 As for the experimental results of Chpoun et al., 3 ;4 some details of this work, such as the angle of transition from RR to MR, ® tr , do not correspond to what comes from the hypothesis of Hornung et al. 1 (® tr was 37.2 deg instead of ® D D 39:3 deg for M D 4:96). This was probably caused by three-dimensionaleffects, which were fairly signi cant in these experiments, where a wedge model with a small spanwise size was used. The contradiction motivated conducting new experiments 10 where different aspect ratios, i.e., ratios of spanwise to streamwisesize, from 0.66 up to 3.75, were used. The existence of hysteresis was con rmed there, but the total agreement of experimental and numerical data was not obtained.The dif culties of experimental studies of the hysteresis phenomenon are caused by acoustic and other perturbations inherent in any aerodynamic wind tunnel and also the problem of obtaining results with no in uence of three-dimensionality.These dif culties may be easily avoided if a numerical simulation is performed. The numerical approach gives an opportunity of not only assessing the impact of different perturbations and three-dimensionality but also elaborating a strategy for future experimental work. This paper is aimed at continuing the numerical study of various aspects of the pr...

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Dependence of Steady Mach Reflections on the Reflecting-Wedge Trailing-Edge Angle

Cited by 9 publications

References 7 publications

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

The influence of the downstream pressure on the shock wave reflection phenomenon in steady flows

Mach Stem Height and Growth Rate Predictions

Numerical Analysis of Shock Wave Reflection Transition in Steady Flows

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