ALBERT

Description:    This paper investigates the flow field near three intersecting shock waves appearing in steady Mach reflection. Results of numerical computations reveal a “von Neumann Paradox”—like feature for weak shock waves, in which the flow field between the reflected and the Mach stem is smooth with no distinct slip flow region and changes rather smoothly. An analytical solution of the Navier–Stokes equations constructed using a polar–coordinate system gives a flow field with the same properties as the numerical simulation. Content Type Journal Article Pages 1-6 DOI 10.1007/s00193-011-0329-8 Authors A. Sakurai, Tokyo Denki University, Kanda, Tokyo, Japan M. Tsukamoto, Tokyo Denki University, Kanda, Tokyo, Japan D. Khotyanovsky, Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia M. Ivanov, Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    The propagation and attenuation of an initial shock wave through a mm-scale channel of circular cross-section over lengths up to 2,000 diameters is examined as a model problem for the scaling of viscous effects in compressible flows. Experimental wave velocity measurements and pressure profiles are compared with existing data and theoretical predictions for shock attenuation at large scales and low pressures. Significantly more attenuation is observed than predicted based on streamtube divergence. Simulations of the experiment show that viscous effects need to be included, and the boundary layer behavior is important. A numerical model including boundary layer and channel entrance effects reproduces the wave front velocity measurements, provided a boundary layer transition model is included. A significant late-time pressure rise is observed in experiments and in the simulations. Content Type Journal Article Pages 1-11 DOI 10.1007/s00193-011-0330-2 Authors J. M. Austin, Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA D. J. Bodony, Department of Aerospace Engineering, University of Illinois, Urbana, IL 61801, USA Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    An investigation into a three-dimensional, curved shock wave interacting with a three-dimensional, curved boundary layer on a slender body is presented. Three different nose profiles mounted on a cylindrical body were tested in a supersonic wind tunnel and numerically simulated by solving the Navier–Stokes equations. The conical and hemispherical nose profiles tested were found to generate shock waves of sufficient strength to separate the boundary layer on the cylinder, while the shock wave generated by the ogival profile did not separate the boundary layer. For the separated flow, separation was found to occur predominantly on the windward side of the cylinder with the lee-side remaining shielded from the direct impact of the incident shock wave. A thickening of the boundary layer on the lee-side of all the profiles was observed, and in the conical and hemispherical cases this leads to the re-formation of the incident shock wave some distance away from the surface of the cylinder. A complex reflection pattern off the shock wave/boundary layer interaction (SWBLI) was also identified for the separated flow cases. For comparative purposes, an inviscid simulation was performed using the hemispherical profile. Significant differences between the viscous and inviscid results were noted including the absence of a boundary layer leading to a simplified shock wave reflection pattern forming. The behaviour of the incident shock wave on the lee-side of the cylinder was also affected with the shock wave amalgamating on the surface of the cylinder instead of away from the surface as per the viscous case. Test data from the wind tunnel identified two separation lines present on the cylindrical surface of the hemispherical SWBLI generator. The pair of lines were not explicitly evident in the original CFD simulations run, but were later identified in a high-resolution simulation. Content Type Journal Article Pages 1-16 DOI 10.1007/s00193-011-0322-2 Authors S. Mowatt, Flow Research Unit, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Private Bag 3, Johannesburg, Wits 2050, South Africa B. Skews, Flow Research Unit, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Private Bag 3, Johannesburg, Wits 2050, South Africa Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent energy created by the flow–area change interaction is determined by a specific estimate of the surface pressure integral. Model’s predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler equations and is able to reproduce the main flow features. Content Type Journal Article Pages 1-16 DOI 10.1007/s00193-011-0321-3 Authors R. Menina, LESEI, Department of Mechanical Engineering, Faculty of Technology, Batna University (UHLB), 1 Avenue Chahid Mohamed El Hadi, 05000 Batna, Algeria R. Saurel, IUSTI, Polytech Marseille, Aix-Marseille University, 5 rue E. Fermi, 13453 Marseille Cedex 13, France M. Zereg, LPEA, Department of Physics, Faculty of Sciences, Batna University (UHLB), 1 Avenue Chahid Mohamed El Hadi, 05000 Batna, Algeria L. Houas, IUSTI, Polytech Marseille, Aix-Marseille University, 5 rue E. Fermi, 13453 Marseille Cedex 13, France Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    An experimental investigation has been carried out to study dual-bell transition behavior in different set ups inside a high-altitude test facility. Cold gas tests were carried out under two different operating conditions namely (i) test nozzle operating in self-evacuation mode and, (ii) test nozzle operating with an additional ejector nozzle (pre-evacuated condition). Although forward transition nozzle pressure ratio does not show any change in its value irrespective of the type of test facility and test set up, the re-transition nozzle pressure ratio shows a significant increase (7–8%) in its value when tested in the high-altitude facility. The latter is caused due to plume blowback effect which dominates during shut down transients in such facilities. Driven by the high atmospheric pressure, the jet exhaust is pushed backwards into the altitude chamber causing the re-transition to occur earlier than that observed in sea-level tests. Further the reduced mass flow rates for nozzle operation in different test set ups in a high-altitude test facility also reduces the magnitude of side-load peaks during the dual-bell transitions. Content Type Journal Article Pages 1-10 DOI 10.1007/s00193-011-0302-6 Authors S. B. Verma, Experimental Aerodynamics Division, CSIR-National Aerospace Laboratories, Bangalore, 560017 India R. Stark, Nozzle Flow Group, DLR Lampoldshausen, Lampoldshausen, Germany C. Génin, Nozzle Flow Group, DLR Lampoldshausen, Lampoldshausen, Germany O. Haidn, Nozzle Flow Group, DLR Lampoldshausen, Lampoldshausen, Germany Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    Results of one-dimensional numerical simulations of the parameters of the converging strong shock wave generated by electrical underwater explosions of a cylindrical wire array with different array radii and different deposited energies are presented. It was shown that for each wire array radius there exists an optimal duration of the energy deposition into the exploding array, which allows one to maximize the shock wave pressure and temperature in the vicinity of the implosion axis. The simulation results agree well with the 130-GPa pressure in the vicinity of the implosion axis that was recently obtained, which strongly indicates the azimuthal symmetry of the converging shock wave at these extreme conditions. Also, simulations showed that using a pulsed power generator with a stored energy of ~200 kJ, the pressure and temperature at the shock wave front reaches ~220 GPa and 1.7 eV at 0.1 mm from the axis of implosion in the case of a 2.5 mm radius wire array explosion. It was found that, in spite of the complicated equation of state of water, the maximum pressure at the shock wave front at radius r can be estimated as P ≈ ( P *( r */ r ) α , where P * is the known value of pressure at the shock wave front at radius r * ≥ r and α is a parameter that equals 0.62±0.02. A rough estimate of the implosion parameters of the hydrogen target after the interaction with the converging strong shock wave is presented as well. Content Type Journal Article Pages 1-9 DOI 10.1007/s00193-011-0320-4 Authors G. Bazalitski, Physics Department, Technion, Haifa, 32000 Israel V. Ts. Gurovich, Physics Department, Technion, Haifa, 32000 Israel A. Fedotov-Gefen, Physics Department, Technion, Haifa, 32000 Israel S. Efimov, Physics Department, Technion, Haifa, 32000 Israel Ya. E. Krasik, Physics Department, Technion, Haifa, 32000 Israel Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description: Report on the 28th International Symposium on Shock Waves Content Type Journal Article Category Report Pages 1-2 DOI 10.1007/s00193-011-0337-8 Authors K. Kontis, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M13 9PL UK Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall. Content Type Journal Article Category Original Article Pages 1-10 DOI 10.1007/s00193-011-0338-7 Authors J. Yoo, High Temperature Gasdynamics Laboratory, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA D. Mitchell, High Temperature Gasdynamics Laboratory, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA D. F. Davidson, High Temperature Gasdynamics Laboratory, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA R. K. Hanson, High Temperature Gasdynamics Laboratory, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    The existence and characteristics of shock wave triple points are examined. The analysis utilizes a single flow plane for the three shocks and is local to the triple point. It applies when the flow is unsteady, three-dimensional, and the upstream flow is nonuniform. Under more restrictive conditions, a relation is also derived for the ratio of the curvature of the Mach stem to that of the reflected shock. For given values of the ratio of specific heats, γ , and the upstream Mach number, M 1 , a solution window is established. A parametric set of solutions is generated within the window for γ  = 1, 1.4, and 5/3 and for 16 values of M 1 ranging from solution onset to M 1 = 6.A solution can be one of three types, these stem from the velocity tangency condition along the slip stream. Topics are addressed such as solution multiplicity, shock wave and slip stream orientation, the nature of the reflected wave (weak, strong, inverted, normal), the nature of the Mach stem (weak, strong, normal), and differences due to changes in γ and M 1 . Content Type Journal Article Category Original Article Pages 1-11 DOI 10.1007/s00193-011-0339-6 Authors H. Hekiri, Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019-0390, USA G. Emanuel, Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019-0018, USA Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287

Description:    It is well accepted that the persistence of regular reflection of a shock wave off a wedge beyond the ideal theoretical prediction is due to viscous and thermal boundary layers induced behind the reflection point. Experiments have been done by reflecting two shock waves of equal strength off each other so that the plane of symmetry between them becomes an ideal inviscid and adiabatic reflection plane thereby experimentally mimicking the assumptions of the theory. There is one definitive experiment done at a wall angle of 40° using a bifurcated shock tube that indicates that the actual transition angle is the theoretical detachment condition. This paper extends these results to two cases near limiting conditions; one at a very low incidence shock Mach number and one at a wall angle very close to the theoretical transition limit. The first confirms the reasons for the von Neumann Paradox but cannot discriminate between sonic and detachment conditions, but is within about 0.5% of them, and the second shows transition much closer to the sonic than the detachment condition but with both within the experimental error bounds. In both cases, the results are notably different from transition conditions off a wedge and confirm the effects of transport properties being the cause of persistence of regular reflection. Content Type Journal Article Category Technical Note Pages 1-6 DOI 10.1007/s00193-011-0341-z Authors T. Herron, Flow Research Unit, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, PO WITS, 2050 Johannesburg, South Africa B. Skews, Flow Research Unit, School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, PO WITS, 2050 Johannesburg, South Africa Journal Shock Waves Online ISSN 1432-2153 Print ISSN 0938-1287