A soap film shock tube to study two-dimensional compressible flows

 A new experimental approach to the study of the two-dimensional compressible flow phenomena is presented. In this technique, a variety of compressible flows were generated by bursting plane vertical soap films. An aureole and a “shock wave” preceding the rim of the expanding hole were clearly observed using traditional high-speed flash photography and a fast line-scan charge coupled device (CCD) camera. The moving shock wave images obtained from the line-scan CCD camera were similar to the x–t diagrams in gas dynamics. The moving shock waves cause thickness jumps and induce supersonic flows. Photographs of the supersonic flows over a cylinder and a wedge are presented. The results suggest clearly the feasibility of the “soap film shock tube”. Received: 11 May 2000/Accepted: 2 November 2000     

Experiments on free and impinging supersonic microjets

The fluid dynamics of microflows has recently commanded considerable attention because of their potential applications. Until now, with a few exceptions, most of the studies have been limited to low speed flows. This experimental study examines supersonic microjets of 100–1,000 μm in size with exit velocities in the range of 300–500 m/s. Such microjets are presently being used to actively control larger supersonic impinging jets, which occur in STOVL (short takeoff and vertical landing) aircraft, cavity flows, and flow separation. Flow properties of free as well as impinging supersonic microjets have been experimentally investigated over a range of geometric and flow parameters. The flowfield is visualized using a micro-schlieren system with a high magnification. These schlieren images clearly show the characteristic shock cell structure typically observed in larger supersonic jets. Quantitative measurements of the jet decay and spreading rates as well as shock cell spacing are obtained using micro-pitot probe surveys. In general, the mean flow features of free microjets are similar to larger supersonic jets operating at higher Reynolds numbers. However, some differences are also observed, most likely due to pronounced viscous effects associated with jets at these small scales. Limited studies of impinging microjets were also conducted. They reveal that, similar to the behavior of free microjets, the flow structure of impinging microjets strongly resembles that of larger supersonic impinging jets.     

Triple configurations of traveling shock waves in inviscid gas flows

Triple configurations of shock waves in supersonic inviscid flows of a perfect gas are considered. The basic parameters of triple configurations are determined, and the conditions of solution existence are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 3–10, May–June, 2008.     

Special and extreme triple shock-wave configurations

Triple shock-wave configurations in steady supersonic flows of an inviscid perfect gas are considered. Triple configurations with special intensities of shock waves and extreme ratios of various flow parameters behind these configurations are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 39–53, July–August, 2006.     

Three-dimensional imaging of a turbulent jet using shearing interferometry and optical tomography

The 3-D density field of a round, neutrally buoyant turbulent jet is obtained using a finite-fringe, shearing interferometer. A He–Ne laser beam (λ=632.8 nm) is subdivided into six beams of equal intensity, which intersect a helium–argon jet flowing from a vertical nozzle. Two-dimensional projection data of the jet are captured simultaneously from six viewing directions distributed over 140°. The desired phase is removed from the spatial carrier using the Fourier transform method. A tomographic reconstruction technique, using a truncated Fourier–Bessel expansion is performed to obtain the complete 3-D density field. The Reynolds number, based on the exit mean velocity and the nozzle diameter, is 5890. Received: 22 December 1999/Accepted: 20 January 2000     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

Entropy method for calculating separated-flow parameters

A variational method of calculating two-dimensional supersonic turbulent separated flows, based on the Prigogine principle (minimum entropy production), the relations of irreversible-process thermodynamics, and the integral energy equation of a viscous gas, is suggested. An application of this method is illustrated by an example of the calculations of the parameters of separated flows with a fixed separation point. The outer flow in the inviscid region is calculated by known methods. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 122–132, January–February, 1997.     

Local subsonic zones in supersonic jet flows

The results of the experimental investigation of supersonic turbulent jets with local subsonic zones of forward and reverse flow exhausting into the ambient atmosphere or an outer stream, either parallel or transverse to the jet, are presented. Some gasdynamic features of the flows containing these zones, which have not been adequately addressed in the literature, are analyzed. Thus, supersonic flows with back pressure, e.g., highly overexpanded and underexpanded jet flows, and those upstream and downstream of a jet on the leeward side of a cone in a supersonic gas stream, are studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–150, January–February, 1998.     

Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections

We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C ^1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C ^1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance.     

Turbulent flow visualization by interferometric integral imaging and computed tomography

An experimental system using integral interferometric imaging and computer tomography for visualizing the structure of a turbulent, vertical helium jet is described. Integral images and tomographic integral data were obtained using a pulsed phase-shifted interferometer. The integral images revealed a sinuous overall jet structure and large-scale buckling motions in the far-field. Tomographic reconstruction of jet cross-sections at numerous axial locations were made for three turbulent jets at two different Reynols numbers, 2,800 and 4,300. Tomographic images revealed unmixed ambient fluid far inside the jet boundary and a bimodal concentration distribution. Image interpretation and experimental errors are discussed.     

Unsteady and nonequilibrium airflow near a stagnation line

The propagation of shock waves in a medium with a nonuniform distribution of the parameters is the subject of recently published research [1–3]. The present paper deals with the problem of the gas flow ahead of the forward point of a blunt body moving at supersonic speed in air with variable parameters. The chemical reaction processes behind the shock front are taken into account. As a result of numerical calculations by the method of characteristics with isolation of the forward shock the time-dependent position of the shock front and the distributions of the composition and gas dynamic parameters in the shock layer are found. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–172, November–December, 1986.     

OH-PLIF visualisation of radical farming supersonic combustion flows

Experimental investigations employing Planar Laser-induced fluorescence visualisation of the qualitative distribution of the OH radical (OH-PLIF), coupled with surface pressure measurements, have been made of flow in a generic, nominally two-dimensional inlet-injection radical farming supersonic combustion scramjet engine model. The test flows were provided by a hypersonic shock tunnel, and covered total enthalpies corresponding to the flight Mach number range 8.7–11.8 and approximately 150 kPa dynamic pressure. The surface pressure measurements displayed radical farming behaviour, that is a series of adjacent high and low pressure regions corresponding to successive shock/expansion structures, with no significant combustion-induced pressure rise until the second structure. OH-PLIF imaging between the first two structures provides the first direct experimental evidence of significant OH radical concentrations upstream of the ignition point in this mode of scramjet operation and shows that combustion reactions were occurring in highly localised regions in a complex turbulent and poorly micromixed fuel/air mixing layer confined to the fuel injection side of the combustor.     

Shock waves in dense granular flows down a chute

Large scale, three dimensional computer simulations of monosized, viscoelastic, spherical glass particles flowing in an inclined duct were performed using a phenomenological model based on the modified Kelvin–Maxwell model. The particle flow rate in the model duct was regulated using a stationary wedge located in the middle of the duct. At low flow rates of glass particles, a continuous flow was observed similar to that excited by steadily and rapidly adding glass particles to the top of a heap. However, at high flow rates, a totally different situation arises where a flow with a different nature was established in the duct. The situation was found to be analogous to the case of a supersonic gas flow in a duct, where a curved-bow shock was observed to have formed on the upper edges of the duct adjacent to the wedge. In addition, in supersonic granular flows the viscous and conductance effects spread the shock changes over a finite shock layer.     

Collision of supersonic flows in vacuum and ambient space

Based on numerical Monte Carlo simulation, the collision of plane-parallel supersonic flows in vacuum and ambient space is studied. The study of the transonic zone of a plane source instantaneously switched on in vacuum made it possible to establish the regular features of the flow parameters in the critical cross section and the validity of using gas-dynamic dependences obtained in the continuum approach for simulating gas exhaustion. Evolution of the structure of a compressed shock layer arising in the region of flow collision is studied. It is found that a collision of flows in the ambient space leads to a more significant increase in temperature in the compressed layer than in the case of a collision in vacuum. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 44–50, July–August, 1999.     

Visual hull method for tomographic PIV measurement of flow around moving objects

Tomographic particle image velocimetry (PIV) is a recently developed method to measure three components of velocity within a volumetric space. We present a visual hull technique that automates identification and masking of discrete objects within the measurement volume, and we apply existing tomographic PIV reconstruction software to measure the velocity surrounding the objects. The technique is demonstrated by considering flow around falling bodies of different shape with Reynolds number?~1,000. Acquired image sets are processed using separate routines to reconstruct both the volumetric mask around the object and the surrounding tracer particles. After particle reconstruction, the reconstructed object mask is used to remove any ghost particles that otherwise appear within the object volume. Velocity vectors corresponding with fluid motion can then be determined up to the boundary of the visual hull without being contaminated or affected by the neighboring object velocity. Although the visual hull method is not meant for precise tracking of objects, the reconstructed object volumes nevertheless can be used to estimate the object location and orientation at each time step.     

Tomographic shadowgraphy for three-dimensional reconstruction of instantaneous spray distributions

Tomographic shadowgraphy is an image-based optical technique capable of reconstructing the three dimensional instantaneous spray distributions within a given volume. The method is based on a multiple view imaging setup with inline illumination provided by current-pulsed LEDs, which results in droplet shadows being projected onto multiple sensor planes. Each camera records image pairs with short inter-framing times that allow the trajectories of the individual droplets to be estimated using conventional three-dimensional particle tracking approaches. The observed volume is calibrated with a traversed micro-target. A comparison is made between several photogrammetric and polynomial least-square camera calibration techniques regarding their accuracy in deep volume calibration at magnifications close to unity. A calibration method based on volume calibration from multiple planar homographies at equally spaced z-planes was found to produce the most reliable calibration. The combination of back-projected images at each voxel plane efficiently reproduces the droplet positions in three-dimensional space by line-of-sight (LOS) intensity reconstruction. Further improvement of the reconstruction can be achieved by iterative tomographic reconstruction, namely simultaneous multiplicative algebraic reconstruction technique (SMART). The quality of spray reconstruction is investigated using experimental data from multiple view shadowgraphs of hollow cone and flat fan water sprays. The investigations are further substantiated with simulations using synthetic data.     

Stability of Transonic Shock Solutions for One-Dimensional Euler–Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler–Poisson systems are investigated. First, a steady transonic shock solution with a supersonic background charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with a supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and on a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler–Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role.     

Simulation of Solute Transport Through Fractured Rock: A Higher-Order Accurate Finite-Element Finite-Volume Method Permitting Large Time Steps

Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fastest flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure–(semi)-implicit transport scheme for the advection–diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2–4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a highly accurate overall solution. Numerical and fracture-related mechanical dispersions are compared in the realistic DFM models using second-order accurate runs as reference cases. With a CFL histogram, we establish target error criteria for CFL overstepping. This analysis indicates that for extreme fracture heterogeneity, only a few transport steps can be sufficient to analyse macro-dispersion. This makes our implicit method attractive for quick analysis of transport properties on multiple realisations of DFM models.     

An extended algebraic reconstruction technique (ART) for density-gradient projections: laser speckle photographic tomography

An extended algebraic reconstruction technique (ART) is presented for tomographic image reconstruction from the density-gradient projections, such as laser speckle photography. The essence of the extended ART is that the density-gradient projection data of speckle photography (Eq. (1)) are first numerically integrated to the algebraic representation of interferometric fringe number data (Eq. (12)), which ART can readily reconstruct into the cross-sectional field. The extended ART is numerically examined by using two computer synthesized phantom fields, and experimentally by using asymmetric single and double helium jets in air. The experimentally reconstructed images were also compared with the direct measurements of helium concentration using an oxygen analyzing probe. The extended ART method shows an improved accuracy and is proposed to use to tomographically reconstruct the density-gradient projections over the previous Fourier convolution (FC) method (Liu et al. 1989). Received: 26 June 1998/Accepted: 18 March 1999