A comprehensive study of measurement uncertainty in tomographic reconstruction of void-profiles in a mercury-nitrogen flow

 The liquid–metal magneto-hydrodynamic (LMMHD) facility at the Bhabha Atomic Research Centre (Mumbai) has a two-phase mercury–nitrogen flow system which is currently used for various studies related to void-fraction, flow, pressure, slip-ratio, of the flow system. Non-invasive measurements of steady-state void-fraction profiles has been carried out by a 60 mCi Cesium-137 gamma-ray source and a NaI(Tl) detector mounted on a trolley. The reconstructed cross-sectional void-fraction profiles were in the riser section of the LMMHD loop, and in this process radial tomographic methods were used, e.g. least-squares and chord-segment-inversion (CSI). The present work investigates the possible uncertainties in the profiles thus measured. A simple statistical model has been developed for the CSI algorithm due to the inherent “square nature” of the data matrix. The inherent Poisson error has been also investigated in this exercise. Received: 1 December 1997/Accepted: 30 May 1998     

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     

An Experimental Study of Mobilization and Creeping Flow of Oil Slugs in a Water-Filled Capillary

An experimental investigation was carried out on mobilization and very slow flow of oil slugs in a capillary tube. The pressure drop of the slug flow was measured at every stage of mobilizing and moving the oil slugs as a function of capillary number in the range of 4 × 10⁻⁷–6 × 10⁻⁶. The pressure drop across the oil slug experienced three stages: build-up, hold-up, and steady stages. During the build-up stage, the convex rear end of the slug was becoming concave into the oil slug and the convex front end of the slug moved ahead to form a new portion of the slug. At the hold-up stage, both the concave rear end and the front end continued to advance, and the initial contact line of the oil slug with the tube wall through a very thin water film was being shortened. At this stage, the pressure drop reached a maximum value and remained nearly constant. At the steady stage, after the oil slug was completely mobilized out of the original contact region, the differential pressure had a step-drop first, and then the oil slug flowed at a lower differential pressure depending on the flow rate. Numerous slug flow tests of this study showed that the hold-up pressure drop was always higher than the steady stage pressure drop. Results also showed that the measured extra pressure drop was significantly high compared to the pressure drop calculated from Poiseuille equation, which is still commonly used in network modeling of multiphase flow in porous media.     

Asymptotic properties of solutions of the Cauchy problem for a degenerate singularly perturbed system of differential equations in the case of the multiple spectrum of the principal operator

We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions are asymptotic expansions of the corresponding exact solutions. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007.     

Tomographic reconstruction of shock layer flows

The tomographic reconstruction of supersonic flows faces two challenges. Firstly, techniques used in the past, such as the direct Fourier method (DFM) (Gottlieb and Gustafsson in On the direct Fourier method for computer tomography, 1998; Morton in Tomographic imaging of supersonic flows, 1995) or various backprojection (Kak and Slaney in Principles of computerized tomographic imaging, vol. 33 in Classics in Applied Mathematics, 2001) techniques, have only been able to reconstruct areas of the flow which are upstream of any opaque objects, such as a model. Secondly, shock waves create sharp discontinuities in flow properties, which can be difficult to reconstruct both in position and in magnitude with limited data. This paper will present a reconstruction method, matrix inversion using ray-tracing and least squares conjugate gradient (MI-RLS), which uses geometric ray-tracing and a sparse matrix iterative solver (Paige and Saunders in ACM Trans. Math. Softw. 8(1):43–71, 1982) to overcome both of these challenges. It will be shown, through testing with a phantom object described in tomographic literature, that the results compare favourably to those produced by the DFM technique. Finally, the method will be used to reconstruct three-dimensional density fields from interferometric shock layer images, with good resolution (Faletič in Tomographic reconstruction of shock layer flows, 2005). This paper was based on work that was presented at the 3rd International Symposium on Interdisciplinary Shock Wave Research, Canberra, Australia, March 1–3, 2006.     

Gas-dynamic signs of explosive eruptions of volcanoes. 2. Model of homogeneous-heterogeneous nucleation. Specific features of destruction of the cavitating magma

The dynamics of state of the crystallite-containing magma is studied within the framework of the gas-dynamic model of bubble cavitation. The effect of crystallites on flow evolution is considered for two cases: where the crystallites are cavitation nuclei (homogeneous-heterogeneous nucleation model) and where large clusters of crystallites are formed in the magma in the period between eruptions. In the first case, decompression jumps are demonstrated to arise as early as in the wave precursor; the intensity of these jumps turns out to be sufficient to form a series of discrete zones of nucleation ahead of the front of the main decompression wave. Results of experimental modeling of an explosive eruption with ejection of crystallite clusters (magmatic “bombs”) suggest that a cocurrent flow of the cavitating magma with dynamically varying properties (mean density and viscosity) transforms to an independent unsteady flow whose velocity is greater than the magma flow velocity. Experimental results on modeling the flow structure during the eruption show that coalescence of bubbles in the flow leads to the formation of spatial “slugs” consisting of the gas and particles. This process is analyzed within a combined nucleation model including the two-phase Iordansky-Kogarko-van Wijngaarden model and the model of the “frozen” field of mass velocities in the cavitation zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 167–177, March–April, 2009.     

Imaging spectroscopy of the nonequilibrium shock front radiation in air

The nonequilibrium radiation of shock fronts in air is experimentally investigated by means of the imaging spectroscopy technique. Shock velocity ranges from 9.7 to 11.6 km/s and initial pressure from 13.3 to 41.6 Pa. The spectral diagnostic system consists of an imaging spectrograph, a streak camera, a gated image-intensified CCD camera and a personal computer for data acquisition/processing. This spectral diagnostic system is capable of simultaneous wavelength-, intensity- and time-resolved spectroscopic measurements in the nanosecond order. The image processing of the streak images includes a combined smoothing/deconvolution process in the time direction to diminish experimental noise effects and the temporal broadening due to the streak camera entrance slit. Wavelength range is chosen to investigate the first negative band of . “Large” and “slim” streak image types are observed. In the “large” streak images greater contribution from (1-)(1,0) behind the radiation peak is observed. Experimental data are compared with a streak image numerically simulated. The numerical simulation agrees better with the “slim” streak image. Received 7 July 1995 / Accepted 10 January 1996     

Ideal incompressible flow around a wedge tip

A planar analog of conical flows is considered: an inviscid incompressible fluid flow around a wedge tip. A class of conical flows is found where vorticity is transported along streamlines by the potential component of velocity. Problems of a wave “locked” in the corner region and of a flow accelerating along the rib of a dihedral angle are considered. By analogy with an axisymmetric quasi-conical flow, a planar quasi-conical flow of the fluid is determined, namely, the flow inside and outside the region bounded by tangent curves described by a power law. Conditions are found where vorticity and swirl produce a significant effect. An approximate solution of the problem of the fluid flow inside a “zero” angle is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 57–65, March–April, 2007.     

A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—part I. Theoretical development and asymptotic analyses

In this paper a rigorous dual-porosity model is formulated, which accurately represents the coupling between large-scale fractures and the micropores within dual porosity media. The overall structure of the porous medium is conceptualized as being blocks of diffusion dominated micropores separated by natural fractures (e.g. cleats for coal) through which Darcy’s flow occurs. In the developed model, diffusion in the matrix blocks is fully coupled to the pressure distribution within the fracture system. Specific assumptions on the pressure behaviour at the matrix boundary, such as step-time function employed in some earlier studies, are not invoked. The model involves introducing an analytical solution for diffusion within a matrix block, and the resultant combined flow equation is a nonlinear integro-(partial) differential equation. Analyses to the equation in this text, in addition to the theoretical development of the proposed model, include: (1) discussion on the “fading memory” of the model; (2); one-dimensional perturbation solution subject to a specific condition; and (3) asymptotic analyses of the “long-time” and “short-time” responses of the flow. Two previous models, the Warren-Root and the modified Vermeulen models, are compared with the proposed model. The advantages of the new model are demonstrated, particularly for early time prediction where the approximations of these other models can lead to significant error.     

Numerical investigation on the flowfield of ＂swallowtail＂ cavity for supersonic mixing enhancement

A ＂swallowtail＂ cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the ＂swallow- tail＂ cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-e turbulence model in a multi-block mesh. Turbu- lence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the ＂swallowtail＂ cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the ＂swallowtail＂ cavity structure.     

Decentralized adaptive neural control of nonlinear systems with unknown time delays

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, and three problems of “computational explosion,” “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Stability of equilibrium for an inverted two-link mathematical pendulum with critical tracking forces

We investigate nonlinear stability for equilibrium of a pendulum with viscoelastic components. The tracking force is chosen so that the matrix of the linearized part of the perturbed motion has two purely imaginary roots or one zero and one negative root. The other two roots are complex with negative real part. The boundary of the domain of stability is divided into “dangerous” and “safe” (in the sense of Bautin) zones. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 100–105, September, 1999.     

A Study of the Behavior of Implicit Pressure Explicit Saturation (IMPES) Schedules for Two-phase Flow in Dynamic Pore Network Models

We focus on the numerical difficulties that typify implicit pressure explicit saturation (IMPES) schedules in dynamic “ball-and-stick” pore network models for two-phase flow. We show that a time stepping procedure based on a prescribed maximum variation of the local capillary pressure rather than on a (usual) maximum variation of the local saturation along with the addition in the solution algorithm of suitable “flow constraints” (in Koplik and Lasseter, Soc. Pet. Eng. J. 25(1):89–100, 1985) provide more stability and a significant run time speed up. In particular, the slow convergence and the oscillatory behavior that typify IMPES schemes at low Ca values due to capillary pinning are efficiently suppressed.     

STREAMLINE-BASED MATHEMATICAL MODEL FOR CO2 MISCIBLE FLOODING

According to the research theory of improved black oil simulator, a practical mathematical model for C02 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening andmiscible oil field.reservoir dynamic management of the CO2 miscible oil field.     

Simultaneous density-field visualization and PIV of a shock-accelerated gas curtain

We describe a highly-detailed experimental characterization of the Richtmyer-Meshkov instability (the impulsively driven Rayleigh-Taylor instability) (Meshkov 1969; Richtmyer 1960). In our experiment, a vertical curtain of heavy gas (SF₆) flows into the test section of an air-filled, horizontal shock tube. The instability evolves after a Mach 1.2 shock passes through the curtain. For visualization, we pre-mix the SF₆ with a small (∼10⁻⁵) volume fraction of sub-micron-sized glycol/water droplets. A horizontal section of the flow is illuminated by a light sheet produced by a combination of a customized, burst-mode Nd:YAG laser and a commercial pulsed laser. Three CCD cameras are employed in visualization. The “dynamic imaging camera” images the entire test section, but does not detect the individual droplets. It produces a sequence of instantaneous images of local droplet concentration, which in the post-shock flow is proportional to density. The gas curtain is convected out of the test section about 1 ms after the shock passes through the curtain. A second camera images the initial conditions with high resolution, since the initial conditions vary from test to test. The third camera, “PIV camera,” has a spatial resolution sufficient to detect the individual droplets in the light sheet. Images from this camera are interrogated using Particle Image Velocimetry (PIV) to recover instantaneous snapshots of the velocity field in a small (19 × 14 mm) field of view. The fidelity of the flow-seeding technique for density-field acquisition and the reliability of the PIV technique are both quantified in this paper. In combination with wide-field density data, PIV measurements give us additional physical insight into the evolution of the Richtmyer-Meshkov instability in a problem which serves as an excellent test case for general transition-to-turbulence studies. Received: 26 June 1999/Accepted: 29 October 1999     

The rheological behaviour of Ca(OH)2 suspensions

The rheological behaviour of Ca(OH)₂ suspensions is investigated, predominantly at a solid volume fraction of 0.25. The influence of standing without being subject to shear (“contact time”) is distinguished from that of being sheared (“shearing time”). The results are interpreted on the basis of the “elastic floc” model of energy dissipation during flow, with a view to the problem whether, in addition to an energy dissipation term related to the viscous drag experienced by particles moving within flocs, there should be an independent energy dissipation term related to fluid movement in the flocs when they change volume or shape. It appears that this additional energy dissipation term is not necessary, if the increase in viscous friction, experienced by two particles which are close together, is taken into account. Paper, presented at the First Conference of European Rheologists at Graz, April 14–16, 1982. A short version has been published in [18].     

Interfacially active particles in droplet/matrix blends of model immiscible homopolymers: Particles can increase or decrease drop size

Particles have been shown to adsorb at the interface between immiscible homopolymer melts and to affect the morphology of blends of those homopolymers. We examined the effect of such interfacially active particles on the morphology of droplet/matrix blends of model immiscible homopolymers. Experiments were conducted on blends of polydimethylsiloxane and 1,4-polyisoprene blended in either a 20:80 or 80:20 weight ratio. The effects of three different particle types, fluoropolymer particles, iron particles, and iron oxyhydroxide particles, all at a loading of 0.5 vol.%, were examined by rheology and by direct flow visualization. Particles were found to significantly affect the strain recovery behavior of polymer blends, increasing or decreasing the ultimate recovery, slowing down or accelerating the recovery kinetics, and changing the dependence of these parameters on the applied stress prior to cessation of shear. These rheological observations were found to correlate reasonably well with particle-induced changes in drop size. The particles can both increase as well as decrease the drop size, depending on the particle type, as well as on which phase is continuous. The cases in which particles cause a decrease in drop size are analogous to the particle stabilization of “Pickering emulsions” well-known from the literature on oil/water systems. We hypothesize that cases in which particles increase drop size are analogous to the “bridging–dewetting” mechanism known in the aqueous foam literature.     

Normal mode analysis of the fully developed free convection flow in a vertical slot with open to capped ends

The fully developed free convection flow in a differentially heated vertical slot with open to capped ends investigated recently by Bühler (Heat Mass Transf 39:631–638, 2003) and Weidman (Heat Mass Transf Online First, February 2006) is revisited in this paper. A new method of solution of the corresponding fourth order boundary value problem, based on its reduction to “normal modes” by a complex matrix similarity transformation is presented. As a byproduct of the method, some invariant relationships involving the heat flux and the shear stress in the flow could be found.     

Investigation of high-speed combustible gas ignited by a hot gas jetproduced in the shock tube

The high-speed combustible gas ignited by a hot gas jet, which is induced by shock focusing, was experimentally investigated. By use of the separation mode of shock tube, the test section of a single shock tube is split into two parts, which provide the high-speed flow of combustible gas and pilot flame of hot gas jet, respectively. In the interface of two parts of test sections the flame of jet was formed and spread to the high-speed combustible gas. Two kinds of the ignitions, 3-D “line-flame ignition” and 2-D “plane-flame ignition”, were investigated. In the condition of 3-D “line-flame ignition” of combustion, thicker hot gas jet than pure air jet, was observed in schlieren photos. In the condition of 2-D “plane-flame ignition” of combustion, the delay time of ignition and the angle of flame front in schlieren photos were measured, from which the velocity of flame propagation in the high-speed combustible gas is estimated in the range of 30–90m/s and the delay time of ignition is estimated in the range of 0.12–0.29ms. PACS 47.40.Nm; 82.40.FpPart of this paper was presented at the 5th International Workshop on Shock/Vortex Interaction, Kaohsiung, October 27–31, 2003.     

A Conceptual Study of Cavity Aeroacoustics Control Using Porous Media Inserts

In this study, an integrated flow simulation and aeroacoustics prediction methodology is applied to testing a sound control technique using porous inserts in an open cavity. Large eddy simulation (LES) combined with a three-dimensional Ffowcs Williams–Hawkings (FW–H) acoustic analogy is employed to predict the flow field, the acoustic sources and the sound radiation. The Darcy pressure – velocity law is applied to conceptually mimic the effect of porous media placed on the cavity floor and/or rear wall. Consequently, flow in the cavity could locally move in or out through these porous walls, depending on the local pressure differences. LES with “standard” subgrid-scale models for compressible flow is carried out to simulate the flow field covering the sound source and near fields, and the fully three-dimensional FW–H acoustic analogy is used to predict the sound field. The numerical results show that applying the conceptual porous media on cavity floor and/or rear wall could decrease the pressure fluctuations in the cavity and the sound pressure level in the far field. The amplitudes of the dominant oscillations (Rossiter modes) are suppressed and their frequencies are slightly modified. The dominant sound source is the transverse dipole term, which is significantly reduced due to the porous walls. As a result, the sound pressure in the far field is also suppressed. The preliminary study reveals that using porous-inserts is a promising technology for flow and sound radiation control.