Gas dynamics with local energy release in subsonic and supersonic flow

The flows developing in the interaction of a supersonic gas stream with a continuously operating axisymmetric energy release source or as a result of the action of pulsed periodic energy injection on a subsonic gas stream are investigated numerically. For a continuously operating energy source two types of flow can be distinguished: with a shock wave detached from the source and with a shock attached to it. Approximate formulas for the gas density in the center of the energy release zone are obtained for the cases of constantly operating and periodic energy sources.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 142–148, March–April, 1995.     

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.      

3D numerical simulation of compressible swirling flow induced by means of tangential inlets

The objective of the present work is to predict compressible swirl flow in the nozzle of air‐jet spinning using the realizable k–ε turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free‐vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.     

脉冲激光等离子体与正激波相互作用的PIV实验研究

脉冲激光等离子体与超声速流场相互作用在飞行器减阻隔热、点火助燃等方面具有重要的应用价值.纹影实验方法只能定性或半定量地反映流动状态.为定量研究速度分布和旋涡结构,针对激光等离子体及其与正激波相互作用过程开展粒子图像测速PIV实验研究.在激波管实验平台上建立了纳秒脉冲激光能量沉积系统和PIV测量系统,通过定量测量,探明了激光等离子体引致的激光空气泡以及热核的流动特性,揭示了激光等离子体在正激波冲击下的流动特性与演化规律,并给出了激光能量大小和位置对相互作用过程的影响.结果表明:激光空气泡内的速度分布在激光入射方向上并不关于击穿点对称,而是在靠近激光入射方向一侧的流速略大于远离激光入射方向一侧;斜压导致热核在演化初期产生涡环,后期则由剪切主导;正激波与激光空气泡界面、热核界面相互作用时,产生斜压涡量,当激光能量为87.8 mJ、正激波马赫数1.4时,热核在正激波作用下产生的涡量比在静止空气中演化时大1个数量级;激光与正激波相互作用的关键过程是热核在正激波冲击下演化成涡环,在激波波前注入激光能量能够获得更加显著的涡环.     

Interaction of a Streamwise Vortex with an Oblique Shock Wave

Interaction of a supersonic streamwise vortex with an oblique shock wave is considered. A mathematical model of the streamwise vortex is constructed. Three interaction regimes (weak, moderate, and strong) are found. It is shown numerically that vortex breakdown is possible in the case of strong interaction. The influence of the governing parameters on the interaction type is studied. It is shown that the main effect on the interaction type is exerted by the streamwise velocity and angle of the wedge forming the shock wave. The effect of splitting of the primary vortex on the shock wave in the case of moderate and strong interaction regimes is found.     

Ideal gas flows with separation zones and time-dependent contact discontinuities of complicated shape

Some examples of flows with separation zones andmovable contact discontinuities obtained as a result of the numerical integration of the time-dependent equations for an ideal gas are presented. The examples concern a steady annular separation zone on the blunt nose of a body in a supersonic flow, periodic shedding of unsteady discontinuities from a cylinder in a steady uniform subsonic flow with a supercritical Mach number, and the complicated deformation of a contact (tangential) discontinuity, namely, the boundaries of a two-dimensional jet, either subsonic or supersonic, flowing into a cocurrent subsonic low-velocity flow. A multiple increase in the difference grid capacity in the numerical integration of the Euler equations indicates the absence of a noticeable scheme viscosity effect in the examples calculated. The inviscid nature of the separation flows obtained is also confirmed by their well-known counterparts constructed in the ideal incompressible fluid approximation. The time-average velocity fields of the two-dimensional jet and the intensity of its sound field are in reasonable agreement with the available data.     

Contribution de l'éclatement tourbillonnaire à la réduction de la traînée des véhicules automobiles : approche numériqueVortex breakdown contribution to the drag reduction of automotive vehicles: numerical approach

The breakdown of a longitudinal vortex originating from a three-dimensional dihedral body is examined in the perspective of reducing the aerodynamic drag of bluff bodies. The vortex breakdown is induced by a continuous and uniform blowing distributed on the separation line related to the formation and the development of the vortex. The breakdown is characterized by an abrupt disintegration of the vortical core and the appearance of a recirculation zone. Numerical results obtained with and without blowing show the crucial impact of the Swirl parameter on the vortex breakdown. Drag reductions close to 6% are found. To cite this article: B. Lehugeur et al., C. R. Mecanique 334 (2006).     

Starting of an axisymmetric convergent-divergent nozzle in a hypersonic flow

The starting of an axisymmetric convergent-divergent nozzle, with the result that supersonic flow is formed within almost the entire channel, is modeled, as applied to the hypersonic aerodynamic setup of the Institute of Mechanics of Moscow State University. A successful starting is realized when the nozzle is thrown in a uniform supersonic air flow at a fairly high Mach number. The steady flow structure is studied. It is numerically shown that in the convergent section of the channel there arises an oblique shock wave whose interaction with the nozzle axis leads to the formation of a reflected shock and a curvilinear Mach disk with a region of unsteady subsonic flow in the vicinity of the throat. The mathematical model is based on the two-dimensional Euler equations for axisymmetric gas flows.     

COMPUTATION OF SUPERSONIC TURBULENT FLOWFIELD WITH TRANSVERSE INJECTION

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Mass and momentum transport in the near field of swirling turbulent jets. Effect of swirl rate

Local transport of the flow momentum and scalar admixture in the near-field of turbulent swirling jets (Re = 5,000) has been investigated by using a combination of the particle image velocimetry and planar laser-induced fluorescence methods. Advection and turbulent and molecular diffusions are evaluated based on the measured distributions of the mean velocity and concentration and the Reynolds stresses and fluxes. As has been quantified from the data, the flow swirl intensifies the entrainment of the surrounding fluid and promotes mass and momentum exchange in the outer mixing layer. A superimposed swirl results in the appearance of a wake/recirculation region at the jet axis and, consequently, the formation of an inner shear layer. In contrast to the scalar admixture, the momentum exchange in the inner shear layer is found to be strongly intensified by the swirl. For the jet with the highest considered swirl rate, a substantial portion of the surrounding fluid is found to enter the unsteady central recirculation zone, where it mixes with the jet that is issued from the nozzle. The contribution of the coherent velocity fluctuations, which are induced by large-scale vortex structures, to the turbulent transport has been evaluated based on triple decomposition, which was based on proper orthogonal decomposition analysis of the velocity data sets. For the considered domain of the jet with the highest swirl rate and vortex breakdown, the contributions of detected helical vortex structures, inducing pressing vortex core, to the radial fluxes of the flow momentum and the scalar admixture are found to locally exceed 65% and 80%, respectively.     

Transonic crossflow of condensing wet steam past a cylinder

The shadow and interferometric methods and the laser probe method are used to investigate crossflow past a cylinder on the free-stream Mach number interval M _a =0.5–1.2 for subcritical Reynolds numbers Re _d and various initial steam states. Detailed pressure distributions are obtained and the pressure fluctuations on the cylinder surface are measured. The dependence of the Strouhal number on the velocity and thermodynamic parameters of the flow are determined. In single-phase steam flow past a cylinder the greatest fluctuations occur in the separation zone in regimes corresponding to transonic drag crisis. It is shown that spontaneous condensation in the turbulent wake and local supersonic zones may cause an increase in the periodic pressure fluctuations in the separation zone, the maximum increase in the fluctuations being noted when the critical pressure ratio is reached at the rear of the cylinder. The initial wetness of the steam has the greatest effect on the periodic separation characteristics at subsonic flow velocities, and in the case of supersonic flow leads to a substantial increase in the level of the low-frequency pressure fluctuations at the front of the cylinder.(deceased)Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 118–138, November–December, 1994.     

Flow Structure of Swirling Turbulent Propane Flames

Flow structure of premixed propane–air swirling jet flames at various combustion regimes was studied experimentally by stereo PIV, CH* chemiluminescence imaging, and pressure probe. For the non-swirling conditions, a nonlinear feedback mechanism of the flame front interaction with ring-like vortices, developing in the jet shear layer, was found to play important role in the stabilisation of the premixed lifted flame. For the studied swirl rates (S = 0.41, 0.7, and 1.0) the determined domain of stable combustion can be divided into three main groups of flame types: attached flames, quasi-tubular flames, and lifted flames. These regimes were studied in details for the case of S = 1.0, and the difference in the flow structure of the vortex breakdown is described. For the quasi-tubular flames an increase of flow precessing above the recirculation zone was observed when increased the stoichiometric coefficient from 0.7 to 1.4. This precessing motion was supposed to be responsible for the observed increase of acoustic noise generation and could drive the transition from the quasi-tubular to the lifted flame regime.     

Downstream boundary effects on the spectral characteristics of a swirling flowfield

The spectral characteristics and the structural response of a swirling flowfield are investigated subject to a non-axisymmetric disturbance and a contraction imposed downstream. Two natural frequencies are noted in different regions of the undisturbed swirling flowfield, one is due to a precessing vortex core and the other to the most amplified downstream azimuthal instability. The downstream contraction usually causes compression of the central recirculation zone into two side-lobes, increases the dominant frequencies and forms a straight central vortex core with a high axial velocity. The dominant downstream instability frequency depends linearly on the inlet Reynolds number and on the mode of the breakdown. For the downstream non-axisymmetric disturbance, such as the passing of the turbine blades, the fundamental frequency is not altered by the disturbance and the oscillation strength of the downstream instability is greatly reduced as the excitation frequency remains unmatched with the dominant downstream natural frequency. Downstream azimuthal instability promotes the breakdown recirculation.A version of this paper was presented at the 26th AIAA Aerospace Sciences Meeting, Reno, Nevada, 11–14, Jan. 1988     

Effect of volume energy supply on swirled flows in a subsonic cocurrent stream

The results of a numerical investigation of the effect of thermal energy supply on a swirling viscous heat-conducting gas flow in a subsonic cocurrent stream are presented. The initial stage of development of the swirling flow in the neighborhood of the vortex axis with constant circulation in the outer flow region is considered for two different distributions of the streamwise velocity vector component which simulate a swirling jet-type flow and a wake flow with a streamwise velocity deficit. The effect of local volume energy supply in the neighborhood of the vortex axis, the circulation of the azimuthal velocity component, and the longitudinal pressure gradient in the inviscid stream on the development of the swirling flow and the process of breakdown of cocurrent vortex flows is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 47–53, November–December, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Solution of the direct problem of the mixed flow of a conducting gas in a laval nozzle with a meridional magnetic field

We consider the direct problem in the theory of the axisymmetric Laval nozzle (including sonic transition) for the steady flow of an inviscid and nonheat-conducting gas of finite electrical conductivity. The problem is solved by numerical integration of the equations of unsteady gas flow using an explicit difference scheme that was proposed by Godunov [1,2], and was used to calculate steady and unsteady flows of a nonconducting gas in nozzles by Ivanov and Kraiko [3]. The subsonic and the supersonic flows of a conducting gas in an axisymmetric channel when there is no external electric field, the magnetic field is meridional, and the magnetic Reynolds numbers are small have previously been completely investigated. Thus, Kheins, Ioller and Élers [4] investigated experimentally and theoretically the flow of a conducting gas in a cylindrical pipe when there is interaction between the flow and the magnetic field of a loop current that is coaxial with the pipe. Two different approaches were used in the theoretical analysis in [4]: linearization with respect to the parameter S of the magnetogasdynamic interaction and numerical calculation by the method of characteristics. The first approach was used for weakly perturbed subsonic and supersonic flows and the solutions obtained in analytic form hold only for small S. This is the approach used by Bam-Zelikovich [5] to investigate subsonic and supersonic jet flows through a current loop. The numerical calculations of supersonic flows in a cylindrical pipe in [4] were restricted to comparatively small values of S since, as S increases, shock waves and subsonic waves appear in the flow. Katskova and Chushkin [6] used the method of characteristics to calculate the flow of the type in the supersonic part of an axisymmetric nozzle with a point of inflection. The flow at the entrance to the section of the nozzle under consideration was supersonic and uniform, while the magnetic field was assumed to be constant and parallel to the axis of symmetry. The plane case was also studied in [6]. The solution of the direct problem is the subject of a paper by Brushlinskii, Gerlakh, and Morozov [7], who considered the flow of an electrically conducting gas between two coaxial electrodes of given shape. There was no applied magnetic field, and the induced magnetic field was in the direction perpendicular to the meridional plane. The problem was solved numerically in [7] using a standard process. However, the boundary conditions adopted, which were chosen largely to simplify the calculations, and the accuracy achieved only allowed the authors [7] to make reliable judgments about the qualitative features of the flow. Recently, in addition to [7], several papers have been published [8–10] in which the authors used a similar approach to solve the direct problem in the theory of the Laval nozzle (in the case of a nonconducting gas).Translated from Izvestiya Akademiya Nauk SSSR, Mekhanika Zhidkosti i Gaza., No. 5, pp. 14–20, September–October, 1971.In conclusion the author wishes to thank M. Ya. Ivanov, who kindly made available his program for calculating the flow of a conducting gas, and also A. B. Vatazhin and A. N. Kraiko for useful advice.     

Numerical investigation of a perturbed swirling annular two-phase jet

A swirling annular gas–liquid two-phase jet flow system has been investigated by solving the compressible, time-dependent, non-dimensional Navier–Stokes equations using highly accurate numerical methods. The mathematical formulation for the flow system is based on an Eulerian approach with mixed-fluid treatment while an adjusted volume of fluid method is utilised to account for the gas compressibility. Surface tension effects are captured by a continuum surface force model. Swirling motion is applied at the inlet while a small helical perturbation is also applied to initiate the instability. Three-dimensional spatial direct numerical simulation has been performed with parallelisation of the code based on domain decomposition. The results show that the flow is characterised by a geometrical recirculation zone adjacent to the nozzle exit and by a central recirculation zone further downstream. Swirl enhances the flow instability and vorticity and promotes liquid dispersion in the cross-streamwise directions. A dynamic precessing vortex core is developed demonstrating that the growth of such a vortex in annular configurations can be initiated even at low swirl numbers, in agreement with experimental findings. Analysis of the averaged results revealed the existence of a geometrical recirculation zone and a swirl induced central recirculation zone in the flow field.     

Interaction of heat release and vortex breakdown during flame flashback driven by combustion induced vortex breakdown

The interaction of heat release by chemical reaction and the flow dominates flame transition in swirling flows caused by combustion induced vortex breakdown (CIVB). The simultaneous application of 1 kHz high-speed particle imaging velocimetry (PIV) for the analysis of the flow field and OH planar laser-induced fluorescence for the detection of the flame front is particularly useful for the improvement of the understanding of the observed fast CIVB driven flame propagation. For the first time, the combination of both techniques was successfully applied to confined swirling flows. In the study, the flow field characteristics of an aerodynamically stabilized burner system with CIVB are analyzed in great depth. The influence of geometric parameters of the swirl generator was investigated and conclusions concerning the proper burner design of vortex breakdown premix burners are drawn from the experimental results. In particular, the effect of the vortex core with respect to the stability of the swirl stabilized burner is analyzed. The contribution of combustion to vortex breakdown is shown comparing isothermal and reacting flows. The presented data reveals that at the onset of CIVB driven flame transition, the azimuthal vorticity leads to the formation of a closed recirculation bubble at the tip of the internal recirculation zone. Once this bubble propagates upstream, the flame is able to follow and propagate relative to the bulk flow velocity with a velocity far beyond the turbulent flame speed. The interaction of reaction and flow was observed for different volumetric heat releases. The experiments confirm the CIVB theory of the authors, which was initially developed on the basis of a CFD study alone. Both the volume expansion and the baroclinic torque have an effect on whether fast flame propagation occurs. Whereas the volume expansion caused by the heat release stabilizes the flow field and the reaction, the baroclinic torque stimulates flame transition. For upstream propagation the flame tip has to have a position downstream of the stagnation point of the bubble. Else, the required transition inducing force is insufficient and the flame remains stable. In case the flame reaches positions too close or even upstream of the stagnation point, the fast propagation is interrupted or even prohibited. The key finding that the relative position of flame and stagnation bubble governs CIVB is discussed on the basis of high-speed LIF/PIV data as well as chemiluminescence. Since essentially the same behavior has been observed before in tests of a totally different swirler design and flow field, the conclusion can be made that the root cause for CIVB independent of the special geometry has been found.     

Interaction of a line vortex with a round parachute canopy

The interaction of a rectilinear vortex with an inflated round parachute canopy model was studied experimentally in a water tunnel where the vortex core was aligned with the axis of the canopy. Three different canopy diameters were used, and the canopy model was attached to a streamlined forebody. Dye flow visualization indicated that vortex breakdown was present when the core trajectory was within the canopy opening. Vortex breakdown occurred about one to two canopy diameters upstream of the canopy opening. The vortex core completely disintegrated when it interacted with the forebody near the canopy centerline. The vortex breakdown and disintegration caused unsteady, asymmetric deformations on the canopy surface. A reduction in the time-averaged drag and an increase in the fluctuating drag was observed when the vortex core was within the canopy opening. The disintegration of the vortex core near the canopy centerline lessened the drag reduction brought on by the presence of the core.     

Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equations

A variational method for solving directly the full steady Euler equations is presented. This method is based on both Newton's linearization and a least squares formulation. The validity of the Euler model and boundary conditions to capture the vortex sheet is discussed. A finite element approximation of the groups of conservative variables is described and results are given for 3D subsonic flows as well as supersonic flows past a flat plate at high angle of attack.