An experimental investigation of a large-scale structure of a two-dimensional backward-facing step by using advanced multi-point LDV

Measurements of spatio–temporal velocity fields at the separated shear layer and reattachment region of a two-dimensional backward-facing step flow are carried out simultaneously using a multi-point LDV. The objective of this paper is to clarify experimentally the structure of a large-scale structure of this flow field using a space and time correlation and conditional average. From the results of the correlation of the velocity fluctuation, the moving path of the vortex shedding from the separated shear layer to the reattachment region exhibits two patterns which it moves to near the wall region or the middle of the step height at the reattachment region. Especially, it moves to near the wall region when it grows larger in the separated shear layer. Moreover, the turbulence concerned with reattachment phenomenon transports from the reattachment region to a separated shear layer by recirculation flow. According to these transports of turbulence, a model for large-scale fluctuation is proposed as a self-excitation motion.     

Dynamic response in a poro-elastic ground induced by a moving air pressure

A steady-state theory is worked out for the dynamic response of a saturated poro-elastic ground to pressure distribution travelling along the ground surface. A boundary layer approximation is applied to Biot's equations for two phases. Sample result for supersonic, transonic and subsonic loads are presented.     

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.     

Coupled fluid structure analysis for wing 445.6 flutter using a fast dynamic mesh technology

The flow around wing 445.6 was modelled using Navier–Stokes equations and S-A model. The wing vibration and flow mesh deformation were computed using a fast dynamic mesh technology proposed by our own group. Wing 445.6 flutter was analysed through a strong coupling between the wing vibration and flow. The reduced flutter velocity was predicted and results are in good agreement with the experimental data. It is found that the subsonic flutter is mainly induced by the flow separation and the transonic and supersonic flutter are mainly caused by the oscillating shock wave and its induced flow separation. The positive aerodynamic work increases due to the oscillating shock wave when the subsonic flow becomes transonic reducing the flutter velocity. While the positive aerodynamic work induced by the oscillating shock wave decreases when the transonic flow becomes supersonic increasing the flutter velocity. That is why the transonic dip exists.     

Assessment of the organization of a turbulent separated and reattaching flow by measuring wall pressure fluctuations

The effect of local forcing on the organization of a turbulent separated and reattaching flow was assessed by measuring wall pressure fluctuations. Multi-arrayed microphones were installed on the surface to measure the simultaneous spatial and temporal wall pressure fluctuations. Local forcing at the separation edge was applied to the separated flow over a backward-facing step through a thin slit. The organization of the separated and reattaching flow was found to be greatest at the effective forcing frequency. The flow structure was diagnosed by analyzing several characteristics of the wall pressure fluctuations: the wall pressure fluctuation coefficients, wall pressure spectrum, wavenumber-frequency spectrum, coherence, cross-correlation, and multi-resolution autocorrelations of pressure fluctuations using the maximum overlap discrete wavelet transform and continuous wavelet transform. Features indicative of the amalgamation of vortices under the local forcing were observed; this amalgamation process accounted for the observed reduction of the reattachment length. Examination of the wall pressure fluctuations revealed that introduction of local forcing enhanced flapping motion as well as the streamwise and spanwise dispersions of vortical structures.     

Characterization of Turbulent Structures in a Transonic Backward-Facing Step Flow

A transonic backward-facing step flow, at a free stream Mach number of 0.8 and a Reynolds number of 1.86 × 10⁵ with respect to the step height, was investigated experimentally by means of planar and stereo Particle Image Velocimetry (PIV) measurements for multiple fields of view. The primary aim of this analysis is to examine whether the large temporal variations of the reattachment location is associated with the presence of large scale coherent flow structures. The mean flow reattaches ≈6.1±0.2 times the step height downstream of the step. This value fluctuates temporally as much as ±3 step heights. Measurements of the wake flow in horizontal planes show that the strong variations of the reattachment length are associated with spanwise variations of the streamwise velocity. Two-point correlations revealed large–scale coherent regions with a length of up to 7 step heights and a dominant spanwise wave-length of 1.5…2.5 step heights. Furthermore, close to the step large structures are found, which span more than 5 step heights in spanwise direction. The Reynolds stress distribution of the separated region strongly suggests that the initial streamwise momentum is transferred to the vertical component as well as to the spanwise component in comparable portions by the deformation of the initial Kelvin-Helmholtz vortices and the generation of secondary ones. As a result, the separated shear layer is characterized by eddies of various sizes and orientations. The mean flow field only shows the primary separation bubble and a secondary recirculation region. No stationary streamwise vortices could be found for the tested Reynolds number.     

Flow visualization of supersonic laminar flow over a backward-facing step via NPLS

An experimental study on a supersonic laminar flow over a backward-facing step of 5 mm height was undertaken in a low-noise indraft wind tunnel. To investigate the fine structures of Ma = 3.0 and 3.8 laminar flow over a backward-facing step, nanotracer planar laser scattering was adopted for flow visualization. Flow structures, including supersonic laminar boundary layer, separation, reattachment, redeveloping turbulent boundary layer, expansion wave fan and reattachment shock, were revealed in the transient flow fields. In the Ma = 3.0 BFS (backward-facing step) flow, by measuring four typical regions, it could be found that the emergence of weak shock waves was related to the K–H (Kelvin–Helmholtz) vortex which appeared in the free shear layer and that the convergence of these waves into a reattachment shock was distinct. Based on large numbers of measurements, the structure of time-averaging flow field could be gained. Reattachment occurred at the location downstream from the step, about 7–7.5 h distance. After reattachment, the recovery boundary layer developed into turbulence quickly and its thickness increased at an angle of 4.6°. At the location of X = 14h, the redeveloping boundary layer was about ten times thicker than its original thickness, but it still had not changed into fully developed turbulence. However, in the Ma = 3.8 flow, the emergence of weak shock waves could be seen seldom, due to the decrease of expansion. The reattachment point was thought to be near X = 15h according to the averaging result. The reattachment shock was not legible, which meant the expansion and compression effects were not intensive.     

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.     

Turbulent mixed convection flow over a backward-facing step––the effect of the step heights

Effect of the backward-facing step heights on turbulent mixed convection flow along a vertical flat plate is examined experimentally. The step geometry consists of an adiabatic backward-facing step, an upstream wall and a downstream wall. Both the upstream and downstream walls are heated to a uniform and constant temperature. Laser–Doppler velocimeter and cold wire anemometer were used, respectively, to measure simultaneously the time-mean velocity and temperature distributions and their turbulent fluctuations. The experiment was carried out for step heights of 0, 11, and 22 mm, at a free stream air velocity, u_∞, of 0.41 m/s, and a temperature difference, ΔT, of 30 °C between the heated walls and the free stream air. The present results reveal that the turbulence intensity of the streamwise and transverse velocity fluctuations and the intensity of temperature fluctuations downstream of the step increase as the step height increases. Also, it was found that both the reattachment length and the heat transfer rate from the downstream heated wall increase with increasing step height.     

Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Experimental investigation of flow over a backward-facing step in proximity to a flexible wall

Turbulent flow between a flexible wall and a solid surface containing a backward-facing step (BFS) was investigated using digital particle image velocimetry and high-speed photography. Stationary sheet of paper under tension was positioned above the solid surface in proximity to the BFS. The incoming air flow emerged from a planar nozzle that was located in the solid wall upstream of the BFS. Flows corresponding to two values of the Reynolds number (3,000 and 3,600) based on the step height and the maximum flow velocity at the step location were characterized in terms of patterns of time-averaged velocity, out-of-plane vorticity, streamline topology, and turbulence statistics. In addition, paper sheet oscillation was characterized using high-speed photography. For the control case of a solid upper wall with the geometry that represented the time-averaged paper profile, hydrodynamic frequencies were characterized using unsteady pressure measurements. Frequencies of the natural vibration modes of the paper sheet were well separated from the hydrodynamic frequencies corresponding to the oscillations of the shear layer downstream of the BFS. As the inflow velocity increased, the paper sheet was pulled closer to the solid surface, which resulted in increased confinement of the incoming jet. The flow reattachment length calculated on the basis of time-averaged flow patterns increased with the increasing Reynolds number.     

Experimental study of the separated flow structure behind a backward-facing step and a passive disturbance

The flow in a channel with a backward-facing step and a rib mounted upstream of the step and generating flow disturbances is studied experimentally by the method of particle image velocimetry. It is demonstrated that mounting of a single rib leads to deformation of the profiles of the mean streamwise velocities and turbulent fluctuations. The effect of the position and height of a single rib on the recirculation region behind the backward-facing step is analyzed. Reduction of the recirculation region size behind the step in the case of flow reattachment upstream of the step is validated.     

Performance evaluation of an inverse integral equation method applied to turbomachine cascades

An improved formulation of the inverse integral equation method proposed in Reference 1 is presented which allows, in particular, a well-posed problem to be ensured. The corresponding computation code is tested in an exhaustive manner for axial and radial compressor and turbine cascades. The agreement between the velocity field obtained with the inverse method and that resulting from a direct calculation is examined for subsonic, transonic and supersonic flows. Accuracy and reliability of the solution to the boundary condition problem are excellent for the subsonic and transonic flows. However, for the supersonic flow, the application of the method seems to be limited by the use of elementary solutions of the Laplace operator.     

基于当地流活塞理论的气动弹性计算方法研究

发展了一种高效、高精度的超音速、高超音速非定常气动力计算 方法------基于定常CFD技术的当地流活塞理论. 运用当地流活塞理论计算非定常 气动力，耦合结构运动方程，实现超音速、高超音速气动弹性的时域模拟. 运用这 种方法计算了一系列非定常气动力算例和颤振算例，并和原始活塞理论、非定 常Euler方程结果作了比较. 由于局部地使用活塞理论假设，这种方法大大地克服 了原始活塞理论对飞行马赫数、翼型厚度和飞行迎角的 限制. 与非定常Euler方程方法相比，当地流活塞理论的效率很高.     

Large eddy simulation of separation control over a backward-facing step flow by suction

Separation control over a backward-facing step (BFS) flow by continuous suction was numerically investigated using the turbulence model of large eddy simulation (LES). The effect of suction control on the flow fields was scrutinised by altering the suction flow coefficient, and the results indicate that suction is not only very effective in shortening the reattachment length but also very influential in reducing the tangential velocity gradient and turbulence fluctuations of the reattached flows. With increasing increments of the absolute suction flow coefficient, the effect of suction control is more significant. Furthermore, the detailed flow fields (including the time-averaged stream and velocity fields) and turbulence characteristics (including the time-averaged resolved kinetic energy and RMS velocity) for the BFS models with or without suction are presented to discuss the mechanism of suction control. Comparisons of the time-averaged statistics between the numerical simulations and corresponding experiments are conducted, and it shows that the LES based on the dynamic kinetic energy subgrid-scale model (DKEM) can acquire exact results. Therefore, feasibility of the numerical methods to simulate suction-controlled models is validated.     

Laval nozzle flow calculation

The inverse problem of the theory of the Laval nozzle is considered, which leads to the Cauchy problem for the gasdynamic equations; the streamlines and the flow parameters are found from the known velocity distribution on the axis of symmetry.The inverse problem of Laval nozzle theory was considered in 1908 by Meyer [1], who expanded the velocity potential into a series in powers of the Cartesian coordinates and constructed the subsonic and supersonic solutions in the vicinity of the center of the nozzle. Taylor [2] used a similar method to construct a flowfield which is subsonic but has local supersonic zones in the vicinity of the minimal section. Frankl [3] and Fal'kovich [4] studied the flow in the vicinity of the nozzle center in the hodograph plane. Their solution, just as the Meyer solution, made it possible to obtain an idea of the structure of the transonic flow in the vicinity of the center of the nozzle.A large number of studies on transonic flow in the vicinity of the center of the nozzle have been made using the method of small perturbations. The approximate equation for the transonic velocity potential in the physical plane, obtained in [3–6], has been studied in detail for the plane and axisymmetric cases. In [7] Ryzhov used this equation to study the question of the formation of shock waves in the vicinity of the center of the nozzle, and conditions were formulated for the plane and axisymmetric cases under which the flow will not contain shock waves. However, none of the solutions listed above for the inverse problem of Laval nozzle theory makes it possible to calculate the flow in the subsonic and transonic parts of the nozzles with large gradients of the gasdynamic parameters along the normal to the axis of symmetry.Among the studies devoted to the numerical calculation of the flow in the subsonic portion of the Laval nozzle we should note the study of Alikhashkin et al., and the work of Favorskii [9], in which the method of integral relations was used to solve the direct problem for the plane and axisymmetric cases.The present paper provides a numerical solution of the inverse problem of Laval nozzle theory. A stable difference scheme is presented which permits analysis with a high degree of accuracy of the subsonic, transonic, and supersonic flow regions. The result of the calculations is a series of nozzles with rectilinear and curvilinear transition surfaces in which the flow is significantly different from the one-dimensional flow. The flowfield in the subsonic and transonic portions of the nozzles is studied. Several asymptotic solutions are obtained and a comparison is made of these solutions with the numerical solution.The author wishes to thank G. D. Vladimirov for compiling the large number of programs and carrying out the calculations on the M-20 computer.     

Transonic separation flow of water past a circular cone

The problem of subsonic, transonic, and supersonic separation flow of water past a circular cone of finite length is solved. The water is assumed to be an ideal compressible fluid. A steady flow picture is obtained in a process of stabilization with respect to the time by means of a two-dimensional finite-difference scheme [1]. The dependence of the drag coefficient on the Mach number of the oncoming flow, the distribution of the pressure over the conical surface, and the shape of the free surface formed behind the cone are investigated.     

Experimental study on the flow field behind a backward-facing step using a detonation-driven shock tunnel

The supersonic combustion RAM jet (SCRAM jet) engine is expected to be used in next-generation space planes and hypersonic airliners. To develop the engine, stabilized combustion in a supersonic flow field must be attained even though the residence time of flow is extremely short. A mixing process for breathed air and fuel injected into the supersonic flow field is therefore one of the most important design problems. Because the flow inside the SCRAM jet engine has high enthalpy, an experimental facility is required to produce the high-enthalpy flow field. In this study, a detonation-driven shock tunnel was built to produce a high-enthalpy flow, and a model SCRAM jet engine equipped with a backward-facing step was installed in the test section of the facility to visualize flow fields using a color schlieren technique and high-speed video camera. The fuel was injected perpendicularly to a Mach 3 flow behind the backward-facing step. The height of the step, the injection distance and injection pressure were varied to investigate the effects of the step on air/fuel mixing characteristics. The results show that the recirculation region increases as the fuel injection pressure increases. For injection behind the backward-facing step, mixing efficiency is much higher than with a flat plate. Also, the injection position has a significant influence on the size of the recirculation region generated behind the backward-facing step. The schlieren photograph and pressure histories measured on the bottom wall of the SCRAM jet engine model show that the fuel was ignited behind the step.Communicated by K. Takayama PACS 47.40.Ki     

Experimental study of heat transfer due to interaction of two separated flows of different scales

This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers Re = 5000-15 000. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.     

Asymptotic analysis of transonic flows

In this paper we derive the equations of the second and third approximations for the stream function of two-dimensional and axisymmetric potential transonic flow of an inviscid gas and find their particular solutions corresponding to certain transonic flows.A similar study concerning the second approximation of subsonic and supersonic flow was made by Van Dyke [1] and Hayes [2]. The second approximation for the velocity potential of transonic flow has been examined in detail by Hayes [3]. Euvrard [4, 5] has investigated the asymptotic behavior of transonic flow far from a body, while Fal'kovich, Chernov, and Gorskii [6] have studied the flow in a nozzle throat.The transonic asymptotic analysis for the stream function is presented in this paper.