Computational analysis and flow structure of a transitional separated-reattached flow over a surface mounted obstacle and a forward-facing step

Large-eddy simulation (LES) of transitional separating-reattaching flow on a two-dimensional square surface mounted obstacle and a forward facing step has been performed using a dynamic sub-grid scale model. The Reynolds number based on the uniform inlet velocity and the obstacle/step height is 4.5 × 10³. The mean LES results for both the obstacle and step flow compare reasonably well with the available experimental and DNS data.

The flow structures upstream of the surface-mounted obstacle (referred to hereafter as obstacle) and the forward-facing step (referred to hereafter as FFS) consist of unstable two-dimensional structures and coherent rib-shaped structures. These structures with the aid of 3D streamline visualisation strongly indicate that the upstream separation bubble is a closed one rather than an open one in the sense that there is little evidence to suggest that there is fluid injection from the upstream separation region into the downstream separated region for the two geometries. The spectra and time history for the velocities and pressure fields at locations immediately upstream of the obstacle and FFS (including the recirculation region) were analysed using both the Fourier and wavelet transforms and revealed the unsteady nature of the recirculation region upstream of the obstacle and FFS.

The transition process has been elucidated using both 2D and 3D flow visualisation of the flow. In both geometries (obstacle and FFS), the separated boundary layer downstream of the leading edge shows 2D nature and roll-up shortly downstream of the separation line leading to 2D K-H rolls to be shed from the leading edge. Coherent structures such as the λ-shaped and rib-like vortices commonly associated with a flat plate boundary layer and also found in the separated-reattached flow of a blunt leading edge plate aligned horizontally to a flow are not common in the separated-reattached flow over the obstacle and FFS.     

Vortex identification methods based on temporal signal-processing of time-resolved PIV data

The lack of a universally accepted mathematical definition of a vortex structure has led to a considerable number of Eulerian criteria to identify coherent structures. Most are derived from the instantaneous local velocity gradient tensor and its derivatives and require appropriate thresholds to extract the boundaries of the structures. Notwithstanding their great potential for studying coherent structures, most criteria are not frame-independent and they lack a clear physical meaning. The Lyapunov exponent, a popular tool in dynamical system theory, appears as a promising alternative. This Lagrangian criterion does not suffer from the drawbacks of the Eulerian criteria and is constructed on a simple physical interpretation that includes information on the history of the flow. However, since the computation of the Lyapunov exponent involves the knowledge of fluid particle trajectories, experimental applications are currently restricted to laminar flows and two-dimensional turbulence, provided that velocity fields are time-resolved. In this work, we explore temporal post-treatment methods to extract vortical structures developing in a flow through a smooth axisymmetric constriction. Data from planar time-resolved Particle image velocimetry, measuring two or three components of the velocity vectors, are transformed via the Taylor hypothesis to quasi-instantaneous three-dimensional velocity field and are interpreted in terms of the discrete wavelet decomposition, the finite-time Lyapunov exponent, and the linear stochastic estimation. It appears that these methods can concurrently provide very rich and complementary scalar fields representing the effects of the vortical structures and their interactions in the flow.     

Numerical Simulation of the Flow in the Carotid Bifurcation

Pulsatile flow through the three-dimensional carotid artery bifurcation has been studied using the artificial-compressibility method. The part of the flow with large inertia bifurcates and creates a very steep velocity gradient on the divider walls. The flow near the nondivider walls slows down because of dilation of the cross section and strong adverse pressure gradient. The secondary flow in the bifurcation region, which is similar to the Dean vortex in a curved pipe, is strong and very complex. The region of separation is not closed for the cases of steady and pulsatile flow. The extent of this region is small and the streamlines are smooth except in the decelerating phase of systole. The change of common-internal bifurcation angle (25°± 15°) for fixed internal–external bifurcation angle of 50° has more effect on the shear on the bifurcation-internal carotid wall and less effect on the shear on the common-internal carotid wall. The mean wall shears are not sensitive to the input flow-rate waveform for constant mean flow, but the maximum wall shears are. Received 3 January 1997 and accepted 11 April 1997     

Measurements of a stator-induced circumferentially varying flow

The flow physics associated with the generation of both axisymmetric and non-axisymmetric swirl by various deflection patterns of a stator array was investigated experimentally through surface pressure and Stereoscopic Particle Image Velocimetry measurements. A three-dimensional rendering technique was developed to reconstruct the flow field around the model and in its wake. The three-dimensional fluid volume was reconstructed from multiple two-dimensional measurement planes. A cyclic distribution of the stators’ deflections resulted in non-axisymmetric distributions of the surface pressure and the flow field downstream of the stator array. The addition of a shroud had an amplifying effect: accelerating the flow through the stator array while reducing the non-uniform tangential velocity component generated by the stators. In the model near wake the flow field is associated with secondary flow patterns in the form of coherent streamwise vortical structures that can be described by potential flow mechanisms. The collective pitch distribution of the stators produces a flow field that resembles a potential Rankine vortex, whereas the cyclic pitch distribution generates a flow pattern that can be described by a potential vortex pair in a cross-flow.     

Cycle resolved multi-planar flow measurements in a four-valve combustion engine

The non-reacting flow in a one-cylinder four-valve combustion engine is measured via cycle resolved two-component/two-dimensional (2C/2D) particle-image velocimetry (PIV). The three-dimensional structure of the velocity field is analyzed based on the flow field measured in eight planar planes within the cylinder for several crank angles during the intake and compression phase. Using the mean and statistical values of the single planes quasi three-dimensional flow fields are reconstructed for crank angles of 80°, 160°, and 240° atdc. This enables the detailed analysis of the spatial distribution of the large and small scale flow structures, e.g., by visualizing large vortical structures and the distribution of the turbulent kinetic energy. It was found that two ring vortices evolving beneath the inlet valves are the dominant large scale structures that seem to be of major concern for the mixing process in the cylinder of a four-valve combustion engine operated at 1500 rpm. Furthermore, the temporal evolution of the flow field within the symmetry plane of the cylinder, measured for crank angles between 40° and 320° atdc in steps of 20°, is discussed. The results give new insight into the complex three-dimensional flow in the combustion chamber of a one-cylinder four-valve combustion engine. That is, the tumble vortex only seems to be of secondary importance for the flow concerning the mixing process at 1500 rpm. This is an essential result for future work considering the fluid mechanics of fuel-air-interaction processes and mixing principles in combustion engines.     

LDV measurements in lateral model aneurysms of various sizes

 Laser Doppler velocimetry (LDV) measurements are presented of three-dimensional flow fields in lateral model aneurysms arising from a straight parent vessel at a 90° angle. The flow considered was pulsatile and the aneurysm wall was rigid. The mean, peak, and minimal Reynolds numbers based on the bulk average velocity and diameter of the parent vessel were 550, 790, and 375, respectively. Comparisons among present in vitro studies, previous in vitro studies, computational simulations, and in vivo studies were made. It was found that the inflow angle into the lateral aneurysm, the maximum wall shear stress acting on the distal lip of the lateral aneurysm, and the intra-aneurysmal vortical motion increased with decreasing aneurysm size. This fact together with the impingement bifurcation of the inflow at the aneurysm dome provide possible hemodynamic factors for the rupture of the lateral aneurysm at small critical size. Received: 15 March 1996/Accepted: 13 March 1997     

Assessment of 2D/3D numerical modeling for deep dynamic stall experiments

The results of computational fluid dynamics (CFD) simulations in two and three spatial dimensions are compared to pressure measurements and particle image velocimetry (PIV) flow surveys to assess the suitability of numerical models for the simulation of deep dynamic stall experiments carried out on a pitching NACA 23012 airfoil. A sinusoidal pitching motion with a 10° amplitude and a reduced frequency of 0.1 is imposed around two different mean angles of attack of 10° and 15°. The comparison of the airloads curves and of the pressure distribution over the airfoil surface shows that a three-dimensional numerical model can better reproduce the flow structures and the airfoil performance for the deep dynamic stall regime. Also, the vortical structures observed by PIV in the flow field are better captured by the three-dimensional model. This feature highlighted the relevance of three-dimensional effects on the flow field in deep dynamic stall.     

湍流边界层拟序结构的实验研究

20世纪60年代后, 先后从流动显示发现了快慢斑、猝发、上升流、下扫流和多种涡结构等湍流边界层的拟序结构. 它们对湍流边界层的摩阻、传热传质和湍动能的产生等特性有重要影响. 涡结构是上述拟序结构的核心, 它影响其它拟序结构的发展和演变. 发卡涡通常被认为是基本涡结构. 发卡涡等涡结构的再生, 是湍流边界层拟序结构能够自持续的必要的因素.壁面低速流上升产生猝发, 是湍流边界层湍能的主要来源; 条件采样是测量猝发频率和其它拟序结构出现频率的重要手段. 流动显示对湍流边界层拟序结构作了大量定性观察, 有许多减阻和增加传热率等应用性研究在此基础上发展起来. 80年代后, 出现了测量湍流边界层的瞬时流速矢量场的多热线法和PIV技术, 三维PIV技术可望将来为湍流边界层的实验研究带来重大进展. 本文评述了流动显示法、多热线法和PIV技术的优点和不足之处, 以及它们在对湍流边界层拟序结构的研究中的贡献.      

Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder

A coupled experimental/numerical analysis of turbulent flow past a square cylinder is performed at the ERCOFTAC Reynolds number Re = U_∞D/ν = 21,400, where U_∞ is the inflow velocity and D the cylinder height. Complementary Laser Doppler Velocimetry (LDV) and high-order large-eddy simulations (LES) approaches, based on a spectral vanishing technique (SVV-LES), provide a comprehensive data base including both instantaneous data and post-processed statistics. Beyond these results, an achievement of the paper is to investigate the coherent structures developing on the sides and in the wake of the cylinder with a special focus on the flow features in the near-wall region. The flow is found to separate at the leading edge of the cylinder with the occurence of three-dimensional Kelvin-Helmholtz (KH) pairings localized in the separating shear layer. The interaction between these KH vortical structures and Von Kármán vortex shedding (VK) in the near wake is discussed based on both visualisations and frequency analysis. In particular, signatures of VK and KH vortical structures are found on velocity time samples.     

Experimental investigation on turbulent flow in a circular-sectioned 90-degree bend

 The steady, turbulent flow in a circular-sectioned 90° bend with smooth walls has been investigated experimentally. The bend had a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. The longitudinal, circumferential and radial components of mean and fluctuating velocities, and the Reynolds stresses in the pipe cross section at several longitudinal stations were obtained with the technique of rotating a probe with an inclined hot wire at a Reynolds number of 6×10⁴. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross section were illustrated. Moreover, other characteristics of the bend flow, such as deviation of the primary flow and intensity of the secondary flow, were presented. Simultaneously, discussions were given on the transition of phenomena in the longitudinal direction and the structures of turbulence in the 90° bend. Received: 21 April 1997/Accepted: 14 November 1997     

Laser photochromic velocimetry estimation of the vorticity and pressure field – two-dimensional flow in a curved vessel

 Laser photochromic velocimetry was successfully used to determine details of a steady two-dimensional flow field. In the plane of symmetry of a 90° curved tube at a Reynolds number of 250, the axial and radial velocity fields were measured using laser photochromic velocimetry combined with a technique involving interpolation of the photochromic data. The wall shear stress, vorticity, and pressure field were also estimated. The experimental results were compared with those from numerical simulation. The agreement was remarkably good lending validity to the interpolation method used for this flow field. Received: 29 May 1997 / Accepted: 13 November 1997     

Evolution of vortex structures in an electromagnetically excited separated flow

Time periodic wall parallel Lorentz forces have been used to excite the separated flow on the suction side of an inclined flat plate. Experiments for a Reynolds number of 10⁴ and an angle of attack of α = 13° are reported. The controlled flow is characterised by a small number of relatively large scale vortices, which are related to the control mechanism. The influence of the main parameters, i.e. the excitation frequency, amplitude and wave form on the suction side flow structures was investigated by analysing time resolved particle image velocimetry (TR-PIV) measurements using continuous wavelet analysis for vortex detection and characterisation. Statistical analysis of the coherent structures of the flow was performed on a large amount of data samples.     

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.     

Simulation of supersonic turbulent flow in the vicinity of an inclined backward-facing step

Large eddy simulation (LES) is a viable and powerful tool to analyse unsteady three-dimensional turbulent flows. In this article, the method of LES is used to compute a plane turbulent supersonic boundary layer subjected to different pressure gradients. The pressure gradients are generated by allowing the flow to pass in the vicinity of an expansion–compression ramp (inclined backward-facing step with leeward-face angle of 25°) for an upstream Mach number of 2.9. The inflow boundary condition is the main problem for all turbulent wall-bounded flows. An approach to solve this problem is to extract instantaneous velocities, temperature and density data from an auxiliary simulation (inflow generator). To generate an appropriate realistic inflow condition to the inflow generator itself the rescaling technique for compressible flows is used. In this method, Morkovin's hypothesis, in which the total temperature fluctuations are neglected compared with the static temperature fluctuations, is applied to rescale and generate the temperature profile at inlet. This technique was successfully developed and applied by the present author for an LES of subsonic three-dimensional boundary layer of a smooth curved ramp. The present LES results are compared with the available experimental data as well as numerical data. The positive impact of the rescaling formulation of the temperature is proven by the convincing agreement of the obtained results with the experimental data compared with published numerical work and sheds light on the quality of the developed compressible inflow generator.     

Coherent Vortex Simulation (CVS), A Semi-Deterministic Turbulence Model Using Wavelets

In the spirit of Ha Minh's semi-deterministic model, we propose a new method for computing fully-developed turbulent flows, called Coherent Vortex Simulation (CVS). It is based on the observation that turbulent flows contain both an organized part, the coherent vortices, and a random part, the incoherent background flow. The separation into coherent and incoherent contributions is done using the wavelet coefficients of the vorticity field and the Biot–Savart kernel to reconstruct the coherent and incoherent velocity fields. The evolution of the coherent part is computed using a wavelet basis, adapted at each time step to resolve the regions of strong gradients, while the incoherent part is discarded during the flow evolution, which models turbulent dissipation. The CVS method is similar to LES, but it uses nonlinear multiscale band-pass filters, which depend on the instantaneous flow realization, while LES uses linear low-pass filters, which do not adapt to the flow evolution. As example, we apply the CVS method to compute a time developing two-dimensional mixing layer and a wavelet forced two-dimensional homogeneous isotropic flow. We also demonstrate how walls or obstacles can be taken into account using penalization and compute a two-dimensional flow past an array of cylinders. Finally, we perform the same segmentation into coherent and incoherent components in a three-dimensional homogeneous isotropic turbulent flow. We show that the coherent components correspond to vortex tubes, which exhibit non-Gaussian statistics and long-range correlation, with the same k ^−5/3power-law energy spectrum as the total flow. In contrast, the incoherent components correspond to an homogeneous random background flow which does not contain organized structures and presents an energy equipartition together with a Gaussian PDF of velocity. This justifies their elimination during the CVS computation to model turbulent dissipation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Wavelet multi-scale analysis of the circular cylinder wake under synthetic jets control

The wavelet method is used to study the multi-scale vortical structures of the flow around a circular cylinder without and with synthetic jet control at Re = 950. The velocity field is decomposed into 9 wavelet components, including one approximation component and 8 detail components. The first component shows the flow characteristics at low frequency. The dominant components represent large-scale vortical structures in the flow and they show similar distributions for the same wake pattern. Other detail components reflect the characteristics of relatively small-scale structures. The individual vortex dynamics underlying the complex flow can be extracted and thus reconstructed by the approximation and dominant components. Thus, we show an effective approach to reveal the flow physics from the complex flow.     

Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

A finite element analysis of the steady laminar entrance flow in a 90° curved tube

A standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier–Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser–Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.     

Direct Numerical Simulation of the Three-Dimensional Transition to Turbulence in the Incompressible Flow around a Wing

The onset of the secondary instability and the successive steps ofthe 3D transition to turbulence are examined in the flow around a wing of NACA0012 section, constant along the spanwise direction. The wing is placed in a uniform flow upstream, at 20° of incidence and at the Reynolds number of 800. The spanwise length is equal to four chords. The objectives of this study are the identification of the three-dimensional transition mechanism and the development of the early stages of turbulence in the present class of unsteady aerodynamic flows. A detailed processing of the DNS signals carried out by an appropriate conditional sampling allows the identification of the physical mechanisms related to the birth of turbulence and to the non-linear interaction with the 3D coherent structures in the near region.     

空腔流动的动量分解及能量输运特性

空腔结构广泛应用于航空航天飞行器部件及地面交通工具中,其复杂的流声特性是相关工程设计中必须考虑的关键问题.空腔流动中的流声相互作用是空腔自持振荡的重要过程,准确识别并解耦空腔内的流体动力学模态和声模态,是深入理解空腔流声相互作用和能量转化机制的关键.通过直接求解二维Navier-Stokes方程数值模拟来流马赫数Ma=...