Numerical study of the turbulent channel flow under space-dependent electromagnetic force control at different Reynolds numbers

In this paper, the control of turbulent channel flow by space-dependent electromagnetic force and the mechanism of drag reduction are investigated with the direct numerical simulation(DNS) methods for different Reynolds numbers. A formulation is derived to express the relation between the drag and the Reynolds shear stress. With the application of optimal electromagnetic force, the in-depth relations among characteristic structures in the flow field, mean Reynolds shear stress, and the effect of drag reduction for different Reynolds numbers are discussed. The results indicate that the maximum drag reductions can be obtained with an optimal combination of parameters for each case of different Reynolds numbers. The regular quasi-streamwise vortex structures, which appear in the flow field, have the same period with that of the electromagnetic force.These structures suppress the random velocity fluctuations, which leads to the absolute value of mean Reynolds shear stress decreasing and the distribution of that moving away from the wall. Moreover, the wave number of optimal electromagnetic force increases,and the scale of the regular quasi-streamwise vortex structures decreases as the Reynolds number increases. Therefore, the rate of drag reduction decreases with the increase in the Reynolds number since the scale of the regular quasi-streamwise vortex structures decreases.     

NUMERICAL STUDY FOR RESONANT TRIAD INTERACTION AND SECONDARY INSTABILITY IN TWO-DIMENSIONAL SUPERSONIC BOUNDARY LAYER

By direct numerical simulation, a supersonic boundary layer was studied to see whether the mechanism for the generation of sub-harmonic waves, similar to those for the incompressible flows, existed in the process of laminar-turbulent transition. The results showed that mechanisms of both resonant triad and secondary instability did exist. Discussions were made on whether these two mechanisms are really important in laminarturbulent transition.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer

The late stages of transition to turbulence in a Mach two boundary layer are investigated by direct numerical simulation of the compressible Navier-Stokes equations. The primary instability at this Mach number consists of oblique waves, which are known to form a pattern of quasi-streamwise vortices. It is found that breakdown does not follow immediately from these vortices, which decay in intensity. The generation of new vortices is observed by following the evolution of the pressure and vorticity in the simulation, and analysed by consideration of vorticity stretching. It is found that the slight inclined and skewed nature of the quasi-streamwise vortices leads to a production of oppositely signed streamwise vorticity, which serves as a strong localised forcing of the shear layer alongside the original vortices, formed by convection and stretching of spanwise vorticity. The shear layer rolls up into many new vortices, and is followed by a sharp increase in the energy of higher frequencies and in the skin friction.     

Coherent structures and riblets

This work deals with the effect of the riblets on the coherent structures near the wall. The emphasis is put on the genesis of the quasi-streamwise vortices in the presence of the riblets. The quasi-streamwise vortices regenerate by the tilting of wall normal vorticity induced by prevailing structures. This requires a mechanism which leads to a temporal streamwise dependence near the elongated flow structures and to a subsequent formation of new wall normal vorticity. It is suggested here that the action of existing quasi-streamwise vortices on the sidewalls of wall normal vorticity may create a local, streamwise dependent spanwise velocity and therefore, a secondary wall normal vorticity field. A preliminary analysis of the set-up and the time and space development of this secondary three-dimensional flow associated with the regeneration mechanism, is given. An attempt is made, in order to explain the drag reduction performed by the riblets through an intermittent model, based on the protrusion height. Logical estimates of the amount of drag reduction are obtained. The differences between the mechanism suggested here and those based on forced control experiments are also discussed.     

Vortical Structures in Rotating Uniformly Sheared Turbulence

Rotating homogeneous turbulence with and without mean uniform shear is investigated numerically. It is found that in the shearless case the two-dimensionalization process is most effective when the initial small-scale Rossby number is around unity and the resonant triad interactions play a central role in the process. The vortical structures are studied systematically by changing the relative strength of the mean shear and the system rotation as well as the sense of rotation. (The system is called cyclonic (or anti-cyclonic) when the direction of the vorticity associated with the rotation is the same as (or opposite to) that of the mean shear.) A distinct coherent structure appears in the anti-cyclonic system when the vorticities associated with the rotation and the mean shear cancel out, i.e. the absolute vorticity of the mean shear vanishes. For the linearly most unstable case in the anti-cyclonic system, the vortex tubes develop in the sheared direction, which is caused by instability of vortex layers. For linearly stable cases in both the cyclonic and the anti-cyclonic systems, there appear three typical structures, that is, the oblique vortex tubes, the pancake-like structures and the ribbon-like structures. It is interesting that the flow behaves quite differently between the cyclonic and anti-cyclonic systems even at the same Bradshaw number.     

A combined analytical and numerical analysis of the flow-acoustic coupling in a cavity-pipe system

The generation of sound by flow through a closed, cylindrical cavity (expansion chamber) accommodated with a long tailpipe is investigated analytically and numerically. The sound generation is due to self-sustained flow oscillations in the cavity. These oscillations may, in turn, generate standing (resonant) acoustic waves in the tailpipe. The main interest of the paper is in the interaction between these two sound sources. An analytical, approximate solution of the acoustic part of the problem is obtained via the method of matched asymptotic expansions. The sound-generating flow is represented by a discrete vortex method, based on axisymmetric vortex rings. It is demonstrated through numerical examples that inclusion of acoustic feedback from the tailpipe is essential for a good representation of the sound characteristics.     

Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition

The present study develops a 2‐D numerical scheme that combines the vortex method and the boundary integral method by a Helmholtz decomposition to investigate the interaction of water waves with submerged obstacles. Viscous effects and generation of vorticity on the free surface are neglected. The second kind of Fredholm integral equations that govern the strengths of vortex sheets along boundaries are solved iteratively. Vorticity is convected and diffused in the fluid via a Lagrangian vortex (blob) method with varying cores, using the particle strength exchange method for diffusion, with particle redistribution. A grid‐convergence study of the numerical method is reported. The inviscid part of the method and the simulation of the free‐surface motion are tested using two calculations: solitary wave propagation in a uniform channel and a moving line vortex in the fluid. Finally, the full model is verified by simulating periodic waves travelling over a submerged rectangular obstacle using nonuniform vortex blobs with a mapping of the redistribution lattice. Overall, the numerical model predicts the vortices' evolution and the free‐surface motion reasonably well. Copyright © 2008 John Wiley & Sons, Ltd.     

Flow-acoustic coupling in coaxial side branch resonators with rectangular splitter plates

Flow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. The acoustically-coupled flows were investigated using digital particle image velocimetry (PIV) in conjunction with unsteady pressure measurements. Global instantaneous, phase- and time-averaged flow images were evaluated to provide insight into the flow physics during flow tone generation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and frequency of the resonant pressure peak. Structure of the acoustic noise source was discussed in terms of patterns of generated acoustic power, which was evaluated by applying the vortex sound theory in conjunction with global quantitative flow imaging and numerical simulation of the acoustic field. In addition to the basic side branch configuration, the effect of bluff rectangular splitter plates located along the centerline of the main duct was investigated. The first mode of the shear layer oscillation was inhibited by the presence of the plates, which resulted in substantial reduction of the amplitude of acoustic pulsations and the strength of the acoustic source.     

Vortex formation mechanisms in the wake behind a sphere for 200 < Re < 380

Direct numerical simulation and visualization of three-dimensional separated flows of a homogeneous incompressible viscous fluid are used to comprehensively describe different mechanisms of vortex formation behind a sphere at moderate Reynolds numbers (200 ≤ Re ≤ 380). For 200 < Re ≤ 270 a steady-state rectilinear double-filament wake is formed, while for Re > 270 it is a chain of vortex loops. The three unsteady periodic flow patterns corresponding to the 270 < Re ≤ 290, 290 < Re ≤ 320, and 320 < Re ≤ 380 ranges are characterized by different vortex formation mechanisms. Direct numerical simulation is based on the Meranzh (SMIF) method of splitting in physical factors with an explicit hybrid finite-difference scheme which possesses the following properties: secondorder approximation in the spatial variables, minimal scheme viscosity and dispersion, and monotonicity. Two different vortex identification techniques are used for visualizing the vortex structures within the wake.     

槽道湍流近壁区相干结构的数值模拟

从流动稳定性理论中的共振三波出发，采用类似湍流直接数值模拟中的最小单元概念，用伪谱方法，对槽道湍流近壁区的单个相干结构进行了数值模拟，得到了与实验基本一致的结果，同时也搞清楚了在谱方法中用Ｃｈｅｂｙｓｈｅｖ－τ方法和配置点法哪个更精确的问题。     

Communication between the buffer layer and the wall in a turbulent channel flow

Direct numerical simulations obtained in large computational domains of a fully developed turbulent channel flow up to the Karman number 1100 are analyzed to determine the scaling of the spanwise correlation coefficients and the effect of the outer eddies. The local fluctuating velocity field is narrow-band-pass and low-pass filtered along the streamwise wavenumber. The spanwise correlations of the narrow-band passed signals in the low buffer layer adequately provide length scales and signatures of the active structures. The low-pass filtering is used to investigate the relative role of the outer eddies. The impact of the active and passive eddies on the wall is analyzed separately through the cross-correlations of the filtered velocity field with the wall shear stress fluctuations. Characteristic length-scales resulting from the analysis of the velocity field differ depending on the quantity and some are related to the conventional streak spacing but not all. The quasi-streamwise vortex paradigm, for the most part, allows the interpretation of these characteristics, but fails in some cases.     

Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil

Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.     

Reynolds stress modelling of rectangular open‐channel flow

A Reynolds stress model for the numerical simulation of uniform 3D turbulent open‐channel flows is described. The finite volume method is used for the numerical solution of the flow equations and transport equations of the Reynolds stress components. The overall solution strategy is the SIMPLER algorithm, and the power‐law scheme is used to discretize the convection and diffusion terms in the governing equations. The developed model is applied to a flow at a Reynolds number of 77000 in a rectangular channel with a width to depth ratio of 2. The simulated mean flow and turbulence structures are compared with measured and computed data from the literature. The computed flow vectors in the plane normal to the streamwise direction show a small vortex, called inner secondary currents, located at the juncture of the sidewall and the free surface as well as the free surface and bottom vortices. This small vortex causes a significant increase in the wall shear stress in the vicinity of the free surface. A budget analysis of the streamwise vorticity is carried out. It is found that both production terms by anisotropy of Reynolds normal stress and by Reynolds shear stress contribute to the generation of secondary currents. Copyright © 2006 John Wiley & Sons, Ltd.     

涡旋波流场的涡量测试与计算及特征参数的影响

从实验和模拟计算两个方面,对涡旋波流场的速度矢量图和涡量进行了定量测试和综合分析,并对涡旋波流动与其特征影响参数之间的关系进行了研究。结果表明:涡旋波流动只在二维层流状态下产生,涡旋波形成后,Re数对旋涡尺寸的影响较小,涡量随Re数的增大而增大,但涡量不随时间的增加而单调增加。随着St数的减小,旋涡尺寸明显增大,涡量却随之减小。本文也对不同槽道内的涡旋波流场进行了数值模拟计算,进而确定了涡旋波流场的形成条件。     

Simulation of the aerodynamics of buildings and structures by means of the closed vortex loop method

Problems of the numerical simulation of the air flow past buildings and structures are considered using the closed vortex loop method. A mathematical model, based on the vortex approach, of the time-dependent ideal incompressible fluid flow past a system of bodies is proposed. A numerical scheme for solving the problem and an algorithm for calculating the distributed wind loads over the body surface are outlined. An example of calculating the aerodynamic loads is given for a real building and the results are compared with the known results of testing a model of the building in a wind tunnel. An example of the calculation and analysis of the wind distribution over a system of several buildings is also presented.     

Large eddy simulation of aircraft wake vortex with self-adaptive grid method

A self-adaptive-grid method is applied to numerical simulation of the evolution of aircraft wake vortex with the large eddy simulation(LES). The Idaho Falls(IDF)measurement of run 9 case is simulated numerically and compared with that of the field experimental data. The comparison shows that the method is reliable in the complex atmospheric environment with crosswind and ground effect. In addition, six cases with different ambient atmospheric turbulences and Brunt V¨ais¨al¨a(BV) frequencies are computed with the LES. The main characteristics of vortex are appropriately simulated by the current method. The onset time of rapid decay and the descending of vortices are in agreement with the previous measurements and the numerical prediction. Also, secondary structures such as baroclinic vorticity and helical structures are also simulated.Only approximately 6 million grid points are needed in computation with the present method, while the number can be as large as 34 million when using a uniform mesh with the same core resolution. The self-adaptive-grid method is proved to be practical in the numerical research of aircraft wake vortex.     

Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

Study on multiple ring-like vortex formation and small vortex generation in late flow transition on a flat plate

A high-order direct numerical simulation (DNS) of flow transition over a flat plate at a free stream Mach number 0.5 has been carried out. During the simulation, we cannot find, according to the classical theory of boundary layer transition, the “hairpin vortex breakdown to smaller structures” in the last stage of flow transition on a flat plate. However, we did discover the so-called spikes as a result of a multibridge or multiring formation. This indicated a large and stable vortex structure which can travel for a long distance. We believe that this is a result of ring heads that are located in an inviscid region. These heads of the “turbulence spot” never seem to break down and persist as a stable structure. In addition, we discovered that the U-shaped vortex is a part of an existing coherent structure instead of a newly generated one. The U-shaped vortex also provides an additional channel to transfer vorticity to the ring from the wall. During travel, the leading primary ring in the front of the spot is sloped and skewed, causing disappearance of the second sweep. As a consequence, no energy is brought down to the lower boundary layer near the vortex ring head of the spot. Thus, the small length scale structures become damped and the existing U-shaped vortex structure becomes distinguishable. So, the question is where do the turbulent small length scale vortices come from? We will address this with a new theory which states that all of small length scales (turbulence) are generated by high-shear (HS) layers rather than being produced by “vortex breakdown.” The new DNS shows that the HS layers are produced by strong positive spikes surrounded by low-speed fluids and by the interaction between the secondary and higher-level vortices and the wall surface especially near the ring neck. This multiple ring-like vortex generation also follows the first Helmholtz vortex conservation law. Furthermore, the Λ-shaped vortex is formed and rolling up, and the Λ-vortex is stretched and narrowed, and a new bridge is generated after the neck. The bridge will further become a second ring and so on. Besides the original vortex legs, there are also U-shaped vortex tubes. Finally, the multiple ring vortex structure is formed. From this process, no evidence is found to support that two consequent multiring circles are mixed to generate small vortices. The connection of downdraft/updraft motions is also studied.     

Numerical prediction of turbulent flow structure generated by a synthetic cross‐jet into a turbulent boundary layer

A detailed numerical study using large‐eddy simulation (LES) and unsteady Reynolds‐averaged Navier–Stokes (URANS) was undertaken to investigate physical processes that are engendered in the injection of a circular synthetic (zero‐net mass flux) jet in a zero pressure gradient turbulent boundary layer. A complementary study was carried out and was verified by comparisons with the available experimental data that were obtained at corresponding conditions with the aim of achieving an improved understanding of fluid dynamics of the studied processes. The computations were conducted by OpenFOAM C++, and the physical realism of the incoming turbulent boundary layer was secured by employing random field generation algorithm. The cavity was computed with a sinusoidal transpiration boundary condition on its floor. The results from URANS computation and LES were compared and described qualitatively and quantitatively. There is a particular interest for acquiring the turbulent structures from the present numerical data. The numerical methods can capture vortical structures including a hairpin (primary) vortex and secondary structures. However, the present computations confirmed that URANS and LES are capable of predicting current flow field with a more detailed structure presented by LES data as expected. Copyright © 2011 John Wiley & Sons, Ltd.