Study on forced shear flow by a oscillating spoiler

In the present paper, numerical solution of the two-dimensional unsteady Navier-Stokes equations is used to study the forced shear flow induced by a spoiler's periodical up and down oscillation on a flat plate. The paper studies the evolution of growing, shedding, merging and decaying of vortices due to the spoiler's oscillation, particularly the dependence of the forced shear flow on the reduced frequency. Results show that the reduced frequency is a key factor in controlling the growing and the shedding of vortices in the shear layer. The instantaneous streamlines and the equi-vorticity contours, as well as the surface pressure distributions, have also been investigated. Numerical results agree well with corresponding experimental ones. The study is helpful for understanding the physical mechanism of shear flow control.     

Wall shear stress modified by bubbles in a horizontal channel flow of silicone oil in the transition region

We performed laboratory experiments on bubbly channel flows using silicone oil, which has a low surface tension and clean interface to bubbles, as a test fluid to evaluate the wall shear stress modification for different regimes of bubble migration status. The channel Reynolds numbers of the flow ranged from 1000 to 5000, covering laminar, transition and turbulent flow regimes. The bubble deformation and swarms were classified as packing, film, foam, dispersed, and stretched states based on visualization of bubbles as a bulk void fraction changed. In the dispersed and film states, the wall shear stress reduced by 9% from that in the single-phase condition; by contrast, the wall shear stress increased in the stretched, packing, and foam states. We carried out statistical analysis of the time-series of the wall shear stress in the transition and turbulent-flow regimes. Variations of the PDF of the shear stress and the higher order moments in the statistic indicated that the injection of bubbles generated pseudo-turbulence in the transition regime and suppressed drag-inducing events in the turbulent regime. Bubble images and measurements of shear stress revealed a correlated wave with a time lag, for which we discuss associated to the bubble dynamics and effective viscosity of the bubble mixture in wall proximity.     

On separated shear layer of blunt circular cylinder

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8×10³ to 1.0×10⁵, with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2–3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5–6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed. The project supported by the National Natural Science Foundation of China and the Key Laboratory for Hydrodynamics of NDCST.     

Experiment and prediction of a cavity type separated flow

A detail study involving flow visualization, Laser Doppler Velocimeter (LDV) measurements and numerical prediction is presented. The visualization experiments revealed striking results of a pulsatile motion in the separated flow region associated with the formation and passage of large eddy structures. Measurements of mean velocities and turbulence intensity profiles across the separated flow field, provided information about the separated shear layer development and the recirculating flow pattern. The numerical predictions, obtained with a two-layer turbulence model in conjunction with the SIMPLE algorithm, failed to reproduce the coherent eddies and the pulsatile motion, but the mean velocities are reasonably reproduced.     

On the measurement of normal stress differences in steady shear flow

Summary Compared to the similar pressure-distribution cone-and-plate apparatus of Adams and Lodge (4), the new apparatus' improvements include: temperature control of the cone (as well as the plate); increased stiffening of the frame; four (not three) pressuremeasuring holes in the cone/plate region; inclusion of a pressure-measuring hole on the axis under the cone truncation; exclusive use of a vertical free liquid boundary at the cone rim (without a sea of liquid). Temperature control of the rotating cone and of the fixed plate leads to acceptable temperature uniformity in the test liquid for working temperatures within 10°C or 20°C of ambient; the corresponding interval is about 1°C if the cone temperature control is abandoned. Pressure gradients measured using a Newtonian liquid agree with those calculated using Walters' eq. (3). For a viscoelastic liquid, after subtracting inertial contributions, pressure distributions measured at a given shear rate in the cone/plate region do not change when the gap angle is changed from 2° to 3°, showing that the effects of secondary flow are negligible. Values ofN ₃ =N ₁ + 2N ₂ obtained from the gradients of these distributions are believed to be in error by not more than ±1 Pa, in favorable cases. The present most useful ranges are: 10 to 5000 Pa forN ₃; 0.1 to 200 sec^–1 for shear rate; up to 5 Pa s for viscosity; and 5 to 40°C for temperature. As an application, it is shown that adding 0.1% of a high molecular weight polyisobutylene to a 2% polyisobutylene solution doublesN ₃ and has no detectable effect on the viscosity measured at low shear rates with a Ferranti-Shirley viscometer.

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Zusammenfassung Im Vergleich zu dem ähnlichen Kegel-Platte-Gerät von Adams und Lodge (4) zur Messung der Druckverteilung wurden an dem neuen Gerät die folgenden Verbesserungen vorgenommen: Temperaturregelung an Kegel und Platte, Versteifung des Rahmens, vier (anstatt drei) Druckmeßlöcher im Kegel-Platte-Bereich, ein zusätzliches Druckmeßloch auf der Achse unter der Kegelstumpf-Deckfläche, ausschließliche Verwendung einer vertikalen freien Grenzfläche der Flüssigkeit am Kegelrand (ohne umgebenden Flüssigkeitssee). Die Temperaturregelung des rotierenden Kegels und der festen Platte führt zu einer ausreichenden Temperaturgleichförmigkeit in der Testflüssigkeit für Betriebstemperaturen, die höchstens um 10–20°C von der Umgebungstemperatur abweichen. Dieses Intervall beträgt dagegen nur etwa 1°C, wenn auf die Temperaturregelung am Kegel verzichtet wird. Für newtonsche Flüssigkeiten entsprechen die gemessenen Druckgradienten den mittels der Gleichung von Walters (3) berechneten. Für viskoelastische Flüssigkeiten zeigen sich bei der Änderung des Spaltwinkels von 2° auf 3° nach Abzug der Trägheitsbeiträge keine Änderungen der bei einer bestimmten Schergeschwindigkeit gemessenen Druckverteilung. Dies zeigt, daß Sekundärströmungseffekte vernachlässigbar sind. Es darf angenommen werden, daß die Werte vonN ₃ =N ₁ + 2N ₂, die man aus den Gradienten dieser Verteilungen erhält, unter günstigen Umständen mit einem Fehler von nicht mehr als ±1 Pa behaftet sind. Gegenwärtig liegen die günstigsten Bereiche bei 10 bis 5000 Pa fürN ₃, 0,1 bis 200 s^–1 für die Schergeschwindigkeit, unterhalb von 5 Pa s für die Viskosität und 5 bis 40°C für die Temperatur. Als Anwendung wird gezeigt, daß ein Zusatz von 0,1% hochmolekularen Polyisobutylens zu einer 2%igen Polyisobutylenlösung den Wert vonN ₃ verdoppelt, aber keinen erkennbaren Einfluß auf die (bei geringen Schergeschwindigkeiten mit einem Ferranti-Shirley-Viskosimeter gemessen) Viskosität hat.

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udsf unidirectional shear flow - TCP truncated-cone and plate - N ₁,N ₂ 1st and 2nd normal stress differences in udsf - N ₃ N ₁ + 2N ₂ - : = A is defined by the equationA := B - P ^* hole pressurePw – Pm; Pw, Pm = pressures measured by flush transducer and by hole-mounted transducer - t time - , strain rate, shear rate - (P,t) covariant body metric tensor at particleP and timet - ⁱ , _i covariant and contravariant udsf body base vectors (i = 1, 2, 3) - ^–1 inverse of - R, plate radius, cone/plate gap angle - r ₀,h ₀ radius and height of cone truncation - r,, spherical polar coordinates; cone axis = 0; plate surface = /2 - physical components of stress; for a tensile component - cone angular velocity - p on the plate = /2 - ,T, density, absolute temperature, viscosity - P 0.15 ²(r ² –R ²) (inertial contribution) [2.7] - P _ve contribution [2.8] from flow perturbations of viscoelastic origin - r _i i = 1,2,3,4; values ofr at centers of holes in cone/plate region - P _i () pressure change recorded by transducerTi when cone angular velocity goes from zero to - 1/2 {P _i ()+ P _i (–)} (average for 2 senses of rotation) - rim pressure, from least-squares line through four points - Re Reynolds' number:R ²/ - (P,t)/t With 11 figures and 2 tables     

双柱状颗粒在线性剪切流场中的动力学分析

为研究柱状颗粒在线性剪切流场中的运动状态和受力情况,本文以颗粒长径比为2,颗粒之间的初始距离ΔS_Py=4D为例,基于直接力浸入边界法数值模拟了双柱状颗粒在三维线性剪切流场中的运动过程。根据模拟结果分析了柱状颗粒周围流场参数分布,在考虑壁面对颗粒的影响和颗粒之间相互影响的条件下,研究了颗粒的受力和运动的变化,探索了流体曳力导致柱状颗粒迁移和转动的规律。研究结果表明,双柱状颗粒在线性剪切流场中易向速度大的流体区域运动;前后两颗粒运动状态和轨迹不同,颗粒之间距离较近时,曳力会产生较大的波动;只有当颗粒在壁面附近时,滞后颗粒才能追上领先颗粒,两颗粒发生牵引、翻滚和分离过程。     

Transient shear flow properties of fiber-filled polyethylene melts

The growth and relaxation of shear and normal stresses have been investigated for glass and carbon fiber-filled polyethylene melts over a wide range of shear rates and temperatures by means of a cone-and-plate rheogoniometer. Flow parameters and flow curves characterizing the stress overshoot and relaxation phenomena of the fiber-filled systems were determined experimentally. The influence of fiber loading, fiber size and temperature on the transient flow parameters are discussed.Predictions by the Meister and Bogue constitutive equations were compared with the experimental data for the transient shear and normal stresses. These equations predict satisfactorily the non-linear transient shear flow of polymer melts and its fiber-filled systems.     

Thermal and dynamic characteristics of the separated flow behind a flat rib with different angles of alignment toward the flow

Results of an experimental study of a turbulent flow past a flat rib with different angles of alignment toward the flow and with different rib heights are presented. The angle of rib alignment toward the flow is varied within ϕ = 50–90°. Vortex formation is visualized, and the coordinates of the reattachment line are determined. It is demonstrated that a decrease in the angle ϕ forms a reattachment region and makes the flow behind the rib more three-dimensional. Pressure coefficients are measured in different longitudinal sections of the channel behind the rib with a varied angle of rib alignment ϕ. Temperature fields on the surface behind the rib are measured by means of an infrared imager and by thermocouples, and the corresponding heat-transfer coefficients are calculated. The effect of the angle of rib alignment toward the flow and the rib height on dynamic and thermal characteristics of the separated flow is analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 103–109, January–February, 2007.     

用三分量LDV测量壁湍流边界层

本文用三分量激光多普勒测速仪对壁湍流边界层进行了测量，经过数据处理后，给出了各湍流参数的分布曲线，并与Ｄｊｅｎｉｄｉ等的测量结果进行了比较，吻合得很好。结果表明，用３Ｄ－ＬＤＶ研究湍流是可行的     

Wall pressure fluctuations of a turbulent separated and reattaching flow affected by an unsteady wake

The spatio-temporal characteristics of the wall-pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated through pressure-velocity joint measurements carried out using multiple-arrayed microphones and split-film probes. A spoke-wheel-type wake generator was installed upstream of the backward-facing step. The flow structure at the effective forcing frequency (St _f=0.2) was found to be well organized in terms of wall pressure spectrum, cross-correlation, wavenumber-frequency spectrum, and wavelet auto-correlation. Introduction of the unsteady wake (St _f=0.2) reduced the reattachment length by 10%. In addition, the unsteady wake enhanced the turbulence intensity near the separation edge and, as a consequence, enhanced the quadrupole sound sources; however, the turbulence intensity near the reattachment region was weakened and the overall flow noise was attenuated. The greater organization of the flow structure induced by the unsteady wake led to a weakening of the dipole sound sources, which are the dominant sound sources in this system. The dipole sound sources generated by wall pressure fluctuations were calculated using Curles integral formula.Abbreviations AR Aspect ratio - SBF Spatial box filtering Roman symbols C _p Wall pressure fluctuation coefficient, p/0.5U ² - H Step height of backward-facing step (mm) - H _s Shape factor (H _s = ^*/) - R _s Distance from acoustic source point to observation point (m) - Re _H Reynolds number, U H/ - St The reduced frequency, fH/U - St _f Normalized forcing frequency by unsteady wake, f _p H/U - T Vortex shedding period (s) - U Free-stream velocity (m/s) - a Speed of sound (m/s) - f Frequency (Hz) - f _p Wake passing frequency (Hz) - k Turbulent kinetic energy (m²/s²) - k _x Streamwise wave number (1/m) - k _z Spanwise wave number (1/m) - l _j Cosine of angle - p Instantaneous wall pressure (Pa) - p _rms Root-mean-square of wall pressure (Pa) - p _SBF Spatial box filtered wall pressure (Pa) - p _d Dipole sound source (Pa) - p _w Conditionally-averaged wall pressure (Pa) - q Dynamic pressure, 0.5U ² (Pa) - r Distance from origin to observation point (mm) - u _c Convection velocity (m/s) - u_max Root-mean-square of streamwise velocity (m/s) - x _R Time-mean reattachment length (mm) Greek symbols _p Forward-flow time fraction - Auto-correlation of pressure at x ₀ - Two-dimensional cross-correlation of pressure with streamwise separation interval , spanwise separation interval , and time delay , at (x ₀, z ₀) - Boundary layer thickness (mm, _99%) - ^* Displacement thickness (mm, ) - _ij Kroneckers delta function - Phase angle (°) - Wavelength (mm) - Momentum thickness (mm, ) - Angle between vertical axis and observation point (°) - Density (kg/m³) - Time delay (s) - Streamwise separation interval (m) - Spanwise separation interval (m) - _p (f; x ₀) Autospectrum of pressure measured at x ₀ (Pa² s) - _pp (, ; x ₀) Streamwise cross spectrum of pressure at x ₀ (Pa² s) - _pp (, , ; x ₀, z ₀) Streamwise and spanwise cross spectrum of pressure at (x ₀, z ₀) (Pa² s) - _pp (kx, ; x ₀) Streamwise wavenumber-frequency spectrum of pressure at x ₀ (Pa² s) - _pp (kx, kz, ; x ₀, z ₀) Two-dimensional wavenumber-frequency spectrum of pressure at (x ₀, z ₀) (Pa² s)     

Instability of the separated shear layer in flow past a cylinder: Forced excitation

The receptivity of the separated shear layer for Re = 300 flow past a cylinder is investigated by forced excitation via an unsteady inflow. In order to isolate the shear layer instability, a numerical experiment is set up that suppresses the primary wake instability. Computations are carried out for one half of the cylinder, in two dimensions. The flow past half a cylinder with steady inflow is found to be stable for Re = 300. However, an inlet flow with pulsatile perturbations, of amplitude 1% of the mean, results in the excitation of the shear layer mode. The frequency of the perturbation of the inlet flow determines the frequency associated with the shear layer vortices. For a certain range of forced frequencies the recirculation region undergoes a low‐frequency longitudinal contraction and expansion. An attempt is made to relate this instability to a global mode of the wake determined from a linear stability analysis. Interestingly, this phenomenon disappears when the outflow boundary of the computational domain is shifted sufficiently downstream. This study demonstrates the need of carefully investigating the effect of the location of outflow boundaries if the computational results indicate the presence of low‐frequency fluctuations. The effect of Re and amplitude of unsteadiness at the inlet are also presented. All computations have been carried out using a stabilized finite element formulation of the incompressible flow equations. Copyright © 2007 John Wiley & Sons, Ltd.     

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.     

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.     

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.     

一种确定均匀动脉壁面切应力的非线性方法

从Ling和Atabek提出的``局部流'理论出发，提出一种利用测量血液黏度、管轴上 的血流速度、压力和管径波形计算均匀动脉管壁切应力的非线性方法. 将这种方法与柳兆荣 等提出的利用测量血液黏度、管轴上的血流速度和平均管径计算切应力的线性方法比较，结 果表明，当管壁脉动幅度较小时，两种方法计算的压力梯度、流速剖面和管壁切应力差别较 小；而当管壁脉动幅度增大时，两种方法计算的压力梯度、流速剖面和管壁切应力差别增大. 对于小幅脉动均匀动脉，用线性方法计算管壁切应力有较高的精度；而对于大变形 均匀动脉，则需要考虑非线性因素对管壁切应力的影响. 由于作为输入量的血液黏度、轴心 血流速度、压力波形和管径波形可在活体上通过无损伤或微损伤的检测方法得到， 所提出的计算切应力的方法为在体或离体研究切应力与动脉重建的关系提供了方法学基础.     

空间曲梁单元的扭转修正系数研究

三维空间曲梁有限单元模型是模拟曲梁结构的有效数值方法,可以考虑曲梁的弯扭耦合特性,最为符合曲梁的几何和受力特征.由于有限元法采用梁理论的平截面假定,空间曲梁单元上的扭转剪应力分布与实际曲梁截面上的扭转剪应力不同,从而会导致扭转刚度和扭转变形的计算失真.本文基于剪切应变能等效原理,推导了不同长宽比的矩形截面空间曲梁单元的...     

Near wall characterization of the flow over a two-dimensional steep smooth hill

Near-wall data for the strongly perturbed flow in a neutrally stable boundary layer encountering a steep, smooth, two-dimensional hill are presented. Observations were made on the centerplane of a water channel at thirteen stations relative to the hill by laser Doppler anemometry. The large reverse flow region that is formed on the lee of the hill was particularly scrutinized through seven measuring stations. Results are presented for the mean and turbulent properties of the flow. Wall shear stress was evaluated through fitting procedures that resorted to the near wall behavior of the velocity profile. Logarithmic fits as well as predictions through the Reynolds stress profiles are also presented.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Simulation of unsteady laminar flow in models of terminal aneurysm of the basilar artery

Blood flow dynamics play an important role in the pathogenesis and treatment of intracranial aneurysms. The evaluation of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils, in addition the temporal and spatial variations of wall shear stress in the aneurysm are correlated with its growth and rupture. The present numerical investigation describes the hemodynamics in two models of terminal aneurysm of the basilar artery. Aneurysm models with an aspect ratio of 1.0 and 1.67 were studied. Each model was subject to a steady, sinusoidal and physiologically representative waveform of inflow for a mean Reynolds number of 560. Symmetric and asymmetric outflow conditions in the branches were also studied.

The three-dimensional continuity and the Navier-Stokes equations for incompressible, unsteady laminar flow with Newtonian properties were solved with a commercial software using non structured grids with 61334 and 65961 cells for models 1 and 2, respectively. The grids were primarily composed of tetrahedral elements.

The intra-aneurysmal flow was unsteady for all input conditions and in both models, the flow always showed a complex vortex structure. The inflow and outflow zones in the aneurysm neck were determined. The wall shear stress on the aneurysm showed large temporal and spatial variations. The asymmetric outflow increased the wall shear stress in both models.     

水平旋转空腔环流的壁面应力

通过对典型的水平旋转内消能泄洪洞空腔环流的试验观测，研究了其壁面应力的变化规律。空腔环流的壁面压强在水平洞的起始段壁面压强急剧减小然后回升，具有过渡段的性质，沿程波状减小，符合对数变化规律，但不同的流态，对数律的参数的变化是不同的：内界面相对压强Po/Pwz。在淹沿流流态时，随(H-h)/h的变化率显著不同，在吸允流流态时却基本相同；壁面切应力沿z的变化规律为先急剧减小，随后缓慢减小至零，主要与环流特性有密切的关系。