Reynolds Number Dependence of Velocity Structure Functions in a Turbulent Pipe Flow

Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR _λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized second-order structure functions show a continuous evolution withR _λ. In particular, the scaling exponentζ _v , corresponding to the v structure function, continues to increase with R _λ in contrast to the nearly unchanged value of ζ _u . The Kolmogorov constant for δu shows a smaller rate of increase with R _λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR _λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the centreline of a fully developed channel flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Lower Critical Reynolds Number for Flow in a Circular Pipe

Flow in a circular pipe is investigated experimentally at Reynolds numbers higher than that at which the resistance coefficients calculated from the Blasius formula for laminar flow and from the Prandtl formula for turbulent flow are equal. The corresponding Reynolds number based on the mean-flow velocity and the pipe diameter is about 1000. The experiments were performed at a high level of inlet pulsations produced by feeding gas into the pipe through a hole with a diameter several times smaller than the pipe diameter. In our experiments the critical Reynolds number was determined as the value, independent of the distance from the inlet, at which the ratio of the axial to the mean-flow velocity as a function of the Reynolds number deviated from 2. At the maximum ratio of the pipe cross-sectional area to the area of the hole through which the gas entered the pipe, equal to 26, the critical Reynolds number was about 2300. After a fivefold increase in the hole area the critical Reynolds number increased by approximately 4%.At Reynolds numbers below 2000, after at a high level of the inlet pulsations an almost laminar flow had developed in the pipe, a perturbation was introduced by inserting a diametrically oriented cylindrical rod with a diameter 10–20 times smaller than the pipe diameter. In these experiments, at Reynolds numbers higher than 1000, at a distance from the rod equal to 50 pipe diameters the axial to mean-flow velocity ratio was less than 2, approaching this value again at large distances from the rod. The insertion of the rod led to a decrease in the critical Reynolds number by approximately 12%.     

黏弹性流体扩展及收缩流动的格子Boltzmann模拟分析

本文应用格子Boltzmann 方法(LBM)并结合Oldroyd-B 模型,讨论了不可压缩的 Navier-Stokes 方程和平流扩散本构方程的解耦及各自求解方法,以及两类问题的边界处理格式,实现了黏弹性流体在二维1:3 扩展流道以及3:1 收缩流道中的流动的数值模拟．获得了不同雷诺数Re 和维森伯格数Wi 以及黏度vs 下流动的流线分布,计算给出了漩涡的涡心位置和大小,并分析了参数Re、Wi 和vs 对流动特点的影响．模拟结果表明本文所采用模型和边界处理方法具有良好的精度和稳定性．     

Hydraulic Resistance of a Pipe with a Surface Film

The results of a laboratory investigation of the effect of a liquid film covering the inner surface of a circular gas pipe on its hydraulic resistance are given. The problems of the similarity of liquid film flows are considered. It is shown that the liquid film increases the resistance of a hydraulically smooth pipe but can reduce that of a rough pipe due to the decrease in the equivalent roughness.     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

Flow Rate Prediction for a Semi-permeable Membrane at Low Reynolds Number in a Circular Pipe

Transport in Porous Media - A concise and accurate prediction method is required for membrane permeability in chemical engineering and biological fields. As a preliminary study on this topic, we...     

Asymptotic solution of the thin viscous shock layer equations at low Reynolds numbers for a cold surface

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies in the neighborhood of the stagnation line is considered. The question of the applicability of the gasdynamic thin viscous shock layer model [1] is investigated for the transition flow regime from continuum to free-molecular flow. It is shown that for a power-law temperature dependence of the viscosity coefficient T the quantity (Re)^1/(1+), where = ( – 1)/2 and is the specific heat ratio, is an important determining parameter of the hypersonic flow at low Reynolds numbers. In the case of a cold surface approximate asymptotic solutions of the thin viscous shock layer equations are obtained for noslip conditions on the surface and generalized Rankine-Hugoniot relations on the shock wave at low Reynolds numbers. These solutions give simple analytic expressions for the thermal conductivity and friction coefficients as functions of the determining flow parameters. As the Reynolds number tends to zero, the values of the thermal conductivity and friction coefficients determined by this solution tend to their values in free-molecular flow for an accommodation coefficient equal to unity. This tending of the thermal conductivity and friction coefficients to the free-molecular limit takes place for both two-and three-dimensional flows. The asymptotic solutions are compared with numerical calculations and experimental data.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 159–170. Original Russian Text Copyright © 2004 by Brykina.     

Solution of the Reynolds Equation for Viscous-Fluid Flow in the Clearance between a Rotating Ellipsoid and a Surface

Slow viscous-fluid flows in the narrow clearance (i) between a moving ellipsoid and a straight tube of elliptic cross section and (ii) between a rotating ellipsoid and a toroidal tube, including the case of an ellipsoid near a plane, are considered. A solution of the boundary-value problem for the Reynolds equation describing the flow in the clearance is found. The similarity of the pressure profiles in the “ellipsoid-plane” and “ cylinder-plane” systems is indicated.     

Effects of Periodic Excitation on the Flow Around a D-Shaped Cylinder at Low Reynolds Numbers

The baseline and forced flow around a bluff body with semi-elliptical D-shape was investigated by solving the 2D Navier–Stokes equations at low Reynolds numbers. A D-shape rather than the canonic circular-cylinder was selected due to the fixed separation points in the latter, enabling to study a pure wake rather than boundary-layer control. The correlation between Strouhal and Reynolds numbers, the mean drag, the lift and drag oscillations vs. the Reynolds number and wake structure were investigated and compared to experimental and numerical data. Effects of open-loop forcing, resulting from the influence of zero-mass-flux actuators located at the fixed separation points, were studied at a Reynolds number of 150. Fluidic rather than body motion or volume forcing was selected due to applicability considerations. The motivation for the study was to quantify the changes in the flow field features, as captured by Proper Orthogonal Decomposition (POD) analysis, due to open-loop forcing, inside and outside the “lock-in” regime. This is done in order to evaluate the suitability of low-order-models based on POD modes of this changing flow field, for future feed-back flow control studies. The evolution of the natural and the excited vortices in the Kármán wake were also investigated. The formation and convection regions of the vortex evolution were documented. It was found that the forcing causes an earlier detachment of the vortices from the boundary-layers, but does not affect their circulation or convection speeds. The results of the POD analysis of the near-wake flow show that the influence of the bluff body shape (“D”-shaped versus circular cylinder) on the baseline POD wake modes is small. It was found that the eigenfunctions (mode-shapes) of the POD velocity modes are less sensitive to slot excitation than the vorticity modes. As a result of the open-loop excitation, two types of mode-shape-change were observed: a mode can be exchanged with a lower-energy mode or shifted to a low energy level. In the latter case, the most energetic mode becomes the “actuator” mode. The evolution of one-slot excitation on still fluid (“Synthetic jet”) was studied and compared to published data and to “actuator” modes with external flow present. Based on the current findings, it is hypothesized that the cross-flow velocity POD modes are suitable for feedback control of wake flow using periodic excitation, due to their low sensitivity to the excitation as compared to the streamwise velocity or vorticity modes.     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Asymptotic Investigation of the Thin Viscous Shock Layer Equations in the Neighborhood of the Stagnation Point for Low Reynolds Numbers

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies is investigated in the neighborhood of the stagnation point. The problem of applicability of the model of a thin viscous shock layer to the regime of transition from continuum to free-molecular flow is considered. In [1], it was shown that at low Reynolds numbers three hypersonic flow regimes can be distinguished and one of those regimes was investigated. In the present study an asymptotic solution of the thin viscous shock layer equations is obtained for another flow regime. With decrease in the Reynolds number the heat transfer coefficient determined by the solution obtained approaches its free-molecular value and the friction coefficient approaches its free-molecular limit, provided that the shock layer thickness is small. The analytical solution is compared with a numerical solution and the results of calculations based on direct Monte Carlo simulation.     

微尺度圆管内气体流量的实验测量

以氮气和氦气为工作介质,研究了微尺度(φ=17.6μm,17.9μm)圆管内压力驱动的气体流动,测量了在不同进出口压力下的流量,并与计算值进行了比较.结果表明,即使对于极低Mach数(M=0.003～0.03)流动,其可压缩性仍十分明显,它来源于微尺度效应.在本文的实验参数下,Kundsen数范围为3×10-3～7×10-3,表面滑移不明显,稀薄气体效应可以忽略.     

Asymptotic solutions of the two-dimensional equations for a thin viscous shock layer in a rarefied gas

Two-dimensional hypersonic rarefied gas flow around blunt bodies is investigated for the continuum to free-molecular transition regime. In [1], as a result of an asymptotic analysis, three rarefied gas flow regimes, depending on the relationship between the problem parameters, were detected and one of these regimes was investigated. In the present study, asymptotic solutions of the thin viscous shock layer equations at small Reynolds numbers are obtained for the other two flow regimes. Analytical expressions for the heat transfer, friction and pressure coefficients are obtained as functions of the incident flow parameters and the body geometry and temperature. As the Reynolds number tends to zero, the values of these coefficients approach their values in free-molecular flow. The scaling parameters of hypersonic rarefied gas flow around bodies are determined for different regimes. The asymptotic solutions are compared with the results of direct Monte Carlo simulation.     

Reynolds数对大攻角细长旋成体绕流滚转角效应影响的数值研究

使用低耗散的Roe格式,数值模拟了Reynolds数(Re)对大攻角细长旋成体绕流滚转角效应的影响.模型头部加了几何小扰动块以引发流场的不对称.在较大的Re数(Re=10 5)下,本文的计算结果与实验是相符的,此时细长体的滚转会导致双稳态、双周期现象,即侧向力随滚转角呈现类似方波形式的双周期变化,方波中侧向力基本保持不变的状态对应于流场的正则态,且两个正则态的侧向力方向相反,方波中侧向力基本保持不变的状态对应于流场的正则态,且两个正则态的侧向力方向相反;而在较小的Re数(Re=4 000)下,如果扰动足够大,细长体的滚转将导致不同的双稳态现象,此时两个正则态的侧向力方向相同,而在较小扰动下双稳态现象不再出现;Re数更小时(Re=1 000),即使在较大的扰动下,双稳态现象也不再出现,侧向力随滚动角仍是连续变化的.本文的计算结果表明,Re数越小,流场对头部扰动的感受性越弱.     

Exact Solutions of the Problem of Unsteady Flow of a Viscoplastic Medium in a Circular Pipe

Two one-parameter series of real solutions describing the process of deceleration and acceleration of a viscoplastic medium under the action of a time-varying pressure gradient are obtained. The problem of axisymmetric unsteady viscoplastic flow is reduced to the solution of the Stefan boundary-value problem for the heat conduction equation with a nonlinear condition on the boundary of the quasi-rigid core. By a self-similar change of variables the problem can be reduced to a second-order ordinary differential equation. The solutions of this equation are represented in terms of Bessel and elementary functions. As a result, two one-parameter series of solutions, the first of which describes the acceleration and the second the deceleration of a viscoplastic medium in a pipe under the action of a time-varying pressure gradient are obtained.     

Similarity Laws for the Velocity Distribution and the Reynolds Tensor Components in the Wall Region of a Turbulent Boundary Layer with Injection and Suction

Similarity laws of the distributions of the average velocity, tangential stress, and mean-square transverse velocity fluctuation are established in an intermediate zone of a turbulent boundary layer with injection and suction. This zone is located in the neighborhood of the wall outside the viscous sublayer. The similarity relationship for the velocity profile is a generalization of the well-known logarithmic law to include the case of the presence of a mass flow at the wall.     

应用二维频移LDV测量多孔板管流的湍流特性

采用二维ＬＤＶ系统对圆管中装有四孔板和三孔板的湍流特性进行了实验研究．在孔板下游射流沿管轴逐渐混合．沿管壁可以观察到反向流区域．经足够长距离后，轴向和切向湍流度逐渐趋于相同数量级．实验结果表明，孔板结构和开孔度对湍流特性有重要影响．     

Analysis of the aerodynamic interaction between two plunging plates in tandem at low Reynolds number for maximum propulsive efficiency

The thrust generated by two heaving plates in tandem is analyzed computationally by solving the Navier–Stokes equations for an incompressible and two-dimensional flow at low Reynolds numbers. We consider with detail two particular sets of configurations of interest in forward flight in a wide range of heaving amplitudes and frequencies: a plunging leading plate with the trailing plate at rest, and the two plates heaving with the same frequency and amplitude, but varying the phase difference. In almost all cases the thrust efficiency of the leading plate is augmented in relation to a single plate heaving with the same frequency and amplitude. In the first configuration with a trailing plate at rest, we characterize the range of nondimensional heaving frequencies and amplitudes of the leading plate for which the stationary trailing plate contributes positively to the global thrust. The maximum global thrust efficiency of this configuration, reached for an advance ratio slightly less than unity and a reduced frequency close to 5, is about the same as the maximum efficiency for an isolated plate, reached for slightly smaller frequencies. But for low frequencies the tandem configuration with the trailing plate at rest is more thrust efficient than the isolated plate. We also characterize the nondimensional frequency and amplitude regions for which the flow becomes chaotic. In the second configuration, the maximum of the total thrust efficiency is reached for a phase lag of 180° (counterstroking), particularly for an advance ratio unity and a reduced frequency 4.4. It is almost the same as the maximum thrust efficiency in the other configuration with the trailing plate at rest and that of a single plate. We discuss the flow structures and the aerodynamic interaction between plates responsible for the optimal thrust configuration in both cases.     

Analysis of Streamwise Velocity Fluctuations in Turbulent Pipe Flow with the Use of an Ultrasonic Doppler Flowmeter

Data collected from several studies of experimental and numerical nature in wall-bounded turbulent flows and in particular in internal flows (channel and pipe flows, Mochizuki and Nieuwstadt [1]) at different Reynolds numbers R ⁺(Ru _*/ν), indicate that: (i) the peak of the rms-value (normalized by u _*) of the streamwise velocity fluctuations (σ _u ⁺|_peak) is essentially independent of the Reynolds number, (ii) the position of the rms peak value (y ⁺|_peak) is weakly dependent of the Reynolds number, (iii) the skewness of the streamwise velocity fluctuations (S _u ) is close to zero at the position in which the variance has its peak. A series of measurements of streamwise velocity fluctuations has been performed in turbulent pipe flow with the use of an Ultrasonic Doppler Velocimeter and our results support those reported in [1]. This revised version was published online in July 2006 with corrections to the Cover Date.