Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity

The magnetohydrodynamic(MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.     

Analysis of turbulent axisymmetric inner near wake

An analysis is presented describing the characteristics of mean velocity profile in the axisymmetric turbulent inner near-wake flow behind a body of revolution. The near wake is developing under zero streamwise pressure gradient and the upstream turbulent boundary layer is fully developed. It is shown that the boundary layer condition that exists at the trailing edge can be used to describe the mean velocity profiles in the inner near wake. It is shown that the logarithmic layer of the upstream turbulent boundary layer continues to be valid for some more distance in the near wake, and as the streamwise distance is increased, the logarithmic layer is slowly getting destroyed. It is also shown that the central line velocity exhibits a logarithmic behaviour for large streamwise distance. Results of the analysis have been validated using available experimental data.     

Simulation of a thick turbulent boundary layer via a rod grid

A possibility to simulate a thick Clauser-equilibrium incompressible turbulent boundary layer on a flat plate of finite length with the help of a grid formed by cylindrical rods was experimentally examined. A grid with rods oriented parallel to the streamlined surface proved to be an efficient tool enabling modification of the turbulent boundary layer. In most cases, at a distance of 600 rod diameters the time-average and fluctuation characteristics of the modified boundary layer exhibited values typical of a natural turbulent boundary layer. It is shown that the mean velocity profiles with artificially increased boundary-layer thickness can be represented, to a good accuracy, in terms of law-of-the-wall variables, and they can be generalized with a single dependence using an empirical velocity scale in the outside region. The use of a combined method for exerting an influence on the shear flow capable of improving the modeling procedure for turbulent velocity fluctuations in boundary layer is proposed.     

氩等离子体射流在空气环境中冲击平板层流流动与传热的数值模拟

本文采用组合扩散系数方法处理不同气体组分之间的扩散，对氩等离子体的流射入空气环境并撞击平板时的层流流动和传热进行了数值模拟．这种新的处理混合气体中质量扩散的方法有助于更准确地描述等离子体条件下的组分扩散与能量输运。文中给出了射流中速度、温度及氩质量分数的分布情况，以及基板处热流密度分布的若干典型的数值模拟结果．     

Near Continuum Velocity and Temperature Coupled Compressible Boundary Layer Flow over a Flat Plate

The problem of a compressible gas flows over a flat plate with the velocity-slip and temperature-jump boundary conditions are being studied. The standard single- shooting method is applied to obtain the exact solutions for velocity and temperature profiles when the momentum and energy equations are weakly coupled. A double-shooting method is applied if these two equations are closely coupled. If the temperature affects the velocity directly, more significant velocity slip happens at locations closer to the plate’s leading edge, and inflections on the velocity profiles appear, indicating flows may become unstable. As a consequence, the temperature-jump and velocity-slip boundary conditions may trigger earlier flow transitions from a laminar to a turbulent flow state.     

Mixed Convective Viscoelastic Nanofluid Flow Past a Porous Media with Soret-Dufour Effects

The present study is carried out to see the thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method (OHAM) is best candidate to handle highly nonlinear system of differ-ential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.     

Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow

The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model(DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation.It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model.Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model.To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified.     

Micro-PIV measurement and CFD analysis of a thin liquid flow between rotating and stationary disks

Abstract  

A strongly sheared flow in a thin liquid layer between rotating and stationary disks is studied experimentally and numerically to clarify the characteristics of the flow in rotation-shearing chemical reactors. The disk diameter is 10 mm and the separation between the disks is 500 μm. The rotational speeds that are examined are 300, 500 and 700 rpm. The micro-PIV technique is used to measure the velocity in the liquid layer. A commercial CFD software is also used to obtain the results for the comparison and validation purposes. The overall velocity distributions revealed by the micro-PIV measurement are in good agreement with the CFD results. Both results show some interesting characteristics of the flow field, including the presence of a secondary flow and its influence on the tangential velocity profiles. The near-wall measurement in the micro-PIV technique is appreciably improved by the use of a simple digital, high-pass filtering technique that is applied to the acquired particle images. It is found that the flow characteristics in the thin liquid layer can be evaluated efficiently if the micro-PIV technique is used together with the high-pass filtering technique that is examined here.     

Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet

The entrained flow of an electrically conducting non-Newtonian, viscoelastic second grade fluid due to an axisymmetric stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero (total adhesion) and infinity (full slip). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equation into an ordinary differential equation. The issue of paucity of boundary conditions is addressed, and an effective numerical scheme has been adopted to solve the obtained differential equation even without augmenting the boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and skin friction coefficient. It is observed that in presence of slip, the velocity decreases with an increase in the magnetic parameter. That is, the Lorentz force which opposes the flow leads to enhanced deceleration of the flow. Moreover, it is interesting to find that as slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid.     

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.     

Improvement of ultrasound speckle image velocimetry using image enhancement techniques

Ultrasound-based techniques have been developed and widely used in noninvasive measurement of blood velocity. Speckle image velocimetry (SIV), which applies a cross-correlation algorithm to consecutive B-mode images of blood flow has often been employed owing to its better spatial resolution compared with conventional Doppler-based measurement techniques. The SIV technique utilizes speckles backscattered from red blood cell (RBC) aggregates as flow tracers. Hence, the intensity and size of such speckles are highly dependent on hemodynamic conditions. The grayscale intensity of speckle images varies along the radial direction of blood vessels because of the shear rate dependence of RBC aggregation. This inhomogeneous distribution of echo speckles decreases the signal-to-noise ratio (SNR) of a cross-correlation analysis and produces spurious results. In the present study, image-enhancement techniques such as contrast-limited adaptive histogram equalization (CLAHE), min/max technique, and subtraction of background image (SB) method were applied to speckle images to achieve a more accurate SIV measurement. A mechanical sector ultrasound scanner was used to obtain ultrasound speckle images from rat blood under steady and pulsatile flows. The effects of the image-enhancement techniques on SIV analysis were evaluated by comparing image intensities, velocities, and cross-correlation maps. The velocity profiles and wall shear rate (WSR) obtained from RBC suspension images were compared with the analytical solution for validation. In addition, the image-enhancement techniques were applied to in vivo measurement of blood flow in human vein. The experimental results of both in vitro and in vivo SIV measurements show that the intensity gradient in heterogeneous speckles has substantial influence on the cross-correlation analysis. The image-enhancement techniques used in this study can minimize errors encountered in ultrasound SIV measurement in which RBCs are used as flow tracers instead of exogenous contrast agents.     

Distribution of mean velocity in turbulent boundary layer over permeable surface with air blowing

In the present article, we investigate the possibility of using simple physical models for predicting properties of incompressible turbulent boundary layer on permeable wall at various values of air-microblowing mass flow rate. It is shown that the velocity scaling U _??*/?? ₉₉ can be successfully used to approximate the distribution of mean velocity in the outer region of the boundary layer. The use of this scaling makes the velocity profiles invariant with respect to Reynolds-number variation; this circumstance largely facilitates the analysis of experimental data, making it independent of upstream flow conditions. The distribution of mean velocity in the logarithmic flow region of the boundary layer over permeable surface can be described with a modified law of the wall involving a constant C ₀ equal to the same constant for canonical boundary layer, and a quantity K being a weak function of blowing ratio.     

Flow measurements in liquid metals by means of the ultrasonic Doppler method and local potential probes

Substantial research activities have been carried out at HZDR during the last 15 years on the development and qualification of various methods to measure the velocity field in liquid metal flows. In this paper we report on two complementary methods for measuring the local velocity. The potential difference probe is a local sensor which is immersed into the liquid. Such sensors are very effective for investigations of the turbulent fluctuations at a local point. However, the installation of the probe in the bulk of the liquid might disturb the flow to be measured. Ultrasonic techniques are non-invasive, but need a continuous path from the ultrasonic transducer to the liquid under investigation. The ultrasound Doppler method delivers instantaneous profiles of the local velocity. Experimental applications of these measuring techniques in diverse liquid metal flows under the influence of magnetic fields will be presented here showing the capabilities and limitations of both methods.     

Large-scale PIV surface flow measurements in shallow basins with different geometries

Shallow depth flow fields and low velocity magnitudes are often challenges for traditional velocity measuring instruments. As such, new techniques have been developed that provide more reliable velocity measurements under these circumstances. In the present study, the two-dimensional (2D) surface velocity field of shallow basins is assessed by means of Large-Scale Particle Image Velocimetry (LSPIV). The measurements are carried out at the water surface, which means that a laser light sheet is not needed. Depending on the time scales of the flow and the camera characteristics, it is even possible to work with a constant light source. An experimental application of this method is presented to analyze the effects of shallow basin geometry on flow characteristics in reservoirs where large coherent two-dimensional flow structures in the mixing layer dominate the flow characteristics. The flow and boundary conditions that give rise to asymmetric flow are presented. Asymmetric flow structures were observed starting from basin shape ratios that are less than or equal to 0.96. By decreasing the basin length and increasing the shape ratio to greater than 0.96, the flow structure generally tends towards a symmetric pattern.     

3D imaging of evaporating fuel droplets by stereoscopic PIV

A gun-type burner is a widely used oil burner for industrial and domestic applications. The oil is pressure-atomized and mixed with air generating a recirculating, swirling flow. Because of the surrounding flame, fuel droplets evaporate, being difficult to obtain information on droplets’ dynamics. Several laser techniques have been applied to this burner for spray diagnosis. PDA provides information about droplet size and velocity but can say little about the instantaneous spatial structures in the flow. Planar laser techniques as PIV can describe the 2D instantaneous spatial structures, but cannot provide information about the 3D structures in the flow. Then Stereoscopic PIV was applied. This technique allows us to measure the full 3D velocity vector map in a whole fluid plane. This paper has a double purpose. Firstly, to visualize the 3D structures which are present in the burner; secondly, to show that Stereoscopic PIV is an applicable technique for the diagnosis of an evaporating spray.     

Velocity,temperature, and Reynolds-stress scaling in the wall region of turbulent boundary layer on a permeable surface

A finite total number of flow parameters in the wall region of a turbulent boundary layer points to universal behavior of turbulent shear stress as a function of mean-velocity gradient and turbulent heat flux as a function of both mean-velocity and mean-temperature gradients. Combined with dimensional arguments, this fact is used to reduce the momentum and heat equations to first-order ordinary differential equations for temperature and velocity profiles amenable to general analysis. Scaling laws for velocity and temperature in boundary layer flows with transpiration are obtained as generalizations of well-known logarithmic laws. Scaling relations are also established for shear stress and rms transverse velocity fluctuation. The proposed method has substantial advantages as compared to the classical approach (which does not rely on fluid-dynamics equations [1–3]). It can be applied to establish scaling laws for a broader class of near-wall turbulence problems without invoking closure hypotheses.     

Mean velocity behaviour in the near wake of long slender cylinder with a sharp trailing edge at a high Reynolds number

A simple eddy viscosity model is applied to the governing equations to establish the behaviour of the mean velocity in the turbulent axisymmetric near wake. The near wake develops from a long slender cylinder which is kept parallel to the flow and is developing under zero streamwise pressure gradient. The upstream turbulent boundary layer on the body of revolution is fully developed. In the inner layer of the flow downstream of the trailing edge, the turbulent inner layer of the upstream boundary layer grows into the initial logarithmic layer, and as a consequence, the centreline velocity in the near wake is shown to increase logarithmically with streamwise distances for large streamwise distances. The analysis further leads to two regions of the near wake flow (the inner near wake and the outer near wake), similar to that of a fully developed turbulent boundary layer, for which the governing equations have been derived. The matching between these two regions leads to a logarithmic variation in the normal direction. Also shown is the variation of the square of the wake width which varies logarithmically with streamwise distance in the near wake. These features are validated by comparison with available experimental data.     

旋转盘腔流场速度与压力的实验研究

本文描述一个旋转盘腔流场的实验研究。该盘腔由一个旋转盘，一个静止盘及静止的外围屏组成．实验表明在盘腔的两个盘面上都有边界层形成，在边界层中，流体除有切向速度外，还有沿径向的二次流存在。在边界层外的核心区中径向速度为零。一般来说，静盘边界层比转盘边界层向紊流转捩地要早。另外，压力的测量表明，在半径较大的区域中压力分布可由“流体以恒角速度旋转”的假设所得的结果近似。     

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method(OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fourier's law of heat conduction.     

Studying effect of MHD on thin films of a micropolar fluid

This paper deals with the study of the effect of MHD on thin films of a micropolar fluid. These thin films are considered for three different geometries, namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The transformed boundary layer governing equations of a micropolar fluid and the resulting system of coupled non-linear ordinary differential equations are solved numerically by using shooting method. Numerical results were presented for velocity and micro-rotation profiles within the boundary layer for different parameters of the problem including micropolar fluid parameters, magnetic field parameter, etc., which are also discussed numerically and illustrated graphically.