Kutta-Joukowski force expression for viscous flow

The Kutta Joukowski(KJ) theorem, relating the lift of an airfoil to circulation, was widely accepted for predicting the lift of viscous high Reynolds number flow without separation. However, this theorem was only proved for inviscid flow and it is thus of academic importance to see whether there is a viscous equivalent of this theorem. For lower Reynolds number flow around objects of small size, it is difficult to measure the lift force directly and it is thus convenient to measure the velocity flow field solely and then, if possible, relate the lift to the circulation in a similar way as for the inviscid KJ theorem. The purpose of this paper is to discuss the relevant conditions under which a viscous equivalent of the KJ theorem exists that reduces to the inviscid KJ theorem for high Reynolds number viscous flow and remains correct for low Reynolds number steady flow. It has been shown that if the lift is expressed as a linear function of the circulation as in the classical KJ theorem, then the freestream velocity must be corrected by a component called mean deficit velocity resulting from the wake. This correction is small only when the Reynolds number is relatively large. Moreover, the circulation, defined along a loop containing the boundary layer and a part of the wake, is generally smaller than that based on inviscid flow assumption. For unsteady viscous flow, there is an inevitable additional correction due to unsteadiness.     

Response of force behaviors of a spherical particle to an oscillating flow

Combined multi-direct forcing technique and the immersed boundary method is applied to investigate the response of force behaviors of a fixed spherical particle to an oscillating flow. The influences of the inlet oscillating flow at a mean Reynolds number of 300 with six different oscillating frequencies and three oscillating amplitudes are investigated. Three different zones with different behaviors are identified and the specific behaviors of the drag and the lift coefficients are analyzed. The averaged drag coefficient and the maximum lift force exerted on the particle increase with the increment of the oscillating Reynolds number or the oscillating amplitude. When the frequency of the inlet flow is equal to the natural vortex shedding frequency, the average drag coefficient reaches the maximum value. A linear relation between the gradient of the maximum lift coefficient and the frequency as well as the amplitude of the inlet oscillating flow is observed in certain regime.     

Hydrodynamic binary coalescence of droplets under air flow in a hydrophobic microchannel

Based on the volume of fluid(VOF) method, we conduct a numerical simulation to study the hydrodynamic binary coalescence of droplets under air flow in a hydrophobic rectangular microchannel. Two distinct regimes, coalescence followed by sliding motion and that followed by detaching motion, are identified and discussed. Additionally, the detailed hydrodynamic information behind the binary coalescence is provided, based on which a dynamic mechanical analysis is conducted to reveal the hydrodynamic mechanisms underlying these two regimes. The simulation results indicate that the sliding motion of droplets is driven by the drag force and restrained by the adhesion force induced by the interfacial tension along the main flow direction. The detachment(i.e., upward motion) of the droplet is driven by the lift force associated with an aerodynamic lifting pressure difference imposed on the coalescent droplet, and also restrained by the adhesion force perpendicular to the main flow direction. Especially, the lift force is mainly induced by an aerodynamic lifting pressure difference imposed on the coalescent droplet. Two typical regimes can be quantitatively recognized by a regime diagram depending on Re and We. The higher Re and We respectively lead to relatively larger lift forces and smaller adhesion forces acting on the droplet, both of which are helpful to detachment of the coalesced droplet.     

基于转捩SST模型凸起圆柱绕流数值研究

为了研究局部凸起对边界层转捩的影响,采用转捩SST模型分别对亚临界、临界和超临界状态下带突起的圆柱绕流问题进行了数值模拟,分析了不同Reynolds数下带突起的圆柱绕流问题的近壁面流动特征以及表面时均压力与摩擦力系数的分布和凸起对圆柱表面流动分离以及转捩的影响,对比了有无凸起两侧圆柱表面时均压力、摩擦力系数的不同. 结果表明:当来流Reynolds数处于临界区时,气流在圆柱上表面凸起处形成了3个反向旋转的漩涡,之后随着θ的增大,发生了流动分离和流动转捩现象;对于不同Reynolds数下的来流,圆柱上表面的凸起可以使气流发生转捩的位置提前;圆柱上表面的凸起使流速增大、压强降低,从而导致圆柱产生升力,随着来流Reynolds数的增大,其升力逐渐变大.      

Flow visualization and aerodynamic-force measurement of a dragonfly-type model

An unsteady flow visualization and force measurement were carried out in order to investigate the effects of the reduced frequency of a dragonfly-type model. The flow visualization of the wing wake region was conducted by using a smoke-wire technique. An electronic device was mounted below the test section in order to find the exact position angle of the wing for the visualization. A load-cell was employed in measuring aerodynamic forces generated by a plunging motion of the experimental model. To find the period of the flapping motion in real time, trigger signals were also collected by passing laser beam signals through the gear hole. Experimental conditions were as follows: the incidence angles of the foreand hind-wing were 0° and 10°, respectively, and the reduced frequencies were 0.150 and 0.225. The freestream velocities of the flow visualization and force measurement were 1.0 and 1.6m/sec, respectively, which correspond to Reynolds numbers of 3.4 × 10³ and 2.9 × 10³. The variations of the flow patterns and phase-averaged lift and the thrust coefficients during one cycle of the wing motion were presented. Results showed that the reduced frequency was closely related to the flow pattern that determined flight efficiency, and the maximum lift coefficient and lift coefficient per unit of time increased with reduced frequency.     

Deriving forces from 2D velocity field measurements

We discuss how to derive a force or a force density from a measured velocity field. The first part focuses on the integral force a fluid exerts on a body, e.g. lift and drag on an airfoil. Obtaining the correct pressure is crucial; however, it cannot be measured within the flow non-intrusively. Using numerical and experimental test cases, we compare the accuracy achievable with three methods: pressure reconstruction from velocity fields via (1) the differential momentum equation, or (2) the Poisson equation, furthermore, (3) Noca’s momentum equation [Noca, JFS 13(5), 1999], which does not require pressure explicitly. The latter gives the best results for the lift, whereas the first or second approach should be used for the drag. The second part deals with obtaining the distribution of a body force density generated by an actuator. Using a stream function ansatz, we obtain a Laplace equation that allows us to compute the solenoidal part of the force distribution; however, the irrotational part is lost. Furthermore, the wall pressure must be known. We validate this approach using numerical data from a wall jet flow in a rectangular box, driven by a fictitious, solenoidal body force. Reconstructing the force distribution yields an error of less than 10^?2 for most of the domain.     

电磁力控制湍流边界层分离圆柱绕流场特性数值分析

在亚临界区高雷诺数Re=1.4×105下,采用脱体涡模拟结合湍流分离的方法对弱电解质中电磁力作用下湍流边界层分离圆柱绕流场及其升(阻)力特性进行了数值模拟和分析.结果表明,电磁力可以提高圆柱体湍流边界层内的流体动能,延缓圆柱体湍流边界层的流动分离,减弱圆柱体湍流绕流场中在流向和展向上大尺度漩涡的强度,减小圆柱体阻力时均值及其升力脉动幅值.当电磁力作用参数大于某个临界值后,湍流边界层流动分离消失,在圆柱体尾部产生射流现象,从而电磁力对圆柱体产生净推力作用,出现负阻力现象,而且升力脉动幅值接近于零,出现圆柱体升力消失现象.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Thermophoresis-Assisted Microscale Magnus Effect in Optical Traps

The Magnus effect, commonly observed on the macroscale, has been considered to be negligible at the microfluidic limit. However, the thermophoretic effect at the microscale leads to a strong lift force that acts on the optically trapped and heated microparticles rotating in a liquid flow. This thermophoresis-assisted Magnus effect is experimentally observed and explained through the inhomogeneity of temperature distribution in the flow around the absorbing microparticles rotated by magnetic forces within the limit of ultralow Reynolds numbers.

     

Visualization of flapping wing of the drone beetle

Investigation of flapping wings of insect are focused on low Reynolds number effect and the unsteady aerodynamic properties. Interaction between flapping wing of insects and the air flow became one of important and fundamental research topics in micro air vehicle. The present work is aim to investigate the flow behavior of flapping wings of tethered scarab beetle. The generation mechanisms of velocity field and vortex formation are visualized with smoke-wire method. Tethered flight of the drone beetle shows the motion with elastic deformation of flapping wing. Measured flapping frequency is about 71 Hz and its frequency is higher than for dragonfly and butterfly. Beetle decreases negative lift by feathering motion in the upstroke process and increase positive lift by effect of wake capture in the downstroke process.     

Investigation on the drives of the poloidal flow in the ohmic and biased electrode experiments

The experimental investigation on the drives of the poloidal flow in KT-5 D tokamak are presented. It is found that the poloidal flow is the main contributor to the radial electric field, and the Reynolds stress can drive significant poloidal flows in ohmic discharges. The investigation on the relationship between the radial gradient of Reynolds stress and the poloidal flow in biasing discharges indicates that not only Reynolds stress but also the Lorentz's force can drive the poloidal flow.     

Similarity solutions of the Navier-Stokes equations for an injection-driven flow between two orthogonally moving porous discs

An incompressible fluid is in motion after injection in the space between two parallel porous discs that can move away or come closer along the same axis passing perpendicular to the midpoints of their respective surfaces. The desire of well describing the incompressible fluid flow patterns and the fact that the velocity field of the axisymmetric flow has two components lead to introduce the stream function in the governing equations. A similarity method is applied to transform the vorticity equation satisfied by the stream function into a nonlinear ordinary differential equation. Thus, the analysis is restricted to solving a two-point boundary-value problem containing two control parameters, notably the Reynolds number and a nondimensional parameter representing the measure of the increase or the decrease in volume of the flow domain. Among the main results, it is found that, the high expansion in volume of the flow domain causes flow reversal for low values of the injection Reynolds number, while the contraction in volume of the flow domain creates a linear behavior of the axial velocity for a small injection Reynolds number and a flattening of the radial velocity profile for all the Reynolds numbers.     

Aerodynamic and energy-efficiency-based assessment of plasma actuator's position on a NACA0015 airfoil

In recent years, there has been an increase in the number of research papers on plasma and its use in active flow control applications. The main objective of this study is to assess the plasma actuator's position on a NACA0015 airfoil in terms of aerodynamic forces. In addition, optimization of the plasma actuator's position and its configuration are studied in order to identify the optimum configuration for improvement in lift coefficient. The experiments are conducted in an open-suction-type wind tunnel at Reynolds numbers of 48,000, 75,000, and 100,000. The plasma actuators are mounted on various positions (x/C) starting from the leading edge to trailing edge of the airfoil. The experimental results on aerodynamic force measurement are presented to illustrate the increasing lift effect of the generated plasma. It is also shown that the plasma actuators used as an active flow control device appears to shift the stall angle of the airfoil. The results of the experimental study suggest that the energy efficiency of airborne systems can be improved with the use of plasma actuators due to its increasing lift coefficient effect. This result becomes a vital finding considering that the same flight can be achieved with less fuel and less amount of environmental pollution for the same distance of journey. It is also worth mentioning that increasing lift effect would mean taking off from a shorter runway or allowing the airborne vehicle with the ability to fly with additional payload.     

Azimuthal distributions of radial momentum and velocity in relativistic heavy ion collisions

Azimuthal distributions of radial (transverse) momentum, mean radial momentum, and mean radial velocity of final-state particles are suggested for relativistic heavy ion collisions. Using the AMPT transport model with string melting, the distributions of Au+Au collisions at 200 GeV are presented and studied. It is demonstrated that the distribution of total radial momentum is more sensitive to the anisotropic expansion, as the anisotropies of final-state particles and their associated transverse momentums are both counted in the measurement. The mean radial velocity distribution is compared with the radial flow velocity. The thermal motion contributes an isotropic constant to the mean radial velocity.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dlmensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling fit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic depinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

On the variable order dynamics of the nonlinear wake caused by a sedimenting particle

In this work we develop a variable order (VO) differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid. In particular, we examine the various force terms in the equation of motion and propose a new form for the history drag acting on the particle. We show that the variable order formulation allows for an effective way to express the dynamic transition of the dominant forces over the entire time of the motion of the particle from rest to terminal velocity. The use of VO operators also allows us to examine the evolving dynamics of the wake during sedimentation. Using numerical data from a finite element simulation of a sedimenting particle, we first solve for the order of the derivative that returns the correct decay of the history force. We then propose a relatively simple expression for the history force that is a function of the Reynolds number and particle-to-fluid density ratio. The new history drag expression correlates very well (R²>0.99) with the numerical data for terminal Reynolds numbers ranging from 2.5 to 20, and for particle-to-fluid density ratios of interest in practice (1<β<10).     

Flow pattern and lift evolution of hydrofoil with control of electro-magnetic forces

The initial responses and evolutions of the flow pattern and lift coefficient of a hydrofoil under the action of electro-magnetic (Lorentz) force have been studied experimentally and numerically, and trace particle methods are employed for them. With the introduction of BVF (boundary vortex flux), the quantitative relation among Lorentz forces, BVF and lifts is deduced. The influences of flow patterns on the hydrofoil lift coefficient have been discussed based on the BVF distribution, and the flow control mechanism of Lorentz force for a hydrofoil has been elucidated. Our results show that the flow pattern and lift of the hydrofoil vary periodically without any force. However, with the action of streamwise Lorentz forces, the separation point on the hydrofoil surface moves backward with a certain velocity, which makes the flow field steady finally. The streamwise Lorentz force raises the foil lift due to the increase of BVF intensity. On the other hand, Lorentz force also increases the hydrofoil surface pressure, which makes the lift decrease. However, the factor leading to the lift enhancement is determinant, therefore, the Lorentz force on the suction side can increase the lift, and the stronger the Lorentz force, the larger the lift enhancement. Our results also show that the localized Lorentz force can also both suppress the flow separation and increase the hydrofoil lift coefficient, furthermore, the Lorentz force located on the tail acts better than that located on the front.     

垂直管内油水两相流局部相分布特性实验研究

应用双头电导探针测量系统,对垂直上升管内油水两相分散流局部相分布特性进行了系统测量。得到了油水两相分散流的局部含油率分布类型图。研究结果表明低折算水速和低折算油速条件下,局部含油率在实验段截面上呈抛物线型局部分布特征,局部最大值出现在实验段中心区域。随折算油速增大,油滴受到横向力如升力的作用,逐渐向实验段壁面区域迁移,形成局部含油率的壁面峰值分布特性。当折算水速大于0．8 m／s时,局部含油率在实验段截面上呈均匀分布。     

纤维悬浮湍流的方程和解及其在管流中的应用

推导了纤维悬浮流的平均运动方程和纤维平均取向角的概率密度函数方程，提出了计算纤维平均取向角分布和悬浮流平均量与脉动量关联函数的逐级迭代方法。将推导的方程和提出的方法用于纤维悬浮管流场的计算并进行了相应的实验，计算和实验结果吻合很好。研究结果表明，在相同的压力降下，与没有纤维的牛顿流相比，纤维悬浮流具有较大的流量，因而纤维在流场中起着减阻的作用，减阻的量随着纤维浓度的增加而增大。在相同情况下，纤维悬浮流的相对湍流强度和雷诺应力比牛顿流小，这说明纤维能够抑制湍流，抑制的量与纤维的质量浓度成正比。