STUDY ON TURBULENT SPOTS IN PLANE COUETTE FLOW

Turbulent spots play a key role in the formation of the turbulence and the transition. The generation and evolution of turbulent spots using the wall impulse model in the plane Couette flow are studied by direct numerical simulation of Navier-Stokes equations. A group of three-dimensional coupling compact difference schemes with high accuracy and high resolution is used in the numerical calculation. The important characteristics of turbulent spots based on the results of examples are analyzed, including the formation of random pulse, the generation of Reynolds stress, the growth of disturbance amplitude, and the continuous change of spot shape, especially the complex evolution process of the streamwise vortices. Computational results confirm that basic properties of turbulent spots in the laminar flow are similar to those in the turbulent flow.

Thermal Influence of the Couette Flow in a Hydrostatic Spindle on the Machining Precision

Hydrostatic spindles are increasingly used in precision machine tools. Thermal error is the key factor affecting the machining accuracy of the spindle, and research has focused on spindle thermal errors through examination of the influence of the temperature distribution, thermal deformation and spindle mode. However, seldom has any research investigated the thermal effects of the associated Couette flow. To study the heat transfer mechanism in spindle systems, the criterion of the heat transfer direction according to the temperature distribution of the Couette flow at different temperatures is deduced. The method is able to deal accurately with the significant phenomena occurring at every place where thermal energy flowed in such a spindle system. The variation of the motion error induced by thermal effects on a machine work-table during machining is predicated by establishing the thermo-mechanical error model of the hydrostatic spindle for a high precision machine tool. The flow state and thermal behavior of a hydrostatic spindle is analyzed with the evaluated heat power and the coefficients of the convective heat transfer over outer surface of the spindle are calculated, and the thermal influence on the oil film stiffness is evaluated. Thermal drift of the spindle nose is measured with an inductance micrometer, the thermal deformation data 1.35 μm after running for 4 h is consistent with the value predicted by the finite element analysis’s simulated result 1.28 μm, and this demonstrates that the simulation method is feasible. The thermal effects on the processing accuracy from the flow characteristics of the fluid inside the spindle are analyzed for the first time.

Effects of the computational domain on the secondary flow in turbulent plane Couette flow

A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000（based on the relative wall speed and half the channel height h） with different streamwise and spanwise lengths are conducted to investigate the effects of the computational box sizes on the secondary flow（SF）. Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean flow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette flow is found, for the first time, within 4（1 ± 0.25）h despite the domain sizes.

Regular perturbation solution of Couette flow(non-Newtonian)between two parallel porous plates: a numerical analysis with irreversibility

The unavailability of wasted energy due to the irreversibility in the process is called the entropy generation.An irreversible process is a process in which the entropy of the system is increased.The second law of thermodynamics is used to define whether the given system is reversible or irreversible.Here,our focus is how to reduce the entropy of the system and maximize the capability of the system.There are many methods for maximizing the capacity of heat transport.The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy.The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel.For this,we choose two different fluid models,namely,the plane and generalized Couette flows.The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid.The present analysis shows the effects of the fluid parameters on the velocity,the temperature,the entropy generation,and the Bejan number.The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method.To validate the perturbation solution,a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0.The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters.It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number.Whenηi→0(i=1,2,3),the Eyring-Powell fluid is transformed into a Newtonian fluid.

Linear stability of plane creeping Couette flow for Burgers fluid

It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simpli- fied perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.

Determination of Slip Length in Couette Flow Based on an Analytical Simulation Incorporating Surface Interaction

An analytical simulation based on a new model incorporating surface interaction is conducted to study the slip phenomenon in the Couette flow at different scales. The velocity profile is calculated by taking account of the micro-force between molecules and macro-force from the viscous shearing effect, as they contribute to the achieve- ment of the slip length. The calculated results are compared with those obtained from the molecular dynamics simulation, showing an excellent agreement. Further, the effect of the shear rate on the slip is investigated. The results can well predict the fluid flow behaviors on a solid substrate, but has to be proved by experiment.

Radiation effect on temperature distribution in three-dimensional Couette flow with suction or injection

A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidat one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number, radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the.temperature distribution than the injection or radiation parameter.

Three dimensional free convection couette flow with transpiration cooling

Free convection flow between two vertical parallel plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion has been analyzed. Due to this type of injection velocity, the flow becomes three-dimensional. Analytical expressions for the velocity, temperature, skin friction and rate of heat transfer were obtained. The important characteristics of the problem, namely the skin friction and the rate of heat transfer are discussed in detail with the help of graphs.

Time-dependent MHD Couette flow of rotating fluid with Hall and ion-slip currents

The unsteady magnehydrodynamics （MHD） Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration. The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique. The unified closed-form expressions axe obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate. The effects of various parameters on the velocity and the skin friction axe discussed by graphs. The results reveal that the primary and secondary velocities increase with the Hall current. An increase in the ion-slip paxameter also leads to an increase in the primary velocity but a decrease in the secondary velocity. It is also shown that the combined effect of the rotation, Hall, and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.

Oscillatory Couette flow of rotating Sisko fluid

The oscillatory Couette flow of a magnetohydrodynamic （MHD） Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Three dimensional Couette flow and heat transfer through a porous medium with variable permeability

This paper reports research on the effects of variations in injectio n velocity and perm eability on the heat transfer and flow through a highly porous medium betwee n two horizontal parallel plates situated at constant distance with constant suc tion by the upper plate.Due to this type of variation in injection velocity and in permeability the flow becomes three dimensional.The governing equations are sol ved by adopting complex variable notations to obtain the expressions for the ve locity and temperature field. The skin-friction along the main flow direction and rate of heat transfer are discussed with the help of graphs.

3D couette flow of dusty fluid with transpiration cooling

The couette dusty flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the dusty fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion was analyzed. Due to this type of injection velocity the dusty flow becomes 3D. Perturbation method is used to obtain the expressions for the velocity and temperature fields of both the fluid and dust. It was found that the velocity profiles of both the fluid and dust in the main flow direction decrease with the increase of the mass concentration of the dust particles, and those in cross flow direction increase with an increase in the mass concentration of the dust particles up to the middle of the channel and thereafter decrease with increase in mass concentration of the dust particles. The skin friction components Tx and Tz in the main flow and transverse directions respectively increase with an increase in the mass concentration of the dust particles (or) injection parameter. The heat transfer coefficient decreases with the increase of the injection parameter and increases with the increase in the mass concentration of the dust particles.

Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case).

Irreversibility analysis of unsteady couette flow with variable viscosity

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.

Benchmark for scale-resolving simulation with curved walls: the Taylor Couette flow

Flow between rotating concentric cylinders,or the Taylor Couette flow,has been studied extensively because of its rich physics,ranging from axisymmetric steady laminar flow,to fully developed turbulent flow.In the present study,we advocate the use of this problem as a benchmark case for scale-resolving simulation,such as large eddy simulation(LES)and direct numerical simulation(DNS).The problem is attractive because of its simple geometry,simple boundary conditions,and complex physics involving wall-shear induced and centrifugal instability.Unlike the wellknown fully developed channel flow,this problem has a curved wall boundary,and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow.A p-refinement study for Re=4000 is performed first to establish DNS data,including the time history of enstrophy,which can be used as an accuracy and resolution indicator to evaluate numerical methods,and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution quality.Finally,an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

Computer Experiments on Rapidly Rotating Plane Couette Flow

The turbulence in plane Couette flow subjected to system rotation is investigated. The anti-cyclonic rotation rate is well above the range in which roll-cells occurand close to the upper bound, beyond which no stationary turbulent states of motionexist. The mean velocity profile exhibits a linear region over 80% of the cross-section, inwhich the mean absolute vorticity is driven to zero. Viscous effects still prevail in narrow regions next to the walls, whereas the quasi-homogeneous central core exhibitsabnormal anisotropies of the Reynolds stress tensor, the vorticity tensor and the energy dissipation rate tensor. In spite of the distinctly higher turbulence level observed,a 13% drag reduction is found. This paradoxical finding is ascribed to configurationalchanges in the turbulence field brought about by the system rotation.

Numerical study of multiple periodic flow states in spherical Couette flow

The supercritical flow states of the spherical Couette flow between two concentric spheres with the inner sphere rotating are investigated via direct numerical simulation using a three-dimensional finite difference method.For comparison with experiments of Nakabayashi et al.And Wimmer,a narrow gap and a medium gap with clearance ratioβ=0.06 and 0.18 respectively areconsidered for the Reynolds number range covering the first Hopfbifurcation point.With adequate initial conditions and temporaryimposition of small wave-type perturbation,multiple periodicflow states with three different pair numbers of spiralTaylor-Gortler(TG)vortices have been simulated successfullyforβ=0.06,of which the 1-pair and 2-pair of spiral Tgvortices are newly obtained.Three different periodic flow stateswith shear waves,Stuart vortices or wavy outflow boundary,have been obtained forβ=0.18.Analysis of the numerical resultsreveals these higher flow modes in terms of fundamental frequency,wave number and spatial structure.

Slip in Couette flow with pressure gradient:Theoretical and experimental investigation of hydrodynamic characteristics considering slip effect

A new slip velocity model based on molecular potential theory and macro-force analysis,which is applied in Couette flow with pressure gradient,is built up.The model is validated by later being introduced in hydrodynamic system to predict film distribution,which shows a good agreement with experimental data obtained from multi-beam intensity-based tests with Fe and Cu ball materials under accurate controlled temperature,load and different wall velocities.Results show that the slip length for Fe case is ignorable so it seems like no slip,but for Cu case,the slip length is large to make 20%discrepancy with no slip simulation and also behaves shear-dependently.Moreover,during the experimental cases when both Fe and Cu ball velocities rise from-133 mm/s to 1330 mm/s,the slip velocity changes its direction with entrainment velocity and thus contributes to first enhance and then diminish the hydrodynamic film,but due to slip length on Cu case varying largely than that on Fe case,the film from Cu case and from Fe case has a clear cross-point between uh=80 mm/s and uh=220 m m/s(ub is the ball speed).The results above support strongly that Cu surface will lead to stronger slip than Fe case because of its smaller solid-liquid interaction,and obviously slip will influence hydrodynamic characteristics prominently.

Unsteady Hydromagnetic Couette Flow within Porous plates in a Rotating System

Unsteady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system is studied when the fluid flow within the channel is induced due to the impulsive movement of the one of the plates of the channel.The plates of the channel are considered porous and the magnetic field is fixed relative to the moving plate.Exact solution of the governing equations is obtained by Laplace transform technique.The expression for the shear stress at the moving plate is also obtained.Asymptotic behaviour of the solution is analyzed for small as well as large values of time t to highlight the transient approach to the final steady state flow and the effects of rotation,magnetic field and suction/injection.It is found that suction has retarding influence on the primary as well as secondary flow where as injection and time have accelerating influence on the primary and secondary flows.