Turbulence in plane Couette flow

Experimental results for fully developed turbulent plane Couette flow are reported and compared to earlier experimental and numerical results. In addition some turbulent statistics not previously reported are shown.     

Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady Couette flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field are applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.     

Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation

Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying turbulent flow simulation. We determined that a decrease in the number of velocities, in particular, 13-velocities, which can be used in the quasi-equilibrium lattice Boltzmann and in the multiple-relaxation time models (MRT), could considerably decrease the computational effort. However, decreasing the number of velocities deteriorates the stability and the accuracy of the results. By comparing the collision models, we also determined that the stability of the entropic lattice Boltzmann model (ELBM), and 19- and 27- velocity MRT is much higher than in other models. However, the numerical viscosity introduced by the ELBM underestimates the enstrophy, and the computational effort increases because of the calculation overhead required to solve the additional equations if special care is not given to the calculation.     

Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases

In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. The first-order approximation of slip velocity at the boundaries is used in the formulation. The solution is also applicable for Couette flow in micro-channels under certain circumstances. The influences of mass transfer and a nondimensional slip parameter on slip velocities are discussed. It is also found that the transient slip velocities at the walls are greatly different from the steady-state velocity slips. The influences of velocity slip and temperature slip parameters on the temperature distribution and heat transfer at the walls are analyzed and discussed. It is shown that the slip parameters can greatly change the temperature profiles and heat transfer characteristics at the walls.     

Particle tracking in Taylor–Couette flow

The paths of small inertial particles are computed in a steady Taylor vortex background flow. When buoyancy effects are neglected we find that particles denser than the background fluid tend to a limit orbit in the meridional plane. The difference in settling time and orbit size, with varying Reynolds number of the background flow, is investigated. We also consider the effect of the various forces on the limit orbit of the particle.     

Spots and turbulent domains in a model of transitional plane Couette flow

A review of the globally subcritical transition to turbulence in shear flows is presented, with an emphasis on the cases of plane and circular Couette flows (pCf and cCf, respectively). A Swift–Hohenberg-like model is next proposed to interpret the behavior of plane Couette flow in the vicinity of its global stability threshold. We present results of numerical simulations supporting this proposal and helping us to raise good questions about the growth and decay of intermittent turbulent domains in this precise context, and more generally about the coexistence of laminar flow and turbulence in other spatio-temporally intermittent flows. PACS 47.27.-i, 47.54.-r, 05.45.-a     

Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

The Couette flow of binary gaseous mixtures is studied on the basis of the McCormack model of the Boltzmann equation, which was solved numerically by the discrete velocity method. The calculations were carried out for three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. The stress tensor and bulk velocity of both species were calculated for several values of the gas rarefaction in the range from 0.01 to 40 for three values of the molar concentrations: 0.1,0.5 and 0.9. The numerical solution together with an analytical solution based on the slip boundary condition cover the whole range of the gas rarefaction. It was showed that the Couette flow is weakly affected by the intermolecular interaction law.     

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 are 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 are discussed by graphs.The results reveal that the primary and secondary velocities increase with the Hall current.An increase in the ion-slip parameter 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.     

From global to local bifurcations in a forced Taylor–Couette flow

The unfolding due to imperfections of a gluing bifurcation occurring in a periodically forced Taylor–Couette system is analyzed numerically. In the absence of imperfections, a temporal glide-reflection Z₂ symmetry exists, and two global bifurcations occur within a small region of parameter space: a heteroclinic bifurcation between two saddle two-tori and a gluing bifurcation of three-tori. As the imperfection parameter increase, these two global bifurcations collide, and all the global bifurcations become local (fold and Hopf bifurcations). This severely restricts the range of validity of the theoretical picture in the neighborhood of the gluing bifurcation considered, and has significant implications for the interpretation of experimental results. PACS 47.20.Ky, 47.20.Lz, 47.20.Ft     

Three-dimensional analysis of the flow in the cyclones

Sincethecycloneisextensivelyusedinindustry,themechanismofitsstreamhasbeeninvestigatedandanalysed.Buttheprocessofthepreviousdiscussionstaysattheleveloftwo-dimensionedmodelanalysis,withtheaddedconsiderationabouttheaxialIysymmetry.lntheseyears,somespecialistshavediscusseditinthelightofthetotalthree-dimensionview.Thispapertriestogivesystematicanddetai]edexp1anationsandtopresentacorrectresultofRef[1].I.GeneralEquationEstablishedFirstweestablishmathematicalexpressionofflowinthecyclone.Wecanimaget…     

Velocity and temperature dissimilarity in fully developed turbulent channel and plane Couette flows

The natural dissimilarity or decorrelation of stream-wise velocity and temperature fluctuations in fully developed turbulent channel and plane Couette flows was studied using direct numerical simulation (DNS). For both of the flow configurations, a Reynolds number of about 150 was used based on the friction velocity and half the distance between walls. Buoyancy effects were neglected, and only results with a molecular Prandtl number, Pr, equal to 1 are presented. The boundary conditions for the thermal field were a uniform source of energy in the domain and isothermal wall temperature for the channel and Couette flow, respectively. The importance of those events responsible for wall-normal turbulent fluxes in the generation of axial velocity and temperature dissimilarity was examined using conditional probability. It was found that the dissimilarity in the whole domain was higher in Couette than in channel flow. It was also found that for wall-normal turbulent fluxes (momentum and heat), the averaged dissimilarity in the whole domain was slightly more correlated with those events in the second or fourth quadrant, according to the quadrant analysis technique. For channel flow, the importance of both kinds of events was similar, while for Couette flow there was a predominance in the generation of dissimilarity by those events in the fourth quadrant. Also, for both flow configurations and throughout the wall-normal direction, it was found that in the buffer region there was a predominance of events in the fourth quadrant associated with dissimilarity for both wall-normal turbulent fluxes. In the frequency domain, the distribution of energy showed that there was a high-frequency shift experienced from the wall towards the centerline by the temperature spectrum with regards to the axial velocity spectrum, for which the action of the fluctuations of the wall-normal velocity was the main cause. In the central region of the flow, on the other hand, there was a global convergence of all spectra towards the pressure spectrum, with this convergence lower for Couette flow. Finally, it is shown that the dissimilarity in developed conditions is caused by the greater correlation existing for the temperature fluctuation with the instantaneous axial pressure gradient than for the velocity fluctuation with the instantaneous axial pressure gradient.     

A three-dimensional fictitious domain method for incompressible fluid flow problems

A new Galerkin finite element method for the solution of the Navier–Stokes equations in enclosures containing internal parts which may be moving is presented. Dubbed the virtual finite element method, it is based upon optimization techniques and belongs to the class of fictitious domain methods. Only one volumetric mesh representing the enclosure without its internal parts needs to be generated. These are rather discretized using control points on which kinematic constraints are enforced and introduced into the mathematical formulation by means of Lagrange multipliers. Consequently, the meshing of the computational domain is much easier than with classical finite element approaches. First, the methodology will be presented in detail. It will then be validated in the case of the two-dimensional Couette cylinder problem for which an analytical solution is available. Finally, the three-dimensional fluid flow inside a mechanically agitated vessel will be investigated. The accuracy of the numerical results will be assessed through a comparison with experimental data and results obtained with a standard finite element method. © 1997 John Wiley & Sons, Ltd.     

Spectral methods for the viscoelastic time-dependent flow equations with applications to Taylor–Couette flow

The time evolution of finite amplitude axisymmetric perturbations (Taylor cells) to the purely azimuthal, viscoelastic, cylindrical Couette flow was numerically simulated. Two time integration numerical methods were developed, both based on a pseudospectral spatial approximation of the variables, efficiently implemented using fast Poisson solvers and optimal filtering routines. The first method, applicable for finite Re numbers, is based on a time-splitting integration with the divergence-free condition enforced through an influence matrix technique. The second one, is based on a semi-implicit time integration of the constitutive equation with both the continuity and the momentum equations enforced as constraints. Stability results for an upper convected Maxwell fluid were obtained for the supercritical bifurcations, either steady or time-periodic, developed after the onset of instabilities in the primary flow. At small elasticity values, ? ≡ De/Re, the time integration of finite amplitude disturbances confirms the stability of the single branch of steady Taylor cells. At intermediate ? values the rotating wave family of time-periodic solutions developed at the onset of instability is stable, whereas the standing wave is found to be unstable. At high ? values, and in particular for the limit of creeping flow (? = ∞), the present study shows that the rotating wave family is unstable and the standing (radial) wave is stable, in agreement with previous finite-element investigations. It is thus shown that spectral techniques provide a robust and computationally efficient method for the simulation of complex, non-linear, time-dependent viscoelastic flows.     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.     

Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid

An analysis is made of the steady flow of a non-Newtonian fluid past an infinite porous flat plate subject to suction or blowing. The incompressible fluid obeys Ostwald-de Waele power-law model. It is shown that steady solutions for velocity distribution exist only for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 0<n<1 provided that there is suction at the plate. Velocity at a point is found to increase with increase in n. No steady solution for velocity distribution exists when there is blowing at the plate. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subject to uniform suction reveals that temperature at a given point near the plate increases with n but further away, temperature decreases with increase in n. A novel result of the analysis is that both the skin-friction and the heat flux at the plate are independent of n.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions

Stokes and Couette flows produced by an oscillatory motion of a wall are analyzed under conditions where the no-slip assumption between the wall and the fluid is no longer valid. The motion of the wall is assumed to have a generic sinusoidal behavior. The exact solutions include both steady periodic and transient velocity profiles. It is found that slip conditions between the wall and the fluid produces lower amplitudes of oscillations in the flow near the oscillating wall than when no-slip assumption is utilized. Further, the relative velocity between the fluid layer at the wall and the speed of the wall is found to overshoot at a specific oscillating slip parameter or vibrational Reynolds number at certain times. In addition, it is found that wall slip reduces the transient velocity for Stokes flow while minimum transient effects for Couette flow is achieved only for large and small values of the wall slip coefficient and the gap thickness, respectively. The time needed to reach to steady periodic Stokes flow due to sine oscillations is greater than that for cosine oscillations with both wall slip and no-slip conditions.