On laminar two-phase flows in magnetohydrodynamics

We consider the Hartmann flow of a conducting fluid in the channel between two horizontal insulating plates of infinite extent, there being a layer of non-conducting fluid between the conducting liquid and the upper channel wall. A suitable volumetric flow-rate factor is defined, and it is shown that significant increases can be obtained in the flow-rate of the conducting fluid for suitable ratios of the depths and viscosities of the two fluids.     

Concerning inviscid solutions for large-scale separated flows

Summary The large-scale separated eddies set up behind a bluff body at high Reynolds number are considered, for steady laminar planar flow. The main eddies are massive and are controlled predominantly by inviscid mechanics, with uniform vorticity inside. Analytical and computational solutions of the massive-eddy (vortex-sheet) problem are then described. A further possibility studied is that, even with lateral symmetry assumed, there may still be an extra degree of nonsymmetry of skewing with respect to the streamwise direction. Small-scale separations, where a Benjamin-Ono equation also possibly yielding nonsymmetric solutions can come into play, are discussed briefly.     

The Oseen model for internal separated flows

Summary The flow field studied in this paper is the viscous laminar, separated flow downstream of a sudden expansion in a two-dimensional duct. The flow is modelled by the Oseen equations and a solution is sought for the downstream flow given the conditions at the sudden expansion. First, the exact solution to a high-Reynolds-number limit equation suggested by Kumar and Yajnik [6] is obtained. Next, the solution to the full equations is sought in terms of an eigenfunction-expansion procedure which leads to a non-standard eigenvalue problem. A detailed study is made of the latter and a number of expansion procedures are considered for the boundary-value problem. Specific calculations of the separated flow are presented for Reynolds numbers R=10 ⁿ , n=0–5. It is found that as R the solution of the full equation does indeed agree with the solution of the high-Reynolds-number limit equation. In particular it is found that the length of the recirculating region x _r scales with R as R.     

An Oseen-type model for swirling internal separated flows

The viscous, laminar, separated flow downstream of a sudden expansion in a pipe is studied. The flow is modeled by an Oseen-type equation, but with the additional feature that the nonlinearity in the swirl is retained. Exact solutions are obtained for a high-Reynolds-number limit and for arbitrary Reynolds number by use of an eigenfunction-expansion procedure, in the presence of swirl. This leads to a non-standard eigenvalue problem. When the swirl is sufficiently large, a central recirculating region is observed. The effect of the pressure gradients on the velocity profiles and the central recirculating eddy is discussed. The low-Reynolds-number solutions go over smoothly to the large Reynolds number solution as the Reynolds number increases. Good agreement is obtained with the numerically computed value of the reattachment length.     

Mathematical simulation of heat- and mass-transfer processes in separated flows with a laminar mixing region at low reynolds numbers

The lower limit of applicability of the mathematical model of heat and mass transfer constructed by Batchelor and Lavrent'ev for separated flow past a bottom trench is extended.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 5, pp. 847–855, May, 1977.     

On the asymptotics of the fluid flow past an array of fixed obstacles

It is known that the asymptotics of slow fluid flow past an array of fixed obstacles is described in several situations by Brinkman's law or Darcy's law (with or without interaction between different obstacles). We show that there exists a continuous transition between the asymptotic structures corresponding to the different situations. Consequently, the asymptotic structure for concentrations of particles 0(1) gives by a limit process the asymptotic schemes for small concentration. Some results of existence, uniqueness and symmetry of the translation tensor are given for flow in 2 dimensions.     

A finite difference calculation procedure for three-dimensional turbulent separated flows

A general finite difference scheme has been proposed along with a three-dimensional co-ordinate transformation procedure for the prediction of three-dimensional fully elliptic flows. This numerical scheme has been successfully employed for the calculations of the three-dimensional turbulent separated flow in a rectangular diffuser. The complexity of the phenomena is seen to increase tremendously for the three-dimensional flows of this class.     

The Navier-Stokes solution for laminar flow past a semi-infinite flat plate

Summary A numerical solution joining Carrier and Lin's solution near the leading edge to the boundary layer solution at large distance of the leading edge is presented. The solution is valid for any Reynolds number. Results are given for the skin friction, the integrated skin friction, the displacement thickness, the pressure along the plate and the velocity ahead of the plate. The asymptotic value of the integrated skin friction agrees very well with the exact value. The displacement thickness is already different from zero for small distances ahead of the plate.     

Method and automated equipment for investigation of the thermophysical properties of liquid laminar polymer flows

Translated from Izmeritel'naya Tekhnika, No. 11, pp. 37–39, November, 1992.     

Three-dimensional full Navier–Stokes solvers for incompressible flows past arbitrary geometries

The computation of the three-dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds-Averaged Navier-Stokes Equations written in a non-orthogonal curvilinear body-fitted co-ordinate system. Results of the computation are compared with available experiments.     

Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate

Laminar free convection boundary layer flow of a thermomicropolar fluid past a non-isothermal vertical flat plate has been studied in detail. It has been established that the flow problem has similarity solutions when the variation in the temperature of the plate is a linear function of the distance from the leading edge measured along the plate. The resulting system of the nonlinear ordinary differential equations has been solved numerically by “Shooting Method” for various values of the material parameters. The effects of these parameters has been studied on the velocity and microrotation fields graphically. Also “Tables” have been given for the values of temperature, skin-friction parameter, microrotation gradient on the wall and Nusselt number. Two types of boundary conditions are prescribed for the microrotation on the wall.     

Vortex shedding suppression for laminar flow past a square cylinder near a plane wall: a two-dimensional analysis

Summary A numerical study on the uniform shear flow past a long cylinder of square cross-section placed parallel to a plane wall has been made. The cylinder is considered to be within the boundary layer of the wall. The maximum gap between the plane wall to the cylinder is taken to be 0.25 times the cylinder height. We investigated the flow when the regular vortex shedding from the cylinder is suppressed. The governing unsteady Navier-Stokes equations are discretized through the finite volume method on staggered grid system. A pressure correction based iterative algorithm, SIMPLER, has been used to compute the discretised equations iteratively. We found that the critical value of the gap height for which vortex shedding is suppressed depends on the Reynolds number, which is based on the height of the cylinder and the incident stream at the surface of the cylinder. At high Reynolds number (Re ≥ 500) however, a single row of negative vortices occurs for wall to cylinder gap height L ≥ 0.2. The shear layer that emerges from the bottom face of the cylinder reattaches to the cylinder itself at this gap hight.     

The use of the hybrid RANS/ILES approach for the investigation of three-dimensional separated turbulent flows in curvilinear diffusers

The hybrid RANS/ILES approach is used for the investigation of turbulent separated flow in curvilinear annular diffusers with the area ratio of 2.04 and 2.7. The effect of geometry on the loss of symmetry of flow in an axisymmetric annular diffuser is considered. The effect of pressure difference in the diffuser on the flow and on the characteristics of turbulence in this diffuser is investigated. The effect of nonuniform total pressure at the channel inlet on the distribution of parameters in the outlet section of the diffuser is determined. The loss of total pressure in diffusers is determined for all of the considered modes. The accuracy of the results is confirmed by comparison with the experimental data available for these diffusers.     

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

In this paper, a novel characteristic–based penalty (CBP) scheme for the finite‐element method (FEM) is proposed to solve 2‐dimensional incompressible laminar flow. This new CBP scheme employs the characteristic‐Galerkin method to stabilize the convective oscillation. To mitigate the incompressible constraint, the selective reduced integration (SRI) and the recently proposed selective node–based smoothed FEM (SNS‐FEM) are used for the 4‐node quadrilateral element (CBP‐Q4SRI) and the 3‐node triangular element (CBP‐T3SNS), respectively. Meanwhile, the reduced integration (RI) for Q4 element (CBP‐Q4RI) and NS‐FEM for T3 element (CBP‐T3NS) with CBP scheme are also investigated. The quasi‐implicit CBP scheme is applied to allow a large time step for sufficient large penalty parameters. Due to the absences of pressure degree of freedoms, the quasi‐implicit CBP‐FEM has higher efficiency than quasi‐implicit CBS‐FEM. In this paper, the CBP‐Q4SRI has been verified and validated with high accuracy, stability, and fast convergence. Unexpectedly, CBP‐Q4RI is of no instability, high accuracy, and even slightly faster convergence than CBP‐Q4SRI. For unstructured T3 elements, CBP‐T3SNS also shows high accuracy and good convergence but with pressure oscillation using a large penalty parameter; CBP‐T3NS produces oscillated wrong velocity and pressure results. In addition, the applicable ranges of penalty parameter for different proposed methods have been investigated.     

On pullback attractors for a class of two-dimensional turbulent shear flows

We consider a two-dimensional Navier–Stokes shear flow with time dependent boundary driving. We establish the existence of a unique global in time solution of the considered problem and then the existence of the pullback attractor for the associated evolutionary process. In the end, we estimate from above the dimension of the attractor in terms of given data.This research is motivated by a problem from lubrication theory.     

On the use of boundary-integral equation methods for unsteady free-surface flows

The Mixed Eulerian-Lagrangian Methods (MEL) forfree-surface potential flows solved by boundary-integral equations (BIEs) is considered, and the diffusion and dispersion errors are studied in the discrete linearized problem. The diffusion error is the base for the stability analysis of the scheme; both the errors give indications on the accuracy of the numerical solution. The study is divided into two steps: comparison of the discrete dispersion relation with the analytical solution and coupling with different time-integration schemes. In particular, a stability analysis of the Runge-Kutta and Taylor-expansion schemes, previously not given in the literature, is addressed. It is shown that MEL methods based on first- and second-order explicit Runge-Kutta and Taylor-expansion schemes are unstable, regardless of the technique adopted to discretize the BIEs. Higher-order Runge-Kutta and Taylor-expansion schemes lead to conditionally stable methods. Known results for explicit, implicit and explicit-implicit Euler schemes are recovered by the present analysis. The theoretical predictions of the errors are confirmed for two different boundary-element techniques: a high-order panel method based on B-Splines to solve for the velocity potential and a spectrally-accurate method based on the Euler-McLaurin summation formula to solve directly for the velocity field.     

On nonlinear models for the pressure-strain rate correlations in turbulent flows

Simple inequalities are obtained that can be used for direct verification of the adequacy of nonlinear models describing a rapid part of the pressure-strain rate correlation tensor. Analysis of a quadratic model shows that such models cannot be accepted in a most part of the physical domain because of violation of the condition of positive definiteness of the spectral matrix of two-point correlations of the pulsation velocity. The boundaries of such “forbidden” zones can be even wider than those for the classical linear models.     

Development of computationally efficient augmented Lagrangian SPH for incompressible flows and its quantitative comparison with WCSPH simulating flow past a circular cylinder

In Lagrangian particle-based methods such as smoothed particle hydrodynamics (SPH), computing totally divergence-free velocity field in a flow domain with the smallest error possible is the most critical issue, which might be achieved through solving pressure Poisson equation implicitly with higher particle resolutions. However, implicit solutions are computationally expensive and may be particularly challenging in the solution of multiphase flows with highly nonlinear deformations as well as fluid-structure interaction problems. Augmented Lagrangian SPH (ALSPH) method is a new alternative algorithm as a prevalent pressure solver where the divergence-free velocity field is achieved by iterative calculation of velocity and pressure fields. This study investigates the performance of the ALSPH technique by solving a challenging flow problem such as two-dimensional flow around a cylinder within the Reynolds number range of 50 to 500 in terms of improved robustness, accuracy, and computational efficiency. The same flow conditions are also simulated using the conventional weakly compressible SPH (WCSPH) method. The results of ALSPH and WCSPH solutions are not only compared in terms of numerical validation/ verification studies, but also rigorous investigations are performed for all related physical flow characteristics, namely, hydrodynamic coefficients, frequency domain analyses, and velocity divergence fields.