Heat transfer enhancement with deformation of the velocity profile

The problem of enhancing the heat transfer in channels and boundary layers by the appropriate deformation of the fluid velocity profile is considered. The resulting additional hydraulic losses, the price of heat transfer enhancement, are determined. The possibilities of controlling heat transfer by redistributing the fluid velocity in channels are demonstrated with reference to flows at low Prandtl numbers. Laminar and turbulent liquid and gas flows with heat transfer in channels and boundary layers are numerically modeled on the basis of modern models of turbulence (flow development in channels with different initial velocity profiles, flows with wall roughness and boundary layer flows with forces acting on the flow to cause deformation of the velocity profile). In all cases it is found that the heat transfer can be enhanced only at the expense of a considerable increase in the hydaulic losses. A class of self-similar thermal problems for flows in plane diffusers is formulated. The eigenfunctions — temperature modes — for various velocity profiles are determined with allowance for the nonuniqueness of the solution of the classical dynamical problem for a plane diffuser and the corresponding heat transfer coefficients are found.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 94–105, May–June, 1993.The authors are grateful to A. Yu. Klimenko for useful discussions.     

高温仪器化压入测试中热接触对位移测量漂移的影响

基于对室温压头和热试样接触后传热过程的分析, 重点研究热接触引起的压头基托热膨胀对高温仪器化压入测试中位移测量漂移的影响. 首先, 通过热传导理论分析, 获得热接触后基托内温度场分布的解析解, 进而研究基托热膨胀引起的位移测量漂移量; 然后, 建立有限元分析模型, 数值模拟高温仪器化压入过程, 验证理论模型的准确性. 研究发现, 压头与热试样接触面间的热传导性质显著影响基托内的温度场分布; 对于不同材料的试样, 接触面间传热性能不同, 基托的热膨胀量差异可以达到几个数量级. 研究结果有助于优化高温压入测试程序, 提高测试的可靠性.      

Prediction of Local Losses of Low <Emphasis Type="Italic">Re</Emphasis> Flows in Non-uniform Media Composed of Parrallelpiped Structures

A method is presented to predict the local losses of low Re flow through a porous matrix composed of layers of orthogonally oriented parallelepipeds for which the local geometry varies discreetly in the direction of bulk flow. In each layer, the variations in the pore lengths perpendicular to and parallel to the direction of bulk flow are restricted to be proportional to one another so that the variation in the geometry of each layer may be characterized by a single parameter, \(\beta \). The solutions to the Navier–Stokes equations are determined for flows through geometries that vary in a forward expansion about this parameter. These provide the data used in the development of a correlation that is able to directly relate local hydraulic permeability to the variation in local pore geometry. In this way, the local pressure losses (as well as the relationship between the volumetric flow rate and the total pressure drop) may be determined without requiring the explicit solution of the entire flow field. Test cases are presented showing that the correlation predicts the local pressure losses to be within 0.5% of the losses determined from the numerical solution to the Navier–Stokes equations. When the magnitude of the variation to the geometry is such that the change in the parameter \(\beta \) between layers is constant throughout the medium, a reduced form of the correlation (requiring the evaluation of only three constants) is able to provide predictions of flow rate and interface pressures that agree to within about 1% with the results of the numerical solutions to the Navier–Stokes equations.     

Thermocapillary convection stability in a cylindrically-symmetric two-phase system

Thermocapillary flows in an infinitely long liquid cylinder surrounded by a coaxial gas layer with a controlled flow rate and the stability of such flows are investigated. In the layers a constant axial temperature gradient is maintained. An exact solution of the equations of motion describing the steady-state flow in this two-phase system is derived. Possible flow regimes and their stability in the linear approximation are studied. It is shown that in the liquid phase the thermocapillary flow can be completely stopped by the gas flow at the expense of the interaction between mechanical stresses at the interface. The results obtained indicate the possibility of controlling thermocapillary flows and their stability by means of gas flows.     

The Effect of Thermal Expansion on Porous Media Convection Part 1: Thermal Expansion Solution

The effect of thermal expansion on porous media convection is investigated by isolating first the solution of thermal expansion in the absence of convection which allows to evaluate the leading order effects that need to be included in the convection problem that is solved later. A relaxation of the Boussinesq approximation is applied and the relevant time scales for the formulated problem are identified from the equations as well as from the derived analytical solutions. Particular attention is paid to the problem of waves propagation in porous media and a significant conceptual difference between the isothermal compression problem in flows in porous media and its non-isothermal counterpart is established. The contrast between these two distinct problems, in terms of the different time scales involved, is evident from the results. While the thermal expansion is identified as a transient phenomenon, its impact on the post-transient solutions is found to be sensitive to the symmetry of the particular temperature initial conditions that are applied.     

Mass flow rate prediction of pressure–temperature-driven gas flows through micro/nanoscale channels

In this paper, we study mass flow rate of rarefied gas flow through micro/nanoscale channels under simultaneous thermal and pressure gradients using the direct simulation Monte Carlo (DSMC) method. We first compare our DSMC solutions for mass flow rate of pure temperature-driven flow with those of Boltzmann-Krook-Walender equation and Bhatnagar-Gross-Krook solutions. Then, we focus on pressure–temperature-driven flows. The effects of different parameters such as flow rarefaction, channel pressure ratio, wall temperature gradient and flow bulk temperature on the thermal mass flow rate of the pressure–temperature-driven flow are examined. Based on our analysis, we propose a correlated relation that expresses normalized mass flow rate increment due to thermal creep as a function of flow rarefaction, normalized wall temperature gradient and pressure ratio over a wide range of Knudsen number. We examine our predictive relation by simulation of pressure-driven flows under uniform wall heat flux (UWH) boundary condition. Walls under UWH condition have non-uniform temperature distribution, that is, thermal creep effects exist. Our investigation shows that developed analytical relation could predict mass flow rate of rarefied pressure-driven gas flows under UWH condition at early transition regime, that is, up to Knudsen numbers of 0.5.     

The flow of thin liquid films around corners

Situations arise where it is required to strip a moving liquid film from a boundary wall. The need to sample wet steam isokinetically is one such situation. Equally it is sometimes desirable for a film not to separate from a boundary wall as in, for example, liquid separators. A theoretical analysis is developed to examine the radial stress distribution within a uniformly thin liquid film flowing around a sharp bend of fixed radius. The results of the analysis are discussed in the light of experimental observations. The controlling parameters in the film flow are identified and are evaluated for a given situation.     

Foam flowing vertically upwards in pipes through expansions and contractions

The drift-flux analysis of one-dimensional two-phase flow of Wallis (Wallis, G.B., 1969. One-dimensional two-phase flow. McGraw-Hill Book Company, New York.) is utilised for the first time to model the behaviour of pneumatic foam flowing vertically through an expansion or an contraction. It is demonstrated that, although a sudden contraction of flow area decreases the liquid fraction, it does not affect the volumetric liquid over-flow rate. It is also demonstrated that a sudden expansion of flow area decreases both the liquid fraction and the volumetric liquid over-flow rate. The liquid fraction of a foam stabilised by 2.92 g/L sodium dodecyl sulphate (SDS) solution flowing through a sudden contraction or expansion was measured by an improved pressure gradient method. The results were found to be consistent with the theoretical analysis. This study has implications for foam fractionation device design, optimisation and process intensification.     

The effects of rate of expansion and injection of water droplets on the entropy generation of nucleating steam flow in a Laval nozzle

The entropy generation due to irreversible heat transfer between vapor and liquid phases in a nucleating steam flow in a Laval nozzle is studied. To calculate the entropy generation due to self-condensation in transonic steam flow, a thermodynamic model is presented. The calculations of nucleating steam flow and the predictions of entropy generation rely on one-dimensional two-phase model. This model shows that the most of the thermodynamic losses take place during the nucleation phenomena. The effect of rate of expansion on the exergy losses is considered by decreasing the divergent angle of nozzle. Also micro-sized pure water droplets is injected theoretically to supercooled steam right after the nozzle throat at the onset of divergent section and the effects of injected droplets on thermodynamic losses and nucleation phenomena are investigated. The results indicate that decreasing the divergent angle and also injection of droplets diminishes the pressure rise in transonic steam flow and decreases the thermal entropy generation due to nucleation.     

Optimization of two-phase flows using the solution of an inverse problem

The results of optimizing two- phase flows on the basis of the solution of an inverse problem with the pressure distribution given by a two-parameter function are presented. The efficiency of the developed approach is illustrated with reference to nozzle and ejector flows with large liquid phase flow rates (the liquid droplet flow rate being greater than that of the gas by a factor of several tens).     

Wave induced thermal boundary layers in a compressible fluid: analysis and numerical simulations

The response of a semi-infinite compressible fluid to a step-wise change in temperature of its boundary is investigated analytically and numerically. Numerical results of the boundary layer structure are compared with Clarke’s analytical solution for a gas with thermal conductivity proportional to temperature. To avoid unwanted numerical dissipation in the numerical analysis, the space-time conservation element and solution element (CESE) method has been adopted to solve the unsteady 1-D Navier-Stokes equations. Good agreement between analytical and numerical results has been found for the development of the thermal boundary layer on a long time scale. Weak shock waves and expansion waves induced by the thermal boundary layer due to its compressibility, are observed in the numerical simulation. Finally, the numerical method has been applied to the reflection of a non-linear expansion wave and to a shock wave from an isothermal wall, thereby illustrating the effect of the boundary layer on the external flow field.     

Experimental and numerical investigation of separated flows in subsonic diffusers

The results of a special investigation of the diffuser flowfield are presented for two models of curvilinear diffuser channels with annular and rectangular cross-sections. The flow is visualized and the total pressure fields are measured by means of low-inertia transducers. At the same time, the flows are numerically calculated using commercial programs, together with codes developed by the authors. In these calculations the stationary and time-dependent Reynolds equations closed by different turbulence models, as well as the time-dependent Navier-Stokes equations, were integrated. A considerable difference between the measured data and the results of the numerical calculations in the stationary formulation is found to exist. At the same time, it has been possible to describe the occurrence of spatial inhomogeneities, the flow pattern, and the level of the experimentally observed aerodynamic losses on the basis of the solution of time-dependent problems.     

An asymptotic iteration method for the numerical analysis of near-critical free-surface flows

Satisfying the boundary conditions at the free surface may impose severe difficulties to the computation of turbulent open-channel flows with finite-volume or finite-element methods, in particular, when the flow conditions are nearly critical. It is proposed to apply an iteration procedure that is based on an asymptotic expansion for large Reynolds numbers and Froude numbers close to the critical value 1.The iteration procedure starts by prescribing a first approximation for the free surface as it is obtained from solving an ODE that has been derived previously by means of an asymptotic expansion (Grillhofer and Schneider, 2003). The numerical solution of the full equations of motion then gives a surface pressure distribution that differs from the constant value required by the dynamic boundary condition. To determine a correction to the elevation of the free surface we next solve an ODE that is obtained from the asymptotic analysis of the flow with a prescribed pressure disturbance at the free surface. The full equations of motion are then solved for the corrected surface, and the procedure is repeated until criteria of accuracy for surface elevation and surface pressure, respectively, are satisfied.The method is applied to an undular hydraulic jump as a test case.     

ADVECTION–DIFFUSION PROCESSES AND RESIDENCE TIMES IN SEMIENCLOSED MARINE BASINS

This paper addresses the problem of estimating the residence times in a marine basin of a passive constituent released in the sea. The dispersion process is described by an advection–diffusion model and the hydrodynamics is assumed to be known. We have performed the analysis of two different scenarios: (i) basins with unidirectional flows, in three space dimensions and under the rigid lid approximation, and (ii) basins with flows forced by the tide, under the shallow water approximation. Let the random variable τ be defined as the time spent in the basin by a particle released at a given point. The probability distribution of τ is obtained from the solution of the advection–diffusion problem and the residence time of a particle is defined as the mean value of τ. Two different numerical approximations have been used to solve the continuous problem: the finite volume and Monte Carlo methods. For both continuous and discrete formulations it is proved that if all the particles eventually leave the basin, then the residence time has a finite value. We present here the results obtained for two study cases: a two- dimensional basin with a steady flow and a one-dimensional channel with flow induced by the tide. The results obtained by the finite volume and Monte Carlo methods are in very good agreement for both scenarios.     

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.     

Hydrodynamics of swirling flow in a circular tube with sudden increase in cross-section and of the flow through a borda mouthpiece

By applying the mass, momentum, and angular momentum conservation laws and the maximum flow rate principle to swirling, effectively inviscid, incompressible flows in a circular tube with a sudden expansion and in direct-flow and reversed-flow Borda mouthpieces the dependence of the flow rate coefficient and mechanical energy losses on the radius ratio and nondimensional circulation is obtained. Several calculating approaches with potential and helical motion are introduced and investigated. In the case of helical motion, as the swirl decreases the axial core of the flow is found to close with a sudden change of the flow parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 51–66, May–June, 1994.     

A high‐resolution wetting and drying algorithm for free‐surface hydrodynamics

A new wetting and drying algorithm for numerical modeling free‐surface flows is proposed and analyzed. A well structured, mildly nonlinear system for the discrete water surface elevation is derived from the governing differential equations by requiring a correct mass balance in wet areas as well as in the region of transition from wet to dry and from dry to wet. Existence and uniqueness of the numerical solution, along with a convergence analysis of an iterative scheme for the mildly nonlinear system, is provided. The present algorithm is devised to use high‐resolution bathymetric data at subgrid level. The resulting model is quite efficient, does not require a threshold value for minimal water depth, does not produce un‐physical negative water depths and generates accurate results with relatively coarse mesh and large time step size. These features are illustrated on a severe test‐case with known analytical solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonboussinesq Thermal Convection in Microgravity under Nonuniform Heating

The model of subsonic flows is used to numerically the effect of thermal expansion of a fluid on the formation of naturally convective flows for small Rayleigh numbers (microconvection) and spatially periodic distribution of heat flows on the boundaries of the domain occupied by the fluid.     

Influence of elongational properties on the contraction flow of polyisobutylene in a mixed solvent

Over the last decade several international programmes have been developed around different standard fluids, one of which is the so-called S1 fluid. This is a solution of polyisobutylene in a mixed solvent and the aim of the programme has been to study the rheology of polymer solutions from the dilute solution to the melt. The focus of this paper will be on the flow visualisation of contraction flows of S1 through orifice dies and on the estimation of some of its extensional properties. The contraction ratios range from 24.4:1 and 124.3:1. The measured entry pressure drops will be correlated with contraction ratio and apparent wall shear rate. Experimental evidence will show that, when regarded as a function of wall shear rate, the entry pressure drops are independent of the contraction ratios. The flow fields for different contraction ratios, at any constant apparent wall shear rate, however, differ substantially. The evolution of the flow fields is monitored and it is shown that an initial increase in vortex size is followed by a slower decrease, this happening at a constant Weissenberg number. At the same Weissenberg number, small scale instabilities start occurring near the office. As the shear rate is increased further, these instabilities grow in size until, eventually, the flow structure is destroyed. An extensional viscosity is evaluated using a modified form of the Binding analysis for contraction flows and we show that the results are not only in qualitative agreement with those from other groups, but also that the analysis is able to predict exactly the onset of the aforementioned flow instabilities. Received: 20 March 1997 Accepted: 18 September 1997