Lighthill–Levich problem for a non-Newtonian fluid

Mass transfer with a heterogeneous chemical reaction of the first order in boundary layer flows of non-Newtonian power-law fluids is investigated. The problem is solved by the method of Laplace transform following the approach suggested by Apelblat [1] [A. Apelblat, Chemical Engineering Journal 19 (1980) 19]. The solution is obtained in a closed analytical form.     

Analytical and numerical solutions to a problem of convection in a porous media with lateral mass flux

We consider the problem of convection in a porous medium adjacent to a heated vertical porous plate. This problem has applications in the re-injection of hot water into a geothermal reservoir [1]. For large Rayleigh numbers, thermal boundary layers are formed and boundary layer theory is the obvious method of investigation. A similarity solution can be obtained when it is stipulated that the wall temperature and the lateral mass flux are power law functions of distance along the plate. In two particular cases, analytical solutions are found. In other cases, the profiles of the normalized velocity and temperature are obtained with accute accuracy using the “quasilinerization” method.     

Boundary stabilization of elastodynamic systems, II. The case of a linear feedback

In this paper, we extend some previous results published in [5]. We consider an elastodynamic system damped by a linear boundary feedback of Neumann type. We prove stabilization results by using the multipliers method and Rellich-type relations given in the first part [6]. Especially, we take in account singularities which appear when changing boundary conditions.     

A note to the solution of cheng-minkowycz equation arising in free convection flow in porous media

In this paper we reconsider the problem of boundary layer free convection flow along a vertical flat plate with a power law surface temperature and embedded in a fluid-saturated porous medium. The resulting ordinary differential equation is solved numerically using the method of perturbation series in combination with Shanks transformation. The accuracy of the present solution is discussed and is found to be in excellent agreement with theoretical predictions of Banks[7].     

Validation of a three-dimensional viscous–inviscid interactive solver for wind turbine rotors

MIRAS is a newly developed computational model that predicts the aerodynamic behavior of wind turbine blades and wakes subject to unsteady motions and viscous effects. The model is based on a three-dimensional panel method using a surface distribution of quadrilateral singularities with a Neumann no penetration condition. Viscous effects inside the boundary layer are taken into account through the coupling with the quasi-3D integral boundary layer solver Q³UIC. A free-wake model is employed to simulate the vorticity released by the blades in the wake. In this paper the new code is validated against measurements and/or CFD simulations for five wind turbine rotors, including three experimental model rotors [20–22], the 2.5 MW NM80 machine [23] and the NREL 5 MW virtual rotor [24]. Such a broad set of operational conditions and rotor sizes constitutes a very challenging validation matrix, with Reynolds numbers ranging from 5.0⋅10⁴ to 1.2⋅10⁷.     

Feedback-Invariant Optimal Control Theory and Differential Geometry, II. Jacobi Curves for Singular Extremals

This is the second article in the series that began in [4]. Jacobi curves were defined, computed, and studied in that paper for regular extremals of smooth control systems. Here we do the same for singular extremals. The last section contains a feedback classification and normal forms of generic single-input affine in control systems on a 3-dimensional manifold.     

两类边界条件下管外对流换热性能实验研究

采用实验研究的方法,分别对针翅管、平直翅片管和光管在同一风洞实验台上进行实验。采用管内电加热法模拟第二类边界条件,管内流体加热,管外空气横掠模拟第三类边界条件,实验的管外雷诺数范围为Re=5000—35000。实验结果表明：光管在第三类边界条件下的Nu是第二类边界条件下的1．048倍,翅片管在第三类边界条件下的Nu是第二类边界条件下的1．073倍,针翅管第三类边界条件下的Nu是第二类边界条件下的1．1倍,且这个比例关系与Re的变化无关。     

Immersed boundary method for the simulation of heat transfer and fluid flow based on vorticity–velocity formulation

ABSTRACT

The present paper, based on the vorticity–velocity formulation of the Navier–Stokes equations, proposes an immersed boundary method for the simulation of heat transfer problems within a geometrically complex domain. The desired boundary conditions are imposed by the direct modification of the initial conditions of vorticity transport and energy equations using smooth interpolations. The time advancement of both transport equations is performed by the explicit fourth-order Runge–Kutta method. One of the main objectives of this paper is to present global smooth interpolations to evaluate the local Nusselt number. The forced convection of moving and fixed circular cylinders, natural convection problem in complex geometries, and the mixed convection between two concentric cylinders—at various Reynolds numbers—are studied.     

The inward solidification of cylinders with a slightly perturbed temperature distribution at the boundary

This paper is concerned with the inward solidification of infinite liquid cylinders, where the boundary values (the cases of specified temperature distribution and specified heat flux are considered) vary slightly with position around the cylinder. This paper is therefore the cylindrical geometry analogue of the spherical problems considered in Gammon and Howarth [1]. The problems are solved analytically by means of a large Stefan number approximation.     

Measurement of Synchronous Machine Parameters by a Modified Frequency Response Method - Part II: Measured Results

De Mello and Hannett [1] have proposed a theoretical method for determining the operational inductances of a synchronous machine at low values of generator speeds. Eitelberg and Harley [2] extended these ideas to obtain the inductances and time constants from the Ld(j2w), Lq(j2w) curves by a numerical curve fitting procedure. Part I [3] of this paper broadens these ideas [1-2] by proposing an improved MODIFIED data-processing method which avoids the tedious integration of the d,q axes flux linkages [1]. Part II continues by performing a line-to-line short-circuit test on a 3 kVA, 220 V microalternator at different speeds covering the range which is of interest to subsynchronous resonance (SSR) studies [4]. Measured results illustrate the practical feasibility of this proposed frequency response method [1-3]. Practical problems associated with this test are also mentioned.     

Investigation of flow boiling in horizontal tubes: Part II—Development of a new heat transfer model for stratified-wavy, dryout and mist flow regimes

The new version of the flow pattern map presented in Part I of this paper has been used to modify the dry angle in the heat transfer model of Kattan-Thome-Favrat [J. Heat Transfer, 120 (1) (1998) 156]. This significantly improves the heat transfer prediction in stratified-wavy flow. Moreover, a new heat transfer prediction method has been developed for the dryout and mist flow regimes, which extends the applicability of the heat transfer model to these flow regimes. An extensive flow boiling heat transfer database has been acquired for R-22 and R-410A to develop and validate the new heat transfer prediction methods. The new model also shows good agreement with the independent heat transfer data of Lallemand et al. [M. Lallemand, C. Branescu, P. Haberschill, Local heat transfer coefficients during boiling of R-22 and R-407C in horizontal smooth and microfin tubes, Int. J. Refrigeration, 24 (2001) 57-72].     

On heat conduction problem in a semi-infinite periodically laminated layer

The paper deals with the heat conduction problem of a semi-infinite periodically stratified layer heated by a constant heat flux directed according to the layering, normal to the boundary being a cross-section of the composite components. The free heat exchange with surroundings is considered on the remaining parts of the boundary. The body is assumed to be composed of n periodically repeated two-layered, perfect bonding lamine. The problem is solved on two ways: (1) directly as heat conduction problem or (2) by using the homogenized model with microlocal parameters [R. Kulchytsky-Zhyhailo, S.J. Matysiak, On some heat conduction problem in a periodically two-layered body. Comparative results, Int. Commun. Heat Mass Transf., in press]. The obtained results are compared and presented in the form of figures.     

The effect of large-amplitude g-jitter vertical free convection boundary-layer flow in porous media

In this paper we consider how the boundary-layer flow induced by a constant temperature vertical surface embedded in a porous medium is modified by time periodic variations in the gravitational acceleration. It is assumed that the amplitude of these variations is comparable with the mean gravitational acceleration. The resulting nonsimilar boundary layer equations are solved using the Keller-box method after using a Fourier decomposition in time to reduce the system to parabolic form with only two independent variables. The main effect of such g-jitter is confined mainly to the region near the leading edge and becomes weak at larger distances from the leading edge. For small g-jitter amplitudes the numerical results compare very well indeed with our earlier analysis in Rees and Pop [Int. Comm. Heat Mass Transfer 27 (2000) 415].     

Solution of transport equations on unstructured meshes with cell-centered colocated variables. Part II: Applications

This paper describes applications of the discretization procedure presented in the companion paper [A.W. Date, Solution of transport equations on unstructured meshes with cell-centered colocated variables. Part I. Discretization, Companion Paper, this volume]. Six problems having different domain complexities, presence of body and surface forces and, boundary conditions are solved. Where possible, the solutions are compared with published experimental or numerical data.     

The effect of Prandtl number on heat transfer from an isothermal rotating disk with blowing at the wall

Numerical results for heat transfer from an isothermal rotating disk with moderate to massive blowing at the wall are presented for a wide range of Prandtl numbers. Results show that for a given finite rate of blowing at the wall, the heat transfer rate first increases, reaching a maximum value before falling sharply, as the Prandtl number is increased. The maximum value of heat transfer rate decreases as the blowing rate increases. The results are compared to the asymptotic expansion results of [13]. The phenomenon of boundary layer blow-off is also investigated.     

Effect of porous coating on critical heat flux

The critical hear flux (CHF) is studied experimentally in vertical tubes heated directly using power current (DC 2500 A, 15 V) and cooled with water at a low mass flow rate (0 ∼ 200 kg/m²s) and at a low pressure (1.0 ∼ 8.0 bar). We used a smooth tube and a tube with a porous coating layer sintered onto the inner surface. The results are compared with each other and with correlations by Katto [1] and Weber [2]. We determined enhancement of heat transfer as well as a negative effect of the porous coating below the expected value of critical heat flux.     

The linear wave instability of boundary layer flow induced by a horizontal heated surface in porous media

In this paper we use the parallel-flow approximation to determine the criterion for the onset of instability in the form of travelling waves in a horizontal thermal boundary layer in porous media. We find that waves grow beyond a nondimensional distance of 28.90 from the leading edge, a result which shows, somewhat surprisingly, that waves are to be preferred over vortices, which have been found to grow beyond 33.47 from the leading edge [1]. We discuss very briefly the implications of our analysis for the use of the parallel flow approximation in the determination of stability criteria for thermal boundary layers.     

NUMERICAL SIMULATION OF BUOYANT AND THERMOCAPILLARY CONVECTION IN A SQUARE CAVITY

Numerical results are presented of the simulation of combined buoyant and thermocapillary convection in a square cavity, and comparison is made with experimental observations of Schwabe and Metzger [1]. The two-dimensional conservation equations for mass, momentum, and thermal energy (temperature) are solved using a multigrid finite-volume method and grids with up to 248 X 200 control volumes. Central differencing is used to discretize both convection and diffusion fluxes, and the coupling of pressure and velocity is achieved via the SIMPLE algorithm for colocated variable arrangement [2]. The discretization accuracy of the results is estimated to be of the order of 1% on the finest grid. The agreement with experimental results is fairly good; the reasons for observed discrepancies are also discussed.     

Simulation of a shock tube with a small exit nozzle

Shock tubes are frequently used to rapidly heat up reaction mixtures to study chemical reaction mechanisms and kinetics in the field of combustion chemistry [1]. In the present work, the flow field inside a shock tube with a small nozzle in the end plate has been investigated to support the analysis of reacting chemical mixtures with an attached mass spectrometer and to clarify whether the usual assumptions for the flow field and the related thermodynamics are fulfilled. In the present work, the details of the flow physics inside the tube and the flow out of the nozzle in the end plate have been investigated. Due to the large differences in the typical length scales and the large pressure ratios of this special device, a very strong numerical stiffness prevails during the simulation process. Second-order ROE numerical schemes have been employed to simulate the flow field inside the shock tube. The simulations were performed with the commercial code ANSYS Fluent [2]. Axial-symmetric boundary conditions are employed to reduce the consumption of CPU time. A density-based transient scheme has been used and validated in terms of accuracy and efficiency. The simulation results for pressure and density are compared with analytical solutions. Numerical results show that a density-based numerical scheme performs better when dealing with shock-tube problems [5]. The flow field near the nozzle is studied in detail, and the effects of the nozzle to pressure and temperature variations inside the tube are investigated. The results show that this special shock-tube setup can be used to study high-temperature gas-phase chemical reactions with reasonable accuracy.     

格子Boltzmann方法模拟土体渗流场研究

格子Boltzmann方法模拟土体渗流场,较传统的数值计算方法具有并行计算能力好、能得到流场细节信息、擅长处理复杂边界的独特优势。通过构建入口边界为非平衡外推格式、出口边界为充分发展格式、左右边界为反弹格式的基于通用渗流模型的LBM模型,编程实现格子Boltzmann方法模拟水在同一级配三种颗粒随机分布的土壤中的渗流情况。通过经典算例验证了所编程序的正确性和有效性,并由得到的渗流场图分析发现,土体颗粒的均匀性和通透性较好时渗流场流线的形状和畅通性也较好。