A numerical study of three-dimensional laminar mixed convection past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective flow over a three-dimensional cavity that lies at the bottom of a horizontal channel. The vertical walls of the cavity are isothermal and all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar and incompressible. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall over a wide range of the Grashof number (10³–10⁶) and two Reynolds numbers Re = 100 and 1000. The computed thermal and flow fields are displayed and discussed in terms of the velocity fields, streamlines, the temperature distribution and the averaged Nusselt number at the heated and cooled walls. It is found that the flow becomes stable at moderate Grashof number and exhibit a three-dimensional structure, while for both high Reynolds and Grashof numbers the mixed convection effects come into play, push the recirculating zone further upstream and the flow becomes unsteady with Kelvin–Helmholtz instabilities at the shear layer.     

Computational and experimental analysis of high temperature thermal treatment of wood based on ThermoWood technology

Heat treatment of wood at relatively high temperatures (in the range of 180–240 °C) is an effective method to improve the dimensional stability and increase biological durability of wood. In this article, a coupling method is presented for high thermal treatment of a wood based on ThermoWood technology. A three-dimensional mathematical model describing simultaneous unsteady heat and moisture transfer between a gas phase and a solid phase during heat treatment has been developed. The conservation equations for the wood sample are obtained using diffusion equation with variable diffusion coefficients and the 3-dimensional incompressible Reynolds averaged Navier–Stokes equations have been solved for the flow field. The experimental results and model predictions were found to be in good agreement.     

A Quasi-Implicit Time-Advancing Scheme for Flow in a Three-Dimensional Curved Duct

A quasi-implicit time-marching scheme for solving unsteady incompressible three-dimensional flows on cell-centered unstructured meshes is developed. The finite-volume formulation is used for the spatial derivatives, and the flow variables at the cell face are obtained using the pressure correction. The nonlinear equations resulting from the fully implicit scheme are linearized without deterioration of the overall super-linear time accuracy. The system matrices are solved using the CG iterative method, known as the P-BiCGSTAB method for the momentum equation and the P-CG method for the pressure Poisson equation. The model is applied to simulate fully developed laminar flow in both a 90° curved 3-D circular duct and a 90° curved 3-D square duct. Steady solution is obtained in an unsteady time-marching manner. Computed results compare well with experimental data and other numerical results. It is demonstrated that the present method can be applied to unsteady incompressible laminar 3-D flow with a complex geometry on the unstructured grid system.     

Laminar flow past a sinusoidal cavity

The dynamic and thermal properties of a laminar flow past a sinusoidal cavity are studied. Velocity and temperature fields inside and above the cavity are numerically determined from the viscous flow equations. Results are compared with the experimental data obtained with a model placed in an incompressible and uniform flow. The good agreement with the dynamic field configuration allows the extension of these calculations to other sinusoidal wall geometries, to other main flow velocities and to cases with suction at the wall. Examples of streamlines and isotherms are given for these various situations.     

Numerical Investigation of Convective Heat Transfer in Unsteady Laminar Flow Over a Square Cylinder in a Channel

Unsteady laminar flow past a heated square cylinder mounted inside a plane channel was investigated numerically. The blockage ratio was chosen as 1/8 and the Reynolds number based on the mean flow velocity and chord length of the square cylinder was selected as less than 200, for which the two-dimensional behavior of the flow is assured. The time-averaged Nusselt number as well as some integral parameters such as drag coefficient, recirculation length, and Strouhal number were obtained and compared with literature. Results show a nearly linear increase in recirculation length and decrease in drag coefficient with increasing Reynolds number for the steady flow regime. There is an increase in the total Nusselt number and drag coefficient with a Reynolds number for unsteady flow regime, where vortex shedding is observed from the cylinder. A correlation was obtained for the variation of the total Nusselt number with the Reynolds number.     

EFFECT OF INCLINED VORTEX GENERATORS ON HEAT TRANSFER ENHANCEMENT IN A THREE-DIMENSIONAL CHANNEL

Three-dimensional unsteady flow and heat transfer in a channel with inclined block shape vortex generators mounted on one side of a channel flow are investigated for different Reynolds numbers, Re _H= 400 - 1500 , and Pr = 0.71. This study was informed to gain an understanding of the flow phenomena and calculate the heat transfer and pressure drop for different Reynolds numbers. The effect of computational domain, angle of incidence, size of the vortex generator, and the discretization schemes on the results are also investigated. Simulations use an incompressible finite volume code, based on a fractional step technique with a multigrid pressure Poisson solver and a nonstaggered grid arrangement.     

Solution of incompressible fluid flow problems with heat transfer by means of an efficient RBF-FD meshless approach

The localized radial basis function collocation meshless method (LRBFCMM), also known as radial basis function generated finite differences (RBF-FD) meshless method, is employed to solve time-dependent, two-dimensional (2D) incompressible fluid flow problems with heat transfer using multiquadric RBFs. A projection approach is employed to decouple the continuity and momentum equations for which a fully implicit scheme is adopted for the time integration. The node distributions are characterized by non-Cartesian node arrangements and large sizes, i.e., in the order of 10⁵ nodes, while nodal refinement is employed where large gradients are expected, i.e., near the walls. Particular attention is given to the accurate and efficient solution of unsteady flows at high Reynolds or Rayleigh numbers, in order to assess the capability of this specific meshless approach to deal with practical problems. Three benchmark test cases are considered: a lid-driven cavity, a differentially heated cavity and a flow past a circular cylinder between parallel walls. The obtained numerical results compare very favorably with literature references for each of the considered cases. It is concluded that the presented numerical approach can be employed for the efficient simulation of fluid-flow problems of engineering relevance over complex-shaped domains.     

Pulsating flow and convective heat transfer in a cavity with inlet and outlet sections

This paper deals with the study of 2-D, laminar, pulsating flow inside a heated rectangular cavity with different aspect ratios. The cooling liquid (water with temperature dependent viscosity and thermal conductivity) comes and leaves the cavity via inlet and outlet ports. The flow topology is characterised by the large recirculation regions that exist at inner corners of the cavity. These low velocity regions cause the heat transfer to be small when compared, for instance, to that of a straight channel. We study the effect that a prescribed pulsation at the inlet port has on the cavity heat transfer. This pulsating boundary condition, of the unsteady Poiseuille type, is described by its frequency and the amplitude of the pressure gradient. The time averaged Reynolds number of the flow, based on the hydraulic diameter of the inlet channel, is 100 and we consider that the dimensionless pulsation frequency (Strouhal number) varies in the range from 0.0 to 0.4. We show that the prescribed pulsation enhances heat transfer in the cavity and that the mechanism that causes this enhancement appears to be the periodic change in the recirculation flow pattern generated by the pulsation. Regarding the quantitative extent of heat transfer recovery, we find that appropriate selection of the pulsation parameters allows for the cavity to behave like a straight channel that is the configuration with the highest Nusselt number.     

MULTIGRID SOLUTION OF UNSTEADY NAVIER-STOKES EQUATIONS USING A PRESSURE METHOD

Abstract

A multigrid relaxation method is applied to a pressure-based implicit procedure to solve the unsteady, incompressible Navier-Stokes equations. The present multigrid method is a correction scheme according to Brandt. This method is used to solve the scalar matrices resulting from the finite-volume formulation and uses flux averaging as the restriction operator. The accuracy and computational efficiency are demonstrated with a steady-state driven cavity flow and an unsteady flow over a circular cylinder case. The results are compared with single-grid results using the OrthoMin conjugate gradient method and experimental data     

Discretized pressure Poisson algorithm for the steady incompressible flow on a nonstaggered grid

In the aspect of numerical methods for incompressible flow problems, there are two different algorithms: semi-implicit method for pressure-linked equations (SIMPLE) series algorithms and the pressure Poisson algorithm. This paper introduced a new discretized pressure Poisson algorithm for the steady incompressible flow based on a nonstaggered grid. Compared with the SIMPLE series algorithms, this paper did not introduce three correction variables. So, there is no need to implement the guess-and-correct procedure for the calculation of pressure and velocity. Compared with the pressure Poisson algorithm, there is no need to calculate unsteady Navier–Stokes equations for steady problems in the new discretized pressure Poisson algorithm. Meanwhile, as the finite volume method and cell-centered grid are used, the governing equation for pressure is obtained from the continuity equation and the boundary conditions for pressure are easily obtained. This new discretized pressure Poisson algorithm was tested at the lid-driven cavity flow problem on a nonstaggered grid and the results are also reliable.     

安装角变化下垂直轴风力机气动性能的研究

建立了3D垂直轴风力机模型,应用FLUENT软件求解三维非定常不可压缩N-S方程和RNGκ-ε湍流模型,采用SIMPLE算法并结合滑动网格技术,数值模拟了安装角变化下垂直轴风力机的三维非定常流场,分析了不同时刻的速度、涡量分布、风力机总转矩的变化规律及风能利用系数。结果表明,计算区域流场复杂,垂直轴风力机的转矩呈周期性变化,风能利用系数随安装角变化而变化。     

发动机冷却水三维流动数值模拟基础研究

本文在作者已完成的不可压缩流体三维流动数值模拟研究的基础上，对发动机冷却水三维流动的数值模拟方法进行了基础性研究。文章对具有发动机冷却水腹复杂形状的箱体内的水进行了三维流动模拟计算，介绍了数值模拟的基本方法，并对计算结果进行了分析，说明了该方法的有效性。该文介绍的内容是深入研究实际发动机冷却水三维流动数值模拟的基础。     

APPLICATION OF THE PIECEWISE PARABOLIC FINITE ANALYTIC METHOD TO THE THREE-DIMENSIONAL CAVITY FLOW

Abstract

The three-dimensional piecewise parabolic finite analytic method (PPFAM3D), with vector potential and vorticity as dependent variables, was used to solve the steady three-dimensional (3-D) laminar cavity flow. Predictions were obtained for Reynolds numbers between 100 and 2000. Results for Re = 100, 400, and 1000 are compared with those available in the literature. The overall agreement is excellent. Results are also compared with the two-dimensional PPFAM cavity flow, showing the effect of three-dimensionality on the velocity predictions at the symmetry plane. The PPFAM3D is a robust numerical algorithm requiring no relaxation to produce physically meaningful and numerically converged solutions. It is a promising tool for solving a variety of flow phenomena governed by unsteady second-order partial differential convection-diffusion equations     

Investigation about the effects of exterior surface paint color on temperature development in aboveground pipeline

A practical analytical model for predicting temperature development of incompressible flow inside an aboveground pipeline has been constructed and presented in this research work. The outer surface of the pipeline is exposed to solar radiation and wind stream. The radiation heat exchange with ambient is also taken into account. The effects of exterior surface paint color represented by emissivity and absorptivity, have been studied. The model has been developed to study crude oil flow temperature development through a specific pipeline. The results obtained by the model show that the bulk temperature inclined to a limiting value in some distance which affected mainly by Reynolds numbers. It is found that emissivity and absorptivity of surface are predominant parameters in temperature development in an aboveground pipeline flow which can increase or decrease pipe surface and fluid temperature especially for low Reynolds number flow. Based on the results which indicated significantly of exterior surface paint color, one should choose the paint color by considering its effects on temperature development.     

Effect of thermal buoyancy on vortex shedding past a circular cylinder in cross-flow at low Reynolds numbers

This paper demonstrates the vortex shedding process behind a heated cylinder in a cross-flow at low Reynolds numbers under the influence of thermal buoyancy. The simulations were performed using an SUPG-based finite element technique. The range of Reynolds numbers was chosen to be 10–45. The flow was steady in the absence of thermal buoyancy. The eddy length and the separation angle were computed for the steady separated flow in the above range of Reynolds numbers. The results were in agreement with those reported in the literature. The Nusselt number distribution around the heated cylinder was also computed in the above range of Reynolds numbers for forced convective flows. The results compared fairly well with available experimental results. The effect of superimposed thermal buoyancy in the same range of Reynolds numbers was studied for various Richardson numbers. The steady separated flows become unsteady periodic in the presence of superimposed thermal buoyancy. For the unsteady periodic flows, the Strouhal numbers were computed. The separation angles and average Nusselt number for such unsteady flows were found to vary with time.     

HEAT TRANSFER AND HYDROMAGNETIC CONTROL OF FLOW EXIT CONDITIONS INSIDE OSCILLATORY SQUEEZED THIN FILMS

The influence of fluids inertia and the effects of the presence of a magnetic field normal to the direction of the flow of an electrically conducting fluid are studied on flow and heat transfer inside a nonisothermal and incompressible thin film undergoing oscillatory squeezing. The governing equations have been nondimensionalized and solved numerically. Further, the influence of the squeezing Reynolds number, thermal squeezing number, Hartmann number, and the squeezing frequency are determined. It is shown that flow instabilities appear at large squeezing Reynolds numbers and that the Nusselt number is affected by inertia effects as a result of increased squeezing Reynolds number. Further, it is found that flow instabilities are reduced when the magnetic field is introduced.     

A VARIABLE-DENSITY PROJECTION METHOD FOR INTERFACIAL FLOWS

General second-order, variable-density, three-step and four-step projection methods are developed to simulate unsteady incompressible interfacial flows. A high-accuracy, variable-density RKCN projection method is presented, in which the three-stage, low-storage Runge-Kutta technique and second-order semi-implicit Crank-Nicholson technique are employed to temporally update the convective and diffusion terms, respectively. To reduce computation cost, a simplified version of the projection method is also presented, in which the pressure Poisson equation (PPE) is solved only at the last substage. The level set approach is employed to implicitly capture the interface for falling droplet flows. Three-dimensional bubble rising flows and two-dimensional falling droplet flows in a small closed channel are studied numerically via the present method. By the definition of the effective pressure, the flow mechanisms for falling droplet flows with different density ratios, viscosity ratios, Weber numbers, and Reynolds numbers are discussed.     

导叶约化中心位置对涡轮非定常气动计算的影响

针对工程上常用的基于叶片数约化的涡轮非定常计算方法,为了掌握导叶约化中心位置对于涡轮内部流动非定常计算结果的影响规律,对导叶前缘约化、导叶尾缘约化、不约化三个算例进行了非定常计算与对比分析.研究结果表明:导叶前缘约化方式对于涡轮气动性能时均值影响量级在1％以上,而导叶尾缘约化方式的影响不到前者的1/2;两种约化方式均能...     

An Experimental Study on 3—D Flow in an Annular Cascade of High Turning Angle Turbine Blades

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