NUMERICAL STUDY OF THE INFLUENCE OF DYNAMIC AND THERMAL EXIT CONDITIONS ON AXISYMMETRIC LAMINAR BUOYANT JET

We propose in our article numerical solutions of the Navier-Stokes equations governing the buoyant round laminar jet. The purpose of this work is to study the influence of the exit conditions at the nozzle exit on the dynamic and thermal parameters of the vertical jet flow. Two emission cases have been considered: Velocity and temperature are uniform or parabolic. The numerical code developed uses a finite difference scheme. The numerical results have been compared with those given by Martynenko, who considered in his analysis only two integration constraints: the momentum at the nozzle exit and the conservation of the energy transported by the jet flow. The obtained results are in good agreement with those proposed in the literature in the plume zone, in which the emission conditions are ignored, and the jet flow is governed mainly by the buoyancy forces. We propose in this paper a correlation to predict the axial virtual origin Xp of the plume zone. Experiments were conducted to validate the numerical model using a nonintrusive method, namely, laser doppler velocimetry.     

NUMERICAL INVESTIGATION OF CONVECTION HEAT TRANSFER IN A HEATED ROOM

We describe numerical investigation of airflow and temperature field in a room with a convective heat source. The simulation involves using computational fluid dynamics (CFD) to validate different turbulence models, i.e., the standard k- k model and the low Reynolds number k- k model. The comparisons between computations and experiments show good and acceptable agreement. It can be concluded that the CFD simulations can capture the main flow features and provide satisfactory results. It can be seen that the thermal wall jet created by the heat source greatly influences airflow pattern and temperature field in the room. It can also be seen that the advanced turbulence model may produce better results than the standard one under a suitable mesh scheme.     

NUMERICAL STUDY OF DEVELOPING NATURAL LAMINAR CONVECTION IN A VERTICAL HYPERBOLIC DUCT OF A FIXED LENGTH AND WITH A CONSTANT WALL TEMPERATURE

The natural laminar convection in a vertical hyperbolic duct of a fixed length and with a constant wall temperature is numerically investigated. The governing equations are solved by a finite difference method. The results are obtained for the velocity, temperature, and pressure fields, and for the mean heat transfer coefficient. The numerical calculations are fulfilled for Rayleigh numbers ( Ra ) ranging from 5 to 3 · 104 and for the numerical eccentricity ranging from 5 to 100. The effects of the numerical eccentricity and Ra are examined and the results are compared with those of a cylindrical vertical duct. It was found that the flow fields and Nusselt number ( Nu ) are affected significantly at small values of the numerical eccentricity and Ra .     

NUMERICAL SIMULATION OF FLOW PATTERN FORMATION IN A BOTTOM HEATED CYLINDRICAL FLUID LAYER

Abstract

The temporal formation of the buoyancy-driven flow structures in a bottom heated, shallow, cylindrical fluid layer was numerically studied. The unsteady three-dimensional Navier-Stokes and energy equations were discretized by the power law scheme and solved by the fully implicit Marker-and-Cell method. Computations were carried out for the pressurized argon (Pr=0·69) and water (Pr=6·1) layers for various Rayleigh numbers and heating rates of the layer. In the pressurized argon layer at a slightly supercritical Rayleigh number with Ra_f;=1·05Ra_c a steady straight roll pattern was formed when the heating rate was very slow (a=0·001) after a long transient stage. When the heating rate was raised to a=0·01, a very different structure tike U-rolls was formed at steady state. In the water layer with Ra_f=l·05Ra_c, a straight roll pattern was again formed, but at a equals;0·07. At Ra_f;=1·13Ra_c, curved rolls with the three foci at the sidewall were formed for a=0·01. A pattern in the form of U-rolls appears at a=0·01. Regular concentric circular rolls prevail at a=1·0. When the Rayleigh number is further raised to 1·23Ra_c, the resulting steady flow is dominated by incomplete circular rolls with open ends near θ=0°     

A NUMERICAL STUDY OF JETS IN A REACTING CROSSFLOW

This article is concerned with computational modeling of the mixing of circumferentially placed round jets with a crossflow in a circular duct. This flow is relevant to many engineering applications including gas turbines and steel melting furnaces. Both nonreacting and reacting flows are considered. The fundamental characteristics that govern the mixing of the air and fuel streams are investigated. Further, the applicability of a laminar flamelet model for prediction of the combustion process is assessed through comparison of code predictions to experimental data.     

蒸汽喷射压缩器喷射系数计算方法研究

对蒸汽喷射压缩器的原理及工作过程进行了较深入的分析，从热力状态变化的角度出发，以索科洛夫计算方法为基础进行简化处理，推导出一种计算喷射系数的简便方法。文中也给出了索科洛夫方程的计算程序。大量对比计算表明，两种方法计算结果一致。     

A NUMERICAL INVESTIGATION OF THE CONVECTIVE HEAT TRANSFER IN UNSTEADY LAMINAR FLOW PAST A SINGLE AND TANDEM PAIR OF SQUARE CYLINDERS IN A CHANNEL

The unsteady laminar flow and heat transfer characteristics from square cylinders located in a channel with a fully developed inlet velocity profile were studied numerically. The time-averaged Nusselt number for each face and the time-averaged cylinder Nusselt number (Nu) were determined, as well as aerodynamic characteristics such as cylinder lift, drag, and eddy-shedding Strouhal number (St) . The results show that the cylinder Nu decreases for both the single and the tandem pair of cylinders as they approach the channel wall. The upstream eddy-promoting cylinder significantly reduces the drag of the downstream cylinder as compared with that of the single cylinder. The St decreases as the wall is approached and is larger for the tandem pair than for the single cylinder for all positions.     

LAMINAR FULLY DEVELOPED MIXED CONVECTION IN INCLINED TUBES UNIFORMLY HEATED ON THEIR OUTER SURFACE

The problem of conjugate heat transfer involving mixed convection laminar ascending flow of water in inclined circular tubes uniformly heated on their outer surface has been studied numerically using a unified formulation for the solid and fluid domains. The highly coupled governing equations were discretized using the control volume approach, and solved according to the SIMPLER algorithm. Results have clearly demonstrated that the conduction within the tube wall has an important influence on both the hydrodynamic and thermal fields. High wall thermal conductivity or large thickness reduces the temperature stratification within the fluid and intensifies the secondary motion, consisting of two symmetrical vortices. The effects of wall conduction are particularly significant for horizontal tubes for which the average Nusselt number is bounded by two limits corresponding to the cases of infinite wall thermal conductivity and zero wall thermal conductivity. For Gr = 2 × 10⁵ these limits are 10.42 and 9.03, respectively. These effects are negligible for tubes inclined at 30° and for Grashof number below 3 × 10⁴.     

NUMERICAL EVALUATION OF WEAKLY TURBULENT FLOW PATTERNS OF NATURAL CONVECTION IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED SIDE WALLS

This article presents the results of numerical evaluation of weakly turbulent natural convection of air in a rectangular enclosure with differentially heated side walls and adiabatic horizontal walls. The turbulence in the natural convection was described by k–ε equations, which were solved by Strang splitting, while average thermal and fluid flow fields were described by statistically averaged equations, which were solved by the projection method PmIII. The combined application of projection method and the Strang splitting characterizes the numerical method in this study. Numerical results for Rayleigh number 1.58 × 10⁹ have revealed reasonable agreement with the existing experimental ones, with some discrepancy attributable to the adiabatic boundary conditions on the horizontal walls. The results are also in good agreement with some published numerical results, particularly at higher Rayleigh numbers. However, comparison with the latest experimental data reveals that the turbulent heat flux model is not quite capable of giving satisfactory temperature distribution.     

NUMERICAL SIMULATION OF LAMINAR FORCED CONVECTION IN AN AIR-COOLED HORIZONTAL PRINTED CIRCUIT BOARD ASSEMBLY

A numerical solution of the steady-state forced convection for air flowing through a horizontally oriented simulated printed circuit board (PCB) assembly under laminar flow condition has been developed. The considered assembly consists of a channel formed by two parallel plates. The upper plate is thermally insulated, whereas the bottom plate is attached with uniformly spaced identical electrically heated square ribs perpendicular to the mean air flow. The bottom plate is used to simulate the PCB, and the ribs with heat generation are used to simulate the electronic components. A second-order upwind scheme is adopted in the calculation and a very fine mesh density is arranged near the obstacle and the channel surface to achieve higher calculation accuracy. Four Nusselt numbers (Nu) are of particular interest in this analysis: local distribution along the rib's surfaces, mean value for individual surfaces of the rib, overall obstacle mean value, and overall PCB mean value between the central lines of two obstacles. The effect of the obstacle size and the separation between two obstacles is discussed systematically.     

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.     

NUMERICAL INVESTIGATION OF TWO-DIMENSIONAL LAMINAR FLOW AND SOLUTE TRANSPORT IN A CHANNEL WITH SOME SYMMETRIC EXPANSIONS AND CONTRACTIONS

Numerical investigation of two-dimensional (2D) laminar flow and solute transport in a channel with some sudden symmetric expansions and contractions has been performed using the fictitious regions method. This method allows us, instead of solving Navier-Stokes equations in a complex domain, to solve equations with suitably continued coefficients in a rectangle. Stream function-vorticity variables are used in the present paper. Dependence of the flow and solute transport from the dimensions of the channel expansions and contractions is numerically investigated for different values of Reynolds and Péclet numbers using a finite differences method on a relatively fine grid.     

LAMINAR IMPINGING JET HEAT TRANSFER WITH A PURELY VISCOUS INELASTIC FLUID

Laminar impinging flow heat transfer is considered with a purely viscous inelastic fluid. The rheology of the fluid is modeled using a strain rate dependent viscosity coupled with asymptotic Newtonian behavior in the zero shear limit. The velocity and temperature fields are computed numerically for a confined laminar axisymmetric impinging flow. Important features of the non-Newtonian developing flow field are described and contrasted with the Newtonian situation. It is demonstrated that very small departures from Newtonian rheology lead to qualitative changes in the Nusselt number distribution along the impinging surface. In particular, a mildly shear thinning fluid displays a pronounced off-stagnation point heat transfer maxima, a feature that is not observed with a Newtonian fluid. Hence, Newtonian fluid approximations cannot adequately describe experimental heat transfer measurements in such situations even though they may be deemed acceptable in terms of describing the velocity field in the incoming nozzle. Numerical results are presented to analyze the effect of the dimensionless nozzle-to-plate distance, the rheological parameters, and the Reynolds and Prandtl numbers on the magnitude of the off-stagnation point peak heat transfer rate. The influence of the rheology of the fluid is particularly significant at low nozzle-to-plate distances since the mean strain rate in the flow field increases as the nozzle-to-plate distance is reduced. The numerical heat transfer results are interpreted in the context of the developing flow field.     

NUMERICAL STUDY OF COMPRESSIBLE TURBULENT FLOW IN MICROTUBES

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line flow and the experimental data assume that the flow is adiabatic, but in reality, compressible, turbulent microtube flows are neither adiabatic nor isothermal, as demonstrated by the numerical results in this study.     

NUMERICAL ANALYSIS OF ULTRAFAST HEAT TRANSFER WITH PHASE CHANGE IN A MATERIAL IRRADIATED BY AN ULTRASHORT PULSED LASER

This study is concerned with problems of ultrafast and high heat flux heat transfer with phase change. We employ the cubic interpolated propagation (CIP) method coupled with a thermoconvective model to examine the history of large-scale phase change, that is, melting and evaporation, and the mechanisms of heat transfer as a wave. It is found that wave-type heat transfer as a shock wave with phase change can be simulated without a hyperbolic heat conduction equation by means of the CIP method. Melting and evaporation occur in the energy deposition region, and energy is transferred by a shock wave beyond an energy penetration depth. The propagation velocity is hardly damped outside the energy deposition region inside aluminum thin foil, but the peak value in density, pressure, and temperature is damped rapidly. For one of the dissipation process mechanisms, generation of thermal stress can be considered. Further, it is found that the initial velocity of shock wave generated inside the energy deposition region is different for each initial incident laser intensities, though the propagation velocity is constant beyond the energy penetration depth in spite of an initial incident laser intensity.     

A NUMERICAL STUDY OF SOLIDIFICATION IN THE PRESENCE OF A FREE SURFACE UNDER MICROGRAVITY CONDITIONS

A numerical study of the relative importance of Marangoni effects under microgravity conditions is presented. The mathematical formulation adopted is based on the enthalpy porosity method. One of the advantages of the fixed grid method is that a unique set of equations and boundary conditions is used for the whole domain, including both solid and liquid phases. The governing equations written in a vorticity-velocity formulation are discretized using a finite volume technique on a staggered grid. A fully implicit method has been adopted for the mass and momentum equations, while the temperature field is solved separately in order to evaluate the variation in the local liquid mass fraction. The resulting algebraic system of equations is solved using a preconditioned BI-CGStab method. Numerical results modelling the free surface, including the effects on it of Marangoni convection, are presented. The influence of the presence of argon in the gap above the free surface is investigated. During the numerical simulations presented in this paper 161 2 41 and 641 2 161 uniform meshes on the whole computational domain for values of Marangoni number ( Ma ) up to 16,120 and Rayleigh number ( Ra ) of 5 have been used.     

NUMERICAL COUPLING OF MULTIPLE-REGION SIMULATIONS TO STUDY TRANSPORT IN A TWIN-SCREW EXTRUDER

A new simplified approach has been proposed toward coupling of the numerical simulation of transport phenomena in multiple regions in order to model complex domains. This approach is employed to study a tangential corotating twin-screw extrusion process. The flow domain in a twin-screw extruder is divided into the translation region (T region) and the intermeshing region (I region) The two regions are simulated separately and then coupled for each screw section, to model the overall transport. A finite difference method is employed in the T region, while a finite element method is employed for the I region. A procedure for coupling of the two flow regions is presented.     

TWO-DIMENSIONAL PROBLEM OF A MOVING HEATED PUNCH IN GENERALIZED THERMOELASTICITY

The two-dimensional equations of generalized thermoelasticity are solved for the case of a heated punch moving across the surface of a semi-infinite thermoelastic half-space subject to appropriate boundary conditions. The exponential Fourier transform with respect to one space variable in a coordinate system moving with the punch is applied. The resulting equations are solved and numerical results are given. The results are compared with those obtained by Roberts for the coupled thermoelastic case.     

土壤源热泵夏季运行特性的实验研究

根据对土壤源热泵夏季运行性能的实测,对夏季制冷工况的启动运行特性与间断运行特性进行了实验研究。实测结果表明,南京地区土壤源热泵夏季运行的启动时间为8～9h,其单位埋管放热量为44～49 W/m,平均传热系数为3.4W/(m·℃)。同时,采用可控间断运行方式可以在有效降低地下土壤温升率及机组进口温度以改善机组运行性能的同时,提高单位埋管的换热能力,从而更有利于提高浅层地热能的利用效率。