摘要:

A computationally efficient and highly accurate solution scheme for phase-change problems is described which combines an implicit treatment of the temperature field equations with an explicit treatment of the interface energy balance (s). This scheme avoids the iterative interaction between the field and interface solutions which characterizes a fully implicit treatment. No time-step limitations were encountered in the wide range of numerical solutions that were carried out with the methodology. The accuracy characteristics were established by comparisons with alternative solutions of a number of specific problems involving plane or radial freezing, one or two solid phases, and, in some cases, convective heating at the solid-liquid interface. Depending on the problem, the alternative solutions were analytical, semianalytical, or numerical. The accuracy level of the solid layer thicknesses given by the solution scheme were found to be in the 0.1% range.

ISSN:0149-5720    

DOI:10.1080/01495728408961808

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Numerical solutions have been carried out for planar or radial freezing on a cooled wall or cylinder maintained at a uniform temperature lower than the fusion temperature. The solutions were obtained by using an implicit/explicit method developed in the preceding paper in this issue. Results are presented for the frozen layer thick-ness, the instantaneous heat flux at the cooled surface, and the time-integrated heat transfer at the surface, all as a function of time from the beginning of the freezing period. These quantities are normalized in various ways to illuminate their short-time and long-time behaviors and to enable comparisons between planar and radial freezing. Convection at the solid-liquid interface had virtually no effect on the freezing process at short times, but at longer times the convection significantly slowed the freezing and ultimately terminated it. Solid-solid transitions tended to slow the freezing and also to increase the heat transfer at the cooled surface.

ISSN:0149-5720    

DOI:10.1080/01495728408961809

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Both the successful determination of the entrainment rate and the calculation of initial values are important aspects of the Patankar-Spatding (P-S) method since they are critical for the attainment of accurate solutions. A new scheme for calculating the entrainment rate, which is very stable and nearly problem-independent, is presented. Here, the main x dependence of the entrainment rate is estimated by using global Quantities known at the previous x step; in particular, it is found to vary inversely with the boundary-layer thickness. This estimation is adjusted by a coefficient which varies very slowly with x and which is determined by a fixed-point method. In addition, a method is given which lets the actual PS computer program generate its own initial values with desired accuracy. Finally, a new explicit formula for the transverse velocity is derived; the formula makes it possible to calculate this velocity component in a very simple manner, using only information already available as part of the solution.

ISSN:0149-5720    

DOI:10.1080/01495728408961810

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A numerical study is reported of flow and heat transfer in the separated and reattached flows created by an abrupt pipe expansion. In the study attention has been given primarily to the development of turbulence near-wall models based on the wall function. An efficient numerical method is also employed for the computation of high-velocity flows. The computed results are compared with experimental data obtained earlier. Generally better results are obtained by employing the present near-wall models, and among them the three-layer model is superior to the two-layer one.

ISSN:0149-5720    

DOI:10.1080/01495728408961811

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A numerical investigation is carried out to determine the temperature and flow pat-terra of a fluid bounded by two horizontal isothermal concentric and eccentric cylinders. The inner cylinder is assumed to be at a higher temperature and rotating. The numerical method involves a mesh transformation technique coupled with the introduction of “false transient“ parameters for the steady-state solution of the problem. The parameters studied were for a Prandtl number of 0.7 and a radius ratio of 2.6 at different Rayleigh numbers, Reynolds numbers, and eccentricities. The results show that the mean Nusselt number increases with Rayleigh number. For a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow.

ISSN:0149-5720    

DOI:10.1080/01495728408961812

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A numerical analysis of laminar flow and heat transfer in a tube bank is described. The two-dimensional Navier-Stokes and energy equations are solved numerically for successive subregions from the inlet to the exit of the bank by a procedure catted the “one step forward and half step backward iteration method” and by using a hybrid grid system. Calculations are carried out for an in-line square tube bank up to five rows deep, with pitch-to-diameter ratios 1.5 × 1.5, under the conditions of uniform tube wall temperature, Re = 60, 120, and 300, and Pr = 0.7. Stream, isovorticity, and isothermal lines through the whole tube bank, local and average Nusselt numbers, pressure distributions along the tube walls and in the flow directions, and friction factor are presented. The friction factor and average Nusselt number agree well with published experimental results. An analogous relation between an in-line tube bank and parallel plates with respect to developing heat transfer characteristics is presented.

ISSN:0149-5720    

DOI:10.1080/01495728408961813

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A numerical solution of transient laminar free convection between two concentric spheres is presented for Pr= 0.7 and Ra =100. The steady average heat transfer coefficient for the inner sphere becomes independent of the radius of the outer sphere when it is more than 40 times that of the inner sphere, and independent of the number of grid points when they are at least 61 and 46 for the radial and azi-muthal directions, respectively. Steady state is reached at a dimensionless time τ = 6 for the average heat transfer coefficient and at τ = 12 for the convection flow. The steady local Nusselt number near the top and bottom stagnation points is different from that of the previous solution of the boundary-layer equations containing curvature terms, while the average Nusselt numbers of both solutions agree within 2%.

ISSN:0149-5720    

DOI:10.1080/01495728408961814

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A numerical experiment was used to evaluate the properties of an upwind differencing scheme for a circular roll rotating at high velocity. Since the roll is rapidly rotated, the temperatures vary only within a thin layer near the outer roll surface, which results in a situation that is numerically favorable for the upwind scheme. Comparison of the present upwind results with a known analytical solution indicates that, with the same number of grid points, better accuracy is achieved at higher Peclet numbers. The present study also indicates that the numerical accuracy is greatly affected by changing mesh size in the radial direction, but is not noticeably affected by changing it in the circumferential direction for the range considered. Some specific features associated with the thermal behavior of a high-speed rotating roil are also presented to explain the numerical findings.

ISSN:0149-5720    

DOI:10.1080/01495728408961815

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor