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RESEARCH PAPERS: Heat and Mass Transfer

Functional or Operator Representation of Numerical Heat and Mass Transport Models

[+] Author and Article Information
G. Danko

 University of Nevada, Reno, 1664 North Virgina Street, Mailstop 173, Reno, NV 89557Danko@unr.edu

J. Heat Transfer 128(2), 162-175 (Aug 05, 2005) (14 pages) doi:10.1115/1.2136919 History: Received December 23, 2004; Revised August 05, 2005

A numerical-computational procedure is described to determine a multidimensional functional or an operator for the representation of the computational results of a numerical transport code. The procedure is called numerical transport code functionalization (NTCF). Numerical transport codes represent a family of engineering software to solve, for example, heat conduction problems in solids using ANSYS (a multiphysics software package by ANSYS, Inc.), heat and moisture transport problems in porous media using NUFT (Non-equilibrium, Unsaturated-saturated Flows and Transport—porous-media transport code, developed by John Nitao at the Lawrence Livermore National Laboratory), or laminar or turbulent flow and transport problems using FLUENT (a software package by Fluent, Inc.), a computational fluid dynamic (CFD) model. The NTCF procedure is developed to determine a model for the representation of the code for a variety of time-dependent input functions. Coupled solution of multiphysics problems often require repeated, iterative calculations for the same model domain and with the same code, but with different boundary condition functions. The NTCF technique allows for reducing the number of runs with the original numerical code to the number of runs necessary for NTCF model identification. The NTCF procedure is applied for the solution of coupled heat and moisture transport problems at Yucca Mountain, NV. The NTCF method and the supporting software is a key element of MULTIFLUX (by University of Nevada, Reno), a coupled thermohydrologic-ventilation model and software. Numerical tests as well as applications for Yucca Mountain, NV are presented using both linear and nonlinear NTCF models. The performance of the NTCF method is demonstrated both in accuracy and modeling acceleration.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Logical and (b) data flow charts of the NTCF model identification

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Figure 2

(a) Stepwise and piecewise input approximations for NTCF algorithm tests. (b) Results of three different NTCF postprocessing methods.

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Figure 3

Stepwise input temperature variations used for NTCF models identification

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Figure 4

Stepwise input temperature variations used for NTCF functional model fitness tests

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Figure 5

Comparison between the first-, second-, and third-order NTCF model results and the NTC (NUFT) results for heat flux; (a) back-calculated results used for model identification, (b) and (c) two NTCF model fitness test results against direct NTC (NUFT) results

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Figure 6

Comparison between the first-, second-, and third-order NTCF model results and the NTC (NUFT) results for moisture flux; (a) back-calculated results used for model identification, (b) and (c) two NTCF model fitness test results against direct NTC (NUFT) results

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Figure 7

Piecewise-linear input temperature variations for Ta and Tb

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Figure 8

All NTCF model results versus the NTC (NUFT) piecewise-linear input boundary function results for heat flux

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Figure 9

All NTCF model results versus the NTC (NUFT) piecewise-linear input boundary function results for moisture flux

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Figure 10

Application example of an NTC model (N index) and corresponding NTCF model (M index) for a four-layer model

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Figure 11

Ventilation calculation results of the NTCF-based MULTIFLUX (solid lines) and ANSYS (dots) (7)

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Figure 12

Air temperature history comparisons at 1m, 250m, and 500m distance along the airway between a reference analytical solution according to Walton, and MULTIFLUX with NUFT as well as Carslaw and Jaeger rock models (4)

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Figure 13

Heat flux response to input variable temperature with time ticks

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Figure 14

Input temperature to NTC (a). Output heat flux response from NTC (b). Output moisture flux response from NTC (c) for low temperature regime. Note the major difference in shape between the heat and the moisture fluxes, the latter being strongly nonlinear.

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Figure 15

Indicinal admittances Ah and Am for heat flux (a); and moisture flux (b), obtained by direct inverse convolution for the low temperature regime. Both Ah and Am are well conditioned.

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Figure 16

Input temperature to NTC (a). Output heat flux response from NTC (b). Output moisture flux response from NTC (c) for high temperature regime.

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Figure 17

Indicinal admittances Ah and Am for heat flux (a); and moisture flux (b) fluxes as a function of time obtained by direct as well as least-square-fit inverse convolutions for high temperature regime. The least-square-fit method provides stable results. The direct method becomes numerically unstable from a point marked in the figure; only a few waves are shown, the rest are omitted.

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Figure 18

Analytical input test functions

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Figure 19

Analytical, strongly nonlinear model response functions

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Figure 20

Analytical test, first-order model fit at the T1 input function

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Figure 21

Analytical test, second-order model fit at T1 and T2 input functions

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Figure 22

Analytical test, third-order model fit at T1, T2, and T3 input functions

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Figure 23

Analytical test, model fit comparison at T4 test input function

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