The Problem of Authenticity of Initial and Thermal Boundary Conditions in the Code Validation Analysis
by
Jerzy Banaszek
Institute of Heat Engineering, Warsaw University of Technology, Poland
Coauthors: Marek Rebow (Institute of Heat Engineering, Warsaw University of Technology)

If a computer simulation is to have a major impact on the design of engineering hardware or to be a desirable supplement to an experimental study of complex phenomena, we first have to be convinced that this simulation has a satisfactory level of confidence. Such analysis consists of two procedures: verification and validation. The former one is the process that demonstrates the ability of a numerical model and its computer program to solve specific set of governing equations. It establishes the level of accuracy and sensitivity of the results to parameters appearing in the discrete formulation through purely numerical experiments. This procedure is based on both grid refinement study and comparison of the results with other available solutions of some benchmark problems. The verification procedure, although indispensable, is not sufficient to establish the confidence of numerically obtained predictions. Indeed, for engineers and physicists the most important issue is the degree to which the computer simulation is an accurate representation of reality, i.e.: the degree to which inevitable simplifications of physical and mathematical models reflect reality. This is established through the code validation procedure where calculations are extensively compared with trustworthy detailed experimental measurements.

In complex phenomena of coupled fluid flow/heat transfer with the solid-liquid isothermal/non-isothermal phase transition an experimental study is very often difficult and prohibitively expensive, particularly for materials with high fusion temperatures (e.g. metallic alloys). Therefore, in such cases the computer code validation procedure is rather performed through comparing the calculations with experimental data for some substitute media, which solidify or melt in the way similar to the materials of interest but in much lower temperatures. For example, in the case of isothermal phase change, melting of gallium [1] or freezing of pure water [2,3] in the differentially heated cavity is studied experimentally, whereas an aqueous ammonium chloride solution [4] is used to mimic the metallic alloy solidification occurring in the range of solidus-liquidus temperatures.

The freezing process of pure water, driven by natural convection in fluid and conduction in both phases, is often used as an experimental benchmark [2,3,5], which is a challenging test for a computer simulation of the solid liquid phase transition. Indeed, water is a fluid that does not obey the Boussinesq approximation of the linear buoyancy force-temperature relation because water density at low temperatures is a non-linear function of temperature. Water density anomaly creates a complex flow pattern that contains two different circulation regions - the hot clockwise vortex and the cold counter-clockwise one. Moreover, experimental investigations of fluid flow and heat transfer processes in the solidifying water are relatively easy to arrange in a small laboratory scale. The up-to-date field acquisition technique, where Thermochromic Liquid Crystal suspended in water as seeding along with the Digital Particle Image Velocimetry and Thermometry can be used here to get detailed, transient, local two-dimensional velocity and temperature fields [2,3,5]. Such experimental findings are commonly acknowledged as exact and reliable enough to be a reference standard for comparison with numerical results [2,3].

However, when water freezes in a small cavity (typically used in experiments), high sensitivity of flow structure and, thus, of the temperature field, to thermal boundary conditions is observed. Moreover, at early times of the process the effect of water super-cooling occurs in the cavity [3,5].

It significantly changes the early-time flow structure and temperature field, and retards the regular ice formation. Therefore, it is reasonable to expect that the calculations can also be affected by some ambiguity of the assumed heat transfer coefficients and by the accuracy of numerical modeling of the real boundary conditions (those that occur during experimental investigations).

To elucidate the problem, the experimental findings reported in [2,3,5], are compared with the results of computer simulation of natural convection of pure water in a square cavity at low but positive temperatures and during the freezing process.

The computationally efficient numerical model has been developed [5] through the combination of the projection method [6], semi-implicit time marching scheme [6,7] and the enthalpy-porosity approach [8] along with equal-order or unequal-order finite element space discretization [9]. This computer code has been used to calculate the natural convection and solidification of pure water inside the cavity and heat conduction in the cavity walls as the conjugate circumstance for diverse thermal boundary conditions imposed on external surfaces of the cavity.

Detailed comparison of the calculated local flow pattern, temperature field and the temporal front shape and position shows significant impact of the initial and thermal boundary conditions on the velocity and temperature distribution in the cavity. Thus, the problem of the authenticity of these conditions is crucial when the above-discussed experimental benchmark is used in the detailed code validation analysis. Special care is needed for precise modeling of realistic boundary and initial conditions to avoid some ad hoc, but not necessary fully correct, conclusions concerning the accuracy and the scope of validity of the computer simulation.

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Date received: May 26, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caco-40.