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Engineering - Refrigeration Insulation
3D Simulation of PU Foaming Flow in a Refrigerator Cabinet

by Young Bae Kim, Kyung Do Kim, Sang Eui Hong, Jong Goo Kim, Man Ho Park, and Ju Hyun Kim, LG Electronics, Korea and Jae Keun Kweon, Korea Polyol Co.

The latest refrigerator-freezer research from LG Electronics focuses on reducing electricity consumption by investigating the foaming flow of PU insulation.

Figure 1. (a) Model of a plate mold; (b) comparison of fronts of a foaming flow in a plate mold between simulation (center) and experiment (right). Velocity vector plots of foaming flows in the center plane are shown in left figures. The grid is in intervals of 5 cm.

To meet the demand for energy-efficient refrigerators, LG Electronics has put significant effort into improving insulation performance. Because consumer demands often require small, mixed production runs, the company has focused on achieving consistent Polyurethane (PU) rigid foam quality for its insulation material.

In order to obtain proper PU foam quality, it is necessary to control formation factors such as parameters, fixture temperature, flow path, air-venting holes, and injection locations of PU liquid mixture. To create a foaming process, physical factors such as viscosity dynamics, bubble dynamics, chemical reaction in the flow, heat transfer, and two-phase flow are taken into consideration.

Because of the complex geometry of a refrigerator cabinet and intricate physical chemical phenomena of PU foaming flow, it would be difficult to investigate foam flow using an empirical approach. A numerical simulation, however, can cut down design time and manufacturing cost, since foam quality is quickly and efficiently predicted.

A three-dimensional (3D) foaming flow simulation program at LG Electronics Digital Appliance Company (DAC) Lab has been developed to not only improve foam quality, but to address the complicated geometry of today’s feature-rich refrigerators (i.e., French door, in-door water/ice dispensers, TV, mini-bar, and etc.). In this study, DAC Lab researchers decided against simulation of chemical reaction and, instead, restricted the simulation scope to projecting flow pattern and filling time. As a part of the simulation, the researchers assumed conditions of uniform density and viscosity in flow domains, which are time-variant. Following is a methodology for 3D numerical simulation of a PU foaming flow and a discussion of its application in an actual refrigerator.


Numerical Methods of Simulation for Polyurethane Foaming Flow

PU foaming flows have been conditioned in compressible, unsteady, and variant-viscosity flow. The governing equation of the flow is defined in continuity and momentum equations as illustrated in Equation 1.

In order to solve the momentum equation (1) and continuity equation (2), the Finite Volume Method (FVM) is applied to spatial discretization. The semi-implicit Eulerian method is applied to temporal discretization. Unstructured brick (hexahedral) meshes are adopted to integrate the governing equations and the SIMPLE algorithm is used to solve the coupled equations[1], [2].

Air in the refrigerator cabinet is not considered in order to project a PU foam flow path without obstruction of air in the cabinet. Once air-venting holes in an actual refrigerator cabinet are properly located, the simulation results are matched with the PU foaming flow. Therefore, the interface between PU foam and air is assumed as a free surface. Free surface of foam can be traced with volume of fluid (VOF) method [3], which is known as a flexible and efficient method to treat a complicated free-surface boundary configuration. Initial condition of a PU foaming flow is determined by an injection process: A PU liquid mixture is released from injection heads that contain a mixture of liquid polyol and isocyanate. The injection process of PU liquid mixture is typically shorter than 7 sec, which is shorter than the cream time of PU. The flow is nearly incompressible. The researchers simulated the injection process of PU liquid mixture with the commercial package FLOW3D and obtained the initial conditions of PU foaming flow from the results of simulation.

Figure 2. (a) Model of a simple refrigerator cabinet; (b) initial location of PU liquid mixture and injection holes (left figure), and filled positions from simulations (right figure) and experiments (blue-filled cycles).

Verification of Numerical Methods

The researchers then conducted experiments and simulations of PU foaming in a plate mold (see Figure 1). The PU liquid mixture from the injection head is put in at the bottom of mold, and foam rises in a vertical direction. The shape of foam front obtained from simulations and experiments can be visually compared in a grid (Figure 1). The shape and location of the foam front in the simulation and the physical results from the experiments were well matched.

In order to examine reliability of the PU foaming flow simulation, the researchers compared the filled position of foam with the results of the experiments. A simple refrigerator is used to fill up the foam for the simulation and experiments (Figure 2). The injection location of PU liquid mixture and the initial position of the mixture in the refrigerator cabinet are shown in two cases. The simulated filled position in each case has been compared with the respective experiment results. The filled position obtained from simulation is highly dependent on the location of the initial PU liquid injection. As a conclusion, the filled position meets the experiment result.

Designing a Refrigerator with Numerical Simulation

Air trapped in PU foam might significantly damage insulation performance of the foam. With flow patterns obtained from simulation of a PU foaming flow, air trapping in the refrigerator cabinet can be avoided. In order to avoid air trapping in the PU foam, it is necessary to find a proper location of air-venting hole and an injection location of PU liquid mixture. An example of a PU foaming flow is shown in Figure 3. Air-venting holes are created to prevent air trapping along the A or BB line.

Another important aspect of PU foaming flow is flow distance in a refrigerator cabinet. If distance of foaming flow is longer than a designated distance, then foam quality gets poor due to surface bubbles on the foam. It is possible to set up design criteria of flow distance from experiments and compare the flow distance in a simulation of PU foaming flow with the design criteria. If a flow distance of PU foaming is longer than the design criterion, it is feasible to reduce it along with injection location of the PU liquid mixture.

Another useful result shows pressure distribution in foaming flow. Pressure distribution of foaming flow shows high correlation with density distribution of PU foam in a refrigerator cabinet. As shown in Figure 4, density of foam on the top of a cabinet is higher than the bottom, and this tendency is the same as the distribution of pressure. It is possible to project the location of maximum density in the cabinet with distribution of pressure. In order to estimate quantitative values of density distribution, it is necessary to solve chemical reaction equation of PU foaming flow.

Figure 3. An example of PU foaming flow in a refrigerator cabinet.

Figure 4. Pressure distribution at the moment of final filling. Density obtained experiments are denoted by arrow and number in the figure. The density of foam (kg/m3) is measured at the location indicated by the arrow.


This study researched 3D simulation of PU foaming flow, which is assumed to have time-variant density and viscosity without considering chemical reaction. Simulation results of foaming flow were matched with the experimental results. It is evident that improvement of foam quality and design cost reduction can come to realization by controlling foaming process in a refrigerator cabinet with numerical simulation. In the future, the researchers plan to develop a more accurate program that includes chemical reaction. This will allow the researchers to accurately project the density distribution of foam, skin layer of foam, and the effects of chemical reactivity on foam. This will be coupled with the simulation of structure and foaming flow of PU foam to study the solidification, deformation after de-mold, and structural strength of refrigerators. References

1. Patankar, S. V. 1980. “Numerical Heat Transfer and Fluid Flow,’’ Hemisphere Publishing Co., New York, USA.
2. Mathur, S. R. and Murthy J. Y. 1997. “A Pressure-Based Method for Unstructured Meshes,” Numerical Heat Transfer, Part B, 31: pp. 195-215.
3. Hirt, C. W. and Nichols, B. D. 1981. “ Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comp. Phys., 39: pp. 201-225.

This is an edited version of a paper presented at the Polyurethanes Conference 2004, held in Oct. 18-20, 2004, Las Vegas, NV, U.S.