1、4767 Development of Computer-Aided Design Program for Refrigerator Duct Systems Youn-Jea Kim, PhD Member ASHRAE S.-K. Park, PhD ABSTRACT In order to effectively design the complex duct systems in a refrigerator, which consists of evaporatol; fan, and various shapes of duct, a computer-aided design p
2、rogram for refrig- erator duct systems is developed by using both the thermal networkandextended T-method. The technique of this program allows rapid and accurate comparison ofthe relative perfor- mance of different designs and suggests different design improvements. The developed program is verifie
3、d by compar- ison of its calculated flow properties with those from CFD analysis for the same model. There are some discrepancies between these results, since the developedprogram has a one- and two-dimensional approach, while the CFD analysis used is a full three-dimensional approach. However, comp
4、arison results show a qualitatively good agreement. INTRODUCTION Many different shapes of ducts (e.g., round, square, rect- angular, and flat-oval, etc.) are used in HVAC (heating, venti- lating, and air-conditioning) systems. As the complexity of the duct system increases, there is an ever-increasi
5、ng demand for tools to improve the quality of the product and the productivity of the designers. A trend accompanying this demand is to design the duct system to be compact and modular. In general, the design of duct systems proceeds through three design stages, i.e., conceptual system design, detai
6、led design, and design verification. A good layout of the system needs to be developed at the end of the conceptual design stage in order to avoid costly design changes later in the design cycle and to meet increasingly stringent time-to-market demands (Stein- brecher 1999). Jang-Hyuk Moon S.-K. Oh,
7、 PhD The traditional approach in designing and analyzing such complex systems is to model the fluid behavior and heat trans- fer using CFD (computational fluid dynamics) analysis. This provides valuable information about the flow and temperature distribution throughout the system. However, such anal
8、ysis for an entire system would be time-intensive in terms of model definition, computation, and visualization of results. More- over, such details may not be necessary for system-level ther- mal design and concept during the early part of the design cycle. There are valuable techniques for quick an
9、d accurate prediction of the system-wide flow and temperature distribu- tion in a duct system design, i.e., the extended T-method and thermal network analysis. Here the extended T-method is modified from the simple T-method (ASHRAE 1997), which employs the Darcy-Weisbach equation to obtain the flow
10、distribution. Also, the temperature distribution is determined from the composition of thermal network. If the heat dissipa- tion is known, the temperature can be determined from the surface heat transfer coefficient. On the other hand, for a component exposed to an external environment, the tempera
11、- ture distribution within a component may be determined from the overall heat transfer coefficient. The formation of empiri- cal correlations are used to determine the Nusselt number for each component that participates in heat transfer. Tsal et al. (1988, 1990) developed a duct analysis program us
12、ing the simple T-method. They predicted the flow rate and the pressure drop at each duct section that was designed by the equal friction method. But the simple T- method can be applicable only to an open duct system in which the flow direction at each duct section is already fixed. Lee et al. (2001)
13、 modified the simple T-method and applied it to actual loop duct systems in a full-scale building. Youn-Jea Kim is a professor and Jang-Hyuk Moon is a student in the School of Mechanical Engineering, Sungkyunkwan University, Suwon, Korea. S.-K. Park is a group leader and S.-K. Oh is director at Sams
14、ung Electronics, Suwon, Korea. 282 02005 ASHRAE. In this study, we have developed a flow analysis program for optimal design of refrigerator duct systems, based on GUI (graphic user interface) and module concepts. Also, the devel- oped program is written on the basis of the extended T-method and the
15、rmal network approach. THEORETICAL BACKGROUND Extended T-Method The purpose of the extended T-method simulation is to determine the flow rate at each section of duct systems that contain loop ducts of known sizes and fan characteristics. This method is applicable to the following major principles: 1
16、. At each node the flow in is equal to the flow out. 2. The overall pressure drop along a possible path connecting an inlet with an exit is equal to the increase in fan pressure. The flow rate and the static pressure of the fan are decided according to the fan characteristic curve. Details on the ex
17、tended T-method and its calculated procedures are found in Lee et al. (2001). Prediction of the system-wide flow distributions requires specification of the flow characteristics of the components used in the model. In particular, the pressure loss per specific weight due to friction can be found fro
18、m the following Darcy-Weisbach relation: 3. where f denotes the friction factor, L is the length of duct, Dh is the hydraulic diameter, and is the minor loss coefficient. For the repetition calculation, Q2 is represented as the multi- fication the flow rate acquired in the previous step (QO) by the
19、flow rate acquired in the present step (Q). Also, C, means all the terms excluding flow rate. Here the minor loss coefficients (Le., entrance, elbow, diverging or converging T, etc.) are found from handbooks (Idelchik 1994; Blevins 1992; ASHRAE 2000). It is noted from the above equation that the pre
20、ssure loss in a component can be represented as a function of flow rate. Moreover, the friction factors of each duct can be defined from the Moody chart and also calculated by follow- ing formula: In the extended T-method, each component in the system is represented by a combination of link and node
21、s. Pressure is calculated at each node, while the flow rates are associated with link. Furthermore, mass conservation is imposed at each node of the network. It has the following form with the sum carried out over all the flow paths that meet at the junction under consideration. n The pressure loss
22、is imposed at eachjunction. AP Zhf = - ?I (3) (4) n I where y denotes the specific weight of the working fluid. By virtue of Equations 3 and 4, the volumetric flow rate and the pressure at each component can be obtained by solving the following form of matrix equation: Thermal Network Analysis A wid
23、ely used discretization method for modeling ther- mal systems in the HVAC industry is the thermal network approach. A thermal network is generally defined by set of nodes and conductances. In this approach, the flow paths and the individual thermal resistance for the entire refrigerator system are i
24、dentified. When the radiation effects are negligi- ble, the steady-state thermal network equation may be written as the following form: N Qi+ R(T.-Ti) IJ J = O i = 1 ,., N (6) j= i where R, represents the thermal conductance and Qi is the heat source or sink. For the case of conduction elements, R,
25、is computed using Fouriers law, (7) where k denotes the thermal conductivity of the material, A, is the cross-sectional area through which the heat flows, and L is the length between nodes i and j. For convection elements, R, can be written as follows: R = hA2 1J where h represents the thermal conve
26、ctive coefficient and A, is the nodal surface area in contact with the fluid. A change in the bulk temperature of the component can be calculated by the heat dissipated from that component. Furthermore, the average temperature of the component is determined from the heat transfer coefficient. In thi
27、s study, the following empirical correlations of the averaged Nusselt numbers are adopted (see Figure I): 1. Free convection with the outside of the duct (Churchill and Chu 1975): 0.387RaY6 NUL = 0.825 + 9/16 8/27 ! i + (0.492,”Pr) J ASHRAE Transactions: Research (a) duct Convection f Using the Eq.
28、(IO) Convection Acrylic Using the Eq. (10) t (b) shelf Figure 1 Heat transfer of uniform cross sections. (a) Conduction and convection in a duct. (b) Conduction and convection in a shelf: where Ra, is the Rayleigh number and Pr is the Prandtl number, respectively. 2. The forced convection with shelf
29、 and inside of the duct (Mills 1999): 0.03(Dh/L)ReDhPr 1 + 0.016(D,/L)ReDhPr23 NuDh = 7.54+ (10) where D, is the hydraulic diameter, ReDh is the Reynolds number, and L is the length within the node. With the help of Equation 6, the temperature distribution can also be found by solving the following
30、matrix equation: Xlrl= yl (11) The above matrix equations (5) and (i 1) are solved by the Gauss-Seidel iteration method. Also, the calculation of the heat loss and gain in each link in combination with the impo- sition of energy balance at each junction enables one to predict the temperature distrib
31、ution in the system. CFD ANALYSIS Figure 2 shows cross-sectional views of a simplified duct system. In this study, the freezing compartment of a side-by- side type of refrigerator is selected. In order to compare the results from the computer-aided design program for refriger- ator duct systems, we
32、performed a CFD analysis of the modeled system. For the purpose of analyzing the flow char- acteristics of inner duct and exits, four different cross sections are selected. Section A represents a cross section in the y- direction along the centerline of branch 1, and Section B is along branch 2 and
33、3, respectively. Sections C and D are paral- lei to the x-z plane and represent upper and center cross sections of duct, respectively. In addition, the modeled duct system has a single inlet and seven exits. All exits have a nearly identical component configuration. The flow is driven by a fan and d
34、ivided into three branches. The dotted-line arrows show the direction of air flow. Governing Equations The equations of continuity and momentum for steady- state turbulent flow can be written in Cartesian tensor notation, as follows: Continuity: a -(puj) = o axi Momentum: where p ,u, r) and Vi are d
35、ensity, dynamic viscosity, pressure, and Cartesian velocity components, respectively. In this study, all three components of the flow velocity are calculated to consider the flow fields. Also, turbulent effects are included in the standard k-E model, which is suitable for turbulent kinetic energy k
36、and its dissipation rate E (Versteeg and Malalasekera 1995). Analytical Technique In order to elucidate the flow characteristics of a duct system, a three-dimensional grid system was made, as shown 284 ASHRAE Transactions: Research Inlet I I I I I , Section A Section B X Figure 2 Overview of the mod
37、eled duct system. in Figure 3, and the Cartesian cut-cell method was used. This method is known as an easier approach to solve this kind of complex geometry problem and to security convergent. The governing equations are solved using PHOENICS, one of the most famous commercial CFD codes. The SIMPLE
38、(semi-implicit method for pressure-linked equations) algo- rithm (Patankar 1980) and hybrid scheme are also employed. In addition, the no-slip condition is used on the wall boundary. It is presumed that there is no mass flux on the walls. In order to reduce the number of cells, the wall function was
39、 used. Also, the Neumann condition, which has zero gradients for all flow variables along the streamline, was applied on the outlet boundary since the flow variables were difficult to know on the exits. At the inlet the flow rate was fixed at 1 CMM, and turbu- lent intensity was given as 5%. Converg
40、ence was determined until residuals were on the order of and the change of number of grid points above about 140,000 did not affect the solutions significantly. FEATURES OF COMPUTER-AIDED DESIGN PROGRAM FOR REFRIGERATOR DUCT SYSTEMS The computer-aided design program for refrigerator duct systems was
41、 developed to help designers do more with fewer opportunities for trial and error. It is an object-oriented program that enables developers to quickly and easily design effective duct systems. The computer-aided design program for refrigerator duct systems is composed of Main Frame, Branch, Solver,
42、and Viewer. Main Frame and Branch are the pre-processor, and Viewer is the post-processor, respectively. Figure 3 Computational domain using Cartesian cut-cell method (1 O0 x 70 x 20). Main Frame We developed the flow and temperature analysis program for optimal design of refrigerator duct systems b
43、ased on GUI (graphic user interface) and module design concepts. Figure 4 shows the Main Frame of the program. In this window, duct designers can change the input values, i.e., units, fluid and material properties, numerics, boundary conditions, file save, and printing command, etc. Branch Figure 5
44、shows the Branch window of the computer-aided design program for refrigerator duct systems. Branch is the ASHRAE Transactions: Research 285 Figure 4 Main frame of computer aided design program for refrigerator duct systems. Figure 5 BRANCH of computer aided design program for refrigerator duct syste
45、ms. 286 ASH RAE Transactions: Research pre-processor of the program. Designers can build effective duct systems by selecting the required elements, e.g., inlet, outlet, elbow, fan, evaporator, etc. In order to prepare an anal- ysis of temperature distribution, shelves and inlet/outlet should be prop
46、erly located. In this window, duct designers are able to easily change several design parameters (Le., duct size, fan type, roughness, heat sink of evaporator, etc.) through additional and eliminative tools. Viewer The computer-aided design program for refrigerator duct systems was developed on the
47、basis of the extended T-method and thermal network approach. In this Viewer window, designers are able to get the information about the predicted results. For instance, calculated results of the flow rate and temperature distribution throughout the duct systems are depicted in Figure 6. The temperat
48、ure distribution in the freezer compartments is displayed on the bottom right comer of the Viewer window (Figure 6b). DISCUSSION The exit flow rates are obtained by three-dimensional calculation of the modeled duct system. Figure 7 shows the velocity contours at different model sections (the relevan
49、t sections of exits and inner duct are illustrated in Figure 2). For instance, S4 and S5 represent the flow patterns of inner duct. Numerical results also show that the flow rate is distributed from 0.1023 to 0.1907 CMM. It is seen that the volumetric flow rate has maximum value at (5) and minimum value at (4). The flow rate at the exits (3 and 4) shows a nearly identical value. Because of the use of overall component characteristics, the computer-aided design program for refrigerator duct systems is very quick in terms of model definition (20 minutes) and computational time (10 seco
