introduction

reliable operation of electronic devices is dependent on maintaining the temperature of the heat dissipating components in a prescribed range. therefore, thermal design constitutes a very important part of the overall design. computational analysis of flow and heat transfer in electronic systems allows thermal designers to perform parametric studies for design optimization.

the technique of computational fluid dynamics (cfd) is widely used by thermal engineers for this purpose. cfd analysis of such systems provides accurate and detailed information about the flow and temperature distribution. with the availability of application specific tools, thermal engineers widely use cfd analysis in the thermal design process.

another technique for the prediction of systemwide distribution of flow and temperature distribution is flow network modeling (fnm). it involves representation of an electronics cooling system as a network of flow paths and components possessing empirically determined flow and thermal characteristics. use of overall component characteristics allows simple, quick, and accurate analysis of flow and temperature distribution of the coolant throughout the system. therefore, fnm is well suited for rapid evaluation of the various design options that is required during the conceptual design of the system.

the purpose of this case study is to present the results of the flow distribution in an electronic cabinet containing a card array computed using cfd (compact [1]) and fnm (macroflow [2]). the flow distribution corresponds to a manifold situation which is encountered in many engineering applications and is known to result in a nonunoform flow distribution. compact-based cfd analysis resolves the details of the flow while macroflow predicts the overall flow distributions. it is of interest to compare the effort and the results of the two approaches.

physical system

figure 1 shows the physical situation that is representative of an electronic cabinet. the geometrical configuration and the boundary conditions are chosen with a view to capture the complexity of the flow distribution in practical forced-flow, air-cooled electronics devices while keeping the problem definition simple. the cabinet contains an array of cards with each card having a surface mounted component represented as a rectangular blockage.

the cards are oriented vertically. the flow enters horizontally in the bottom left corner and exits from the top right corner. the flow distribution in the various passages is governed by the interaction of the flow inertia and the resistance to flow in the individual passages. the assumption of two-dimensionality simplifies the cfd solution while retaining the essential physical phenomena that govern the flow distribution. it corresponds to a combination of forward-flow combining and dividing manifolds.

as such, it constitutes a stringent test for comparing the flow distribution predicted using fnm with the detailed predictions obtained with cfd.

figure 1. physical situation for the electronic cabinet.

the various physical dimensions of the cabinet are shown in figure 1 in centimeters. calculations of the flow distributions are performed with following fluid properties and flow conditions for air.

a flow uniform velocity profile is assumed at the inlet. the resulting reynolds number for the flow (based on the inlet velocity and the hydraulic diameter of inlet opening) is 20000. the flow is assumed to be steady and in the turbulent regime.

computational solution

cfd analysis using compact is based on control volume method of patankar [3] for discretization of the governing equations and incorporates the simpler algorithm for handling the velocity-pressure coupling. results of the grid independence study showed that refining the grid from 60x17 to 104x66 caused only a 1% change in the magnitudes of the overall flow rates in the vertical passages between the cards.

the reported results correspond to a grid size of 104x66. a total of 300 iterations were required to obtain a converged solution with a corresponding cpu time of 9 minutes on a pentium 133 pc. finally, the time required to define the problem using a graphical preprocessor and examination of the results using a postprocessing program required a total of 3 hours. it should be noted that the time required for model setup, calculation and examination of results for a three-dimensional model is an order of magnitude more than that for the two-dimensional model used here.

fnm analysis using macroflow

figure 2 shows the network representation of the electronic cabinet. each part of the network directly corresponds to the relevant portion of the physical system. important features of the model are as follows:

figure 2 - macroflow representation of the flow network for the cabinet.

• each tee junction in the supply channel at the bottom represents division of the incoming flow stream into a stream between the cards and the remaining fraction that continues forward. similarly, each tee junction in the channel at the top represents merging (combining) of the streams from the card array.

• each card passage is represented by three ducts in tandem. the middle duct, which has a smaller cross-section due to the blockage created by the electronic component, is preceded by a sharp area contraction and is followed by an abrupt expansion.

• the incoming flow is specified in the fixed flow link at the inlet while a fixed pressure is specified at the exit.

• the ducts are characterized by appropriate cross-sectional areas and lengths and the friction factor is calculated using the moody chart that is incorporated in macroflow.

• the pressure loss characteristics of all the components in the network, available in macroflow, are taken from idelchik [3] and blevins [4].

network solution for the cabinet requires 25 seconds of cpu time on a pentium 133 pc. also, the time required to define the problem using a graphical preprocessor and examination of the results required a total of 20 minutes.

results

the detailed flow and pressure fields predicted using cfd analysis are shown in figure 3. due to its large inertia (high reynolds number), the fluid continues to flow forward in the supply channel at the bottom. therefore, there is only a small amount of flow in the first few passages between the cards. majority of the flow goes through the last three passages with the last passage carrying the maximum flow. the flow field shows recirculation at the entrance and behind the component blockage in each of the vertical passages between the cards.

it is of interest to examine the variation of the static pressure field in the cabinet. the static pressure in the bottom main channel increases continuously because of a gradual decrease in velocity away from the inlet. further, the pressure is maximum in the right corner because of flow impingement. in the top main channel, the flow streams from the card array passages merge to give rise to a continuous increase in the flow velocity. this causes the pressure in the top channel to decrease from left to right.

figure 3. predicted results using cfd analysis.

fnm predicts the total flow and the end point pressures for each flow path and component in the network. the flow directions in the network, indicated by arrows in figure 2, agree with the detailed flow pattern in figure 3. as seen in the cfd analysis, fluid inertia determines the flow split at junctions. macroflow analysis accounts for the fluid inertia through the nonlinear dependence of branch loss factors in tee junctions on the amount of flow split.

figure 4 shows a comparison of the total flow rates in the card passages predicted by fnm and cfd. the overall flow rate in the cfd calculation is determined by integrating the velocity profile across the passage. it is seen that the flow rates predicted using fnm results agree with the corresponding cfd predictions within 7%. figures 5 and 6 show the variation of the average pressures at the two ends of each card passage in the top and bottom channels respectively.

the fnm values are obtained by averaging the static pressures at the ends of the tee junctions while cfd values are obtained by averaging the static pressure in the volume directly above each card passage. since calculations are done assuming a constant density, variation of the pressure relative to an average pressure is plotted. this average pressure is calculated by averaging the pressures in the top and bottom channels. fnm analysis correctly predicts the increase (decrease) in the static pressure in the top (bottom) channel.

further, the fnm results agree with the cfd results within 15%.

figure 4. comparison of the mass flow distribution in the card array
predicted using cfd and macroflow.

figure 5. comparison of the pressure variation in the bottom channel
predicted using cfd and macroflow.

figure 6. comparison of the pressure variation in the top channel
predicted using cfd and macroflow.

conclusions

this case study demonstrates the use of two flow analysis techniques, computational fluid dynamics (cfd) and flow network modeling (fnm), for the prediction of the flow distribution in an electronic cabinet. cfd analysis is performed using compact while fnm analysis is performed using macroflow. the geometry and boundary conditions for the electronic cabinet are chosen so as to create a simplified representation of a real system while retaining the essential features of the underlying fluid dynamics.

results of the analysis show that the overall flow and pressure distributions predicted using macroflow are in excellent agreement with the compact predictions. further, macroflow analysis requires an order of magnitude less time than the corresponding cfd analysis and is ideally suited for use in the system-level design. it allows rapid evaluation of the thermal performance of various design options in a scientific manner.

use of cfd can then be made in the detailed design for accurate prediction of thermal performance of fewer designs and parts of the overall system. an enhanced design cycle which incorporates this two-level analysis results in a significantly shorter design cycle and improves the productivity of the thermal design engineer.

references

1. compact - users manual, innovative research, inc., 2520 broadway street ne, suite 200, minneapolis, mn 55413.

2. macroflow - users manual, innovative research, inc., 2520 broadway street ne, suite 200, minneapolis, mn 55413.

3. patankar, s. v., 1980, "numerical heat transfer and fluid flow," hemisphere publishing corporation, new york.

4. idelchick, i. e., 1994, "handbook of hydraulic resistance", 3rd edition.

5. blevins, r. d., 1984, "applied fluid dynamics handbook".