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Design and Analysis of Liquid-Cooling Systems Using Flow Network Modeling (FNM)

Liquid cooling is being used more and more for the thermal management of electronics due to increasing power densities in defense, power electronic, medical, and computer applications. These systems involve closed-loop circulation of a coolant and include components for flow distribution (e.g. tubes and pumps), flow control (e.g. valves and orifices), and heat transfer (e.g. cold plates and heat exchangers). The objectives in the design of these systems are to create a sufficient amount of total flow and to distribute the flow to maintain the electronic component temperature at the desired level.

Flow Network Modeling (FNM) can be a powerful tool for the system-level design of liquid-cooling loops. This article describes the design process of a typical liquid cooling loop using the software program MacroFlow™[1], a FNM-based analysis tool, to illustrate its benefits.

Suitability of FNM for System-Level Design of Liquid-Cooling Loops

The FNM technique constitutes a simple, rapid, and accurate method for the analysis of flow and temperature distribution in liquid-cooling systems (Belady et al. [2], Kelkar [3]). It involves the following steps:

  • Network representation of a liquid-cooling system to describe the arrangement of the various components and flow paths.
  • Characterization of components by empirical correlations that relate the overall pressure drop and thermal resistance to the corresponding flow rate using correlations from handbooks (Idelchik [4], Blevins [5]), vendor data, or experimental measurements.
  • Solution of the conservation equations over the network for a rapid determination (less than a minute on a PC) of the pressures, flow rates, and temperatures throughout the system.

The FNM technique is ideally suited for the design of liquid cooling systems because it addresses the interaction among the individual components for determining the system performance. During the design of a liquid-cooling system, it can be used for:

  • Evaluating the thermal performance of different flow configurations
  • Sizing of individual components so that the desired total flow as well as flow balance is achieved
  • Performing "What-if" and contingency studies

Thus, use of the FNM technique at the Conceptual Design stage minimizes costly trial-and-error, significantly shortens the design cycle, and reduces risk of late-cycle design changes later.

Representation of the closed-loop water-cooling system constructed using MacroFlow™ Figure 1 - Flow network representation of the closed-loop water-cooling system constructed using MacroFlow™[1]

Illustrative Application - Design of a Water-Cooled System

Physical System

The liquid-cooling system considered in this study is shown in Fig. 1. It consists of five cold plates, chosen from the products offered by Lytron [6], arranged in a U-shaped manifold. (The U-shaped layout (versus a Z shape) is dictated by system layout. The main orifice controls the total flow while orifices in each of the flow branches control the flow to the individual cold plates based on their cooling requirements.

Table 1 - Heat dissipation in the electronic units and the corresponding cold plates

Electronic Unit Heat Dissipated(kW) Cold Plate Type, Lytron[6]
EU-1 0.3 CP-10 6" 2 Pass
EU-2 0.4 CP-10 6" 2 Pass
EU-3 0.5 CP-10 6" 2 Pass
EU-4 3.0 CP-10 12" 4 Pass
EU-5 4.0 CP-10 12" 4 Pass

As listed in Table 1, a small cost-effective cold plate is used for removing heat from EUs 1-3 while a high-performance cold plate is used to cool EUs 4 and 5. The flow and thermal characteristics of these two cold plate designs are shown in Fig. 2.

CP-10 6" Double Pass

Pressure Drop Thermal Resistance
Flow and thermal resistance characteristics of the Lytron cold plates

CP-10 12" Quadruple Pass

Pressure Drop Thermal Resistance
Flow and thermal resistance characteristics of cold platesFigure 2: Flow and thermal resistance characteristics of cold plates

Design Iterations

The objective of the design process is to keep the average temperature of the surface of each cold plate below 60°C so that the electronic components operate in a reliable fashion. Important steps in the design of the cooling system are now described.

  • Sizing of the Main Orifice, the Pump, and the Heat Exchanger - The first step in the design process is to size the components in the main flow paths based on the total flow rate requirement and to ensure that the system is scalable for accommodating additional electronic units. Network model is used for different combinations of the pump, heat exchanger, main orifice, and filter to determine a scalable configuration that provides the desired flow rate of 6.8 gpm at a temperature of 25°C at the exit of the heat exchanger.
  • Sizing the Orifices in the Branches -As seen in Fig. 3, in the original design that uses identical orifices in the side branches, Units 1 and 2 are cooled excessively while Units 3 and 4 are operating well beyond the permissible temperature of 60°C. Therefore, using the network model, sizes of the branch are adjusted to achieve the desired flow distribution based on either the forward analysis approach or the inverse design method (Kang et al. [7]). Figure 3 shows that flow distribution in the revised design ensures that each cold plate is operating below the maximum allowable temperature.

MacroFlow™-based analysis of each network configuration takes only a few seconds on a PC so that the design modifications are explored in a very rapid fashion.

Cold Plate volumetric flow rate(a) Volumetric Flow Rate
Cold Plate average surface temperature(b) Average Surface Temperature
Figure 3 - Flow rates and average surface temperatures for the cold plates in the original and revised designs

Conclusions

Liquid-cooling system design involves choosing the flow configuration and sizing the individual components to achieve proper flow distribution to the individual cold plates. The technique of Flow Network Modeling (FNM) is ideally suited for evaluating various design options in a simple, rapid, and accurate fashion. The productivity benefits of this technique are illustrated, through the use of the software product MacroFlow™, in its application for the design of a practical closed-loop water-cooled system.

References

  1. MacroFlow Users Manual, Innovative Research, LLC., 3025 Harbor Lane North, Suite 225, Plymouth, MN 55447, www.inresllc.com.
  2. Belady C., Kelkar K.M., and Patankar S.V., "Improving Productivity of Electronic Packaging with Flow Network Modeling (FNM)," Electronics Cooling, Vol. 5, No. 1, pp. 36-40, 1998.
  3. Kelkar K.M., "Enhancing the Productivity of the Thermal Design Process Using Flow Network Modeling (FNM)," Coolingzone Online Magazine, February 2002, www.coolingzone.com
  4. Idelchik I.E., Handbook of Hydraulic Resistance, CRC Press, Florida, 1994.
  5. Blevins R.D., Fluid Dynamics Handbook, Krieger Publishing Company, 1992.
  6. Lytron - Total Thermal Solutions, 2003 Product Catalog, 55 Dragon Court, Woburn, MA 01801, USA, 781-933-7300, www.Lytron.com.
  7. Kang S.S., Schmidt R.C., Kelkar K.M., Radmehr A., and Patankar S.V., "A Methodology for the Design of Perforated Tiles in Raised Floor Data Centers Using Computational Flow Analysis," Proceedings of the Itherm 2000 Conference, pp. 215-224, Las Vegas, May 2000.

Article courtesy of Kanchan Kelkar, Principle Engineer, Innovative Research, 763-519-0105 x 204, kelkar@inresllc.com, www.inresllc.com.