Using FLOTHERM and the Command Center to Exploit the Principle of Superposition

Transcription

1 Using FLOTHERM and the Command Center to Exploit the Principle of Superposition Paul Gauché Flomerics Inc. 257 Turnpike Road, Suite 100 Southborough, MA Phone: (508) Fax: (508) Abstract A set of computational analyses was performed for a system level model to show that the principle of superposition can easily be exploited in a new parametric tool called the Command Center (CC), a module that will be included with Flomerics software from the next release. Thermal superposition implies that the effect of a set of independent sources in an analysis can be studied one by one and a combination of these sources can be added to provide a solution for a system. This implies that the thermal effect of the sources is linearized to enable the superposition principle. For forced convection systems, this assumption is valid for a broad range of boundary conditions whilst for natural convection systems, this principle will only work in a narrow range of source values. The concept of the adiabatic heat transfer coefficient (AHTC) and superposition kernel function (SKF) has been used as a basis for understanding thermal superposition, a very useful tool enabling thermal analysis before the power list for a new design is available. Because CFD solves the physics of flow and heat transfer implicitly for a model, the concept of the AHTC can be used directly without additional analysis methods except for a quick matrix multiplication process. The method in CFD requires that each heat source is activated as a unit value in turn and the results are stored for any number of probed points in the system. These points are then tabulated and post-processed with the actual system heat load to determine the system temperatures. For forced convection systems where radiation and natural convection effects are minimal, the results of this study have shown excellent correlation. Key words: CFD, Adiabatic Heat Transfer Coefficient, Superposition Kernel Function Introduction Thermal analysis using advanced computational tools for the cooling design of electronic equipment is becoming more common and, in many cases essential. The increasing power densities in electronic packages and the increased demand for reliability have forced hardware designers to look closer at the thermal design and optimization of equipment. To satisfy this demand of thermal design optimization in electronics, Flomerics has developed a new module for FLOTHERM used to perform parametric sets of analyses automatically. This module is called the Command Center. Performing a computational analysis on a system requires enough data to model the important geometry of the concept or design, the material properties and the thermal boundary conditions. The thermal boundary conditions include: 1) the ambient or environmental conditions that effect the equipment and 2) the power dissipation rating of each electrical or electronic device. One of the biggest problems in accurate modeling of electronic systems is the reliability or simply the lack of power dissipation ratings. State of the art computational fluid dynamics (CFD) software can perform accurate analyses of complex systems, but if the power rating is off by 100% or more, the model will not provide correct results. The issue of knowing the power in the system has been one of the biggest stumbling blocks in the analysis of equipment that does not yet exist. This is no longer a problem when a prototype exists, but by then it s too difficult to affect the design in any effective way. Knowing

2 the power rating of devices has been a hot topic in recent years and discussions by Kordyban [1] and Addison [2] will confirm this. Pollard et. al. [3] mentions that as the power distribution gets refined during the design cycle, the analyst must perform the thermal analysis again. He goes on to present a superposition method for multi-chip modules (MCMs) using a least squares fitted influence matrix used to determine temperatures for a given power vector without redoing the analysis. His work showed that the method is valid for forced convection and to some extent, natural convection. This paper presents a method reported by Gauché [4] that enables a number of discrete points to be analyzed for temperature by performing a set of CFD runs and then performing a matrix multiplication afterwards. As soon as accurate power values can be obtained, the matrix obtained from the CFD is multiplied with the power vector and the temperature of the discrete points is known to a surprising degree of accuracy. This method makes use of the principle that superposition can be used in forced convection heat transfer by using the concept of the adiabatic heat transfer coefficient and superposition kernel function [5, 6]. An introduction to the Command Center is followed by a description of the numerical method employed in FLOTHERM and an outline of the matrix calculations needed. A couple of examples illustrate the power of the Command Center and the superposition method recommended. A discussion of results and conclusions wrap up the presentation. FLOTHERM s Command Center The Command Center is a module in FLOTHERM for the 2000 release of the software used to automatically run a set of parametrically modified projects. Any variable in a FLOTHERM project, including libraries, can be used as a parameter variable in the Command Center, providing the user with a powerful optimization tool. The Command Center employs a commonsense hierarchical structure with the ability to set a wide variety of parameters for inputs and the user can select any form of outputs based on the data outputted in a project. The following figures show the Input Variables and Scenario Table windows of the Command Center for one of the cases considered in this study. Note that each heat source in turn has a unit value of heat added in the various scenarios. Fig. 1: The Input Variables window in the Command Center for a superposition model.

3 Fig. 2: Part of the Scenario Table window in the Command Center for a superposition model. Numerical Method The electronics cooling CFD package, FLOTHERM by Flomerics, is a computational fluid and heat transfer analysis and design package specifically for the analysis of electronic equipment. FLOTHERM makes use of the finite volume method to analyze three-dimensional geometries from chip level to system level. The conjugate heat and flow solution is performed using the Boussinesq approximation for buoyancy forces. FLOTHERM solves the steady-state as well as the transient governing equations. Turbulence is modeled with a choice of zero or two equation models. The governing equations are shown here in compact form for conservation of mass, momentum (Navier-Stokes) and energy respectively [7]: u r = 0 (1) r u r r 2 r r +?(u )u = P + µ u +?gß(t T ) t (2) T r?c p +?c pu T = k T + S (3) t? These equations are discretized into algebraic expression and solved for iteratively in a computational grid. The numerical solution of the governing equations provides all the characterization necessary for the use of the proposed method. The CFD determines the convective heat transfer through the energy equation implicitly determining the local heat transfer coefficients and thermal kernel for each heated object. The pressure drop is also determined implicitly in the CFD. To emulate and measure the effect of the adiabatic heat transfer phenomena, all heat sources in the model need to be turned off. After this, one unit heat source at a time is activated and the model is converged. This process is repeated as many times as there are discrete heat sources. Fortunately, the process does not take long as the flow solution is converged after the first run. Each consecutive run simply adjusts the temperature in the domain. A selected number of points need to be monitored in the domain of the project. These would usually be critical points of interest such as the die junction temperature of each component; in fact any point of interest can be monitored. At the end of each converged run, the temperatures of these points must be noted. For n discrete heat sources and m discrete monitor points, a matrix is set up. The matrix elements contain the temperature rise above ambient.

4 1,1 2,1 n,1 1,2 (4). 1, m n, m Once the discrete power sources become known, they can be entered into a source vector of n sources. P1 P2 (5) P n A matrix multiplication is then performed with the resulting m dimensional vector representing the temperature rise above ambient of each monitor point. 1, 1,1 1,2 m 2,1 n,1 n, m P1 p1 P2 T p2 = (6) Pn pm This matrix can be augmented by the ambient temperature to give the actual temperature at each monitor point (T pi ). Application Examples Printed Circuit Board Characterization The first case considered is the thermal characterization of a PCB. This PCB contains a central processing unit (CPU) dissipating 11 Watts and 12 additional heat-dissipating devices, each dissipating 1.4 Watts. The CPU has a heat sink attached with the following dimensions: Base Length x Width x Thickness = 40mm x 40mm x 4mm; Number of fins x Fin Thickness = 7 x 1mm. The board is characterized in a wind tunnel at 1m/s. The layout of the board is shown in figure 3. Fig. 3: The Structure of the PCB with components and heat sink. In the FLOTHERM model, the PCB is modeled using orthotropic properties. The CPU is modeled in detail using FLOPACK so that the die junction temperature can be determined accurately. The other components are modeled as lumped objects. In all cases, the monitor points are located at the center of the device/die. Figure 4 is a Command Center output of temperature rise above ambient for all single heated devices. Note that the heated component itself has the highest temperature rise. Personal Computer Analysis The second case considered is a personal computer (PC) containing a motherboard, a CPU with extruded heat sink, 4 other large components, 2 single inline memory modules (SIMMs), a hard drive, a power supply, 2 inlet vents and an exhaust fan. The layout of the PC can be seen in figure 4. The three nearest covers have been removed. The power of each device is listed in table 1. Fig. 4: The Internal Structure of the PC. Figures 5 and 6 show the superposition scenario results in graphical format. Each scenario represents the results of 1 powered device at a time.

5 The superposition matrices are made up out of this information. Now that the matrices have been determined, the actual temperature rise for a given source vector can be determined. In the next section, the results of the matrix multiplication are given together with a discussion of these results. Device Power [W] CPU 16 Chip 1 6 Chip 2 2 Chip 3 2 Chip 4 2 SIMM SIMM Power Supply 16 Hard Drive 15 Table 1: Power Dissipation Table. Fig. 5: Temperature Rise for all components per Scenario PCB model Fig. 6: Temperature Rise for all components per Scenario PC model

6 Discussion of Results The result of both cases show excellent correlation between the direct CFD and the superposition method presented in this paper. Due to the high amount of forced flow in the case of the personal computer, the effect of buoyancy forces was minimal leading to maximum variation between methods of 0.35%. In the case of the PCB, the maximum deviation between methods was slightly higher at a value of 0.65%. This can be attributed to buoyancy effects that were inconsistent between the adiabatic CFD runs and the full CFD analysis. Buoyancy adds a non-linearity to the computation that is not superposition able. This last point is an important one to note if this method is to be employed. Any non-linearities in the model such as the effects of radiation and high amounts of buoyancy will cause deviation from the desired results. A proposal to get around this problem is to continue to use the concept of the adiabatic heat transfer coefficient and superposition kernel function, and avoid turning all components off and keeping one on at a unit value of power. An alternative method would be to have a reasonable estimate of the powers and perturb each power value by a unit value. This will still provide the temperature rise matrix and the result will capture a linearized thermal characterization of all thermal effects around the power range of interest. D Comparison - Direct CFD vs. Superposition Case 1: PCB Superposition CFD Device Fig. 4: Comparison between Direct CFD Analysis and the Superposition Method: PCB. D Comparison: Direct CFD vs. Superposition Case 2: Personal Computer SKF Full CFD Device Fig. 5: Comparison between Direct CFD Analysis and the Superposition Method: Personal Computer.

7 Conclusion This work set out to provide a method complimentary to CFD that will enable the thermal design engineer to continue with data that is given and analyze models before accurate power information is available. Once this power data is received, the CFD analysis does not need to be performed over again. The method fits in with the idea of just-in-time project management. [7] Mills, A.F., Heat and Mass Transfer, Irwin, First Edition, Chicago, pp , The findings were that for forced convection cases, the method works out to be very accurate. For cases where thermal radiation and mixed or natural convection are encountered, the method becomes less viable, although a modification to the method has been proposed. This method could prove to be very valuable in the electronics industry where physical design of hardware needs tighter integration and where time is of the essence. References [1] Kordyban, T., Ten Stupid Things Engineers do to Mess up Their Cooling, Electronics Cooling Magazine, Vol. 6, No. 1, pp , January [2] Addison, S., Thermal Analysis moves into the 21 st Century, Electronics Cooling Magazine, Vol. 6, No. 1, pp , January [3] Pollard, L.L., Salskov, E., and Lee, S., Thermal Analysis and Validation of MCMs, 16 th Annual IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), pp , San Jose, CA, March 21-23, [4] Gauché, P., A Design Approach to Thermal Characterization of Forced Convection Systems using Superposition in CFD, IMAPS 2000 Boston, Boston, MA, September 18-22, [5] Anderson, A.M., and Moffat, R.J., The Adiabatic Heat Transfer Coefficient and Superposition Kernel Function: Part 1 Data for Arrays of Flatpacks for Different Flow Conditions, Journal of Electronic Packaging, Vol. 114, pp.14-21, March [6] Anderson, A.M., and Moffat, R.J., The Adiabatic Heat Transfer Coefficient and Superposition Kernel Function: Part 2 Modeling Flatpack Data as a function of Channel Turbulence, Journal of Electronic Packaging, Vol. 114, pp.22-28, March 1992.