Applied Math Modeling White Paper

Improving Model Geometry for CFD Analysis By Liz Marshall, Applied Math Modeling Inc., Concord, NH

October, 2010 solid objects, and too much detail can make the simulation process more cumbersome than it needs to be. This is certainly true in data centers, where small gaps between equipment are fair game for the CFD solver, but may not be particularly relevant to the large-scale flow patterns in the room. Facility analysts must always consider whether or not the air flow in a narrow gap is an important feature of the flow in the room as a

Introduction

In today’s world, computer-aided engineering (CAE) is an integral part of engineering design and analysis. At the root of all CAE is computer-aided design (CAD), which is used to build virtual models of objects and spaces. CAD models are used as input for a number of engineering software packages, where stress analysis, heat transfer, or fluid flow is simulated. Fluid flow analysis is done using computational fluid dynamics (CFD), and this technology is used for applications ranging from aircraft wings to coal furnaces to room air flows. Despite their close relationship, CAD models differ from CFD models in one important way. With CAD the focus is on solid geometry, so more detail is generally considered better than less detail. Figure 1: An example of a mesh, used for performWith CFD, the focus is on the fluid flow in the space between ing a CFD calculation of the air flow in a room

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whole. It if is not, the geometry should be modified to eliminate such gaps. Cleaning up – or more accurately, dumbing down – the geometry in this manner can make for a much more rapid time to CFD solution with minimal impact on the final results.

cases, the results confirm that the simpler geometry is more cost effective for the application of CFD.

Case 1 Problem Definition

The CFD simulation process begins with the construction of the model geometry. In the case of a data center, this includes the room, the equipment in the room, and perforated floor tiles and ceiling grills to allow for the passage of air, as needed. Once the room geometry is specified, a computational mesh is built. The mesh (Figure 1) is used to break up the air space into thousands or millions of small cells. In each of these cells, the relevant variables are computed and stored. It is widely believed that models with more cells have the potential to offer a more accurate solution, assuming that the equipment is represented correctly. Cells can be wasted, however, if they are used in regions where the information is not relevant. When this happens, the cell count is larger than it needs to be but the accuracy in the solution is no better. Furthermore, the time to solution can be considerably longer than it needs to be.

A 5000 sq.ft. L-shaped data center is in operation at a major medical facility in the Northeast. It has a raised floor and ceiling return. Three downflow CRACs with turning vanes are positioned on the perimeter and an upflow CRAC is positioned in the center of the room. Ductwork is used to pipe the supply air from the upflow CRAC to several locations around the room. Racks with heat loads ranging from 10 Watts to 8 kW comprise a total heat load of 226 kW with a heat density of about 45 kW/sq.ft. Four power density units (PDUs) each add an average of 1 kW of heat to the room. The supply plenum contains a number of pipes and blockages. The rooms adjacent to the data center are at a constant temperature of 72°F, and the wall resistance is 2 ft2-F/(Btu/ Hr). In the original model, the racks – and 1inch gaps between them - were properly sized, as shown in Figure 2 (top). Gaps created in this fashion are assumed to be important details when the automated mesh generator goes to work. However, their importance in the global data center flow is questionable. To find out how important the gaps are, a second model is built in which the racks have the same location but are given a slightly increased width to eliminate the gaps. The

To illustrate this point, two models of medium-sized data centers are considered using CoolSim software. The original models of the data centers are both accurate in the CAD sense. All of the equipment is carefully represented, but as a result, there are gaps between adjacent equipment or there is excessive geometric detail. The models are then “improved” for CFD by simplifying the geometry. The simulations are run and a thorough comparison is done to contrast the original and modified geometries. In both © 2010 Applied Math Modeling Inc.

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shows that the maximum room temperature differs by only 1°F while the maximum rack inlet temperatures are identical. The maximum flowrate through a perforated tile is within 1% while the minimum is within 8%. Taking a closer look at the maximum rack inlet temperatures, 35% have the same value and only 3% have a value that differs by more than 5%. The maximum difference in the average rack inlet temperature is 5% for all racks in the room. Based on these results, simplification of the model has the benefit of reducing the model size and time to solution without introducing negative consequences such as large scale error in the results. Figure 2: In the CAD-style geometry (top), the racks are accurately sized, but have 1 inch gaps between them; a CFD-style geometry (bottom) eliminates the gaps between racks by increasing the widths by 1 inch

modified geometry is shown in Figure 2 Number of Cells (bottom).

With Gaps No Gaps 3.766 M

2.801M

4.53

3.74

81

82

Solution Time (Hours)

Results

Max Room Temperature (°F)

A CFD analysis is done using both of 77 77 the geometries and the results are com- Max Rack Inlet Temperature (°F) pared in Table 1. The results show that Max Perf Tile Flowrate (CFM) 729 734 elimination of the gaps leads to a model 472 436 Min Perf Tile Flowrate (CFM) with about 1 million fewer cells. The time to solution is reduced by about 45 Table 1: A comparison of the size, solution time, and minutes. Comparison of the results a few results for the data center modeled with and without gaps between the equipment © 2010 Applied Math Modeling Inc.

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Case 2

used to guide the return air in an area where a number of geometric constraints are present. The original CFD model of the CRAC and top is shown in Figure 3. While the top is an accurate representation of reality, its complexity is perhaps more than is needed. After all, the fan in the CRAC return will draw the air into the unit. The role of the mounted structure is simply to guide the air into the

Problem Definition

As a second example, consider one of the small data centers at a large collocation facility. The 2500 sq. ft. raised floor data center has two downflow CRACs, one of which is outfitted with a complex structure on the return. The equipment heat load in the room is about 100 W/sq.ft. and the complex top is

Figure 3: A complex structure mounted on the return of a downflow CRAC is used to help guide the return air back to the unit

Figure 4: A simplified structure on the CRAC return does not have all of the features of the original, but does include the essential shielding and open areas © 2010 Applied Math Modeling Inc.

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openings and a much simpler structure could accomplish the same goal.

Looking again at the maximum rack inlet temperatures, half of the racks have identical values and only 1 rack has values that differ by more than 5%. For the average rack inlet temperature, all of the racks in the room agree to within 0 or 1% except two, where the agreement is within 2.5% and 5%. This example further illustrates that less complexity in a CFD model can translate into more in terms of decreased time to solution with negligible loss of accuracy.

An alternative design is shown in Figure 4, where one such simplified structure is shown. It has the same overall dimensions as the complex structure, but avoids the minute detailing. Results

Using the two CRAC top designs as the only difference between the cases, two CFD simulations are performed and the results compared. An overview of the results is summarized in Table 2.

Summary

These examples demonstrate that for the purpose of CFD modeling, simplified geometry has advantages over complex, CADComplex Simple style geometries. In addition to saving 1.590 M 1.168M Number of Cells on the number of computational cells 2.32 1.87 Solution Time (Hours) and solution time, the effort involved in the setup is reduced as well. With 98 96 Max Room Temperature (°F) automatic grid generation and solution 91 90 Max Rack Inlet Temperature (°F) procedures in place for software de2,530 2,515 Max Perf Tile Flowrate (CFM) signed for data center modeling, time 839 818 Min Perf Tile Flowrate (CFM) savings during the setup can be significant. For the complex CRAC top, Table 2: A comparison of the size, solution time, for example, the original structure was and a few results for the data center modeled with a built using 33 baffle objects. By concomplex CRAC top and a simple CRAC top trast, the simple model needed only 9 By changing only the structure on top of one baffles. Even if the final goal is to have a of the CRACs in the room, about 400,000 CFD model with a large amount of geometric cells are saved and the CPU time is reduced detail, these results show that simplified by just under 30 minutes - or 19%. The models are an excellent first pass solution maximum rack inlet temperature differs by and indeed, are usually just as good as mod1°F and the maximum temperature in the els with increased detail. room by 2°F. The maximum and minimum flowrates through the perforated tiles are within 2.5%.

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