# Fluid dynamics

### In this second in David’s tutorial series on thermal management, he discusses the limitations of simple LFM and CFM requirements as they relate to board cooling. Next up: Shelf cooling.

[Editor’s note: The first article in the series is.]

Volumetric airflow (CFM) has been the parameter of choice for both board and shelf airflow characterization in AdvancedTCA, MicroTCA, and other COTS specifications and standards targeting interoperability. CFM is used to determine the temperature rise of air going through any space when a given number of watts are being dissipated in that space.

CFM is only valid when the cooling agent is specified. For this purpose AdvancedTCA specifies its own Standard Air. Other conditions such as altitude, air temperature, and barometric pressure will modify the needed airflow value. Originally used for designing HVAC systems, CFM is not very useful for engineers trying to cool small heat-producing components. While the CFM formula focuses on maintaining proper air temperature, in electronics cooling, we are concerned with maintaining proper component temperatures.

In Equation 1 showing the CFM formula:

n  The constant 1.830 represents air density under one set of conditions only.

n  W is the heat generated in watts.

n  dT is the temperature rise of the air, but not the component.

The only stable value in this formula is the power. The air density is a variable with the dependencies mentioned earlier, and the value selected for dT depends on other conditions. It is the component temperature that is important. With this as the upper limit, the value of dT with a low ambient temperature can be much higher than when the ambient temperature is high. Hence the needed value of the airflow can vary significantly. Note that high values of airflow result in high values of noise.

Volumetric flow can be specified for boards after the board thermal design is completed. Volumetric flow is suitable to define shelf performance for all conditions. For good board airflow design we should concentrate on linear flow velocities. Although the final design results can be presented as a volumetric flow, a single definition in units of mass flow, i.e. kg/s (in English units slugs/m or slugs/s[1]), can be used to cover PICMG and CP-TA requirements.

## Board cooling

It is worth re-examining the behavior of cooling airflow through a typical board in regard to velocities and volumes as well as mass flow.

First some classic definitions. Laminar flow describes a flow that can be visualized as flowing in laminas or layers. Turbulent flow is defined as an irregular condition of flow in which various quantities show a random variation in time and space. While turbulent flow can be empirically analyzed with various models, the use of chaos theories taken from high-energy physics provides the most accurate turbulent modeling. This is really for the dedicated mathematicians to handle, but I introduce it here to point out that mathematical models do not always reflect reality. Board-level airflow epitomizes this[2].

Figure 1 shows a typical velocity and volumetric profile of airflow over a flat plate, for example, a Printed Circuit Board (PCB). Air is a fluid that has several properties including viscosity. Due to the viscosity the air close to the plate has zero velocity, and the distance (called the boundary layer) to where the velocity is 99 percent of the free stream velocity is typically about 2 mm to 4 mm. This is in the range of component height. Adding to the chaotic flow is the roughness of component placement. The size of the arrows represents the velocity (LFM), and the area under the curve equates to CFM. However, this simple diagram does illustrate one key point: LFM does not equate simply to CFM, instead, the cross sectional area of the airflow needs to be taken into account.

Figure 2 represents the conditions of a board in a rack where the height is restricted and the boundary layer conditions of both plates need to be taken into account. The shape of the curve shows that the high-velocity area is concentrated in the center of the board height.

Figure 3 shows several low-profile components and a heat sink. While Figure 1C is not taken from calculations or measurements, it nevertheless shows the volatile movement of air through a typical board cross section.

One (patent pending) board airflow management technique involves a low-cost conformal airflow duct. The duct can be manufactured based on the PCB layout tool component height table or based on a 3D file. Height above each of the components can be added, and the ducting can be made to direct airflow through rather than over heat sinks. The total volumetric flow cannot be ignored, as we still depend on the heat capacity of the air to accept the power being dissipated. Contact author for more information.

Figure 4 represents a cross section of an AdvancedTCA board. It can be seen that side 2 provides an airflow path. The typical side 2 component are capacitors and perhaps low-profile ICs. They all produce a certain amount of heat. But side 1 components also generate heat that flows into the PCB material. BGA packages in particular have significant heat flow into the board. Be aware of the two separate air paths and monitor the benefit of the side 2 airflow. If there is too much airflow then this is a wasted shelf resource, and the flow should be impeded. If the airflow is insufficient then the side 1 airflow may have been to be constrained to allow more side 2 ariflow, or the total board airflow may need to be increased. As the shelf slot airflow has a path to both side 1 and side 2, only the total volumetric or mass board airflow needs to be specified.

## Handling front board, RTM, MicroTCA, and carrier airflow

The airflow needed by a single board or RTM can be simulated or measured whether in terms of volume or mass relatively easily. Deciding the needed airflow for an AdvancedTCA carrier with a variable set of AdvancedMC modules from different suppliers can seem a daunting task, but by reviewing first principles it can be done quite simply. The traditional graphical analysis combines the fan (shelf) pressure flow curve with the board impedance curve. The operating point is where the two curves intercept[3]. For this to work for an AdvancedTCA carrier fitted with a variety of AMCs we need an easy method to derive a composite board airflow impedance. Simulation or measurement, done in the same way as for the carrier, makes finding the AdvancedMC module impedance data possible. Measurement of the carrier impedance needs to be carried out with the AdvancedMC positions blocked off. Note that the AdvancedMC connectors form an effective barrier between the two sites.

When one or more AdvancedMC modules are introduced into the carrier the combination forms two paths in parallel. The series AdvancedMC modules have the same airflow with a total pressure drop that is the sum of the individual module pressures. Find the total impedance of the AdvancedMC combination by taking the sum of the individual impedances with constant airflow. The simplest way to do this is to sum the impedance p/q in its quadratic relationship (Equation 2), where “p” = pressure and “q” = airflow. The impedance value is derived by summing the individual coefficients b = b1 + b2 + bn and so on.

The impedance table or curve for the combination of carrier and AdvancedMC module airflow is solved by summing the two[4] airflow values with the same pressure across the carrier and AdvancedMC combination. One example of software that makes this a relatively simple process is SAAM software from Advanced Platforms. The result for an AdvancedTCA board populated with AdvancedMCs will be given in two parts, the total airflow impedance of the combination and the division of the cooling air in the two sections. This approach, along with the SAAM program, enables a rapid assessment of the airflow conditions in real time for multiple combinations of AdvancedMC modules and carriers.

## Noise

The main contributor to acoustic noise in an installation is the fan assembly. This is not the only contributor, as we will discuss later in this series. Adding to the acoustic noise is the board assembly. Board layout priorities, such as EMC and signal integrity, closely followed by cooling, mean that the board contribution to noise is rarely considered. The earlier part of this article points to balancing air velocity, volumetric flow, and mass flow. Of these factors velocity is the main noise contributor. If cooling can be maintained with a managed mass flow, then the velocity noise contribution should be minimized.

## Airflow management algorithm

In older systems it was deemed sufficient to control fan speed by measuring the exit airflow based on the capacity of a volume of air to move heat. The AdvancedTCA algorithm is based around thermal events generated when a temperature threshold (or other dependent variable) is exceeded, so the board or structure designer must ensure that sensors are in place for all critical components.

## Conformance testing

It has been the aim of PICMG, the Scope Alliance, and to ensure the interoperability of the AdvancedTCA ecosystem. Similar exercises are in place or considered for all mission-critical elements. Thermal interoperability is arguably one of the most important factors, but the existing testing tools have not been successful.

Simulation is essential for board design, but it should be noted that the turbulent flow modeling capabilities of CFD software dedicated to the thermal analysis of electronics have been confined to zero-equation mixing length or standard two-equation high-Reynolds number k-e eddy viscosity turbulence models. These models meet the criteria of robustness, in terms of promoting stable convergence, and to some extent, universality, which makes them popular for practical engineering calculations. They are by far the most widely used and validated and are considered as computationally viable in a design environment. Unfortunately, this approach is not entirely satisfactory for modeling the thermal and kinematic complexity of thermofluid problems in forced air-cooled electronic systems.

For this reason we believe that board airflow measurement needs to be based on the industry standardized ANSI/AMCA 210-99 pressure based methodology. A tester for board airflow does not to be as large as a full chamber[5], but it must meet laboratory standards for accuracy and repeatability. For AdvancedTCA devices the measurement results must be given in terms of standard air. The flow rates and pressures should reflect the expected AdvancedTCA trends towards higher power (100 CFM and board pressures up to 1.5" H2O). We will argue the case for specifying mass flow rather than volumetric flow. The tool must be able to measure front boards, RTM. and preferably AdvancedMC. It would be useful if the tester would also allow powered testing for Front+RTM, complete with functional shelf management and ability to independently measure and control the flow of Front Blade and RTM airflow. The tool should also be small enough to fit into an environmental chamber.

## Next in the series

The next article will look at some of the aspects of the shelf design and examine issues in the conformance testing of the shelf. We shall also discuss the design of the rack and the placement of high-power racks in office layouts. These are outside the scope of the PICMG 3.0 specifications but of critical importance in a systems environment. The final article will look at some new developments.

David Wright has been involved in AdvancedTCA since 2001, and in practical electronics and mathematical modeling for much longer. After working for multinational companies GEC Ltd., MEL, a division of Philips NV, CTS Corp., and Hybricon, Inc. David operated as a consultant for nine years before co-founding Wickenby Ltd. in Israel. After significant investor involvement the company has been renamed as Advanced Platforms Ltd. David functions as the AdvancedTCA, ATCA300, and MicroTCA Systems Architect. Advanced Platforms Ltd. provides third-generation products and services.

References

[1]    In this article we have used the more common English units rather than the internationally recognized MKS units. Note: Advanced Platforms Ltd. uses MKS units.

[2] Eveloy, Valérie and Rodgers, Peter, Application of Low-Reynolds Number Turbulent Flow Models to the Prediction of Electronic Component Heat Transfer, Internet paper from 2004 Inter Society Conference on Thermal Phenomena.

[3] Wright, David AdvancedTCA cooling design from concept to maintenance, CompactPCI and AdvancedTCA Systems April 2006

[4] Three air paths if side 2 flow is simulated or measured separately.

[5] Advanced Platforms Ltd. laboratory board tester.