# Heat Transfer and Pressure Drop Performance of the Air Bearing Heat Exchanger.

INTRODUCTIONThe air bearing heat exchanger (ABHE) is shown in Figure 1 (see Koplow (2010) for a thorough introduction). A thermal load enters the base of the device and passes through a thin (~10 [micro]m [0.39*[10.sup.-3] in]) air gap into a rotating heat-sink-impeller. The rotating heat-sink-impeller, meanwhile, induces a radially outward flow of the ambient surrounding air. Heat transfer into this air flow occurs at the heat-sink-impeller blade surfaces. Since the impeller blades reside in an rotating frame, fluid particles in the boundary layer adjacent to their surfaces experience an outward centrifugal force, an effect which tends to result in thinner boundary layers compared to stationary, pressure-driven flow (see, for example, experimental results of Cobb and Saunders (1956) or theoretical analysis of Schlichting (1979)). Since convective heat transfer is well approximated by conduction across the boundary layer, this thinning of the boundary layer represents an enhancement in the convective heat transfer coefficient.

The ABHE was invented to address the need for compact, high-performance air cooled heat sinks in electronics cooling applications, where the volume occupied by a heat sink is often constrained. As can be seen in Figure 1, the ABHE lies well beyond the performance frontier associated with commercially available heat sinks for cooling desktop CPUs for thermal resistance vs. volume occupied by the heat sink. The potential application of ABHE technology to much larger scales (e.g. HVAC&R) is currently under investigation.

Air cooled heat exchangers are often limited by the convection between the air and the surfaces. In heat exchangers, the overall conductance (UA) determines how much thermal interaction occurs, and thus designers often try to maximize UA to achieve better performance. However, many applications have volume constraints which tend to limit fin surface area (A) and leaves convection enhancement as the only remaining design tool to increase UA.

A wide variety of convection enhancement techniques exist, which are discussed in the comprehensive review of Bergles (1998). These techniques consist of passive (e.g. rough surfaces, extended surfaces, swirl flow devices, etc.) and active (e.g. stirring, surface scraping) methods. The ABHE represents a unique type of active enhancement because the enhancement mechanism (associated with the rotation of the heat-sink-impeller) is also necessary for establishing relative motion between the heat sink fins and ambient air and moving the air through the system.

In the present work, we discuss results of experiments and CFD for two 10 cm [3.9 in] diameter prototype ABHEs with fin heights of approximately 25 mm [1.0 in], which we refer to as "v4" (36 fins) and "v5" (80 fins). We tested the pumping performance using a flow bench to determine the fan curves (pressure rise vs. volume flow) at several rotational speeds. In addition, we conducted steady-state thermal testing to measure the convective thermal resistance (average heat transfer coefficient) of the rotating impellers. Finally, we showed that the performance trends at the free delivery flow rate can be captured with a relatively simple CFD model.

EXPERIMENTS

We performed several experiments to measure the performance of the ABHE. First, we used a custom-built apparatus to measure the fan curves of the device at various speeds. Second, we measured the thermal performance at the free delivery point using a thin film heater and an IR thermometer.

Fan Curve Measurement

The fan testing apparatus, shown in Figure 2, allowed for the flow rate through the impeller to be restricted and the pressure just upstream of the impeller to be measured. In this apparatus, a DC motor drove the impeller, which was situated just underneath a plenum whose pressure was monitored relative to the ambient.

A series of commercial sieves were modified to make up the flow plenum from which the impeller drew air. The mesh sieves (140 and 20 mesh) served to straighten and spread the inlet flow, minimizing jetting onto the impeller. By drawing air from a large volume (305 mm [12.0 in] diameter by 203 mm [8.0 in] height, to the screen nearest the impeller), the flow to the impeller was made to be as natural as possible, with the constraint that the inlet and outlet of the impeller needed to be separated. The system resistance was varied using a butterfly valve just upstream of the plenum. Using a flow booster (Nortel Manufacturing AM750 or AM1000 for low or high flow rates, respectively) increased the volume flow of the pressurized air supply and allowed measurements to be made all the way out to the free delivery point (and also into the negative pressure regime, although this is of little practical interest). A turbine flow meter (Omega FTB-934 or FTB-938, for low or high flow rates, respectively) was used to measure the air flow. A differential pressure transducer (Omega PX275-05DI) was used to measure the pressure rise across the impeller. The rotation was controlled by a DC motor (Pittmann 14204S005) and a variable, computer-controlled power supply (Circuit Specalisits 3646A). The rotational speed was characterized using a stroboscope and related to the motor voltage, which was measured throughout the course of the experiments. Finally, we performed two sensitivity checks to ensure negligible systematic errors due to (1) the position of the impeller relative to the plenum (where there was a small clearance between the top edge of the heat-sink-impeller and the plenum) and (2) the position of the pressure tap in the plenum.

Since the cross sectional area of the plenum is much larger than the cross sectional area of the inlet to the impeller, the velocity in the plenum is relatively small and the dynamic pressure ([[rho]v.sup.2]/2) is negligible compared to the total pressure, meaning that the static and total pressures can be considered equal in the plenum. Thus, the differential pressure measurement in the experimental apparatus represents the total-to-static pressure rise across the impeller (for a discussion of the utility of using the total-to-static pressure as a performance metric, see Epple et al. (2011)). At a given rotational speed, the total-to-static pressure rise across the impeller depends on the flow resistance of the system in which it is installed; this resistance was varied in the experimental apparatus in order to yield fan curves (i.e. total-to-static pressure rise vs. volume flow) at various rotational speeds. These fan curves can be seen in Figure 3 for two impeller designs. At a speed of 2500 rpm, both impellers had a shut-off pressure of 65 Pa [0.26 in[H.sub.2]O] and a volumetric flow rate of order 1500 L/min [53 [ft.sup.3]/min]. Near the free delivery point, the fans (most noticeably the v5 impeller) experienced a hysteresis effect, where either of two stable flow rates were possible depending on the pressure from which the operating point was approached. The fits shown in Figure 3 are based on fits to the dimensionless fan curves (discussed below and shown in Figure 2).

The fan curves were nondimensionalized by dividing the volume flow and pressure rise by reference quantities. The flow coefficient ([phi]) is formed by normalizing the volume flow to a hypothetical flow rate, where the velocity is the impeller tip speed ([omega]d/2) and the cross sectional area is the impeller's exit plane area ([pi]db):

[mathematical expression not reproducible] (1)

where V is the volume flow rate, [omega] is the rotational speed (rad/s), d is the outer diameter of the impeller, and b is the axial breadth (height) of the impeller at the exit plane. The total-to-static head coefficient ([[psi].sub.ts]) is formed by normalizing the total-to-static pressure rise to the dynamic pressure associated with the impeller tip speed ([[rho]v.sup.2]/2):

where [[DELTA]p.sub.ts] is the total-to-static pressure difference and [rho] is the fluid density. Note, however, that for mathematical convenience the denominator is multiplied by 2 (a discussion of this can be found in Epple (2011)). This definition also means that, in relation to the velocity triangle commonly analyzed in fan design, the flow and head coefficients have consistent and direct interpretations as ratios of the meridional and tangential exit velocities to the tip speed, respectively.

By forming these dimensionless quantities, the multitude of fan curves shown in Figure 3 was compressed into a single curve for each impeller, as shown in Figure 2. The curves in Figure 2 can be used to reconstruct the fan curve at any speed or for a different size impeller (provided geometric similarity is maintained and the device is not operated in a different flow regime). The dimensionless fan curves exhibited two parabolic regions; the fits used a sigmoid function to blend these two parabolic regions. Compared to v4, v5 had a similar shut-off head coefficient and a slightly higher free delivery flow coefficient. Also, relative to v4, the kink that occurs at about 2/3 of the free delivery flow coefficient was more pronounced in v5.

Heat Transfer Measurement

The heat transfer performance of the v4 and v5 heat-sink-impellers was measured using the apparatus shown in Figure 4. A Kapton film heater was adhered to the bottom surface of the impeller, covered with insulation and then mounted on a rotating shaft. The contact area between the shaft and the base of the impeller was very small, which, in addition to the insulation, minimized conduction through the shaft. The power leads to the heater were fed through two of the blades of the impeller and into a 305 mm [12 in] long piece of 4.0 mm [0.16 in] hex tubing where they were mated with a rotary electrical contact (Mercotac 205-H). Two IR thermometers (Fluke 80T-IR and Omega OS36-01) aimed at the impeller provided temperature readings. A type-K thermocouple measured the temperature of the inlet air. The voltage and current applied to the heater were measured as well as the rotational speed (by measuring the voltage waveform on one of the phases of the brushless DC motor). All voltages were logged with a data acquisition system (Agilent 34970A).

In these tests, the temperature of the impeller base was measured for various thermal power inputs in the 50-100 W [170-340 Btu/h] range. The overall convective thermal resistance ([R.sub.conv]) was calculated as [R.sub.conv]=([T.sub.base]-[T.sub.amb])/Q, where Q is the heat transfer into the impeller, [T.sub.base] is the temperature of the impeller base, and [T.sub.amb] is the temperature of the surrounding ambient air. Notice that the temperature scale associated with [R.sub.conv] is the inlet temperature difference of the heat sink. In considering the entire ABHE, one must also consider the thermal resistance of the air bearing gap, which can be calculated using Fourier's Law as [R.sub.gap]=[b.sub.gap]/k*[A.sub.base], where [b.sub.gap] is the air gap thickness, k is the thermal conductivity of air, and [A.sub.base] is the area of the impeller base. The optimum air gap is application dependent, due to the tradeoff between lower air gap thermal resistance and higher shearing losses. Typically, we have run these 10 cm [3.9 in] diameter impellers with a 10 [micro]m [0.39*[10.sup.-3] in] air gap, which results in a gap thermal resistance of 0.047 K/W [0.025 h*[degrees]F/Btu] (the thermal resistance per unit gap width is 4700 K/W*m [0.025 h*[degrees]F/Btu*in]) and 1.8 W [1.3 ft*lbf/s] of frictional loss at 2500 rpm. Thus, an air gap distance of 5 [micro]m [0.20*[10.sup.-3] in] would result in an air gap thermal resistance of 0.024 K/W [0.013 h*[degrees]F/Btu] and 3.6 W [2.7 ft*[lb.sub.f]/s] of frictional loss at 2500 rpm.

An "effective" heat exchanger conductance (UA) can be calculated as UA=1/[R.sub.total], where [R.sub.total] is the sum of the convective and gap thermal resistances, which are in series. The overall effective heat transfer coefficient (U) can be calculated as U=1/[([R.sub.conv]+[R.sub.gap])[A.sub.base]]. Again, in considering U one must recall that it refers to the thermal circuit starting at the bottom of the stationary baseplate ([T.sub.bot]) and ending at the ambient surrounding air ([T.sub.amb]), and therefore has the temperature scale [T.sub.bot]-[T.sub.amb]. This is appropriate for heat sink design, where one has knowledge of these temperatures ([T.sub.bot] and [T.sub.amb]) a priori and is not concerned with the temperature profile in the air flow; however, it is different than the temperature scale used in considering the flow of the air in the impeller (for example, in an effectiveness-NTU analysis), which is the log-mean temperature difference. It is straightforward to convert to the log-mean temperature difference by performing an energy balance on the air flow.

Finally, the heat exchanger effectiveness is defined as the increase in the air's bulk temperature relative to the inlet temperature difference: [epsilon]=([T.sub.out]-[T.sub.amb])/([T.sub.base]-[T.sub.amb]). To obtain an estimate of Tout of the air flow, an energy balance on the air was performed, based on the free delivery mass flow rate as measured in the fan testing apparatus. In Figure 5, the convective thermal resistance ([R.sub.conv]), the overall effective heat transfer coefficient (U), and the air-side heat exchanger effectiveness are shown for v4 and v5 as a function of rotational speed.

SIMULATIONS

To better understand the fluid dynamics in the heat-sink-impeller of the ABHE, we developed a computational fluid dynamics (CFD) model using ANSYS CFX. This model consisted of a single unit cell comprising one blade of the heat-sink-impeller, as shown in Figure 6. The conjugate heat transfer capability of CFX was used to include the coupling between the solid conduction in the aluminum fins and convection heat transfer to the air flow. Stationary and rotating domains were used with a frozen rotor frame change model at the stationary-rotating interface. The edges of the unit cell were periodic interfaces. Finally, air was allowed to enter and leave the domain via the top, bottom, and side faces by using an opening boundary condition, which specifies either the static or total pressure for exiting or entering flow, respectively. The openings were far enough from the impeller to allow the flow field to become relatively uniform at the boundary.

The bottom of the impeller was given a constant temperature boundary condition (chosen to be 25 [degrees]C [45 [degrees]F] higher than the ambient surroundings) in order to mimic the surface of a vapor chamber heat pipe, which is used in CPU cooling applications to effectively spread the concentrated thermal load over the entire air gap area. The heat transfer into the impeller was determined with an area integral of the heat flux into the constant temperature boundary. The flow was modeled using the SST turbulence model with the total energy equation. According to a study by Brethouwer (2011), the turbulent Prandtl number associated with heat transfer in rotating channels is lower than the typical value of 0.9 for a stationary channel. Based on this, as well as comparisons to experimental results, the turbulent Prandtl number was set to 0.2 (rather than the default value of 0.9 in CFX).

Representative results from the CFD solutions can be seen in Figure 6, which shows several repeated unit cells of the v5 impeller. The velocity vectors are projected onto a surface running down the middle of a unit cell. This mid-unit-cell surface, a surface parallel to the impeller base and situated at half the blade height, and the exterior surface of the aluminum blades are colored by temperature. The isotherms on the fin surfaces indicate higher heat transfer at the edge of the fin near the inner diameter, where the boundary layer begins. Also, the velocity vectors indicate that air flow enters the channel from the top as well as the inner bore. Finally, the thermal resistance results from the CFD model overpredict the measured thermal resistance, but correctly capture the trends in both v4 and v5. The CFD predictions for volumetric flow rate are typically within 20% of the experimental results.

CONCLUSION

The ABHE, invented for volume-constrained CPU cooling applications, has been shown to have unprecedented compactness and thermal performance. We report experimental results (fan curves and thermal resistance at the free delivery point) for two 10 cm [3.9 in] diameter heat-sink-impeller designs. One of the heat-sink-impellers we tested had an air side primary heat transfer coefficient of 2000 W/[m.sup.2]*K [350 Btu/h*[ft.sup.2]*[degrees]F] at 4500 rpm; when considering a 10 [micro]m [0.39*[10.sup.-3] in] air bearing gap in series, the effective heat transfer coefficient seen on the bottom of the stationary baseplate was 1200 W/[m.sup.2]*K [210 Btu/h*[ft.sup.2]*[degrees]F]. In addition, we observed that its pumping performance surpassed axial fans of comparable diameter (e.g. at 3750 rpm, it had a 150 Pa [0.60 inH2O] shut-off pressure and a 2370 L/min [83.7 [ft.sup.3]/min] free delivery flow rate). Finally, we show that a CFD model of a single-blade unit cell can yield satisfactory predictions that capture the trends in thermal resistance, yielding useful design information.

ACKNOWLEDGMENTS

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. The authors thank the Building Technologies Program (US Department of Energy, Office of Energy Efficiency and Renewable Energy) and the Sandia Laboratory Directed Research & Development (LDRD) program for supporting this research.

REFERENCES

ANSYS CFX, Release 14.5.

Bergles, A.E., Handbook of Heat Transfer, ch. 11: Techniques to Enhance Heat Transfer. McGraw-Hill, 1998.

Brethouwer et al., Turbulence, instabilities and passive scalars in rotating channel flow, J.Phys.: Conf. Ser. 318 032025, 2011.

Cobb, E.C. and Saunders, O.A., "Heat transfer from a rotating disk," Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 236, no. 1206, pp. 343-351, 1956.

Epple, P., Durst, F. and Delgado, A., A theoretical derivation of the Cordier diagram for turbomachines. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 225: 354-368, 2011.

Koplow, J.P., A fundamentally new approach to air-cooled heat exchangers, Technical Report SAND2010-0258, Sandia National Laboratories, 2010.

Page, M., FrostyTech--Best Heat Sinks & PC Cooling Reviews, http://www.frostytech.com. Accessed: March, 2012.

Schlichting, H. "Boundary-layer theory," Seventh edition, McGraw-Hill series in mechanical engineering, pp. 102-107, 1979.

Staats, W.L., Active heat transfer enhancement in integrated fan heat sinks, doctoral dissertation, Massachusetts Institute of Technology. http://hdl.handle.net/1721.1/78179, 2012.

Wayne L. Staats, PhD

Affiliate Member ASHRAE

Terry A. Johnson

Ned Daniel Matthew

Jeff Koplow, PhD

Ethan S. Hecht, PhD

Wayne L. Staats, Ned Daniel Matthew, Ethan S. Hecht, Terry A. Johnson, and Jeff Koplow are researchers at Sandia National Laboratories in Livermore, California.

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Author: | Staats, Wayne L.; Johnson, Terry A.; Matthew, Ned Daniel; Koplow, Jeff; Hecht, Ethan S. |
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Publication: | ASHRAE Conference Papers |

Article Type: | Report |

Date: | Dec 22, 2014 |

Words: | 3204 |

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