3. Characterization of a liquid cooling system using transient effectiveness

This section illustrates an example of investigating a liquid cooling system which has several heat exchanger units using the transient effectiveness method and its corresponding characteristics. Several experimental tests are conducted on a data center liquid cooling test facility and the results are reported in reference [19]. The transient effectiveness method is used to analyze the performance of heat exchangers and the dynamic performance of the entire test facility. The transient effectiveness method provides an analyzing method for investigating and characterizing the transient performance of heat exchangers which are working in the cooling and heating systems with multiple coupled heat transfer loops, in which multiple heat exchanger units are used.

#### 3.1. Description of the test facility and experimental test scenarios

Figure 9 shows the liquid cooling chiller-less data center test facility designed by IBM. Basically the entire system contains a liquid cooling server rack, a liquid to liquid heat exchanger, and a dry cooler. The rack was fully populated with liquid cooled volume servers. Each server dissipates approximately 350 W. Then the total maximum rack power can reach 15 kW. There is also a side car heat exchanger contained within the rack on the side for cooling the rack circulated air. The air is recirculated inside the rack driven by server fans. The CPU and DIMM are cooled using cold plate and cold rails, which are directly attached to them. The heat captured by the rack circulated air and the liquid are then transferred to the atmosphere through the sidecar heat exchanger, the liquid-to-liquid heat exchanger, and the dry cooler. More details in terms of the description of each component and the entire test facility design are reported in references [19, 20].

Temperature sensors (T1–T10) are located at various locations, including the inlet and outlet of each component, including the cold plates, servers, sidecar heat exchanger, buffer unit, and dry cooler, as shown in Figure 8. The detailed description of the sensor locations and functions, as well as the data collection and data processing, is summarized in reference [19]. Three transient test cases were designed and conducted and the detailed experimental designs for the three cases are shown in Table 2.

#### 3.2. Transient effectiveness

#### 3.2.1. Transient effectiveness calculation

The experimental data for the sidecar heat exchanger, the buffer unit, and the dry cooler for all the three cases are used to generate the transient effectiveness curves. The corresponding results are shown in Figure 9(a)–(c) for the buffer unit, the side card heat exchanger, and the dry cooler, respectively. In the current study, Cmin fluid of each heat exchanger unit is used in the current study.

Transient Effectiveness Methods for the Dynamic Characterization of Heat Exchangers http://dx.doi.org/10.5772/67334 203

Figure 8. Schematic representation of the test facility and experimental setup.


Table 2. Transient test cases.

exchanger, initial conditions and some special circumstances such as the cold fluid becoming

3. Characterization of a liquid cooling system using transient effectiveness

This section illustrates an example of investigating a liquid cooling system which has several heat exchanger units using the transient effectiveness method and its corresponding characteristics. Several experimental tests are conducted on a data center liquid cooling test facility and the results are reported in reference [19]. The transient effectiveness method is used to analyze the performance of heat exchangers and the dynamic performance of the entire test facility. The transient effectiveness method provides an analyzing method for investigating and characterizing the transient performance of heat exchangers which are working in the cooling and heating systems with multiple coupled heat transfer loops, in which multiple heat exchanger

Figure 9 shows the liquid cooling chiller-less data center test facility designed by IBM. Basically the entire system contains a liquid cooling server rack, a liquid to liquid heat exchanger, and a dry cooler. The rack was fully populated with liquid cooled volume servers. Each server dissipates approximately 350 W. Then the total maximum rack power can reach 15 kW. There is also a side car heat exchanger contained within the rack on the side for cooling the rack circulated air. The air is recirculated inside the rack driven by server fans. The CPU and DIMM are cooled using cold plate and cold rails, which are directly attached to them. The heat captured by the rack circulated air and the liquid are then transferred to the atmosphere through the sidecar heat exchanger, the liquid-to-liquid heat exchanger, and the dry cooler. More details in terms of the description of each component and the entire test facility design

Temperature sensors (T1–T10) are located at various locations, including the inlet and outlet of each component, including the cold plates, servers, sidecar heat exchanger, buffer unit, and dry cooler, as shown in Figure 8. The detailed description of the sensor locations and functions, as well as the data collection and data processing, is summarized in reference [19]. Three transient test cases were designed and conducted and the detailed experimental designs for

The experimental data for the sidecar heat exchanger, the buffer unit, and the dry cooler for all the three cases are used to generate the transient effectiveness curves. The corresponding results are shown in Figure 9(a)–(c) for the buffer unit, the side card heat exchanger, and the dry cooler, respectively. In the current study, Cmin fluid of each heat exchanger unit is used in

as the hot fluid, Cmin fluid becoming Cmax fluid, and so on.

202 Heat Exchangers– Design, Experiment and Simulation

3.1. Description of the test facility and experimental test scenarios

units are used.

are reported in references [19, 20].

the three cases are shown in Table 2.

3.2.1. Transient effectiveness calculation

3.2. Transient effectiveness

the current study.

For the sidecar heat exchanger:

$$\varepsilon(\tau) = \frac{c\_{air}(\tau) \cdot \left[T\_{Rack\ outlet\ air}(\tau) - T\_{Rack\ inlet\ air}(\tau)\right]}{c\_{min}(\tau) \cdot \left[T\_{Rack\ outlet\ air}(\tau) - T\_{Prand}(\tau)\right]} \tag{5}$$

For the buffer unit:

$$\varepsilon(\tau) = \frac{c\_{internal}(\tau) \cdot \left[T\_{Potrak}(\tau) - T\_{Perack}(\tau)\right]}{c\_{min}(\tau) \cdot \left[T\_{Postack}(\tau) - T\_{Prebffer}(\tau)\right]} \tag{6}$$

For the dry cooler:

$$\varepsilon(\tau) = \frac{c\_{air}(\tau) \cdot \left[T\_{Ambient\\_air}(\tau) - T\_{Exhaust\\_air}(\tau)\right]}{c\_{min}(\tau) \cdot \left[T\_{Ambient\\_air}(\tau) - T\_{Posthuffer}(\tau)\right]} \tag{7}$$

Figure 9. Transient effectiveness curves, (a) case 1; (b) case 3; and (c) case 2.

#### 3.2.2. Transient response analysis using the transient effectiveness

The transient effectiveness for each component is plotted in Figure 9(a)–(c), with the results of the three test cases. Figure 9(a) shows the transient effectiveness for test case 1. It can be seen by comparing the transient effectiveness curves that the transient response time of the buffer unit is very short compared to the other two heat exchangers. Since the two fluids of the buffer unit are constant, the final effectiveness is kept as the same value of 0.8. The dry cooler shows a relatively long response time, since its corresponding transient effectiveness curve takes longer time to approach a steady state. Since there is no fluid mass flow rate changes, the final steady states are the same as the initial one of 0.6. In terms of the side car heat exchanger, it can be seen that a new steady state is reached. This illustrates that the air mass flow has varied in this test case. Figure 9(b) shows the transient effectiveness results for case 2. In this test case, the internal fluid mass flow rate is varied. Therefore, the final steady-state values of the sidecar heat exchanger and the buffer unit are changed. In terms of the buffer unit, the effectiveness curves show a rapid response and rapidly approaches a new steady-state condition. The sidecar heat exchanger shows a similar fast response performance. The dry cooler takes much longer to reach the same steady-state condition (since the dry cooler has no fluid mass flow rate variation), compared to the other two heat exchangers. Figure 9(c) shows the transient effectiveness results for test case 3. Similar to test case 1, the dry cooler and the sidecar heat exchanger take longer time before they settle down and approach a steady state. The buffer unit variation time is much smaller, as shown in the curves. It is also illustrated in the transient effectiveness curves that the air flow within the server rack is varied in this test case, since the sidecar heat exchanger reaches a different final steady-state value. More analysis regarding the cause of the variation in rack air flow is presented in reference [19]. By plotting the transient effectiveness curves, the dynamic performance of each heat exchanger component and the time taken to approach a new steady state can be seen clearly. In addition, based on the characteristics of the transient effectiveness curves, more dynamic performance related to the variation applied to the heat exchanger is illustrated.

For a closed coupled system, especially when multiple heat exchanger units are used, the transient effectiveness can be used to characterize the thermal capacitance effects of each unit. Figure 9(a)–(c) shows that the buffer unit effectiveness reaches steady state much faster than the other two heat exchanger units. The dry cooler takes the longest time, which is seen in all three cases. This illustrates that the thermal capacitance of the buffer unit is much less than that of the dry cooler. Actually, the dry cooler is a much larger unit located outside of the building and the buffer unit is a small plate heat exchanger. The time taken for the sidecar heat exchanger to reach steady state in cases 1 and 3 is long. However, the sidecar heat exchanger takes a much shorter time in case 2. Here are some explanations: in cases 1 and 3, which involve variations in server power, the server thermal mass is involved. The impact of the thermal mass extends the time taken for the rack recirculated air and the entire rack side air dynamic to reach steady state. Then the time taken for the side card heat exchanger to reach steady state is longer in cases 1 and 3. The server thermal mass is not involved in case 2. Therefore, only the thermal capacitance of the side card heat exchanger is dominate in the transient response. Based on this analysis, it can be seen that the thermal capacitance of the sidecar heat exchanger and the buffer unit are much smaller compared with the one of the dry

Figure 9. Transient effectiveness curves, (a) case 1; (b) case 3; and (c) case 2.

204 Heat Exchangers– Design, Experiment and Simulation

cooler heat exchanger. The temperature results are collected at different locations, capturing a detailed response sequence. However, since the heat exchanger units are connected to each other using the internal loop and external loop, it is very difficult to characterize the response time of certain heat exchanger by using any temperature result. The temperature results vary during the entire test run. The transient effectiveness method provides a way to observe individual component performance, even though it is in a closed coupled system, by fliting the influence of the neighbored components. The buffer unit transient effectiveness curves have reached steady-state conditions, while the temperatures are still varying. This illustrates that the buffer unit itself has reached a steady-state thermal-exchange condition during a transient event. This can be understood as a self "steady-state" condition in a transient environment. In this condition, even though the corresponding fluid temperatures vary with time, the heat exchanger has approached a steady-state condition.

#### 3.3. Summary

This section illustrates that the transient effectiveness can be used for characterizing the dynamic response of a closed coupled heat transfer loop, which has multiple heat exchanger units installed. It also represents the thermal capacitance impact of each component during different transient events. In addition, some detailed physical insights, which cannot be directly captured from temperature results, can be indicated by the transient effectiveness results.
