Juan Catano

Dynamic Modeling of Refrigeration Cycle for Electronics Cooling

In this paper a refrigeration cycle consisting of multiple evaporators, liquid accumulator, compressor, condenser and expansion valves is analyzed. In the cycle the evaporators and condenser are treated as dynamic components while the liquid accumulator, compressor and the expansion valve are consider static components. For the dynamic components, equations for conservation of mass, energy and momentum are used to characterize the comprehensive transient behaviors. One of the differences with previous models is the use of the momentum equation which is typically neglected in traditional vapor compression refrigeration systems, but it is important in electronics cooling where microchannels are commonly used and a significant pressure drop is observed in the evaporator. This model is expected to have higher accuracy than previously used lumped parameter approximation while maintaining its simplicity to be useful for control purposes. The compressor and expansion valves are modeled using empirical relations, the accumulator is used to guarantee proper operation of the compressor. Local system stability is analyzed using a linearized model at some operating condition and an experimental testbed is developed to validate the model. The test bed consists of three electrically controlled heaters immersed in the refrigeration loop which act as the evaporators. A heated tank as an accumulator for operation at wide range of operating conditions, including low quality at the evaporator outlets. A reciprocating compressor with variable frequency drive to operate

Experimental identification of evaporator dynamics for vapor compression refrigeration cycle during phase transition

Experimental identification of the evaporator dynamics in a vapor compression cycle (VCC) subjected to imposed heat flux in the evaporator is studied. The imposed heat flux boundary condition represents a specific application of the VCC for electronics cooling. However, this application requires different models and control algorithms than traditional VCCs with fluid-to-fluid heat exchanges because of the faster time response of the imposed heat flux boundary condition and because the refrigerant flow at the exit of the evaporator is expected to be a two-phase mixture. First principle models are highly nonlinear and, hence, are not practical for system control. To obtain a simplified model, a dynamic identification of component response characteristics is performed by applying a pulse change in the system operating conditions (i.e., the heat load to the evaporator, the expansion valve opening, or the compressor speed). It is shown that for changes in expansion valve opening, the temperature of the refrigerant at the exit of the evaporator has opposite trends when the flow is initially in the two-phase region and when the flow is in the superheated region. This phenomena represents a challenge for controller design, and further investigation is required.

Stability analysis of heat exchanger dynamics

In the study of vapor compression cycle, momentum balance equation is often ignored in the heat exchanger model. In this paper, we investigate the effect of the momentum balance through a systematic study of the open loop stability of a heat exchanger. We consider 1-D fluid flow in a pipe in four cases of increasing complexity the most general case corresponds to the heat exchanger model: 1. incompressible flow without heat transfer; 2. incompressible flow with heat transfer; 3. compressible flow without heat transfer; 4. compressible flow with heat transfer. Among the three balance equations, mass, momentum, and energy, case 1 involves only the momentum, case 2 involves both momentum and energy, case 3 involves mass and momentum, and case 4 requires all three equations. It is shown that in cases 1, which corresponding to the incompressible flow without heat input, the system is lumped and always stable, and in cases 2, 3 and 4, the system is stable if and only if the equilibrium flow velocity is sufficiently high. Finite difference approximation and linearization of the dynamic models are used for local stability evaluation in case 3 and 4. The overall cycle analysis as well as a simulation example is also included. The result of this study now forms the foundation to investigate the open loop stability and closed loop control design for vapor compression cycles used in HVAC and electronic cooling systems.

The Steady-State Modeling and Static System Design of a Refrigeration System for High Heat Flux Removal

This paper investigates the steady-state modeling and static system design of a refrigeration system for high heat flux removal of high power electronics system. The refrigeration cycle considered consists of multiple evaporators, liquid accumulator, compressor, condenser and expansion valves. In contrast with conventional refrigeration systems with liquid-to-liquid heat exchangers for temperature control where the critical heat flux (CHF) is not a major concern, refrigeration systems for high heat flux removal have to ensure that the incoming heat flux is lower than the CHF to prevent device burnout. Since the superheated region in the evaporator has much lower heat transfer coefficient than the two-phase region, the evaporator exit should be two-phase for ensure sufficiently high CHF. The two-phase evaporator exit necessitates the inclusion of a heated liquid accumulator for the safe operation of the compressor to ensure only saturated vapor enters the compressor. The evaporators and condenser of the cycle are modeled by the mass balance, momentum balance, and energy balance equations. Due to the future utilization of microchannels to enhance heat transfer in heat exchangers, the momentum equation, rarely seen in previous modeling efforts, is included here to capture potentially significant pressure drops. The expansion valve and compressor are modeled as static components. The accumulator is modeled to regulate the active refrigeration charge of the system and to provide just enough heat to the outflow of the evaporator such that the inflow of the compressor is always saturated vapor. Based on the steady-state model, the static system design issues include determining the total refrigerant charge of the system to accommodate the varying operation conditions, sizing of the compressor and accumulator, and finding the optimal operation condition for given incoming heat flux to optimize the Coefficient of Performance (COP) while satisfying the CHF and other constraints. The steady-state model will be validated on a testbed currently in construction. The testbed consists of a reciprocating compressor with variable frequency drive, a plate condenser, a heated accumulator (tank with electric heater), three evaporators with immersed electrically controlled heaters, and one electronic expansion valve for each evaporator.Copyright

Energy Efficiency of Refrigeration Systems for High-Heat-Flux Microelectronics

Increasingly, military and civilian applications of electronics require extremely high-heat fluxes on the order of 1000 W/cm2. Thermal management solutions for these severe operating conditions are subject to a number of constraints, including energy consumption, controllability, and the volume or size of the package. Calculations indicate that the only possible approach to meeting this heat flux condition, while maintaining the chip temperature below 65°C, is to utilize refrigeration. Here, we report an initial thermodynamic optimization of the refrigeration system design. In order to hold the outlet quality of the fluid leaving the evaporator to less than approximately 20%, in order to avoid reaching critical heat flux, the refrigeration system design is dramatically different from typical configurations for household applications. In short, a simple vapor-compression cycle will require excessive energy consumption, largely because of the additional heat required to return the refrigerant to its vapor state before the compressor inlet. A better design is determined to be a “two-loop” cycle, in which the vapor-compression loop is coupled thermally to a pumped loop that directly cools the high-heat-flux chip.

Experimental Identification of Component Parameters for Multiple-Evaporator Vapor Compression Refrigeration Cycle

Vapor compression refrigeration cycles have become a promising alternative for high-heat-flux electronic cooling. Still, this area of research lacks the modeling and control design tools to facilitate its practical implementation. At Rensselaer simulation models for system level design and algorithms for temperature control are being developed to bridge that gap. However, these models need to be validated by experimental results. Since the models are not entirely based on first-principle equations, the empirical relations should be matched to the particular experimental setup used for validation. Therefore, the first step towards validation is the identification of empirical parameters that are intrinsic to the experimental apparatus and are required for the simulation. Consequently, this paper presents the experimental identification of the expansion valve coefficient, and the compressor’s volumetric efficiency used in the model. Experiments are performed at different expansion valve openings and different compressor speeds until steady-state is reached. The steady-state data is used to obtain the expansion valve coefficients, and the compressor’s volumetric efficiency. Finally, the data is used to obtain correlations, which are adequately accurate with reasonable computation cost, for each of the evaluated parameters to be incorporated into the simulation model.Copyright

The Steady-State Modeling and Analysis of a Two-Loop Cooling System for High Heat Flux Removal

Steady-state modeling and analysis of a two-loop cooling system for high heat flux removal applications are studied. The system structure proposed consists of a primary pumped loop and a vapor compression cycle (VCC) as the secondary loop to which the pumped loop rejects heat. The pumped loop consists of evaporator, condenser, pump, and bladder liquid accumulator. The pumped loop evaporator has direct contact with the heat generating device and CHF must be higher than the imposed heat fluxes to prevent device burnout. The bladder liquid accumulator adjusts the pumped loop pressure level and, hence, the subcooling of the refrigerant to avoid pump cavitation and to achieve high critical heat flux (CHF) in the pumped loop evaporator. The vapor compression cycle of the two-loop cooling system consists of evaporator, liquid accumulator, compressor, condenser and electronic expansion valve. It is coupled with the pumped loop through a fluid-to-fluid heat exchanger that serves as both the vapor compression cycle evaporator and the pumped loop condenser. The liquid accumulator of the vapor compression cycle regulates the cycle active refrigerant charge and provides saturated vapor to the compressor at steady state. The heat exchangers are modeled with the mass, momentum, and energy balance equations. Due to the projected incorporation of microchannels in the pumped loop to enhance the heat transfer in heat sinks, the momentum equation, rarely seen in previous refrigeration system modeling efforts, is included to capture the expected significant microchannel pressure drop witnessed in previous experimental investigations. Electronic expansion valve, compressor, pump, and liquid accumulators are modeled as static components due to their much faster dynamics compared with heat exchangers. The steady-state model can be used for static system design that includes determining the total refrigerant charge in the vapor compression cycle and the pumped loop to accommodate the varying heat load, sizing of various components, and parametric studies to optimize the operating conditions for a given heat load. The effect of pumped loop pressure level, heat exchangers geometries, pumped loop refrigerant selection, and placement of the pump (upstream or downstream of the evaporator) are studied. The two-loop cooling system structure shows both improved coefficient of performance (COP) and CHF overthe single loop vapor compression cycle investigated earlier by authors for high heat flux removal.Copyright

Pre- and Post-Critical Heat Flux Analyses in a Saturated Refrigerant Flow Boiling System

Vapor compression refrigeration (VCR) cooling has been identified as a promising solution to ensure the low-temperature sustainable operation of photonics, avionics and electronics in extreme hot weather. With the inherent benefits of saturated flow boiling in a direct VCR cooling cycle, uniform low surface temperature and low solid/liquid thermal resistances can be achieved. However, flow boiling heat transfer performance is limited by the relatively low critical heat flux (CHF) condition because the evaporator inlet flow is already a liquid/vapor mixture. Moreover, for the aforementioned applications, the dissipated heat loads are usually subject to large and transient changes, which could easily cause the evaporating flow to exceed the CHF point. Therefore, it is important to characterize boiling heat transfer in transient VCR evaporators under both pre-CHF and post-CHF conditions. Comprehensive experimental data are reported in this paper to describe the complete forced convection boiling hysteresis at the evaporator exit. Several well-known boiling heat transfer correlations and flow pattern criteria are used to help understand the physics of the hysteresis. An empirical model is developed to reveal the unstable nature of transition flow boiling dynamics. A probability distribution function model is further proposed to predict the droplet size in mist flow and vapor core of annular flow. This study provides more design and operating guidelines for the application of saturated flow boiling systems in renewable power generation and electronics/photonics/avionics cooling industries.Copyright

Experimental Model Identification and Controller Design of a Vapor Compression Cycle for Electronics Cooling

In this paper dynamic identification of the evaporator dynamics in a vapor compression cycle (VCC) subjected to imposed heat flux is studied. The imposed heat flux boundary condition at the evaporator represents a specific application of the VCC for electronics cooling. However, different models and control algorithms than traditional VCCs are required. First principle models are highly nonlinear and, hence, not practical for system control. A dynamic model identification of the refrigerant temperature at the exit of the evaporator, refrigerant pressure, and temperature of the heating element is performed by varying the expansion valve opening. It is shown that single-input single-output (SISO) identification is not sufficient to capture the dynamics of the evaporator, due to the coupling of the dynamics in the entire system. Including the effect of incoming mass flow rate into the evaporator to the model significantly improves the identification and prediction of the evaporator dynamics. Finally, a SISO controller based on the identified model, is designed and tested experimentally. The control objective is to maintain the temperature of the heating element below a set point, subjected to changes in heat flux.Copyright

Stability analysis of refrigeration systems for electronics cooling

In modeling studies of vapor compression cycles, the momentum balance equation is usually ignored in the dynamic heat exchanger models. However, in micro-scale heat exchangers, significant pressure drop has been observed. In this paper, we investigate the effects of the momentum balance through a systematic study of the open loop stability of a heat exchanger. We consider 1-D compressible fluid flow in a general circular channel with heat transfer exists. The mass, momentum, and energy conservation equations are all included in the analysis. For the complete cycle, we model the compressor and valve as static elements, since they have much faster dynamics. Based on the finite difference approximation of the dynamic model, we obtained a necessary and sufficient condition for the open loop stability of the vapor compression cycle about a given operating point. A simple simulation example shows that the stabilizing condition agrees with the numerical simulation results. The results of this study form the foundation to investigate the open loop stability and closed loop control design for vapor compression cycles used in electronics cooling systems.