## Abstract

Flow boiling in microchannel evaporators is widely recognized and promising for its compact structure, lower coolant usage, high heat transfer coefficient, ability to provide higher heat fluxes, and better temperature uniformity than single-phase liquid cooling. However, critical heat flux (CHF), local dry-outs, and flow instabilities can be significant roadblocks for practical implementation. Flow instabilities, like pressure drop oscillation, could lead to nonuniform wall temperature distribution, flow reversal, and local dryout, which can be detrimental to system performance. We conducted an experimental study of a vapor compression cycle incorporating a microchannel evaporator to investigate the role of evaporator design and various system parameters on the overall performance. These parameters include the expansion valve setting, the accumulator heat load, and the evaporator heat load. While the evaporator design, the testbed, and system parameters affect the system response in unique ways, flow instability can be explained based on the overall pressure drop occurring in the system and how it varies as a function of these factors. Based on the understanding gained from this experimental study, a dynamic control strategy was developed to stabilize the system facing transient heat loads. The system can successfully address transient evaporator heat loads with feedforward control, which would otherwise lead to pressure drop oscillation. We believe this study can be helpful in further development of active control techniques to achieve multiple objectives of maintaining fixed evaporator temperature, allowing higher cooling rates, avoiding CHF, and suppressing flow instabilities, even in the presence of transient heat loads.

## 1 Introduction

There is a significant need for efficient and reliable thermal management to remove high heat fluxes in applications such as light-emitting diodes, laser diodes, high-performance integrated circuits, and data centers [16]. Compared to the traditional macroscale evaporators, flow boiling in microchannel evaporators is particularly attractive due to its potential to achieve high heat transfer coefficients and low thermal resistances, maintaining relatively uniform temperatures, and enabling compact structures and lower coolant usage [7,8]. While flow boiling in microchannels is promising, several challenges impede its implementation, including the occurrence of relatively high pressure drop, critical heat flux, and flow instabilities, such as pressure drop oscillation, flow maldistribution, and density oscillation [9,10].

The two conditions necessary for the occurrence of pressure drop oscillation (PDO) are compressible volume in the system and a negative slope in the demand pressure curve, which causes a decrease in the overall pressure drop in the system with increasing mass flow rate [11,12]. Research shows that even a small compressible volume is sufficient to cause PDO [13]. It can be triggered by bubble growth, confinement, and rupture in the narrow channels. Furthermore, the pressure oscillations show increasing intensity with higher vapor qualities in the microchannel [14,15]. In this regard, many factors could affect the oscillation amplitude and frequency, including the channel geometry, subcooling of refrigerant at the inlet, flow rate, evaporator heat load, and the amount of compressible volume in the system [16,17]. This system-level dynamic instability could result in structural vibrations, premature critical heat flux (CHF), partial dry-outs, and system failure if corrective measures are not taken [18,19].

Various designs and surface modifications of the evaporator have been developed to improve the heat transfer performance and suppress flow instability. These modifications include the use of reentrant cavities [20], interconnected microchannels [21], artificial nucleation sites with nanowires and porous metallic coatings [22], micro- and nanoscale hierarchical structures [23], inlet restrictors, and expanding microchannel geometries [24,25]. A combination of strategies, such as using artificial nucleation sites with inlet restrictors, can address flow instability by suppressing oscillations and enhance the heat transfer coefficient [26]. Similarly, pin fin-interconnected reentrant microchannels combine the merits of reentrant cavities and micropin fins by providing heat transfer enhancement while addressing pressure drop and two-phase flow instabilities [27,28].

Active flow control strategies can also address the challenges posed by PDO and transient heating. These strategies include external pulsation of refrigerant flow [29], jet flow [30], and dynamically controlling the compressor or pump speed [31]. Studies also indicate that high-frequency flow pulsation can reduce PDO. Specifically, with external pulsations, the flow can switch from bubbly to annular, leading to lower pressure fluctuations [32]. Seed bubbles generated upstream using microheaters also provide an active control strategy to improve the flow and heat transfer performance while suppressing instability [33]. For active control, a combination of lumped dynamic and static models for the system can predict PDO occurrence, guiding the development of active feedback control methods. This approach can effectively regulate the evaporator temperature, maintain higher system efficiencies and avoid flow instability [8,3436].

This study demonstrates an actively controlled system based on the vapor compression cycle (VCC) incorporating a microchannel evaporator. We show how PDO depends on the evaporator design and system parameters, including the expansion valve setting, accumulator heat load, evaporator heat load can affect the oscillation characteristics. By understanding how various parameters affect system stability, we developed a simple active control strategy that uses the evaporator heat load as a feedforward signal to control the expansion valve. The experiments demonstrate how the system is stabilized, and PDO is avoided in the presence of dynamically varying heat loads. We believe such simple control strategies can address a wide range of applications facing transient heat loads by providing better cooling performances and higher efficiencies.

## 2 Vapor Compression Cycle Testbed

Figure 1(a) shows the physical layout of the VCC system considered in this study. In this system, the compressor receives the refrigerant as saturated vapor from the accumulator and compresses it to higher pressure and temperature. The refrigerant flows through the condenser, where it condenses and cools by losing heat to an external coolant. After exiting the condenser as a liquid corresponding to the external coolant temperature, the refrigerant flows through an electronic expansion valve to exit as a two-phase mixture at low pressure and temperature. The refrigerant then enters the evaporator, where it absorbs heat from a heat source. After exiting the evaporator, the refrigerant enters the accumulator as a liquid–vapor mixture. It should be noted that the compressor requires refrigerant in the vapor phase to operate safely. Hence, heat input to the accumulator is often necessary to maintain the desired vapor flow rate in the system.

Fig. 1
Fig. 1
Close modal

Figure 1(b) shows the testbed to characterize the VCC system using R134a (1,1,1,2-tetrafluoroethane) as the refrigerant. This testbed used two different compressors—a reciprocating compressor (MTZ 18-3, Danfoss Maneurop, Utica, NY) with a displacement volume of 3.023 $×$ 10−5$m3$ and a nominal cooling capacity of 2904 $W$ and a smaller compressor (FFI10HBX, Embraco, Rochester, NY) with a nominal cooling capacity of 1170 W. A variable frequency drive (VLT 5011, Danfoss, Utica, NY) was used to operate the larger compressor (MTZ 18-3, Danfoss Maneurop), which controlled the compressor frequency between the allowable range of 25–75 $Hz$ with an electric signal varying between 0 and 10 $V$. The smaller compressor was operated at a fixed frequency of 60 $Hz$.

An electronic expansion valve (SER-AA, Parker, Washington, MO) allowed valve openings from 0% to 100$%$. A stepper motor driver (IM483, Intelligent Motion Systems, Champaign, IL), which divides the opening into 6000 microsteps, drove the valve using pulse signals ranging between 0 and 5 $V$. The condenser used in this study was a brazed-plate heat exchanger (C-4AG, Dragon, Troy, MI). The condenser temperature was maintained using a coolant (60$%$ water and 40$%$ glycol by volume) circulated using an external chiller (CFT150, Neslab, Clackamas, OR), which has a maximum cooling capacity of 4500 $W$ at 20 $°C$. The accumulator used in the testbed was a 25 $cm$ diameter and 80 $cm$ long cylinder. A cartridge heater (McMaster-Carr, Albany, NY) was inserted in the accumulator to supply heat to the refrigerant directly. The heater was wired to a DC power supply (BK Precision 1902, Yorba Linda, CA) with a maximum heating power of 900 $W$. A Coriolis mass flow sensor (ACM 300, AW Co., Edina, MN), installed before the expansion valve, measured the mass flow rate through the evaporator within a range of 0–5 $kg/min$. This study used calibrated T-type thermocouples (Omega Engineering, Brooklyn, NY) with an accuracy of ±0.2 $°C$. The testbed used strain gage pressure transducers (PX-303, Omega Engineering, Brooklyn, NY) with an accuracy ±0.25$%$ of the measurement range [37]. Temperature and pressure sensors were placed at the inlet and outlet of the evaporator, the accumulator, the condenser, and the compressor's outlet, as indicated in Fig. 1(a). Table 1 lists the accuracies of various sensors.

Table 1

Measurement uncertainties for various sensors

DescriptionParameterUncertainty
Inlet evaporator pressure$Pei$±0.25 $%$$×$ 1378 $kPa=$ 3.44 $kPa$
Outlet evaporator pressure$Peo$±0.25 $%$$×$689 $kPa =$ 1.72 $kPa$
Accumulator pressure$Pa$±0.25 $%$$×$ 689 $kPa =$ 1.72 $kPa$
Outlet compressor pressure$Pmo$±0.25 $%$$×$ 1378 $kPa =$ 3.44 $kPa$
Temperature sensors$T$±0.2$°C$
Mass flow rate$m˙e$±2$×10−4 kg/s$
Power supply voltage$V$±0.05 $%×$ measured values $+$ 10 $mV$
Power supply current$I$±0.05 $%×$ measured values $+$ 10 $mA$
DescriptionParameterUncertainty
Inlet evaporator pressure$Pei$±0.25 $%$$×$ 1378 $kPa=$ 3.44 $kPa$
Outlet evaporator pressure$Peo$±0.25 $%$$×$689 $kPa =$ 1.72 $kPa$
Accumulator pressure$Pa$±0.25 $%$$×$ 689 $kPa =$ 1.72 $kPa$
Outlet compressor pressure$Pmo$±0.25 $%$$×$ 1378 $kPa =$ 3.44 $kPa$
Temperature sensors$T$±0.2$°C$
Mass flow rate$m˙e$±2$×10−4 kg/s$
Power supply voltage$V$±0.05 $%×$ measured values $+$ 10 $mV$
Power supply current$I$±0.05 $%×$ measured values $+$ 10 $mA$

The testbed used an SCXI-1303 terminal block (National Instruments, Farmingdale, NY) to collect data from the thermocouples and an SCB-68 terminal block (National Instruments) to collect data from the pressure transducers and the refrigerant mass flow sensor. The controller and driver of the power supply, the expansion valve, and the compressor were connected to a desktop computer using a PCI-6723 board with an SCB terminal block (National Instruments). A LabVIEW virtual interface displayed measurements and allowed inputs to adjust operation with a sampling rate of 5 $Hz$ [37].

## 3 Results

### 3.1 Effect of Testbed and Evaporator Design

#### 3.1.1 Evaporator Design 1.

We tested a microchannel evaporator with 42 channels, with the following dimensions for both fluid channels and walls: Width × Depth × Length= 250 $μm×$ 500 $μm×$21.2 $mm$, as shown in Fig. 2. The microchannel evaporator, made of copper, was directly interfaced with resistive heaters to simulate electronic heating between 0 and 900 $W$. The testbed incorporated the larger compressor (MTZ 18-3, Danfoss Maneurop) to enable higher flow rates and heat dissipation.

Fig. 2
Fig. 2
Close modal

Figure 3(a) shows the variations of the condenser pressure ($Pc$), accumulator pressure ($Pa$), and demand pressure drop ($ΔPD=Pc−Pa$) when the evaporator heat load is varied. In this case, the compressor frequency $ω$ = 25 $Hz$, the accumulator heat load $Qa$ = 500 $W$, and the expansion valve opening$Av$= 100$%$. Note that Fig. 3(a) only shows the steady-state pressures by trimming the transition data (denoted by dotted lines) between steady-states when the heat load is increased. With increasing evaporator heat loads ($Qe$ = 0 to 500 $W$), the microchannel pressure drop increases due to higher vapor qualities in the evaporator, which results in larger accelerational and frictional pressure drops. Consequently, there is a three-fold increase in the demand pressure from 50 to 150 $kPa$. Although not shown here, a significantly large evaporator heat load ($≫$500 $W$) could lead to partial dry-out and heater burn-out. More importantly, it is evident that these tests do not show any PDO. In fact, we did not observe PDO for the entire range of operating conditions supported by this experimental testbed.

Fig. 3
Fig. 3
Close modal

The absence of PDO in this testbed, which consisted of evaporator-1, can be explained based on the demand pressure curves. Figure 3(b) shows the microchannel pressure drop versus mass flow rate for different evaporator heat loads, indicating higher pressure drops for lower mass flow rates and larger heat loads due to increasing vapor qualities. The lack of a negative slope region in Fig. 3(b) is apparent, eliminating PDO for these operating conditions. The lack of a negative slope, in this case, can be due to the large compressor used in this testbed, which provided relatively large mass flow rates. Consequently, the exit quality of the evaporator was too small and insufficient to induce PDO. Additionally, the hydraulic diameter of the microchannel was sufficiently small (330 $μ$m) to have an effect similar to the inlet restrictors for preventing flow instability.

#### 3.1.2 Evaporator Design 2.

In design-2, an evaporator with relatively larger dimensions was used. In this design, the evaporator consisted of seven channels with the following dimensions for both fluid channels and walls: Width $×$ Depth $×$ Length = 1 $mm×$1 $mm×$100 $mm$, as shown in Fig. 4. This evaporator was also made of copper with embedded cartridge heaters to simulate electronic heating. In this case, the testbed incorporated a smaller compressor (FFI10HBX, Embraco) to enable lower flow rates. This compressor was operated at a constant frequency of 60 $Hz$.

Fig. 4
Fig. 4
Close modal

Figure 5 shows the condenser pressure ($Pc$), the accumulator pressure ($Pa$), and the demand pressure ($ΔPD=Pc−Pa$) as a function of time when the compressor frequency $ω$ = 60 $Hz$, the accumulator heat load $Qa$ = 400 $W$, the expansion valve opening$Av$= 100$%$ and the evaporator heat load $Qe$ = 300 $W$. It is evident from Fig. 5(a) that PDO occurred for the chosen evaporator design, testbed, and operating conditions. It shows large oscillations in condenser pressure ($Pc$), and relatively uniform pressure ($Pa$) in the accumulator. A nearly static $Pa$ is due to the use of a large accumulator—an effective buffer for suppressing pressure oscillation. Due to the characteristic variations in $Pc$ and $Pa$, the demand pressure drop ($ΔPD$) also shows significant oscillations with an amplitude of 28 $kPa$ and a period of 11 $s$ (Fig. 5(c)).

Fig. 5
Fig. 5
Close modal

These experiments show that the evaporator design and testbed can significantly affect flow instability and pressure drop. Smaller evaporator channels and larger compressors could be operated to lower the vapor quality and avoid PDO. However, in this case, larger mass flow rates (or smaller exit vapor qualities) are not beneficial since they only provide an incremental enhancement in the overall heat transfer coefficient compared to single-phase liquid cooling. The overall system efficiency is not improved significantly.

Finally, it should be noted that local oscillations could still occur in the evaporator channels, although the system-level demand pressure may show relatively static behavior. As stated in other studies [14,15], pressure oscillations and reverse flow in the evaporator can occur due to bubble growth and rupture in the narrow channels. The usage of inlet restrictors or large mass flow rates could, to some extent, prevent the propagation of such oscillations upstream [26].

### 3.2 Effect of System Parameters.

For a system susceptible to PDO instability, parameters like the compressor speed ($ω$), expansion valve setting ($Av$), accumulator heat load ($Qa$), and evaporator heat load ($Qe$) can affect system stability and overall performance. We studied these parameters experimentally. For the results described below, we used evaporator design-2 and the corresponding testbed consisting of the smaller compressor operated at a fixed frequency of 60 $Hz$. Although we do not vary the compressor frequency, its effect on system stability is analogous to the accumulator heat load, as explained in prior computational studies [11,38].

### 3.3 Expansion Valve Setting.

As described before, the testbed allows varying the valve setting by opening or closing it electronically. A variation in the valve opening can change the slope of the pressure drop characteristic curve. It is possible to eliminate the pressure curve's negative slope by closing the expansion valve and introducing additional hydraulic resistance. However, whether a smaller valve opening would cause or suppress oscillation will depend on the operating point - the intersection point of the supply and demand pressure drop curves. Figure 6 demonstrates this aspect and the impact of the valve setting on system stability. These results are obtained for $ω$ = 60 $Hz$, $Qa$ = 300 $W$,$Qe$ = 130 $W$, and $Av$ varied from 50% to 100$%$. Figures 6(a)6(c) show the system demand pressure ($ΔPD=Pc−Pa$) varying with time for different valve settings. Figure 6(d) shows how the demand pressure is a function of mass flow rate and valve setting. It also shows the supply curve, which depends on the compressor (or pump) used in the system and is independent of the valve setting.

Fig. 6
Fig. 6
Close modal

When the valve is fully open ($Av$= 100$%$), the system is stable (Fig. 6(a)). The oscillation occurs by decreasing the valve setting to $Av$= 80$%$. When the valve setting is decreased further ($Av$ = 50$%$), the oscillation is suppressed. For the three cases considered, oscillation occurs only when the demand pressure curve has a negative slope and its intersection with the supply curve ($ΔPs$) is in the negative slope region. While both $Av=100%$ and $Av=80%$ exhibit a negative slope region, only $Av=80%$ represents a case wherein the intersection is in the negative slope region. $Av=50%$ eliminates the negative slope, hence, leaving no scope for oscillation for these operating conditions. However, this freedom from PDO is achieved at the expense of a higher demand pressure drop (compare Figs. 6(a) and 6(c)) and compressor power, which reduces the coefficient of performance (COP) of the VCC system.

Finally, we want to note that Fig. 6(d), illustrating the supply and demand pressure drop curves, only helps explain the impact of system parameters on stability. They do not represent the actual pressure curves for the testbed since a VCC system undergoing pressure drop oscillation cannot be represented with a static operating point from the intersection point of supply and demand curves. We will use a similar approach to explain the role of other system parameters as well.

As indicated in Fig. 6(d), the operating point given by the intersection of the supply and demand pressure drop curves can be changed by the valve setting. The system is stable when the intersection lies in the positive slope region and unstable in the negative slope region [19,21,37]. By changing the valve setting, the pressure drop through the valve would be affected almost immediately, which would change the flow rate through the compressor and affect the system stability. Hence, it is possible to stabilize the system quickly by changing the valve setting or the overall hydraulic resistance in the system. While similar effects have been seen with passive strategies like inlet restrictors in microchannel evaporators [26], the use of an electronically controlled expansion valve provides a dynamically controllable alternative and possibly higher overall efficiencies for a system experiencing dynamic heat loads.

Figures 7(a)7(c) shows the nonlinear impact of the accumulator heat load ($Qa$) on system stability when $ω$ = 60 $Hz$, $Av$ = 100$%$,and $Qe$ = 130 $W$. Figure 7(d) shows the impact of $Qa$ on the supply pressure curve ($ΔPS$) and the intersection point. When the accumulator heat is large (Fig. 7(a), $Qa$ = 500 $W$) or small (Fig. 7(c), $Qa$ = 200 $W$), the demand pressure ($ΔPD$) is relatively static. However, for an intermediate accumulator heat load (Fig. 7(b), $Qa$ = 300 $W$), the oscillation in $ΔPD$ is noticeably larger. Recalling that an accumulator heat load is necessary to maintain the required vapor flow rate to the compressor, these observations can be explained based on how $Qa$ affects the supply pressure curve ($ΔPS$).

Fig. 7
Fig. 7
Close modal

The overall pressure drops for different accumulator heat loads do not differ significantly, as evident in Figs. 7(a)7(c). When the accumulator heat is large ($Qa$ = 500 $W$) or small ($Qa$ = 200 $W$), the intersection point of supply ($ΔPS$) and demand pressure ($ΔPD$) curves will lie in the positive slope region, ensuring system stability. However, for intermediate values ($Qa$ = 300 $W$), the intersection of the curves could lie in the negative slope region, making the system unstable. Thus, like the expansion valve setting, the accumulator heat load can also be used as a controllable parameter for stabilizing the system. However, there is a substantial penalty for using larger accumulator heat loads. The decrease in overall COP can be significant since the amount of energy necessary to generate vapor and affect the supply pressure curve can be quite large. For a small accumulator heat load (a small mass flow rate), there is a risk of CHF due to the increase of vapor quality in the evaporator, which may cause a surge in temperature. Also, note that the system response time to accumulator heat load change is also much longer than the change in valve setting.

Figure 8 shows the impact of evaporator heat load ($Qe$) on system stability and oscillation characteristics when $ω$ = 60 $Hz$, $Av$= 100$%$,and $Qa$ = 400 $W$. Unlike the valve setting and the accumulator heat load, $Qe$ is application-specific and can change dynamically. For example, a multicore computer processor can experience varying computational loads, resulting in a time-varying $Qe$. With all other system parameters held constant, as $Qe$ increases, the overall demand pressure drop $ΔPD$ increases. The increase in $Qe$ can lead to oscillation with rising amplitudes. In this case, the increase in $ΔPD$ is due to a higher vapor quality in the evaporator, which affects the accelerational and frictional pressure drops.

Fig. 8
Fig. 8
Close modal

If the system is initially stable for lower evaporator heat load (Fig. 8(a), $Qe$ = 100 $W$), it could become unstable due to an increase in $Qe$ (Fig. 8(b), $Qe$ = 200 $W$), and a continuous increase in $Qe$ will make PDO in VCC more severe (Fig. 8(c), $Qe$ = 300 $W$). Comparing Figs. 8(b) and 8(c), a change in $Qe$ from 200 to 300 W, will change the amplitude of PDO from 13 to 28 $kPa$. This increase is due to higher $Qe$, which affects the VCC demand pressure drop, as illustrated in Fig. 8(d). A larger $Qe$ will increase the pressure drop in the microchannel evaporator, which is accompanied by a steeper and wider negative slope region in the demand pressure drop curve, resulting in larger amplitudes of oscillation.

### 3.6 System Stability and Control.

Figure 9 shows the system stability map obtained experimentally for the various combinations of accumulator heat load and valve setting and a constant compressor speed $ω$ = 60 $Hz$ and evaporator heat load, $Qe$ = 130 $W$. Such stability maps can be generated for different evaporator heat loads, which could serve as a guideline for developing an active control strategy. Specifically, the evaporator heat load can be used as a feedforward control signal for setting the expansion valve and the accumulator heat load to avoid flow instability.

Fig. 9
Fig. 9
Close modal

As discussed earlier, a smaller valve opening could stabilize the system by changing the slope of the demand pressure drop curve. However, a smaller valve opening may also trigger oscillation, determined by the intersection of supply and demand pressure curves. It is also important to note that the system can be prone to CHF for smaller valve openings due to decreased mass flow rate resulting in higher vapor qualities in the evaporator. Thus, the valve setting should be chosen carefully. With a change in the accumulator heat load, the refrigerant flow rate could either increase or decrease, either stabilizing or destabilizing the system. Using the system stability map (Fig. 9) as a guideline, we can design feedforward and feedback control to stabilize the system and maintain crucial system parameters, like evaporator temperature and pressure, at the desired values.

Figure 10 shows a proportional valve control diagram wherein the evaporator heat load is used as a feedforward signal to control the valve opening as $Av=C+ kpQe=75−0.1 Qe$. Here, $kp$is the proportional gain. This simple implementation of active control can stabilize the system by change the valve setting in response to dynamic heat loads.

Fig. 10
Fig. 10
Close modal

Figure 11(a) shows the system responses when the evaporator heat load increases from 130 to 300 $W$. Without any active control, the amplitude of pressure oscillations becomes larger, changing from 8 to 18.7 $kPa$. Figure 11(b) shows the system responses with a proportional feedforward control of the expansion valve under an identical change in evaporator heat load. In this case, the PDO has been suppressed. In this case, we observe a sharp increase in pressure due to the sudden decrease in the valve opening when the evaporator heat load increases. It took close to 80 $s$ for the system to reach a steady-state. This experiment demonstrates the capability to address PDO in a dynamically changing environment by using feedforward control.

Fig. 11
Fig. 11
Close modal

## 4 Conclusion

This study is based on an experimental investigation of pressure drop oscillation in a testbed utilizing a vapor compression cycle. The overall objective of this study is to gain a better understanding and address flow instability using an active control strategy. The experiments show how two different evaporators with minor modifications to the testbed can result in widely different performances. We observed flow oscillations only for one of the evaporator designs for the range of operating conditions considered in this study. A VCC testbed incorporating an evaporator with microchannels and a large compressor could avoid PDO across a wide range of operating conditions by operating at relatively high mass flow rates. However, this takes place at the penalty of a higher pumping power and lower overall system efficiency. In contrast, using a smaller compressor, allowing lower refrigerant flow rates, and relying more on phase-change can be beneficial. However, we risk the occurrence of flow oscillations and CHF. These risks can be avoided by understanding the effect of various system parameters on flow instability. In this regard, we studied the effect of the expansion valve opening, the accumulator heat load, and the evaporator heat load while maintaining a fixed compressor speed.

In general, system parameters can have a nonlinear effect on the overall performance. We see stable system operation for relatively high and low values of the expansion valve opening and the accumulator heat load. On the other hand, the system is unstable for intermediate values. The system response to an increasing evaporator heat was monotonic, with higher heat loads resulting in pressure drop oscillation with larger amplitudes and severity. The effect of all the parameters on pressure drop oscillation can be explained based on the variation of the system-level supply and demand pressure curves. When these curves intersect in the negative slope region of the demand pressure curve, the system shows flow instability with significant pressure drop oscillations. A change in the valve opening, the accumulator heat load, and the evaporator heat load can affect the supply and demand pressure curves and where they intersect. This understanding of system response is essential and can determine the stability map, which is a collection of stable and unstable operating points based on the various combinations of system parameters.

Furthermore, a simple control strategy can be developed using the system stability map. The experiments in this study demonstrate the possibility of stabilizing the system through active control. Specifically, in a VCC, the use of the expansion valve as a controllable parameter can be more favorable than using the accumulator heat load due to faster response time and higher overall efficiency. This study demonstrated active control of transient heat loads with the evaporator heat load as a feedforward signal. In future studies, a more accurate and effective control strategy could be applied to achieve multiple objectives, including maintaining fixed evaporator temperature, allowing better system performance, CHF avoidance, and suppressing flow instabilities in the presence of transient heat loads.

## Funding Data

• Office of Naval Research (ONR) (Award No. N00014-16-1-2690; Funder ID: 10.13039/100000006).

• New York State Empire State Development Division of Science, Technology and Innovation (NYSTAR) (Center for Automation Technologies and Systems (CATS); Funder ID: 10.13039/100004863).

## Nomenclature

• $m˙$ =

mass flow rate, $kg/s$

•
• $P$ =

pressure, $Pa$

•
• PDO =

pressure drop oscillation

•
• $Q$ =

heat load, $W$

•
• $T$ =

temperature, $° C$

•
• VCC =

vapor compression cycle

•
• $ω$ =

compressor frequency, $Hz$

### Subscripts

Subscripts

• $a$ =

accumulator

•
• $D$ =

demand

•
• $e$ =

evaporator

•
• $err$ =

error

•
• $i$ =

inlet

•
• $m$ =

compressor

•
• $o$ =

outlet

•
• $S$ =

supply

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