Numerical Simulations and Analyses of Mechanically Pumped Two-Phase Loop System for Space Remote Sensor

Abstract

A mechanically pumped two-phase loop (MPTL) system used for the accurate and stable thermal control of orbital heat sources can show excellent characteristics. In order to study the dynamic behaviors of heat and mass transfer of MPTL systems, particularly in response to heat load variations, a transient numerical model was developed by using the time-dependent Navier-Stokes equations. A comparison between the simulation and test results indicated that the errors of mass flow rate were at around ±10%, of which the validity and accuracy were verified. The model was used to study the operating state, and flow and heat characteristics on the basis of the analyses of variations in mass flow rate, temperature, and quality under different operating conditions. Above all, the complex transient behaviors in response to heat load variations in an MPTL system were studied in this model, such as the mass transfer between the accumulator and loop. Results indicate that the phenomenon of mass exchange occurs between the main loop and the accumulator when the heating power increased or decreased. Variations in temperature and pressure in the accumulator were different for the cases of increasing and decreasing power. The slope of the exchange rate curve and the maximal value of the flow rate decreased with the increase in filling amount. The model could be used to guide the design of MPTL systems and to predict the behavior before a system is built.

1. Introduction

A mechanically pumped two-phase loop (MPTL) is a kind of active two-phase heat transfer device through the latent heat of liquid-vapor phase change during the flow boiling process, which possesses the characteristics of large heating power dissipation, the accurate temperature control of multi heat sources, and the high stability of its temperature level [1,2,3]. The mentioned merits give MPTL the advantages of miniaturized, lightweight, and compact heat exchange equipment; thus, MPTL systems have important application values for the development of aerospace and movable antennas, and high-power lasers. For space remote sensors, core optical components and structures are needed to control their temperatures in narrow ranges [4]. Moreover, in order to increase the imaging indices of geometric accuracy and signal-to-noise ratio for a space camera, the temperatures of core photoelectric devices also require to be strictly controlled throughout their entire life cycle [5]. However, the operating modes of a space camera and its external environment are complicated in real application, which brings great difficulties to its thermal design. Therefore, MPTL is of great interest in the thermal control of space optical payloads. Some on-orbit flight cases have proven the excellent working characteristics of the MPTL system in terms of temperature control and heat dissipation [6,7,8,9,10,11]. For example, in 2011, one MPTL system for the thermal control of an alpha magnetic spectrometer could limit the temperature variation in multi heat sources within ±0.30 °C for 192 silicon microstrip detectors. The above-mentioned studies and application cases showed the excellent performance of the MPTL system in the thermal control of space payloads.

Several experimental investigations on MPTL systems have also been carried out to study behaviors under different conditions. Liu et al. [12,13] studied the transient behaviors of start-up temperature control under different heat loads, flow rates, and sink boundaries in the lab, and their results indicated that the MPTL system presented excellent and stable performance for varied conditions. Zhang et al. [14] investigated operating behaviors in a simulated space environment, and MPTL could be smoothly operated under different boundaries. Meng et al. [1,15] studied the transient characteristics during start-up and heating power load on/off for simulating the operating modes of a space camera in the lab and a simulated space environment. MPTL could manage the temperature in small oscillations and provide a uniform temperature boundary during the whole process. Zhang et al. [16] introduced a coupled controller for the temperature control of a microchannel MPTL, and their results indicated that the novel control method performed well in both temperature control and disturbance rejection. Li et al. [17] analyzed the effects of start-up and variation heat load on the dynamic characteristics of an MPTL system, and temperature and pressure presented different phenomena during start-up and regular operation periods.

Comparing with the experimental studies, theoretical analysis and numerical studies can also play a key role in understanding the heat and mass transfer behavior, and underlying mechanisms of MPTL system. Quite a few numerical and theoretical studies have been carried out on the system. Huang et al. [18] studied the coupling behaviors between the accumulator and the main loop of an MPTL system by simulation, and they revealed the mutual disturbance between them. van Gerner et al. [19,20] studied the transient behaviors of an MPTL system with a working fluid of CO₂ and R134a, and the factors that affected the fluid exchange behaviors were analyzed. Chaix et al. [21] carried out steady- and transient-state simulations through dedicated fluidic tools and methodologies, and compared the simulation and experimental results under several flight cases. For a remote-sensing satellite, heat dissipation from these devices to monitor and map certain objects and regions are periodic and intermittent when their operating modes are changed according to demand. The periodic operating modes of this kind of satellite give more challenges to simulation work, especially the dynamical heat and mass transfer processes between the main loop and the accumulator. However, there was a deficiency in the mutual effects between vapor and liquid phases within the accumulator, and the dynamic behaviors of the main loop during the mass transfer process for MPTL systems. In order to assess the behavior and stability of MPTL system for a space camera on the conceptual level, an accurate model is needed to obtain the heat and flow behaviors of the system after these actions. In this study, a transient numerical model is established that is used to study the dynamic behaviors of heat and mass transfer of an MPTL system. In the following, the composition and mathematical model of the MPTL system are given first, followed by a comparison between the test data and simulation results, and results and discussions for the heat and mass transfer processes. Lastly, some conclusions are drawn.

2. Operating Principle

For the purpose of the heat dissipation and temperature control of multiheat sources on a space camera, the schematic diagram of the proposed MPTL system is shown in Figure 1. The MPTL was composed of a pump to transport the fluid through the whole loop, a preheater to heat the subcooled liquid into saturated fluid, several cold plates (evaporators) to collect heat from the heat sources, a condenser to remove the heat from the working fluid to sink, an accumulator to regulate the evaporator temperature and account for the expansion of the working fluid, and liquid and two-phase lines to transport the fluid. Since the saturation states of the fluid in the cold plate and the accumulator are related, the following condition is satisfied [22]:

$$T_E-T_A=\frac{\Delta P_{EA}}{{\left(dP/dT\right)}_{sat}}$$

(1)

where T_E and T_A are the saturation temperatures of the fluid in the cold plate and accumulator, respectively; ∆P_EA is the saturation pressure difference between cold plate and accumulator; and (dP/dT)_sat is the slope value of the pressure-temperature saturation line at T_A. Equation (1) states that, for a given pressure difference between these two elements, a corresponding saturation temperature difference also exists.

The accumulator is the key component of MPTL system, acting like the brain. The accumulator is used to perform vapor and liquid management, to adjust the distribution of the working fluid, and to control the saturation temperature and pressure of the system. For a two-phase fluid, a change in temperature (pressure) can be realized by creating vapor or liquid, which can be achieved by a heater or cooler. In this study, a two-phase thermally controlled accumulator was employed to carry out the control functions. The accumulator requires a fixed volume tank whose temperature is controlled by auxiliary external heating and cooling devices. The fluid state within the accumulator must be two-phase in order to maintain the saturated temperature of the MPTL system. In applications, auxiliary heating and cooling can be accomplished with temperature-controlled heating circuits and Peltier devices. The main advantage of the accumulator is that it is relatively simple and robust. In ground applications, accumulator design is relatively simple, since the liquid and vapor are separated by gravity. For space cases, special capillary structures are designed to ensure that the outlet fluid is pure liquid.

3. Mathematical Model

3.1. Basic Hypotheses

The transient mathematical model developed to simulate the distribution of fluid in the loop, variation in the thermodynamic state, and characteristics of heat and mass transfer was based on the node-network method. The treatment of fluid flow is one-dimensional in nature. In addition, the following hypotheses were supposed:

(1)

The flow state of a single phase in the pipe was considered to be fully developed since there was a large length-to-diameter ratio in the tube.

(2)

The homogeneous equilibrium model was used for the two-phase flow in pipes. The velocities of vapor and liquid phases were the same, and a perfect mixing state between the phases with equal temperature and pressure was assumed.

(3)

Energy variation due to the change in pressure was omitted.

Considering the application features of space camera, the characteristics of the model were as follows:

(1)

The physical parameters within the MPTL system are from NIST REFROP database 23 [23], which can guarantee the simulation precision.

(2)

The phase state of fluid is determined by comparison the value of specific enthalpy of the fluid lump with that of pure liquid phase or gas phase.

(3)

The coupling processes of radiation, heat conduction and phase change of gas and liquid are included in the model.

3.2. Governing Equation

The transient model of MPTL system includes thermal and flow models [24], which is shown in Figure 2. The thermal model is composed by heat conduction and heat radiation, which is mainly used to compute the heat transfer between the walls and heat exchange between the wall and the sink. The flow model consists of the process of flow and convective heat transfer between the fluid and the wall, which is used to analyze the process of flow transfer and heat-fluid coupling.

The governing equation for the thermal nodes is the energy balance equation [25,26], which is given as follows:

$$m_N{C}_N\frac{d{T}_N}{dt}={\displaystyle \sum _i{Q}_{Ci}}+{\displaystyle \sum _j{Q}_{Fj}}+{\displaystyle \sum _k{Q}_{Rk}}+{\displaystyle \sum _l{Q}_{sl}}$$

(2)

where $m_N$ and $C_N$ are the mass and specific heat of node N; Q_C, Q_F, Q_R, Q_S are the conduction heat of node N related with other nodes, convective heat with the fluid for node N, and radiation heat with the sink and the loaded heating power; i, j, k, l are the numbers of Q_C, Q_F, Q_R, Q_S.

The convective heat can be calculated by

$$Q_F=hA\Delta T$$

(3)

where the heat transfer coefficient at the inner wall is determined by

$$h_i=\frac{\left(Nu\right)k_f}{d_i}$$

(4)

where Nu is the Nusselt number; k_f is heat conductivity; d is the diameter or equivalent diameter. When the fluid is single-phase, Nu can be calculated by the following equations [27]:

$$Nu=\left\{\begin{array}{cc}4.36& \mathit{Re}<1960\hfill \\ \frac{\left(f/8\right)\left(Re-1000\right)Pr}{1+12.7{\left(f/8\right)}^{1/2}\left({Pr}^{2/3}-1\right)}& 1960<Re<6420\hfill \\ 0.023{Re}^{0.8}{Pr}^n& Re>6420\hfill \end{array}\right.$$

(5)

where Re is the Reynolds number; f is the friction parameter; and Pr is the Prandtl number. When the temperature of the thermal node was higher than that of the fluid, n was equal to 0.4; otherwise, its value was 0.3. When the fluid was in two-phase, the Shah correlation was used to calculate Nu as follows [28]:

$$Nu=0.023{Re}_l^{0.8 }{Pr}_l^{0.4}\left[{\left(1-x\right)}^{0.8}+\frac{3.8x^{0.76}{\left(1-x\right)}^{0.04}}{P^{*}{}^{0.38}}\right]$$

(6)

where

$${Pr}_l=\frac{{\mu }_l{c}_{p_l}}{k_l}$$

(7)

$$P^{*}=\frac{P}{P_c}$$

(8)

The qualitative temperature in Equations (6)–(8) adopts the saturation temperature of the two-phase section. x in Equation (6) is the mass fraction (i.e., quality).

A flow model includes the flow lumps and flow path. The mass equation of a flow lump is given by

$$\frac{d{m}_i}{dt}={\displaystyle \sum _k\left(e_k\cdot {\dot{m}}_{ik}\right)}$$

(9)

where m_i is the mass of lump i; e_k is the symbol of direction; $\dot{m}$ is the mass flow rate. When the fluid enters lump i, e_k = 1; when the fluid flows out of lump i, e_k = −1; when no fluid exchange between lump i and other lumps occurs, e_k = 0.

The energy balance equation is determined as follows:

$$\frac{d\left(m_i{\gamma }_i\right)}{dt}={\displaystyle \sum _k\left(e_k\cdot {\dot{m}}_{ik}{\gamma }_{ik}\right)}+{\displaystyle \sum _j{Q}_{Fj}}$$

(10)

where γ is the specific enthalpy of the fluid.

The momentum equation of flow path ij (i.e., the flow section between adjacent lumps i and j) is given by

$$\frac{d\left({\dot{m}}_{ij}\right)}{dt}=\frac{A_{ij}}{L_{ij}}\left(P_i-P_j-\Delta P_f\right)$$

(11)

where A_ij and L_ij are the sectional area and length of the pipe between lumps I and j, respectively. P is pressure, and ∆P_f is the friction pressure drop of the section of the pipe.

When single-phase flow is in the pipe, ∆P_f is calculated by [29]:

$$\Delta P_f=\frac{2f{L}_{ij}}{\rho d}{\left(\frac{{\dot{m}}_{ij}}{A_{ij}}\right)}^2$$

(12)

where f is calculated by the Churchill equation [21], which is given by

$$f=8{\left[{\left(\frac{8}{Re}\right)}^{12}+\frac{1}{{\left(\alpha +\beta \right)}^{1.5}}\right]}^{1/12}$$

(13)

where α and β are calculated as follows:

$$\alpha ={\left\{-2.457\times \ln \left[{\left(\frac{7}{\mathrm{Re}}\right)}^{0.9}+\frac{0.27\epsilon }{d}\right]\right\}}^{16}$$

(14)

$$\beta ={\left(\frac{\mathrm{37,530}}{\mathrm{Re}}\right)}^{16}$$

(15)

where ε is the roughness of the inner wall of the pipe.

There were some bends for the pipes on the condenser, so extra local pressure loss was needed to consider them. Pressure drop at the bends is given by

$$\Delta P_f=\frac{2f{L}_{ij}}{\rho d}{\left(\frac{{\dot{m}}_{ij}}{A_{ij}}\right)}^2+\frac{\zeta }{2}{\left(\frac{{\dot{m}}_{ij}}{\rho A_{ij}}\right)}^2$$

(16)

where ρ is the density of the gas or liquid phase; and ζ is the local friction parameter.

When two-phase flow was in the pipe, the Friedel model was used to calculated the two-phase pressure drop [30]. The model was calculated as follows:

$$\Delta P_f={\Phi }_{l0}^2\Delta P_l$$

(17)

where the parameter of the two-phase flow resistance is given by

$${\Phi }_{l0}^2=E+\frac{3.24FH}{F{r}^{0.045}W{e}^{0.035}}$$

(18)

where

$$E={\left(1-x\right)}^2+\frac{x^2{\rho }_l{f}_v}{{\rho }_v{f}_l}$$

(19)

$$F=x^{0.78}{\left(1-x\right)}^{0.22}$$

(20)

$$H={\left(\frac{{\rho }_l}{{\rho }_v}\right)}^{0.91}{\left(\frac{{\mu }_v}{{\mu }_l}\right)}^{0.19}{\left(1-\frac{{\mu }_v}{{\mu }_l}\right)}^{0.7}$$

(21)

$$Fr=\frac{{\dot{m}}^2}{gd{\rho }_{tp}^2}$$

(22)

$$We=\frac{{\dot{m}}^{2}d}{{\rho }_{tp}\sigma }$$

(23)

where μ, g, and σ are the dynamic viscosity, gravitational acceleration, and surface tension coefficient, respectively. Subscripts v and l represent the gas and liquid phases. ρ_tp is calculated by

$${\rho }_{tp}=\frac{1}{\left(x/{\rho }_v-\left(1-x\right)/{\rho }_l\right)}$$

(24)

where ρ_v and ρ_l are the density of the gas and liquid phases, respectively.

There were processes of gas-liquid phase changes in the preheater, evaporators, and condenser. In this study, the phase state of the fluid was determined by comparing the values of the specific enthalpy of the fluid lump and of the pure liquid phase or gas phase.

When γ < γ_{sat_l}, the state of the fluid was a single liquid phase. The absorbed or released heat could increase or decrease the fluid temperature. The following equation is satisfied as follows:

$${\gamma }_{sat\_l}-\gamma =C_{pl}\dot{m}\Delta t$$

(25)

where γ_{sat_l} is the specific enthalpy of the saturated liquid; C_pl is the specific heat of the liquid phase; and ∆t is value of the temperature increase or decrease.

When ${\gamma }_{sat\_l}\le \gamma <{\gamma }_{sat\_v}$, there was two-phase fluid in the pipe. The quality of the fluid increased or decreased when heat was loaded or removed from the lump. Equation (26) was used to calculate the quality:

$$\gamma -{\gamma }_{sat\_l}=x\cdot {\gamma }_{lv}$$

(26)

where γ_lv is the latent heat of vaporization.

When γ > γ_{sat_v}, the state of the fluid was a single gas phase. The following equation is satisfied as follows:

$$\gamma -{\gamma }_{sat\_v}=C_{pv}\dot{m}\Delta t$$

(27)

where γ_{sat_v} is the specific enthalpy of the gas phase, and C_pv is the specific heat of the liquid phase.

In the accumulator, there was a nonequilibrium thermodynamic state, which is different from the single equilibrium thermodynamic state. In the last state, the heat transfer and mixing processes were assumed to occur over a negligibly small time scale. To model the phasic nonequilibrium in which the vapor and liquid within a two-phase control volume may not be at the same temperature (and in some instances, not the same pressure), two control equations for vapor and liquid phase are required [30]:

$$m_{al}{C}_{pl}\cdot \frac{d{T}_{al}}{dt}=-{\dot{m}}_a{C}_{pl}\left(T_{al}-T_l\right)+\frac{\Delta m_{al,av}}{\Delta t}{\gamma }_{lv}\frac{{\rho }_v}{{\rho }_l-{\rho }_v}+U_{lT}\cdot A_{sT}\left(T_I-T_{al}\right)$$

(28)

$$m_{av}{C}_{pv}\cdot \frac{d{T}_{av}}{dt}=\frac{\Delta m_{al,av}}{\Delta t}{\gamma }_{lv}\frac{{\rho }_v}{{\rho }_l-{\rho }_v}+U_{vT}\cdot A_{sT}\left(T_I-T_{av}\right)+Q_a$$

(29)

where m_al is the mass of the liquid within the accumulator; ${\dot{m}}_a$ is the exchange flow rate of the fluid; T_al is the temperature of the liquid phase; T_l is the temperature of the subcooled fluid; ∆m_{al, av}/∆t is the exchange rate between the gas and liquid phases; U_lT is the heat transfer coefficient of the liquid phase; A_sT is the interface area between the liquid and gas phases; m_av is the mass of the gas phase within the accumulator; T_av is the temperature of the gas phase; U_vT is the heat transfer coefficient of the gas phase; Q_a is the heating or cooling power loaded on the accumulator.

3.3. Boundary and Initial Conditions

To validate the model, the simulation results of the model were compared with the experimental data. The boundary and initial conditions of the simulation model were consistent with the test setup. In terms of physical boundaries, several conditions for different components of MPTL system were considered. The temperature of the accumulator’s wall was precisely controlled in a narrow range, and the aimed temperature was between 19.7 and 20.3 °C. During the test, the temperature of the condenser was set between 9.5 and 10.5 °C, and it was used to dissipate the heat from the system. In addition, the walls of all the components were impermeable to the working fluid. The initial conditions mainly included the temperature, pressure, and quality of the fluid, and the wall temperature of each component, which are determined by the physical state of the system. Then, the relevant thermophysical parameters of the working fluid that were relevant with temperature, pressure, and vapor were obtained with a program.

3.4. Discretization and Computation Method

The computational model was discretized by the staggered grid method (shown in Figure 2). Two kinds of parameters, namely, scalar and vector variables, were defined at different locations. The scalar parameters of pressure, temperature, and quality were defined on the lumps. Vector parameters, for example, the mass flow rate of $\dot{m}$, were located on the interfaces between the adjacent lumps (i.e., junctions), which were staggered half-step lengths from main lumps. The nodes were also defined to represent the thermal parameters, such as the wall temperature and heat capacity.

To better understand how the mesh resolution affects the simulation results, mesh dependence combined with the experimental results was established. Three different sets of meshes with the numbers of 300, 600, and 900 for the main loop were used to evaluate the model’s precision and convergence, and determine the optimal number of meshes. The optimal number of meshes was 600 by considering the simulation errors, and computational accuracy and efficiency.

A set of coupled nonlinear equations were obtained from Equations (2)–(29). In this model, all the relevant thermophysical parameters of the working fluid, such as vapor or liquid density, viscosity, saturated pressure, latent heat of evaporation, and the thermal conductivity of the liquid and vapor, were obtained with the use of the NIST REFPROP database 23 for each volume node and junction area at each time step. The time terms used an implicit finite difference scheme, the main variables of pressure, flow rate, and specific enthalpy used the fully implicit scheme, and other parameters used the explicit scheme. The obtained nonlinear equations were first linearized with the Newton-Raphson method and then solved with the Gaussian iteration.

3.5. Experimental Verification Setup

Figure 3 shows the experimental setup of the MPTL system. A two-phase thermally controlled accumulator was used in this setup. The temperature of the accumulator walls was controlled at 20 ± 0.3 °C during the tests and simulations. Two mass flowmeters were installed in the setup located downstream of the pump and of the condenser. The mass flow rate was 1.0 g/s, which was realized by pump electronics in a fraction of a second. Hence, this can set the pump outlet mass flow rate to be a constant value and simplify the simulation. The heat input of the heat source varied in the range of 0–100.0 w. The temperature of the accumulator was controlled with a PID regulator. The temperature of the condenser was controlled in the range of 10 ± 0.5 °C. In order to decrease the heat leakage from the environment to the MPTL system, all pipes were covered by heat insulation material. During the test, the temperature of the lab was controlled at 20.0 ± 1.0 °C.

Table 1. Parameters of the MPTL system.

Component	Description
Pump	Flow rate: 1.0 g/s
Accumulator	Volume: 200 mL; temperature range: 20 ± 0.3 °C
Preheater	Power: 50 W
Cold plates	Power: 100 W
Condenser	Temperature range: 10 ± 0.5 °C
Tubes	OD: 3.0 mm; ID: 2.0 mm
Working fluid	Ammonia

gives the main parameters of the MPTL system. Flat-plate heat exchangers with small channels were used as the preheater and cold plates. The rectangular section area of the inner flow channel was 2.0 × 1.5 mm, which is equivalent to a hydraulic diameter of 1.7 mm. The heating powers loaded on the preheater and cold plates were uniformly distributed on the top areas. The contact heat transfer coefficient between pipe and condenser was tested with a thermal contact resistance tester in the lab, and it was 1500 W/(m²·°C). The working fluid for the MPTL system was ammonia, possessing the characteristics of large latent heat of evaporation, highly efficient heat transfer, and stable properties. Ammonia is the common working fluid of two-phase heat transfer devices (such as heat pipes and loop heat pipes) for the thermal control of spacecraft.

4. Results and Discussion

4.1. Model Verification

Figure 4 shows the comparison of the mass flow rate between the simulation results and test data. Numerical and experimental results were consistent after studying the exchange rate between the accumulator and main loop when the heat load changed. The error range for the predicted numerical results was between −10% and +10% because the thermal resistance between the heater and the wall of the accumulator, and the thermal capacity of the accumulator in the model were neglected, and the fluid in the accumulator heated up slightly quicker in the simulation than it did in the test. The slightly quicker response of the simulation resulted in a higher flow rate peak from the main loop to the accumulator. With regard to the phenomenon of mass exchange, as a result of the increase or decrease in the cold plates’ heat input, liquid flowed into or out of the accumulator. When the heat load increased, a large amount of vapor in the cold plates was suddenly generated, and the volume of the pipe located downstream of the cold plates was occupied by the generated vapor, which gave rise to flow from the main loop to the accumulator, as shown in Figure 4a. In addition, there was a clear discrepancy between the simulation and test data at around 690 and 720 s. During this period, the values of the simulation results were higher than those of the test results, which may have been caused by the neglected thermal capacity of the model accumulator. The extra fluid also flowed from the accumulator to the main loop. When the heat load decreased, vapor in the cold plates was quickly reduced, and the pipe located downstream of the cold plates was refilled by the fluid from the accumulator, which caused the backflow phenomenon from the accumulator to the main loop, as shown in Figure 4b. In the latter case, fluid from the accumulator must be pure, which is important for the safety of a continuously running pump.

4.2. Parameter Variations in the MPTL System

Figure 5 gives the temporal evolution of the pressure and temperature of the working fluid in the evaporator. After the heating power had increased from 0 to 100 W, a sudden rise in the pressure curve occurred. In the evaporator, the quality was quickly increased to 0.08, which was caused by the increased heat input. The fluid with increased quality traveled through the MPTL system with increased fluid velocity. Downstream of this increased quality front, the fluid adopting the velocity of the front with higher density was sped up. The excess mass flow rate led to higher pressure at the evaporator outlet. Since the value of the latent heat of evaporation γ_lv was decreased when the saturated pressure decreased, there was a short increase in the quality curve.

The temporal evolutions of temperature and pressure for the vapor and liquid phases in the accumulator when the heat load increased and decreased are shown in Figure 6. Since the variation processes of temperature and pressure were concentrated between 600 and 700 s, the time periods in Figure 6 are between 570 and 750 s. As shown in Figure 6a,b, the temperature and pressure in the accumulator changed as a result of the increasing power, and the variation trends of temperature for the gas and liquid phases were different, while the pressure difference between them was very small. The changing processes of temperature for the gas and liquid phases can be explained as follows. The cold liquid from the main loop flowed into the accumulator and then mixed with the liquid inside it. Quickly compressing the space of the gas phase led to the temperature rapidly rising. The maximal value of the temperature increase was 0.6 °C as the flow rate reached the peak value. After that, the flow rate gradually decreased, and the temperature of the gas phase dropped until it was the same as that of the liquid phase as a result of the heat exchange at the gas and liquid interphase. Influenced by the larger thermal capacity of the liquid phase in the accumulator, the drop temperature of the liquid phase was delayed and slower, and the peak value of the drop temperature was 0.25 °C. As shown in Figure 6b, there was little difference in pressure between the gas and liquid phases, and the variations in pressure for the two phases were consistent. In addition, the changing trend of pressure was the same as the temperature trend of the gas phase in the accumulator. Figure 6a,c,d show the temporal evolution of temperature and pressure for the vapor and liquid phases in the accumulator when the heat load decreased. Unlike the variation trend of the parameters in the case of power increasing, the differences in temperature and pressure between the gas and liquid phases were small, and variations in temperature and pressure were consistent. In this case, the backflow rate from accumulator to the main loop was relatively low; thus, the decreasing rate of volume for gas-phase changes was small, which led to the low variations in temperature and pressure for the gas and liquid phases.

Figure 7a shows temporal evolution of temperature at different locations of the transport pipe between the accumulator and main loop. L1, L2, and L3 represent the different locations of the bypass pipe. L1 was 10 mm near the main loop, L3 was 10 mm near the accumulator, and L2 was in the middle location of the pipe (the length of the pipe was 200 mm). Since the variation process of temperature in Figure 7a was mainly concentrated at between 600 and 700 s, the time periods in Figure 7a are between 0 and 2400 s. When the heat was increased from 0 to 100 W, a large amount of cold liquid flowed into the accumulator though the connection pipe; hence, the temperature of the pipe wall decreased. When the heat was decreased from 100 to 0 W, hot liquid flowed out of the accumulator, which resulted in the temperature of the pipe wall increasing. Figure 7b shows the profiles of the mass flow rate of the main loop along the flow distance at two time instants that correspond to the moment of the maximal values when the flows into and out of the accumulator were at their peak. After the heat load increased or decreased, the flow rates from the pump exit to the cold plates’ inlet were the same, while the rates in other locations were affected by the power change. When the heat load increased, the mass flow rates of the two phases between the cold plates’ outlet and the condenser’s inlet are linearly increased.

4.3. Effects of Different Working Fluid Charges

The heat and mass transfer processes when the heat load increased and decreased under different working fluid charges (Case 1: 37 g, Case 2: 77 g; Case 3: 117 g) are studied in this section.

Figure 8 gives the temporal evolution of temperature and pressure in an accumulator with a refrigerant charge. When the heat load increased, the increment in the temperature and pressure of the gas phase increased, and the decrement in the liquid temperature decreased, as shown in Figure 8a,b. This was mainly because the relative volume change in the gas phase increased, and the relative volume change in the liquid phase decreased with the filling amount. When the heat load decreased, the differences in temperature and pressure between the gas and liquid phases were small, as shown in Figure 8c,d. In addition, when the heat load increased, the temperature and pressure of the gas phase first increased and then decreased under the function of the heat transfer between the gas and liquid phases. The decrement in temperature and pressure of the gas phase decreased with filling amount, which was affected by the total heat capacity of the accumulator.

Figure 9 shows the temporal evolution of the exchange rate and the profile of the mass flow rate along the flow distance with different working fluid charges. As shown in Figure 9a, when the heat load increased, both the slope of the exchange rate curve and the maximal value of the flow rate decreased with the increase in filling amount. An explanation for this is that, with the increasing amount of ammonia, the increment in gas phase pressure increased, which increased the flow resistance from the main loop to the accumulator. When the heat load decreased, the exchange rates changed little for different working fluid charges, as shown in Figure 9b. This was mainly because the distribution of the gas phase was not associated with the filling amount. Figure 9c,d show the profiles of the mass flow rate of the main loop along the flow distance with charges at two time instants that corresponded to the moment of the maximal values when the flows into and out of the accumulator were at their peak. The volumes of the liquid phase increased, and the volumes of the gas phase decreased in the accumulator with the working fluid charges. When the heat load increased, the maximal values of the main loop decreased with the increase of ammonia charges in Figure 9c; when the heat load decreased, the minimal values of the main loop remained the same, as shown in Figure 9d. The distribution of the flow rate was only affected in the case of a filling amount increase, which is consistent with the results shown in Figure 8c,d.

5. Conclusions

A transient mathematical model was established for the better understanding of the phenomenon of heat and mass transfer between the accumulator and main loop, temperature and pressure variations in the gas and liquid phases in the accumulator, and the variation in the mass flow rate of the main loop. The model validation was demonstrated by comparing the simulation results with the experimental data through a verification setup. The main conclusions from the numerical simulations are given as follows:

(1)

The phenomenon of mass exchange occurred between the main loop and the accumulator when the heating power increased or decreased. The generating process of a large amount of vapor gave rise to the fluid flowing from the main loop into the accumulator when the heating power increased. The reducing process of vapor in the main loop, on the other hand, led to the backflow phenomenon from the accumulator to the main loop.

(2)

Temperature and pressure in the accumulator changed as a result of the increasing power, and the variation trends of temperature for the gas and liquid phases were different, while the pressure difference between them is very small. The differences for the temperature and pressure between the gas and liquid phases were small, and variations in temperature and pressure were consistent when heating power decreased.

(3)

Both the slope of the exchange rate curve and the maximal value of the flow rate decreased with the increase in filling amount due to the increase in flow resistance from the main loop to the accumulator when the heat load increased, while the exchange rates changed little for different working fluid charges because the distribution of the gas phase was not associated with the filling amount.

The model can be used for predicting the transient characteristics of MPTL systems, and for understanding and analyzing MPTL performance.