Subcooled Liquid Research Articles

Advanced model for a non-adiabatic capillary tube considering both subcooled liquid and non-equilibrium two-phase states of R-600a

Previous empirical correlations have largely failed to predict the mass flow rate variations of R-600a during the transient pull-down operation of household refrigerators. This shortcoming is attributed to the fact that these correlations were developed for specific thermodynamic states of the refrigerant at the capillary inlet, whereas the thermodynamic state varies during transient operations, particularly involving non-equilibrium two-phase states. To address these limitations, a novel model has been developed. This model comprises two distinct sub-models corresponding to the refrigerant state at the capillary tube inlet: one for the subcooled liquid state and the other for the non-equilibrium two-phase state. These sub-models are integrated to account for the transitions in the thermodynamic state of R-600a at the capillary inlet. The integrated model demonstrates excellent agreement with observed variations in the R-600a mass flow rate during the pull-down operation of actual refrigerators. The mean absolute percentage error between the measured and estimated mass flow rates is approximately 10 % over the entire period of pull-down operations tested under various environmental conditions.

Development and Optimization of a Micro-Baffle for the Enhancement of Heat Transfer in Film Boiling

This study represents the development and optimization of a micro-baffle design to enhance heat transfer in film boiling. Numerical simulations are performed using an open-source computational fluid dynamics (CFD) model, which incorporates the Lee model for momentum source associated with the phase change, and the Volume of Fluid (VOF) method to capture bubble dynamics. A comparison of the numerical results with the previous numerical and experimental data confirmed the validity of the numerical model. The influence of key design parameters was systematically investigated. The results revealed that a vertical baffle provided the maximum performance. The optimal baffle design achieved a 57.4% improvement in the Nusselt number and a 66.4% increase in critical heat flux (CHF). Furthermore, the proposed design facilitated continuous bubble formation, even with a reduced temperature difference between the heated surface and the subcooled liquid, which is crucial for energy-efficient thermal management in engineering systems. Ultimately, this study demonstrates the potential of micro-baffle designs in controlling bubble dynamics and improving heat transfer in film boiling, thereby aiding the design of efficient thermal systems.

Experimental study of the influence of bubble interaction on their characteristics during transient boiling in a flow of subcooled liquid

Experimental study of the influence of bubble interaction on their characteristics during transient boiling in a flow of subcooled liquid

Modeling the Characteristics During the Flow of a Subcooled Liquid Out of Geometrically Similar Laval Nozzles

Modeling the Characteristics During the Flow of a Subcooled Liquid Out of Geometrically Similar Laval Nozzles

Numerical study of flow boiling on microcavity surface under the action of an electric field using lattice Boltzmann method

The microcavity setting promotes bubble nucleation, and the presence of an electric field enables bubble detachment. In this study, the synergistic effect of electric field and microcavity in improved flow boiling heat transfer was analyzed based on the pseudopotential lattice Boltzmann method. The investigation was focused on the influence of wall superheat, Reynolds (Re) number, electric field intensity, liquid subcooling, and gravitational acceleration on the flow boiling performance under two forms of electric field distributions for uniform conducting microcavity surface (MC–UCS) and conducting–insulating microcavity surface (MC–CIS). Compared with the MC–UCS, the MC–CIS maintained a stable wetting state in the microcavity through inhibition of sliding and merging of bubbles. The increase in electric field intensity and Re number improved convective heat transfer in the microcavity but at the expense of a larger frictional pressure drop. The boiling phenomenon on the microcavity surface weakened with the increase in liquid subcooling, which caused difficulty for the electric field to improve the heat transfer performance by improving bubble behavior. Electrical force can replace buoyancy force to perturb the vapor–liquid interface under low gravitational acceleration. This condition allows the fluid shear force to drive bubbles away from the microcavity surface quickly. The results can provide theoretical and technical guidance for the realization of the enhanced synergistic heat transfer between electric fields and microstructures.

Experimental investigation of pressure drop oscillation and active mitigation in a pumped two-phase loop

A pumped two-phase loop (P2PL) integrated with a microchannel evaporator is the most favored design for advanced thermal management of modern electronic devices. However, these systems are susceptible to two-phase flow instabilities, in particular pressure drop oscillation (PDO), which can compromise their performance by premature initiation of critical heat flux (CHF), deterioration of the heat transfer capabilities, and inducing severe thermal and pressure fluctuations. This study experimentally investigates PDO in a P2PL with a microchannel evaporator, exploring the underlying mechanisms and mitigation strategies. The range of parameters are: heat flux from 0 to 56 W/cm2, mass flux from 47.9 to 95.9 kg/m2-s, a fixed inlet temperature of 10 °C, initial accumulator gas pressure from 620.5 to 827.3 kPa, and vapor quality from zero (subcooled liquid) to one (pure vapor close to dryout). A consistent trend of high-amplitude, low-frequency PDO at low heat fluxes transitioning to low-amplitude, high-frequency PDO at high heat fluxes was observed across all operating conditions. PDO originating in the evaporator propagated to other loop components with similar characteristics, underscoring the systemic nature of PDO. Further, PDO-driven thermal oscillations were observed to propagate through the evaporator, reaching the heater (heat source) temperature with maximum amplitude of 3.4 °C. These oscillations had a detrimental impact on the heat transfer coefficient by altering the flow boiling regimes within the microchannels. Notably, the subcooled liquid temperatures remained stable, indicating the absence of pressure-induced thermal effects in single-phase regions. Finally, an active control technique, based on controlling the pump flow rate using continuous feedback of flow rate was implemented to mitigate PDO, eliminating both pressure and temperature oscillations, achieving an average reduction of 69.8 % in PDO amplitude.

3D Numerical Investigation of Bubble Upflow Condensation Behaviors During Subcooled Flow Boiling in Mini-Channel with VOSET

In the subcooled flow boiling process, bubble condensation is an inevitable basic phenomenon. This paper studies the condensation phenomenon of the single, double vertical/horizontal saturated bubbles rising in a three-dimensional mini-rectangular channel based on the interface capture method VOSET (coupled volume-of-fluid and level set method) and the phase transition model. Bubble condensation behaviors are investigated at different initial diameters, inlet velocity distributions, subcooling temperatures, bubble gaps, and arrangement for the two-bubble condensing system especially. The effects of these parametric on bubble motion trajectory, shape evolution, volume variation, and condensation rate are presented. The numerical results indicated that the initial bubble size and liquid subcooling play an important role in influencing the shape and volume variation of condensing bubble behaviors significantly, while the inlet velocity distribution only affects bubble motion trajectory. Furthermore, the interaction and coalescence between the bubbles will affect the bubble behaviors and the condensation rate. Finally, the condensation heat transfer coefficients at the bubble surfaces for different cases simulated in this paper are presented, seemingly first in the literature.

Saturated/subcooled flow boiling heat transfer characteristics for R134a, HFE-7100 and Deionized water inside micro/mini-channels: Part Ⅱ – New CHF prediction model establishment

A new flow pattern map has been developed and presented in Part Ⅰ of this paper for R134a, HFE-7100 and Deionized water inside micro/mini-channels. To further explain the phenomenon and understand the mechanism of triggering critical heat flux (CHF), the theoretical model to predict the CHF of saturated/subcooled flow boiling inside the micro/mini-channels is proposed based on the liquid layer dry-out and Helmholtz instability (intermittent and continuous vapor blanket) theories. Both the effect of the dry-out flows and the liquid sublayer under the vapor blanket were taken into consideration. For saturated and subcooled boiling, the two mechanisms of triggering the CHF were revealed based on different flow patterns and experimental phenomena, respectively. The boiling heat transfer performance has been experimentally investigated under different liquid subcoolings, mass fluxes and geometry parameters. By analyzing the previous models and establishing a database, the comparison of new model predictions with present experimental data shows good agreement within a standard deviation of ± 10 %. Besides, prior CHF data were used to verify this new model, which also presents varying degrees of success in predicting the CHF.

Analysis of an evaporator with single horizontal circular micro-tube using FC-72 as working fluid for electronic cooling applications

Flow boiling in micro-channels is one of the most efficient methods for heat rejection in electronics, necessitating proper system design. Numerical simulations are the most suitable tool for this purpose, with most literature focusing on CHF situations, while few studies address conditions bellow it. This paper presents a parametric analysis of an evaporator with a horizontal circular micro-tube, maintaining a fixed outlet quality, using numerical simulation. The simulation employs a one-dimensional steady-state model with FC-72 as the working fluid, considering both subcooled liquid and two-phase lengths, computed using theoretical equations and correlations. The effects of inner tube diameter, heat flux, inlet pressure, and subcooling level on key evaporator design parameters are discussed in detail. Results indicate that to minimize hydraulic pumping power, fluid temperature difference, and inlet temperature are required, the evaporator should operate with the lowest heat flux (50kW∙m-2), the largest inner tube diameter (1.3mm), the highest subcooling level (30K), and the lowest inlet pressure (2bar). Under these conditions, hydraulic pumping power can be reduced by up to 86%. Furthermore, to achieve the minimum fluid temperature difference along the tube (approximately 4.9K) and avoid CHF situation, operation with the lowest subcooling level (5K) is necessary. Finally, the ratio of the heat flux to the critical heat flux, q"/CHF, increases with rising inlet pressure and subcooling level, and/or decreasing inner tube diameter. The minimum q"/CHF ratio of 43.9% was obtained at pin=2bar, q"=50kW∙m-2, D=0.9mm, and ΔTsub=5K. These findings provide insights into optimal design parameters for evaporators in micro-electronics cooling applications.

Saturated/subcooled flow boiling heat transfer characteristics for R134a, HFE-7100 and Deionized water inside micro/mini-channels: Part I - Visualization of flow patterns and new diabatic two-phase flow pattern transition regimes

An experimental investigation on flow saturated/subcooled flow boiling heat transfer for R134a, HFE-7100 and Deionized water inside micro/mini-channels (L/dh = 40/53/70) was presented. Flow patterns and their transitions of three working fluids at various liquid subcoolings (0 ∼ 70 K) were visualized and analyzed. Experiments were carried out at a saturated pressure of 770 kPa for R134a and at atmospheric pressure for HFE-7100 and Deionized water. The mass flux varied from 400 to 800 kg/m2s, and heat fluxes up to 270.1 W/cm2 over the entire range of vapor quality (0 ∼ 1). The effects of mass flux, heat flux, liquid subcoolings and geometry parameters on flow pattern evaluation and transition were discussed. Bubble (isolated and confined bubbles), slug, churn, annular and dry-out flows were observed for the micro/mini-channels. The results indicated that the flow patterns have a significant difference on flow boiling under different liquid subcoolings. There is obvious flow pattern transition from slug flow to annular flow for nearly saturated boiling (ΔTsub ≤ 10 K). However, with the increase of inlet liquid subcooling, only obvious bubble flow and slug flow were observed during the entire boiling process, and the annular flow was not obvious before triggering the CHF. Besides, the flow pattern transition criterion is modified and the new flow pattern transition regimes including saturated/subcooled flow boiling for different working fluids are developed based on present experimental results.

Investigation of Wall Boiling Closure, Momentum Closure and Population Balance Models for Refrigerant Gas–Liquid Subcooled Boiling Flow in a Vertical Pipe Using a Two-Fluid Eulerian CFD Model

The precise design of heat exchangers in automobile air conditioning systems for more sustainable electric vehicles requires an enhanced assessment of CFD mechanistic models for the subcooled boiling flow of pure eco-friendly refrigerant. Computational Multiphase Flow Dynamics (CMFDs) relies on two-phase closure models to accurately depict the complex physical phenomena involved in flow boiling. This paper thoroughly examines two-phase CMFD flow boiling, incorporating sensitivity analyses of critical parameters such as boiling closures, momentum closures, and population balance models. Three datasets from the DEBORA experiment, involving vertical pipes with subcooled boiling flow of refrigerant at three different pressures and varying levels of inlet liquid subcooling, are used for comparison with CFD simulations. This study integrates nucleate site density and bubble departure diameter models to enhance wall boiling model accuracy. It aims to investigate various interfacial forces and examines the S-Gamma and Adaptive Multiple Size-Group (A-MuSiG) size distribution methods for their roles in bubble break up and coalescence. These proposed approaches demonstrate their efficacy, contributing to a deeper understanding of flow boiling phenomena and the development of more accurate models. This investigation offers valuable insights into selecting the most appropriate sub-closure models for both boiling closure and momentum closure in simulating boiling flows.

Flow boiling heat transfer enhancement of R134a in additively manufactured minichannels with microengineered surfaces

Additive manufacturing (AM) of metal components has opened new frontiers in heat transfer applications owing to its wide design freedom, which enables previously unexplored geometries with enhanced thermal performance to be developed. Open minichannels, on the other hand, consist of an extra manifold situated above the common flow channels, have been demonstrated to effectively reduce pressure drop and two-phase flow instability by mitigating backflow and maldistribution. In this paper, we synergized open minichannel design methodology with an ultrascalable surface microstructuring method for AM AlSi10Mg to improve flow boiling heat transfer performance of R134a. Experiments were conducted at the refrigerant mass flow rates (ṁ) of 0.005 kg/s to 0.01 kg/s (corresponding to mass fluxes of 73 to 146 kg/m2⋅s), and effective heat fluxes (qeff) of 1.8 kW/m2 to 141 kW/m2, by supplying 2 ℃ subcooled liquid to the minichannel inlet at saturation pressure (Psat) of 7.27 bar. The effects of heat flux, nucleation site density, mass flow rate and location of nucleation sites on the harmonic-average heat transfer coefficient (have) and pressure drop (ΔP) along the flow direction are investigated and compared against a conventionally manufactured (Al6061) counterpart. Our results show that the proposed etching process significantly improves the cooling performance of AM microstrucured minichannels, resulting in 210% higher have than Al6061 with negligible pressure drop penalty. The flow visualization results reveal a sequential order of nucleation site activation with increasing heat flux for microstructured open minichannels, which starts from the top of fins, followed by the corners and other three surfaces within the channels. This also results in the non-negligible effects of mass flow rate on cooling performance for microstructured minichannels, with approximately 10%–66% higher have at the lowest mass flow rate. Besides, the pressure drop penalty resulting from plain AM rough surface is also reduced by up to 13% through the proposed microstructuring process. In all, this work not only successfully identifies the dominant mechanisms in AM microstructured open minichannels, but it also provides useful minichannel design guidelines for high-performance two-phase cooling devices by AM.

Optimizing CO2 Purification in a Negative CO2 Emission Power Plant

AbstractIn the pursuit of mitigating CO2 emissions, this study investigates the optimization of CO2 purification within a negative CO2 emission power plant using a spray ejector condenser (SEC) coupled with a separator. The approach involves direct‐contact condensation of vapor, primarily composed of an inert gas (CO2), facilitated by a subcooled liquid spray. A comprehensive analysis is presented, employing a numerical model to simulate a cyclone separator under various SEC outlet conditions. Methodologically, the simulation, conducted in Fluent, encompasses three‐dimensional, transient, and turbulent characteristics using the Reynolds stress model turbulent model and mixture model to replicate the turbulent two‐phase flow within a gas–liquid separator. Structural considerations are delved into, evaluating the efficacy of single‐ and dual‐inlet separators to enhance CO2 purification efficiency. The study reveals significant insights into the optimization process, highlighting a notable enhancement in separation efficiency within the dual‐inlet cyclone, compared to its single inlet counterpart. Specifically, a 90.7 % separation efficiency is observed in the former, characterized by symmetrical flow patterns devoid of wavering CO2 cores, whereas the latter exhibits less desirable velocity vectors. Furthermore, the investigation explores the influence of key parameters, such as liquid volume fraction (LVF) and water droplet diameter, on separation efficiency. It is ascertained that a 10 % LVF with a water droplet diameter of 10 µm yields the highest separation efficiency at 90.7 %, whereas a 20 % LVF with a water droplet diameter of 1 µm results in a reduced efficiency of 50.79 %. Moreover, the impact of structural modifications, such as the addition of vanes, on separation efficiency and pressure drop is explored. Remarkably, the incorporation of vanes leads to a 9.2 % improvement in separation efficiency and a 16.8 % reduction in pressure drop at a 10 % LVF. The findings underscore the significance of structural considerations and parameter optimization in advancing CO2 capture technologies, with implications for sustainable energy production and environmental conservation.

Enhanced CHF of pool boiling and its predictive correlation for heterogeneous distributed composite microstructured surfaces with microcavities on micro-pin-fins

In the present study, several heterogeneous distributed composite microstructured surfaces (HDCMs) with different geometry parameters were prepared. The effect of the widths of the composite microstructured region, the widths of the smooth channels, the pitch of the micro-pin-fins, and the porosity of the surfaces on the pool boiling performance in HFE-7100 was examined under different liquid subcoolings. During the experiments, the three-phase contact lines of bubbles can be restricted by composite microstructured regions. Thus, reasonable geometry parameters can further enhance the liquid supply, promoting pool boiling heat transfer performance. The maximum critical heat flux of the HDCM is 14.1 % higher than that of the uniformly distributed composite microstructured surface (UDCM). Considering the effects of subcooled Jakob number (Jasub), composite microstructured region density number (SD), capillary resistance number (CR), and porosity (φ) on the critical heat flux (CHF) of HDCMs, an empirical correlation predicted the CHF for DCMs with different geometry parameters was proposed. The prediction results meet well with the experimental data, with an error within ±15 %.

Impact of solvent dry down, phase change, vehicle pH and slowly reversible keratin binding on skin penetration of cosmetic relevant compounds: II. Solids

We extended a mechanistic, physics-based framework of the dry down process, previously developed for liquids and electrolytes, to solids and coded it into the latest UB/UC/P&G skin permeation model, herein renamed DigiSkin. The framework accounts for the phase change of the permeant from dissolved in a solvent (liquid) to precipitated on the skin surface (solid). The evaporation rate for the solid is reduced due to lower vapor pressure for the solid state versus subcooled liquid. These vapor pressures may differ by two orders of magnitude. The solid may gradually redissolve and penetrate the skin. The framework was tested by simulating the in vitro human skin permeation of the 38 cosmetically relevant solid compounds reported by Hewitt et al., J. Appl. Toxicol. 2019, 1–13. The more detailed handling of the evaporation process greatly improved DigiSkin evaporation predictions (r2 = 0.89). Further, we developed a model reliability prediction score classification using diverse protein reactivity data and identified that 15 of 38 compounds are out of model scope. Dermal delivery predictions for the remaining chemicals have excellent agreement with experimental data. The analysis highlighted the sensitivity of water solubility and equilibrium vapor pressure values on the DigiSkin predictions outcomes influencing agreement with the experimental observations.

Heat capacities of active pharmaceutical ingredients nifedipine, griseofulvin, probucol and 5,5-diphenylhydantoin

The isobaric condensed-phase heat capacities of selected pharmaceutical active ingredients (APIs), namely nifedipine (CAS RN: 21829-25-4), griseofulvin (CAS RN: 126-07-8), probucol (CAS RN: 23288-49-5) and 5,5-diphenylhydantoin (CAS RN: 57-41-0), were determined over a wide temperature range starting from 2 K by combination of relaxation (heat pulse) calorimetry, Tian-Calvet calorimetry and power-compensated differential scanning calorimetry. Heat capacity measurements were taken for clearly specified polymorphs, a liquid phase (including subcooled liquid) and a glassy amorphous phase, if feasible. For 5,5-diphenylhydantoin, a heat capacity anomaly was detected in the temperature range 160 to 190 K and interpreted based on additional calorimetric and temperature-variable crystallographic measurements as a sequence of two phase transitions, which are reported for the first time in this work. Based on the determined phase behavior and heat capacity data from near 0 K, standard thermodynamic functions for crystalline and liquid phases were calculated for all APIs studied. This work significantly extends the availability of reliable heat capacity data and related thermodynamic properties for APIs required for modeling their solubility and other applications involving thermodynamic modeling.

Study of operational modes of cool-down and warm-up processes for the ESS large-scale 20 K helium refrigeration system

In the beginning, the European Spallation Source (ESS) will install two hydrogen moderators where the nuclear heating is estimated to be 6.7 kW at 5 MW proton beam power. The ESS cryogenic moderator system (CMS) has the function to circulate a subcooled liquid hydrogen through the moderatos. It is cooled through a heat exchanger by a large-scale 20 K helium refrigeration system with a cooling capacity of 30.3 kW at 15K, which is called Target Moderator Cryoplant (TMCP). The commissioning of the TMCP cold box and the two compressor skids was completed in 2019. Cryogenic transfer lines with a length of 300 m (CTL) and a valve box located next to the CMS cold box were installed during the summer of 2022. In this paper, the TMCP cool-down and warm-up processes have been studied and the operational parameters have been optimized based on the result of the CMS cool-down simulation.

Simulation of the cool-down process for the ESS cryogenic moderator system

The ESS cryogenic Moderator System (CMS) has been designed to supply a subcooled liquid hydrogen (17.5 K and 1.0 MPa) to two hydrogen moderators where the nuclear heating is estimated to be 6.7 kW (to be increased to four in the future). The CMS is cooled by a helium refrigerator system with a cooling power of 30.3 kW at 15 K. In this study, a one-dimensional simulation code has been developed to understand temperature behaviors during the cool-down process. The operational methods and parameters have been optimized. The CMS cool-down process is divided into three phases (I: gaseous hydrogen above 36 K, II: condensation from 36 to 31 K, and III: liquid hydrogen below 31 K). It turns out from the simulation result that the CMS would be able to be cooled down to the nominal condition of 17 K within 27 hours.

Review of “cold shock” cases in operation of loop heat pipes and related thermal instabilities

Loop Heat Pipes (LHP) are passive two-phase heat transfer devices, driven by capillary pumps that source energy for circulation of working fluid solely from the heat source. They have a proven track record in spacecraft thermal control as well as terrestrial applications. However, LHP may experience partial or complete wick dryout and thermal instabilities at rapid power-up steps or (and) rapid condenser cooling conditions change due to a rapid inflow of subcooled liquid from the condenser into the evaporator. Such cases do not have very wide coverage in literature and are usually presented as a little nuisance in testing of a particular LHP, for which some design workaround was found. Oftentimes suggested solutions trade performance or other design merits for robustness of operation. This article aims to review such case studies where phenomena similar to the described “cold shock” affected LHP performance. The aforementioned instabilities become even more pronounced in grid-like multievaporator LHP having multiple parallel connections between capillary pumps and compensation chambers, as heat and mass transfer between those elements becomes less definite and can eventually increase the heat leak into compensation chambers. Vulnerability of LHP with distributed network of evaporators to seemingly “safe” transient regimes fosters deeper analysis of the “cold shock” phenomenon. With comprehensive definition to the problem and a list of research questions, technical measures for getting rid of it in perspective LHP designs can be foreseen.

Influence of subcooling conditions on pool boiling in microgravity conditions: Single artificial case

A series of boiling experiments on a single artificial nucleation site has been carried out on the International Space Station (ISS) in the framework of the Multiscale Boiling (RUBI) setup installed in space in 2019. The aim of these unique experiments is to understand the bubble nucleation-growth mechanisms involved in heat transfer during boiling under well-controlled operating conditions without being masked/impeded by gravity and natural convection. The bubbles can grow to large sizes that are inaccessible in the presence of gravity. They are observed by a side-view black-and-white camera and by an infrared camera through a transparent heated substrate. In this paper, we present the results of a single-bubble pool-boiling experiment with an emphasis upon the role of the surrounding liquid subcooling, several values of which are investigated. The experimental results are complemented by numerical simulations using a previously developed model. However, the model is slightly modified to account in a simplest way for possible non-condensable residuals, without which we would have a hard time to explain certain observed behaviors.