CRYOGENIC FLOW BOILING PHYSICS IN TERRESTRIAL, PARTIAL, AND MICROGRAVITY CONDITIONS

With the growing interest in space exploration, cryogenic technologies involving two-phase flow and heat transfer are in high demand to successfully procure advanced space applications such as fuel depots and nuclear thermal propulsion (NTP) systems for deep space missions. However, the unique and extreme thermal properties of cryogenic fluids introduce distinct flow boiling fluid physics and energy transport phenomena, which differ significantly from those observed with conventional fluids. Understanding the unique two-phase physics in cryogenic flow boiling remains an ongoing challenge. Furthermore, the lack of readily available microgravity cryogenic steady-state heat transfer data hinders the assessment of gravitational effects on cryogenic flow boiling. This study aims to elucidate the fundamental two-phase flow and heat transfer physics of cryogenic flow boiling system by conducting (i) experimental, (ii) theoretical/empirical, and (iii) computational investigations of cryogenic flow boiling using liquid nitrogen (LN2) under various gravity environments, encompassing terrestrial, partial, and microgravity conditions.

The first part of this study investigates 1-ge horizontal flow boiling of liquid nitrogen with a near-saturated inlet along a circular tube of dimensions 8.5-mm inner diameter and 680-mm heated length. Experiments are conducted using a payload developed for eventual parabolic flight experiments. The operating parameters varied are mass velocity of 406.76–1572.77 kg/m2s, inlet quality of -0.05 to -0.01, and inlet pressure of 336.29–493.07 kPa. High speed video recordings are presented to explain two-phase flow structure and regime transitions which are visualized through a transparent tube in a visualization section situated downstream of the heated tube. Recognized flow patterns are bubbly, plug, slug, stratified annular, and annular. Heat transfer results are presented and discussed in terms of flow boiling curve trends, streamwise wall temperature profiles, streamwise heat transfer coefficient (HTC) profiles, and average HTCs. Previous HTC correlations are evaluated against the measured HTC data, of which two are identified for superior accuracy in predicting cryogen data. This particular experimental study confirms the reliability and readiness of the payload for subsequent parabolic flight experiments intended for acquisition of microgravity data.

The second part of this study aims to elucidate the gravitational effects on two-phase fluid physics and heat transfer by conducting the first-ever experimental measurement of cryogenic flow boiling performance using a steady-state heated method in a reduced gravity environment. Parabolic flight experiments were performed to acquire both heat transfer measurements and high-speed video of interfacial behaviors, under varying gravity levels (microgravity, hypergravity, Lunar gravity, and Martian gravity). The experiments involved flow boiling of liquid nitrogen (LN2) with a near-saturated inlet along a circular heated tube of dimensions 8.5-mm inner diameter and 680-mm heated length. The operating parameters varied are mass velocity of 398.3 – 1342.8 kg/m2s, inlet quality of -0.08 to -0.01, and inlet pressure of 413.68 – 689.48 kPa. Captured microgravity flow patterns range from bubbly to annular, all having vapor structures that are larger than those under higher gravity levels. Under microgravity, absence of buoyancy yields symmetrical vapor structures without flow stratification, laying a physical foundation for the distinct two-phase heat transfer trends during LN2 flow boiling in microgravity. Transient data collected during the flight parabolas exhibited decreasing heated wall temperature as the aircraft transitioned from hypergravity to microgravity phases. The temperature variation indicated an enhancement in flow boiling heat transfer with decreasing gravity levels and a reduction with increasing gravity levels. The effect of reduced gravity on cryogenic flow boiling heat transfer coefficient (HTC) is discussed based on steady state heat transfer analysis. Seminal HTC correlations are evaluated against the measured microgravity HTC data, of which one is identified for superior accuracy in predicting microgravity data.

The third part of this study discusses the two-phase flow and heat transfer performance of LN2 flow boiling across five distinct flow orientations: vertical upflow, vertical downflow, horizontal flow, 45° inclined upflow, and 45° inclined downflow. The study employed the steady-state heating method within a circular heated tube featuring an 8.5-mm inner diameter and a 680-mm heated length. High-speed video recordings were utilized to capture two-phase flow patterns and interfacial behaviors across various flow orientations. The experiments covered a wide range of operating conditions, including mass velocities ranging from 351.80 to 1572.77 kg/m²s and inlet pressures from 297.14 to 1032.97 kPa, primarily with near-saturated inlet subcooling. Distinct two-phase flow patterns and regime transitions were identified for each flow orientation. Symmetrical flow patterns were evident in vertical orientations, whereas non-vertical orientations exhibited asymmetric flow stratifications, primarily influenced by the buoyancy force in a terrestrial gravity environment. Bubble dynamic parameters were quantified, and bubble collision and dispersion phenomena were visualized. Analyzing heat transfer performance based on local flow boiling curves and variations in heat transfer coefficients (HTCs), it was observed that vertical upflow demonstrated the most enhanced heat transfer performance, while vertical downflow exhibited the lowest. As mass velocity exceeded 830 kg/m²s, the differences in heat transfer among orientations became less distinct, emphasizing the role of flow inertia in mitigating the influence of flow orientation. A direct comparison of microgravity HTC data from a recent study by the authors against the 1-ge HTC data indicated enhanced heat transfer performance in microgravity for flow orientation configurations in terrestrial gravity. However, this enhancement progressively diminished as the heat flux increased. Distinct HTC trends were observed as mass velocity increased for different flow orientations and gravity levels.

The fourth part of this study analyzes the consolidated experimental database and discusses the development of universal heat transfer coefficient correlations for both saturated and subcooled cryogenic flow boiling. The escalating interest in cryogenic technologies for space-related applications has led to an unprecedented demand for reliable prediction methods for cryogenic two-phase flow and heat transfer. Regrettably, existing heat transfer coefficient (HTC) correlations developed for conventional fluids prove inadequate and provide subpar predictions when applied to cryogenic flow boiling conditions. Therefore, it is imperative to develop a set of new HTC correlations specifically tailored for cryogenic flow boiling. Comprehensive databases are constructed consolidating all the experimental data of the author’s and historical data extracted from open literatures, spanning a wide range of operating conditions, flow orientations, and various cryogenic fluids. Subsequently, based on the constructed databases, an assessment of the predictive accuracy of seminal HTC correlations is conducted, followed by the development of new HTC correlations for cryogenic saturated and subcooled flow boiling. The newly developed correlations demonstrate very good predictive accuracy, with an overall mean absolute error (MAE) of 23.84% and 21.24% for LN2 saturated and subcooled HTC, respectively, under terrestrial gravity conditions. When assessed against a microgravity dataset, these correlations exhibit equally good predictive accuracy, yielding MAE values of 20.78% and 25.99% for LN2 saturated and subcooled HTC, respectively. Furthermore, the universal applicability of the new HTC correlations is ascertained by assessing the correlations across a multitude of cryogenic fluids, including LN2, LHe, LAr, LCH4, and LH2. Impressively, these correlations display outstanding predictive accuracy, with MAE values of 24.01% and 21.29% for saturated and subcooled HTC, respectively, underscoring their superior performance across a wide range of cryogenic fluids, validated against 2,445 saturated cryogenic HTC datapoints and 1,553 subcooled cryogenic HTC datapoints. Overall, the new HTC correlations consistently outperform all prior seminal correlations, yielding good predictive accuracy across a diverse spectrum of operating conditions, irrespective of flow orientation and gravity level, for various cryogenic fluids.

The fifth part of this study aims to elucidate the gravitational effects on cryogenic two-phase fluid physics and CHF by conducting the first-ever experimental measurements of cryogenic flow boiling using a steady-state heating method in a reduced and partial gravity environment. Using liquid nitrogen (LN2) as the working fluid, parabolic flight experiments were conducted to obtain both CHF measurements and high-speed video recordings of interfacial behavior under varying gravity levels, including microgravity and both Lunar and Martian gravities. Additionally, terrestrial ground experiments were performed across five distinct flow orientations: vertical upflow, vertical downflow, horizontal flow, 45° inclined upwards, and 45° inclined downwards. The study employed a circular heated tube featuring an inner diameter of 8.5 mm and a heated length of 680 mm. Vertical upflow exhibited the most enhanced CHF performance, while vertical downflow showed the poorest performance. Increasing gravitational acceleration—from microgravity to Lunar to Martian—reduced CHF due to intensified flow stratification caused by the strengthening buoyancy force. The gravitational effect was mitigated by increasing the mass velocity above a threshold of 700 kg/m²s. Finally, existing CHF correlations were evaluated, revealing a need for a new correlation specific to cryogenic fluids under reduced gravity conditions. Consequently, a new CHF correlation was developed and tested using datasets from microgravity as well as both Lunar and Martian gravities. The new correlation shows excellent predictive accuracy, evidenced by a mean absolute error (MAE) of 7.54%, against eleven newly acquired microgravity, Lunar and Martian CHF datapoints.

The sixth part of this study investigates the performance of 2-D axisymmetric computational fluid dynamics (CFD) in predicting boiling characteristics of liquid nitrogen flowing vertically upwards along a uniformly heated circular tube. Investigation of the popular Volume of Fluid (VOF) model reveals (a) inaccurate surface tension calculation which degrades interface tracking, and (b) under-representation of bubble-to-bubble interaction, which stems from the innate nature of employing a single momentum equation in VOF. To alleviate VOF shortcomings, Coupled Level Set VOF (CLSVOF) is adopted in ANSYS FLUENT, including a user defined function to account for the crucial effects of bubble collision dispersion force. The CFD simulation results are validated against wall temperature and volume fraction results from prior benchmark experiments corresponding to four different wall heat flux conditions at nearly identical mass velocities. Predictions are also provided for axial variations of interfacial flow pattern, fluid temperature, and fluid velocity, flow characteristics that are very difficult to measure in cryogenic experiments. The CFD simulation results are shown to be highly accurate at predicting the nucleate boiling portion of the flow boiling curve.

The seventh part of this study investigates numerical simulations and their validation for flow boiling of liquid nitrogen (LN2) in a vertical upflow orientation, with a primary aim to understand the complex two-phase flow and heat transfer phenomena important to space applications. The computational fluid dynamics (CFD) model utilized the coupled level set volume of fluid (CLSVOF) method, incorporating additional source terms for bubble collision dispersion force and shear lift force in the momentum conservation equation to enhance simulation accuracy. The simulations were conducted for two mass velocities (G = 526 and 804 kg/m²s) and three different heat flux levels (approximately 10%, 30%, and 70% of critical heat flux (CHF)) under Earth gravity. The model was validated against measured wall temperature data acquired from the authors’ previous experimental studies, demonstrating average deviations of less than 2.8 K across all operating conditions. The simulated two-phase flow contours illustrated various flow patterns, including bubbly, slug, churn, and annular. Both mass velocity and heat flux were observed to impact the onset of nucleate boiling (ONB), bubble nucleation, growth, and coalescence, and overall vapor structure. The simulations also offered insight into axial and radial void fraction and velocity profiles, revealing local flow acceleration trends synchronized with void fraction development. A comparison between predicted and measured bulk fluid temperature profiles showed excellent agreement, further validating the CFD model's accuracy and practical usefulness for two-phase cryogenic flow boiling simulations in space applications.

The eighth part of this study investigates numerical simulations and validation of liquid nitrogen flow boiling under two gravity conditions: microgravity and Earth gravity. The primary objective is to assess the impact of gravity on two-phase flow and heat transfer behavior. A previously developed and validated multiphase CFD model—based on the Coupled Level Set Volume-of-Fluid (CLSVOF) method and enhanced with additional source terms—was utilized to simulate cryogenic flow boiling in microgravity. In the first part of the study, microgravity simulations were carried out at a mass velocity of 696 kg/m²·s and three heat flux levels: 11%, 23%, and 45% of the critical heat flux. Model validation was performed against wall temperature data obtained during parabolic flight experiments conducted by the same authors. The simulation results showed strong agreement with experimental measurements, with a maximum temperature deviation of 3.3 K and a mean absolute error (MAE) of 1.33% across all tested conditions. In the second part of the study, the validated CFD model was used to conduct three additional flow boiling simulations under terrestrial Earth gravity, with identical operating conditions, to systematically evaluate the effect of gravity. Direct comparisons were made between the microgravity and Earth gravity cases, focusing on key results from the simulations, such as two-phase flow contours, fluid temperature spatial distributions, axial wall temperature profiles, fluid vorticity contours, and mean velocity differences. The comparison results are discussed in detail in this paper, highlighting the impact of gravity on the thermal-hydraulic characteristics of cryogenic flow boiling, which is otherwise extremely challenging to quantify or measure experimentally.