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A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Two-Phase Equation of State for Al 2 O 3

Two-phase equation of state (EOS) for AI 2 O 3 (alumina) is calibrated using the experimental/simulation calibration data uploaded to the caldata repository. The two phases are solid α-Al 2 O 3 (corundum, sapphire, ruby) and its melt. The enthalpy of formation is set to that available from the NIST-JANAF database at T = 0K, P =1 bar. The expected applicability range of the EOS is from the ambient conditions to temperatures of ~ 5000 K and pressures of ~ 50-100 GPa.

36 MATERIALS SCIENCE↗

Insights into the rapid two-phase transport dynamics in different structured porous transport layers of water electrolyzers through high-speed visualization

In proton exchange membrane electrolyzer cells (PEMECs), maintaining efficient two-phase transport is one of the most important functions of porous transport layers (PTLs). To enhance the two-phase transport in PTLs, thin/titanium liquid/gas diffusion layers (TT-LGDLs) are introduced in PEMECs, and their difference from the conventional Ti felt PTLs are analyzed in-situ through high-speed and microscale visualization and electrochemical characterizations. The visualization results show that unfavorable large slugs can be greatly reduced in the PEMEC with a TT-LGDL compared to the PEMEC with a Ti felt PTL. More importantly, the recovery capability of water starvation with different PTLs is studied. After water starvation, the PEMEC with the TT-LGDL can recover the water starvation much more rapidly than the Ti felt cell, benefiting from its short and straight-through flow paths. Furthermore, the TT-LGDL tends to generate oxygen bubbles that are almost six times smaller and 236 times more frequently than the Ti felt PTL, indicating significantly boosted removal efficiency of produced oxygen and PEMEC performance. Finally, this study offers new insights into the dynamic processes of two-phase transport and the recovery capability of water starvation for different PTLs, which will provide valuable guidance for further optimization of PTLs and performance enhancement of PEMECs.

08 HYDROGEN↗

Simultaneous imaging of two-phase velocities in particle-laden flows by two-color optical phase discrimination

In this Letter, we present a particle image/tracking velocimetry (PIV/PTV) technique for simultaneous velocity measurement of both fluid and particle phases, adopting newly developed optical phase discrimination methods and novel optical particles. Spherical acrylic (PMMA) particles of diameter ∼ <#comment/> O ( 100 µ <#comment/> m ) were used as the particle phase, while fine B A M : E u 2 + phosphors of diameter ∼ <#comment/> O ( 1 µ <#comment/> m ) were used as the fluid tracer. Under Nd:YAG 355 nm laser excitation, both the laser-induced fluorescence (LIF) from PMMA and laser-induced phosphorescence (LIP) from B A M : E u 2 + provided sufficiently strong signals for PIV imaging with two non-intensified cameras and were clearly separable for phase discrimination using spectral filters and temporal profiles. The advantages of the PIV/PTV method include the relatively low cost of B A M : E u 2 + phosphors, high sphericity and narrow size distribution of PMMA particles with LIF emission, and direct optical discrimination eliminating artifacts, while requiring much less computational capacity for PIV/PTV processing of complex particle-laden flows.

Bi, Xiaopeng (ORCID:0000000190847325)↗

SiPM-matrix readout of two-phase argon detectors using electroluminescence in the visible and near infrared range

Proportional electroluminescence (EL) in noble gases is used in two-phase detectors for dark matter searches to record (in the gas phase) the ionization signal induced by particle scattering in the liquid phase. The “standard” EL mechanism is considered to be due to noble gas excimer emission in the vacuum ultraviolet (VUV). In addition, there are two alternative mechanisms, producing light in the visible and near infrared (NIR) ranges. The first is due to bremsstrahlung of electrons scattered on neutral atoms (“neutral bremsstrahlung”, NBrS). The second, responsible for electron avalanche scintillation in the NIR at higher electric fields, is due to transitions between excited atomic states. In this work, we have for the first time demonstrated two alternative techniques of the optical readout of two-phase argon detectors, in the visible and NIR range, using a silicon photomultiplier matrix and electroluminescence due to either neutral bremsstrahlung or avalanche scintillation. The amplitude yield and position resolution were measured for these readout techniques, which allowed to assess the detection threshold for electron and nuclear recoils in two-phase argon detectors for dark matter searches. To the best of our knowledge, this is the first practical application of the NBrS effect in detection science.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Advanced two-phase subchannel method via non-linear iteration

A fast-running, robust two-phase flow, sub-channel model is presented based on non-linear solution of the steady-state subchannel fluid flow equations. The drift-flux model solves for conservation of liquid and vapor mass, mixture energy, and axial and transverse mixture momentum as part of an efficient planar marching scheme and nonlinear, nested outer and inner iteration. Here, models based on mechanistic subcooled boiling, two-phase turbulent void mixing, and drift are included. Solution verification and mesh convergence studies were performed for modern GE 10 × 10 fuel geometry and are shown to have excellent convergence behavior. Run time performance for a 50 axial mesh model showed 2.2 seconds on a single CPU core to tightly converge all 3D distributions (flow, void, pressure) for the GE 10 × 10 fuel geometry, supporting its efficient use within the Virtual Environment for Reactor Applications boiling water reactor framework.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

The role of the spatial heterogeneity and correlation length of surface wettability on two-phase flow in a CO 2 -water-rock system

This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.

58 GEOSCIENCES↗

Visualization of Two-phase Flow Maldistribution in Brazed Plate Heat Exchangers

Brazed plate heat exchangers (BPHEs) are widely used in refrigeration and HVAC applications, but are susceptible to two-phase flow maldistribution especially when operated as evaporators. Existing visualization approaches are either limited to idealized conditions or suffer from poor optical transparency. This paper presents a novel visualization method in which one edge of a BPHE, parallel to the refrigerant inlet or outlet port, is removed by wire electrical discharge machining and replaced with a flat, transparent plate. The planar geometry allows the use of optically and infrared (IR)-transparent materials, enabling both high-speed videography and IR thermography of the two-phase flow at the channel entrances and exits. Preliminary tests with R134a and R1234ze(Z) at saturation temperatures between 5 °C and 15 °C demonstrate that distinct two-phase flow patterns in the inlet header can be clearly identified and differentiated under realistic operating conditions. Potentials of optical flow analysis of high-speed videos are shown to provide objective, quantitative indicators for flow regime characterization and comparison. IR imaging of the outlet port reveals non-uniform temperature distributions at the channel exits, providing independent evidence of maldistribution across the channel stack. Limitations of IR temperature accuracy due to the spectral properties of the sapphire window are discussed, and directions for improvement are identified.

Hausherr, Carsten [Technical University of Berlin ↗

Improvement of two-phase closure models in CTF using Bayesian inference

Under the Consortium for Advanced Simulation of Light Water Reactors (CASL) program, extensive capabilities have been developed in CTF to analyze light-water reactors (LWRs) for normal operating conditions, departure from nucleate boiling (DNB), and system transients. However, further improvements are required in the modeling and simulation of boiling water reactors (BWRs), which is a focus of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, CTF validation results were used to optimize selected modeling coefficients by calibrating to experimental data using a Bayesian inference approach. Here, calibration studies were conducted to improve (vapor) void fraction prediction without worsening the two-phase pressure drop prediction, as well as to improve the two-phase pressure drop prediction. Calibration was performed for interfacial drag and wall shear models. Surrogates were developed to alleviate the computational expense required for sampling the parameter space using Markov chain Monte Carlo (MCMC). An assessment performed with calibrated models demonstrated an improvement of CTF in its prediction of key parameters such as void fraction and two-phase pressure drop.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

High-speed characterization of two-phase flow and bubble dynamics in titanium felt porous media for hydrogen production

Bubble dynamics and two-phase flow phenomena are closely related to the performance of proton exchange membrane electrolyzer cells (PEMECs). This paper reports an in-situ study of the oxygen bubble behavior and associated multiphase evolutions in the anode side of PEMECs with titanium (Ti) felt liquid gas diffusion layers (LGDLs) by a high-speed visualization system. The micro oxygen bubble dynamics was captured and analyzed at different locations and virous operating conditions. The results show that the bubble detachment frequency and detachment diameter greatly increase with the operating current density. Additionally, they are significantly impacted by the local pore structure and morphology of Ti felt LGDLs. In the flow channels, there exist only several discrete micro bubbles at a low current density (0.04 A/cm 2 ) and a large flow velocity (133 mm/s). At a current density (0.2 A/cm 2 ) and a flow velocity (67 mm/s), a number of gas slugs are formed in the follow channels, in addition to discrete micro bubbles. At a high current density (1 A/cm 2 ) and a flow velocity (67 mm/s), more bubbles appear in the channel, and the flow field is dominated by slug or annular flows. These investigations can help to better understand the two-phase flow and bubble detachment mechanism, and provide a foundation for electrochemical reaction, multiphase flow studies and optimize the design of gas diffusion layers and flow fields for PEMECs in the future.

08 HYDROGEN↗

FY23 Report on Water NSTF Testing at Two-Phase Conditions: Off-normal Scenarios

Under support from the Department of Energy (DOE) and the Office of Advanced Reactor Technologies (ART), a large-scale test facility has been constructed at Argonne National Laboratory to generate NQA-1 qualified validation data for passive decay heat removal systems in advanced reactors. The Natural convection Shutdown heat removal Test Facility (NSTF) reflects key features of a ½ scale, water-based, Reactor Cavity Cooling System (RCCS) and is intended to study the behavior, bound performance, and ultimately guide design decisions for passive decay heat removal systems for advanced reactors. In addition to the experimental activities detailed in this report, a supportive computational modeling effort is on-going which has been demonstrated to significantly strengthen the experimental program while also improving accuracy of the computer models. Together these create a mutually beneficial relationship integral to meeting the overall program objective of examining the heat removal performance of the RCCS concept. This report details the experimental activities and upgrades performed during the program’s fifth year of water-based operation. The theme of this year of testing was examining off-normal scenarios. In practice, that meant examining scenarios with blockages or other design basis conditions. From a maintenance and capability standpoint that meant assessing valving options for implementing blockages, assessing drain and refill capabilities, and ensuring in all cases that operators could safely, efficiently, and repeatably bring the facility to an off-normal condition and return it to the normal operating state. In one notable case, no solution existed, nor was a solution commercially available, that met the facility needs for implementing blockages within the two-phase region of the chimney. A valve and feedthrough were custom-designed for NSTF to operate submerged in saturated water while being safely actuated from outside the tank. The fifth year of testing included eight matrix tests consisting of 162 hours of active heating, 9,735 kWh of electrical heating, with seven tests classified as Accepted per NQA-1 and one as Trending. All matrix tests were performed at two-phase flow conditions. The power parametric series from previous years was extended to include another scenario with a decay load equivalent to 1.75 MWt, full scale, further resolving the system flow oscillation response as a function of input power. A depletion test was performed to extend previous work and examine the system’s approach to stagnation and geysering that were not previously observed. This test began at an initial inventory level of 50%, prototypic power of 2.1 MWt, and employed an accelerated drain of 0.75 gpm plus boiloff until stagnation conditions were achieved and multiple geysering events were recorded. Further exploring the geysering phenomenon was a separate effects test examining static boiling in the risers and chimney. This static boiling test was performed at 48 kWe, a higher power than testing in the previous year, and included enhancements to the drain system to remove inventory in a better-controlled and more reliable manner. Two tests were performed, at prototypic conditions of 1.4 MWt and 2.4 MWt, respectively, examining the system response to throttled conditions in the singlephase region of the piping. A ball valve immediately before he riser inlet header was increasingly throttled, progressing the system through a repeatable pattern of two-phase oscillations and stable regimes before ultimately inducing stagnation and geysering. Concluding the year, two tests were performed at baseline conditions of 70% initial inventory level and 2.1 MWt of prototypic decay heat to examine both repeatability and the response to throttling within the two-phase region, at the inventory tank inlet using the custom valve mentioned above. The first such test repeated transient operating conditions and revealed significant sensitivity t

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Extension of Clad Damage Propagation Model for Fission Gas Dispersal and Two-Phase Flow Effects in MOOSE SubChannel Module

This report presents an extension of the Clad Damage Propagation (CDAP) model implemented in the MOOSE SubChannel Module (SCM) to capture post-failure fission-gas dispersal and two-phase flow effects in sodium-cooled fast reactor assemblies. The extended model tracks discharged gas axially and radially, computes channel-averaged flow quality and void fraction using a Lockhart–Martinelli framework, evaluates two-phase frictional pressure-drop multipliers, determines inlet mass-flow degradation under fixed core pressures, and applies an intensified-void-based heat-transfer degradation to affected fuel pins. Radial plume expansion is parameterized using mineral-oil jet experiments mapped to sodium conditions via Reynolds–Weber similarity. Implementation details are documented, along with the new methods and user inputs needed to control plume mapping and two-phase behavior. Demonstration simulations for 19- and 37-pin bundles show that breach size and inlet velocity strongly influence propagation potential: small breaches (≤0.5 mm) produce limited degradation while larger breaches (~1 mm) can drive oscillatory temperature spikes and enhanced failure propagation, especially at higher velocities. These results demonstrate that the extended CDAP model provides a more complete framework for quantifying cladding damage propagation and evaluating propagation potential in transient scenarios. The approach remains computationally efficient, consistent with subchannel-level analysis, yet incorporates sufficient physics to bridge localized post-failure effects with bundle- and assembly-scale degradation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Study of the film boiling heat transfer and two-phase flow interface behavior using image processing

Here, in this study, based on a small-scale quench test facility, the two-phase flow interface behavior during quench transients is visualized and analyzed utilizing an image processing framework. The high-fidelity experimental results obtained for two-phase flow in the current framework can support various studies both in the time domain and in the frequency domain. In particular, visualization of the data obtained from different heating surfaces under different test conditions are used to perform a full-scale transient 2-D vapor film reconstruction. The liquid-vapor interface variations in various heat transfer regimes as well as at the initial film breakup point can be directly obtained through the processed data. Moreover, the temporal variation of the interfacial wave frequency approaching quench is investigated in detail. Based on the high-resolution data obtained for the liquid-vapor interface, the detailed phase velocity and temperature profiles are obtained through theoretic analysis, based on which the film boiling heat transfer coefficient (HTC) can be determined. In addition, an improved film boiling HTC model is developed considering the effects of wall superheat, liquid subcooling temperature, vapor film thickness as well as fluid properties. The model is found to predict film boiling HTC well within 15% error.

42 ENGINEERING↗

Two-phase separator device for removing condensate or particulate from a gas stream

This disclosure provides a two-phase separator device for separating condensate or particulate from a gas stream. In some implementations, the separator device removes water from air and may operate under micro-gravity conditions. The gas stream flows through the two-phase separator device and passes through a rotatable vane assembly along a flow path without being redirected in another flow path. Condensate or particulate in the gas stream is impacted by a plurality of vanes of the rotatable vane assembly, and the condensate is captured by features formed within the plurality of vanes. The captured condensate is accelerated radially outwardly along the each of the plurality of vanes towards a sloped inner wall, and further moved along the sloped inner wall in a direction against the flow path of the gas stream during rotation.

Cognata, Thomas↗

A multi-dimensional dataset for two-phase instability in low pressure natural circulation based on direct transient local measurement

Thermal hydraulic instability can challenge the control and the safety of nuclear reactors. This experimental research captures and investigates the instability in a low-pressure (1–10 atmospheres) natural circulation loop with an adiabatic chimney installed above the heated section. Direct transient local measurement of two-phase flow is performed at multiple axial locations along the flow channel with thermocouples and conductivity probes traversed by customized high-precision mechanisms. Based on the periodicity of oscillations, a post-processing method is proposed to align the data captured non-simultaneously to reconstruct the instability behavior in one representative period. The averaging operation over multiple oscillation cycles is performed to reduce the random errors. Cyclic phenomena are clearly demonstrated by the post-processed data, and rapid void fraction change induced by the flashing is observed to be significant in the driving mechanism for low pressure oscillations. Parametric effects of inlet subcooling, heat flux, inlet flow restriction and system pressure are studied within the experiment range, and qualitative results are explained and compared with existing literature. The ratio between the oscillation period and the travelling time of the fluid particle through the test section is compared with the theoretical value for the density wave oscillation. The new dataset contains directly measured transient multi-dimensional two-phase data along the flow channel for natural circulation under density wave oscillations. The generated dataset is valuable for the validation of system analysis codes and CFD codes in the simulation of natural circulation phenomena and dynamic two-phase flow.

42 ENGINEERING↗

Upgrade of the mechanically pumped CO 2 two-phase cooling system for the alpha magnetic spectrometer on the international space station

This study describes the successful upgrade of a mechanically pumped CO 2 two-phase cooling system in space by designing a new pump module for the Alpha Magnetic Spectrometer-02 on the International Space Station. Key factors for mission success are emphasized, including achieving high coolant filling accuracy within 10% of the target and maintaining system stability within ±1 °C. The impact of adding radiators to improve cooling efficiency is examined, and it is found that operating multi-radiators out-of-phase does not significantly affect system reliability. The centrifugal pump design is shown to allow for better lubricant circulation, while the in-house designed controller incorporates protective measures to prevent cavitation, overheating, and over-current. Further, this research advances the understanding of circulation loop systems and their upgrades in space and demonstrates the potential for extending the lifetime of space-borne mechanically pumped two-phase cooling systems.

42 ENGINEERING↗

Generic two-phase coexistence in a type-2 Schloegl model for autocatalysis on a square lattice: Analysis via heterogeneous master equations

Schloegl's second model (also known as the quadratic contact process) on a square lattice involves spontaneous annihilation of particles at lattice sites at rate p, and their autocatalytic creation at unoccupied sites with n ≥ 2 occupied neighbors at rate k n . Here, kinetic Monte Carlo (KMC) simulation reveals that these models exhibit a nonequilibrium discontinuous phase transition with generic two-phase coexistence: the p value for equistability of coexisting populated and vacuum states, p eq (S), depends on the orientation or slope, S, of a planar interface separating those phases. The vacuum state displaces the populated state for p > eq (S), and the opposite applies for p < p eq (S) for 0 < S < ∞. The special “combinatorial” rate choice k n = n(n–1)/12 facilitates an appealing simplification of the exact master equations for the evolution of spatially heterogeneous states in the model, which aids analytic investigation of these equations via hierarchical truncation approximations. Truncation produces coupled sets of lattice differential equations which can describe orientation-dependent interface propagation and equistability. The pair approximation predicts that p eq (max) = p eq (S = 1) = 0.09645 and p eq (min) = p eq (S → ∞) = 0.08827, values deviating less than 15% from KMC predictions. In the pair approximation, a perfect vertical interface is stationary for all p < p eq (S = ∞) = 0.08907, a value exceeding p eq (S → ∞). One can regard an interface for large S → ∞ as a vertical interface decorated with isolated kinks. For p < p eq (S = ∞), the kink can move in either direction along this otherwise stationary interface depending upon p, but for p = p eq (min) the kink is also stationary.

97 MATHEMATICS AND COMPUTING↗