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Evolution of Two-Phase High Explosive Reactive Flow [Slides]
Reactive hydrodynamics involve rapid conversion of reactants to products along a detonation wave and needs a closure rule: P-T equilibrium. To calculate P-T equilibrium, we use a root finding method, which can be a computational bottleneck. We evolve the guess for the root finder rather than using the previous value to reduce iterations. Evolving products volume fraction Φ p for an initial root finding guess does reduce root finding iterations and seems to give the best results immediately following a detonation wave (reducing root finding iterations from 5 to 2).
Thermodynamically consistent Cahn–Hilliard–Navier–Stokes equations using the metriplectic dynamics formalism
Cahn–Hilliard–Navier–Stokes (CHNS) systems describe flows with two-phases, e.g., a liquid with bubbles. Obtaining constitutive relations for general dissipative processes for such systems, which are thermodynamically consistent, can be a challenge. We show how the metriplectic 4-bracket formalism (Morrison and Updike, 2024) achieves this in a straightforward, in fact algorithmic, manner. First, from the noncanonical Hamiltonian formulation for the ideal part of a CHNS system we obtain an appropriate Casimir to serve as the entropy in the metriplectic formalism that describes the dissipation (e.g. viscosity, heat conductivity and diffusion effects). General thermodynamics with the concentration variable and its thermodynamics conjugate, the chemical potential, are included. Having expressions for the Hamiltonian (energy), entropy, and Poisson bracket, we describe a procedure for obtaining a metriplectic 4-bracket that describes thermodynamically consistent dissipative effects. The 4-bracket formalism leads naturally to a general CHNS system that allows for anisotropic surface energy effects. Furthermore, this general CHNS system reduces to cases in the literature, to which we can compare.
Experimentation on Finned-Tube Microchannel Heat Exchanger Incorporating Phase Change Material and R-410A
Integrating latent heat thermal energy storage, particularly phase change materials (PCM), in building heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems, offers substantial benefits for peak load shifting and energy efficiency. While numerous studies explore PCM-embedded heat exchangers (PCM-HX) using single-phase heat transfer fluids, there needs to be more investigation regarding PCM-HX utilizing two-phase refrigerant flow. This gap is even more pronounced for microchannel heat exchanger (MCHX) configurations. In this study, an MCHX-based PCM-HX was built and tested to analyze and evaluate the performance of a PCM-HX operating with a two-phase refrigerant as the working fluid. A commercially available MCHX condenser unit was embedded with 2.6 kg of RT35 PCM and tested using R-410A as the working fluid, using an in-house test loop to control the refrigerant inlet conditions precisely. Thin and minimally invasive T-type thermocouples traced the temperature evolution along MCHX channels and tube banks. Additional larger T-type thermocouple probes at the refrigerant inlet and outlet measured the average power of the PCM-HX during condensing tests, ranging from 0.7 kW to 1.6 kW based on mass flow rates varying from 3.5 g/s to 8 g/s. This experimental study on MCHX-based PCM-HX with a two-phase refrigerant has the potential to offer practical design guidelines for the direct integration of PCM-TES in HVAC&R systems without the use of a secondary loop, while caution is advised to avoid a substantial increase in the refrigerant charge amount.
Uncertainty analysis of PIV measurements in bubbly flows considering sampling and bubble effects with ray optics modeling
In this report, a modeling-based approach is developed to investigate the external sources of uncertainty in particle image velocimetry (PIV) measurements for two-phase bubbly flows. Primarily relied on ray optics modeling, this study focuses on the uncertainty in PIV measurements due to bubble-induced light distortion. In addition, the uncertainty due to sampling is also considered through synthetic PIV images generated from Monte Carlo sampling. Based on a PIV-planar laser induced florescence (PLIF) measurement system, three case studies are performed and discussed, considering respectively the sampling effect, bubble effect, and the combination of these two effects. These case studies confirm the validity of the ray optics modeling in obtaining accurate particle images through a benchmark test. Furthermore, it is also found that the bubble effect could significantly influence the particle images. On the other hand, the result of the case study with synthetic PIV images indicates that the bubble effect on particle images can be minimized by removing “outliers” in the obtained velocity vector field through a multi-pass post-processing procedure. However, the uncertainty of the velocity measurements will still increase.
Advanced Steam-Electric Power Cycle for Advanced Reactor Concepts
This report presents improvements made to RELAP-7 for modeling Rankine power cycles, which are used on the secondary side of some advanced reactor concepts. For example, for a High-Temperature gas-cooled Reactor Pebble bed Module (HTR-PM), in the primary loop, helium transfers heat from the fuel to a steam generator, and on the secondary side, dry steam from the steam generator applies work to a turbine, which is converted into electrical power by a generator. After passing through the turbine, the steam passes through a condenser and pumped to the steam generator inlet, completing a Rankine cycle on the secondary side. This HTR-PM concept is used as an example to demonstrate a steam-electric power cycle capability in RELAP-7. This power cycle requires a number of different physical components, including a pump, compressor, turbine, steam generator, and condenser. The steam generator is modeled using a heat exchange between primary and secondary loops, and the condenser is modeled using a cooling source term. Recent efforts demonstrated preliminary models for the turbomachinery components (pump/compressor and turbine), but more physical models were required. Furthermore, several improvements were made for the robustness of mixed single-phase/two-phase flow present in a Rankine cycle.
FY2022 Progress on Imbibition Testing in Containment Science
Estimation of two-phase fluid flow properties is important to understand and predict water and gas movement through the vadose zone for agricultural, hydrogeological, and engineering applications, such as for vapor-phase contaminant transport and/or containment of noble gases in the subsurface. In this second progress report of FY22, we present two ongoing activities related to imbibition testing on volcanic rock samples. We present the development of a new analytical solution predicting the temperature response observed during imbibition into dry samples, as discussed in our previous first progress report for FY22. We also illustrate the use of a multi-modal capillary pressure distribution to simulate both early- and late-time imbibition data collected on tuff core that can exhibit multiple pore types. These FY22 imbibition tests were conducted for an extended period (i.e., far beyond the time required for the wetting front to reach the top of the sample), which is necessary for parameter estimation and characterization of two different pore types within the samples.
NIOBIUM-1% ZIRCONIUM, NATURAL-CIRCULATION, BOILING-POTASSIUM CORROSION LOOP TEST
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Continuum shock mixture models for Ni+Al multilayers: Individual layers and bulk equations of state
Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni x Al y , as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni x Al y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.
COMPUTATION FLUID DYNAMICS ANALYSIS FOR GENERIC SMALL MODULAR REACTOR CONTAINMENT SEPARATE EFFECTS TEST
It is desirable for fourth-generation Small Modular Reactors to be passively cooled in standard and accident operations. Passive Containment Cooling Systems can reject heat from the containment structure, without using pumps or blowers. The targeted design containment structure is a large, domed, stainless steel, cylindrical vessel. In a postulated Design Basis Accident, steam will flash inside containment. Steam condensation occurs on the inner containment wall and transfers heat through the steel containment into a large body of water known as the annular reservoir (AR) surrounding the vessel serving as the ultimate heat sink. Natural circulation drives the flow in the AR and heat will be released to the environment by evaporation of water. Unique containment geometry requires a separate effects test (SET) facility for the verification and validation of the computer code and evaluation model development and assessment for reactor licensing efforts. In this study, STAR-CCM+, a computational fluid dynamics (CFD) code was used to inform the decision-making process on the design of the SET. The CFD simulation modeled, a two-phase turbulent flow with fluid film development and heat transfer for different containment geometries. The Reactor Excursion and Leak Analysis Program will also be used in a code-to-code verification against the CFD results.
Parametric and Sensitivity Analysis of a Steam Generator Model Using Python and Machine-Learning Tools
For this study, we used Python and machine-learning tools to perform a comprehensive parametric and sensitivity analysis on a steam generator (SG) model. (The Python model was based on a previously completed MATLAB framework for the Holtec SMR-160 SG.) We investigated the influence of various input parameters (e.g., heat transfer coefficient [HTC], Nusselt number, and heat exchanger effectiveness) on the system’s output. With machine-learning tools such as the Risk Analysis Virtual Environment (RAVEN), which was developed at Idaho National Laboratory, we were then able to perform an automated analysis of the SG inputs’ effect on the HTC. The analysis results give valuable insights into the performance and optimization of SG systems. We found the inlet mass flow rate (MFR) to have the greatest impact on the HTC, followed closely by the inlet temperature, and then pressure. Shifting of the input parameters causes the location of the maximum HTC along the SG length to change incrementally. The cold leg (CL) MFR was also found to impact the HTC magnitude as well as the location of the maximum HTC. At between 0.4–0.9 of the total SG length, the input parameters experience maximum impact on the HTC, leading us to suggest that sensors be efficiently placed on the SG so as to closely and effectively monitor thermal-hydraulic properties during reactor operation. We also found that the sensitivity data calculated manually agrees with the RAVEN – based data, confirming the same range of maximum sensitivity. However, the RAVEN-based analysis showed that cold leg pressure and hot leg temperature have a greater impact on the heat transfer coefficient than the mass flow rate, implying that a manual sensitivity study taking only two samples is not accurate.
Thermochemical reduction modeling in a high-temperature moving-bed reactor for energy storage: 1D model
The design of robust and efficient high-temperature thermochemical reactors and determination of operating conditions are critical steps toward enabling high-efficiency long-duration solar energy storage. This work presents a computational model for the thermal reduction of a metal oxide material (Mg-Mn-O) up to 1450 °C and the coupled complex transport phenomena in a novel tubular thermal reactor design that features the capability for a high extent-of-reduction (high energy storage density) and inherent heat recuperation. A one-dimensional model coupling counter-current gas–solid flow, two-phase heat transfer, thermochemical redox reactions, and species transport in a moving-bed reactor is developed. Simplified versions of the model are validated with published results in the literature for packed beds with both inert and reactive particles; the fully coupled model is also validated with experimental measurements of a moving-bed reactor in terms of local temperatures and oxygen release at the exit. Detailed comparisons on the effects of different boundary conditions in the reaction zone (prescribed wall temperature vs. heat flux conditions) and formulations based on a simple uniform flow assumption vs. plug flow using Ergun equation for gas flow are investigated. The results are compared with experimental measurements, and for all cases, the energy flow components in the reactor system and the thermal to chemical conversion efficiency and overall system efficiency are computed. Finally, the predicted high thermal-to-chemical efficiency ~95% and system efficiency ~30% agree with experimental measurements.
FY22 Progress on Multicontinuum Methods in Containment
Estimation of two-phase fluid flow properties is important to understand and predict water and gas movement through the vadose zone for agricultural, hydrogeological, and engineering applications, such as containment transport and/or containment of gases in the subsurface. To estimate rock fluid flow properties and subsequently predict physically realistic processes such as patterns and timing of water, gas, and energy (e.g., heat) movement in the subsurface, laboratory spontaneous water imbibition with simultaneous temperature measurement and numerical modeling methods are presented in the FY22 progress report. A multiple-overlapping-continua conceptual model is used to explain and predict observed complex multi-phenomenological laboratory test behavior during spontaneous imbibition experiments. This report primarily addresses two complexities that arise during the experiments: 1) capturing the late-time behavior of spontaneous imbibition tests with dual porosity; and 2) understanding the thermal perturbation observed at or ahead of the imbibing wetting front, which are associated with adsorption of water in initially dry samples. We use numerical approaches to explore some of these issues, but also lay out a plan for further laboratory experimentation and modeling to best understand and leverage these unique observations.
Experimental study of three-dimensional CO 2 -water drainage and fracture-matrix interactions in fractured porous media
Estimation of CO 2 storage capacity in fractured porous reservoirs requires a better understanding of the CO 2 -water flow fundamentals in fracture-matrix systems. There are few core-flood experiments on three-dimensional CO 2 -water drainage in a fracture-matrix system, yet none have examined the impacts of the capillary continuity of fractures and fracture-matrix interactions. In this study, twelve drainage experiments were conducted in four fracture-matrix columns, each comprising a vertical stack of a cylindrical rock core, a filter paper serving as an analogue to a horizontal fracture, and a ceramic plate. Here, the core sample was surrounded by open space at the top and circumferential sides to model fractures, allowing for 3-D CO 2 -water drainage in the rock core and displaced water draining across the horizontal fracture. X-ray computed tomography was conducted to visualize the dynamic invasion/drainage processes in four rock core samples showing contrasts in anisotropy, permeability, and heterogeneity. Experimental results show (1) the equilibrium CO 2 saturations in the rock matrix vary from 0.10 to 0.60 at controlled capillary pressures up to 200 kPa, (2) the CO 2 saturations in the matrix increase with water saturation in the horizontal fracture resulting in better capillary continuity for water to drain across the fracture, and (3) the fracture water saturation can be enhanced by the non-uniform fracture capillary pressure and countercurrent flow of CO 2 and water across the fracture-matrix interface. In the case of high fracture water saturation, matrix CO 2 saturation largely depends on matrix anisotropy and heterogeneity. The core-scale experimental results contribute to understand the fracture-matrix interactions and CO 2 storage efficiency in fractured porous media.
Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO 2 Leakage through a Compromised Well
Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO 2 ) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO 2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.
First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs
ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.
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.
Non-dimensional performance and safety parameters for heat pipes
The use of heat pipes in safety-critical systems such as nuclear microreactors dictates the development of generalized, practical, scalable performance and safety parameters. Traditional dimensional metrics, while informative, lack the universality required for comparative analysis across varying designs and operating regimes. Here, this work introduces a comprehensive set of non-dimensional parameters to characterize heat pipe performance and safety, including capillary performance, effective thermal conductivity, response time, exergetic efficiency, allowable temperature gradients, allowable rate of temperature change, priming coefficients, and factor of safety. A reference heat pipe design representative of microreactor applications was analyzed via the developed parameters using both traditional analytical models and Sockeye simulations under transient and steady-state conditions. Sodium, potassium, and water were evaluated as working fluids to demonstrate the applicability of the framework across a broad temperature range. The proposed non-dimensional parameters effectively captured key thermal-hydraulic behaviors and safety concerns, as was demonstrated via Sockeye simulations. This framework supports the development of design optimization strategies, operational protocols, and safety assurance practices for advanced reactor systems and other high-reliability applications.