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At least 19 records

Numerical simulation of compressible, turbulent, two-phase flow

A computer program for numerically simulating compressible, turbulent, two-phase flows is described and applied. Special attention is given to flows in which dust is ingested into the turbulent boundary layer behind shock waves moving over the earth's surface. it is assumed that the two phases are interpenetrating continua which are coupled by drag forces and heat transfer. The particle phase is assumed to be dilute, and turbulent effects are modeled by zero- and two-equation eddy viscosity models. An important feature of the turbulence modeling is the treatment of surface boundary conditions which control the ingestion of particles into the boundary layer by turbulent friction and diffusion. The numerical method uses second-order implicit upwind differencing of the inviscid terms of the equations and second-order central differencing of the viscous terms. A diagonal form of the implicit algorithm is used to improve efficiency, and the transformation to a curvilinear coordinate system is accomplished by the finite volume techniques. Applications to a series of representative flows include a two-phase nozzle flow, the steady flow of air over a sand bed, and the air flow behind a normal shock wave in uniform motion over a sand bed. Results of the latter two applications are compared with experimental results.

Coakley, t. J.↗

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.

36 MATERIALS SCIENCE↗

Construction of an Exact Pressure-Equilibrium Scheme for the Five-Equation Two-Phase Flow Model With Thermal Relaxation

Numerical simulation of compressible multiphase flows based on the four-equation (homogeneous relaxation) model is known to suffer from two fundamental difficulties with (a) wave propagation and (b) pressure equilibrium preservation. First, the mixture sound speed exhibits non-monotonic dependency with respect to the volume fraction, which leads to robustness issues in the resolution of shocks and acoustic wave propagation across two-phase regions. This difficulty can be mitigated by solving Allaire’s five-equation model augmented with infinitely fast phasic temperature equilibrium, from which solutions of the four-equation model can be recovered. However, when temperature is non-uniform, this augmented five-equation formulation still fails to preserve pressure equilibrium across material interfaces. In this work, we propose a fully conservative numerical scheme that exactly preserves pressure equilibrium at the discrete level for the augmented five-equation model, for arbitrary initial distributions of temperature and volume fraction. Combined with the monotonic sound speed property of the five-equation formulation, the proposed pressure-equilibrium preserving scheme significantly improves robustness in the presence of strong multiphase interactions, including shock–interface interactions and advection of material interfaces.

ESG↗

Magnetohydrodynamic generators using two-phase liquid-metal flows

Two-phase flow generator cycle of a magnetohydrodynamic /MHD/ generator uses a working fluid which is compressible and treated as an expanding gas. The two-phase mixture passes from the heat source through the MHD generator, where the expansion process takes place and the electrical energy is extracted.

Petrick, M.↗

Transient engine performance with water ingestion

The immediate effects on the transient performance of a generic, high bypass ratio jet engine on account of water ingestion are discussed. The air compression subsystem has been analyzed with respect to four aerothermodynamic and mechanical processes associated with two-phase fluid flow and the engine simulation has been carried out under three limiting cases of interest in practice, one pertaining to draining of water at the end of compression and the other two, to partial evaporation at two different locations in the burner. General observations are made on engine operability as a function of engine and control design under various engine and (control input) sensor operating conditions, with various mass fractions of water in the air-water mixture entering the engine, during various pilot-initiated power demand changes.

Haykin, T.↗

Use of two-phase flow heat transfer method in spacecraft thermal system

In space applications, weight, volume and power are critical parameters. Presently liquid freon is used in the radiator planels of the Space Shuttle to dissipate heat. This requires a large amount of freon, large power for pumps, large volume and weight. Use of two-phase flow method to transfer heat can reduce them significantly. A modified commercial vapor compression refrigerator/freezer was sucessfully flown in STS-4 to study the effect of zero-gravity on the system. The duty cycle was about 5 percent higher in flight as compared to that on earth due to low flow velocity in condenser. The vapor Reynolds number at exit was about 4000 as compared to about 12,000. Efforts are underway to design a refrigerator/freezer using an oil-free compressor for Spacelab Mission 4 scheduled to fly in January 1986. A thermal system can be designed for spacecraft using the two-phase flow to transfer heat economically.

Hye, A.↗

Heat Transfer and Fluid Mechanics Institute, Meeting, 26th, Washington State University, Pullman, Wash., June 26-28, 1978, Proceedings

Papers are presented on the heat transfer and fluid mechanics in energy systems including diesel combustion analysis using rapid sampling and the numerical simulation of thermal response of architectural structures. Experiments associated with hypersonic boundary layers, the prediction of nozzle-wall pressure distribution, and the effects of nozzle geometry on an axisymmetric thrust augmentor are outlined. Predictions are made of film thickness on a roll-metering device and the thermal characteristics of multiple-surface submerged condenser modules are described. Numerical studies are made of the interaction between natural and forced convection in a complex geometry and of pressure drop and holdup in two-phase stratified flow. A numerical solution is given for viscous flows at high Reynolds numbers and for compressible boundary layer flows near separation or reattachment. The structure and transport properties in turbulent shear flows are reviewed along with the spectra of Reynolds stresses in a developing pipe flow.

Crowe, C. T.↗

Heat Transfer and Fluid Mechanics Institute, Meeting, 25th, University of California, Davis, Calif., June 21-23, 1976, Proceedings

Major research advances in heat transfer and fluid dynamics are outlined, with particular reference to relevant energy problems. Of significant importance are such topics as synthetic fuels in combustion, turbulence models, combustion modeling, numerical methods for interacting boundary layers, and light-scattering diagnostics for gases. The discussion covers thermal convection, two-phase flow and boiling heat transfer, turbulent flows, combustion, and aerospace heat transfer problems. Other areas discussed include compressible flows, fluid mechanics and drag, and heat exchangers. Featured topics comprise heat and salt transfer in double-diffusive systems, limits of boiling heat transfer in a liquid-filled enclosure, investigation of buoyancy-induced flow stratification in a cylindrical plenum, and digital algorithms for dynamic analysis of a heat exchanger. Individual items are announced in this issue.

Mckillop, A. A.↗

Spacecraft heat transfer by two-phase flow method

A refrigerator/freezer has been designed with an oil-free compressor to provide an economical two-phase flow system for heat transfer. A computer simulation has been done for the condenser and evaporator to determine the design parameters, such as length, diameter, and flow regimes, for different refrigerants and load requirements. A large Reynolds number was considered to ensure annular flow (in order to maximize heat transfer coefficients) and large Froude number. The simulation was correlated with the test data of a vapor compression refrigerator/freezer flown on STS-4 (which provided information on vapor compression in a zero-gravity environment). The two-phase system will be used for the Spacelab mission SLS-1 and can be used in future spacecraft and high-speed aircraft, where weight, volume, and power requirements are critical.

Hye, A.↗

Using X-ray radiography to study oxygen flow in a proton exchange membrane electrolyzer operating under balanced pressure conditions

Of the various water electrolyzer technologies, the proton exchange membrane electrolyzer (PEMWE) is one of the best solutions for producing clean hydrogen without releasing CO 2 . In order to allow for widespread use of clean hydrogen, it is necessary to decrease its cost, which is intrinsically related to system operation. Current PEMWE plants operate in differential mode, directly pressurizing hydrogen and benefiting from thermodynamic compression, which increases overall system efficiency. However, high differential pressure above 30 bar can cause membrane stress, resulting in membrane creeping and failure. Pressurizing the water and operating at balanced pressure allows hydrogen to be produced at higher pressures while preserving the integrity of the membrane and porous layers. Nevertheless, the impact of pressurizing water on PEMWE performance must be better understood to maximize performance under balanced pressure conditions. Here, this study examined the impact of water pressure on two-phase flow. A high-pressure electrolyzer setup was developed to perform operando X-ray radiography and examine oxygen transport with high temporal resolution. The imaging segmentation process, developed to capture bubble properties in the channel, was applied to a specific experiment. The results clearly showed that as pressure increased up to 30 bars, the initial bubbly flow transitioned to slug flow, which led to channel saturation with oxygen. This work demonstrates that two-phase flow in an electrolyzer can be studied using X-ray radiography, which has the advantages of fast measurements and the ability to probe dense materials, such as those required for pressurized electrolyzers.

Balanced high pressure operation↗

SSME thrust chamber modeling with Navier Stokes equations

The capability of predicting two-dimensional, compressible and reacting flow in the combustion chamber and nozzle of the Space Shuttle Main Engine (SSME) is demonstrated. A nonorthogonal body fitted coordinate system has been used to represent the combustor and nozzle geometry. The Navier-Stokes equations are solved for the entire thrust chamber with the k-epsilon turbulence model accounting for compressibility and large pressure gradients effects. Results of the computational test cases reveal all expected features of the transonic nozzle flows including location of sonic line, internal shock and boundary layer build-up. Calculated performance parameters such as thrust, flow rate, and specific impulse are also in reasonble agreement with available data. The results show promising potential of solving full Navier-Stokes equations with heat transfer and two-phase combustion in truly comprehensive modeling of rocket engines.

Przekwas, A. J.↗

Characterization of Inlet Guide Vane Performance for Discharge Compressor Operation near the Dome of an sCO 2 Pumped Heat Energy Storage

Southwest Research Institute® (SwRI®) developed and tested a Variable Inlet Guide Vane (IGV herein) assembly on an integrally-geared sCO 2 compressor (IGC) to demonstrate compressor operation at both the compressor design point and near the dome and to define the operating limits of the compressor by monitoring for two-phase flow, flow turbulence from the IGVs, and compressor choke and surge as the CO 2 inlet temperature is varied. Performance testing was conducted on an existing integrally-geared, two-stage main compressor designed for near-critical-point operation with CO 2 . This testing campaign validated the IGV design and operation, as well as improved the understanding and confidence in operating compressors and predicting performance characteristics near the critical point where fluid properties change rapidly with temperature. In addition to improving the robust operating limits of an sCO 2 compressor, the development of an IGV for the IGC system improved off-design compressor efficiency by 12%.

25 ENERGY STORAGE↗

Laboratory evaluation of cyclic underground hydrogen storage in the Temblor sandstone of the San Joaquin Basin, California

Underground Hydrogen Storage (UHS) in depleted oil and gas reservoirs could provide a cost-effective solution to balance seasonal fluctuations in renewable energy generation. However, data and knowledge on UHS at subsurface conditions are limited so it is difficult to estimate how effective this type of storage could be. In this study, we perform high pressure experiment to measure the effectiveness of cyclic hydrogen (H 2 ) storage in a specimen of Temblor sandstone retrieved from the San Joaquin Basin of California. Our experiment mimics reservoir pressure conditions to measure H 2 -brine relative permeability and fluid-rock interactions over the course of ten charging and discharging cycles. Initial gas breakthrough occurred at 15 % to 25 % H2 saturation in the specimen with 3 % NaCl brine as the resident fluid. Continuing injecting to 4 pore volumes (PV) of H 2 yielded an asymptotic H 2 saturation of 38 % to 41 %, a level often referred to as the irreducible gas saturation based on two-phase flow. The boundary condition in this study mimics the near wellbore region, which experiences bi-directional H 2 flow. This bi-directional flow led to evaporative drying of the specimen resulting in 94 % H 2 saturation at the end of 10th cycle. This indicates that cyclic flow and evaporative drying can lead to more efficient reservoir storage where a larger fraction of the reservoir porosity is usable to store H 2 . The produced gas stream consisted of H 2 mixed with 8 % to 22 % H 2 O, indicating formation dry-out by evaporation. Meanwhile, produced water chemistry indicated calcite and silicate dissolution, with calcite sourced from fossil fragments. This led to a loss of cementation and weakened the rock sample. Combined, our results indicate dry-out, compaction, increased H 2 saturation, rock weakening, and permeability loss during cyclic UHS. Overall, we anticipate that the combined effects should lead to higher than anticipated UHS storage efficiency per volume of sandstone reservoir rock.

08 HYDROGEN↗

Phenomena Identification and Ranking Table (PIRT) for heat pipes

Heat pipes are advanced passive thermal management devices that utilize phase change and capillary action to achieve efficient heat transfer. However, due to the complexity of the phenomena coupled in heat pipes, including capillary, phase change, turbulence, and compressibility effects, there are high uncertainties in the predictability of their operational regimes and performance. This PIRT exercise, conducted as a collaborative effort involving the Department of Energy (DOE) Microreactor Program (MRP), the Nuclear Regulatory Commission (NRC), and university partners systematically identifies, reviews, and prioritizes critical phenomena affecting the operation of heat pipes based on their importance and knowledge levels. Additional analyses and discussion are provided for phenomena with high importance and low knowledge, such as wick de-wetting, critical heat flux, contact angles, and pressure dynamics. The discussions included the recognizing challenges and proposing future research directions for both modeling and simulation and experimental efforts. Additionally, the report addresses phenomena with medium importance and low knowledge that could impact heat pipe operation during non-normal or transient operation, including frozen startup, laminar to turbulent transition, geyser boiling, wick priming, underfilling conditions, surface roughness of the wick, NCGs trapped in the wick, and the timescales of startup and shutdown. In conclusion, this comprehensive evaluation serves as a valuable resource for guiding future research and development efforts, supporting the successful integration of heat pipes into critical applications such as nuclear reactors, and contributing to the advancement of heat pipe technologies in safety-critical industries.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

A Finite Element Method for Compressible and Turbulent Multiphase Flow Instabilities with Heat Transfer

We present a new finite element framework for modeling compressible, turbulent multiphase flows with heat transfer. For two-fluid systems with a free surface, the Volume of Fluid (VOF) method is implemented without the need for interface reconstruction, while turbulence is resolved using a dynamic Vreman large eddy simulation (LES) model. Unlike most two-phase VOF studies, which neglect heat transfer, the present approach incorporates energy transport equations within the VOF formulation to account for heat exchange, an effect particularly important in turbulent flows. Conjugate heat transfer is often challenging in finite volume methods, which require explicit specification of heat fluxes at the solid–fluid interface, limiting accuracy and predictive capability. By contrast, the finite element formulation does not require heat flux inputs, allowing more accurate and robust simulation of heat transfer between solids and fluids. The method is demonstrated through three representative cases. First, a two-fluid instability with a single-mode perturbation is simulated and validated against analytical growth rates. Second, conjugate heat transfer is examined in a high-temperature flow over a cold metal cylinder, with validation performed both quantitatively—via pressure coefficient comparisons with experimental data—and qualitatively using vector field topology. Finally, compressible spray injection and breakup are modeled, demonstrating the ability of the framework to capture interfacial dynamics and atomization under turbulent, high-speed conditions. In the compressible spray injection and breakup case, the results indicate that the finite element formulation achieved higher predictive accuracy and robustness than the finite-volume method. With the same mesh resolution, the FEM reduced the root mean square error (RMSE) and mean absolute percentage error (MAPE) from 6.96 mm and 26.0% (for the FVM) to 4.85 mm and 12.7%, respectively, demonstrating improved accuracy and robustness in capturing interfacial dynamics and heat transfer. The study also introduced vector field topology to visualize and interpret coherent flow structures and instabilities, offering insights beyond conventional scalar-field analyses.

97 MATHEMATICS AND COMPUTING↗

Two-phase flows within systems with ambient pressure

In systems where the design inlet and outlet pressures are maintained above the thermodynamic critical pressure, it is often assumed that two phase flows within the system cannot occur. Designers rely on this simple rule of thumb to circumvent problems associated with a highly compressible two phase flow occurring within the supercritical pressure system along with the uncertainties in rotordynamics, load capacity, heat transfer, fluid mechanics, and thermophysical property variations. The simple rule of thumb is adequate in many low power designs but is inadequate for high performance turbomachines and linear systems, where two phase regions can exist even though outlet pressure is greater than critical pressure. Rotordynamic-fluid-mechanic restoring forces depend on momentum differences, and those for a two phase zone can differ significantly from those for a single-phase zone. Using the Reynolds equation the angular velocity, eccentricity, geometry, and ambient conditions are varied to determine the point of two phase flow incipience.

Hendricks, R. C.↗