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At least 55 records · Page 3

A New Unsteady Model for Dense Cloud Cavitation in Cryogenic Fluids

Contents include the following: Background on thermal effects in cavitation. Physical properties of hydrogen. Multi-phase cavitation with thermal effect. Solution procedure. Cavitation model overview. Cavitation source terms. New cavitation model. Source term for bubble growth. One equation les model. Unsteady ogive simulations: liquid nitrogen. Unsteady incompressible flow in a pipe. Time averaged cavity length for NACA15 flowfield.

Hosangadi, Ashvin↗

Multiphysics Modeling of a Single Channel in a Nuclear Thermal Propulsion Grooved Ring Fuel Element

In the past, fuel rods have been used in nuclear propulsion applications. A new fuel element concept that reduces weight and increases efficiency uses a stack of grooved discs. Each fuel element is a flat disc with a hole on the interior and grooves across the top. Many grooved ring fuel elements for use in nuclear thermal propulsion systems have been modeled, and a single flow channel for each design has been analyzed. For increased efficiency, a fuel element with a higher surface-area-to-volume ratio is ideal. When grooves are shallower, i.e., they have a lower surface area, the results show that the exit temperature is higher. By coupling the physics of turbulence with those of heat transfer, the effects on the cooler gas flowing through the grooves of the thermally excited solid can be predicted. Parametric studies were done to show how a pressure drop across the axial length of the channels will affect the exit temperatures of the gas. Geometric optimization was done to show the behaviors that result from the manipulation of various parameters. Temperature profiles of the solid and gas showed that more structural optimization is needed to produce the desired results. Keywords: Nuclear Thermal Propulsion, Fuel Element, Heat Transfer, Computational Fluid Dynamics, Coupled Physics Computations, Finite Element Analysis

Kim, Tony↗

Modification of favorable average curvature effect by changing parallel sound wave behavior in tokamak plasmas

Abstract The favorable average curvature effect, also known as the GGJ effect (Glasser et al 1975 Phys. Fluids 18 875), is intrinsically associated with parallel sound wave propagation in a tokamak plasma. This work investigates how the GGJ effect is modified by changing the parallel sound wave behavior. Two physics models beyond the standard single fluid theory, i.e. an anisotropic thermal transport model and a parallel sound wave damping model, are employed to change parallel sound waves in a toroidal plasma, and the consequence on the GGJ effect is demonstrated for two important classes of problems, i.e. the resistive plasma response to the applied resonant magnetic perturbation and the stability of the tearing mode. Toroidal modeling reveals that the GGJ effect is significantly altered by both of the aforementioned physics effects. Compared to the thermal transport physics, which completely removes the GGJ effect, the sound wave damping effect only offers partial mitigation. The differences between these two models are further illustrated in terms of the radial structure of the shielding current and the eigenfunction of the tearing instability. In particular, a fundamental reason for complete suppression of the GGJ effect by the thermal transport is identified as an extra toroidal coupling of the poloidal harmonics.

Physics↗

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Constrained Vapor Bubble

The nonisothermal Constrained Vapor Bubble, CVB, is being studied to enhance the understanding of passive systems controlled by interfacial phenomena. The study is multifaceted: 1) it is a basic scientific study in interfacial phenomena, fluid physics and thermodynamics; 2) it is a basic study in thermal transport; and 3) it is a study of a heat exchanger. The research is synergistic in that CVB research requires a microgravity environment and the space program needs thermal control systems like the CVB. Ground based studies are being done as a precursor to flight experiment. The results demonstrate that experimental techniques for the direct measurement of the fundamental operating parameters (temperature, pressure, and interfacial curvature fields) have been developed. Fluid flow and change-of-phase heat transfer are a function of the temperature field and the vapor bubble shape, which can be measured using an Image Analyzing Interferometer. The CVB for a microgravity environment, has various thin film regions that are of both basic and applied interest. Generically, a CVB is formed by underfilling an evacuated enclosure with a liquid. Classification depends on shape and Bond number. The specific CVB discussed herein was formed in a fused silica cell with inside dimensions of 3x3x40 mm and, therefore, can be viewed as a large version of a micro heat pipe. Since the dimensions are relatively large for a passive system, most of the liquid flow occurs under a small capillary pressure difference. Therefore, we can classify the discussed system as a low capillary pressure system. The studies discussed herein were done in a 1-g environment (Bond Number = 3.6) to obtain experience to design a microgravity experiment for a future NASA flight where low capillary pressure systems should prove more useful. The flight experiment is tentatively scheduled for the year 2000. The SCR was passed on September 16, 1997. The RDR is tentatively scheduled for October, 1998.

Huang, J.↗

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Water Transport and the Evolution of CM Parent Bodies

Extraterrestrial water-bearing minerals are of great importance both for understanding the formation and evolution of the solar system and for supporting future human activities in space. Asteroids are the primary source of meteorites, many of which show evidence of an early heating episode and varying degrees of aqueous alteration. The origin and characterization of hydrated minerals (minerals containing H2O or OH) among both the main-belt and near-earth asteroids is important for understanding a wide range of solar system formation and evolutionary processes, as well as for planning for human exploration. Current hypotheses postulate asteroids began as mixtures of water ice and anhydrous silicates. A heating event early in solar system history was then responsible for melting the ice and driving aqueous alteration. The link between asteroids and meteorites is forged by reflectance spectra, which show 3-μm bands indicative of bound OH or H2O on the C-class asteroids, which are believed to be the parent bodies of the carbonaceous chondrites in our collections. The conditions at which aqueous alteration occurred in the parent bodies of carbonaceous chondrites are thought to be well-constrained: at 0-25 C for less than 15 Myr after asteroid formation. In previous models, many scenarios exhibit peak temperatures of the rock and co-existing liquid water in more than 75 percent of the asteroid's volume rising to 150 C and higher, due to the exothermic hydration reactions triggering a thermal runaway effect. However, even in a high porosity, water-saturated asteroid very limited liquid water flow is predicted (distances of 100's nm at most). This contradiction has yet to be resolved. Still, it may be possible for water to become liquid even in the near-surface environment, for a long enough time to drive aqueous alteration before vaporizing or freezing then subliming. Thus, we are using physics- and chemistry-based models that include thermal and fluid transport as well as the effects of relevant chemical reactions, to investigate whether formation of hydrated minerals can occur in the surface and near-surface environments of carbonaceous type asteroids. These models will elucidate how the conditions within the parent body that cause internal aqueous alteration play themselves out at the asteroid's surface. We are using our models to determine whether the heat budget of 20-100-km bodies is sufficient to bring liquid water to the near-surface and cause mineral alteration, or whether additional heat input at the surface (i.e, by impacts) is needed to provide a transient liquid water source for mineral hydration without large- scale liquid water transport.

Coker, R.↗

Stability of a viscous fluid in a rectangular cavity in the presence of a magnetic field

The stability of an electrically conducting fluid subjected to two dimensional disturbance was investigated. A physical system consisting of two parallel infinite vertical plates which are thermally insulated was studied. An external magnetic field of constant strength was applied to normal plates. The fluid was heated from below so that a steady temperature gradient was maintained in the fluid. The governing equations were derived by perturbation technique, and solutions were obtained by a modified Galerkin method. It was found that the presence of the magnetic field increases the stability of the physical system and instability can occur in the form of neutral or oscillatory instability.

Liang, C. Y.↗

Computational Prediction of Pressure and Thermal Environments in the Flame Trench With Launch Vehicles

One of the key objectives for the development of the 21st Century Space Launch Com- plex is to provide the exibility needed to support evolving launch vehicles and spacecrafts with enhanced range capacity. The launch complex needs to support various proprietary and commercial vehicles with widely di erent needs. The design of a multi-purpose main ame de ector supporting many di erent launch vehicles becomes a very challenging task when considering that even small geometric changes may have a strong impact on the pressure and thermal environment. The physical and geometric complexity encountered at the launch site require the use of state-of-the-art Computational Fluid Dynamics (CFD) tools to predict the pressure and thermal environments. Due to harsh conditions encountered in the launch environment, currently available CFD methods which are frequently employed for aerodynamic and ther- mal load predictions in aerospace applications, reach their limits of validity. This paper provides an in-depth discussion on the computational and physical challenges encountered when attempting to provide a detailed description of the ow eld in the launch environ- ment. Several modeling aspects, such as viscous versus inviscid calculations, single-species versus multiple-species ow models, and calorically perfect gas versus thermally perfect gas, are discussed. The Space Shuttle and the Falcon Heavy launch vehicles are used to study di erent engine and geometric con gurations. Finally, we provide a discussion on traditional analytical tools which have been used to provide estimates on the expected pressure and thermal loads.

thermal↗

Numerical Investigation of the Spark Discharge Process in a Crossflow

The present study numerically investigates the spark discharge process under crossflow conditions using a thermal equilibrium plasma solver that fully couples the electromagnetic physics and fluid dynamics in a computational framework. Numerical results are validated by the comparison with experimental data. Here, the spark discharge experiment is performed in a constant volume vessel using an inductive coil ignition system for automotive applications, and the evolution of the spark channel is measured using high-speed imaging. The crossflow in the gap between the spark-plug electrodes is generated by a rotating fan with two different fan speeds, and the flow velocity across the gap is characterized by particle image velocimetry (PIV) measurement. A computational fluid dynamics (CFD) solver is employed to simulate the crossflow and provide the flow field variables (velocity, pressure, temperature) to the plasma solver. The crossflow velocity predicted in the flow simulation agrees well with the PIV data in that the non-uniform velocity profiles at monitoring points are reproduced by the CFD code. With the crossflow initialization in the plasma solver, the simulated spark discharge process from the breakdown to spark discharge matches the experimental data, including the voltage and circuit waveforms and the high-speed images of the spark channel evolution. The stretch of spark channel captured by plasma simulations agrees with the measured data. The plasma simulation reveals that the mean temperature of the spark channel is maintained at 5000 K during the discharge phase, and the temperature varies along the spark channel so that the highest value is obtained at the spark root on the center electrode. Overall, the results presented in this paper are meant to provide valuable information about the properties of the plasma generated by the spark discharge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Advanced thermal energy management: A thermal test bed and heat pipe simulation

Work initiated on a common-module thermal test simulation was continued, and a second project on heat pipe simulation was begun. The test bed, constructed from surplus Skylab equipment, was modeled and solved for various thermal load and flow conditions. Low thermal load caused the radiator fluid, Coolanol 25, to thicken due to its temperature avoided by using a regenerator-heat-exchanger. Other possible solutions modeled include a radiator heater and shunting heat from the central thermal bus to the radiator. Also, module air temperature can become excessive with high avionics load. A second preoject concerning advanced heat pipe concepts was initiated. A program was written which calculates fluid physical properties, liquid and vapor pressure in the evaporator and condenser, fluid flow rates, and thermal flux. The program is directed to evaluating newer heat pipe wicks and geometries, especially water in an artery surrounded by six vapor channels. Effects of temperature, groove and slot dimensions, and wick properties are reported.

Barile, Ronald G.↗

High-Speed Diagnostic and Simulation Capabilities for Reacting Hypersonic Reentry Flows (LDRD Final Report)

High-enthalpy hypersonic flight represents an application space of significant concern within the current national-security landscape. The hypersonic environment is characterized by high-speed compressible fluid mechanics and complex reacting flow physics, which may present both thermal and chemical nonequilibrium effects. We report on the results of a three-year LDRD effort, funded by the Engineering Sciences Research Foundation (ESRF) investment area, which has been focused on the development and deployment of new high-speed thermochemical diagnostics capabilities for measurements in the high-enthalpy hypersonic environment posed by Sandia's free-piston shock tunnel. The project has additionally sponsored model development efforts, which have added thermal nonequilibrium modeling capabilities to Sandia codes for subsequent design of many of our shock-tunnel experiments. We have cultivated high-speed, chemically specific, laser-diagnostic approaches that are uniquely co-located with Sandia's high-enthalpy hypersonic test facilities. These tools include picosecond and nanosecond coherent anti-Stokes Raman scattering at 100-kHz rates for time-resolved thermometry, including thermal nonequilibrium conditions, and 100-kHz planar laser-induced fluorescence of nitric oxide for chemically specific imaging and velocimetry. Key results from this LDRD project have been documented in a number of journal submissions and conference proceedings, which are cited here. The body of this report is, therefore, concise and summarizes the key results of the project. The reader is directed toward these reference materials and appendices for more detailed discussions of the project results and findings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Approach for the Aluminum-clad Dry Storage Pilot using HFIR Fuel

To confirm that the dry storage of aluminum-clad research reactor spent nuclear fuel (ASNF) will remain within the safety envelope after applied drying schemes and that the resulting evolution of the gas space composition, temperature, and pressure conditions are understood, a dry storage pilot project is being established. The pilot will incorporate an instrumented lid for discrete interval or for on-demand gas composition and temperature monitoring of two DOE Standard Canisters (DSCs) loaded with three High Flux Isotope Reactor (HFIR) inner cores per DSC. Each DSC would be subjected to a separate alternative candidate drying scheme. Canisters will undergo 1 to 5 years of monitoring, including internal temperature and gas sampling to track pressure and composition changes. This report outlines the approach for modeling the ASNF-in-canister behavior in terms of evolving gas space conditions for the ASNF dry storage pilot using HFIR fuel. The ASNF has an adherent surface oxyhydroxide layer comprised of boehmite/bayerite that generates hydrogen when subjected to irradiation. Three-dimensional multi-physics computational fluid dynamics simulations will be executed to compute the thermal field within the DSC and provide inputs to a chemical model employed to compute pressure buildup as hydrogen is generated in the system. Implemented in Cantera, the chemical model solves gas phase and aluminum oxyhydroxide surface-mediated radiolysis reactions. Gas phase reactions are sourced from Wittman and Hanson (2015), whereas surface-mediated reactions are incorporated by fitting experimental data using an optimization algorithm (Abboud, 2023). Water radiolysis reactions from Wren and Ball (2001) are adopted with modifications as described in Abboud (2023c). Understanding the effect of the hydrogen buildup over time is important for long-term storage safety considerations. Modeling results will include the canister pressure, temperature, and composition evolution from the initial helium backfill with the addition of radiolytically-evolved chemical species (e.g., hydrogen and oxygen). The specific HFIR cores for the pilot program have not yet been selected, and the overall design is still in development. The CFD-chemical model used for this work will be based on prior models with necessary updates to allow for improved accuracy and efficiency. The experimental data obtained from the HFIR demonstration will be used to improve and validate the computational models to predict the ASNF-in-canister behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Technical accomplishments of the NASA Lewis Research Center, 1989

Topics addressed include: high-temperature composite materials; structural mechanics; fatigue life prediction for composite materials; internal computational fluid mechanics; instrumentation and controls; electronics; stirling engines; aeropropulsion and space propulsion programs, including a study of slush hydrogen; space power for use in the space station, in the Mars rover, and other applications; thermal management; plasma and radiation; cryogenic fluid management in space; microgravity physics; combustion in reduced gravity; test facilities and resources.

Source record↗

Effects of Gravity on Supercritical Water Oxidation (SCWO) Processes

The effects of gravity on the fluid mechanics of supercritical water jets are being studied at NASA to develop a better understanding of flow behaviors for purposes of advancing supercritical water oxidation (SCWO) technologies for applications in reduced gravity environments. These studies provide guidance for the development of future SCWO experiments in new experimental platforms that will extend the current operational range of the DECLIC (Device for the Study of Critical Liquids and Crystallization) Facility on board the International Space Station (ISS). The hydrodynamics of supercritical fluid jets is one of the basic unit processes of a SCWO reactor. These hydrodynamics are often complicated by significant changes in the thermo-physical properties that govern flow behavior (e.g., viscosity, thermal conductivity, specific heat, compressibility, etc), particularly when fluids transition from sub-critical to supercritical conditions. Experiments were conducted in a 150 ml reactor cell under constant pressure with water injections at various flow rates. Flow configurations included supercritical jets injected into either sub-critical or supercritical water. Profound gravitational influences were observed, particularly in the transition to turbulence, for the flow conditions under study. These results will be presented and the parameters of the flow that control jet behavior will be examined and discussed.

aqueous solutions↗

A Generalized Multi-Phase Framework for Modeling Cavitation in Cryogenic Fluids

A generalized multi-phase formulation for cavitation in fluids operating at temperatures elevated relative to their critical temperatures is presented. The thermal effects and the accompanying property variations due to phase change are modeled rigorously. Thermal equilibrium is assumed and fluid thermodynamic properties are specified along the saturation line using the NIST-12 databank. Fundamental changes in the physical characteristics of the cavity when thermal effects become pronounced are identified; the cavity becomes more porous, the interface less distinct, and has increased entrainment when temperature variations are present. Quantitative estimates of temperature and pressure depressions in both liquid nitrogen and liquid hydrogen were computed and compared with experimental data of Hord for hydrofoils. Excellent estimates of the leading edge temperature and pressure depression were obtained while the comparisons in the cavity closure region were reasonable. Liquid nitrogen cavities were consistently found to be in thermal equilibrium while liquid hydrogen cavities exhibited small, but distinct, non-equilibrium effects.

Dorney, Dan↗

Experimental evaluation of thermal-fluids performance of Helium-Cooled Flat Plate (HCFP) divertor

Various helium (He)-cooled solid-tungsten (W) divertor concepts have been proposed for long-pulse magnetic fusion energy reactors. Among these concepts, the He-cooled flat plate divertor (HCFP) modules have the largest plasma-facing surface area of ~0.2 m 2 . Simulations have shown that the most recent version of the design can withstand heat fluxes as great as 8 MW/m 2 . Earlier experimental studies of a single shortened HCFP cooling unit with a slot length of 7.6 cm used air at ambient temperature and pressures below 0.6 MPa. Here, we present initial experimental studies of a copper alloy and steel test section modeling a shortened HCFP cooling unit using He at prototypical pressure of 10 MPa, inlet temperatures T i ≤ 200 °C and steady-state incident heat fluxes q" ≤ 1.2 MW/m 2 . Results for Nusselt number Nu as a function of Reynolds number Re were obtained for Re = 1.2×10 4 –3.4×10 4 , and used to develop a Nu(Re) correlation and validate numerical models of the test section using commercial computational fluid dynamics (CFD) software. Simulations with this model are performed to evaluate the effect of the shortened slot. Furthermore, these analyses are used to estimate the thermal-fluids performance of the HCFP under prototypical conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Two-fluid simulations of galaxy formation

We investigate the formation of galaxies and larger structure with a simulation modeling two gravitationally coupled fluids representing dark matter and baryons. The baryon gas dynamics are calculated with a smoothed particle hydrodynamics (SPH) method, and the physics modeled includes thermal pressure, shock heating, and radiative cooling. We simulate a 16 Mpc periodic cube with 64(exp 3) particles in each fluid and 10% baryon mass fraction. We confirm, for the first time experimentally, disk formation as a natural consequence of hierarchical clustering in a large-scale cosmological environment. The majority of isolated galaxies exhibit centrifugally supported disks. A power-law relation between cold baryonic mass and maximum rotation velocity is found, M varies as nu(sub rot)(exp alpha) with alpha = 2.5 after correcting for differential numerical resolution. Both the spatial and velocity distributions of the simulated galaxies are biased with respect to the dark matter. A counts-in-cells analysis indicates that an unphysical degree of merging in the central cluster is likely responsible for the antibias signal in the correlation function. A robust, scale-dependent velocity bias is measured. The ratio of galaxy to dark matter pairwise velocity dispersions on a scale of 1 Mpc is 0.7. The amplitude is only mildly dependent on redshift or mass cutoff and scales with separation as r(exp 0.2). The degree to which these results depend on numerical parameters is discussed. Mass resolution plays a key role in controlling the resulting fraction of cold, dense baryons. The mass fraction associated with galaxies decreases by a factor of approximately greater than 3 when the mass per particle is increased by a factor 8. Photoionization and energy input from supernova will have to be included to determine more carefully the fraction of highly dissipated material and the characteristics of the stellar component of galaxies.

Evrard, August E.↗