Computational Fluid Dynamics and Magnetohydrodynamics Modeling of Liquid Metal Flows for Fusion Blanket Applications
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The AeroServoElasticity task under the NASA Supersonics Project is developing dynamic models of the propulsion system and the vehicle in order to conduct research for integrated vehicle dynamic performance. As part of this effort, a nonlinear quasi 1-dimensional model of an axisymmetric external compression supersonic inlet is being developed. The model utilizes compressible flow computational fluid dynamics to model the internal inlet segment as well as the external inlet portion between the cowl lip and normal shock, and compressible flow relations with flow propagation delay to model the oblique shocks upstream of the normal shock. The external compression portion between the cowl-lip and the normal shock is also modeled with leaking fluxes crossing the sonic boundary, with a moving CFD domain at the normal shock boundary. This model has been verified in steady state against tunnel inlet test data and it s a first attempt towards developing a more comprehensive model for inlet dynamics.
The solid rocket boosters (SRBs) on the Space Launch System (SLS) generate powerful ignition overpressure (IOP) waves that can potentially damage the vehicle and surrounding ground structures. Based on historical Shuttle experience, the IOP will be mitigated by utilizing an IOP/Sound Suppression (SS) water system which sprays water in and around the SRB and RS-25 engine plumes. However, the complex multiphase physics of the resulting plume-water interaction can lead to undesirable effects, such as high velocity water spray onto the engine nozzles and SRB nozzle side loads. Prior to launch, insight into this environment can be achieved through scale model testing and predictive computational fluid dynamics (CFD) modeling. The Scale Model Acoustic Test (SMAT) was conducted at Marshall Space Flight Center to provide the data necessary to develop the SLS liftoff acoustic environments by using a 5% scale SLS vehicle, fully integrated with a scaled IOP/SS water system, mobile launcher (ML), and tower. NASA engineers have put forth significant effort in validating the Loci/CHEM-Real Fluids multiphase CFD solver on a wet hold down test from the SMAT series. In this paper, the IOP acoustics and plume-water interactions predicted by the CFD model are compared and validated against the experiment, enabling relatively inexpensive, rapid turnaround for multiphase launch environment analyses to support future flights and design evolutions of SLS and other launch vehicles.
A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.
Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.
Electrically enhanced condensation achieved by an electrospray system can enhance dehumidification in HVAC applications if successfully scaled up. The first step towards scale-up is identifying critical design and operating parameters that significantly impact dehumidification for the electrospray system. Sensitivity analysis is one approach for identifying critical parameters. This paper presents a methodology that can efficiently perform quantitative sensitivity analysis on a computationally expensive high fidelity simulation model, which is a computational fluid dynamics (CFD) model of the electrospray system. The methodology employs surrogate modeling and Sobol sensitivity analysis. We estimate the main and total effect Sobol sensitivity indices of four operating parameters of the electrospray system. The results reveal that the most important parameter is the size of the sprayed droplets, followed by the volumetric flow rate of the bulk air and injected water in the system. The water injection velocity of the spray was found to have little to no impact on dehumidification.
As one of the primary users of the electric grid, buildings and building equipment, including heating, ventilation, and air conditioning (HVAC) systems, can be leveraged to provide the flexible demand needed to balance the grid. Typical strategies to achieve demand flexibility are to reduce electricity use during peak or critical periods by shutting down equipment or relaxing system setpoints, which will inevitably impact the occupants’ comfort. When occupants feel uncomfortable, they may take actions to regain their comfort, and some of those actions (such as turning on a personal fan) may have a negative impact on meeting the demand response goal. Therefore, it is important to incorporate occupant behaviors into the assessment ofthe building demand flexibility potential. In this study, a simulation framework that includes simulation of zone thermal loads, an HVAC system, and occupant behaviors, was developed to investigate the impact of occupant behaviors on demand flexibility. A case study was conducted using a small office model from the U.S. Department of Energy (DOE) Commercial Prototype Building Models to simulate the building envelope and zone loads. An agent-based occupant thermal behavior model was adapted to forecast occupants’ thermal comfort and their resulting thermal behaviors. An artificial neural network (ANN) based airflow model trained from a computational fluid dynamics (CFD) model of the zone was adopted to better predict the ambient environment of each occupant. An air-source heat pump simulation model that was calibrated from a real two-stage air-source heat pump system was used as the HVAC system. A typical load shedding event during peak hours was studied. Repeated simulations were conducted to capture the stochastic effects of occupant behaviors. The interplay between the demand flexibility, occupant comfort and behavior were analyzed by evaluating key performance indicators, including the energy use, occupant discomfort duration, and occupant behavior duration during the peak period. The results suggest that this framework can be used to analyze typical commercial buildings and their HVAC systems in terms ofdemand flexibility potential under the impact of occupant behaviors.
Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.
A physics-based model was developed to simulate the behavior of material in a self-reacting friction stir welding (SR-FSW) process for the joining of metals. This steady-state model builds upon fundamental computational fluid dynamic (CFD) principles within Ansys Fluent to solve the discretized equations. The effective viscosity is calculated using a viscoplastic model using a Sheppard-Wright formulation of flow stress. Numerous advancements have been made in the incorporated physics including (1) temperature-dependent material properties; (2) locally adaptable flow and thermal boundary conditions; and (3) adapting material properties in nugget in response to microstructural changes. Simulation strategies to accelerate computation and improve numerical stability include adapting the mesh refinement and solver relaxation factors during simulation. The result is a highly robust and computationally efficient model capable of providing the material flow and temperature history across the domain. As material history determines the local microstructure and ultimately weld strength, an accurate and detailed physics-based model has the potential to accelerate SR-FSW process development. The model is highly adaptable to changes in process parameters, tool design, or alloy.
This document contains presentations given at Workshop on Computational Turbulence Modeling held 15-16 Sep. 1993. The purpose of the meeting was to discuss the current status and future development of turbulence modeling in computational fluid dynamics for aerospace propulsion systems. Papers cover the following topics: turbulence modeling activities at the Center for Modeling of Turbulence and Transition (CMOTT); heat transfer and turbomachinery flow physics; aerothermochemistry and computational methods for space systems; computational fluid dynamics and the k-epsilon turbulence model; propulsion systems; and inlet, duct, and nozzle flow.
The dataset includes computational fluid dynamics (CFD) models and simulation files for crossflow turbines as well as a detailed project report. The report documents the project undertaken by the Ocean Renewable Power Company (ORPC) to design and optimize a modular fairing for the Modular RivGen Marine Hydrokinetic (MHK) turbine, which enhances the efficient deployment and operation of turbine arrays. The project focused on optimizing the hydrodynamic performance of the fairing using CFD, with an emphasis on two key geometric parameters: the fairing's cross-sectional shape and the spacing between the rotor and the fairing. The analysis aimed to maximize net power output while also assessing discretized loading to evaluate ultimate and fatigue loads on the turbine components. The numerical modeling was conducted using both the commercial CFD software Star-CCM+ and the open-source code openFOAM, with the latter utilizing the actuator line library, turbinesFOAM. This dual-code approach was intended to increase confidence in the results and demonstrate the viability of using open-source tools for high-fidelity marine energy modeling. This dataset includes all necessary files for actuator line simulations in openFOAM, as well as 2D blade-resolved CFD results, along with Python and Java scripts for setting up and post-processing simulations.
One of NASA's objectives is to be able to perform a complete, pre-flight, evaluation of cardiovascular changes in astronauts scheduled for prolonged space missions. Computational fluid dynamics (CFD) has shown promise as a method for estimating cardiovascular function during reduced gravity conditions. For this purpose, MRI can provide geometrical information, to reconstruct vessel geometries, and measure all spatial velocity components, providing location specific boundary conditions. The objective of this study was to investigate the reliability of MRI-based model reconstruction and measured boundary conditions for CFD simulations. An aortic arch model and a carotid bifurcation model were scanned in a 1.5T Siemens MRI scanner. Axial MRI acquisitions provided images for geometry reconstruction (slice thickness 3 and 5 mm; pixel size 1x1 and 0.5x0.5 square millimeters). Velocity acquisitions provided measured inlet boundary conditions and localized three-directional steady-flow velocity data (0.7-3.0 L/min). The vessel walls were isolated using NIH provided software (ImageJ) and lofted to form the geometric surface. Constructed and idealized geometries were imported into a commercial CFD code for meshing and simulation. Contour and vector plots of the velocity showed identical features between the MRI velocity data, the MRI-based CFD data, and the idealized-geometry CFD data, with less than 10% differences in the local velocity values. CFD results on models reconstructed from different MRI resolution settings showed insignificant differences (less than 5%). This study illustrated, quantitatively, that reliable CFD simulations can be performed with MRI reconstructed models and gives evidence that a future, subject-specific, computational evaluation of the cardiovascular system alteration during space travel is feasible.
As a result of certain transient scenarios, a thermally stratified layer of liquid sodium can develop in the bulk coolant volumes of a sodium-cooled fast reactor (SFR). In addition to the effects a stratification layer has on the temperature of the heat transport system, a stratification layer can also influence the transition to and establishment of natural circulation flow, which plays an important role in passive cooling and the inherent safety of a pool-type SFR. Therefore, the ability to accurately capture thermal stratification phenomena is important when demonstrating the safety basis of a pool-type SFR during transient sequences. The present work assesses various computational models with different fidelities in their ability to predict thermal stratification in the upper plenum of an SFR. Each computational model will be assessed using the data generated at the Thermal Stratification Test Facility (TSTF) located at the University of Wisconsin-Madison. Using measured flow rate and inlet temperature data, the measured temperature distributions of the tests are compared to the predictions of the lumped volume-based models in SAS4A/SASSYS-1, a 1D-based model in SAM, and a 3-D computational fluid dynamics (CFD) model using STAR-CCM+. The relative performance of the various computational methods is assessed with respect to key metrics such as bulk coolant temperature distribution and plenum exit temperature. A total of eight tests are analyzed, covering different combinations of flow rates (3 and 10 GPM) and upper internal structure (UIS) configurations (none, solid, porous, and open) The perfect mixing model of SAS4A/SASSYS-1 provides the highest accuracy when the flow rate is high and there is no UIS in the test vessel, as high flow rate injection promotes thermal mixing of the sodium in the test vessel. For most of the analyzed tests, the stratified volume model of SAS4A/SASSYS-1 is able to predict the delay in the outlet temperature drop and temperature distribution in the test vessel by a small number of layers to represent thermal stratification. However, the stratified volume model can only simulate a maximum of three temperature layers within a volume and when a layer approaches the elevation of the outlet, the predicted outlet temperature can demonstrate rapid, non-physical changes. The 1-D axial mixing model of SAM provides results that agree reasonably well with the measured data in the prediction of the temporal evolution of the outlet temperature with the exception of the case with a high flow rate and no UIS. The SAM 1-D model has a similar level of accuracy to CFD results when it comes to predicting the outlet temperature. CFD shows overall good agreement in predicting the temperature distribution in the test vessel and outlet temperature. As CFD can model the test vessel geometry in detail, it performs well in the cases of complex geometries such as tests that included a UIS and internal flow through the UIS resulting in active mixing of the coolant in the test vessel. Each of the models discussed in the present work has the potential to be useful during the various stages of reactor design, analysis, and licensing. The lumped-volume approach can be applied for fast turnaround safety calculations to obtain overall reactor behavior during transients. The 1-D models provide improved accuracy when stratification is expected for a relatively low increase in the computational cost. The CFD model can be utilized for confirmatory analysis of the 1-D model, when experimental measurements are not available.
NovoNutrients’ fermentation technology uses energy from hydrogen to transform industrial CO2 emissions into premium animal feed ingredients and other valuable products. A single NovoNutrients’ commercial manufacturing plant will capture and convert over 200,000 tons/yr of CO2 into over 100,000 tons/yr of high-protein feed. Key to the rapid and widespread deployment of the technology is maximization of its productivity and energy efficiency. Robust, physically based computational models of the technology will significantly increase productivity and efficiency, accelerating NovoNutrients’ technology to manufacturing scale. NREL has unique capabilities for creating and running such computational models. NREL's existing aerobic bioreaction computational fluid dynamics (CFD) models will be adapted to NovoNutrients’ gas fermentation (CO2, H2, O2) technology. The multiphysics CFD simulations require thousands of high-performance computing (HPC) node hours to simulate the complex geometries and contents of NovoNutrients’ industrial bioreactors. The experimentally validated CFD models were used to identify optimally efficient and productive bioreactor designs and operating conditions.
Dispersed particle-laden flows are encountered in many building and industrial applications, such as flow in a fluidized bed, hydrocarbon transportation in pipelines, and the fouling of air-cooled heat exchangers (Kuruneru et al., 2016; Ray et al., 2019; Wang et al., 2019). Computational fluid dynamic (CFD) models have been developed in recent years to depict particle-fluid and particle-particle interactions in laminar or turbulent flows with increasing accuracy and stability. One particular particle-laden system of interest for moisture control is electrically-enhanced condensation in air and water droplet flows. Electrically-enhanced condensation consists of the use of highly charged water droplets injected in the moist air. The droplets become electric seeds that attract polar water vapor molecules to their surfaces and promote condensation. The nucleation and growth of the charged droplets deplete the vapor phase near a droplet, which is compensated for by the dielectrophoresis flow and diffusion. Dielectrophoresis flow involves surrounding vapor at a distance of about 10 to 100 nm for droplets charged by an electrospray compared to ~2 nm for a single electron charge in a droplet. As the vapor molecules collapse on the surface of the droplets, their initial electrical charge decreases with time due to the neutralization of the ions. While the physics of this phenomena is well known, engineering models for predicting the condensation rates are not available. This work computationally investigates dehumidification of moist airflow in a converging rectangular duct. The objective is to develop an engineering model that predicts water vapor condensation by employing dielectrophoresis principles. We construct a Computational Fluid Dynamics (CFD) model of the duct with electrically-enhanced condensation. The model is implemented in the open-source software OpenFOAM. We utilize the Multi-Phase Particle-In-Cell (MP-PIC) method coupled with a Population Balance Equation (PBE) approach to simulate the particle-laden system. This methodology is an Eulerian-Lagrangian approach used to simulate the droplets' behavior in the humid air. The MP-PIC approach (Andrews and O'Rourke, 1996) mitigates the computational cost by parceling several fundamental particles with similar properties (such as types, sizes, and temperature) into one computational particle. Thus, the billions of particles can be substituted by millions of computational particles without significant loss of information. The PBE was considered with the Lagrangian frame to combine the particle distribution function used in MP-PIC (Kim et al., 2020). This approach preserves mass and energy conservation between the phases in the Eulerian and Lagrangian structures. The PBE in this procedure was directly linked to the discrete parcels, making the simulation of the particle distribution computationally efficient and robust. The MP-PIC-PBE approach used in the present work was applied to the dehumidification of air. Water droplets were injected in the air stream and forced to grow according to experimentally derived correlation. The experiments were conducted on a converging duct with the same geometry and boundary conditions used to build the CFD model. This approach enabled us to approximate the effect of dielectrophoresis phenomena on the droplet and air interface. This presentation will discuss the details of the new CFD model built for the duct, the implementation of the model in OpenFOAM CFD programming language, and the experimental validation of the newly developed model. The results revealed a moderate yet measurable increase in droplet diameter due to water vapor condensation at the vapor-liquid interface of the electrically charged droplets' surface. The seed water droplet particles grew in size by capturing the water vapor in the surrounding air. The OpenFOAM model predicted reductions of humidity in the air from 5 to 10 percent.
Regulatory agencies are considering alternative approaches to assessing inhalation toxicity that utilizes in vitro studies with human cells and in silico modeling in lieu of additional animal studies. In support of this goal, computational fluid-particle dynamics models were developed to estimate site-specific deposition of inhaled aerosols containing the fungicide, chlorothalonil, in the rat and human for comparisons to prior rat inhalation studies and new human in vitro studies. Under bioassay conditions, the deposition was predicted to be greatest at the front of the rat nose followed by the anterior transitional epithelium and larynx corresponding to regions most sensitive to local contact irritation and cytotoxicity. For humans, simulations of aerosol deposition covering potential occupational or residential exposures (1–50 µm diameter) were conducted using nasal and oral breathing. Aerosols in the 1–5 µm range readily penetrated the deep region of the human lung following both oral and nasal breathing. Under actual use conditions (aerosol formulations >10 µm), the majority of deposited doses were in the upper conducting airways. Beyond the nose or mouth, the greatest deposition in the pharynx, larynx, trachea, and bronchi was predicted for aerosols in the 10–20 µm size range. Only small amounts of aerosols >20 µm penetrated past the pharyngeal region. Using the ICRP clearance model, local retained tissue dose metrics including maximal concentrations and areas under the curve were calculated for each airway region following repeated occupational exposures. These results are directly comparable with benchmark doses from in vitro toxicity studies in human cells leading to estimated human equivalent concentrations that reduce the reliance on animals for risk assessments.
Gas fermentation has emerged as a promising new technology for the generation of fuels and chemicals from mixtures of greenhouse and energy rich gas streams (CO2/CH4/H2/CO) via microbial bioreaction. Example pathways include biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Effective Gas-liquid mass-transfer is an important physical phenomenon that determines the design and scale-up of these systems. There is currently a knowledge-gap regarding bubble-size distributions when using a mixture of gases with vastly different properties, which can have a significant impact on overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a detailed multiphase computational-fluid-dynamics (CFD) model to study the impact of gas-mixtures on overall mass-transfer in bubble column and air-lift reactors. The CFD tool previously developed by the authors (1) for simulating aerobic fermentation reactors at scale is used in this study. The Reynolds-averaged mass, momentum, energy, and species transport equations are solved for interpenetrating gas and liquid phase in this model. We use a population balance-based bubble-size-distribution model that is validated against small-scale experiments in our solver. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient is analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors.
Information is given in viewgraph form for turbulence modeling in computational fluid dynamics (CFD). The Eddy Viscosity Models (EVM), Algebraic Second Moment Closures (ASM), and Differential Second-Moment Closures (DSM) are considered. It is concluded that EVM's, ASM's, and DSM's will remain in use, though with a steady decline in importance of EVM's and ASM's in favor of DSM's. Improved versions of low-Re two-equation EVM's should lead to more reliable predictions of separated flows than are achievable at present. Further refinement of sub-models in second moment closures can be expected throughout this decade. There will be increasing attention given to interfacing SMC with higher order approaches such as LES, and an increased use of two-time-scale schemes providing distinct time scales for large and fairly small eddies.