Search NASA⌕ Search

SEARCH · Search NASA

Results for “PRANDTL NUMBER”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

High-Fidelity Numerical Investigation on Elucidating Sodium Heat Transfer Characteristics for 37-Pin Wire-Wrapped Fuel Bundle in the PLANDTL Facility

This study involved a Reynolds-averaged Navier-Stokes- (RANS-) based computational fluid dynamics (CFD) analysis of the 37-pin wire-wrapped fuel bundle of the PNC Plant dynamics test loop (PLANDTL) facility. Previously, mainly the hydrodynamic phenomena of the wire-wrapped fuel bundle were analyzed, but the present study additionally included heat transfer analysis through conjugate heat transfer. The main purpose of the study was to benchmark the experimental data of the PLANDTL 37-pin wire-wrapped fuel bundle to investigate the heat transfer phenomena. In addition, the aim was to verify the accuracy of the RANS-based CFD analysis method using the STAR-CCM+ simulation software in comparison with the experimental data. The grid used for verification was an innovative grid system consisting of hexahedra using Fortran-based code. The development of the RANS-based CFD methodology included grid sensitivity analysis, turbulence model sensitivity analysis, and turbulent Prandtl number sensitivity analysis. Information on the temperature, mass flow rate, and area of the CFD results for each subchannel was provided for the top of the heated section and is expected to serve as a reference for future studies aiming to perform the validation and verification of a PLANDTL facility. In addition, the dependence of the peak temperature on the azimuth angle of each pin was analyzed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Development of an Efficient Meso- scale Multi-phase Flow Solver in Nuclear Applications

The proposed research aims at formulating a predictive high-order Lattice Boltzmann Equation for multi-phase flows relevant to nuclear energy related application - namely, saturated and sub-cooled boiling in reactors, and liquid- liquid mixing and extraction for fuel cycle separation. An efficient flow solver will be developed based on the Finite Element based Lattice Boltzmann Method (FE- LBM), accounting for phase-change heat transfer and capable of treating multiple phases over length scales from the submicron to the meter. A thermal LBM will be developed in order to handle adjustable Prandtl number, arbitrary specific heat ratio, a wide range of temperature variations, better numerical stability during liquid-vapor phase change, and full thermo-hydrodynamic consistency. Two-phase FE-LBM will be extended to liquid–liquid–gas multi-phase flows for application to high-fidelity simulations building up from the meso-scale up to the equipment sub-component scale. While several relevant applications exist, the initial applications for demonstration of the efficient methods to be developed as part of this project include numerical investigations of Critical Heat Flux (CHF) phenomena in nuclear reactor fuel bundles, and liquid-liquid mixing and interfacial area generation for liquid-liquid separations. In addition, targeted experiments will be conducted for validation of this advanced multi-phase model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

SAM Theory Manual

The System Analysis Module (SAM) is an advanced and modern system analysis tool being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM development aims for advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability for reactor transient analyses. To facilitate the code development, SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SAM focuses on modeling advanced reactor concepts such as SFRs (sodium fast reactors), LFRs (lead-cooled fast reactors), and FHRs (fluoride-salt-cooled high temperature reactors) or MSRs (molten salt reactors). These advanced concepts are distinguished from light-water reactors in their use of single-phase, low-pressure, high-temperature, and low Prandtl number (sodium and lead) coolants. As a new code development, the initial effort has been focused on modeling and simulation capabilities of heat transfer and single-phase fluid dynamics responses in Sodium-cooled Fast Reactor (SFR) systems. The system-level simulation capabilities of fluid flow and heat transfer in general engineering systems and typical SFRs have been verified and validated. This document provides the theoretical and technical basis of the code to help users understand the underlying physical models (such as governing equations, closure models, and component models), system modeling approaches, numerical discretization and solution methods, and the overall capabilities in SAM. As the code is still under ongoing development, this SAM Theory Manual will be updated periodically to keep it consistent with the state of the development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Thermal-Hydraulics Modeling and Simulations of Hot Pool Using the SAS-CFD Coupled Code

The main goal of this activity is to test the dynamic coupling of the SAS4A/SASSYS-1 (SAS) and CFD models, using a recently patched version of the SAS code intended to address an undocumented limitation that hindered the Versatile Test Reactor (VTR) simulation efforts in FY21. As described in previous VTR calculation reports, the undocumented limitation in SAS v5.4 does not allow the user to activate the CFD coupling option during restart calculations. Since the analysts were unaware of this limitation, prior SAS-CFD simulation results for the protected station blackout (PSBO) transient were erroneous. Root-cause analysis was performed to determine the cause of this undocumented limitation in SAS v5.4, the SAS software was updated in a new patch, and the SAS-CFD simulations were repeated with this patched software. The results of the SAS-CFD simulations documented in this report show that the software patch does address the cited issue, and that the patched software indeed supports the activation of the CFD coupling model in restart calculations. The SAS development team will determine the schedule for implementing the patch in an official software release. This report documents updated SAS-CFD simulations of the PSBO transient response in the VTR. The hot pool is modeled with the CFD code STAR-CCM+, which is coupled at the flow boundaries to the SAS model of the primary heat transport system. SAS computes the mass flow rate and temperature at each core subassembly outlet, the thermal insulation cavity bypass, and the IHX inlet windows. CFD in turn computes the absolute pressure and temperature at each of these boundaries. The SAS code will ignore the temperature data at flow boundaries where flow is directed into the hot pool, i.e., at the core subassembly outlets unless flow reversal occurs. Similarly, CFD will ignore temperature data at boundaries where the flow is directed out of the hot pool, i.e., at the IHX inlets except under flow reversal. The focus of this work is to ensure that the SAS software patch addresses the undocumented limitation described in prior VTR calculation reports, rather than the accurate assessment of thermal stratification in the VTR during protected transients. This motivates the development of a new, simplified CFD model with a coarser mesh to accelerate the testing process. The updated model, and simplifying assumptions, are documented in this report. In future work, the thermal stratification assessment should be performed in more detail. The simplified CFD model can be improved by performing grid convergence studies sensitivity studies of turbulence parameters (e.g., Prandtl number, turbulence production and dissipation parameters) on temperature distributions and thermal stratification.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Parametric model-order-reduction development for unsteady convection

A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.

leray regularization↗
DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗
DOE OSTI2018

Fluctuation Dynamo in a Collisionless, Weakly Magnetized Plasma

Results from a numerical study of fluctuation dynamo in a collisionless, weakly magnetized plasma are presented. The key difference between this dynamo and its magnetohydrodynamic (MHD) counterpart is the adiabatic production of magnetic-field-aligned pressure anisotropy by the amplification of a weak seed field. This, in turn, drives kinetic instabilities on the ion-Larmor scale—namely, firehose and mirror—which sever the adiabatic link between the thermal and magnetic pressures, thereby allowing the dynamo to proceed. After an initial phase of rapid growth driven by these instabilities, the magnetic energy grows exponentially and exhibits a ${k}^{3/2}$ spectrum that peaks near the resistive scale, similar to the large-magnetic-Prandtl-number ($\mathrm{Pm}\gg 1$) MHD dynamo. The magnetic field self-organizes into a folded-sheet topology, with direction reversals at the resistive scale and field lines curved at the parallel scale of the flow. The effective $\mathrm{Pm}$ is determined by whether the ion-Larmor scale is above or below the field-reversing scale: in the former case, particles undergo Bohm-like diffusion; in the latter case, particles scatter primarily off of firehose fluctuations residing at the ends of the magnetic folds, and the viscosity becomes anisotropic. The magnetic field ultimately saturates at dynamical strengths, with its spectral peak migrating toward larger scales. This feature, along with an anti-correlation of magnetic-field strength and field-line curvature and a gradual thinning of magnetic sheets into ribbons, resembles the saturated state of the large-$\mathrm{Pm}$ dynamo, the primary differences manifesting in firehose/mirror-unstable regions. Furthermore, these results have implications for magnetic-field growth in the weakly collisional intracluster medium of galaxy clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Estimating turbulent energy flux vertical profiles from uncrewed aircraft system measurements: exemplary results for the MOSAiC campaign

This study analyzes turbulent energy fluxes in the Arctic atmospheric boundary layer (ABL) using measurements with a small uncrewed aircraft system (sUAS). Turbulent fluxes constitute a major part of the atmospheric energy budget and influence the surface heat balance by distributing energy vertically in the atmosphere. However, only few in situ measurements of the vertical profile of turbulent fluxes in the Arctic ABL exist. The study presents a method to derive turbulent heat fluxes from DataHawk2 sUAS turbulence measurements, based on the flux gradient method with a parameterization of the turbulent exchange coefficient. This parameterization is derived from high-resolution horizontal wind speed measurements in combination with formulations for the turbulent Prandtl number and anisotropy depending on stability. Measurements were taken during the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) expedition in the Arctic sea ice during the melt season of 2020. For three example cases from this campaign, vertical profiles of turbulence parameters and turbulent heat fluxes are presented and compared to balloon-borne, radar, and near-surface measurements. The combination of all measurements draws a consistent picture of ABL conditions and demonstrates the unique potential of the presented method for studying turbulent exchange processes in the vertical ABL profile with sUAS measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Time-resolved turbulent dynamo in a laser plasma

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas (Pm<1). However, the same framework proposes that the fluctuation dynamo should operate differently when Pm≳1, the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports an experiment that creates a laboratory Pm≳1 plasma dynamo. We provide a time-resolved characterization of the plasma’s evolution, measuring temperatures, densities, flow velocities, and magnetic fields, which allows us to explore various stages of the fluctuation dynamo’s operation on seed magnetic fields generated by the action of the Biermann-battery mechanism during the initial drive-laser target interaction. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude and saturate dynamically. It is shown that the initial growth of these fields occurs at a much greater rate than the turnover rate of the driving-scale stochastic motions. Our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized magnetohydrodynamics (MHD) simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1962

Thermodynamic and Transport Property Correlation Formulas for Equilibrium Air from 1,000 Degrees Kelvin to 15,000 Degrees Kelvin

The thermodynamic properties, density and temperature, as well as transport property parameters involving viscosity, Prandtl number (including diffusion effects), and gaseous radiation absorption coefficients have been correlated as a function of enthalpy at four pressure levels (10 (sup -1), 10 (sup 0), 10, and 10 (sup 2) atmospheres). The correlation formulas are written in a generalized form for which coefficients for a particular property and pressure level are tabulated. The correlation formulas are useful in digital computer programs for non-adiabatic viscous flow problems.

AIR↗
NASA NTRS1969

Properties of air and combustion products of fuels with air

Thermodynamic and transport properties include ratio of specific heats, molecular weight, viscosity, heat capacity, thermal conductivity, and Prandtl number. Properties are calculated from 300 to 2500 degrees K and for pressures of three and ten atmospheres.

Lewandowski, K.↗
NASA NTRS1971

Transient-forced convection film boiling on an isothermal flat plate

An approach for the solution of transient-forced convection film boiling on an isothermal flat plate using the boundary layer model is developed. The similarity variables are used to convert the governing partial differential equations to ordinary ones. The results of numerical solutions of these ordinary equations indicate that the transient process can be classified as one-dimensional conduction, intermediate, and the steady state regions. The time required for the one-dimensional conduction and the time necessary to attain a steady state condition are obtained. The influence of interfacial shear is seen to be negligible while the Prandtl Number and the ratio (C sub p delta T divided by h sub fg times Pr) have major influence. The use of local similarity approximations for the intermediate regime facilitates prediction of complete boundary layer growth. Using the ratio of time at any instant to the steady state time as abscissa, the curves representing the boundary layer growth can be merged into a single mean curve within 5 percent. Further, the analysis shows that the average rate of heat transfer during transient is 50 to 100 percent higher than those at steady state. The average rate of vapor convected away is 10 to 15 percent lower than at steady state while the average rate of accumulation to form the vapor layer is 1 to 14 times larger. Further, the total heat transferred during transient increases and the evaporation decreases for increasing values of C sub p delta T divided by h sub fg times Pr

Nagendra, H. R.↗
NASA NTRS1971

Finite difference solution to the three-dimensional, incompressible thermal energy boundary-layer equation

An implicit numerical method has been adopted for the solution to the three-dimensional, energy boundary-layer equation. The energy equation is written in terms of a dimensionless temperature function, the relative stagnation-enthalpy difference, and transformed by the introduction of a Blasius-type transformation of coordinates as well as dimensionless stream functions. The method is applied to the problem consisting of an infinite cylinder joined with its axis perpendicular to a thin, flat, heated plate. A Prandtl number equal to one is simply considered.

Fillo, J. A.↗
NASA NTRS1972

Computer program for solving compressible nonsimilar-boundary-layer equations for laminar, transitional, or turbulent flows of a perfect gas

A computer program is described which solves the compressible laminar, transitional, or turbulent boundary-layer equations for planar or axisymmetric flows. Three-point implicit difference relations are used to reduce the momentum and energy equations to finite-difference form. These equations are solved simultaneously without iteration. Turbulent flow is treated by the inclusion of either a two-layer eddy-viscosity model or a mixing-length formulation. The eddy conductivity is related to the eddy viscosity through a static turbulent Prandtl number which may be an arbitrary function of the distance from the wall boundary. The transitional boundary layer is treated by the inclusion of an intermittency function which modifies the fully turbulent model. The laminar-boundary-layer equations are recovered when the intermittency is zero, and the fully turbulent equations are solved when the intermittency is unity.

Price, J. M.↗
NASA NTRS1972

Thermophysical properties of parahydrogen from the freezing liquid line to 5000 R for pressures to 10000 psia

The tables include entropy, enthalpy, internal energy, density, volume, speed of sound, specific heat, thermal conductivity, viscosity, thermal diffusivity, Prandtl number, and the dielectric constant for 65 isobars. Quantities of special utility in heat transfer and thermodynamic calculations are also included in the isobaric tables. In addition to the isobaric tables, tables for the saturated vapor and liquid are given, which include all of the above properties, plus the surface tension. Tables for the P-T of the freezing liquid, index of refraction, and the derived Joule-Thomson inversion curve are also presented.

Mccarty, R. D.↗
NASA NTRS1971

The three-dimensional steady radial expansion of a viscous gas from a sonic source into a vacuum.

The three-dimensional steady radial expansion of a viscous, heat-conducting, compressible fluid from a spherical sonic source into a vacuum is analyzed using the Navier-Stokes equations as a basis. It is assumed that the model fluid is a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Limiting forms for the flow variable solutions are studied for the Reynolds number based on the sonic source conditions, going to infinity and the Newtonian parameter both fixed and going to zero. For the case of the viscosity-temperature exponent between .5 and 1, it is shown that the velocity as well as the pressure approach zero as the radial distance goes to infinity. The formulations of the distinct regions that span the domain extending from the sonic source to the vacuum are presented.

Bush, W. B.↗
NASA NTRS1971

A numerical investigation into the effects of compressibility and total enthalpy difference on the development of a laminar free shear layer.

A method is presented for integrating numerically the equations of motion for a compressible free shear layer developing from a boundary-layer profile of arbitrary shape. Sutherland's law is used to determine the coefficient of viscosity and the Prandtl number is taken as 0.72. Calculated results are reported for free-stream Mach numbers ranging from 0 to 10 and for stagnation-enthalpy ratios ranging from 0 to 5.0. The effects of varying the initial boundary-layer profile and of a discontinuity in temperature at the origin are also studied. The results include graphs showing the development of dividing-streamline velocity, of local Nusselt number, and of dividing-streamline location.

Carpenter, P. W.↗