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Latest developments in the MOOSE fluid properties module

The fluid properties module in MOOSE serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, SAM~\cite{sam}, the MOOSE thermal hydraulics module, RELAP-7~\cite{relap7} and subchannel~\cite{subchannel}. It is used for coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled simulations~\cite{anl_sam_pgh}. The module offers a consistent set of interfaces to implement to create a new fluid property. There are numerous fluid properties of interest in the entirety of all fields of fluid flow simulations, and this is exacerbated by the use of different variable sets depending on the compressibility of the fluid. For single-phase fluids, the following variable sets may be used to compute fluid properties: (pressure, temperature) and (specific volume, specific internal energy). Some properties may also be computed using the (pressure, density) or the (specific volume, specific enthalpy) variable sets. In order to reduce the challenge of adding a new fluid property, properties may be implemented partially.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The MOOSE fluid properties module

The fluid properties module in MOOSE~\cite{lindsay2022moose} serves a variety of fluid simulation applications based on MOOSE, including the MOOSE Navier Stokes module~\cite{moose_ns}, Pronghorn~\cite{pgh}, the MOOSE thermal hydraulics module, SAM~\cite{sam}, RELAP-7~\cite{relap7}, Sockeye~\cite{sockeye}, Pronghorn-subchannel~\cite{subchannel} and the MOOSE porous flow module~\cite{porous}. These applications are used to solve coarse mesh multi-dimensional thermal-hydraulics~\cite{pgh}, 1D systems analysis~\cite{sam,relap7} in nuclear reactor analysis, heat pipe modeling~\cite{sockeye} and porous flow simulations~\cite{porous} for underground gas storage and water seepage. The use of consistent fluid properties across fluid flow applications facilitates coupled flow simulations~\cite{anl_sam_pgh,osti_1889653}. Each application has historically driven the implementation of several fluid properties, which were later extended to be compatible with other applications. The unique diversity of applications of the module, due to its presence in MOOSE, has driven its expansion to new fluids, such as advanced nuclear reactor coolants and, more recently, arbitrary functions or tables-based property definitions, as detailed in section~\ref{content}, as well as numerous thermophysical properties and variable sets, as detailed in subsection~\ref{sec:prop}. The need for different discretizations of flow equations based on the compressibility of the fluid has motivated support for both primitive (pressure- and temperature-based) and conservative (internal energy- and specific volume-based) flow variables in the module. Thermodynamic relations are used to convert between these two formulations, as needed. The module serves a dual purpose of providing fluid properties for direct use in flow simulations and facilitating the implementation of user-specific fluid properties. Contributions of new properties for existing fluids or new fluids are strongly encouraged.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The MOOSE fluid properties module

The Fluid Properties module within the Multiphysics Object-Oriented Simulation Environment (MOOSE) is used to compute fluid properties for numerous applications, ranging from nuclear reactor thermal hydraulics to geothermal energy. Those applications drove the development of the module to enable numerous different fluid equations of states, property lookups with primitive and conserved flow variable to cater to pressure and density-driven solvers, and an object-oriented design facilitating expansion and maintenance. Each fluid property is implemented in its own class but inherits capabilities such as automatic differentiation, automated out-of-bounds handling or variable conversion capabilities. Here, this paper presents the module, its design, its user and developer interface, its content in terms of fluids and properties, and several of its applications showing its major role in the MOOSE simulation ecosystem.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fluid property measurements study

Fluid properties of refrigerant-21 were investigated at temperatures from the freezing point to 423 Kelvin and at pressures to 1.38 x 10 to the 8th power N/sq m (20,000 psia). The fluid properties included were: density, vapor pressure, viscosity, specific heat, thermal conductivity, thermal expansion coefficient, freezing point and bulk modulus. Tables of smooth values are reported.

Devaney, W. E.↗

Tabulated Fluid Properties Research Report

The Multiphysics Object-Oriented Simulation Environment (MOOSE) enables a wide range of advanced nuclear reactor simulations.[6] Under the guidance of MOOSE’s Thermal Hydraulics Team,I worked to expand the capabilities of Tabulated Fluid Properties (TFP) in the fluid properties module. The fluid properties module allows the user to determine a variety of fluid properties by interpolating points between tabulated data. I implemented the ability to use bilinear interpolation instead of bicubic interpolation for interpolating tabulated data. I also changed the method of variable set inversions to use a 2-dimensional Newton’s Method utility that I created. Variable set inversions are often done from (v,e) to (p,T), where v is specific volume, e is specific internal energy, p is pressure and T is temperature. New routines have also been added into TFP such that it can be used with more applications, such as the Navier Stokes and Thermal Hydraulics modules in MOOSE for Pronghorn[5] and RELAP-7[1] respectively. This work was spurred by interest from NASA in testing a Nuclear Thermal Propulsion (NTP) engine system. NTP engines have drastically different fluid properties throughout the engine and Tabulated Fluid Properties provides the flexibility needed to properly simulate and test these engines.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Engineering Approach to the Variable Fluid Property Problem in Free Convection

An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Gregg, J. L.↗

Fluid Properties for MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) enables a wide range of advanced nuclear reactor simulations. Under the guidance of MOOSE's Finite Volume Team, we worked on the fluid properties module. Significant contributions include enabling Tabulated Fluid Properties (TFP) for systems thermal hydraulics analysis, Temperature and Pressure functionalized Fluid Properties, and Lead & Lead-Bismuth properties. Along with improving the capabilities of the fluid properties module, we also improved the documentation to allow for future users and developers to understand how the module works.

97 MATHEMATICS AND COMPUTING↗

Fluid property and operational effects on swirl injector atomization

Results of atomization tests of rocket injection elements are correlated in terms of the test fluid properties and the injection element operating conditions. The type of element modeled has a central, swirling liquid oxidizer flow; and a coaxial, axial gaseous fuel flow. Results of the correlations describe the effect of geometry, fluid properties, and operating conditions on liquid atomization. The ranges of test conditions allow reasonable extrapolation to actual high-pressure engine operating conditions. At such conditions, the swirl element should produce exceptionally finely-atomized and well-distributed spray for high combustion performance. United Technologies Research Center (UTRC) completed a test program to measure fluid spray atomization, in terms of droplet size and droplet size distributions, for swirling-flow injection elements. Element sizes and dimensions covered ranges of dimensions representative of typical cryogenic (O2/H2) liquid rocket engine practice. Relevant dimensions include the element diameter, the tangential-entry metering slot length, and the coastal fuel slot radial gap. Test fluids included water, simulated Jet-A, and Freon 113. These fluids cover ranges of properties which include or approach those of liquid oxygen. Gaseous nitrogen simulated the coaxial gaseous hydrogen fuel flow.

Cox, G. B., Jr.↗

Analytical investigation of fully developed laminar flow in tubes with heat transfer with fluid properties variable along the radius

Relations were analytically obtained for the prediction of radial distributions of velocity and temperature for fully developed laminar flow of gases and of liquid metals in tubes with fluid properties variable along the radius. The relations are applicable to both heating and cooling of the fluid. By use of the relations for velocity and temperature distributions, relations were obtained among Nusselt number, friction parameter, and ratio of wall to bulk temperature. The Nusselt number and friction parameter were found to be independent of Reynolds number and Prandtl number. The effects of ratio of wall to bulk temperature on Nusselt number and friction parameter could be eliminated by evaluating the fluid properties at specified temperatures in the fluid.

Deissler, Robert G↗

Extension of Generalized Fluid System Simulation Program's Fluid Property Database

This internship focused on the development of additional capabilities for the General Fluid Systems Simulation Program (GFSSP). GFSSP is a thermo-fluid code used to evaluate system performance by a finite volume-based network analysis method. The program was developed primarily to analyze the complex internal flow of propulsion systems and is capable of solving many problems related to thermodynamics and fluid mechanics. GFSSP is integrated with thermodynamic programs that provide fluid properties for sub-cooled, superheated, and saturation states. For fluids that are not included in the thermodynamic property program, look-up property tables can be provided. The look-up property tables of the current release version can only handle sub-cooled and superheated states. The primary purpose of the internship was to extend the look-up tables to handle saturated states. This involves a) generation of a property table using REFPROP, a thermodynamic property program that is widely used, and b) modifications of the Fortran source code to read in an additional property table containing saturation data for both saturated liquid and saturated vapor states. Also, a method was implemented to calculate the thermodynamic properties of user-fluids within the saturation region, given values of pressure and enthalpy. These additions required new code to be written, and older code had to be adjusted to accommodate the new capabilities. Ultimately, the changes will lead to the incorporation of this new capability in future versions of GFSSP. This paper describes the development and validation of the new capability.

Patel, Kishan↗

Real fluid properties of normal and parahydrogen

Computer program calculates the real fluid properties of normal or parahydrogen using a library of single function calls without initial estimates. Accurate transport and thermodynamic properties of molecular hydrogen are needed for advanced propulsion systems.

Goldberg, F. N.↗

Analysis of Turbulent Flow and Heat Transfer on a Flat Plate at High Mach Numbers with Variable Fluid Properties

A previous analysis of turbulent heat transfer and flow with variable fluid properties in smooth passages is extended to flow over a flat plate at high Mach numbers, and the results are compared with experimental data. Velocity and temperature distributions are calculated for a boundary layer with appreciative effects of frictional heating and external heat transfer. Viscosity and thermal conductivity are assumed to vary as a power or the temperature, while Prandtl number and specific heat are taken as constant. Skin-friction and heat-transfer coefficients are calculated and compared with the incompressible values. The rate of boundary-layer growth is obtained for various Mach numbers.

Deissler, R. G.↗

Updated, expanded, fluid properties handbook

Revised handbook presents quantitative data, in the form of graphs and charts, pertaining to thermodynamic properties of specific cryogenic fluids and several metals. References to sources of data are cited.

Gershman, R.↗

Consideration of Alternate Working Fluid Properties in Gas Lubricated Foil Journal Bearings

The Oil-Free Turbomachinery Program at the NASA Glenn Research center is committed to, revolutionary improvements in performance, efficiency and reliability of turbomachinery propulsion systems. One of the key breakthroughs by which this goal is being achieved is the maturation of air lubricated foil bearing technology. Through experimental testing, foil bearings have demonstrated a variety of exceptional qualities that show them to have an important role in the future of rotordynamic lubrication. Most of the work done with foil bearings thus far has considered ambient air at atmospheric pressure as the working fluid or lubricating fluid in the bearing. However, special applications of oil-free technology require the use of air at non- standard ambient conditions or completely different working fluids altogether. The NASA Jupiter Icy Moon Orbiter program presents power generation needs far beyond that of any previous space exploration effort. The proposed spacecraft will require significant power generation to provide the propulsion necessary to reach the moons of Jupiter and navigate between them. Once there, extensive scientific research will be conducted that will also present significant power requirements. Such extreme needs require exploring a new method for power generation in space. A proposed solution involves a Brayton cycle nuclear fission reactor. The nature of this application requires reliable performance of all reactor components for many years of operation under demanding conditions. This includes the bearings which will be operating with an alternative working fluid that is a combination of Helium and Xenon gases commonly known as HeXe. This fluid has transport and thermal properties that vary significantly from that of air and the effect of these property differences on bearing performance must be considered. One of the most promising applications of oil-free technology is in aircraft turbine engines. Eliminating the oil supply systems from aircraft engines will lead to significant weight and maintenance reduction. In such applications, the lubricating fluid will be high altitude air. This air will be at much lower pressure than that at sea level. Again this property change will result in a change in bearing performance, and analysis is required to quantify this effect. The study of these alternate working fluid properties will be conducted in two ways: analytically and experimentally. Analytical research will include the use of a mathematical code that can predict film thickness profiles for various ambient conditions. Estimations of load capacity can be made based upon the film thickness trends. These values will then be compared to those obtained from classical rigid bearing analysis. Experimental Research will include testing a foil bearing at a variety of ambient air pressures. The analytical and experimental data will be compared to draw conclusions on bearing performance under alternate working fluid properties.

Smith, Matthew J.↗

Implementation of High Temperature and Pressure fluid property interpolation tables

This document describes the use of module property_interpolate by John Doherty (Doherty,2006). The document “Fast Lookup of CO 2 Properties” describes the numerical details associated with lookup table. Rajeh Pawar modified property_interpolate for easier implementation in the FEHM code. George Zyvoloski modified the package to produce tables for water and air at very high temperatures and pressures. He also modified the auxiliary codes(drivers) to use newer datasets from the National Institute of Standards and Technology. We note here that within the files associated with FEHM there three property_interpolate modules. They are interpolate_2a.f90 (water), interpolate_2b.f90 (air) , and interpolate_2c.f90(CO 2 ). The interpolate_2c module is different than the earlier module produced by Rajeh Pawar in that it includes high temperature and pressure data. While FEHM has a number of fluid physics modules, this document will describe only the software and algorithms associated with water, water vapor, and heat (WH).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗