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NASA NTRS2010

Turbulence and Global Properties of the Solar Wind

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations was noted. The high corrections suggest that the fluctuations are Alfven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations. The plasma in the magnetic tail of Earth's magnetosphere also shows aspects of turbulence, as does the plasma in the dayside magnetosphere near the poles the dayside cusps. Recently, new analyses of high time resolution magnetic field data from Cluster have offered a glimpse of how turbulence is dissipated, thus heating the ambient plasma.

Goldstein, Melvyn L.↗
NASA NTRS1999

Overview of Fluid Dynamics Activities at the Marshall Space Flight Center

Since its inception 40 years ago, Marshall Space Flight Center (MSFC) has had the need to maintain and advance state-of-the-art flow analysis and cold-flow testing capability to support its roles and missions. This overview discusses the recent organizational changes that have occurred at MSFC with emphasis on the resulting three groups that form the core of fluid dynamics expertise at MSFC: the Fluid Physics and Dynamics Group, the Applied Fluid Dynamics Analysis Group, and the Experimental Fluid Dynamics Group. Recently completed activities discussed include the analysis and flow testing in support of the Fastrac engine design, the X-33 vehicle design, and the X34 propulsion system design. Ongoing activities include support of the RLV vehicle design, Liquid Fly Back Booster aerodynamic configuration definition, and RLV focused technologies development. Other ongoing activities discussed are efforts sponsored by the Center Director's Discretionary Fund (CDDF) to develop an advanced incompressible flow code and to develop optimization techniques. Recently initiated programs and their anticipated required fluid dynamics support are discussed. Based on recent experiences and on the anticipated program needs, required analytical and experimental technique improvements are presented. Due to anticipated budgetary constraints, there is a strong need to leverage activities and to pursue teaming arrangements in order to advance the state-of-the-art and to adequately support concept development. Throughout this overview there is discussion of the lessons learned and of the capabilities demonstrated and established in support of the hardware development programs.

Garcia, Roberto↗
NASA NTRS2005

Users' Manual for Computer Code SPIRALI Incompressible, Turbulent Spiral Grooved Cylindrical and Face Seals

The SPIRALI code predicts the performance characteristics of incompressible cylindrical and face seals with or without the inclusion of spiral grooves. Performance characteristics include load capacity (for face seals), leakage flow, power requirements and dynamic characteristics in the form of stiffness, damping and apparent mass coefficients in 4 degrees of freedom for cylindrical seals and 3 degrees of freedom for face seals. These performance characteristics are computed as functions of seal and groove geometry, load or film thickness, running and disturbance speeds, fluid viscosity, and boundary pressures. A derivation of the equations governing the performance of turbulent, incompressible, spiral groove cylindrical and face seals along with a description of their solution is given. The computer codes are described, including an input description, sample cases, and comparisons with results of other codes.

Walowit, Jed A.↗
NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗
NASA NTRS1986

Influence of friction dampers on torsional blade flutter

This paper deals with the stabilizing effects of dry friction on torsional blade flutter. A lumped parameter model with single degree of freedom per blade has been used to represent the rotor stage. The well-known cascade theories for incompressible and supersonic flows have been used to determine the allowable increase in fluid velocity relative to the blade. It has been found that the effectiveness of friction dampers in controlling flutter can be substantial.

Sinha, A.↗
NASA NTRS1989

Galerkin/least-squares procedures in computational fluid dynamics

The application of Galerkin/least-squares methodology to computational fluid dynamics is reviewed. Applications to advective-diffusive systems of equations and incompressible and compressible Euler and Navier-Stokes equations are described. Space-time finite-element methodology for time-dependent problems is emphasized and the status and role of so-called 'discontinuity-capturing operators' is reviewed.

Hughes, Thomas J. R.↗
NASA NTRS1991

CFD Applications in Propulsion

An overview of various applications of Computational Fluid Dynamics (CFD) algorithms to propulsion problems is given. Topics of interest include incompressible, low speed compressible, transonic, and supersonic problems. A common family of algorithms is used for all applications and emphasis is placed on maintaining accuracy and convergence efficiency for all problems. Specific problems include pump hydrodynamics, simultaneous combustion and mixing in rocket engines, viscous nozzle flow, and CFD applications to combustion stability.

Merkle, Charles L.↗
NASA NTRS1991

Development of an integrated BEM approach for hot fluid structure interaction

The development of a boundary element formulation for the study of hot fluid-structure interaction in earth-to-orbit engine hot section components is described. The initial primary thrust of the program to date was directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state. This required the development of integral formulations for both the solid and fluid, and some preliminary infrastructural enhancements to a boundary element code to permit coupling of the fluid-structure problem. Boundary element formulations are implemented in two dimensions for both the solid and the fluid. The solid is modeled as an uncoupled thermoelastic medium under plane strain conditions, while several formulations are investigated for the fluid. For example, both vorticity and primitive variable approaches are implemented for viscous, incompressible flow, and a compressible version is developed. All of the above boundary element implementations are incorporated in a general purpose two-dimensional code. Thus, problems involving intricate geometry, multiple generic modeling regions, and arbitrary boundary conditions are all supported.

Dargush, Gary F.↗
NASA NTRS1994

Hydrodynamics of rotating stars and close binary interactions: Compressible ellipsoid models

We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids, and the hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. Both viscous dissipation and the gravitational radiation reaction are incorporated. We establish the validity of our approximations and demonstrate the simplicity and power of the method by rederiving a number of known results concerning the stability and dynamical oscillations of rapidly rotating polytropes. In particular, we present a generalization to compressible fluids of Chandrasekhar's classical results for the secular and dynamical instabilities of incompressible Maclaurin spheroids. We also present several applications of our method to astrophysical problems of great current interest, such as the tidal disruption of a star by a massive black hole, the coalescence of compact binaries driven by the emission of gravitational waves, and the development of instabilities in close binary systems.

Lai, Dong↗
NASA NTRS2007

Turbulence and Global Properties of the Solar Wind

The solar wind shows striking characteristics that suggest that it is a turbulent magnetofluid, but the picture is not altogether simple. From the earliest observations, a strong correlation between magnetic fluctuations and plasma velocity fluctuations as noted. The high corrections suggest that the fluctuations are Alven waves. In addition, the power spectrum of the magnetic fluctuation showed evidence of an inertial range that resembled that seen in fully-developed fluid turbulence. Alfven waves, however, are exact solutions of the equations of an incompressible magnetohydrodynamics. Thus, there was a puzzle: how can a magnetofluid consisting of Alfven waves be turbulent? The answer lay in the role of velocity shears in the solar wind that could drive turbulent evolution. Puzzles remain: for example, the power spectrum of the velocity fluctuations is less steep than the slope of the magnetic fluctuations. The plasma in the magnetic tail of Earth's magnetosphere also shows aspects of turbulence, as does the plasma in the dayside magnetosphere near the poles--the so-called dayside cusps.

Goldstein, Melvyn L.↗
NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗
NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗
NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗
NASA NTRS2015

OpenFOAM Simulations of Atmospheric-Entry Capsules in the Subsonic Regime

The open-source Computational Fluid Dynamics software OpenFOAM is gaining wider acceptance in industry and academia for incompressible flow simulations. To date, there has been relatively little utilization of OpenFOAM for compressible external aerodynamic applications. The numerous turbulence models available in OpenFOAM makes it an attractive option for evaluating alternate Reynolds-Averaged Navier-Stokes (RANS) turbulent models to assess separated flow on atmospheric entry vehicles in the subsonic regime, where traditional turbulent models show reduced accuracy. This paper presents simulations of an axisymmetric capsule geometry at subsonic conditions using an OpenFOAM compressible flow solver. These results are compared with results from the NASA CFD code OVERFLOW and experimental data. These OpenFOAM simulations serve as a basis to explore OpenFOAMs extended turbulence models on compressible separated flows such as found on entry capsules.

Nikaido, Ben E.↗
NASA NTRS2001

Restraint of Liquid Jets by Surface Tension in Microgravity Modeled

Tension in Microgravity Modeled Microgravity poses many challenges to the designer of spacecraft tanks. Chief among these are the lack of phase separation and the need to supply vapor-free liquid or liquidfree vapor to the spacecraft processes that require fluid. One of the principal problems of phase separation is the creation of liquid jets. A jet can be created by liquid filling, settling of the fluid to one end of the tank, or even closing a valve to stop the liquid flow. Anyone who has seen a fountain knows that jets occur in normal gravity also. However, in normal gravity, the gravity controls and restricts the jet flow. In microgravity, with gravity largely absent, jets must be contained by surface tension forces. Recent NASA experiments in microgravity (Tank Pressure Control Experiment, TPCE, and Vented Tank Pressure Experiment, VTRE) resulted in a wealth of data about jet behavior in microgravity. VTRE was surprising in that, although it contained a complex geometry of baffles and vanes, the limit on liquid inflow was the emergence of a liquid jet from the top of the vane structure. Clearly understanding the restraint of liquid jets by surface tension is key to managing fluids in low gravity. To model this phenomenon, we need a numerical method that can track the fluid motion and the surface tension forces. The fluid motion is modeled with the Navier-Stokes equation formulated for low-speed incompressible flows. The quantities of velocity and pressure are placed on a staggered grid, with velocity being tracked at cell faces and pressure at cell centers. The free surface is tracked via the introduction of a color function that tracks liquid as 1/2 and gas as -1/2. A phase model developed by Jacqmin is used. This model converts the discrete surface tension force into a barrier function that peaks at the free surface and decays rapidly. Previous attempts at this formulation have been criticized for smearing the interface. However, by sharpening the phase function, double gridding the fluid function, and using a higher order solution for the fluid function, interface smearing is avoided. These equations can be rewritten as two coupled Poisson equations that also include the velocity. The method of solution is as follows: first, the phase equations are solved from this solution, a velocity field is generated, then a successive overrelaxation scheme is used to solve for a pressure field consistent with the velocity solution. After the code was implemented in axisymmetric form and verified by several test cases, the drop tower runs of Aydelott were modeled. The model handed the free-surface deformation quite nicely, even to the point of modeling geyser growth in the regime where the free surface was no longer restrained. A representative run is shown.

Chato, David J.↗
NASA NTRS2003

Numerical Models of Human Circulatory System under Altered Gravity: Brain Circulation

A computational fluid dynamics (CFD) approach is presented to model the blood flow through the human circulatory system under altered gravity conditions. Models required for CFD simulation relevant to major hemodynamic issues are introduced such as non-Newtonian flow models governed by red blood cells, a model for arterial wall motion due to fluid-wall interactions, a vascular bed model for outflow boundary conditions, and a model for auto-regulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models are solved iteratively using the pseudocompressibility method and dual time stepping. Moving wall boundary conditions from the first-order fluid-wall interaction model are used to study the influence of arterial wall distensibility on flow patterns and wall shear stresses during the heart pulse. A vascular bed modeling utilizing the analogy with electric circuits is coupled with an auto-regulation algorithm for multiple outflow boundaries. For the treatment of complex geometry, a chimera overset grid technique is adopted to obtain connectivity between arterial branches. For code validation, computed results are compared with experimental data for steady and unsteady non-Newtonian flows. Good agreement is obtained for both cases. In sin-type Gravity Benchmark Problems, gravity source terms are added to the Navier-Stokes equations to study the effect of gravitational variation on the human circulatory system. This computational approach is then applied to localized blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other model using an anatomical data set. A three- dimensional anatomical Circle of Willis configuration is reconstructed from human-specific magnetic resonance images using an image segmentation method. The blood flow through these Circle of Willis models is simulated to provide means for studying gravitational effects on the brain circulation under auto-regulation.

Kim, Chang Sung↗
NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗
NASA NTRS2015

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.↗