Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “mass conservation”

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 235 records · Page 13

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, C. M.↗

Impact ejecta on the moon

The response of a lunar-sized object to the impact of meteoroids no more than about 100 km in radius is studied by means of a numerical model. The partitioning of impact energy into the kinetic and internal energy of the ejecta is obtained by using the conservation of mass, momentum, and energy conservation equations in finite-difference form within an Eulerian framework with approximate equations of state. The calculations are performed for a 15 km/sec impact of an iron object 5 cm in radius on a gabbroic anorthosite surface. Ejecta ballistic analysis is then performed. Most of the material lost escaping the moon is lunar crust material. Only 0.2% of the meteoroid escapes, all in the vapor phase.

Okeefe, J. D.↗

Turbulence And Evaporation In Clusters Of Drops

Report presents theoretical model of evaporation of cluster of drops of single-component liquid fuel in and of processes of exchange between cluster and gas surrounding it. Formulation of model has three components: description of conservation of mass, molecular species, and enthalpy in sphere of influence of each drop; description of conservation of mass, molecular species, and enthalpy in cluster volume; description of convective effects by use of differential equations expressing conservation of momentum for gases and drops. Results obtained from analysis show turbulence enhances evaporation and controlling factor in evaporation of very dense clusters. Practical implication of findings evaporation of fuel controlled more readily near fuel injector than farther along combustor.

Bellan, Josette↗

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Tao, W.-K.↗

Parametric Study of 239 Pu and 235 U Mass Equivalency in Spherical Geometries

In this technical document, parametric studies were performed to determine if a bounding mass equivalency can be used to simplify multi-material models in MCNP6 for criticality evaluations. The studies explored the simplification of MCNP6 models by substituting materials, particularly 239 Pu for 235 U. The initial hypothesis for the material simplification is based on the subcritical mass limits from the ANSI/ANS- 8.1 standard which states that for water reflected metal spheres the limits are 20.1 kg 235 U and 5.0 kg 239 Pu. Using those masses, it was hypothesized that a 20.1 kg sphere of 235 U and a 5.0 kg sphere of 239 Pu could be considered to have the same multiplication. Given that equivalency, 4kg 235 U could be modeled by 1kg 239 Pu (i.e., a mass ratio of 4:1). The parametric studies compare the materials 239 Pu and 235 U independently and in multi-material spherical models. Critical mass, critical thickness, critical mass ratio and critical thickness ratio values are presented as functions of inner radius. keff values are presented as a function of inner radius at different mass ratios and total masses. Results indicate that the conservative bounding mass equivalency is one. That is, if substituting 239 Pu for 235 U it should be done on a gram for gram basis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Global End-Member Approach to Derive aCDOM(440) from Near-Surface Optical Measurements

This study establishes an optical inversion scheme for deriving the absorption coefficient of colored (or chromophoric, depending on the literature) dissolved organic material (CDOM) at the 440 nm wavelength, which can be applied to global water masses with near-equal efficacy. The approach uses a ratio of diffuse attenuation coefficient spectral end members, i.e., a short and long wavelength pair. The global perspective is established by sampling "extremely" clear water plus a generalized extent in turbidity and optical properties that each span three decades of dynamic range. A unique data set was collected in oceanic, coastal, and inland waters (as shallow as 0.6 m) from the North Pacific Ocean, the Arctic Ocean, Hawaii, Japan, Puerto Rico, and the east and west coasts of the United States. The data were partitioned using subjective categorizations to define a validation quality subset of conservative water masses, i.e., the inflow and outflow of properties constrain the range in the gradient of a constituent, plus 15 subcategories of water masses that were not evolving conservatively. The dependence on subcategories was confirmed with an objective methodology based on cluster analysis techniques. The latter defined five distinct classes with validation quality data present in all classes, but which also decreased in percent composition as a function of increasing class number and optical complexity. Four different algorithms based on different validation quality end members were validated with accuracies of 1.–6.2 %, wherein pairs with the largest spectral span were most accurate. Although algorithm accuracy decreased with the inclusion of more subcategories containing non-conservative water masses, changes to the algorithm fit were small when a preponderance of subcategories were included. The high accuracy for all end-member algorithms was the result of data acquisition and data processing improvements, e.g., increased vertical sampling resolution to less than 1mm and a boundary constraint to mitigate wave focusing effects, respectively. An independent evaluation with a historical database confirmed the consistency of the algorithmic approach and its application to quality assurance, e.g., to flag data outside expected ranges, identify suspect spectra, and objectively determine the in-water extrapolation interval by converging agreement for all applicable end-member algorithms. The legacy data exhibit degraded performance (as 44 % uncertainty) due to a lack of high-quality near-surface observations, especially for clear waters wherein wave-focusing effects are problematic. The novel optical approach allows the in situ estimation of an in-water constituent in keeping with the accuracy obtained in the laboratory.

Stanford B Hooker↗

Numerical Modeling of Flow Distribution in Micro-Fluidics Systems

This paper describes an application of a general purpose computer program, GFSSP (Generalized Fluid System Simulation Program) for calculating flow distribution in a network of micro-channels. GFSSP employs a finite volume formulation of mass and momentum conservation equations in a network consisting of nodes and branches. Mass conservation equation is solved for pressures at the nodes while the momentum conservation equation is solved at the branches to calculate flowrate. The system of equations describing the fluid network is solved by a numerical method that is a combination of the Newton-Raphson and successive substitution methods. The numerical results have been compared with test data and detailed CFD (computational Fluid Dynamics) calculations. The agreement between test data and predictions is satisfactory. The discrepancies between the predictions and test data can be attributed to the frictional correlation which does not include the effect of surface tension or electro-kinetic effect.

Majumdar, Alok↗

A Constrained Data Assimilation Algorithm Based on GSI Hybrid 3D-EnVar and Its Application

Abstract Data assimilation (DA) at mesoscales is important for severe weather forecasts, yet the techniques of data assimilation at this scale remain a challenge. This study introduces dynamical constraints in the Gridpoint Statistical Interpolation (GSI) three-dimensional ensemble variational (3D-EnVar) data assimilation algorithm to enable the use of high-resolution surface observations of precipitation to improve atmospheric analysis at mesoscales. The constraints use the conservations of mass and moisture. Mass constraint suppresses the unphysical high-frequency oscillation, while moisture conservation constrains the atmospheric states to conform with the observed high-resolution precipitation. We show that the constrained data assimilation (CDA) algorithm significantly reduced the spurious residuals of the mass and moisture budgets compared to the original data assimilation (ODA). A case study is presented for a squall line over the Southern Great Plains on 20 May 2011 during Midlatitude Continental Convective Clouds Experiment (MC3E) of the Atmospheric Radiation Measurement (ARM) program by using ODA or CDA analysis as initial condition of forecasts. The state variables, and the location and intensity of the squall line are better simulated in the CDA experiment. Results show how surface observation of precipitation can be used to improve atmospheric analysis through data assimilation by using the dynamical constraints of mass and moisture conservations.

Wang, Jia↗

Calculation of unsteady airfoil loads with and without flap deflection at -90 degrees incidence

A method has been developed for calculating the viscous flow about airfoils with and without deflected flaps at -90 deg incidence. This unique method provides for the direct solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body-fitted computational mesh incorporating a staggered grid method. The vorticity is determined at the node points, and the velocity components are defined at the mesh-cell sides. The staggered-grid orientation provides for accurate representation of vorticity at the node points and for the conservation of mass at the mesh-cell centers. The method provides for the direct solution of the flow field and satisfies the conservation of mass to machine zero at each time-step. The results of the present analysis and experimental results obtained for a XV-15 airfoil are compared. The comparisons indicate that the calculated drag reduction caused by flap deflection and the calculated average surface pressure are in excellent agreement with the measured results. Comparisons of the numerical results of the present method for several airfoils demonstrate the significant influence of airfoil curvature and flap deflection on the predicted download.

Stremel, Paul M.↗

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

SanAndres, Luis↗

A two-layer multiple-time-scale turbulence model and grid independence study

A two-layer multiple-time-scale turbulence model is presented. The near-wall model is based on the classical Kolmogorov-Prandtl turbulence hypothesis and the semi-empirical logarithmic law of the wall. In the two-layer model presented, the computational domain of the conservation of mass equation and the mean momentum equation penetrated up to the wall, where no slip boundary condition has been prescribed; and the near wall boundary of the turbulence equations has been located at the fully turbulent region, yet very close to the wall, where the standard wall function method has been applied. Thus, the conservation of mass constraint can be satisfied more rigorously in the two-layer model than in the standard wall function method. In most of the two-layer turbulence models, the number of grid points to be used inside the near-wall layer posed the issue of computational efficiency. The present finite element computational results showed that the grid independent solutions were obtained with as small as two grid points, i.e., one quadratic element, inside the near wall layer. Comparison of the computational results obtained by using the two-layer model and those obtained by using the wall function method is also presented.

Kim, S.-W.↗

Calculation of three-dimensional (3-D) internal flow by means of the velocity-vorticity formulation on a staggered grid

A method has been developed to accurately compute the viscous flow in three-dimensional (3-D) enclosures. This method is the 3-D extension of a two-dimensional (2-D) method developed for the calculation of flow over airfoils. The 2-D method has been tested extensively and has been shown to accurately reproduce experimental results. As in the 2-D method, the 3-D method provides for the non-iterative solution of the incompressible Navier-Stokes equations by means of a fully coupled implicit technique. The solution is calculated on a body fitted computational mesh incorporating a staggered grid methodology. In the staggered grid method, the three components of vorticity are defined at the centers of the computational cell sides, while the velocity components are defined as normal vectors at the centers of the computational cell faces. The staggered grid orientation provides for the accurate definition of the vorticity components at the vorticity locations, the divergence of vorticity at the mesh cell nodes and the conservation of mass at the mesh cell centers. The solution is obtained by utilizing a fractional step solution technique in the three coordinate directions. The boundary conditions for the vorticity and velocity are calculated implicitly as part of the solution. The method provides for the non-iterative solution of the flow field and satisfies the conservation of mass and divergence of vorticity to machine zero at each time step. To test the method, the calculation of simple driven cavity flows have been computed. The driven cavity flow is defined as the flow in an enclosure driven by a moving upper plate at the top of the enclosure. To demonstrate the ability of the method to predict the flow in arbitrary cavities, results will he shown for both cubic and curved cavities.

Stremel, Paul M.↗

(U) A Linear Response Model Predicts Reactivity From a Density Profile

We tested the ability to predict the system reactivity, described by alpha, given a density profile using a simple linear system response. We generated a suite of 1-dimensional density profiles that consisted of nominal density, a discontinuity, and a decay. These profiles were prescribed a functional form and the mass was conserved in all cases. From these density profiles, we calculated the alpha value of the 3-dimensional system.We calculated a linear response function given a training set of the 1-dimensional density profiles, and the system reactivity described by alpha. We tested the robustness of the response function using the remaining test data. Our results showed very good agreement between the predicted and calculated test values, where the distribution of alpha differences was centered about zero and had a standard deviation of 0.005 gens/shake. The predicted and calculated alpha values did not significantly differ (t=-0.0009 p<0.99). We used Singular Value Decomposition (SVD) to reduce the matrix rank by retaining95% of the cumulative singular value contributions. This reduced the matrix rank by 91.7%. We generated the linear response matrix and calculated the difference between the predicted and calculated alpha values. Using the reduced order matrix, we showed good agreement between the predicted and calculated alpha values where the distribution of differences was centered near zero, the standard deviation was 0.006 gens/shake, and the statistical t-test showed good agreement (t=0.02, p<0.98). These results show a linear relationship between a series of 1-dimensional density profiles,where the mass was conserved, and the system reactivity. The next steps of this work will be to investigate the linear response using 2-dimensional density profiles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver

In this work, we develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multigrid, Fractional-Step Computation Of Flow

Speed of computer code solving three-dimensional Navier-Stokes equations of flow of incompressible fluid by fractional-step method increased significantly by use of multigrid procedures. In method, equations solved on general nonorthogonal curvilinear coordinate grid, using volume fluxes. At each time step, computations performed in two fractional steps. In first step, equations of conservation of momentum solved by use of gradient of pressure from previous time step via explicit approximate-factorization method, yielding approximate flow field that does not satisfy equation of conservation of mass. In second step, discrete Poisson-like equation with Neumann-type boundary conditions, formed by combining equations of conservation of momentum and mass, solved iteratively.

Kwak, Dochan↗

Predictions for a Low-mass Cutoff for the Primordial Black Hole Mass Spectrum

In this note, we outline how a modest violation in the conservation of mass during the merger of two PBHs affects the PBH mass spectrum that we previously obtained using a Boltzmann equation model for the evolution of the mass spectrum with no mass loss. We find that if the initial cosmological redshift is of the order of 10 12 , then the fraction of primordial holes with masses greater than 10 3 solar masses appears to be close to what is required to provide the seeds for galaxies. In addition, we note that as a result of rapid collisions and strong coupling to electromagnetic radiation for temperatures > GeV, there will be an effective low-mass cutoff in the mass spectrum for PBH masses less than a certain PBH mass less than 0.1M ⊙ . We also point out that this cutoff in the mass spectrum below ~ 0.1M ⊙ can be confirmed by combining future microlensing observations from the Roman Space Telescope and the Vera C. Rubin Observatory with astrometric observations.

79 ASTRONOMY AND ASTROPHYSICS↗

A physics-based model for frost buildup under turbulent flow using direct numerical simulations

We present a new model for frost buildup under turbulent (and laminar) flow using direct numerical simulations. The physical model consists of two layers, the air and the frost. The air layer is fully resolved and consists of solving for the velocity, temperature, and vapor mass fraction fields. The frost layer thickness is resolved using conservation of mass and energy. Both phases are dynamically coupled using the immersed boundary method. Three-dimensional simulations are conducted in an open-channel configuration. A number of challenges need to be overcome to make these simulations feasible. First, to enforce far-field conditions of zero gradient and prescribed mean temperature and humidity, a source term is added to the energy and transport equations in the flow solver. Second, the mean frost thickness is subtracted after each time step to ensure a constant mean flow thickness and level of turbulence in the numerical domain. Third, a slow-time acceleration approach, which accelerates the frost buildup by a predetermined factor, is employed to bridge the gap between the fast turbulent and slow frost buildup time scales. Finally, a frost densification scheme is used to overcome the difficulties of vertically varying frost properties. The model is validated by comparing the frost thickness and frost thickness buildup rate over a period of one hour from a cooled flat plate experiment. As a result, both quantities compare favorably with experiments.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗