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NASA NTRS1983

Computation of viscous flows in turbomachinery cascades

Analytic and numerical experiments involving the use of the space-marching method for the prediction of the viscous flow field in turbomachinery cascades indicate that the grid lines in the physical domain must be nearly orthogonal in order to arrive at accurate predictions. For staggered cascades, a nonperiodic grid system was used and appropriate approximations were applied in place of the periodicity boundary conditions upstream and downstream of the cascade. Predicted drag coefficient, turning angle, boundary layer momentum thicknesses, and velocity profiles are compared with experimental data. Good agreement is obtained in most cases.

Pouagare, M.↗

NASA NTRS1987

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗

NASA NTRS1996

Comparative Study of Advanced Turbulence Models for Turbomachinery

A computational study has been undertaken to study the performance of advanced phenomenological turbulence models coded in a modular form to describe incompressible turbulent flow behavior in two dimensional/axisymmetric and three dimensional complex geometry. The models include a variety of two equation models (single and multi-scale k-epsilon models with different near wall treatments) and second moment algebraic and full Reynolds stress closure models. These models were systematically assessed to evaluate their performance in complex flows with rotation, curvature and separation. The models are coded as self contained modules that can be interfaced with a number of flow solvers. These modules are stand alone satellite programs that come with their own formulation, finite-volume discretization scheme, solver and boundary condition implementation. They will take as input (from any generic Navier-Stokes solver) the velocity field, grid (structured H-type grid) and computational domain specification (boundary conditions), and will deliver, depending on the model used, turbulent viscosity, or the components of the Reynolds stress tensor. There are separate 2D/axisymmetric and/or 3D decks for each module considered. The modules are tested using Rocketdyn's proprietary code REACT. The code utilizes an efficient solution procedure to solve Navier-Stokes equations in a non-orthogonal body-fitted coordinate system. The differential equations are discretized over a finite-volume grid using a non-staggered variable arrangement and an efficient solution procedure based on the SIMPLE algorithm for the velocity-pressure coupling is used. The modules developed have been interfaced and tested using finite-volume, pressure-correction CFD solvers which are widely used in the CFD community. Other solvers can also be used to test these modules since they are independently structured with their own discretization scheme and solver methodology. Many of these modules have been independently tested by Professor C.P. Chen and his group at the University of Alabama at Huntsville (UAH) by interfacing them with own flow solver (MAST).

Hadid, Ali H.↗

NASA NTRS1995

Technical report series on global modeling and data assimilation. Volume 5: Documentation of the AIRES/GEOS dynamical core, version 2

A detailed description of the numerical formulation of Version 2 of the ARIES/GEOS 'dynamical core' is presented. This code is a nearly 'plug-compatible' dynamics for use in atmospheric general circulation models (GCMs). It is a finite difference model on a staggered latitude-longitude C-grid. It uses second-order differences for all terms except the advection of vorticity by the rotation part of the flow, which is done at fourth-order accuracy. This dynamical core is currently being used in the climate (ARIES) and data assimilation (GEOS) GCMs at Goddard.

Suarez, Max J.↗

NASA NTRS1993

Viscous analysis of three-dimensional rotor flows using a multigrid method

A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

Arnone, A.↗

NASA NTRS1986

The grid array antenna

Attention is called to the grid array as a possible useful antenna design for UHF clear air radars. This type of antenna integrates radiating elements and the feed network into a single structure so that a fairly large array can be driven from a single feed point. Figures are given which demonstrate the basic principle of the grid array, which are adapted from Conti et al. (1981). Conductors are arranged above a ground plane in a repeating, staggered array of connected rectangles. Each rectangular element is approximately one by one-half wavelength in size. The currents on the conductors at resonance is indicated. The grid array illustrated can be expanded in both vertical and horizontal directions about the feed point by adding additional rectangular conductors. The design eliminates the feed network and would provide a thin, panel-like antenna that could be easily built and transported.

Ecklund, W. L.↗

NASA NTRS1981

Finite element analysis of transonic flows in highly staggered cascades

Finite element method is employed in the solution of full-potential equation for analyzing steady, transonic flows through a series of highly staggered cascades. Convergence characteristics and efficiency of the developed numerical procedure are discussed. Accuracy of the mathematical model is investigated in terms of the employed computational grid. In particular, the importance of accurate representation of the trailing edge together with the shock on the obtained flow results are studied. Numerical results include choked flows, for a cascade of NACA 0012 airfoils with pitch/chord length = 1, and stagger angle of 45 deg.

Akay, H. U.↗

NASA NTRS2019

Using Power Diagrams to Build Optimal Unstructured Meshes for C-Grid Models

The Model for Prediction Across Scales (MPAS) for Ocean (-O), Sea-Ice (-SI) and Land-Ice (-LI), in addition to the Coastal Ocean Marine Prediction Across Scales (COMPAS) are two novel general circulation models designed to resolve coupled ocean-ice dynamics over variable spatial scales using non-uniform unstructured grids. Both models are based on a conservative mimetic finite-difference/volume formulation (TRiSK), in which staggered momentum, vorticity and mass-based degrees- of-freedom are distributed over an orthogonal 'primal-dual' mesh.

Engwirda, Darren↗

NASA NTRS1999

Heat Transfer on a Film-Cooled Blade: Effect of Hole Physics

A multiblock, three-dimensional Navier Stokes code has been used to study the within-hole and near-hole physics in relation to heat transfer on a film-cooled blade. The flow domain consists of the coolant flow through the plenum and hole-pipes for the three staggered rows of shower-head holes on the VKI rotor, and the main flow over the blade. A multiblock grid is generated that is nearly orthogonal to the various surfaces. It may be noted that for the VKI rotor the shower-head holes are inclined at 30 deg to the spanwise direction, and are normal to the streamwise direction on the blade. Wilcox's k-omega turbulence model is used. The present study provides a much better comparison for the span-averaged heat transfer coefficient on the blade surface with the experimental data than an earlier analysis wherein coolant velocity and temperature distributions were specified at the hole exits rather than extending the computational domain into the hole-pipe and plenum. Details of the distributions of coolant velocity, temperature, k and omega at the hole exits are also presented.

Garg, Vijay K.↗

NASA NTRS1998

Heat Transfer on a Film-Cooled Blade - Effect of Hole Physics

A multi-block, three-dimensional Navier-Stokes code has been used to study the within-hole and near-hole physics in relation to heat transfer on a film-cooled blade. The flow domain consists of the coolant flow through the plenum and hole-pipes for the three staggered rows of shower-head holes on the VK1 rotor, and the main flow over the blade. A multi-block grid is generated that is nearly orthogonal to the various surfaces. It may be noted that for the VK1 rotor the shower-head holes are inclined at 30 deg. to the spanwise direction, and are normal to the streamwise direction on the blade. Wilcox's k-omega turbulence model is used. The present study provides a much better comparison for the heat transfer coefficient at the blade mid-span with the experimental data than an earlier analysis wherein coolant velocity and temperature distributions were specified at the hole exits rather than extending the computational domain into the hole-pipe and plenum. Details of the distributions of coolant velocity, temperature, k and omega at the hole exits are also presented.

Garg, Vijay K.↗

NASA NTRS1999

Heat Transfer on a Film-Cooled Rotating Blade

A multi-block, three-dimensional Navier-Stokes code has been used to compute heat transfer coefficient on the blade, hub and shroud for a rotating high-pressure turbine blade with 172 film-cooling holes in eight rows. Film cooling effectiveness is also computed on the adiabatic blade. Wilcox's k-omega model is used for modeling the turbulence. Of the eight rows of holes, three are staggered on the shower-head with compound-angled holes. With so many holes on the blade it was somewhat of a challenge to get a good quality grid on and around the blade and in the tip clearance region. The final multi-block grid consists of 4784 elementary blocks which were merged into 276 super blocks. The viscous grid has over 2.2 million cells. Each hole exit, in its true oval shape, has 80 cells within it so that coolant velocity, temperature, k and omega distributions can be specified at these hole exits. It is found that for the given parameters, heat transfer coefficient on the cooled, isothermal blade is highest in the leading edge region and in the tip region. Also, the effectiveness over the cooled, adiabatic blade is the lowest in these regions. Results for an uncooled blade are also shown, providing a direct comparison with those for the cooled blade. Also, the heat transfer coefficient is much higher on the shroud as compared to that on the hub for both the cooled and the uncooled cases.

Garg, Vijay K.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

A compressible, unsteady, full Navier-Stokes, finite difference code was developed for modeling transonic flow through two-dimensional, oscillating cascades. The procedure introduces a deforming grid technique to capture the motion of the airfoils. Results using a deforming grid are presented for both isolated and cascaded airfoils. The load histories and unsteady pressure distributions are predicted for the NASA 64A010 isolated airfoil and compared with existing experimental data. Results show that the deforming grid technique can be used to successfully predict the unsteady flow properties around an oscillating airfoil. The deforming grid technique was extended for modeling unsteady flow in a cascade. The use of a deforming grid simplifies the specification of boundary conditions. Unsteady flow solutions similar to the isolated airfoil predictions are found for a NACA 0012 cascade with zero interblade phase angle and zero stagger. Experimental data for these cases are not available for code validation, but computational results are presented to show sample predictions from the code. Applications of the code to typical turbomachinery flow conditions will be presented in future work.

Huff, Dennis L.↗

NASA NTRS1987

Numerical simulations of unsteady, viscous, transonic flow over isolated and cascaded airfoils using a deforming grid

Huff, Dennis L.↗

NASA NTRS2007

Impact of MODIS High-Resolution Sea-Surface Temperatures on WRF Forecasts at NWS Miami, FL

Over the past few years,studies at the Short-term Prediction Research and Transition (SPoRT) Center have suggested that the use of Moderate Resolution Imaging Spectroradiometer (MODIS) composite sea-surface temperature (SST) products in regional weather forecast models can have a significant positive impact on short-term numerical weather prediction in coastal regions. The recent paper by LaCasse et al. (2007, Monthly Weather Review) highlights lower atmospheric differences in regional numerical simulations over the Florida offshore waters using 2-km SST composites derived from the MODIS instrument aboard the polar-orbiting Aqua and Terra Earth Observing System satellites. To help quantify the value of this impact on NWS Weather Forecast Offices (WFOs), the SPoRT Center and the NWS WFO at Miami, FL (MIA) are collaborating on a project to investigate the impact of using the high-resolution MODIS SST fields within the Weather Research and Forecasting (WRF) prediction system. The scientific hypothesis being tested is: More accurate specification of the lower-boundary forcing within WRF will result in improved land/sea fluxes and hence, more accurate evolution of coastal mesoscale circulations and the associated sensible weather elements. The NWS MIA is currently running the WRF system in real-time to support daily forecast operations, using the National Centers for Environmental Prediction Nonhydrostatic Mesoscale Model dynamical core within the NWS Science and Training Resource Center's Environmental Modeling System (EMS) software; The EMS is a standalone modeling system capable of downloading the necessary daily datasets, and initializing, running and displaying WRF forecasts in the NWS Advanced Weather Interactive Processing System (AWIPS) with little intervention required by forecasters. Twenty-seven hour forecasts are run daily with start times of 0300,0900, 1500, and 2100 UTC on a domain with 4-km grid spacing covering the southern half of Florida and the far western portions of the Bahamas, the Florida Keys, the Straights of Florida, and adjacent waters of the Gulf of Mexico and Atlantic Ocean. Each model run is initialized using the Local Analysis and Prediction System (LAPS) analyses available in AWIPS, invoking the diabatic. "hot-start" capability. In this WRF model "hot-start", the LAPS-analyzed cloud and precipitation features are converted into model microphysics fields with enhanced vertical velocity profiles, effectively reducing the model spin-up time required to predict precipitation systems. The SSTs are initialized with the NCEP Real-Time Global (RTG) analyses at l/12 degree resolution (approx. 9 km); however, the RTG product does not exhibit fine-scale details consistent with its grid resolution. SPoRT is conducting parallel WRF EMS runs identical to the operational runs at NWS MIA in every respect except for the use of MODIS SST composites in place of the RTG product as the initial and boundary conditions over water. The MODIS SST composites for initializing the SPoRT WRF runs are generated on a 2-km grid four times daily at 0400, 0700, 1600, and 1900 UTC, based on the times of the overhead passes of the Aqua and Terra satellites. The incorporation of the MODIS SST composites into the SPoRTWRF runs is staggered such that the 0400UTC composite initializes the 0900 UTC WRF, the 0700 UTC composite initializes the 1500 UTC WRF, the 1600 UTC composite initializes the 2100 UTC WRF, and the 1900 UTC composite initializes the 0300 UTC WRF. A comparison of the SPoRT and Miami forecasts is underway in 2007, and includes quantitative verification of near-surface temperature, dewpoint, and wind forecasts at surface observation locations. In addition, particular days of interest are being analyzed to determine the impact of the MODIS SST data on the development and evolution of predicted sea/land-breeze circulations, clouds, and precipitation. This paper will present verification results comparing the NWS MIA forecasts the SPoRT experimental WRF forecasts, and highlight any substantial differences noted in the predicted mesoscale phenomena.

Case, Jonathan L.↗

NASA NTRS2008

A Multi-Season Study of the Effects of MODIS Sea-Surface Temperatures on Operational WRF Forecasts at NWS Miami, FL

Studies at the Short-term Prediction Research and Transition (SPORT) Center have suggested that the use of Moderate Resolution Imaging Spectroradiometer (MODIS) sea-surface temperature (SST) composites in regional weather forecast models can have a significant positive impact on short-term numerical weather prediction in coastal regions. Recent work by LaCasse et al (2007, Monthly Weather Review) highlights lower atmospheric differences in regional numerical simulations over the Florida offshore waters using 2-km SST composites derived from the MODIS instrument aboard the polar-orbiting Aqua and Terra Earth Observing System satellites. To help quantify the value of this impact on NWS Weather Forecast Offices (WFOs), the SPORT Center and the NWS WFO at Miami, FL (MIA) are collaborating on a project to investigate the impact of using the high-resolution MODIS SST fields within the Weather Research and Forecasting (WRF) prediction system. The project's goal is to determine whether more accurate specification of the lower-boundary forcing within WRF will result in improved land/sea fluxes and hence, more accurate evolution of coastal mesoscale circulations and the associated sensible weather elements. The NWS MIA is currently running WRF in real-time to support daily forecast operations, using the National Centers for Environmental Prediction Nonhydrostatic Mesoscale Model dynamical core within the NWS Science and Training Resource Center's Environmental Modeling System (EMS) software. Twenty-seven hour forecasts are run dally initialized at 0300, 0900, 1500, and 2100 UTC on a domain with 4-km grid spacing covering the southern half of Florida and adjacent waters of the Gulf of Mexico and Atlantic Ocean. Each model run is initialized using the Local Analysis and Prediction System (LAPS) analyses available in AWIPS. The SSTs are initialized with the NCEP Real-Time Global (RTG) analyses at 1/12deg resolution (approx.9 km); however, the RTG product does not exhibit fine-scale details consistent with its grid resolution. SPORT is conducting parallel WRF EMS runs identical to the operational runs at NWS MIA except for the use of MODIS SST composites in place of the RTG product as the initial and boundary conditions over water, The MODIS SST composites for initializing the SPORT WRF runs are generated on a 2-km grid four times daily at 0400, 0700, 1600, and 1900 UTC, based on the times of the overhead passes of the Aqua and Terra satellites. The incorporation of the MODIS SST data into the SPORT WRF runs is staggered such that SSTs are updated with a new composite every six hours in each of the WRF runs. From mid-February to July 2007, over 500 parallel WRF simulations have been collected for analysis and verification. This paper will present verification results comparing the NWS MIA operational WRF runs to the SPORT experimental runs, and highlight any substantial differences noted in the predicted mesoscale phenomena for specific cases.

Case, Jonathan L.↗

NASA NTRS1987

Time-partitioning simulation models for calculation on parallel computers

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Milner, Edward J.↗

NASA NTRS1987

Time-partitioning simulation models for calculation of parallel computers

Milner, Edward J.↗

NASA NTRS1991

Unsteady-flow-field predictions for oscillating cascades

The unsteady flow field around an oscillating cascade of flat plates with zero stagger was studied by using a time marching Euler code. This case had an exact solution based on linear theory and served as a model problem for studying pressure wave propagation in the numerical solution. The importance of using proper unsteady boundary conditions, grid resolution, and time step size was shown for a moderate reduced frequency. Results show that an approximate nonreflecting boundary condition based on linear theory does a good job of minimizing reflections from the inflow and outflow boundaries and allows the placement of the boundaries to be closer to the airfoils than when reflective boundaries are used. Stretching the boundary to dampen the unsteady waves is another way to minimize reflections. Grid clustering near the plates captures the unsteady flow field better than when uniform grids are used as long as the 'Courant Friedrichs Levy' (CFL) number is less than 1 for a sufficient portion of the grid. Finally, a solution based on an optimization of grid, CFL number, and boundary conditions shows good agreement with linear theory.

Huff, Dennis L.↗