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At least 541 records · Page 30

Reynolds-Stress Budgets in an Impinging Shock Wave/Boundary-Layer Interaction

Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Comparisons with experimental data showed a sensitivity of the current prediction to the modeling of the sidewalls. This was found to be common among various computational studies in the literature where periodic boundary conditions were used in the spanwise direction, as was the case in the present work. Thus, although the experiment was quasi-two-dimensional, the present simulation was determined to be two-dimensional. Quantities present in the exact equation of the Reynolds-stress transport, i.e., production, molecular diffusion, turbulent transport, pressure diffusion, pressure strain, dissipation, and turbulent mass flux were calculated. Reynolds-stress budgets were compared with past large-eddy simulation and direct numerical simulation datasets in the undisturbed portion of the turbulent boundary layer to validate the current approach. The budgets in SBLI showed the growth in the production term for the primary normal stress and energy transfer mechanism was led by the pressure strain term in the secondary normal stresses. The pressure diffusion term, commonly assumed as negligible by turbulence model developers, was shown to be small but non-zero in the normal stress budgets, however it played a key role in the primary shear stress budget.

shock wave/boundary-layer interactio↗

Flow Physics at a Large Rotor Tip Gap in a Multi-Stage Axial Compressor

The flow physics in a large rotor tip gap in a 1.5-stage axial compressor is investigated in the current study. The flow structure in the rotor tip region is complex with several dominant vortical structures of opposite rotation, resulting in inhomogeneous and highly anisotropic turbulence. Earlier measurements show that eddy viscosity is negative over large parts of the tip region and eddy viscosity varies among stress/strain components. The present study aims to understand how the complex nature of rotor tip leakage flow affects compressor performance when the tip gap size is greater than 4–5% of the rotor span, which is typical of advanced small core engines. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques are applied to study flow physics in a large rotor tip gap (5.5% of rotor span) in a 1.5-stage axial compressor. Calculated flow fields from the two different approaches are compared with available measurements and examined in detail. LES calculates the pressure rise in the present compressor fairly well, while URANS with a standard two-equation turbulence closure underpredicts the pressure rise by 15-20% of the measured values. The current study shows that URANS with the current turbulence closure produces much higher all-positive eddy viscosity in the tip-gap region compared to measurements and LES. The distribution of eddy viscosity in the URANS simulation is also wrong. Consequently, the flow in the tip region is highly damped with significantly larger blockage generation, which results in the tip leakage vortex (TLV) staying closer to the blade suction side compared to the measurement. When the TLV stays closer to the blade, both flow turning and the pressure rise across the compressor are reduced compared to the measurements. It appears that this effect is amplified by a large rotor tip gap.

tip gap↗

Seasat detection of waves, currents and inlet discharge

A new era of remote sensing for coastal and oceanographic monitoring was born on June 26, 1978 with the launch of Seasat. Duck-X was a 2 month experiment conducted during August to October 1978 off the east coast of the U.S.A. for the validation of the Seasat synthetic aperture radar (SAR). During this field experiment, various oceanographic phenomena were monitored. Ground truth observations of these phenomena have been correlated with Seasat SAR imagery. The ground truth sensors included airborne photographic and radar imagery, meteorological satellite imagery, land based radars, and conventional wave gauges. The direction and length of the principal ocean wave trains are compared for the periods of Seasat overflight of the Duck-X area. During these overflights significant wave heights were 1.5 m and less and the maximum wave period was 15 sec. The current correlations concentrate on the western boundary of the Gulf Stream and its associated eddy structure. Inlet outflow is shown for inlets on the east coast of the U.S.A. This ground truth study has indicated that the SAR imagery contains an unanticipated abundance of information on a variety of oceanographic and coastal phenomena.

Mattie, M. G.↗

Equatorial long-wave characteristics determined from satellite sea surface temperature and in situ data

SST maps and imagery derived from the NOAA 6 satellite AVHRR for June and July 1981 in the eastern tropical Pacific portray the wavelike structure of the cool water along the equator from 93 deg W to 125 deg W. Cusped waves of approximately 1000-km zonal wavelength and 25-day period propagated westward with a phase speed of 40 km/day. The observed meridional extent between the crest and trough of the waves is about 300 km. Details in the imagery show cooler water at the cusps advected north and then east with the north equatorial countercurrent (NECC), consistent with the suggestion of a series of anticyclonic eddies occupying the shear zone between the NECC and the westward flowing south equatorial current. Absolute SST estimates from the AVHRR data agree to within 0.6 C with shipboard data taken along 110 deg W between 5 deg N and 5 deg S. The wavelike structures in the SST maps are also in agreement at the surface with a vertical expendable bathythermograph temperature section made along the equator between 93 deg W and 125 deg W, which shows the phase of the waves tilting westward with increasing depth over the upper 75 m. Such a phase shift, if it extended 100-200 km meridionally in either direction from the equator, would be associated with an equatorward flux of heat. Similar phase shifts appear in temperature time series at depths of 20 and 50 m, from a mooring at 0-deg 33-min N, 110-deg 30-min W. Near-surface currents measured at this and a second mooring on the equator at 109-deg 40-min W indicate a regular pattern of northward advection when wave cusps pass them, followed by southwest flow during the passage of wave troughs, again consistent with an equatorward flux of heat, as well as with earlier theoretical and drift buoy findings.

Pullen, Patricia E.↗

Computational and Experimental Flow Field Analyses of Separate Flow Chevron Nozzles and Pylon Interaction

A computational and experimental flow field analyses of separate flow chevron nozzles is presented. The goal of this study is to identify important flow physics and modeling issues required to provide highly accurate flow field data which will later serve as input to the Jet3D acoustic prediction code. Four configurations are considered: a baseline round nozzle with and without a pylon, and a chevron core nozzle with and without a pylon. The flow is simulated by solving the asymptotically steady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, up-wind, flux-difference splitting finite volume scheme and standard two-equation kappa-epsilon turbulence model with a linear stress representation and the addition of a eddy viscosity dependence on total temperature gradient normalized by local turbulence length scale. The current CFD results are seen to be in excellent agreement with Jet Noise Lab data and show great improvement over previous computations which did not compensate for enhanced mixing due to high temperature gradients.

Massey, Steven J.↗

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗

Enabling Metric-Based Mesh Adaptation for Advanced Compressible Flow Simulations Using US3D

This work presents a metric-based mesh adaptation capability added to the flow solver US3D that is used to improve the accuracy of atmospheric entry simulations. Flow past an entry vehicle in free-flight is usually unsteady and characterized by anisotropic flow features like a strong bow shock and small-scale isotropic flow features like turbulent eddies in the wake. The results presented in this paper demonstrate that we are currently able to iteratively apply metric-based mesh adaptation to improve the solution accuracy by simultaneously targeting isotropic and anisotropic flow features. A simplified workflow of running CFD simulations for entry vehicles is presented where we start off with a coarse initial mesh to compute a first approximation of the flow. This coarse mesh is then iteratively refined using the newly developed metric to improve the resolution of the CFD computation. Furthermore, we demonstrate that we are able to adapt large mesh sizes in a timely fashion which allows us to start thinking about applying this adaptive framework to unsteady atmospheric entry CFD simulations.

Mesh adaptation↗

Wind Field and Trajectory Models for Tornado-Propelled Objects

A mathematical model to predict the trajectory of tornado born objects postulated to be in the vicinity of nuclear power plants is developed. An improved tornado wind field model satisfied the no slip ground boundary condition of fluid mechanics and includes the functional dependence of eddy viscosity with altitude. Subscale wind tunnel data are obtained for all of the missiles currently specified for nuclear plant design. Confirmatory full-scale data are obtained for a 12 inch pipe and automobile. The original six degree of freedom trajectory model is modified to include the improved wind field and increased capability as to body shapes and inertial characteristics that can be handled. The improved trajectory model is used to calculate maximum credible speeds, which for all of the heavy missiles are considerably less than those currently specified for design. Equivalent coefficients for use in three degree of freedom models are developed and the sensitivity of range and speed to various trajectory parameters for the 12 inch diameter pipe are examined.

Redmann, G. H.↗

The Impacts of Freshwater Input and Surface Wind Velocity on the Strength and Extent of a Large High Latitude River Plume

Arctic Ocean physical and biogeochemical properties are strongly influenced by freshwater input from land and through the Bering Strait, where the mean currents transport water northward from the Bering Sea. The Yukon River is one of the largest rivers in North America and the Arctic, contributing large quantities of freshwater and terrigenous material to the coastal ocean in the northern Bering Sea. However, a detailed analysis of the coastal hydrodynamics at the outflow of the river has not been conducted in this remote but regionally important river. A three-dimensional hydrodynamic model was built to represent the lower Yukon River and coastal ocean for the ice-free months in 7 years. On average, a large anticyclonic eddy persisted at the main outflow of the Yukon that recirculates water back toward the coast where the currents converge to form a mean northward transport along the delta. Interannual spatial variance in salinity was relatively small, while there was substantial variance in u and v current velocity. u velocity spatial variance was correlated to the volume of freshwater discharge across years, while v velocity spatial variance was correlated to the N–S wind velocity. During strong wind events, plume structure was substantially altered: southerly winds deepened the plume and enhanced northward transport, while northerly winds shoaled and strengthened the pycnocline, and reversed the flow toward the south. The variability in plume dispersion on short time scales due to wind forcing has implications for where terrigenous material is processed in and settles out of the water column.

river plume↗

Slow and Steady: Ocean Circulation. The Influence of Sea Surface Height on Ocean Currents

The study of ocean circulation is vital to understanding how our climate works. The movement of the ocean is closely linked to the progression of atmospheric motion. Winds close to sea level add momentum to ocean surface currents. At the same time, heat that is stored and transported by the ocean warms the atmosphere above and alters air pressure distribution. Therefore, any attempt to model climate variation accurately must include reliable calculations of ocean circulation. Unlike movement of the atmosphere, movement of the ocean's waters takes place mostly near the surface. The major patterns of surface circulation form gigantic circular cells known as gyres. They are categorized according to their general location-equatorial, subtropical, subpolar, and polar-and may run across an entire ocean. The smaller-scale cell of ocean circulation is known' as an eddy. Eddies are much more common than gyres and much more difficult to track in computer simulations of ocean currents.

Haekkinen, Sirpa↗

Airborne eddy correlation gas flux measurements - Design criteria for optical techniques

Although several methods exist for the determination of the flux of an atmospheric species, the airborne eddy correlation method has the advantage of providing direct flux measurements that are representative of regional spatial domains. The design criteria pertinent to the construction of chemical instrumentation suitable for use in airborne eddy correlation flux measurements are discussed. A brief overview of the advantages and limitations of the current instrumentation used to obtain flux measurements for CO, CH4, O3, CO2, and water vapor are given. The intended height of the measurement within the convective boundary layer is also shown to be an important design criteria. The sensitivity, or resolution, which is required in the measurement of a scalar species to obtain an adequate species flux measurement is discussed. The relationship between the species flux resolution and the more commonly stated instrumental resolution is developed and it is shown that the standard error of the flux estimate is a complicated function of the atmospheric variability and the averaging time that is used. The use of the recently proposed intermittent sampling method to determine the species flux is examined. The application of this technique may provide an opportunity to expand the suite of trace gases for which direct flux measurements are possible.

Ritter, John A.↗

Study of Convective Flow Effects in Endwall Casing Treatments in Transonic Compressor Rotors

The unsteady convective flow effects in a transonic compressor rotor with a circumferential-groove casing treatment are investigated in this paper. Experimental results show that the circumferential-groove casing treatment increases the compressor stall margin by almost 50% for the current transonic compressor rotor. Steady flow simulation of the current casing treatment, however, yields only a 15% gain in stall margin. The flow field at near-stall operation is highly unsteady due to several self-induced flow phenomena. These include shock oscillation, vortex shedding at the trailing edge, and interaction between the passage shock and the tip clearance vortex. The primary focus of the current investigation is to assess the effects of flow unsteadiness and unsteady flow convection on the circumferential-groove casing treatment. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques were applied in addition to steady Reynolds-averaged Navier-Stokes (RANS) to simulate the flow field at near-stall operation and to determine changes in stall margin. The current investigation reveals that unsteady flow effects are as important as steady flow effects on the performance of the circumferential grooves casing treatment in extending the stall margin of the current transonic compressor rotor. The primary unsteady flow mechanism is unsteady flow injection from the grooves into the main flow near the casing. Flows moving into and out of the grooves are caused due to local pressure difference near the grooves. As the pressure field becomes transient due to self-induced flow oscillation, flow injection from the grooves also becomes unsteady. The unsteady flow simulation shows that this unsteady flow injection from the grooves is substantial and contributes significantly to extending the compressor stall margin. Unsteady flows into and out of the grooves have as large a role as steady flows in the circumferential grooves. While the circumferential-groove casing treatment seems to be a steady flow device, unsteady flow effects should be included to accurately assess its performance as the flow is transient at near-stall operation.

Hah, Chunill↗

Large-Eddy Simulation Code Developed for Propulsion Applications

A large-eddy simulation (LES) code was developed at the NASA Glenn Research Center to provide more accurate and detailed computational analyses of propulsion flow fields. The accuracy of current computational fluid dynamics (CFD) methods is limited primarily by their inability to properly account for the turbulent motion present in virtually all propulsion flows. Because the efficiency and performance of a propulsion system are highly dependent on the details of this turbulent motion, it is critical for CFD to accurately model it. The LES code promises to give new CFD simulations an advantage over older methods by directly computing the large turbulent eddies, to correctly predict their effect on a propulsion system. Turbulent motion is a random, unsteady process whose behavior is difficult to predict through computer simulations. Current methods are based on Reynolds-Averaged Navier- Stokes (RANS) analyses that rely on models to represent the effect of turbulence within a flow field. The quality of the results depends on the quality of the model and its applicability to the type of flow field being studied. LES promises to be more accurate because it drastically reduces the amount of modeling necessary. It is the logical step toward improving turbulent flow predictions. In LES, the large-scale dominant turbulent motion is computed directly, leaving only the less significant small turbulent scales to be modeled. As part of the prediction, the LES method generates detailed information on the turbulence itself, providing important information for other applications, such as aeroacoustics. The LES code developed at Glenn for propulsion flow fields is being used to both analyze propulsion system components and test improved LES algorithms (subgrid-scale models, filters, and numerical schemes). The code solves the compressible Favre-filtered Navier- Stokes equations using an explicit fourth-order accurate numerical scheme, it incorporates a compressible form of Smagorinsky s model for the subgrid-scale turbulence, and it uses generalized curvilinear coordinates to allow analysis of a wide range of geometries. The code runs in parallel on shared memory multiprocessor computers and is written in Fortran 90 with dynamic memory allocation. A sample result for a Mach-1.4 round jet is presented in the figure. Instantaneous Mach number contours in several cross-planes downstream of the nozzle exit are shown, illustrating how an LES captures the large unsteady three-dimensional turbulent structures present in the jet.

DeBonis, James R.↗

Towards large eddy and direct simulation of complex turbulent flows

Recent advances in the methodology for direct numerical simulation of turbulent flows and some of the current applications are reviewed. It is argued that high-order finite difference schemes yield solutions with comparable accuracy to the spectral methods with the same number of degrees of freedom. The effects of random inflow conditions on the downstream evolution of turbulence are discussed.

Moin, Parviz↗

Model capabilities, 2-D

Two dimensional (2-D) atmospheric models provide results for altitude versus latitude as a function of time and are developed primarily for two reasons: to help understand atmospheric occurrences and to give assessments and/or make predictions of future changes in the atmosphere. Historically, the formulation of transport in 2-D models has been a difficult problem. Most current 2-D models have a transport that is either an Eulerian mean circulation with large stratospheric eddy diffusion or a residual (diabatic or Lagragian) mean circulation which typically is accompanied with small stratospheric eddy diffusion. Because of the assumption of zonal averaging, 2-D models are primarily useful in making predictions of atmospheric changes of time scales longer than a season. Although decadel atmospheric changes may be reasonably well represented with a 2-D model, the year to year changes which result from interannual transport differences, stratospheric warmings, semiannual oscillations, or quasi-biennial oscillations may not be well represented in the stratosphere and troposphere.

Jackman, Charles H.↗

Stability of the Martian atmosphere: Is heterogeneous catalysis essential?

A comprehensive homogeneous gas phase photochemical model is developed to study the problem of stability of the Martian atmosphere. The one-dimensional model extends from the ground up to 220 km, passing through the homopause at 125 km. The model thus couples the lower (neutral) atmosphere to the ionosphere above which provides significant downward flux of carbon monoxide and oxygen atoms. It is concluded on the basic of currently accepted values for globally and seasonally averaged water vapor abundance, dust opacity and the middle atmospheric eddy mixing coefficient, as well as the relevant laboratory data (particularly the temperature dependence of CO2 absorption cross section and the rate constant for CO+OH reaction), that the rate of re-formation of carbon dioxide exceeds its photolytic destruction rate by about 40%. Furthermore, it is found that this result is virtually independent of the choice of eddy mixing coefficient, unless its value in the middle atmosphere exceeds 10(exp 8) sq cm/sec or is far smaller than 10(exp 5)sq cm/sec, or the dust opacity, unless it exceeds unity, or the water vapor mixing ratio at the surface, unless it is far smaller (less than or = 1 ppm) or far greater (greater than or = 500 ppm) than the average value (approximately 150 ppm). Since none of these extremes represent globally and seasonally averaged conditions on Mars, we propose that the present model requires existence of a mechanism to throttle down the recycling rate of carbon dioxide on Mars. Therefore, it is suggested that a heterogeneous process which provides a sink to the species that participate in the recycling of CO2, i.e., H2O, H2O2, OH, CO or O, in particular, may be necessary to bring about the balance between the CO2 recycling rate and its photolytic destruction rate. Aerosols of dust or ice (pure or doped water or carbon dioxide ice present in the atmosphere of Mars) can provide the appropriate adsorption sites for the above heterogeneous process. Despite our conclusion that some heterogeneous process may be needed, it is important to recognize that one-dimensional models can only provide first-order results which, most likely, represent globally and seasonally averaged conditions. However, it is only after actual temporal, latitudinal and longitudinal variations of relevant atmospheric parameters are included in the model that one can determine fuly whether the problem of atmospheric stabiltiy still continues to persist and whether some heterogeneous process is required to correct it.

Atreya, Sushil K.↗

Predicting the Effects of Test Media in Ground-Based Propulsion Testing

This paper discusses the progress of work which began in mid-2004 sponsored by the Office of the Secretary of Defense (OSD) Test & Evaluation/Science & Technology (T&E/S&T) Program. The purpose of the work is to improve the state of the art of CFD capabilities for predicting the effects of the test media on the flameholding characteristics in scramjet engines. The program has several components including the development of advance algorithms and models for simulating engine flowpaths as well as a fundamental experimental and diagnostic development effort to support the formulation and validation of the mathematical models. The paper will provide details of current work involving the development of phenomenological models for Reynolds averaged Navier-Stokes codes, large-eddy simulation techniques and reduced-kinetics models. Experiments that will provide data for the modeling efforts will also be described, along with with the associated nonintrusive diagnostics used to collect the data.

Drummond, J. Philip↗

Modeling and Analysis of Stirling Power Convertors

Modeling and Analysis of Stirling Power Convertors Luis A. Rodriguez1 Steven M. Geng, Terry V. Reid, Scott D. Wilson NASA Glenn Research Center, Cleveland, OH, 44135, USA NASA Glenn’s Thermal Energy Conversion Branch is supporting the development of the next generation free-piston Stirling power convertors. American Superconductor (AMSC) and Sunpower Inc. are the two firms under contract to develop the Flexure Isotope Stirling Convertor (FISC) and the Sunpower Robust Stirling Convertor (SRSC), respectively. To comprehend and forecast convertor performance, Sage, ANSYS® Maxwell, and ANSYS® Fluent were used to model the Stirling thermodynamic cycle, alternator electromagnetics, and piston and displacer dynamics. I. Introduction Stirling convertors are being developed by NASA as a potential steady source of electrical power for NASA’s future scientific space missions. Currently, NASA Glenn Research Center has two corporations under contract, American Superconductor (AMSC) and Sunpower Inc., for the development of the next generation of free-piston Stirling convertors for dynamic radioisotope power systems. AMSC is developing the Flexure Isotope Stirling Convertor (FISC), which uses flexures to prevent side motion and rubbing of the piston. Similarly, Sunpower Inc, is developing the Sunpower Robust Stirling Convertor (SRSC). The SRSC uses gas bearings to prevent radial contact of the moving piston. As convertor development continues, it is increasingly important to understand and predict the interactions of components in the system, how they respond to one another, and how they perform as a response to changes in operating conditions. A suitable and enlightening way to demonstrate and foresee these interactions is with the use of accurate modeling software. Sage, ANSYS® Maxwell, and ANSYS® Fluent are the current modeling tools used by NASA to analytically determine convertor performance. Sage is a one-dimensional object-oriented commercial software package used for modeling and optimizing Stirling convertors for Dynamic Radioisotope Power Systems (DRPS) and it is one of the most accurate Stirling convertor codes in use by NASA. This code is the successor to GLIMPS (Globally-Implicit Stirling Cycle Simulation) and GLOP (GLIMPS Optimization) software created by Gedeon Associates [1]. Model input parameters are typically material/gas type, component physical dimensions, temperatures, frequency, charge pressure, and number of time/space nodes. Sage is used to model both the FISC’s and SRSC’s Stirling cycle thermodynamics and piston/displacer dynamics. Performance maps were created and analyzed for both power systems to better understand the relationship between the following conditions: cold-end temperature, hot-end temperature, piston/displacer amplitudes, pressure drop, and thermal input power. The synergy between these conditions will help determine parameter sensitivity. ANSYS® Maxwell was used to create a three-dimensional (3-D) axisymmetric model for both FISC and SRSC alternators. The significant physical components included in each model are the magnets, magnet carrier, outer/inner laminations, and the coil. Inputs to the model are piston amplitude, piston frequency, alternator load, coil resistance, tuning capacitance, and specific material properties. The alternator models calculate terminal voltage, current, piston/current phase, voltage/current phase, coil inductance, terminal power and efficiency. The RI2 losses, core (hysteresis and eddy) losses, and magnet/can eddy losses are also a part of the final results. ANSYS® Fluent is used to build 3-D computational fluid dynamic (CFD) models to examine the Stirling cycle thermodynamics for both the FISC and SRSC systems. Three-dimensional Computer Aided Design (CAD) models were used to create the physical components of each convertor. Steady-state simulations were conducted for hardware testing, prediction of environmental losses during testing, and generation of radiation look-up tables. The model inputs to the aforementioned analysis are the material properties and boundary thermal conditions. The steady-state model calculates temperature and heat flow distributions. Transient 3-D calculations were also part of the CFD analysis. In this study a physically reduced version of the FISC is used to obtain a prediction of available engine power. For the gas bearing SRSC, the transient effort is used to obtain a prediction of bearing pad performance and its sensitivity to micro-channel geometric variation. The model inputs to the transient simulations are the piston amplitude, displacer amplitude, frequency, displacer/piston phase angle, dynamic deforming CFD grid, temperature boundary conditions, and user defined files describing motion profile of piston/displacer. The results of the model are temperature distributions, heat distributions, and PV power produced at pre-determined conditions.

Luis A Rodriguez↗