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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.

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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Role of Meteorology in Flights of a Solar-Powered Airplane

In the summer of 2001, the Helios prototype solar-powered uninhabited aerial vehicle (UAV) [a lightweight, remotely piloted airplane] was deployed to the Pacific Missile Range Facility (PMRF), at Kauai, Hawaii, in an attempt to fly to altitudes above 100,000 ft (30.48 km). The goal of flying a UAV to such high altitudes has been designated a level-I milestone of the NASA Environmental Research Aircraft and Sensor Technology (ERAST) program. In support of this goal, meteorologists from NASA Dryden Flight Research Center were sent to PMRF, as part of the flight crew, to provide current and forecast weather information to the pilots, mission directors, and planners. Information of this kind is needed to optimize flight conditions for peak aircraft performance and to enable avoidance of weather conditions that could adversely affect safety. In general, the primary weather data of concern for ground and flight operations are wind speeds (see Figure 1). Because of its long wing span [247 ft (.75 m)] and low weight [1,500 to 1,600 lb (about 680 to 726 kg)], the Helios airplane is sensitive to wind speeds exceeding 7 kn (3.6 m/s) at the surface. Also, clouds are of concern because they can block sunlight needed to energize an array of solar photovoltaic cells that provide power to the airplane. Vertical wind shear is very closely monitored in order to prevent damage or loss of control due to turbulence.

Donohue, Casey↗
NASA NTRS2018

Transition Delay via Vortex Generators in a Hypersonic Boundary Layer at Flight Conditions

The potential of realizable, stationary streaks undergoing non-modal growth to stabilize a hypersonic boundary-layer flow and, subsequently, delay the laminar-turbulent transition onset, is studied via numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment, namely, a 7-degree half-angle cone with 2.5 mm nose radius, freestream Mach number of 5.30, freestream unit Reynolds number equal to 13.42 x 10(exp 6)/m, and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the test article. This paper investigates flow modifications induced by wall-mounted vortex generators (VGs), followed by an analysis of the modal instability of the perturbed, streaky boundary-layer flow. Results are presented both for a single array of VGs that was designed on the basis of optimal growth theory and for a VG configuration involving two separate arrays with opposite orientations that ware designed to provide staged control of flow instabilities while simultaneously reducing the amplification of streak instabilities resulting from the control devices. Earlier research had shown that the onset of transition during the HIFiRE-1 flight experiment, which did not include any control devices, correlated with an amplification factor of N = 14.7 for the planar Mack modes. If one assumes that the transition N -factor is not affected by the introduction of the VGs, then the control configurations based on a single array of VGs and two separate arrays would result in a transition delay of 17% and 40%, respectively. These findings suggest a passive flow control s to induce streaks that would delay transition in hypersonic boundary dominated by Mack-mode instabilities.

Incompressible boundary layer↗
DOE OSTI2022

Accurate Compression of Tabulated Chemistry Models with Partition of Unity Networks

Tabulated chemistry models are widely used to simulate large-scale turbulent fires in applications including energy generation and fire safety. Tabulation via piecewise Cartesian interpolation suffers from the curse-of-dimensionality, leading to a prohibitive exponential growth in parameters and memory usage as more dimensions are considered. Artificial neural networks (ANNs) have attracted attention for constructing surrogates for chemistry models due to their ability to perform high-dimensional approximation. However, due to well-known pathologies regarding the realization of suboptimal local minima during training, in practice they do not converge and provide unreliable accuracy. Partition of unity networks (POUnets) are a recently introduced family of ANNs which preserve notions of convergence while performing high-dimensional approximation, discovering a mesh-free partition of space which may be used to perform optimal polynomial approximation. In this work, we assess their performance with respect to accuracy and model complexity in reconstructing unstructured flamelet data representative of nonadiabatic pool fire models. Our results show that POUnets can provide the desirable accuracy of classical spline-based interpolants with the low memory footprint of traditional ANNs while converging faster to significantly lower errors than ANNs. For example, we observe POUnets obtaining target accuracies in two dimensions with 40 to 50 times less memory and roughly double the compression in three dimensions. We also address the practical matter of efficiently training accurate POUnets by studying convergence over key hyperparameters, the impact of partition/basis formulation, and the sensitivity to initialization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

CFD Simulation of Helium Flow Loop Test Section

A helium flow loop is being assembled at Oak Ridge National Laboratory to analyze heat transfer enhancement for systems such as blanket and divertor components. To efficiently identify optimum geometries for heat transfer enhancement in these applications, simulation work is performed to optimize test section designs that are built and tested in the helium flow loop that operates at 4 MPa and a mass flow rate of 100 g/s. Different ribbed geometries that examine rib shape, rib height, rib orientation, rib spacing, and three dimensional orientation are modeled and simulated in STAR-CCM+ to compare their ability to remove heat and mitigate pressure drop. Following the simulations, models are selected and manufactured for the helium flow loop tests. Simulations initially focus on a hydrodynamic study to determine the appropriate mesh and physics models and then add a heat flux to analyze the heat transfer abilities of the models. The simulations are run in steady state and use a Reynolds-averaged Navier-Stokes k-ε turbulence model. The helium is modeled as an ideal gas. The simulation explores models of geometries that enhance the heat transfer and decrease pressure drop with an overall goal of increasing fluid collision with the wall. Enhanced geometries are simulated to select appropriate designs for manufacturing, and preliminary experimental results are used to validate the simulations. Furthermore, the factors that are being analyzed in the comparison between the experimental and the simulated results include matching thermocouple temperatures, pressure drop, roughness, and fluid velocity.

42 ENGINEERING↗
NASA NTRS1987

Design and test of a natural laminar flow/large Reynolds number airfoil with a high design cruise lift coefficient

Research activity on an airfoil designed for a large airplane capable of very long endurance times at a low Mach number of 0.22 is examined. Airplane mission objectives and design optimization resulted in requirements for a very high design lift coefficient and a large amount of laminar flow at high Reynolds number to increase the lift/drag ratio and reduce the loiter lift coefficient. Natural laminar flow was selected instead of distributed mechanical suction for the measurement technique. A design lift coefficient of 1.5 was identified as the highest which could be achieved with a large extent of laminar flow. A single element airfoil was designed using an inverse boundary layer solution and inverse airfoil design computer codes to create an airfoil section that would achieve performance goals. The design process and results, including airfoil shape, pressure distributions, and aerodynamic characteristics are presented. A two dimensional wind tunnel model was constructed and tested in a NASA Low Turbulence Pressure Tunnel which enabled testing at full scale design Reynolds number. A comparison is made between theoretical and measured results to establish accuracy and quality of the airfoil design technique.

Kolesar, C. E.↗
NASA NTRS1999

High-Area-Ratio Rocket Nozzle at High Combustion Chamber Pressure: Experimental and Analytical Validation

Experimental data were obtained on an optimally contoured nozzle with an area ratio of 1025:1 and on a truncated version of this nozzle with an area ratio of 440:1. The nozzles were tested with gaseous hydrogen and liquid oxygen propellants at combustion chamber pressures of 1800 to 2400 psia and mixture ratios of 3.89 to 6.15. This report compares the experimental performance, heat transfer, and boundary layer total pressure measurements with theoretical predictions of the current Joint Army, Navy, NASA, Air Force (JANNAF) developed methodology. This methodology makes use of the Two-Dimensional Kinetics (TDK) nozzle performance code. Comparisons of the TDK-predicted performance to experimentally attained thrust performance indicated that both the vacuum thrust coefficient and the vacuum specific impulse values were approximately 2.0-percent higher than the turbulent prediction for the 1025:1 configurations, and approximately 0.25-percent higher than the turbulent prediction for the 440:1 configuration. Nozzle wall temperatures were measured on the outside of a thin-walled heat sink nozzle during the test fittings. Nozzle heat fluxes were calculated front the time histories of these temperatures and compared with predictions made with the TDK code. The heat flux values were overpredicted for all cases. The results range from nearly 100 percent at an area ratio of 50 to only approximately 3 percent at an area ratio of 975. Values of the integral of the heat flux as a function of nozzle surface area were also calculated. Comparisons of the experiment with analyses of the heat flux and the heat rate per axial length also show that the experimental values were lower than the predicted value. Three boundary layer rakes mounted on the nozzle exit were used for boundary layer measurements. This arrangement allowed total pressure measurements to be obtained at 14 different distances from the nozzle wall. A comparison of boundary layer total pressure profiles and analytical predictions show good agreement for the first 0.5 in. from the nozzle wall; but the further into the core flow that measurements were taken, the more that TDK overpredicted the boundary layer thickness.

Jankovsky, Robert S.↗
NASA NTRS1998

Minimum Climb to Cruise Noise Trajectories Modeled for the High Speed Civil Transport

The proposed U.S. High Speed Civil Transport (HSCT) will revolutionize commercial air travel by providing economical supersonic passenger service to destinations worldwide. Unlike the high-bypass turbofan engines that propel today's subsonic airliners, HSCT engines will have much higher jet exhaust speeds. Jet noise, caused by the turbulent mixing of high-speed exhaust with the surrounding air, poses a significant challenge for HSCT engine designers. To resolve this challenge, engineers have designed advanced mixer rejector nozzles that reduce HSCT jet noise to airport noise certification levels by entraining and mixing large quantities of ambient air with the engines' jet streams. Although this works well during the first several minutes of flight, far away from the airport, as the HSCT gains speed and climbs, poor ejector inlet recovery and ejector ram drag contribute to poor thrust, making it advantageous to turn off the ejector. Doing so prematurely, however, can cause unacceptable noise levels to propagate to the ground, even when the aircraft is many miles from the airport. This situation lends itself ideally to optimization, where the aircraft trajectory, throttle setting, and ejector setting can be varied (subject to practical aircraft constraints) to minimize the noise propagated to the ground. A method was developed at the NASA Lewis Research Center that employs a variation of the classic energy state approximation: a trajectory analysis technique historically used to minimize climb time or fuel burned in many aircraft problems. To minimize the noise on the ground at any given throttle setting, high aircraft altitudes are desirable; but the HSCT may either climb quickly to high altitudes using a high, noisy throttle setting or climb more slowly at a lower, quieter throttle setting. An optimizer has been programmed into NASA's existing aircraft and noise analysis codes to balance these options by dynamically choosing the best altitude-velocity path and throttle setting history. The noise level standard, or metric, used in the optimizer should be one that accurately reflects the subjective annoyance levels of ground-based observers under the flight path. A variety of noise metrics are available, many of which are practical for airport-vicinity noise certification. Unlike airport noise, however, the HSCT's climb noise will be characterized by relatively low noise levels, long durations, and low-frequency spectra. The noise metrics used in these calculations are based on the recommendations of researchers at the NASA Langley Research Center, who have correlated the flyover noise annoyance levels of actual laboratory subjects with a variety of measurements. Analysis of data from this optimizer has shown that significant reductions in noise may be obtained with trajectory optimization. And since throttling operations are performed in the subsonic portion of the climb path (where thrust is plentiful), only small penalties in HSCT range or fuel performance occur.

Berton, Jeffrey J.↗
NASA NTRS2001

Microgravity Combustion Science and Fluid Physics Experiments and Facilities for the ISS

At the NASA Glenn Research Center, the Microgravity Science Program supports both ground-based and flight experiment research in the disciplines of Combustion Science and Fluid Physics. Combustion Science research includes the areas of gas jet diffusion flames, laminar flames, burning of droplets and misting fuels, solids and materials flammability, fire and fire suppressants, turbulent combustion, reaction kinetics, materials synthesis, and other combustion systems. The Fluid Physics discipline includes the areas of complex fluids (colloids, gels, foams, magneto-rheological fluids, non-Newtonian fluids, suspensions, granular materials), dynamics and instabilities (bubble and drop dynamics, magneto/electrohydrodynamics, electrochemical transport, geophysical flows), interfacial phenomena (wetting, capillarity, contact line hydrodynamics), and multiphase flows and phase changes (boiling and condensation, heat transfer, flow instabilities). A specialized International Space Station (ISS) facility that provides sophisticated research capabilities for these disciplines is the Fluids and Combustion Facility (FCF). The FCF consists of the Combustion Integrated Rack (CIR), the Fluids Integrated Rack (FIR) and the Shared Accommodations Rack and is designed to accomplish a large number of science investigations over the life of the ISS. The modular, multiuser facility is designed to optimize the science return within the available resources of on-orbit power, uplink/downlink capacity, crew time, upmass/downmass, volume, etc. A suite of diagnostics capabilities, with emphasis on optical techniques, will be provided to complement the capabilities of the subsystem multiuser or principal investigator-specific experiment modules. The paper will discuss the systems concept, technical capabilities, functionality, and the initial science investigations in each discipline.

Lauver, Richard W.↗
NASA NTRS2016

Analysis of the Capacity Potential of Current Day and Novel Configurations for New York's John F. Kennedy Airport

In 2015, a series of systems analysis studies were conducted on John F. Kennedy Airport in New York (NY) in a collaborative effort between NASA and the Port Authority of New York and New Jersey (PANYNJ). This work was performed to build a deeper understanding of NY airspace and operations to determine the improvements possible through operational changes with tools currently available, and where new technology is required for additional improvement. The analysis was conducted using tool-based mathematical analyses, video inspection and evaluation using recorded arrival/departure/surface traffic captured by the Aerobahn tool (used by Kennedy Airport for surface metering), and aural data archives available publically through the web to inform the video segments. A discussion of impacts of trajectory and operational choices on capacity is presented, including runway configuration and usage (parallel, converging, crossing, shared, independent, staggered), arrival and departure route characteristics (fix sharing, merges, splits), and how compression of traffic is staged. The authorization in March of 2015 for New York to use reduced spacing under the Federal Aviation Administration (FAA) Wake Turbulence Recategorization (RECAT) also offers significant capacity benefit for New York airports when fully transitioned to the new spacing requirements, and the impact of these changes for New York is discussed. Arrival and departure capacity results are presented for each of the current day Kennedy Airport configurations. While the tools allow many variations of user-selected conditions, the analysis for these studies used arrival-priority, no-winds, additional safety buffer of 5% to the required minimum spacing, and a mix of traffic typical for Kennedy. Two additional "novel" configurations were evaluated. These configurations are of interest to Port Authority and to their airline customers, and are believed to offer near-term capacity benefit with minimal operational and equipage changes. One of these is the addition of an Optimized Profile Descent (OPD) route to runways 22L and 22R, and the other is the simultaneous use of 4 runways, which is not currently done at Kennedy. The background and configuration for each of these is described, and the capacity results are presented along with a discussion of drawbacks and enablers for each.

Glaab, Patricia↗
NASA NTRS1991

Flow of superfluid helium in tubes with heated walls

The equations for superfluid helium flowing through a straight tube with heated walls are integrated. The model equations are based on those of Landau as modified for superfluid turbulence by Gorter and Mellink (1949). The model is implemented by the program SUPERFLOW which runs on a personal computer. The effect of the heating level on the mass flux, the energy flux, and the pressure and temperature profiles is investigated. The four types of profiles which occur without sidewall heating are also found with heated walls. The progression through these four types is shown to depend primarily on the dimensionless parameter, defined previously to characterize the unheated profiles, and a dimensionless ratio of heat fluxes. The pressure and temperature maxima which rise well above the boundary values increase significantly with sidewall heating. Approximate design equations for estimating the mass flux and the profiles are presented. The physical basis of the results is discussed. These results are useful in the design of optimal cooling loops and other superfluid flow systems.

Snyder, H. A.↗
NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗
DOE OSTI2021

Vertical-Axis Wind Turbine Steady and Unsteady Aerodynamics for Curved Deforming Blades

Vertical-axis wind turbines’ simpler design and low center of gravity make them ideal for floating wind applications. However, efficient design optimization of floating systems requires fast and accurate models. Low-fidelity vertical-axis turbine aerodynamic models, including double multiple streamtube and actuator cylinder theory, were created during the 1980s. Commercial development of vertical-axis turbines all but ceased in the 1990s until around 2010 when interest resurged for floating applications. Despite the age of these models, the original assumptions (2-D, rigid, steady, straight bladed) have not been revisited in full. When the current low-fidelity formulations are applied to modern turbines in the unsteady domain, aerodynamic load errors nearing 50% are found, consistent with prior literature. However, a set of steady and unsteady modifications that remove the majority of error is identified, limiting it near 5%. This paper shows how to reformulate the steady models to allow for unsteady inputs including turbulence, deforming blades, and variable rotational speed. A new unsteady approximation that increases numerical speed by 5–10× is also presented. Combined, these modifications enable full-turbine unsteady simulations with accuracy comparable to higher-fidelity vortex methods, but over 5000× faster.

17 WIND ENERGY↗
NASA NTRS1991

Evaluation of tunnel sidewall boundary-layer-control systems for high-lift airfoil testing

An experimental study was conducted in the NASA Langley Low-Turbulence Pressure Tunnel to evaluate a suction sidewall boundary-layer-control (BLC) technique used in testing 2D high-lift airfoils. Sidewall BLC is required to maintain spanwise two-dimensionality of the flow over the airfoil at large angles of attack. A supercritical-type high-lift air-foil, equipped with a double-slotted flap and a leading-edge slat, was used for the study which was conducted at a Mach number of 0.2 and Reynolds numbers based on chord of 9 and 16 million. The sidewall BLC technique, which features distributed suction through porous endplates connected to a venting system, was able to control sidewall boundary-layer separation and maintain two-dimensional flow over the high-lift configuration for both Reynolds numbers tested. Discussions on porous endplate optimization and effects of suction on section lift are presented. Results obtained with the suction system were also compared with previous data obtained with a tangential blowing BLC system for the same high-lift configuration.

Paschal, K.↗
NASA NTRS2004

Model of Atmospheric Links on Optical Communications from High Altitude

Optical communication links have the potential to solve many of the problems of current radio and microwave links to satellites and high-altitude aircraft. The higher frequency involved in optical systems allows for significantly greater signal bandwidth, and thus information transfer rate, in excess of 10 Gbps, and the highly directional nature of laser-based signals eliminates the need for frequency-division multiplexing seen in radio and microwave links today. The atmosphere, however, distorts an optical signal differently than a microwave signal. While the ionosphere is one of the most significant sources of noise and distortion in a microwave or radio signal, the lower atmosphere affects an optical signal more significantly. Refractive index fluctuations, primarily caused by changes in atmospheric temperature and density, distort the incoming signal in both deterministic and nondeterministic ways. Additionally, suspended particles, such as those in haze or rain, further corrupt the transmitted signal. To model many of the atmospheric effects on the propagating beam, we use simulations based on the beam-propagation method. This method, developed both for simulation of signals in waveguides and propagation in atmospheric turbulence, separates the propagation into a diffraction and refraction problem. The diffraction step is an exact solution, within the limits of numerical precision, to the problem of propagation in free space, and the refraction step models the refractive index variances over a segment of the propagation path. By applying refraction for a segment of the propagation path, then diffracting over that same segment, this method forms a good approximation to true propagation through the atmospheric medium. Iterating over small segments of the total propagation path gives a good approximation to the problem of propagation over the entire path. Parameters in this model, such as initial beam profile and atmospheric constants, are easily modified in a simulation such as this, which allows for the rapid analysis of different propagation scenarios. Therefore, this method allows the development of a near-optimal system design for a wide range of situations, typical of what would be seen in different atmospheric conditions over a receiving ground station. A simulation framework based upon this model was developed in FORTRAN, and for moderate grid sizes and propagation distances these simulations are computable in reasonable time on a standard workstation. This presentation will discuss results thus far.

Subich, Christopher↗
DOE OSTI2023

Entropy-driven Optimal Sub-sampling of Fluid Dynamics for Developing Machine-learned Surrogates

Optimal sub-sampling of large datasets from fluid dynamics simulations is essential for training reduced-order machine learned models. A method using Shannon entropy was developed to weight flow features according to their level of information content, such that the most informative features can be extracted and used for training a surrogate model. The method is demonstrated in the canonical flow over a cylinder problem simulated with OpenFOAM. Both time-independent predictions and temporal forecasting were investigated as well as two types of prediction targets: local per-grid-point predictions and global per-time-step predictions. When tested on training a surrogate model, results indicate that our entropy-based sampling method typically outperforms random sampling and yields more reproducible results in less iterations. Finally, the method was used to train a surrogate model for modeling turbulence in magnetohydrodynamic flows, which revealed various challenges and opportunities for future research.

Brewer, Wes↗
NASA NTRS2004

The Impact of Model Uncertainty on Spatial Compensation in Active Structural Acoustic Control

Turbulent boundary layer (TBL) noise is considered a primary factor in the interior noise experienced by passengers aboard commercial airliners. There have been numerous investigations of interior noise control devoted to aircraft panels; however, practical realization is a challenge since the physical boundary conditions are uncertain at best. In most prior studies, pinned or clamped boundary conditions have been assumed; however, realistic panels likely display a range of varying boundary conditions between these two limits. Uncertainty in boundary conditions is a challenge for control system designers, both in terms of the compensator implemented and the location of actuators and sensors required to achieve the desired control. The impact of model uncertainties, uncertain boundary conditions in particular, on the selection of actuator and sensor locations for structural acoustic control are considered herein. Results from this research effort indicate that it is possible to optimize the design of actuator and sensor location and aperture, which minimizes the impact of boundary conditions on the desired structural acoustic control.

Cabell, Randolph H.↗
NASA NTRS2021

Determining Planetary Boundary Layer Height by Micro-pulse Lidar with Validation by UAV Measurements

Planetary boundary layer height (PBLH) is often used to characterize the structure of the lower atmosphere. Aerosol lidar, a ground-based remote sensing method, provides the vertical distribution of aerosol at a high temporal resolution observation data, from which, the PBL structure and the position of the PBL top can be comprehensively studied. PBLH determination with lidar data depends primarily on the characteristic turbulent motions in the atmosphere and the geophysical location. However, lidar determination of PBLH over densely populated subtropical locations has rarely been discussed; thus, developing retrieval techniques suitable to these areas is necessary. In this study, four PBLH determination methods (Gradient, δ–threshold, Haar wavelet transform, and hybrid image processing) are applied to estimate the PBLH from lidar observations over an urban area in East Asia, and one—the Gradient method—relied on potential temperature measurements from an unmanned aerial vehicle (UAV) flights to validate our results. Our results indicate that a combination of the gradient method and δ-threshold method can provide better results, in terms of diurnal pattern, than using either method individually. Furthermore, the Haar wavelet and the Hybrid image processing can detect the PBL development comparably well, but both methods are dependent on their initial conditions and optimized algorithm settings. In addition, the accompanying UAV observations are conclusively shown to have a high degree of efficacy for validating the lidar data. This research highlights that a combination of PBLH determination methods can better describe the PBLH evolution throughout a day in some cases, while in others less common determination methods are proving useful, and a suite of retrieval methods should still be explored for precisely mapping the PBL in densely populated subtropical areas.

Yueh-Chen Wang↗
NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗