Search NASA⌕ Search

SEARCH · Search NASA

Results for “wake model validation”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Validation of a flight simulation model of the AH-64 Apache attack helicopter against flight test data

The FLYRT simulation model of the U.S. Army/McDonnell Douglas AH-64 Apache attack helicopter is validated against flight test data. The approach used for validation involves matching static trim attitudes and control positions and driving the model with measured control time histories to compare dynamic responses such as angular rates and normal acceleration. Flight test data is processed to determine kinematic consistency in the angular degrees of freedom. Modeling problems associated with aerodynamic interaction of the main rotor wake on the horizontal stabilator and engine response timing are identified. Appropriate model updates are made which result in good overall model correlation throughout the flight regime investigated.

Harding, J. W.↗
DOE OSTI2021

Design and analysis of a wake model for spatially heterogeneous flow

Abstract. Methods of turbine wake modeling are being developed to more accurately account for spatially variant atmospheric conditions within wind farms. Most current wake modeling utilities are designed to apply a uniform flow field to the entire domain of a wind farm. When this method is used, the accuracy of power prediction and wind farm controls can be compromised depending on the flow-field characteristics of a particular area. In an effort to improve strategies of wind farm wake modeling and power prediction, FLOw Redirection and Induction in Steady State (FLORIS) was developed to implement sophisticated methods of atmospheric characterization and power output calculation. In this paper, we describe an adapted FLORIS model that features spatial heterogeneity in flow-field characterization. This model approximates an observed flow field by interpolating from a set of atmospheric measurements that represent local weather conditions. The objective of this method is to capture heterogeneous atmospheric effects caused by site-specific terrain features, without explicitly modeling the geometry of the wind farm terrain. The implemented adaptations were validated by comparing the simulated power predictions generated from FLORIS to the actual recorded wind farm output from the supervisory control and data acquisition (SCADA) recordings and large eddy simulations (LESs). When comparing the performance of the proposed heterogeneous model to homogeneous FLORIS simulations, the results show a 14.6 % decrease for mean absolute error (MAE) in wind farm power output predictions for cases using wind farm SCADA data and a 18.9 % decrease in LES case studies. The results of these studies also indicate that the efficacy of the proposed modeling techniques may vary with differing site-specific operational conditions. This work quantifies the accuracy of wind plant power predictions under heterogeneous flow conditions and establishes best practices for atmospheric surveying for wake modeling.

17 WIND ENERGY↗
DOE OSTI2021

Wind Energy Forecasting with the Weather Research and Forecasting Model

This was a collaborative effort between Lawrence Livermore National Security, LLC as manager and operator of Lawrence Livermore National Laboratory (LLNL) and Siemens Energy, Inc. (Siemens) to develop a wind resource forecasting tool. LLNL was to develop an independent high-resolution mesoscale modeling capability forecasting tool that could be implemented in conjunction with existing wind farm control and monitoring software to provide forecasting of wind resources using local observations of winds and temperature. Research with LLNL’s state-of-the-art large-eddy simulation meteorological prediction model, based on the community WRF model and innovative turbulence parameterizations, would improve that model’s applicability to large wind farms offshore and in complex terrain. The modeling capability would include uncertainty quantification. Finally, the application of the modeling tool and existing global climate change predictions would enable the delineation of the likely effects of climate change on wind resources. Siemens was to provide high time resolution hub-height wind speed and other meteorological data streams, including temperature profiles from wind farms, for LLNL to incorporate into the modeling system, to validate and tune this forecasting model for their locations of interest. These data streams would also be used for longer-term studies of correlations of wind resources to climate oscillations to indicate how long-term climate change trends may affect the available wind resource. Siemens would also provide information and observations of turbine wakes for incorporation into the modeling tool. By implementing state-of-the-art turbulence parameterizations into a simulation model and/or ensembles of simulation models, and by integrating real-time hub height wind speed and other meteorological datastreams from wind farms into that model or ensemble of models, LLNL would develop a forecasting tool that could be implemented by Siemens as an add-on to existing wind farm control and monitoring software to provide owners with useful resource forecasting. The desired outcome was that the accuracy level of the output would be sufficient to substantiate power output commitments. The final deliverable for this work would consist of a document outlining the algorithms and software tools that could be integrated into Siemens Wind Park Supervisor.

17 WIND ENERGY↗
NASA NTRS2001

A Model Rotor in Axial Flight

A model rotor was mounted horizontally in the settling chamber of a wind tunnel to obtain performance and wake structure data under low climb conditions. The immediate wake of the rotor was carefully surveyed using 3-component particle image velocimetry to define the velocity and vortical content of the flow, and used in a subsequent study to validate a theory for the separate determination of induced and profile drag. Measurements were obtained for two collective pitch angles intended to render a predominately induced drag state and another with a marked increase in profile drag. A majority of the azimuthally directed vorticity in the wake was found to be concentrated in the tip vortices. However, adjacent layers of inboard vorticity with opposite sense were clearly present. At low collective, the close proximity of the tip vortex from the previous blade caused the wake from the most recent blade passage to be distorted. The deficit velocity component that was directed along the azimuth of the rotor blade was never more that 15 percent of the rotor tip speed, and except for the region of the tip vortex, appeared to have totally disappeared form the wake left by the previous blade.

McAlister, K. W.↗
NASA NTRS2015

Unsteady Thick Airfoil Aerodynamics: Experiments, Computation, and Theory

An experimental, computational and theoretical investigation was carried out to study the aerodynamic loads acting on a relatively thick NACA 0018 airfoil when subjected to pitching and surging, individually and synchronously. Both pre-stall and post-stall angles of attack were considered. Experiments were carried out in a dedicated unsteady wind tunnel, with large surge amplitudes, and airfoil loads were estimated by means of unsteady surface mounted pressure measurements. Theoretical predictions were based on Theodorsen's and Isaacs' results as well as on the relatively recent generalizations of van der Wall. Both two- and three-dimensional computations were performed on structured grids employing unsteady Reynolds-averaged Navier-Stokes (URANS). For pure surging at pre-stall angles of attack, the correspondence between experiments and theory was satisfactory; this served as a validation of Isaacs theory. Discrepancies were traced to dynamic trailing-edge separation, even at low angles of attack. Excellent correspondence was found between experiments and theory for airfoil pitching as well as combined pitching and surging; the latter appears to be the first clear validation of van der Wall's theoretical results. Although qualitatively similar to experiment at low angles of attack, two-dimensional URANS computations yielded notable errors in the unsteady load effects of pitching, surging and their synchronous combination. The main reason is believed to be that the URANS equations do not resolve wake vorticity (explicitly modeled in the theory) or the resulting rolled-up un- steady flow structures because high values of eddy viscosity tend to \smear" the wake. At post-stall angles, three-dimensional computations illustrated the importance of modeling the tunnel side walls.

Strangfeld, C.↗
NASA NTRS1994

Validation of Vortex-Lattice Method for loads on wings in lift-generated wakes

A study is described that evaluates the accuracy of vortex-lattice methods when they are used to compute the loads induced on aircraft as they encounter lift-generated wakes. The evaluation is accomplished by use of measurements made in the 80- by 120-foot wind tunnel of the lift, rolling-moment, and downwash in the wake of three configurations of a model of a subsonic transport aircraft. The downwash measurements are used as input for a vortex-lattice code in order to compute the lift and rolling moment induced on wings that have a span of 0.186, 0.510, or 1.022 times the span of the wake-generating model. Comparison of the computed results with the measured lift and rolling moment distributions are used to determine the accuracy of the vortex-lattice code. It was found that the vortex-lattice method is very reliable as long as the span of the encountering of following wing is less than about 0.2 of the generator span. As the span of the following wing increases above 0.2, the vortex-lattice method continues to correctly predict the trends and nature of the induced loads, but it overpredicts the magnitude of the loads by increasing amounts. The increase in deviation of the computed from the measured loads with size of the following wing is attributed to the increase in distortion of the structure of the vortex wake as it approaches and passes the larger following wings.

Rossow, J.↗
NASA NTRS1995

Validation of Vortex-Lattice Method for Loads on Wings in Lift-Generated Wakes

A study is described that evaluates the accuracy of vortex-lattice methods when they are used to compute the loads induced on aircraft as they encounter lift-generated wakes. The evaluation is accomplished by the use of measurements made in the 80 by 120 ft Wind Tunnel of the lift, rolling moment, and downwash in the wake of three configurations of a model of a subsonic transport aircraft. The downwash measurements are used as input for a vortex-lattice code in order to compute the lift and rolling moment induced on wings that have a span of 0.186, 0.510, or 1.022 times the span of the wake-generating model. Comparison of the computed results with the measured lift and rolling-moment distributions the vortex-lattice method is very reliable as long as the span of the encountering or following wing is less than about 0.2 of the generator span. As the span of the following wing increases above 0.2, the vortex-lattice method continues to correctly predict the trends and nature of the induced loads, but it overpredicts the magnitude of the loads by increasing amounts.

Rossow, Vernon J.↗
DOE OSTI2022

Scientific challenges to characterizing the wind resource in the marine atmospheric boundary layer

Abstract. With the increasing level of offshore wind energy investment, it is correspondingly important to be able to accurately characterize the wind resource in terms of energy potential as well as operating conditions affecting wind plant performance, maintenance, and lifespan. Accurate resource assessment at a particular site supports investment decisions. Following construction, accurate wind forecasts are needed to support efficient power markets and integration of wind power with the electrical grid. To optimize the design of wind turbines, it is necessary to accurately describe the environmental characteristics, such as precipitation and waves, that erode turbine surfaces and generate structural loads as a complicated response to the combined impact of shear, atmospheric turbulence, and wave stresses. Despite recent considerable progress both in improvements to numerical weather prediction models and in coupling these models to turbulent flows within wind plants, major challenges remain, especially in the offshore environment. Accurately simulating the interactions among winds, waves, wakes, and their structural interactions with offshore wind turbines requires accounting for spatial (and associated temporal) scales from O(1 m) to O(100 km). Computing capabilities for the foreseeable future will not be able to resolve all of these scales simultaneously, necessitating continuing improvement in subgrid-scale parameterizations within highly nonlinear models. In addition, observations to constrain and validate these models, especially in the rotor-swept area of turbines over the ocean, remains largely absent. Thus, gaining sufficient understanding of the physics of atmospheric flow within and around wind plants remains one of the grand challenges of wind energy, particularly in the offshore environment. This paper provides a review of prominent scientific challenges to characterizing the offshore wind resource using as examples phenomena that occur in the rapidly developing wind energy areas off the United States. Such phenomena include horizontal temperature gradients that lead to strong vertical stratification; consequent features such as low-level jets and internal boundary layers; highly nonstationary conditions, which occur with both extratropical storms (e.g., nor'easters) and tropical storms; air–sea interaction, including deformation of conventional wind profiles by the wave boundary layer; and precipitation with its contributions to leading-edge erosion of wind turbine blades. The paper also describes the current state of modeling and observations in the marine atmospheric boundary layer and provides specific recommendations for filling key current knowledge gaps.

17 WIND ENERGY↗
NASA NTRS1991

The power induced effects module: A FORTRAN code which estimates lift increments due to power induced effects for V/STOL flight

A user friendly FORTRAN code that can be used for preliminary design of V/STOL aircraft is described. The program estimates lift increments, due to power induced effects, encountered by aircraft in V/STOL flight. These lift increments are calculated using empirical relations developed from wind tunnel tests and are due to suckdown, fountain, ground vortex, jet wake, and the reaction control system. The code can be used as a preliminary design tool along with NASA Ames' Aircraft Synthesis design code or as a stand-alone program for V/STOL aircraft designers. The Power Induced Effects (PIE) module was validated using experimental data and data computed from lift increment routines. Results are presented for many flat plate models along with the McDonnell Aircraft Company's MFVT (mixed flow vectored thrust) V/STOL preliminary design and a 15 percent scale model of the YAV-8B Harrier V/STOL aircraft. Trends and magnitudes of lift increments versus aircraft height above the ground were predicted well by the PIE module. The code also provided good predictions of the magnitudes of lift increments versus aircraft forward velocity. More experimental results are needed to determine how well the code predicts lift increments as they vary with jet deflection angle and angle of attack. The FORTRAN code is provided in the appendix.

Sandlin, Doral R.↗
NASA NTRS1999

Numerical Simulation of Complex Turbomachinery Flows

An unsteady, multiblock, Reynolds Averaged Navier Stokes solver based on Runge-Kutta scheme and Pseudo-time step for turbo-machinery applications was developed. The code was validated and assessed against analytical and experimental data. It was used to study a variety of physical mechanisms of unsteady, three-dimensional, turbulent, transitional, and cooling flows in compressors and turbines. Flow over a cylinder has been used to study effects of numerical aspects on accuracy of prediction of wake decay and transition, and to modify K-epsilon models. The following simulations have been performed: (a) Unsteady flow in a compressor cascade: Three low Reynolds number turbulence models have been assessed and data compared with Euler/boundary layer predictions. Major flow features associated with wake induced transition were predicted and studied; (b) Nozzle wake-rotor interaction in a turbine: Results compared to LDV data in design and off-design conditions, and cause and effect of unsteady flow in turbine rotors were analyzed; (c) Flow in the low-pressure turbine: Assessed capability of the code to predict transitional, attached and separated flows at a wide range of low Reynolds numbers and inlet freestream turbulence intensity. Several turbulence and transition models have been employed and comparisons made to experiments; (d) leading edge film cooling at compound angle: Comparisons were made with experiments, and the flow physics of the associated vortical structures were studied; and (e) Tip leakage flow in a turbine. The physics of the secondary flow in a rotor was studied and sources of loss identified.

Chernobrovkin, A. A.↗
DOE OSTI2024

The 2023 National Offshore Wind data set (NOW-23)

Abstract. This article introduces the 2023 National Offshore Wind data set (NOW-23), which offers the latest wind resource information for offshore regions in the United States. NOW-23 supersedes, for its offshore component, the Wind Integration National Dataset (WIND) Toolkit, which was published a decade ago and is currently a primary resource for wind resource assessments and grid integration studies in the contiguous United States. By incorporating advancements in the Weather Research and Forecasting (WRF) model, NOW-23 delivers an updated and cutting-edge product to stakeholders. In this article, we present the new data set which underwent regional tuning and performance validation against available observations and has data available from 2000 through, depending on the region, 2019–2022. We also provide a summary of the uncertainty quantification in NOW-23, along with NOW-WAKES, a 1-year post-construction data set that quantifies expected offshore wake effects in the US Mid-Atlantic lease areas. Stakeholders can access the NOW-23 data set at https://doi.org/10.25984/1821404 (Bodini et al., 2020).

17 WIND ENERGY↗
NASA NTRS1997

The LaRC Wake Vortex Modelling Effort

The purpose of the modelling effort at NASA Langley, including goals, is outlined in this presentation. Included, is a description of the numerical model that is used for the NASA wake vortex modeling effort and the approach that is taken in order to achieve the stated goals. Also shown are: 1) a demonstration of using the model in a fog environment; 2) preliminary results from a 3-D simulation in a nonturbulent and thermally-stable environment with comparison to a comparable 2-D simulation of the same event; and 3) several validation cases from the Idaho-Falls and Memphis field studies where results from the 2-D version of the model are compared with Lidar and tower data.

Proctor, Fred↗
NASA NTRS2011

Modeling of Supersonic Film Cooling on the J-2X Nozzle Extension

Supersonic film cooling (SSFC) of nozzles has been used in several liquid rocket engine designs, and is being applied to the nozzle extension (NE) of the J-2X upper stage engine currently under development. Turbine exhaust gas (TEG) is injected tangentially from a manifold along the NE, and provides a thermal barrier from the core nozzle flow for the NE. As the TEG stream mixes with the nozzle flow, the effectiveness of the thermal barrier is reduced. This paper documents computational fluid dynamics (CFD) analysis work performed by NASA Marshall Space Flight Center (MSFC) to model the flow of the TEG through the manifold, into the nozzle, and the subsequent mixing of the TEG stream with the core flow. The geometry and grid of the TEG manifold, structural support ribs, and the NE wall will be shown, and the CFD boundary conditions described. The Loci-CHEM CFD code used in this work will also be briefly described. A unique approach to modeling the combined TEG manifold/thrust chamber assembly (TCA) was employed, as it was not practical to model the entire 360 circumferential range in one simulation. Prior CFD validation work modeling Calspan SSFC experiments in the early 1990s, documented in a previous AIAA paper, will also be briefly discussed. The fluid dynamics of the TEG flow through the manifold, into and between the structural support ribs, and into the nozzlette that feeds the TCA will be described. Significant swirl and non-uniformities are present, which along with the wakes from the ribs, act to degrade the film cooling effectiveness compared to idealized injection of TEG gas. The effect of these flow characteristics on the adiabatic wall temperature profile on the NE will be discussed.

Ruf, Joseph H.↗
NASA NTRS1990

Numerical investigation of laminar-turbulent transition in a flat plate wake

Lamina-turbulent transition of high-deficit flat plate wakes is investigated by direct numerical simulations using the complete Navier Stokes equations. The simulations are based on a spatial model so that both the base flow and the disturbance flow can develop in the downstream direction. The Navier Stokes equations are used in a vorticity-velocity form and are solved using a combination of finite difference and spectral approximations. Fourier series are used in the spanwise direction. Second-order finite-differences are used to approximate the spatial derivatives in the streamwise and transverse directions. For the temporal discretion, a combination of ADI, Crank-Nicolson, and Adams-Bashforth methods is employed. The discretized velocity equations are solved using fast Helmholtz solvers. Code validation is accomplished by comparison of the numerical results to both linear stability and to experiments. Calculations of two- and/or three-dimensional sinuous and mode disturbances in the wake of flat plate are undertaken. For calculations of two-dimensional disturbances, the wake is forced at an amplitude level so that nonlinear disturbance development may be observed. In addition, the forcing amplitude is varied in order to determine its effect on the disturbance behavior. To investigate the onset of three-dimensionality, the wake is forced with a small-amplitude three-dimensional disturbance and a larger amplitude two-dimensional disturbance. The two-dimensional forcing amplitude is varied in order to determine its influence on the three-dimensional flow field.

Fasel, Hermann F.↗
NASA NTRS2014

Materials International Space Station Experiment (MISSE): Overview, Accomplishments and Future Needs

Materials and devices used on the exterior of spacecraft in low Earth orbit (LEO) are subjected to environmental threats that can cause degradation in material properties, possibly threatening spacecraft mission success. These threats include: atomic oxygen (AO), ultraviolet and x-ray radiation, charged particle radiation, temperature extremes and thermal cycling, micrometeoroid and debris impacts, and contamination. Space environmental threats vary greatly based on spacecraft materials, thicknesses and stress levels, and the mission environment and duration. For more than a decade the Materials International Space Station Experiment (MISSE) has enabled the study of the long duration environmental durability of spacecraft materials in the LEO environment. The overall objective of MISSE is to test the stability and durability of materials and devices in the space environment in order to gain valuable knowledge on the performance of materials in space, as well as to enable lifetime predictions of new materials that may be used in future space flight. MISSE is a series of materials flight experiments, which are attached to the exterior of the International Space Station (ISS). Individual experiments were loaded onto suitcase-like trays, called Passive Experiment Containers (PECs). The PECs were transported to the ISS in the Space Shuttle cargo bay and attached to, and removed from, the ISS during extravehicular activities (EVAs). The PECs were retrieved after one or more years of space exposure and returned to Earth enabling post-flight experiment evaluation. MISSE is a multi-organization project with participants from the National Aeronautics and Space Administration (NASA), the Department of Defense (DoD), industry and academia. MISSE has provided a platform for environmental durability studies for thousands of samples and numerous devices, and it has produced many tangible impacts. Ten PECs (and one smaller tray) have been flown, representing MISSE 1 through MISSE 8, yielding long-duration space environmental performance and durability data that enable material validation, processing recertification and space qualification; improved predictions of materials and component lifetimes in space; model verification and development; and correlation factors between space-exposure and ground-facilities enabling more accurate in-space performance predictions based on ground-laboratory testing. A few of the many experiment results and observations, and their impacts, are provided. Those highlighted include examples on improved understanding of atomic oxygen scattering mechanisms, LEO coating durability results, and polymer erosion yields and their impacts on spacecraft design. The MISSE 2 Atomic Oxygen Scattering Chamber Experiment discovered that the peak flux of scattered AO was determined to be 45 deg from normal incidence, not the model predicted cosine dependence. In addition, the erosion yield (E(sub y)) of Kapton H for AO scattered off oxidized-Al is 22% of the E(sub y) of direct AO impingement. These results were used to help determine the degradation mechanism of a cesium iodide detector within the Hubble Space Telescope Cosmic Origins Spectrograph Experiment. The MISSE 6 Indium Tin Oxide (ITO) Degradation Experiment measured surface electrical resistance of ram and wake ITO coated samples. The data confirmed that ITO is a stable AO protective coating, and the results validated the durability of ITO conductive coatings for solar arrays for the Atmosphere-Space Transition 2 Explorer program. The MISSE 2, 6 and 7 Polymer Experiments have provided LEO AO Ey data on over 120 polymer and composites samples. The flight E(sub y) values were found to range from 3.05 x 10(exp -26) cu cm/atom for the AO resistant polymer CORIN to 9.14 x 10(exp -26) cu cm/atom for polyoxymethylene (POM). In addition, flying the same polymers on different missions has advanced the understanding of the AO E(sub y) dependency on solar exposure for polymers containing fluorine. The MISSE polymer results are highly requested and have impacted spacecraft design for WorldView-2 & -3, the Global Precipitation Measurement-Microwave Imager, and other spacecraft. The flight data has enabled the development of an Atomic Oxygen Erosion Predictive Tool that allows the erosion prediction of new and non-flown polymers. The data has also been used to develop a new NASA Technical Standards Handbook "Spacecraft Polymers Atomic Oxygen Durability Handbook." Many intangible benefits have also been derived from MISSE. For example, over 40 students have collaborated on Glenn's MISSE experiments, which have resulted in greater than $80K in student scholarships and awards in national and international science fairs. Students have also given presentations and won poster competition awards at international space conferences.

Flight Experiment↗
NASA NTRS1992

Validation and applications of the POLAR code

The Potentials of Large Objects in the Auroral Region (POLAR) code was written to model the charging of large spacecraft by auroral electrons in low polar orbit. It has also proven to be a powerful tool for analysis of active and voltage-plasma interactions. POLAR combines 3-D object definition, direct solution to Poisson's equation, space charge transport, and surface charge computation. Physical effects treated by POLAR include the plasma wake and ram, the geomagnetic field, ionization, sheath and barrier formation, and photo and secondary electron generation and transport. Polar development is complete and it is now available to the aerospace community. The methodology of POLAR is reviewed but concentration is on the applications of POLAR to physical problems and observations with the intent of demonstrating both the code's capabilities, and its limitations. These applications include the Space Shuttle, the Defense Meteorological Satellite Program (DMSP) satellites, sounding rockets, plasma chamber experiments, and things not yet flown.

Cooke, David L.↗
DOE OSTI2025

AMR-Wind: A Performance-Portable, High-Fidelity Flow Solver for Wind Farm Simulations

We present AMR-Wind, a verified and validated high-fidelity computational-fluid-dynamics code for wind farm flows. AMR-Wind is a block-structured, adaptive-mesh, incompressible-flow solver that enables predictive simulations of the atmospheric boundary layer and wind plants. It is a highly scalable code designed for parallel high-performance computing with a specific focus on performance portability for current and future computing architectures, including graphical processing units (GPUs). In this paper, we detail the governing equations, the numerical methods, and the turbine models. Establishing a foundation for the correctness of the code, we present the results of formal verification and validation. The verification studies, which include a novel actuator line test case, indicate that AMR-Wind is spatially and temporally second-order accurate. The validation studies demonstrate that the key physics capabilities implemented in the code, including actuator disk models, actuator line models, turbulence models, and large eddy simulation (LES) models for atmospheric boundary layers, perform well in comparison to reference data from established computational tools and theory. We conclude with a demonstration simulation of a 12-turbine wind farm operating in a turbulent atmospheric boundary layer, detailing computational performance and realistic wake interactions.

17 WIND ENERGY↗
NASA NTRS1983

Numerical solution of three-dimensional unsteady transonic flow over wings including inviscid/viscous interactions

A numerical procedure is presented for computing the unsteady transonic flow field about three dimensional swept wings undergoing general time dependent motion. The outer inviscid portion of the flow is assumed to be governed by the modified unsteady transonic small disturbance potential equation which is integrated in the time domain by means of an efficient alternating direction implicit approximate factorization algorithm. Gross dominant effects of the shock boundary layer interaction are accounted for by a simple empirically defined model. Viscous flow regions adjacent to the wing surface and in the trailing wake are described by a set of integral equations appropriate for compressible turbulent shear layers. The two dimensional boundary layer equations are applied quasi-statically stripwise across the span. Coupling with the outer inviscid flow is implemented through use of the displacement thickness concept within the limitations of small disturbance theory. Validity of the assumptions underlying the method is established by comparison with experimental data for the flow about a high aspect ratio transport wing having an advanced airfoil section.

Rizzetta, D. P.↗