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NASA NTRS1959

Formulas Pertinent to the Calculation of Flow-Field Effects at Supersonic Speeds Due to Wing Thickness

Expressions based on linearized supersonic-flow theory are derived for the perturbation velocity potential in space due to wing thickness for rectangular wings with biconvex airfoil sections and for arrow, delta, and quadrilateral wings with wedge-type airfoil sections. The complete range of supersonic speeds is considered subject to a minor aspect-ratio-Mach number restriction for the rectangular plan form and to the condition that the trailing edge is supersonic for the sweptback wings. The formulas presented can be utilized in determining the induced-flow characteristics at any point in the field and are readily adaptable for either numerical computation or analytical determination of any velocity components desired.

Margolis, Kenneth↗

NASA NTRS1983

Linearized potential solution for an airfoil in nonuniform parallel streams

A small perturbation potential flow theory is applied to the problem of determining the chordwise pressure distribution, lift and pitching moment of a thin airfoil in the middle of five parallel streams. This theory is then extended to the case of an undisturbed stream having a given smooth velocity profile. Two typical examples are considered and the results obtained are compared with available solutions of Euler's equations. The agreement between these two results is not quite satisfactory. Possible reasons for the differences are indicated.

Prabhu, R. K.↗

DOE OSTI2022

An Open-Source Frequency-Domain Model for Floating Wind Turbine Design Optimization

A new frequency-domain dynamics model has been developed that uses open-source components to efficiently represent a complete floating wind turbine system. The model, called RAFT (Response Amplitudes of Floating Turbines), incorporates quasi-static mooring reactions, strip-theory and potential-flow hydrodynamics, blade-element-momentum aerodynamics, and linear turbine control. The formulation is compatible with a wide variety of support structure configurations and no manual or time-domain preprocessing steps are required, making RAFT very practical in design and optimization workflows. The model is applied to three reference floating wind turbine designs and its predictions are compared with results from time-domain OpenFAST simulations. There is good agreement in mean offsets as well the statistics and spectra of the dynamic response, verifying RAFT’s general suitability for floating wind analysis. Follow-on work will include verification of potential-flow and turbine-control features and application to optimization problems.

17 WIND ENERGY↗

NASA NTRS1995

Sensitivity analysis for aeroacoustic and aeroelastic design of turbomachinery blades

A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.

Lorence, Christopher B.↗

NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

NASA NTRS1954

Lift and moment coefficients expanded to the seventh power of frequency for oscillating rectangular wings in supersonic flow and applied to a specific flutter problem

Linearized theory for compressible unsteady flow is used to derive the velocity potential and lift and moment coefficients in the form of oscillating rectangular wing moving at a constant supersonic speed. Closed expressions for the velocity potential and lift and moment coefficients associated with pitching and translation are given to seventh power of the frequency. These expressions extend the range of usefulness of NACA report 1028 in which similar expressions were derived to the third power of the frequency of oscillation. For example, at a Mach number of 10/9 the expansion of the potential to the third power is an accurate representation of the potential for values of the reduced frequency only up to about 0.08; whereas the expansion of the potential to the seventh power is an accurate representation for values of the reduced frequency up to about 0.2. The section and total lift and moment coefficients are discussed with the aid of several figures. In addition, flutter speeds obtained in the Mach number range from 10/9 to 10/6 for a rectangular wing of aspect ratio 4.53 by using section coefficients derived on the basis of three-dimensional flow are compared with flutter speeds for this wing obtained by using coefficients derived on the basis of two-dimensional flow.

Nelson, Herbert C↗

NASA NTRS1993

Turbine blade forced response prediction using FREPS

This paper describes a software system called FREPS (Forced REsponse Prediction System) that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced response dynamic stresses in axial flow turbomachinery blades due to aerodynamic and mechanical excitations. A flutter analysis capability is also incorporated into the system. The FREPS system performs aeroelastic analysis by modeling the motion of the blade in terms of its normal modes. The structural dynamic analysis is performed by a finite element code such as MSC/NASTRAN. The steady aerodynamic analysis is based on nonlinear potential theory and the unsteady aerodynamic analyses is based on the linearization of the non-uniform potential flow mean. The program description and presentation of the capabilities are reported herein. The effectiveness of the FREPS package is demonstrated on the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine. Both flutter and forced response analyses are performed and typical results are illustrated.

Murthy, Durbha, V.↗

NASA NTRS1974

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method. Part 1. Theory and results

The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The analysis uses parabolic elements and linearly-varying source density. The result is a large increase in computing speed and accuracy. The theory is described, and the effectiveness of the modification is illustrated.

Hess, J. L.↗

NASA NTRS1953

Steady vibrations of wing of circular plan form

This paper treats the problem of determining the lift, moment, and induced drag of a thin wing of circular plan form in uniform incompressible flow on the basis of linearized theory. As contrasted to a similar paper by Kinner, in which the acceleration potential method was used, the present paper utilizes the concept of the velocity potential. Calculations of the lift and moment are presented for several deformed shapes. It is shown that considerable deviations exist between the strip theory analysis and the more exact theory. The lift, moment, and induced drag are also determined for a harmonically oscillatory circular plan form wing. As contrasted to a similar paper by Schade, in which the acceleration potential method was used, the present paper utilizes the concept of the velocity potential. Expressions for lift, moment, and induced drag are given and finally specialized to the case of a slowly oscillating circular wing.

FLUTTER - WINGS↗

NASA NTRS1941

The elliptic wing based on the potential theory

This article is intended as a contribution to the theory of the lifting surface. The aerodynamics of the elliptic wing in straight and oblique flow are explored on the basis of potential theory. The foundation of the calculation is the linearized theory of the acceleration potential in which all small quantities of higher order are disregarded.

Krienes, Klaus↗

NASA NTRS1958

Drag Minimization for Wings and Bodies in Supersonic Flow

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Heaslet, Max A↗

NASA NTRS1948

A linearized solution for time-dependent velocity potentials near three-dimensional wings at supersonic speeds

Explore the source record for details and available documents.

SUPERSONIC↗

NASA NTRS2020

Convolutional Neural Network for Transition Modeling Based on Linear Stability Theory

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based empirical formulas based on integral quantities such as the shape factor of the boundary layer. However, in many applications of computational fluid dynamics, the shape factor is not straightforwardly available or not well-defined. We propose using the complete velocity profile along with other quantities (e.g., frequency, Reynolds number) to predict the perturbation amplification factor. While this can be achieved with regression models based on a classical fully connected neural network, such a model can be computationally more demanding. We propose a novel convolutional neural network inspired by the underlying physics as described by the stability equations. Specifically, convolutional layers are first used to extract integral quantities from the velocity profiles, and then fully connected layers are used to map the extracted integral quantities, along with frequency and Reynolds number, to the output (amplification ratio). Numerical tests on classical boundary layers clearly demonstrate the merits of the proposed method. More importantly, we demonstrate that, for Tollmien-Schlichting instabilities in two-dimensional, low-speed boundary layers, the proposed network encodes information in the boundary layer profiles into an integral quantity that is strongly correlated to a well-known, physically defined parameter – the shape factor.

Laminar-turbulent transition↗

NASA NTRS1987

Winglets on low aspect ratio wings

The drag reduction potentially available from the use of winglets at the tips of low aspect ratio (1.75-2.67) wings with pronounced (45-60 deg) leading edge sweep is assessed numerically for the case of a cruise design point at Mach of 0.8 and a lift coefficient of 0.3. Both wing-winglet and wing-alone design geometries are derived from a linear-theory, minimum induced drag design methodology. Relative performance is evaluated with a nonlinear extended small disturbance potential flow analysis code. Predicted lift coefficient/pressure drag coefficient increases at equal lift for the wing-winglet configurations over the wing-alone planform are of the order of 14.6-15.8, when boundary layer interaction is included.

Kuhlman, John M.↗

NASA NTRS1992

FREPS - A forced response prediction system for turbomachinery blade rows

FREPS (Forced REsponse Predicition System) is a software system that integrates structural dynamic, steady and unsteady aerodynamic analyses to efficiently predict the forced dynamic stresses of turbomachinery blades to aerodynamic and mechanical excitations. The program performs flutter analysis also. The FREPS system uses a modal approach for aeroelastic analysis. The structural dynamic analysis is based on MSC/NASTRAN, the steady aerodynamic analysis is based on potential theory and the unsteady aerodynamic analysis is based on a linearization of the non-uniform potential mean flow. The capabilities of the program are described and illustrated by application to the High Pressure Oxygen Turbopump turbine of the Space Shuttle Main Engine.

Murthy, Durbha V.↗

NASA NTRS1986

An analysis for the sound field produced by rigid wide cord dual rotation propellers of high solidarity in compressible flow

An unsteady lifting service theory for the counter-rotating propeller is presented using the linearized governing equations for the acceleration potential and representing the blades by a surface distribution of pulsating acoustic dipoles distributed according to a modified Birnbaum series. The Birnbaum series coefficients are determined by satisfying the surface tangency boundary conditions on the front and rear propeller blades. Expressions for the combined acoustic resonance modes of the front prop, the rear prop and the combination are also given.

Ramachandra, S. M.↗

NASA NTRS1986

An approach to the calculation of the pressure field produced by rigid wide chord dual rotation propellers of high solidity in compressible flow

Ramachandra, S. M.↗

NASA NTRS1989

Influence of thickness and camber on the aeroelastic stability of supersonic throughflow fans: An engineering approach

An engineering approach was used to include the nonlinear effects of thickness and camber in an analytical aeroelastic analysis of cascades in supersonic acial flow (supersonic leading-edge locus). A hybrid code using Lighthill's nonlinear piston theory and Lanes's linear potential theory was developed to include these nonlinear effects. Lighthill's theory was used to calculate the unsteady pressures on the noninterference surface regions of the airfoils in cascade. Lane's theory was used to calculate the unsteady pressures on the remaining interference surface regions. Two airfoil profiles was investigated (a supersonic throughflow fan design and a NACA 66-206 airfoil with a sharp leading edge). Results show that compared with predictions of Lane's potential theory for flat plates, the inclusion of thickness (with or without camber) may increase or decrease the aeroelastic stability, depending on the airfoil geometry and operating conditions. When thickness effects are included in the aeroelastic analysis, inclusion of camber will influence the predicted stability in proportion to the magnitude of the added camber. The critical interblade phase angle, depending on the airfoil profile and operating conditions, may also be influenced by thickness and camber. Compared with predictions of Lane's linear potential theory, the inclusion of thickness and camber decreased the aerodynamic stifness and increased the aerodynamic damping at Mach 2 and 2.95 for a cascade of supersonic throughflow fan airfoils oscillating 180 degrees out of phase at a reduced frequency of 0.1.

Ramsey, John K.↗