Results for “AIRFOILS - CIRCULAR TRANSFORMATION” — Page 6

NASA NTRS1980

Lear jet boundary layer/shear layer laser propagation experiments

Optical degradations of aircraft turbulent boundary layers with shear layers generated by aerodynamic fences are analyzed. A collimated 2.5 cm diameter helium-neon laser (0.63 microns) traversed the approximate 5 cm thick natural aircraft boundary layer in double pass via a reflective airfoil. In addition, several flights examined shear layer-induced optical degradation. Flight altitudes ranged from 1.5 to 12 km, while Mach numbers were varied from 0.3 to 0.8. Average line spread function (LSF) and Modulation Transfer Function (MTF) data were obtained by averaging a large number of tilt-removed curves. Fourier transforming the resulting average MTF yields an LSF, thus affording a direct comparison of the two optical measurements. Agreement was good for the aerodynamic fence arrangement, but only fair in the case of a turbulent boundary layer. Values of phase variance inferred from the LSF instrument for a single pass through the random flow and corrected for a large aperture ranged from 0.08 to 0.11 waves (lambda = .63 microns) for the boundary layer. Corresponding values for the fence vary from 0.08 to 0.16 waves. Extrapolation of these values to 10.6 microns suggests negligible degradation for a CO2 laser transmitted through a 5 cm thick, subsonic turbulent boundary layer.

Gilbert, K.↗

NASA NTRS1983

Design of shock-free compressor cascades including viscous boundary layer effects

A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta's turbulence model and assumes transition region of zero length.

Dulikravich, G. S.↗

NASA NTRS1979

A comparison of the pitching and plunging response of an oscillating airfoil

An oscillating SC1095 airfoil model was tested for its aerodynamic stability in a rigid body with a single degree of freedom pitch about its quarter chord, and also in a rigid body with single degree of freedom plunge. The ability of pitching data to model plunging motions was evaluated. A one to one correspondence was established between pairs of pitching and plunging motions according to the potential flow transformation formula alpha=ikh. The imposed variables of the experiment were mean incidence angle, amplitude of motion, free stream velocity, and oscillatory frequency. Results indicate that significant differences exist between the aerodynamic responses to the motions, particularly at high load conditions. At high load conditions, the normal force for equivalent pitch is significantly greater than that for true pitch at the geometric incidence angle.

Carta, F. O.↗

NASA NTRS2012

Simulation Tools Model Icing for Aircraft Design

Here s a simple science experiment to try: Place an unopened bottle of distilled water in your freezer. After 2-3 hours, if the water is pure enough, you will notice that it has not frozen. Carefully pour the water into a bowl with a piece of ice in it. When it strikes the ice, the water will instantly freeze. One of the most basic and commonly known scientific facts is that water freezes at around 32 F. But this is not always the case. Water lacking any impurities for ice crystals to form around can be supercooled to even lower temperatures without freezing. High in the atmosphere, water droplets can achieve this delicate, supercooled state. When a plane flies through clouds containing these droplets, the water can strike the airframe and, like the supercooled water hitting the ice in the experiment above, freeze instantly. The ice buildup alters the aerodynamics of the plane - reducing lift and increasing drag - affecting its performance and presenting a safety issue if the plane can no longer fly effectively. In certain circumstances, ice can form inside aircraft engines, another potential hazard. NASA has long studied ways of detecting and countering atmospheric icing conditions as part of the Agency s efforts to enhance aviation safety. To do this, the Icing Branch at Glenn Research Center utilizes a number of world-class tools, including the Center s Icing Research Tunnel and the NASA 607 icing research aircraft, a "flying laboratory" for studying icing conditions. The branch has also developed a suite of software programs to help aircraft and icing protection system designers understand the behavior of ice accumulation on various surfaces and in various conditions. One of these innovations is the LEWICE ice accretion simulation software. Initially developed in the 1980s (when Glenn was known as Lewis Research Center), LEWICE has become one of the most widely used tools in icing research and aircraft design and certification. LEWICE has been transformed over the years from strictly a research tool to one used routinely by industry and other government agencies. Glenn contractor William Wright has been the architect of this development, supported by a team of researchers investigating icing physics, creating validation data, and ensuring development according to standard software engineering practices. The program provides a virtual simulation environment for determining where water droplets strike an airfoil in flight, what kind of ice would result, and what shape that ice would take. Users can enter geometries for specific, two-dimensional cross sections of an airfoil or other airframe surface and then apply a range of inputs - different droplet sizes, temperatures, airspeeds, and more - to model how ice would build up on the surface in various conditions. The program s versatility, ease of use, and speed - LEWICE can run through complex icing simulations in only a few minutes - have contributed to it becoming a popular resource in the aviation industry.

Source record↗

NASA NTRS2012

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Hartshom, Fletcher↗

NASA NTRS1978

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗

NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗

NASA NTRSDate not supplied

A Design Exploration of Natural Laminar Flow Applications for the SUSAN Electrofan Concept

A trade study supported by the NASA Convergent Aeronautics Solutions (CAS) Project is presently underway to explore the desirability, feasibility, and viability of a new vehicle concept. The vehicle under development is the SUbsonic Single Aft eNgine (SUSAN) Electrofan configuration, which is a subsonic regional jet with the transformative concept of combining wing-mounted distributed electrified aircraft propulsion with a single engine design. The multidisciplinary team is investigating several potential technologies that would help the SUSAN Electrofan configuration achieve its performance goals, one of which is the application of Natural Laminar Flow (NLF) to the main wing. The present computational study utilizes the Crossflow Attenuated Natural Laminar Flow (CATNLF) design method to reshape the wing airfoils to obtain significant extents of NLF at the cruise condition. Fully-turbulent and laminar designs were performed to quantify the aerodynamic performance potential of NLF on the SUSAN Electrofan configuration. The laminar design supported laminar flow on53% of the area of the wing upper surface, resulting in a 19count (8.8%) drag reduction for the wing-fuselage configuration. The near-cruise off-design characteristics are also studied and illustrate that the robust laminar design sustains an NLF performance benefit through perturbations in Mach and angle of attack. A discussion is also included on multidisciplinary implications of utilizing NLF for the configuration, including design, manufacturing, and operational considerations required to support NLF on the main wing, as well as the interaction between the potential wing-mounted boundary layer ingestion technology that is also being explored for the SUSAN Electrofan configuration.

Natural Laminar Flow↗

NASA NTRS1991

A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

Scott, James R.↗

NASA NTRS1981

A diagonal form of an implicit approximate-factorization algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced to 24-34%.

Pulliam, T. H.↗

NASA NTRS1984

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Tseng, K.↗

NASA NTRS1981

A Diagonal Form of an Implicit Approximate-Factorization Algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced 24-34%.

Pulliam, T. H.↗

NASA NTRS1982

Coordinate generation with precise controls over mesh properties

Powerful local controls have been developed for mesh generation with the class of multisurface coordinate transformations. The controls come from local piecewise linear interpolants, and the resulting coordinates have continuous first derivatives. At the boundaries, the mesh controls provide the capability of joining distinct coordinate systems together with continuous derivatives. Away from boundaries, a local region can be given a particular mesh form to model internal objects or to simplify a problem. Applications of the controls are illustrated with a sequence of two-dimensional examples. For simplicity, each is generated about a NACA0012 airfoil which is of unit length and with leading edge pointed in a negative x-direction.

Eiseman, P. R.↗

NASA NTRS1991

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time-marching Full-Potential cascade solver are developed and verified. In the first method, the Influence Coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.

Bakhle, Milind A.↗

NASA NTRS1982

Analysis of separated boundary-layer flows

A method for predicting the strong interaction between the viscous and inviscid flows which occurs in flow separation is reviewed. An inverse boundary-layer procedure approximately accounts for normal pressure gradients that may be important in strongly interacting flows. Transformed boundary-layer equations are written in which the pressure gradient is set equal to the inviscid pressure gradient. As the boundary-layer edge is approached and the viscous shear and heat conduction terms vanish, the viscous flow solution is required to asymptotically approach the inviscid solution over the generalized displacement body. Attention is then focused on viscous-inviscid interacting flows with a first-order viscous formulation and constant pressure across the boundary layer. Results obtained with this procedure are presented for: (1) transitional separation bubbles near an airfoil leading edge, (2) subsonic boattail separated turbulent flow, and (3) transonic turbulent shock wave boundary-layer interaction on an axisymmetric bump configuration.

Carter, J. E.↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

Boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗