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NASA NTRS1993

Multiblock Navier-Stokes solutions about the F/A-18 wing-LEX-fuselage configuration

Three-dimensional thin-layer Navier-Stokes computations are presented for the F/A-18 configuration. The modeled configuration includes an accurate surface representation of the fuselage, leading-edge extension (LEX), and wing, both with and without leading-edge flap deflection. A multiblock structured grid strategy is employed to decompose the computational flowfield domain around the subject configuration. Steady-state solutions are obtained from an algorithm that solves the compressible Navier-Stokes equations with an upwind-biased, flux-difference splitting approach. The results presented are based on a fully turbulent flow assumption, simulating the high Reynolds number flow conditions that correspond to a recent FI A-18 flight experiment. Good agreements between the computations and the flight test results are obtained for both surface flow patterns as well as surface pressure distributions. Furthermore, a correlation between the computed LEX vortex-core and the flight test results, observed by way of smoke visualization, is also presented.

Aircraft configurations↗

NASA NTRS1941

Methods of analyzing wind-tunnel data for dynamic flight conditions

The effects of power on the stability and the control characteristics of an airplane are discussed and methods of analysis are given for evaluating certain dynamic characteristics of the airplane that are not directly discernible from wind-tunnel tests alone. Data are presented to show how the characteristics of a model tested in a wind tunnel are affected by power. The response of an airplane to a rolling and a yawing disturbance is discussed, particularly in regard to changes in wing dihedral and fin area. Solutions of the lateral equations of motion are given in a form suitable for direct computations. An approximate formula is developed that permits the rapid estimation of the accelerations produced during pull-up maneuvers involving abrupt elevator deflections.

Donlan, C J↗

NASA NTRS1995

A 3-D Navier-Stokes CFD study of turbojet/ramjet nozzle plume interactions at Mach 3.0 and comparison with data

Advanced airbreathing propulsion systems used in Mach 4-6 mission scenarios, usually consist of a single integrated turboramjet or as in this study, a turbojet housed in an upper bay with a separate ramjet housed in a lower bay. As the engines transition from turbojet to ramjet, there is an operational envelope where both engines operate simultaneously. One nozzle concept under consideration has a common nozzle, where the plumes from the turbojet and ramjet interact with one another as they expand to ambient conditions. In this paper, the two plumes interact at the end of a common 2-D cowl, when they both reach an approximate Mach 3.0 condition and then jointly expand to Mach 3.6 at the common nozzle exit plane. At this condition, the turbojet engine operated at a higher NPR than the ramjet, where the turbojet overpowers the ramjet plume, deflecting it approximately 12 degrees downward and in turn the turbojet plume is deflected 6 degrees upward. In the process, shocks were formed at the deflections and a shear layer formed at the confluence of the two jets. This particular case was experimentally tested and the data used to compare with the PARC3D code with k-kl two equation turbulence model. The 2-D and 3-D centerline CFD solutions are in good agreement, but as the CFD solutions approach the outer sidewall, a slight variance occurs. The outer wall boundary layers are thin and do not present much of an interaction, however, where the confluence interaction shocks interact with the thin boundary layer on the outer wall, strong vortices run down each shock causing substantial disturbances in the boundary layer. These disturbances amplify somewhat as they propagate downstream axially from the confluence point. The nozzle coefficient (CFG) is reduced 1/2 percent as a result of this sidewall interaction, from 0.9850 to 0.9807. This three-dimensional reduction is in better agreement with the experimental value of 0.9790.

Chang, Ing↗

NASA NTRS2002

An Interactive Excel Program for Tracking a Single Droplet in Crossflow Computation

Spray jet in crossflow has been a subject of research because of its wide application in systems involving pollutant dispersion, jet mixing in the dilution zone of combustors, and fuel injection strategies. The focus of this work is to investigate dispersion of a 2-dimensional atomized spray jet into a 2-dimensional crossflow. A quick computational method is developed using available software. The spreadsheet can be used for any 2D droplet trajectory problem where the drop is injected into the free stream eventually coming to the free stream conditions. During the transverse injection of a spray into high velocity airflow, the droplets (carried along and deflected by a gaseous stream of co-flowing air) are subjected to forces that affect their motion in the flow field. Based on the Newton's Second Law of motion, four ordinary differential equations were used. These equations were then solved by a fourth-order Runge-Kutta method using Excel software. Visual basic programming and Excel macrocode to produce the data facilitate Excel software to plot graphs describing the droplet's motion in the flow field. This program computes and plots the data sequentially without forcing users to open other types of plotting programs. A user's manual on how to use the program is also included in this report.

Urip, E.↗

NASA NTRS1998

Effect of Apex Flap Deflection on Vertical Tail Buffeting

A computational study of the effect of vortex breakdown location on vertical tail buffeting is conducted. The position of the breakdown is modified by employing an apex flap deflected by an experimentally determined optimal angle. The delayed breakdown flow and buffeting response is then compared to the nominal undeflected case. This multidisciplinary problem is solved sequentially for the fluid flow, the elastic tail deformations and the grid displacements. The fluid flow is simulated by time accurately solving the unsteady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, upwind, flux-difference splitting finite volume scheme. The elastic vibrations of the tails are modeled by uncoupled bending and torsion beam equations. These equations are solved accurately in time using the Galerkin method and a five-stage Runge-Kutta-Verner scheme. The grid for the fluid dynamics calculations is continuously deformed using interpolation functions to disperse the displacements smoothly throughout the computational domain. An angle-of-attack of 35 deg.is chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on tile vertical tails. The dimensions and material properties of the vertical tails are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. Results are presented for a baseline uncontrolled buffeting case and a delayed breakdown case in which the apex flap has been deflected 15 deg. The flap was found to be very effective in delaying the breakdown, increasing the location from 50%c to 94%c, which resulted in a 6% increase in lift coefficient and pitching moment. However, the integrated buffet loads and tip responses were roughly equivalent for the two cases.

Massey, Steven J.↗

NASA NTRS1977

Nonplanar wing load-line and slender wing theory

Nonplanar load line, slender wing, elliptic wing, and infinite aspect ratio limit loading theories are developed. These are quasi two dimensional theories but satisfy wing boundary conditions at all points along the nonplanar spanwise extent of the wing. These methods are applicable for generalized configurations such as the laterally nonplanar wing, multiple nonplanar wings, or wing with multiple winglets of arbitrary shape. Two dimensional theory infers simplicity which is practical when analyzing complicated configurations. The lateral spanwise distribution of angle of attack can be that due to winglet or control surface deflection, wing twist, or induced angles due to multiwings, multiwinglets, ground, walls, jet or fuselage. In quasi two dimensional theory the induced angles due to these extra conditions are likewise determined for two dimensional flow. Equations are developed for the normal to surface induced velocity due to a nonplanar trailing vorticity distribution. Application examples are made using these methods.

Deyoung, J.↗

NASA NTRS1980

High-frequency sound propagation in a spatially varying mean flow

An equation for acoustic ray paths in a spatially varying mean flow was examined to determine some of the characteristics of the flow gradient effects on sound propagation. In a potential flow, the acoustic rays are deflected in the direction of increasing mean flow, and the gradient of the mean flow speed is the dominant factor causing the ray deflection. In contrast, in a sheared mean flow, the vorticity is the dominant factor in deflection of the acoustic rays.

Cho, Y. C.↗

NASA NTRS1991

Finite element analysis of nonlinear flutter of composite panels

A finite element formulation is developed to analyze large-amplitude panel flutter of arbitrary laminated plates. The plates considered are anisotropic composite, thin rectangular panels. The equations of motion for an oscillating plate are determined and solved by linearizing the nonlinear stiffness matrices. The solution procedure is presented to determine the limit-cycle motions which are caused by the large deflections and vibrations induced by the areodynamic load. The aerodynamic load is defined by the first-order piston theory. Examples studied include cross-ply laminates with various numbers of layers and three-layer angle-ply laminates with different lamination angles. The effects of simply supported and clamped boundary conditions of a cross-ply laminate are also examined.

Dixon, Iain R.↗

NASA NTRS1990

Vibration and wave propagation characteristics of multisegmented elastic beams

Closed form analytical solutions are derived for the vibration and wave propagation of multisegmented elastic beams. Each segment is modeled as a Timoshenko beam with possible inclusion of material viscosity, elastic foundation and axial forces. Solutions are obtained by using transfer matrix methods. According to these methods formal solutions are first constructed which relate the deflection, slope, moment and shear force of one end of the individual segment to those of the other. By satisfying appropriate continuity conditions at segment junctions, a global 4x4 matrix results which relates the deflection, slope, moment and shear force of one end of the beam to those of the other. If any boundary conditions are subsequently invoked on the ends of the beam one gets the appropriate characteristic equation for the natural frequencies. Furthermore, by invoking appropriate periodicity conditions the dispersion relation for a periodic system is obtained. A variety of numerical examples are included.

Nayfeh, Adnan H.↗

NASA NTRS1993

A numerical investigation of a subsonic jet in a crossflow

The flowfield induced by a single, subsonic jet exhausting perpendicularly from a flat plate into a subsonic crossflow has been numerically investigated. The test case was chosen to match available experimental data where the jet Mach number was 0.78, and the freestream Mach number was 0.13. Time-averaged solutions were obtained using the thin-layer Navier-Stokes equations and two overlapping grids. The solutions were sensitive to the radial grid clustering near the edge of the jet and to the far-field boundary conditions. Experimental data comparisons were required to determine the most appropriate jet grid and satisfactory boundary conditions. Globally, the solutions converged in about 6000 iterations. The computational results accurately showed the deflected jet and associated contrarotating vortices. The fine clustered grid in the region upstream of the jet exit allowed the horseshoe vortex in the boundary layer near the jet exit to be captured. Most importantly for aircraft applications, the computed plate pressure distributions compared favorably with the experimental data over most of the surface. However, in the wake region immediately downstream of the jet exit, where there is extensive flow separation, some discrepancies with experimental data were observed. Two turbulence models were used in this study: (1) the zero-equation, two layer Baldwin-Lomax turbulence model; and (2) one-equation Baldwin-Barth turbulence model. The turbulence models gave results which generally compared no better with experimental data than the laminar computation results.

Chiu, Stephen H.↗

NASA NTRS1980

Vibration characteristics of a steadily rotating slender ring

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Lallman, F. J.↗

NASA NTRS1981

High-frequency sound propagation in a spatially varying mean flow

An equation for acoustic ray paths in a spatially varying mean flow has been examined to determine some of the characteristics of the flow gradient effects on sound propagation. In a potential flow the acoustic rays are deflected in the direction of increasing mean flow, and the gradient of the mean flow speed is the dominant factor causing the ray deflection. In contrast, in a sheared mean flow, the vorticity is the dominant factor in deflection of the acoustic rays.

Cho, Y. C.↗

NASA NTRS1988

Digital active control law synthesis for aeroservoelastic systems

This paper presents a formulation for synthesis of digital active control laws for aeroservoelastic systems, which are typically modeled by large order equations in order to accurately represent the rigid and flexible body modes, unsteady aerodynamic forces, actuator dynamics, and gust spectra. The control law is expected to satisfy multiple design requirements on the dynamic loads, responses, actuator deflection and rate limitations, as well as maintain certain stability margins, yet should be simple enough to be implemented by an onboard digital microprocessor. The synthesis procedure minimizes a linear quadratic Gaussian type cost function, by updating selected free parameters of the control law, while satisfying a set of inequality constraints on the design loads, responses and stability margins. A stable classical control law or an estimator based full or reduced order control law can be used as an initial design starting point. The gradients of the cost function and the constraints, with respect to the digital control law design variables are derived analytically, to facilitate rapid convergence. Selected design responses can be treated as constraints instead of lumping them into the cost function, in order to satisfy individual root-mean-square load and response limitations. Constraints are also imposed on the minimum singular value requirements for stability robustness improvement.

Mukhopadhyay, Vivekananda↗

NASA NTRS1959

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Bennett, Floyd V.↗

NASA NTRS1977

Effect of a nonconstant C/m-alpha/ on the stability of rolling aircraft

An analytical study is carried out of the behavior of modern high-speed aircraft of inertially slender configurations in maneuvers involving large rates of roll. Inertia cross-coupling, as well as a linear variation of longitudinal static stability (C/m-alpha/) with angle of attack, are considered. The steady-state solutions of the nonlinear equations of motion, based on principal inertia axes, are studied to obtain useful information on the response behavior of the state variables during roll maneuvers. It is shown that, in addition to the critical values of aileron deflection that have been previously found to limit a steady-state roll with constant longitudinal static stability, there can be two new critical values introduced by a linear decrease of the absolute value of longitudinal static stability with angle of attack. For aileron deflections near these critical values, the response of the aircraft exhibits violent oscillations and dangerous peak loads, due to the cross-coupled motion accompanying a roll maneuver. These critical values define a new range of aileron deflections in which no steady-state roll is possible.

Davari, B.↗

NASA NTRS1982

Flow induced force of labyrinth seal

Flow induced instability force due to a labyrinth seal is analyzed. An approximate solution is given for the partial differential equation representing the flow in labyrinth seal and it is compared with the finite difference method in order to verify the accuracy of both methods. The effects of difference of inlet and outlet pressures of the seal, deflection of pressure and mass flow from the steady state, rotor diameter, seal clearance, seal interval and seal number on the flow induced force of the seal are investigated and it is known that some of these factors are very influential on the flow induced force.

Iwatsubo, T.↗

NASA NTRS1983

Nonlinear aerodynamic modeling of flap oscillations in transonic flow - A numerical validation

The regime of validity of a nonlinear aerodynamic force and moment formulation, based on concepts from nonlinear functional analysis and applicable to a transonic airfoil with a deflecting flap, is investigated. A time-dependent finite difference technique is used to evaluate the aerodynamic data of the formulation in terms of specified, characteristic motions. Flap-motion histories are generated from the flap inertial equations of motion, with aerodynamic reactions specified by the moment formulation. The motion histories depicting the cases of decaying and growing flap oscillations are compared with histories generated through simultaneous, coupled solution of the fluid-dynamic equations and flap inertial equations of motion. The range of applicability of the formulation is discussed.

Chyu, W. J.↗

NASA NTRS1987

Modeling of joints for the dynamic analysis of truss structures

An experimentally-based method for determining the stiffness and damping of truss joints is described. The analytical models use springs and both viscous and friction dampers to simulate joint load-deflection behavior. A least-squares algorithm is developed to identify the stiffness and damping coefficients of the analytical joint models from test data. The effects of nonlinear joint stiffness such as joint dead band are also studied. Equations for predicting the sensitivity of beam deformations to changes in joint stiffness are derived and used to show the level of joint stiffness required for nearly rigid joint behavior. Finally, the global frequency sensitivity of a truss structure to random perturbations in joint stiffness is discussed.

Belvin, W. Keith↗