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NASA NTRS1997

The Reduction of Ducted Fan Engine Noise Via A Boundary Integral Equation Method

The development of a Boundary Integral Equation Method (BIEM) for the prediction of ducted fan engine noise is discussed. The method is motivated by the need for an efficient and versatile computational tool to assist in parametric noise reduction studies. In this research, the work in reference 1 was extended to include passive noise control treatment on the duct interior. The BEM considers the scattering of incident sound generated by spinning point thrust dipoles in a uniform flow field by a thin cylindrical duct. The acoustic field is written as a superposition of spinning modes. Modal coefficients of acoustic pressure are calculated term by term. The BEM theoretical framework is based on Helmholtz potential theory. A boundary value problem is converted to a boundary integral equation formulation with unknown single and double layer densities on the duct wall. After solving for the unknown densities, the acoustic field is easily calculated. The main feature of the BIEM is the ability to compute any portion of the sound field without the need to compute the entire field. Other noise prediction methods such as CFD and Finite Element methods lack this property. Additional BIEM attributes include versatility, ease of use, rapid noise predictions, coupling of propagation and radiation both forward and aft, implementable on midrange personal computers, and valid over a wide range of frequencies.

Tweed, J.↗

NASA NTRSDate not supplied

Transonic Cruise Slotted Wing Design for Commercial Transport Aircraft using CDISC

A knowledge-based aerodynamic design method, CDISC, has been extended to enable the computational design of transonic cruise slotted wings for commercial transport aircraft. The cruise slotted wing is a multielement wing concept with a forward main element and an aft flap element, separated to form an intermediate slot. This slot favorably redirects airflow from the main element lower surface toward the low-momentum, upper-surface boundary layer of the flap. Relative to the supercritical wing, the cruise slotted wing enables greater aft loading that helps to reduce shock strength and transonic pressure drag. The cruise slotted wing may be considered a passive drag reduction technology with potential fuel-burn savings and increased vehicle range for next-generation aircraft. The current paper seeks to quantify the drag-saving benefits of cruise slotted wing technology in application to single-aisle commercial transport aircraft. A series of multielement design constraints were developed within CDISC for the design of a partial-span, cruise slotted wing for a Mach-0.8 variant of the Common Research Model. To mitigate the skin-friction drag penalty associated with cruise slotted wings, the design features a flap with natural laminar flow over approximately 75% of the flap surface area. Cruise drag estimates from the NASA USM3D-ME flow solver between a supercritical wing and the partial-span, cruise slotted wing design were within one drag count. Near-cruise, off-design analyses showed limited laminar-flow sensitivity to angle of attack and a more gradual drag rise compared to a supercritical wing. Based on this observed benefit, future work is motivated to design a cruise slotted wing with laminar flow on both wing elements to achieve a significant reduction in cruise drag while delaying drag divergence.

CDISC↗

NASA NTRSDate not supplied

Transonic Cruise Slotted Wing Design for Commercial Transport Aircraft using CDISC

A knowledge-based aerodynamic design method, CDISC, has been extended to enable the computational design of transonic cruise slotted wings for commercial transport aircraft. The cruise slotted wing is a multielement wing concept with a forward main element and an aft flap element, separated to form an intermediate slot. This slot favorably redirects airflow from the main element lower surface toward the low-momentum, upper-surface boundary layer of the flap. Relative to the supercritical wing, the cruise slotted wing enables greater aft loading that helps to reduce shock strength and transonic pressure drag. The cruise slotted wing may be considered a passive drag-reduction technology with potential fuel burn savings and increased vehicle range for next-generation aircraft. The current paper seeks to quantify the drag-saving benefits of cruise slotted wing technology in application to single-aisle commercial transport aircraft. A series of multielement design constraints were developed within CDISC for the design of a partial-span, cruise slotted wing for a Mach-0.8 variant of the Common Research Model. To mitigate the skin-friction drag penalty associated with cruise slotted wings, the design features a flap with natural laminar flow over approximately 75% of the flap surface area. Cruise drag estimates from the NASA USM3D flow solver between a supercritical wing and the partial-span, cruise slotted wing design were within one drag count. Near-cruise, off-design analyses showed limited laminar flow sensitivity to angle of attack and a more gradual drag rise compared to a supercritical wing. Based on this demonstrated benefit, future work is motivated to design a cruise slotted wing with natural laminar flow on both wing elements to achieve a significant reduction in cruise drag while providing delayed drag divergence.

CDISC↗

NASA NTRS1984

Multi-grid technique for the solution of incompressible Navier-Stokes equations

A computationally efficient method is proposed for obtaining fine-mesh solutions of the Navier-Stokes equations for high-Re flow, including separation. The method involves implementing a multi-grid solution procedure with suitably chosen elements, such that the resulting overall solution technique is efficient as well as robust. The robustness and efficiency of the solution technique are demonstrated by applying it to three model problems: flow in a driven cavity, downstream asymptotic flow in curved ducts of square and polar sections, and Newmann boundary-value problem in clustered curvilinear orthogonal coordinates.

Ghia, K. N.↗

NASA NTRS1992

Contact thermal shock test of ceramics

A novel quantitative thermal shock test of ceramics is described. The technique employs contact between a metal-cooling rod and hot disk-shaped specimen. In contrast with traditional techniques, the well-defined thermal boundary condition allows for accurate analyses of heat transfer, stress, and fracture. Uniform equibiaxial tensile stresses are induced in the center of the test specimen. Transient specimen temperature and acoustic emission are monitored continuously during the thermal stress cycle. The technique is demonstrated with soda-lime glass specimens. Experimental results are compared with theoretical predictions based on a finite-element method thermal stress analysis combined with a statistical model of fracture. Material strength parameters are determined using concentric ring flexure tests. Good agreement is found between experimental results and theoretical predictions of failure probability as a function of time and initial specimen temperature.

Rogers, W. P.↗

NASA NTRS1990

Approximate minimum-time trajectories for two-link flexible manipulators

The method of recursive quadratic programming was used to generate approximate minimum-time tip trajectories for two-link semi-rigid and flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for an n-link, m-joint system with bending only in the horizontal plane. Constraints on the trajectory include boundary conditions on position and energy for a rest-to-rest maneuver, straight-line tracking between boundary positions, and motor torque limits. Trajectory comparisons utilize a change in the link stiffness to compare a semi-rigid configuration to a flexible one. The level of bending flexibility necessary to excite significant modal behavior is demonstrated. Applied torques for minimum-time maneuvers are shown to be very similar between configurations and retain much of the qualitative character of rigid-body slewing motion.

Eisler, G. R.↗

NASA NTRS2014

Flutter Analysis for Turbomachinery Using Volterra Series

The objective of this paper is to describe an accurate and efficient reduced order modeling method for aeroelastic (AE) analysis and for determining the flutter boundary. Without losing accuracy, we develop a reduced order model based on the Volterra series to achieve significant savings in computational cost. The aerodynamic force is provided by a high-fidelity solution from the Reynolds-averaged Navier-Stokes (RANS) equations; the structural mode shapes are determined from the finite element analysis. The fluid-structure coupling is then modeled by the state-space formulation with the structural displacement as input and the aerodynamic force as output, which in turn acts as an external force to the aeroelastic displacement equation for providing the structural deformation. NASA's rotor 67 blade is used to study its aeroelastic characteristics under the designated operating condition. First, the CFD results are validated against measured data available for the steady state condition. Then, the accuracy of the developed reduced order model is compared with the full-order solutions. Finally the aeroelastic solutions of the blade are computed and a flutter boundary is identified, suggesting that the rotor, with the material property chosen for the study, is structurally stable at the operating condition, free of encountering flutter.

computational fluid dynamics↗

NASA NTRSDate not supplied

Supersonic Traveling Crossflow Wave Characteristics in Ground and Flight Tests

This paper continues analysis of data acquired in a series of supersonic crossflow transition experiments on a 65° swept- wing model tested in both wind tunnel and flight. Flow visualization data are summarized to provide context for the swept-wing instability mechanisms of interest. Unsteady pressure measurements obtained near the wing model leading edge (LE) are studied using 2nd- and 3rd-order statistical methods to extract traveling crossflow wave characteristics from these data. Comparisons between tunnel and flight data with boundary-layer (BL) Linear Stability Theory (LST) predictions provide insights into BL transition phenomena similarities and differences observed in tests using the same swept-wing model configurations. Comparisons of unsteady pressure data results for wing LE configurations with and without distributed-roughness-element (DRE) patterns installed, suggest traveling crossflow disturbance growth is reduced when this type of flow control is applied. A brief stud y of different background surface roughness levels on the wing LE suggests the potential for another flow control approach to promote laminar flow on swept wings using streamwise-biased surface finishes.

Lewis R Owens↗

NASA NTRS1977

Structural analysis of ultra-high speed aircraft structural components

The buckling characteristics of a hypersonic beaded skin panel were investigated under pure compression with boundary conditions similar to those found in a wing mounted condition. The primary phases of analysis reported include: (1) experimental testing of the panel to failure; (2) finite element structural analysis of the beaded panel with the computer program NASTRAN; and (3) summary of the semiclassical buckling equations for the beaded panel under purely compressive loads. A comparison of each of the analysis methods is also included.

Lenzen, K. H.↗

NASA NTRS1985

Elevated temperature crack growth

The purpose is to determine the ability of currently available P-I integrals to correlate fatigue crack propagation under conditions that simulate the turbojet engine combustor liner environment. The utility of advanced fracture mechanics measurements will also be evaluated during the course of the program. To date, an appropriate specimen design, a crack displacement measurement method, and boundary condition simulation in the computational model of the specimen were achieved. Alloy 718 was selected as an analog material based on its ability to simulate high temperature behavior at lower temperatures. Tensile and cyclic tests were run at several strain rates so that an appropriate constitutive model could be developed. Suitable P-I integrals were programmed into a finite element post-processor for eventual comparison with experimental data.

Malik, S. N.↗

NASA NTRS1987

Calculation of skin-stiffener interface stresses in stiffened composite panels

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Cohen, David↗

NASA NTRS1991

Structural reliability methods: Code development status

The Probabilistic Structures Analysis Method (PSAM) program integrates state of the art probabilistic algorithms with structural analysis methods in order to quantify the behavior of Space Shuttle Main Engine structures subject to uncertain loadings, boundary conditions, material parameters, and geometric conditions. An advanced, efficient probabilistic structural analysis software program, NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a deliverable. NESSUS contains a number of integrated software components to perform probabilistic analysis of complex structures. A nonlinear finite element module NESSUS/FEM is used to model the structure and obtain structural sensitivities. Some of the capabilities of NESSUS/FEM are shown. A Fast Probability Integration module NESSUS/FPI estimates the probability given the structural sensitivities. A driver module, PFEM, couples the FEM and FPI. NESSUS, version 5.0, addresses component reliability, resistance, and risk.

Millwater, Harry R.↗

NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗

NASA NTRS1974

An analytic method to account for drag in the Vinti Satellite theory

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Watson, J. S.↗

NASA NTRS2002

Analytical Modal Analysis for Thin-Film Flat Lenses

Due to strong potential applications and more demanding requirements imposed upon thin-film structures for space deployable, there has been increasing research and development activities during recent years in the field of vibration analysis of these types of structures. Moreover, interests in employing these structural components have received renewed emphasis in recent years within NASA and the Air Force. This is due to their inherent lightweight, low packaging and launch volume, and relative simplicity of deployment. Among the potential mission concepts for which these structural elements are included, one can mention solar sails, space solar power generation systems, solar thermal propulsion vehicles, large space telescopes, and inflatable communication antennas. This paper presents analytical procedures to determine vibration and physical characteristics of thin film lenses with circular and elliptical shapes membranes considered in design of a solar concentrator. In general, three methods are used to obtain approximate solutions of Helmholtz boundary value problems. One method requires that solution satisfy the differential equation exactly and the boundary condition approximately. Another method demands a solution that satisfies the boundary conditions exactly and the governing equations approximately. The third method sees a solution that satisfies both the governing equation and boundary conditions approximately. Extensive reviews of vibrations of membrane and plates are provided by Leissa and Mazumdar.

Hamid R. Hamidzadeh↗

NASA NTRS2012

A New Approach in Force-Limited Vibration Testing of Flight Hardware

The force-limited vibration test approaches discussed in NASA-7004C were developed to reduce overtesting associated with base shake vibration tests of aerospace hardware where the interface responses are excited coherently. This handbook outlines several different methods of specifying the force limits. The rationale for force limiting is based on the disparity between the impedances of typical aerospace mounting structures and the large impedances of vibration test shakers when the interfaces in general are coherently excited. Among these approaches, the semi-empirical method is presently the most widely used method to derive the force limits. The inclusion of the incoherent excitation of the aerospace structures at mounting interfaces has not been accounted for in the past and provides the basis for more realistic force limits for qualifying the hardware using shaker testing. In this paper current methods for defining the force limiting specifications discussed in the NASA handbook are reviewed using data from a series of acoustic and vibration tests. A new approach based on considering the incoherent excitation of the structural mounting interfaces using acoustic test data is also discussed. It is believed that the new approach provides much more realistic force limits that may further remove conservatism inherent in shaker vibration testing not accounted for by methods discussed in the NASA handbook. A discussion on using FEM/BEM analysis to obtain realistic force limits for flight hardware is provided.

force limiting responses↗

NASA NTRS1992

An interactive boundary-layer approach to multielement airfoils at high lift

A calculation method based on an interactive boundary-layer approach to multielement airfoils is described and is applied to three types of airfoil configurations with and without flap-wells in order to demonstrate the applicability of the method to general high-lift configurations. This method, well tested for single airfoils as a function of shape, angle of attack, and Reynolds number, is here shown to apply equally well to two-element airfoils and their wakes, to a flap-well region, and to a three-element arrangement which includes the effects of co-flowing regions, a flap well, and the wake of the elements. In addition to providing accurate representation of these flows, the method is general so that its extension to three-dimensional arrangements is likely to provide a practical, accurate and efficient tool to assist the design process.

Cebeci, Tuncer↗

NASA NTRS2000

Computational Aeroacoustics by the Space-Time CE/SE Method

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a newly developed numerical method for conservation laws. Despite its second order accuracy, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide spectrum of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its novel, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for CAA (computational aeroacoustics). In this seminar, the 1-D and 2-D unstructured version of the CE/SE schemes are first briefly described. Secondly, some discussions on the NRBC are given. Then, various examples for linear, nonlinear aeroacoustics are presented.

Loh, Ching Y.↗