Results for “coupled problems” — Page 23

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

A standing wave approach is applied to the analysis of the flutter and forced response of tuned and mistuned rotors. The traditional traveling wave cascade airforces are recast into standing wave arbitrary motion form using Pade approximants, and the resulting equations of motion are written in the matrix form. Applications for vibration modes, flutter, and forced response are discussed. It is noted that the standing wave methods may prove to be more versatile for dealing with certain applications, such as coupling flutter with forced response and dynamic shaft problems, transient impulses on the rotor, low-order engine excitation, bearing motions, and mistuning effects in rotors.

Dugundji, J.↗

NASA NTRS1983

Flutter and forced response of mistuned rotors using standing wave analysis

A standing wave approach is applied to the analysis of the flutter and forced response of tuned and mistuned rotors. The traditional traveling wave cascade airforces are recast into standing wave arbitrary motion form using Pade approximants, and the resulting equations of motion are written in the matrix form. Applications for vibration modes, flutter, and forced response are discussed. It is noted that the standing wave methods may prove to be more versatile for dealing with certain applications, such as coupling flutter with forced response and dynamic shaft problems, transient impulses on the rotor, low-order engine excitation, bearing motion, and mistuning effects in rotors.

Bundas, D. J.↗

NASA NTRS1987

Development of an integrated BEM (Boundary Element Mesh) for hot fluid-structure interaction

A boundary integral representation for a coupled approach to fluid flow and solid deformation problems associated with the design of hot-section components such as those in the Space Shuttle Main Engine is discussed. The formulation is based on the fundamental analytical solution of the Navier-Stokes equation for fluid velocity in an infinite domain. This fundamental solution was obtained by decomposing a Navier-Stokes equation into vorticity and dilation transport equations. A boundary integral involving convolutions in time was then constructed in which the convective terms appear in the volume integral.

Dargush, G. F.↗

NASA NTRS1992

Using Derivatives Of Higher Order In Sensitivity Analysis

"What if" questions answered exactly, without using "increment-and-reevaluate" approach, and without finite differencing of system analysis, by use of sensitivity analysis to calculate first derivatives of behaviors of coupled systems with respect to design variables. If problem strongly nonlinear, efficiency improved by making derivatives of higher orders available to search algorithms. Extension effected by recursive application of same implicit function theorem that underlies previous method. Useful in design calculations for almost any system, including structures, machines, and distribution networks. Feedback control of processes improved by inclusion of derivative terms of higher order.

Sobieski, Jaroslaw↗

NASA NTRS1998

Optimization of Supersonic Transport Trajectories

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗

NASA NTRS1998

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗

NASA NTRS2000

Control of Shock Loading from a Jet in a Flexible Structure's Presence

The control of shock noise or screech from a jet near a flexible structure is discussed. The pressure from the supersonic jet consists of a shock with spiral and flapping nonaxisymmetric modes superimposed on broadband response. This shock induces a nonlinear-nonstationary loading problem associated with acoustic wave generation and propagation coupled with structural vibration. Control of the shock is achieved by placing a ring at the nozzle lip oscillating at the shock fundamental frequency. The ring prevents the shock characteristics originating in the column of the shear layer from sustaining connection with the out-of-phase surface vibration. Shock-free flow is maintained over a large pressure ratio. The peak power spectral density of the pressure due to shock fundamental and harmonics is converted to broadband level. The experiment is motivated by consideration of aircraft structural fatigue and interior noise.

Maestrello, Lucio↗

NASA NTRS2001

Field Effects of Buoyancy on Lean Premixed Turbulent Flames

Buoyancy affects the entire flowfield of steady turbulent flames and this aspect of flame buoyancy coupling is largely unexplored by experiments or by theory. Open flames and flames within large confinements are free to expand and interact with the surrounding environment. In addition to fluid and combustion conditions, their aerodynamic flowfields are determined by the flame brush orientation and geometry, wake of the stabilizer, enclosure size, and of course, the gravitational field. Because the flowfield consists mainly of cold reactants (mostly in the nearfield) and hot products (mostly in the farfield), buoyancy effects are manifested in the farfield region. In upward pointing flames, an obvious effect is a favorable axial pressure gradient that accelerates the products thereby increasing the axial aerodynamic stretch rate. Intrinsic to turbulent flows, changes in mean aerodynamic stretch also couple to the fluctuating pressure field. Consequently, buoyancy can influence the turbulence intensities upstream and downstream of the flame. Flame wrinkling process, and heat release rate are also directly affected. This backward coupling mechanism is the so-called elliptic problem. To resolve the field effects of buoyancy would require the solution of three-dimensional non-linear Navier Stokes equations with full specification of the upstream, wall and downstream boundary conditions.

Cheng, R. K.↗

NASA NTRS1998

Three Program Architecture for Design Optimization

In this presentation, I would like to review historical perspective on the program architecture used to build design optimization capabilities based on mathematical programming and other numerical search techniques. It is rather straightforward to classify the program architecture in three categories as shown above. However, the relative importance of each of the three approaches has not been static, instead dynamically changing as the capabilities of available computational resource increases. For example, we considered that the direct coupling architecture would never be used for practical problems, but availability of such computer systems as multi-processor. In this presentation, I would like to review the roles of three architecture from historical as well as current and future perspective. There may also be some possibility for emergence of hybrid architecture. I hope to provide some seeds for active discussion where we are heading to in the very dynamic environment for high speed computing and communication.

Miura, Hirokazu↗

NASA NTRS1999

Control of Shock Loading from a Jet in the Presence of a Flexible Structure

The control of shock noise or screech from a jet near a flexible structure is discussed. The pressure from the supersonic jet consists of a shock with spiral and flapping nonaxisymmetric modes superimposed on broadband response. This shock induces a nonlinear-nonstationary loading problem associated with acoustic wave generation and propagation coupled with structural vibration. Control of the shock is achieved by placing a ring at the nozzle lip oscillating at the shock fundamental frequency. The ring prevents the shock characteristics originating in the column of the shear layer from sustaining connection with the out-of-phase surface vibration. Shock-free flow is maintained over a large pressure ratio. The peak power pressure level is reduced by 40 dB.

Maestrello, Lucio↗

NASA NTRS2003

Development of Probabilistic Life Prediction Methodologies and Testing Strategies for MEMS and CMC's

This effort is to investigate probabilistic life prediction methodologies for ceramic matrix composites and MicroElectroMechanical Systems (MEMS) and to analyze designs that determine stochastic properties of MEMS. For CMC's this includes a brief literature survey regarding lifing methodologies. Also of interest for MEMS is the design of a proper test for the Weibull size effect in thin film (bulge test) specimens. The Weibull size effect is a consequence of a stochastic strength response predicted from the Weibull distribution. Confirming that MEMS strength is controlled by the Weibull distribution will enable the development of a probabilistic design methodology for MEMS - similar to the GRC developed CARES/Life program for bulk ceramics. A main objective of this effort is to further develop and verify the ability of the Ceramics Analysis and Reliability Evaluation of Structures/Life (CARES/Life) code to predict the time-dependent reliability of MEMS structures subjected to multiple transient loads. A second set of objectives is to determine the applicability/suitability of the CARES/Life methodology for CMC analysis, what changes would be needed to the methodology and software, and if feasible, run a demonstration problem. Also important is an evaluation of CARES/Life coupled to the ANSYS Probabilistic Design System (PDS) and the potential of coupling transient reliability analysis to the ANSYS PDS.

Jadaan, Osama↗

NASA NTRS2006

Analyzing Aeroelastic Stability of a Tilt-Rotor Aircraft

Proprotor Aeroelastic Stability Analysis, now at version 4.5 (PASTA 4.5), is a FORTRAN computer program for analyzing the aeroelastic stability of a tiltrotor aircraft in the airplane mode of flight. The program employs a 10-degree- of-freedom (DOF), discrete-coordinate, linear mathematical model of a rotor with three or more blades and its drive system coupled to a 10-DOF modal model of an airframe. The user can select which DOFs are included in the analysis. Quasi-steady strip-theory aerodynamics is employed for the aerodynamic loads on the blades, a quasi-steady representation is employed for the aerodynamic loads acting on the vibrational modes of the airframe, and a stability-derivative approach is used for the aerodynamics associated with the rigid-body DOFs of the airframe. Blade parameters that vary with the blade collective pitch can be obtained by interpolation from a user-defined table. Stability is determined by examining the eigenvalues that are obtained by solving the coupled equations of motions as a matrix eigenvalue problem. Notwithstanding the relative simplicity of its mathematical foundation, PASTA 4.5 and its predecessors have played key roles in a number of engineering investigations over the years.

Kvaternil, Raymond G.↗

NASA NTRSDate not supplied

A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

CFD-based multidisciplinary models are the fundamental building blocks of multidis- ciplinary design optimization frameworks. Linear and nonlinear solutions of these coupled models are difficult, especially when the Jacobian matrices represent a saddle point problem, where a block-diagonal corresponding to a discipline is non-invertible. These scenarios necessitate the use of a coupled solver algorithm such as the Newton’s method instead of the popular block Gauss– Seidel-based methods because of this non-invertible block. To address this challenge, we introduce a nonlinear Schur complement solver suitable for CFD-based multidisciplinary models. The solver leverages the specialized linear and nonlinear solvers of the CFD code, and therefore, does not require the solution of a large coupled linear system as the coupled Newton’s method. Further- more, because the solver primarily uses the specialized linear and nonlinear solvers of the CFD code, it does not suffer from the same robustness limitations as the coupled Newton’s method. In this work, we will implement this solver in NASA’s OpenMDAO framework and demonstrate its effectiveness using a CFD-based aeropropulsive model. The solver will contribute to the develop- ment of aeropropulsive design optimization and CFD-based design optimization methods with the ultimate goal of accelerating the design and integration of advanced propulsion systems.

Nonlinear Solvers↗

NASA NTRS1995

On Developing a Taxonomy for Multidisciplinary Design Optimization: A Decision-Based Perspective

In this paper, we approach MDO from a Decision-Based Design (DBD) perspective and explore classification schemes for designing complex systems and processes. Specifically, we focus on decisions, which are only a small portion of the Decision Support Problem (DSP) Technique, our implementation of DBD. We map coupled nonhierarchical and hierarchical representations from the DSP Technique into the Balling-Sobieski (B-S) framework (Balling and Sobieszczanski-Sobieski, 1994), and integrate domain-independent linguistic terms to complete our taxonomy. Application of DSPs to the design of complex, multidisciplinary systems include passenger aircraft, ships, damage tolerant structural and mechanical systems, and thermal energy systems. In this paper we show that Balling-Sobieski framework is consistent with that of the Decision Support Problem Technique through the use of linguistic entities to describe the same type of formulations. We show that the underlying linguistics of the solution approaches are the same and can be coalesced into a homogeneous framework with which to base the research, application, and technology MDO upon. We introduce, in the Balling-Sobieski framework, examples of multidisciplinary design, namely, aircraft, damage tolerant structural and mechanical systems, and thermal energy systems.

Lewis, Kemper↗

NASA NTRS1982

Integral dependent spin couplings in CI calculations

Although the number of ways to combine Slater determinants to form spin eigenfunctions increases rapidly with the number of open shells, most of these spin couplings will make only a small contribution to a given state, provided the spin coupling is chosen judiciously. The technique of limiting calculations to the interacting subspace pioneered by Bunge (1970) was employed by Munch and Davidson (1975) to the vanadium atom. The use of an interacting space looses its advantage in more complex cases. However, the problem can always be reduced to only one interacting spin coupling by making the coefficients integral dependent. The present investigation is concerned with the performance of integral dependent interacting couplings, taking into account the results of three test calculations.

Iberle, K.↗

NASA NTRS2008

Benchmarking Gas Path Diagnostic Methods: A Public Approach

Recent technology reviews have identified the need for objective assessments of engine health management (EHM) technology. The need is two-fold: technology developers require relevant data and problems to design and validate new algorithms and techniques while engine system integrators and operators need practical tools to direct development and then evaluate the effectiveness of proposed solutions. This paper presents a publicly available gas path diagnostic benchmark problem that has been developed by the Propulsion and Power Systems Panel of The Technical Cooperation Program (TTCP) to help address these needs. The problem is coded in MATLAB (The MathWorks, Inc.) and coupled with a non-linear turbofan engine simulation to produce "snap-shot" measurements, with relevant noise levels, as if collected from a fleet of engines over their lifetime of use. Each engine within the fleet will experience unique operating and deterioration profiles, and may encounter randomly occurring relevant gas path faults including sensor, actuator and component faults. The challenge to the EHM community is to develop gas path diagnostic algorithms to reliably perform fault detection and isolation. An example solution to the benchmark problem is provided along with associated evaluation metrics. A plan is presented to disseminate this benchmark problem to the engine health management technical community and invite technology solutions.

Simon, Donald L.↗

NASA NTRS1978

CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact

CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

Chamis, C. C.↗

NASA NTRS1978

CELFE/NASTRAN Code for the analysis of structures subjected to high velocity impact

The CELFE (Coupled Eulerian Lagrangian Finite Element)/NASTRAN Code three-dimensional finite element code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.

Chamis, C. C.↗