A rapid perturbation procedure for determining nonlinear flow solutions

application to transonic turbomachinery flows
  • 90 Pages
  • 3.66 MB
  • English
National Aeronautics and Space Administration, Scientific and Technical Information Branch, For sale by the National Technical Information Service] , Washington, D.C, [Springfield, Va
Singular perturbations (Mathematics), Turbomachines -- Blades -- Design and constru
StatementStephen S. Stahara, James P. Elliott, and John R. Spreiter
SeriesNASA contractor report -- 3425
ContributionsElliott, J. P. 1929-, Spreiter, John R, United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch, Lewis Research Center
The Physical Object
Paginationiv, 90 p. :
ID Numbers
Open LibraryOL14930715M

This simple procedure, however, only works directly for continuous flows for which the perturbation change does not alter the solution domain. For those perturbations which change the flow domain, coordinate stretching (usually obvious) is necessary to insure proper definition of the unit perturbation solution.

A rapid perturbation procedure for determining nonlinear flow solutions: application to transonic turbomachinery flows. A rapid perturbation procedure for determining nonlinear flow solutions: application to transonic turbomachinery flows / By Stephen S.

Stahara, John R. Spreiter, J. (James Philip) Elliott, Lewis Research Center. and United States. "The author has invested a great amount of effort into determining all the power series and computing the functions depicted in the figures." -Mathematical Reviews, Issue h" an excellent reference to researchers, engineers, and interested individuals in helping them tackle nonlinear problems in an analytical fashiona good subject index and an outstanding list of Cited by: The Mickens iteration procedure for nonlinear second-order differential equations is used for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential.

determining analytical approximate solutions of a nonlinear oscillatory system are the perturbation methods. These methods involve the expansion of a solution to an oscillation equation in a series in a small parameter. Several researchers have studied different nonlinear problems by means of iteration procedures [1,2,3,4,5,6, 7,8].

A perturbation-incremental method is presented for the analysis of strongly non-linear oscillators of the form ẍ + g(x) = λf(x.x).x, where g(x) and f(x.x) are arbitrary non-linear functions of their arguments. The method is an extension of the perturbation-iterative method to the case where λ is not necessarily by:   We apply the asymptotic perturbation (AP) method to the study of the vibrations of Euler--Bernoulli beam resting on a nonlinear elastic foundation.

An external periodic excitation is in primary resonance or in subharmonic resonance in the order of one-half with an nth mode frequency. The AP method uses two different procedures for the solutions: introducing an Cited by: pruned perturbation procedure is that the nth-order pruned perturbation approximation does not deliver an exact –t if the truth is an nth-order polynomial even though pruned perturbation approximations are polynomials.5 This questions the suitability of pruned perturbation approximations when the underlying function is close to a by: Introduction to singular perturbation methods Nonlinear oscillations.

This text is part of a set of lecture notes written by A. Aceves, N. Ercolani, C. Jones, J. Lega & J. Moloney, for a summer school held in Cork, Ireland, from to The links below will take you to online overviews of some of the concepts used Size: KB.

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Step 5 would, therefore, be a second linear perturbation step using the direct steady-state dynamics procedure with a load applied at the point of attachment of the disposal unit. The base state for this step is the state at the end of the previous general step—that is, at the end of the forming process (Step 3).

A unified approach for solving nonlinear regular perturbation problems Article in International Journal of Mathematical Education 39(8). An optimization strategy is used to find the blowing and suction control law at the wall providing the maximum damping of the perturbation energy at a given target time.

Two optimally-growing finite-amplitude initial perturbations have been employed to initialize the : S. Cherubini, J.-C. Robinet, P. De Palma.

An analysis step during which the response can be either linear or nonlinear is called a general analysis step. An analysis step during which the response can be linear only is called a linear perturbation analysis step.

Summary. In this paper, we apply a new perturbation technique coupled with the iteration method. This procedure is obtained by combining the iteration methods of J.

He and Mickens into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of oscillation amplitude, Cited by: Nonlinear and stable perturbation-based approximations Wouter J.

Den Haan and Joris De Wind Decem Abstract Users of regular higher-order perturbation approximations can face two problems: policy functions with odd undesirable shapes and simulated data that explode.

Kim. Perturbation Analysis of Optimization Problems J. Frederic Bonnans1 and Alexander Shapiro2 1INRIA-Rocquencourt, Domaine de Voluceau, B.P.Rocquencourt, France, and Ecole Polytechnique, France 2School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GeorgiaUSA.

Perturbation theory leads to an expression for the desired solution in terms of a formal power series in some "small" parameter – known as a perturbation series – that quantifies the deviation from the exactly solvable problem. The leading term in this power series is the solution of the exactly solvable problem, while further terms describe the deviation in the solution, due to the.

Full text of "Power Perturbation Method for Power Flow Analysis" See other formats International Journal of Automation and Power Engineering,1: Published Online April Power Perturbation Method for Power Flow Analysis P. Bhowmik 1, D.

Description A rapid perturbation procedure for determining nonlinear flow solutions PDF

Rajan 2, S. Das 3, 4 'Department of Electrical Engineering, National Institute of. Chapter 4: Linear Perturbation Theory May 4, 1. Gravitational Instability 1As theresult ofa phasetransition very early Universe went through an astonishingly rapid exponential expansion.

moderate imprint and nonlinear features start to emerge. Primordial density perturbations on a small 2.

Exploring the Classic Perturbation Method for Obtaining Single and Multiple Solutions of Nonlinear Algebraic Problems with Application to Microelectronic Circuits - written by M. Sandoval-Hernandez, O. Alvarez-Gasca, A.

Contreras-Hernandez published on /10/01 download full article with reference data and citationsAuthor: M. Sandoval-Hernandez, O. Alvarez-Gasca, A. Contreras-Hernandez, J.

Pretelin-Canela, B.

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By investigation of perturbation solution for nonlinear reaction-diffusion system, we derive related differential model for perturbations that involves weak nonlinearities up to third order. For a first time, this model is shown to result in derivation of the system for amplitude distribution by means of nonlinear integration on orthogonal basis in spatial : Victor F.

Dailyudenko. A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow.

This technique called the Optimal Homotopy Asymptotic Method (OHAM) does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper Cited by: where 헠 is a nonlinear prediction model y = 헠 t 0 →t (x) is a prediction from t 0 to t generated by the model 헠 with x as the initial condition.

Here x b, x, and x′ are all m x-dimensional column vectors, and y and y′ are m y-dimensional column ng n nonzero initial perturbations: x′ 1, x′ 2,x′ n (n ≪ m = m x + m y), which are linearly independent: det Cited by: Newton-Raphson procedure. The Fast decoupled power flow solution requires more iterations than the Newton-Raphson method, but requires considerably less time per iteration and a power flow solution is obtained very rapidly.

This technique is very useful in contingency analysis where numerous outages are to be simulated or a power flow solution isFile Size: 2MB. The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental by: As long as two surfaces move relatively to each other, friction can't be avoided.

And the verse effects of friction are quite obvious. Hence aerodynamics studies the movement of bodies in space (air) or the way air moves over the surface of bodies in order to reduce friction by accurate and stylish streamlining.

• General introduction to Hydrodynamic Instabilities • Linear instability of parallel flows finite-amplitude of the perturbation. Determining the shape and amplitude of Compute an equilibrium solution 𝐐b of the original nonlinear system. Notes on Perturbation Techniques for ODEs James A.

Tzitzouris The idea behind the perturbation method is a simple one. Faced with a problem that we cannot solve exactly, but that is close (in some sense) to an auxiliary problem that we can solve exactly, aFile Size: KB.

details the steps in perturbation computations. Suppose that y(t,ǫ) is the solution of an ordinary differential equation in which the equation and the initial data depend smoothly on a parameter ǫ. Goal. Compute the coefficients in the Taylor polynomials Set ǫ = 0 to determine an initial value problem determiningFile Size: 32KB.

New perturbation iteration solutions for Fredholm and Volterra integral equations. J Appl Math. ; He JH. Iteration perturbation method for strongly nonlinear oscillators. J Vib Control. ; – doi: / Mickens RE. Iteration procedure for determining approximate solutions to nonlinear oscillator by: 1.

The periodic solution in the first approximation is obtained. The solution is compared with the exact one and shows good agreement. Ariel et al investigated the suitability of a homotopy perturbation method for computing the axisymmetric flow of a viscous, incompressible fluid due to the stretching of a sheet.

It is found that the HPM produces Cited by:   Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He’s homotopy perturbation method A. Beléndez et al Nonlinear Analysis Real World Applications 10 Crossref. Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems.