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Academic literature on the topic 'Goldstein equations'

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Published: 1 June 2024

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Journal articles on the topic "Goldstein equations":

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Lam, S. H., and N. Rott. "Eigen-Functions of Linearized Unsteady Boundary Layer Equations." Journal of Fluids Engineering 115, no. 4 (December 1, 1993): 597–602. http://dx.doi.org/10.1115/1.2910185.

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The Lam and Rott theory of linearized unsteady boundary layers is revisited, and some new results are obtained. The exact outer eigen-solution for a flat plate found in the original paper is shown to be a special case of the Prandtl-Glauert transposition theorem. The streamwise coordinate-dependent factor of the inner eigen-solutions, first found by M. E. Goldstein for the flat plate, is generalized for arbitrary pressure gradients.
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Pogorui, Anatoliy A., and Ramón M. Rodríguez-Dagnino. "Goldstein-Kac telegraph equations and random flights in higher dimensions." Applied Mathematics and Computation 361 (November 2019): 617–29. http://dx.doi.org/10.1016/j.amc.2019.05.045.

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FERLINI, VINCENT. "SOLUTIONS TO ZERO-SUM EXPONENT EQUATIONS OVER FINITE CYCLIC GROUPS OF EXPONENT GREATER THAN TWO." International Journal of Algebra and Computation 18, no. 03 (May 2008): 423–41. http://dx.doi.org/10.1142/s0218196708004494.

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Lyndon initiated a study of equations over cyclic groups [8] and his approach led him to consider a class of equations of the form ah= (tpat-p)(tqat-q)(tpat-p)-1(tqat-q)-1where t is the variable and the cyclic group is Cn= 〈a|an〉. Work by Ferlini, Goldstein, and Salpukis [3] concentrated, more generally, on equations with the exponent sum of the variable being zero over C2. This paper continues along the path started by Lyndon and shows that a large class of the equations above do have solutions over Cnwhere n ≥ 4. Our approach involves the use of pictures. We also include a result that the equations with h = 1, 2, p = 1, and q = 2 do not have a solution over C3.
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HILFER, R. "ON FRACTIONAL RELAXATION." Fractals 11, supp01 (February 2003): 251–57. http://dx.doi.org/10.1142/s0218348x03001914.

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Generalized fractional relaxation equations based on generalized Riemann-Liouville derivatives are combined with a simple short time regularization and solved exactly. The solution involves generalized Mittag-Leffler functions. The associated frequency dependent susceptibilities are related to symmetrically broadened Cole-Cole susceptibilities occurring as Johari Goldstein β-relaxation in many glass formers. The generalized susceptibilities exhibit a high frequency wing and strong minimum enhancement.
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Mallier, Roland. "The nonlinear temporal evolution of a disturbance to a stratified mixing layer." Journal of Fluid Mechanics 291 (May 25, 1995): 287–97. http://dx.doi.org/10.1017/s0022112095002709.

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Using a nonlinear critical layer analysis, Goldstein & Leib (1988) derived a set of nonlinear evolution equations governing the spatial growth of a two-dimensional instability wave on a homogeneous incompressible tanh y mixing layer. In this study, we extend this analysis to the temporal growth of the García model of an incompressible stratified shear layer. We consider the stage of the evolution in which the growth first becomes nonlinear, with the nonlinearity appearing inside the critical layer. The Reynolds number is assumed to be just large enough so that the unsteady, nonlinear and viscous terms all enter at the same order of magnitude inside the critical layer. The equations are solved numerically for the inviscid case.
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Galaktionov, V. A., and I. V. Kamotski. "On nonexistence of Baras–Goldstein type for higher-order parabolic equations with singular potentials." Transactions of the American Mathematical Society 362, no. 08 (March 17, 2010): 4117–36. http://dx.doi.org/10.1090/s0002-9947-10-04855-5.

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Chalons, Christophe, and Rodolphe Turpault. "High‐order asymptotic‐preserving schemes for linear systems: Application to the Goldstein–Taylor equations." Numerical Methods for Partial Differential Equations 35, no. 4 (February 21, 2019): 1538–61. http://dx.doi.org/10.1002/num.22363.

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El Ibrami, Hassan, and Ahmed Naciri. "Equity Capital-Structure-Based Evaluation Method." International Journal of Accounting and Financial Reporting 2, no. 2 (December 28, 2012): 299. http://dx.doi.org/10.5296/ijafr.v2i2.2537.

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Abstract The main purpose of this paper is to theoretically compare three structural models presenting several similarities and using financial statements within the context of real options theory. The models are those suggested by i) Leland (1994); ii) Goldstein, Ju and Leland (2001) and iii) Sarkar and Zapatero (2003). The analysis emphasizes convergence conditions of the three models based on their respective dynamic equations. The results show that the first two models represent special cases of the third one. The paper also presents a new equity and debt valuation method. Keywords: Structural model, Financial statement, Equity, EBIT, Mean reversion, Contingent claim, Convergence.
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Galaktionov, V. A. "On nonexistence of Baras-Goldstein type without positivity assumptions for singular linear and nonlinear parabolic equations." Proceedings of the Steklov Institute of Mathematics 260, no. 1 (April 2008): 123–43. http://dx.doi.org/10.1134/s0081543808010094.

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Mallier, R., and S. A. Maslowe. "Fully coupled resonant-triad interactions in a free shear layer." Journal of Fluid Mechanics 278 (November 10, 1994): 101–21. http://dx.doi.org/10.1017/s0022112094003630.

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We report the results of an investigation of the weakly nonlinear evolution of a triad of waves, each slightly amplified on a linear basis, that are superimposed on a tanh y mixing layer. The triad consists of a plane wave and a pair of oblique modes that act as a subharmonic of order 1/2. The oblique modes are inclined at approximately ±60°. to the mean flow direction and because the resonance conditions are satisfied exactly the analysis is entirely self-consistent as an asymptotic theory. The nonlinearity first occurs within the critical layer and the initial interaction is of the parametric resonance type. This produces faster than exponential growth of the oblique waves, behaviour observed recently in the experiments of Corke & Kusek (1993). The critical-layer dynamics lead subsequently to coupled integro-differential equations governing the amplitude evolution and, as first shown in related work by Goldstein & Lee (1992) on boundary layers in an adverse pressure gradient, these equations develop singularities in a finite time.
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Journal articles

Dissertations / Theses on the topic "Goldstein equations":

1

Bensalah, Antoine. "Une approche nouvelle de la modélisation mathématique et numérique en aéroacoustique par les équations de Goldstein : Applications en aéronautique." Electronic Thesis or Diss., Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLY008.

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La problématique du bruit fait par les réacteurs d'avions est un des enjeux majeurs de l’industrie aéronautique.C’est dans ce contexte que l’équipe du centre de recherche d'Airbus travaille au développement du code de calcul Actipole de propagation acoustique en présence d'un écoulement porteur.L'approche consiste en un couplage FEM-BEM entre la zone de propagation loin de l'avion où l'écoulement est supposé uniforme (BEM) et la zone plus proche où l'écoulement est supposé potentiel (FEM).Les équations de l'aéroacoustique en régime harmonique se réduisent alors à la simple équation scalaire d'Helmholtz convectée.Nous étudions une reformulation des équations d'Euler linéarisées, les équations de Goldstein, prenant en compte l'interaction entre l'acoustique et l'hydrodynamique, lorsque l'écoulement n'est plus potentiel, par l'ajout d'une inconnue hydrodynamique localisée aux zones fortement rotationnelles.Les équations de Goldstein peuvent être vues comme une perturbation de l'équation d'Helmholtz convectée, couplée à une équation de transport harmonique.Nos approches théorique et numérique restent dans le cadre de cette vision perturbative en étudiant dans une premier temps la résolution de l'équation de transport.Nous montrons ainsi que sous l'hypothèse d'un écoulement domaine-remplissant, l'équation de transport harmonique peut être inversée et sous contrainte d'un faible rotationnel, le caractère Fredholm de l'équation d'Helmholtz convectée se généralise aux équations de Goldstein.Le cas général est un problème ouvert et difficile, nous montrons que l'équation de transport n'est pas toujours inversible et possède des fréquences de résonance auxquelles les og solutionsfg{} tendent à être singulières le long de lignes de recirculation de l'écoulement.Nous montrons qu'il en est de même des équations couplées qui possèdent en plus des fréquences de résonance du transport d'autres résonances, dites critiques.Nous terminons cette thèse par une étude locale des singularités, par la méthode de Frobenius, des solutions modales obtenues par absorption limite, aux fréquences de résonance du transport et critiques, au voisinage de lignes résonantes, montrant que de telles solutions sortent alors du cadre variationnelle classiques
The issue of the noise radiating by reactor engines is one of the most important in the aeronautic industry.It is in this context that the Aribus research department team is working on the code Actipole of acoustic propagation in flow.The approach used is a FEM-BEM coupling between areas far away of the aircraft where the flow is assumed to be uniform (BEM) and the the nearest area where the flow is assumed to be potential (FEM).Then, harmonic aeroacoustic equations simplify in the simpler scalar convected Helmholtz equation.We study the Goldstein formulation, equivalent to the Linearized Euler equations, taking into account the interaction between acoustics and hydrodynamics, where the flow is no more potential, by locally adding a hydrodynamic unknown in most vortical areas.Goldstein equations can be seen as perturbations of the convected Helmholtz equation, coupled with a harmonic transport equation.Our theoritical and numerical approachs take advantage of this perturbative view by studying in a first step the resolution of the transport equation.We then show that under the hypothesis of a domain-filling flow, the harmonic transport equation can be solved and under the assumption of a small vorticity, the Fredholm property of the convected Helmholtz equation can be generalized to Goldstein equations.The general case is an open problem and is much more difficult, we show that the transport equation is not always well-posed and admits some resonance frequencies for which og solutions fg{} tend to be singular along some closed streamlines of the flow.We show that the same phenomena occurs with the coupled equations which admit, in addition to resonance frequencies due to transport, other resonances so called critic resonances.We end this thesis by studying the local singularities, by Frobenius method, of modal solutions obtained using limitting absoprtion principle when we are at the resonance frequencies around a resonant streamline.We show that these solutions are then no more in the classical functionnal framework used for variational formulation

Books on the topic "Goldstein equations":

1

1941-, Goldstein Jerome A., Goldstein Gisèle Ruiz 1958-, Nagel R, and Neubrander Frank 1954-, eds. Evolution equations: Proceedings in honor of J.A. Goldstein's 60th birthday. New York: M. Dekker, 2003.

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Ruban, Anatoly I. Trailing-Edge Flow. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199681754.003.0004.

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Chapter 3 focuses on the high-Reynolds number flow of an incompressible fluid near the trailing edge of a flat plate. It begins with Goldstein’s (1930) solution for a viscous wake behind the plate, and shows that the displacement effect of the wake produces a singular pressure gradient near the trailing edge. It further shows that this singularity leads to a formation triple-deck viscous-inviscid interaction region that occupies a small vicinity of the trailing edge. A detailed analysis of the flow in each tier of the triple-deck structure is conducted based on the asymptotic analysis of the Navier–Stokes equations. As a result, the so-called ‘interaction problem’ is formulated. It concludes with the numerical solution of so-called ‘interaction problem’.

Book chapters on the topic "Goldstein equations":

1

Adam, John A. "Atmospheric Waves." In Rays, Waves, and Scattering. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691148373.003.0014.

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This chapter deals with the underlying mathematics of atmospheric waves. Gravity waves occur between any stable layers of fluids that differ in density. When the fluid boundary is disturbed, buoyancy forces try to restore the equilibrium. The fluid returns to its original shape and overshoots before oscillations finally set in that propagate as waves. Internal gravity or buoyancy waves are often observed in the stable density layering of the upper atmosphere. The chapter first describes the linearized equations governing atmospheric waves before introducing a mathematical model of lee/mountain waves over an isolated mountain ridge, focusing on the basic equations and solutions, trapped lee waves, and billow clouds. It also considers wind shear, Howard's semicircle theorem, and the Taylor–Goldstein equation.

Conference papers on the topic "Goldstein equations":

1

Smith, Lelanie, Josua P. Meyer, Oliver F. Oxtoby, and Arnuad G. Malan. "An Interactive Boundary Layer Modeling Methodology for Aerodynamic Flows." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62075.

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Computational Fluid Dynamics (CFD) simulation is a computational tool for exploring flow applications in science and technology. Of central importance in many flow scenarios is the accurate modeling of the boundary layer phenomenon. This is particularly true in the aerospace industry, where it is central to the prediction of drag. Modern CFD codes as applied to modeling aerodynamic flows have to be fast and efficient in order to model complex realistic geometries. When considering viscous flows the boundary layer typically requires the largest part of computational resources. To simulate boundary layer flow with most current CFD codes requires extremely fine mesh spacing normal to the wall and is consequently computationally very expensive. Boundary layer modeling approaches have by contrast received relatively little attention, while having the potential of offering considerable computational cost savings. One boundary layer method which has proven to be very accurate is the two-integral method of Drela (1986). Coupling the boundary layer solution to inviscid external flow is, however, a challenge due to the Goldstein singularity, which occurs as separation is approached. We propose to develop a new method to couple Drela’s two-integral equations with a generic outer flow solver in an iterative fashion. We introduce an auxiliary equation which is solved along with the displacement thickness to overcome the Goldstein singularity without the need to solve the entire flow domain simultaneously. In this work the incompressible Navier-Stokes equations will be used for the outer flow. In the majority of previous studies the boundary layer thickness is simulated using a wall transpiration boundary condition at the interface between viscous and inviscid flows. This boundary condition is inherently non-physical since it adds extra mass into the system to simulate the effects of the boundary layer. Here, we circumvent this drawback by the use of a mesh movement algorithm to shift the surface of the body outward without regridding the entire mesh. This replaces the transpiration boundary condition. The results obtained show that accurate modeling is possible for laminar incompressible flow and that the solutions obtained compare well to similarity solutions in the cases of flat and inclined plates and to the results of a NACA 0012 airfoil produced by the validated XFOIL code (Drela and Youngren, 2001).
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Semiletov, Vasily, and Sergey A. Karabasov. "Adjoint Linearised Euler solver for Goldstein acoustic analogy equations for 3D non-uniform flow sound scattering problems: verification and capability study." In 20th AIAA/CEAS Aeroacoustics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2014. http://dx.doi.org/10.2514/6.2014-2318.

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Semiletov, Vasily A., and Sergey A. Karabasov. "A 3D frequency-domain linearised Euler solver based on the Goldstein acoustic analogy equations for the study of nonuniform meanflow propagation effects." In 19th AIAA/CEAS Aeroacoustics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2019.

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Morfey, Christopher, Brian Tester, and Christopher Powles. "Numerical and Asymptotic Lilley-Equation Solutions for the Goldstein Jet-Noise Source Model." In 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference). Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-3592.

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Chattot, Jean-Jacques. "Optimization of Wind Turbines Using Helicoidal Vortex Model." In ASME 2003 Wind Energy Symposium. ASMEDC, 2003. http://dx.doi.org/10.1115/wind2003-522.

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The problem of the design of a wind turbine for maximum output is addressed from an aerodynamical point of view. It is shown that the optimum inviscid design, based on the Goldstein model, satifies the minimum energy condition of Betz only for light loading. The more general equation governing the optimum is derived and an integral relation is obtained, stating that the optimum solution satisfies the minimum energy condition of Betz in the Trefftz plane “in the average”. The discretization of the problem is detailed, including the viscous correction based on the 2-D viscous profile data. A constraint is added to account for the force on the tower. The minimization problem is solved very efficiently by relaxation. Several optimized solutions are calculated and compared with the NREL rotor, using the same profile, but different chord and twist distributions. In all cases, the optimization produces a more efficient design.
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Amouzgar, Kaveh, and Niclas Stromberg. "An Approach Towards Generating Surrogate Models by Using RBFN With a Priori Bias." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34948.

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In this paper, an approach to generate surrogate models constructed by radial basis function networks (RBFN) with a priori bias is presented. RBFN as a weighted combination of radial basis functions only, might become singular and no interpolation is found. The standard approach to avoid this is to add a polynomial bias, where the bias is defined by imposing orthogonality conditions between the weights of the radial basis functions and the polynomial basis functions. Here, in the proposed a priori approach, the regression coefficients of the polynomial bias are simply calculated by using the normal equation without any need of the extra orthogonality prerequisite. In addition to the simplicity of this approach, the method has also proven to predict the actual functions more accurately compared to the RBFN with a posteriori bias. Several test functions, including Rosenbrock, Branin-Hoo, Goldstein-Price functions and two mathematical functions (one large scale), are used to evaluate the performance of the proposed method by conducting a comparison study and error analysis between the RBFN with a priori and a posteriori known biases. Furthermore, the aforementioned approaches are applied to an engineering design problem, that is modeling of the material properties of a three phase spherical graphite iron (SGI). The corresponding surrogate models are presented and compared.
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Kurup, Nishu V., Shan Shi, Zhongmin Shi, Wenju Miao, and Lei Jiang. "Study of Nonlinear Internal Waves and Impact on Offshore Drilling Units." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50304.

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Internal waves near the ocean surface have been observed in many parts of the world including the Andaman Sea, Sulu Sea and South China Sea among others. The factors that cause and propagate these large amplitude waves include bathymetry, density stratification and ocean currents. Although their effects on floating drilling platforms and its riser systems have not been extensively studied, these waves have in the past seriously disrupted offshore exploration and drilling operations. In particular a drill pipe was ripped from the BOP and lost during drilling operations in the Andaman sea. Drilling riser damages were also reported from the south China Sea among other places. The purpose of this paper is to present a valid numerical model conforming to the physics of weakly nonlinear internal waves and to study the effects on offshore drilling semisubmersibles and riser systems. The pertinent differential equation that captures the physics is the Korteweg-de Vries (KdV) equation which has a general solution involving Jacobian elliptical functions. The solution of the Taylor Goldstein equation captures the effects of the pycnocline. Internal wave packets with decayed oscillations as observed from satellite pictures are specifically modeled. The nonlinear internal waves are characterized by wave amplitudes that can exceed 50 ms and the present of shearing currents near the layer of pycnocline. The offshore drilling system is exposed to these current shears and the associated movements of large volumes of water. The effect of internal waves on drilling systems is studied through nonlinear fully coupled time domain analysis. The numerical model is implemented in a coupled analysis program where the hull, moorings and riser are considered as an integrated system. The program is then utilized to study the effects of the internal wave on the platform global motions and drilling system integrity. The study could be useful for future guidance on offshore exploration and drilling operations in areas where the internal wave phenomenon is prominent.
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Liangfeng, Wang, Xiang Kangshen, Mao Luqin, Tong Hang, and Qiao Weiyang. "Numerical Simulation of the Effect of the Tip Clearance Flow on Rotor-Stator Interaction Tone Noise in Axial-Flow Fan." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14179.

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Abstract The present study is focused on the sound generation due to the rotor tip clearance flow interaction with stator in an axial flow fan. A hybrid URANS/Goldstein’s equations method is applied to calculate the unsteady flow and tone noise in a high loaded axial-flow fan with different rotor tip clearance. The numerical simulation results show that the main sound sources of fan tip clearance tone noise are concentrated in the leading edge of downstream stator blades. It is found that when the rotor tip clearance increases from zero to 2.5 mm (0.94% relative blade height), the mass flow of the fan decreases by about 2% and the efficiency of the fan decreases by about 1 percentage, and the sound power level at 1BPF forward tone increases by 1.47dB, and that of backward tone increases by 0.65dB. However, the influence of tip clearance on the tone noise intensity at 2BPF and 3BPF is more complex, and the variation range is less than 1dB. It is found that the wake width and wake strength at the rotor exit increase with the increase of tip clearance. The tip secondary flow caused by rotor clearance seriously affects the circumferential inhomogeneity of stator leading edge inflow conditions.
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Liangfeng, Wang, Mao Luqin, Xiang Kangshen, Duan Wenhua, Tong Hang, and Qiao Weiyang. "Numerical Study on Duct Acoustic Modal and Source Flow Structure of Fan Tones With Leaned and Swept Stator." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14180.

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Abstract The present study is focused on the fan tone noise reduction with leaned and swept stator blade. A hybrid URANS/Goldstein’s equations method is used to calculate the unsteady flow and tone noise of a high loaded axial-flow fan. The numerical simulation results show that the fan tone noise will be increased with negative angle lean, while it will be reduced with positive lean angle. The higher the harmonic number, the larger the noise reduction with positive lean angle blade. It is found that when the stator blade sweeps back of 30 degrees, the fan tone noise at the fan inlet can be reduced by 5.5 dB, while the fan tone noise at the fan outlet can be reduced by 9.8dB. It is also found that the combined leaned and swept blade has the largest noise reduction. When the fan stator blade lean angle and sweep angle are both 30 degrees, the fan inlet tone noise can be reduced by 8.5 dB, while the fan outlet tone noise can be reduced by 17dB. The numerical simulation results indicate that the influence of blade lean and sweep on fan mass flow is less than 1% within the scope of this study. The negative lean angle of stator blade can improve the aerodynamic performance, but the positive lean angle of the stator blade will reduce the total pressure ratio and isentropic efficiency of the fan.

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