Academic literature on the topic 'Falkner–Skan–Cooke boundary layer'
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Journal articles on the topic "Falkner–Skan–Cooke boundary layer"
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Auteri, F., and L. Quartapelle. "Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems." Communications in Computational Physics 12, no. 5 (2012): 1329–58. http://dx.doi.org/10.4208/cicp.130411.230911a.
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AbstractIn this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.
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HÖGBERG, MARKUS, and DAN HENNINGSON. "Secondary instability of cross-flow vortices in Falkner–Skan–Cooke boundary layers." Journal of Fluid Mechanics 368 (August 10, 1998): 339–57. http://dx.doi.org/10.1017/s0022112098001931.
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Linear eigenvalue calculations and spatial direct numerical simulations (DNS) of disturbance growth in Falkner–Skan–Cooke (FSC) boundary layers have been performed. The growth rates of the small-amplitude disturbances obtained from the DNS calculations show differences compared to linear local theory, i.e. non-parallel effects are present. With higher amplitude initial disturbances in the DNS calculations, saturated cross-flow vortices are obtained. In these vortices strong shear layers appear. When a small random disturbance is added to a saturated cross-flow vortex, a low-frequency mode is found located at the bottom shear layer of the cross-flow vortex and a high-frequency secondary instability is found at the upper shear layer of the cross-flow vortex. The growth rates of the secondary instabilities are found from detailed analysis of simulations of single-frequency disturbances. The low-frequency disturbance is amplified throughout the domain, but with a lower growth rate than the high-frequency disturbance, which is amplified only once the cross-flow vortices have started to saturate. The high-frequency disturbance has a growth rate that is considerably higher than the growth rates for the primary instabilities, and it is conjectured that the onset of the high-frequency instability is well correlated with the start of transition.
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CORBETT, PETER, and ALESSANDRO BOTTARO. "Optimal linear growth in swept boundary layers." Journal of Fluid Mechanics 435 (May 25, 2001): 1–23. http://dx.doi.org/10.1017/s0022112001003627.
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Optimal perturbations for the family of three-dimensional boundary layers described by the Falkner–Skan–Cooke similarity solution are obtained using a variational technique in the temporal framework. The disturbances experiencing the most growth take the form of vortices almost aligned with the external streamline at inception and evolve into streaks. In subcritical flows these can attain about twice the transient amplification observed in comparably forced two-dimensional flows. Possible connections between optimal perturbations and exponentially amplified crossflow vortices are explored.
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Brynjell-Rahkola, Mattias, Philipp Schlatter, Ardeshir Hanifi, and Dan S. Henningson. "Global Stability Analysis of a Roughness Wake in a Falkner–Skan–Cooke Boundary Layer." Procedia IUTAM 14 (2015): 192–200. http://dx.doi.org/10.1016/j.piutam.2015.03.040.
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Högberg, Markus, Mattias Chevalier, and Dan S. Henningson. "Linear compensator control of a pointsource induced perturbation in a Falkner–Skan–Cooke boundary layer." Physics of Fluids 15, no. 8 (2003): 2449–52. http://dx.doi.org/10.1063/1.1584434.
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Brynjell-Rahkola, Mattias, Nima Shahriari, Philipp Schlatter, Ardeshir Hanifi, and Dan S. Henningson. "Stability and sensitivity of a cross-flow-dominated Falkner–Skan–Cooke boundary layer with discrete surface roughness." Journal of Fluid Mechanics 826 (August 15, 2017): 830–50. http://dx.doi.org/10.1017/jfm.2017.466.
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With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner–Skan–Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the $\unicode[STIX]{x1D700}$-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.
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SCHRADER, LARS-UVE, LUCA BRANDT, and DAN S. HENNINGSON. "Receptivity mechanisms in three-dimensional boundary-layer flows." Journal of Fluid Mechanics 618 (January 10, 2009): 209–41. http://dx.doi.org/10.1017/s0022112008004345.
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Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.
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CHEVALIER, MATTIAS, JÉRÔME HŒPFFNER, ESPEN ÅKERVIK, and DAN S. HENNINGSON. "Linear feedback control and estimation applied to instabilities in spatially developing boundary layers." Journal of Fluid Mechanics 588 (September 24, 2007): 163–87. http://dx.doi.org/10.1017/s0022112007007392.
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This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Högberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner–Skan–Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.
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TAYLOR, M. J., and N. PEAKE. "The long-time behaviour of incompressible swept-wing boundary layers subject to impulsive forcing." Journal of Fluid Mechanics 355 (January 25, 1998): 359–81. http://dx.doi.org/10.1017/s002211209700788x.
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The long-time limit of the response of incompressible three-dimensional boundary layer flows on infinite swept wedges and infinite swept wings to impulsive forcing is examined using causal linear stability theory. Following the discovery by Lingwood (1995) of the presence of absolute instabilities caused by pinch points occurring in the radial direction in the boundary layer flow of a rotating disk, we search for pinch points in the cross flow direction for both the model Falkner–Skan–Cooke profile of a swept wedge and for a genuine swept-wing configuration. It is shown in both cases that, within a particular range of the parameter space, the boundary layer does indeed support pinch points in the wavenumber plane corresponding to the crossflow direction. These crossflow-induced pinch points do not constitute an absolute instability, as there is no simultaneous pinch occurring in the streamwise wavenumber plane, but nevertheless we show here how they can be used to find the maximum local growth rate contained in a wavepacket travelling in any given direction. Lingwood (1997) also found pinch points in the chordwise wavenumber plane in the boundary layer of the leading-edge region of a swept wing (i.e. at very high flow angles). The results presented in this paper, however, demonstrate the presence of pinch points for a much larger range of flow angles and pressure gradients than was found by Lingwood, and indeed describe the flow over a much greater, and practically significant, portion of the wing.
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HÖGBERG, MARKUS, and DAN S. HENNINGSON. "Linear optimal control applied to instabilities in spatially developing boundary layers." Journal of Fluid Mechanics 470 (October 31, 2002): 151–79. http://dx.doi.org/10.1017/s0022112002001702.
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The work presented extends previous research on linear controllers in temporal channel flow to spatially evolving boundary layer flow. The flows studied are those on an infinite swept wedge described by the Falkner–Skan–Cooke (FSC) velocity profiles, including the special case of the flow over a flat plate. These velocity profiles are used as the base flow in the Orr–Sommerfeld–Squire equations to compute the optimal feedback control through blowing and suction at the wall utilizing linear optimal control theory. The control is applied to a parallel FSC flow with unstable perturbations. Through an eigenvalue analysis and direct numerical simulations (DNS), it is shown that instabilities are stabilized by the controller in the parallel case. The localization of the convolution kernels for control is also shown for the FSC profiles.Assuming that non-parallel effects are small a technique is developed to apply the same controllers to a DNS of a spatially evolving flow. The performance of these controllers is tested in a Blasius flow with both a Tollmien–Schlichting (TS) wave and an optimal spatial transiently growing perturbation. It is demonstrated that TS waves are stabilized and that transient growth is lowered by the controller. Then the control is also applied to a spatial FSC flow with unstable perturbations leading to saturated cross-flow vortices in the uncontrolled case. It is demonstrated that the linear controller successfully inhibits the growth of the cross-flow vortices to a saturated level and thereby delays the possibility of transition through secondary instabilities. It is also demonstrated that the controller works for relatively high levels of nonlinearity, and for stationary as well as time-varying perturbations.
Dissertations / Theses on the topic "Falkner–Skan–Cooke boundary layer"
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Brynjell-Rahkola, Mattias. "Global stability analysis of three-dimensional boundary layer flows." Licentiate thesis, KTH, Stabilitet, Transition, Kontroll, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-175353.
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This thesis considers the stability and transition of incompressible boundary layers. In particular, the Falkner–Skan–Cooke boundary layer subject to a cylindrical surface roughness, and the Blasius boundary layer with applied localized suction are investigated. These flows are of great importance within the aviation industry, feature complex transition scenarios, and are strongly three-dimensional in nature. Consequently, no assumptions regarding homogeneity in any of the spatial directions are possible, and the stability of the flow is governed by an extensive three-dimensional eigenvalue problem. The stability of these flows is addressed by high-order direct numerical simulations using the spectral element method, in combination with a Krylov subspace projection method. Such techniques target the long-term behavior of the flow and can provide lower limits beyond which transition is unavoidable. The origin of the instabilities, as well as the mechanisms leading to transition in the aforementioned cases are studied and the findings are reported. Additionally, a novel method for computing the optimal forcing of a dynamical system is developed. This type of analysis provides valuable information about the frequencies and structures that cause the largest energy amplification in the system. The method is based on the inverse power method, and is discussed in the context of the one-dimensional Ginzburg–Landau equation and a two-dimensional flow case governed by the Navier–Stokes equations.<br><p>QC 20151015</p>
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Chevalier, Mattias. "Adjoint based control and optimization of aerodynamic flows." Licentiate thesis, KTH, Mechanics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1435.
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Brynjell-Rahkola, Mattias. "Studies on instability and optimal forcing of incompressible flows." Doctoral thesis, KTH, Stabilitet, Transition, Kontroll, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-218172.
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This thesis considers the hydrodynamic instability and optimal forcing of a number of incompressible flow cases. In the first part, the instabilities of three problems that are of great interest in energy and aerospace applications are studied, namely a Blasius boundary layer subject to localized wall-suction, a Falkner–Skan–Cooke boundary layer with a localized surface roughness, and a pair of helical vortices. The two boundary layer flows are studied through spectral element simulations and eigenvalue computations, which enable their long-term behavior as well as the mechanisms causing transition to be determined. The emergence of transition in these cases is found to originate from a linear flow instability, but whereas the onset of this instability in the Blasius flow can be associated with a localized region in the vicinity of the suction orifice, the instability in the Falkner–Skan–Cooke flow involves the entire flow field. Due to this difference, the results of the eigenvalue analysis in the former case are found to be robust with respect to numerical parameters and domain size, whereas the results in the latter case exhibit an extreme sensitivity that prevents domain independent critical parameters from being determined. The instability of the two helices is primarily addressed through experiments and analytic theory. It is shown that the well known pairing instability of neighboring vortex filaments is responsible for transition, and careful measurements enable growth rates of the instabilities to be obtained that are in close agreement with theoretical predictions. Using the experimental baseflow data, a successful attempt is subsequently also made to reproduce this experiment numerically. In the second part of the thesis, a novel method for computing the optimal forcing of a dynamical system is developed. The method is based on an application of the inverse power method preconditioned by the Laplace preconditioner to the direct and adjoint resolvent operators. The method is analyzed for the Ginzburg–Landau equation and afterwards the Navier–Stokes equations, where it is implemented in the spectral element method and validated on the two-dimensional lid-driven cavity flow and the flow around a cylinder.<br><p>QC 20171124</p>
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Bertolotti, Fabio P. "Temporal and spatial growth of subharmonic disturbances in Falkner-Skan flows." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/90912.
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The transition from laminar to turbulent flow in boundary-layers occurs in three stages: onset of two-dimensional TS waves, onset of three-dimensional secondary disturbances of fundamental or subharmonic type, and onset of the turbulent regime. In free flight conditions, subharmonic disturbances are the most amplified.
Recent modeling of the subharmonic disturbance as a parametric instability arising from the presence of a finite amplitude TS wave has given results in quantitative agreement with experiments conducted in a Blasius boundary-layer. The present work extends the analysis to the Falkner-Skan family of profiles, and develops a formulation for spatially growing disturbances to exactly match the experimental observations.
Results show that subharmonic disturbances in Falkner-Skan flows behave similarly to those in a Blasius flow. The most noticeable effect of the pressure gradient is a decrease (favorable) or an increase (adverse) of the disturbance's growth rate. Due to the lack of experimental data, a comparison of subharmonic growth rates from theory and experiment is limited to the Blasius boundary-layer. A comparison of results from the spatial formulation with those previously obtained from a temporal formulation shows the difference to be small. A connection between disturbance growth in a separating boundary-layer profile and a free shear layer is presented. A modification of Caster's transformation from temporal to spatial growth rates for secondary disturbances is given.<br>M.S.
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Mello, Hilton Carlos de Miranda. "Estudo dos efeitos de um jato sintético simulado numericamente no atraso da separação de uma camada limite sobre um aerofólio hipotético." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/18/18135/tde-26022006-111816/.
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A realização deste trabalho tem como objetivo fundamental estudar os efeitos dos atuadores de jato sintético no escoamento de uma camada limite desenvolvida sobre uma placa plana e um aerofólio hipotético. A interação dos jatos sintéticos com um escoamento transversal pode conduzir a uma aparente modificação da forma aerodinâmica de corpos rombudos e, dessa forma, fornecer uma maneira de controle da separação na camada limite. Estudos recentes demonstram que tipos diferentes de escoamentos podem ser produzidos pelo atuador dependendo da oscilação da membrana. Um método numérico para solução das equações de Navier-Stokes incompressíveis bidimensionais na formulação vorticidade-velocidade é utilizado neste trabalho. As equações governantes são discretizadas utilizando-se métodos de diferenças finitas compactas de sexta ordem para as derivadas espaciais. A equação de Poisson para a componente da velocidade normal é resolvida por um método iterativo de sobre-relaxação em linhas sucessivas usando um esquema com malha composta para acelerar a convergência. Os resultados de simulações com diferentes valores de freqüência, amplitude e comprimento de fenda foram verificados através de uma análise de Fourier temporal. Através desta análise é verificado qual a melhor situação para se atrasar a separação da camada limite<br>This work has as a fundamental objective the study of the effects of synthetic jet actuators on the boundary layer flow on a flat plate and on a hypothetical airfoil. The interaction of synthetic jets with transverse flow can lead to an apparent modification in the aerodynamic shape of blunt bodies and, in that way, supply a means of control of transition within the boundary layer. Recent studies demonstrate that different types of flow may be produced by the actuator, depending on the amplitude of oscillation of the membrane. A numerical method for the solution of two-dimensional incompressible Navier-Stokes equations written in vorticity-velocity formulation is used in this work. The spatial derivatives are discretized with a sixth order compact finite differences scheme. The Poisson equation for the normal velocity component is solved by an iterative line successive over relaxation method and uses a multigrid full approximation scheme to accelerate the convergence. The results of simulations with different values of frequency, amplitude and slot length were verified through a temporal Fourier analysis. By way of this analysis it is verified which are the better parameters for the controlled delay of boundary layer separation
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Sinha, Roy Arijit. "Analysis and control of boundary layer transition on a NACA 0008 wing profile." Thesis, KTH, Mekanik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-239931.
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The main aim of this thesis was to understand the mechanism behind the classical transition scenario inside the boundary layer over an airfoil and eventually attempting to control this transition utilizing passive devices for transition delay. The initial objective of analyzing the transition phenomenon based on TS wave disturbance growth was conducted at 90 Hz using LDV and CTA measurement techniques at two different angles of attack. This was combined with the studies performed on two other frequencies of 100 and 110 Hz, in order to witness its impact on the neutral stability curve behavior. The challenges faced in the next phase of the thesis while trying to control the transition location, was to understand and encompass the effect of adverse pressure gradient before setting up the passive control devices, which in this case was miniature vortex generators. Consequently, several attempts were made to optimize the parameters of the miniature vortex generators depending upon the streak strength and stability. Finally, for 90 Hz a configuration of miniature vortex generators have been found to successfully stabilize the TS wave disturbances below a certain forcing amplitude, which also led to transition delay.
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Yu-ChenWu and 吳昱成. "Applications of the Hybrid Laplace Adomian Decomposition Method to Non-Newtonian Power-Law Fluid Falkner-Skan Boundary Layer Flow and Heat Transfer Under Magnetic Field Effect." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/uxbd84.
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碩士<br>國立成功大學<br>機械工程學系<br>107<br>The problem of magnetohydrodynamic flow, heat transfer and entropy generation rate for a non-Newtonian power-law fluid past a stationary wedge in the presence of a transverse magnetic field is analyzed. The Falkner-Skan equation is applied for the wedge flow. The magnetic field density and surface temperature of the wedge are assumed to vary with the distance from the origin. The governing equations are transformed to nonlinear ordinary differential equations by similarity transformation and several physical parameters related to flow behavior of power-law fluid, magnetic field, angle and surface temperature are introduced.
The governing equations are solved numerically by Hybrid Laplace Adomian Decomposition Method. Laplace Adomian Decomposition Method (LADM) combines the Laplace transformation and Adomian Decomposition Method and is used to solve the nonlinear differential equations. In order to make the result of LADM converge, Padé approximant is employed and the method is named Hybrid Laplace Adomian Decomposition Method.
The results of this study concerns with the velocity and temperature profiles. The Second-law of characteristic of the system is considered and computed from the velocity and temperature. Parameters effecting velocity, temperature and entropy generation rate will be discussed in this study. The local skin-friction coefficient and the local Nusselt number are also tabulated and analyzed.
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Bernhard, Stefan. "Transient integral boundary layer method to simulate entrance flow conditions in one-dimensional arterial blood flow." Doctoral thesis, 2006. http://hdl.handle.net/11858/00-1735-0000-0006-B443-0.
Full textBooks on the topic "Falkner–Skan–Cooke boundary layer"
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Choudhari, Meelan. Acoustic receptivity due to weak surface inhomogeneities in adverse pressure gradient boundary layers. National Aeronautics and Space Administration, Langley Research Center, 1995.
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Ruban, Anatoly I. Classical Boundary-Layer Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199681754.003.0002.
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Chapter 1 discusses the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including the Blasius boundary layer on a flat plate and the Falkner–Skan solutions for the boundary layer on a wedge surface. It presents Schlichting’s solution for the laminar jet and Tollmien’s solution for the viscous wake. These are followed by analysis of Chapman’s shear layer performed with the help of Prandtl’s transposition theorem. It also considers the boundary layer on the surface of a fast rotating cylinder with the purpose of linking the circulation around the cylinder with the speed of its rotation. It concludes discussion of the classical boundary-layer theory with analysis of compressible boundary layers, including the interactive boundary layers in hypersonic flows.
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Escudier, Marcel. Laminar boundary layers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0017.
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This chapter starts by introducing the concept of a boundary layer and the associated boundary-layer approximations. The laminar boundary-layer equations are then derived from the Navier-Stokes equations. The assumption of velocity-profile similarity is shown to reduce the partial differential boundary-layer equations to ordinary differential equations. The results of numerical solutions to these equations are discussed: Blasius’ equation, for zero-pressure gradient, and the Falkner-Skan equation for wedge flows. Von Kármán’s momentum-integral equation is derived and used to obtain useful results for the zero-pressure-gradient boundary layer. Pohlhausen’s quartic-profile method is then discussed, followed by the approximate method of Thwaites. The chapter concludes with a qualitative account of the way in which aerodynamic lift is generated.
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L, Ng Lian, Streett Craig L, and Langley Research Center, eds. Acoustic receptivity due to weak surface inhomogeneities in adverse pressure gradient boundary layers. National Aeronautics and Space Administration, Langley Research Center, 1995.
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Ruban, Anatoly I. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199681754.003.0001.
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This book investigates high-Reynolds number flows, and analyses flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including Blasius’s boundary layer on a flat plate, Falkner–Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers the so-called ‘self-induced separation’ in supersonic flow, and which led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate, and then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It covers the Marginal Separation theory—a special version of the triple-deck theory—and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.
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Ruban, Anatoly I. Fluid Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199681754.001.0001.
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This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture courses, and then progressing through more advanced material up to the level of modern research in the field. This book is devoted to high-Reynolds number flows. It begins by analysing the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory. These analyses include the Blasius boundary layer on a flat plate, the Falkner-Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers first the so-called ‘self-induced separation’ in supersonic flow that was studied in 1969 by Stewartson and Williams, as well as by Neiland, and led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate first investigated in 1969 by Stewartson and in 1970 by Messiter. It then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It concludes by covering the Marginal Separation theory, which represents a special version of the triple-deck theory, and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.
Book chapters on the topic "Falkner–Skan–Cooke boundary layer"
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Shang, Deyi. "Review of Falkner-Skan Type Transformation for Laminar Forced Convection Boundary Layer." In Theory of Heat Transfer with Forced Convection Film Flows. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12581-2_3.
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Attili, Basem. "Numerical Solution of the Falkner-Skan Equation Arising in Boundary Layer Theory Using the Sinc-Collocation Method." In Trends in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49716-3_7.
Full textConference papers on the topic "Falkner–Skan–Cooke boundary layer"
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Li, Hongwei, M. Razi Nalim, and Charles L. Merkle. "Transient Thermal Response of Turbulent Compressible Boundary Layers." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68788.
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A general numerical method is developed with the capability to predict the transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature was numerically studied on a 2-D semi-infinite flat plate. The Reynolds-averaged boundary-layer equations are solved based on the compressible Falkner-Skan transformation. Turbulence is modeled using a two-layer eddy-viscosity model developed by Cebeci and Smith, and the turbulent Prandtl number formulation originally developed by Kays and Crawford. The governing differential equations are discretized with the Keller-box method. The numerical accuracy is validated through grid independence studies and comparison with the steady state solution. In turbulent flow as in laminar, heat transfer coefficient is initially very different from that obtained from quasi-steady analysis. It is found that, both the transient time scale and the magnitude of the transient heat transfer coefficients differ significantly between turbulent and laminar flow. The more complex variation of transient heat transfer rate in turbulent flow is evident, and needs further study.
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Fakheri, Ahmad. "Flow Separation." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12409.
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In thermal science courses, flow over curved objects, like cylinders or spheres are generally discussed qualitatively, followed by the presentation of numerical or experimental results for the drag coefficient, Nusselt number, and flow separation. Rarely, there is much discussion of how solutions are obtained. In this paper the flow separation is first introduced by solving the Falkner-Skan flow. The process for numerical solution of equations is presented to show that the flow separates at a plate angle of about −18°. Comparisons are drawn between this and flow over a cylinder. The non-similar boundary layer equations are then solved flow over a cylinder, using potential flow results for the velocity outside of the boundary layer. This solution shows that the flow separates at 103.5°, which is significantly more than the experimental value of 80°. Using a more realistic velocity for flow outside of the boundary layer, the numerical solution obtained predicts flow separation at an angle of 79°, which is close to the experimental results. All the solutions are obtained using spreadsheets that greatly simplify the analysis.
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Argaw, Yacob M., and John P. Kizito. "Heat Transfer Enhancement Through Impingement Surface Shape Modification." In ASME 2013 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/fedsm2013-16364.
Full textAbstract:
Free stream flow past a heated wedge can be modeled and solved using Falkner-Skan equation when the wedge angle is within a limit. These types of flows at times, depending on the wedge angle or impingement direction, are referred to as Blasius and/or Hiemenz flows. When the impingement surface is constrained between walls from the side to create a cavity, these methods are no longer valid where the side walls significantly affect the flow field. We have used a numerical simulation to determine the effect of impingement shape described by wedge angle. The cooling process described by maximum heat flux with minimum surface temperature is the overall goal of the present study. The results show that the presence of side walls does affect the boundary layer of flow across the impingement surface. The results computed using similarity solution method in Matlab and a commercial CFD code simulation validates shape modification enhances the heat transfer process and the side wall’s effect is significant.