Relevant bibliographies by topics / Orr-Sommerfeld equation

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  2. Dissertations / Theses
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Academic literature on the topic 'Orr-Sommerfeld equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Orr-Sommerfeld equation"

1

Bridges, Thomas J. "The Orr–Sommerfeld equation on a manifold." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 455, no. 1988 (1999): 3019–40. http://dx.doi.org/10.1098/rspa.1999.0437.

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Herron, Isom H. "The Orr–Sommerfeld Equation on Infinite Intervals." SIAM Review 29, no. 4 (1987): 597–620. http://dx.doi.org/10.1137/1029113.

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Puri, Pratap. "Stability and eigenvalue bounds of the flow of a dipolar fluid between two parallel plates." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2057 (2005): 1401–21. http://dx.doi.org/10.1098/rspa.2004.1434.

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In this article, we derive the Orr–Sommerfeld equation for the stability of parallel flows of a dipolar fluid. The classical results found by Squire, for viscous Newtonian fluids, are generalized to the case of dipolar fluids. A sufficient condition for stability is obtained for dipolar fluids and eigenvalue bounds for the Orr–Sommerfeld equation are found.
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Alvarez, L. M., and V. V. Ditkin. "On the numerical solution of the Orr-Sommerfeld equation." USSR Computational Mathematics and Mathematical Physics 30, no. 2 (1990): 183–86. http://dx.doi.org/10.1016/0041-5553(90)90094-9.

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Pierucci, Mauro, and Pedro G. Morales. "Effect of Finite Thickness Flexible Boundary Upon the Stability of a Poiseuille Flow." Journal of Applied Mechanics 57, no. 4 (1990): 1056–60. http://dx.doi.org/10.1115/1.2897625.

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The stability behavior, the stress, and velocity distributions for a plane Poiseuille flow bounded by a finite thickness elastic layer is studied. The analysis is performed by utilizing the coupled relationships between the Orr-Sommerfeld stability equation for the fluid and the Navier equations for the solid. The numerical instabilities experienced in the solution of the Orr-Sommerfeld equation have been overcome with the use of Davey’s orthonormalization technique. This study focuses only on the Tollimen-Schlichting instabilities. This mode is the most unstable of the three different types of instabilities. The results show that certain combinations of parameters can lead to improved stability conditions. Under these conditions the normal and shear stress distributions may behave completely different in certain regions of the fluid.
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Trinh, Ngoc Anh, and Dong Vuong Lap Tran. "Calculation of the Orr-Sommerfeld stability equation for the plane Poiseuille flow." Science and Technology Development Journal - Natural Sciences 2, no. 5 (2019): 122–29. http://dx.doi.org/10.32508/stdjns.v2i5.787.

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The stability of plane Poiseuille flow depends on eigenvalues and solutions which are generated by solving Orr-Sommerfeld equation with input parameters including real wavenumber and Reynolds number . In the reseach of this paper, the Orr-Sommerfeld equation for the plane Poiseuille flow was solved numerically by improving the Chebyshev collocation method so that the solution of the Orr-Sommerfeld equation could be approximated even and odd polynomial by relying on results of proposition 3.1 that is proved in detail in section 2. The results obtained by this method were more economical than the modified Chebyshev collocation if the comparison could be done in the same accuracy, the same collocation points to find the most unstable eigenvalue. Specifically, the present method needs 49 nodes and only takes 0.0011s to create eigenvalue while the modified Chebyshev collocation also uses 49 nodes but takes 0.0045s to generate eigenvalue with the same accuracy to eight digits after the decimal point in the comparison with , see [4], exact to eleven digits after the decimal point.
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Lie, K. H., and D. N. Riahi. "Numerical solution of the Orr-Sommerfeld equation for mixing layers." International Journal of Engineering Science 26, no. 2 (1988): 163–74. http://dx.doi.org/10.1016/0020-7225(88)90102-4.

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Zakharchuk, V. T., N. P. Savenkova, and S. L. Chernyshov. "An approach to the solution of the Orr?Sommerfeld equation." Computational Mathematics and Modeling 4, no. 2 (1993): 135–39. http://dx.doi.org/10.1007/bf01131207.

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Banerjee, Mihir B., R. G. Shandil, and Balraj Singh Bandral. "Eigenvalue bounds for Orr-Sommerfeld equation ‘No backward wave’ theorem." Proceedings Mathematical Sciences 106, no. 3 (1996): 281–87. http://dx.doi.org/10.1007/bf02867436.

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Sengupta, Tapan K. "Solution of the Orr-Sommerfeld equation for high wave numbers." Computers & Fluids 21, no. 2 (1992): 301–3. http://dx.doi.org/10.1016/0045-7930(92)90027-s.

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Dissertations / Theses on the topic "Orr-Sommerfeld equation"

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Van, der Fort Zareer. "A numerical investigation of the linear hydrodynamic stability of Newtonian and weakly non-Newtonian channel flows as described by the Orr-Sommerfeld equation." Master's thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/4940.

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Includes abstract.<br>Includes bibliographical references (leaves 106-112).<br>The Orr-Sommerfeld equation describes the growth of infinitesimal disturbances to laminar solutions of the Newtonaian Navier-Stokes equations. In this dissertation we consides in part idealised flows between two parallel planes of infinite extent and a finite distance apart. They are referred to as closed channel flows.
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Gennaro, Elmer Mateus. "Análise da instabilidade hidrodinâmica de uma esteira assimétrica." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/18/18148/tde-22042008-112415/.

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Em uma aeronave, dispositivos de hiper-sustentação à altos ângulos de ataque promovem a formação de esteiras. Tais esteiras influenciam o desempenho aerodinâmico. A esteira do eslate, por exemplo, afeta o ponto de transição do elemento principal da asa e é a fonte de ruído mais importante na estrutura do avião. Devido a geração de sustentação estas esteiras são assimétricas. Corpos imersos em escoamento cisalhante também produzem esteiras assimétricas, com importantes aplicações para a indústria petrolífera. Existem aspectos de tais escoamentos que precisam de investigação. Por exemplo, não há consenso sobre se pode ou não a assimetria suprimir desprendimento de vórtice ou como afeta o desprendimento da frequência. Na verdade, existe uma aparente discrepância entre os resultados encontrados na literatura. O objetivo do presente trabalho é contribuir para esta questão. A idéia foi investigar a influência da assimetria em um perfil de esteira bidimensional sob desenvolvimento temporal. O perfil da esteira assimétrica foi obtido por uma combinação entre um perfil de uma esteira gaussiana e um perfil tangente hiperbólico da camada de mistura. Foi desenvolvido uma análise bidimensional (2D) da teoria de estabilidade linear para o perfil. O trabalho também incluiu simulações numéricas diretas (DNS) bidimensionais da evolução da perturbação usando formulação característica das equações compressíveis de Navier-Stokes na forma não-conservativa. Os resultados mostraram que a assimetria reduz o frequência de desprendimento para a faixa investigada do parâmetro de assimetria 0 \'< OU =\' K \'< OU =\' 0,25. Para pequenos valores deste parâmetro os resultados mostraram que a assimetria promove a estabilidade. Efeitos do número de Mach na esteira assimétrica também foram investigados. Os resultados mostraram que o aumento do Ma reduziu a máxima taxa de amplificação e a banda instável. Além disso, os resultados da literatura foram reconciliados, levando-se em conta a variação do coeficiente de arrasto com a assimetria. Portanto, uma possível explicação para a controvérsia foi oferecido.<br>In an aircraft, high-lift devices operating at high angle of attack promote the formation wakes. Such wakes influence the aerodynamic performance. The slat wake, for example, affects the transition point of the wing main element and is the most important source of noise in the airframe. Owing to the generation of lift these wakes are asymmetries. Bodies immersed in a shear flow also produce asymmetric wakes, with important applications to the oil industry. There are aspects of such flows that need investigation. For instance, there is no consensus about whether or not the asymmetry can suppress vortex shedding or how it affects the shedding frequency. Indeed there is an apparent discrepancy between results found in literature. The aim of the present work was to contribute to this issue. The idea was to investigate the influence of asymmetry on a two-dimensional wake profile under temporal development. The asymmetric wake profile was obtained by a combination between a Gaussian wake profile and a hyperbolic tangent mixing layer profile. The bidimensional (2D) linear stability theory analysis of the profile was performed. The work also included 2D Direct Numerical Simulation (DNS) using the characteristic formulation of the compressible Navier-Stokes equations in non-conservative form. The results showed that the asymmetry reduces the shedding frequency for the range of 0 \'< OU =\' K \'< OU =\' 0,25 investigated. For small values of the asymmetric parameter the results showed that the asymmetry promotes stability. Effects of the number of Mach in asymmetric wake also were investigated. The results showed that the increase of Ma reduced the maximum rate amplification and the band unstable. Moreover, the results from literature were reconciled by taking into account the variation of the drag coefficient with the asymmetry. Therefore, a possible explanation for the controversy was offered.
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Scibilia-Cocheril, Marie-Françoise. "Contribution a l'etude des jets parietaux." Paris 6, 1986. http://www.theses.fr/1986PA066539.

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Definition des caracteristiquees du jet parietal. Historique du sujet. Theorie de glauert permettant l'existence d'une solution semblable selon laquelle la forme des profils de vitesse dans chaque section du jet reste inchangee le long du jet. Etude de la stabilite lineaire et non lineaire. Resolution de l'equation d'orr-sommerfeld en theorie temporelle et en theorie spatiale. Etude experimentale: mesure des vitesses en presence d'un corps bidimensionnel ou tridimensionnel, mesures de temperature
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Knotek, Stanislav. "Řešení vývoje nestabilit kapalného filmu s následným odtržením kapek." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-234165.

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This dissertation deals with instabilities of thin liquid films up to entrainment of drops. Four types of instabilities have been classified depending on the type of structure and process on the liquid film surface: two-dimensional slow waves, two-dimensional fast waves, three-dimensional waves, solitary waves and entrainment of drops from the film surface. This thesis analyzes the physical principles of instabilities and deals with the mathematical formulation of the problem. Shear and pressure forces acting on the surface of the liquid film are identified as the cause of instabilities. Mathematical models for predicting instabilities are demonstrated using approaches based on solving the Orr-Sommerfeld equation and the equations of motion in integral form. Models of shear and pressure forces acting on the surface of the film and selected models of film thickness are presented. The work is focused on the prediction of the initiation of two-dimensional waves using the integral approach. Shear stress and pressure forces acting on the liquid film surface have been modeled using the simulation of air flow over a solid surface. Finally, criteria for drop entrainment are presented with their dependence on air velocity and film thickness.
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Högberg, Markus. "Optimal Control of Boundary Layer Transition." Doctoral thesis, KTH, Mechanics, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3245.

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Books on the topic "Orr-Sommerfeld equation"

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Biringen, Sedat. Solution of the Orr-Sommerfeld equation for the Blausius boundary-layer documentation of program ORRBL and a test case. Langley Research Center, 1988.

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Sedat, Biringen, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division, eds. A Chebyshev matrix method for spatial modes of the Orr-Sommerfeld equation. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1989.

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G, Danabasoglu, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. Solution of the Orr-Sommerfeld equation for the Blausius boundary-layer documentation of Program ORRBL and a test case. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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G, Danabasoglu, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. Solution of the Orr-Sommerfeld equation for the Blausius boundary-layer documentation of Program ORRBL and a test case. National Aeronautics and Space Administration, Scientific and Technical Information Division, 1988.

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5

Rajeev, S. G. Spectral Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0013.

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Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.
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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.
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Rajeev, S. G. Instabilities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0008.

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The most well-known of the many instabilities of a fluid is the Rayleigh–Taylor instability. A denser fluid sitting on top of a lighter fluid is in unstable equilibrium, much like a pendulum standing on its head. Kapitza showed that rapidly oscillating the point of support of a pendulum can counteract this instability. The Rayleigh–Taylor instability can also be inhibited by shaking the two fluid layers rapidly. The Orr–Sommerfeld equations are a linear model of instabilities of a steady solution of Navier-Stokes. The Orr–Sommerfeld operator is not normal (does not commute with its adjoint). This means that there are transients (solutions that grow large before dying out) even if the linear equations predict stability. A simple nonlinear model with transients due to Trefethen et al. is studied to gain intuition into fluid instabilities.
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Book chapters on the topic "Orr-Sommerfeld equation"

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Chin, Raymond C. Y. "An Asymptotic-Numerical Method for the Orr-Sommerfeld Equation." In Instabilities and Turbulence in Engineering Flows. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1743-2_5.

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Zhuk, V. I. "On Long Wave Asymptotic Solutions of the Orr-Sommerfeld Equation for Boundary Layer." In Laminar-Turbulent Transition. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82462-3_90.

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YIH, CHIA-SHUN. "Note on eigenvalue bounds for the Orr—Sommerfeld equation." In Selected Papers By Chia-Shun Yih. World Scientific Publishing Company, 1991. http://dx.doi.org/10.1142/9789812813084_0041.

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Conference papers on the topic "Orr-Sommerfeld equation"

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Monschke, Jason, Matthew Kuester, and Edward White. "Acoustic Receptivity Measurements Using Modal Decomposition of a Modified Orr-Sommerfeld Equation." In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-669.

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Bruno Pelisson Chimetta and Erick de Moraes Franklin. "Asymptotic solution of the Orr-Sommerfeld equation for surface waves on an inclined plane." In 23rd ABCM International Congress of Mechanical Engineering. ABCM Brazilian Society of Mechanical Sciences and Engineering, 2015. http://dx.doi.org/10.20906/cps/cob-2015-1657.

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Chimetta, Bruno Pelisson, and Erick De Moraes Franklin. "Numerical solutions of the Orr-Sommerfeld equation for a thin liquid film on an inclined plane." In CNMAC 2017 - XXXVII Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2018. http://dx.doi.org/10.5540/03.2018.006.01.0406.

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Anderson, Theodore R. "Turbulent wall pressure and wall shear fluctuations calculated from the Orr-Sommerfeld equation with nonlinear forcing terms." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51019.

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Doostmohammadi, Amin, and Seyyedeh Negin Mortazavi. "Instability of Viscoelastic Fluids in Blasius Flow." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24315.

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In this paper, we study the hydrodynamic stability of a viscoelastic Walters B liquid in the Blasius flow. A linearized stability analysis is used and orthogonal polynomials which are related to de Moivre’s formula are implemented to solve Orr–Sommerfeld eigenvalue equation. An analytical approach is used in order to find the conditions of instability for Blasius flow and Critical Reynolds number is found for various combinations of the elasticity number. Based on the results, the destabilizing effect of elasticity on Blasius flow is determined and interpreted.
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Gungor, Ayse G., Mark P. Simens, and Javier Jime´nez. "Direct Simulations of Wake-Perturbed Separated Boundary Layers." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46322.

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A wake-perturbed flat plate boundary layer with a stream-wise pressure distribution similar to those encountered on the suction side of typical low-pressure turbine blades is investigated by direct numerical simulation. The laminar boundary layer separates due to a strong adverse pressure gradient induced by suction along the upper simulation boundary, transitions and reattaches while still subject to the adverse pressure gradient. Various simulations are performed with different wake passing frequencies, corresponding to the Strouhal number 0.0043 &lt; fθb/ΔU &lt; 0.0496 and wake profiles. The wake profile is changed by varying its maximum velocity defect and its symmetry. Results indicate that the separation and reattachment points, as well as the subsequent boundary layer development, are mainly affected by the frequency, but that the wake shape and intensity have little effect. Moreover, the effect of the different frequencies can be predicted from a single experiment in which the separation bubble is allowed to reform after having been reduced by wake perturbations. The stability characteristics of the mean flows resulting from the forcing at different frequencies are evaluated in terms of local linear stability analysis based on the Orr-Sommerfeld equation.
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Wu, Xuesong, and Ming Dong. "On Continuous Spectra of the Orr-Sommerfeld/Squire Equations and Entrainment of Free-stream Vortical Disturbances in the Blasius Boundary Layer." In 43rd AIAA Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2465.

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Hu, Xiaoxia, and Ali Dolatabadi. "Linear Stability of a Thin Liquid Film Flowing Along an Inclined Surface." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30279.

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The formation of the waves on a thin liquid water film was analytically investigated by studying its shear mode stability. The inclined angle of the substrate is limited to 8°. The purpose of analytical solution is to determine the maximum growth rate of the generated wave as well as its corresponding wave number, which is realized by solving the Orr-Sommerfeld equations for both gas and liquid phases with the corresponding boundary conditions. The results of wave formations on a surface with a thin liquid film of de-icing are validated by previous experimental data as well as compared with Yih’s theoretical analysis [7]. Studies have also conducted on the effect of surface tension or liquid film depth on the stability of a thin liquid film flowing along a solid substrate.
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Zhang, Ce, Wei Ma, Wensheng Yu, and Jinfang Teng. "Effect of Heat Transfer on Pipe Flow Stability." In ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/gt2017-64451.

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The compressibility of flow field has an important effect on flow stability. However, when the compressibility is considered, the effect of Mach number is often considered while the effect of heat transfer is always neglected in the existing flow stability studies. Linear stability analysis tools based on compressible Orr-Sommerfeld (O-S) equations and linearized Navier-Stokes equations in cylindrical coordinate system are established in this paper. These equations are numerically solved by using Chebyshev spectral collocation method and pseudo-modes are eliminated. Linear stability analysis of pipe flow with heat transfer whose average flow field is obtained by CFD simulation is carried out. The results show that for spatial modes, the heating effect of the wall makes pipe flow more unstable, while cooling effect of the wall makes pipe flow more stable. For global modes of pipe flow, the frequency of global mode decreases when the wall cools the flow and the decrease of mean temperature of pipe flow leads to the improvement of global mode stability.
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