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(PDF) Shape Optimization for Delay of Laminar-Turbulent Transition
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{"work":{"id":31708897,"created_at":"2017-03-04T07:51:19.470-08:00","from_world_paper_id":161154926,"updated_at":"2024-11-27T03:16:25.065-08:00","_data":{"ai_title_tag":"Optimizing Wing Shapes for Delayed Laminar-Turbulent Transition","grobid_abstract":"A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural laminar flow, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are solved to analyze the evolution of convectively unstable disturbances. Laminar-turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.","publication_date":"2012,5,2","publication_name":"Aiaa Journal","grobid_abstract_attachment_id":"52023092"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Shape Optimization for Delay of Laminar-Turbulent Transition","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [60938844]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":52023092,"attachmentType":"pdf"}"><img alt="First page of “Shape Optimization for Delay of Laminar-Turbulent Transition”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/52023092/mini_magick20190123-17346-1i61lmj.png?1548302968" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Shape Optimization for Delay of Laminar-Turbulent Transition</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="60938844" href="https://independent.academia.edu/OlivierAmoignon"><img alt="Profile image of Olivier Amoignon" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/60938844/144425964/133949491/s65_olivier.amoignon.png" />Olivier Amoignon</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2012, Aiaa Journal</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">16 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 31708897; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural laminar flow, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are solved to analyze the evolution of convectively unstable disturbances. Laminar-turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":52023092,"attachmentType":"pdf","workUrl":"https://www.academia.edu/31708897/Shape_Optimization_for_Delay_of_Laminar_Turbulent_Transition"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":52023092,"attachmentType":"pdf","workUrl":"https://www.academia.edu/31708897/Shape_Optimization_for_Delay_of_Laminar_Turbulent_Transition"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas" data-impression-entity-id="31708897" data-impression-entity-type="2" data-impression-source="signup-banner"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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href="https://www.academia.edu/62507712/Control_theory_based_airfoil_design_for_potential_flow_and_a_finite_volume_discretization">Control theory based airfoil design for potential flow and a finite volume discretization</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="22086676" href="https://independent.academia.edu/jreuther">james reuther</a></div><p class="ds-related-work--metadata ds2-5-body-xs">32nd Aerospace Sciences Meeting and Exhibit</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper describes the implementation of optimization techniques based on control theory for airfoil design. In previous studies [6, 71 it was shown that control theory could be used to devise an effective optimization procedure for two-dimensional profiles in which the shape is determined by a conformal transformation from a unit circle, and the control is the mapping function. The goal of our present work is to develop a method which does not depend on conformal mapping, so that it can be extended to treat three-dimensional problems. Therefore, we have developed a method which can address arbitrary geometric shapes through the use of a finite volume method to discretize the potential flow equation. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented, where both target speed distributions and minimum drag are used as objective functions.-Nomenclature A,, grid transformation coefficients b design variable B generic co-state variable c speed of sound C C d coefficient of drag Ci coefficient of lift C, coefficient of pressure bounding surface of flowfield domain on airfoil 'Graduate Student, Student Memher AIAA tJames S. McDomeU Distinguished University Professor Copyright 01994 hy the American Institute of Aeronau-of Aerospace Engineering, AIAA Fellow tics and Astronautics, hc. All rights reserved W C; d</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Control theory based airfoil design for potential flow and a finite volume discretization","attachmentId":75245603,"attachmentType":"pdf","work_url":"https://www.academia.edu/62507712/Control_theory_based_airfoil_design_for_potential_flow_and_a_finite_volume_discretization","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/62507712/Control_theory_based_airfoil_design_for_potential_flow_and_a_finite_volume_discretization"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="74851153" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74851153/An_Interactive_Boundary_Layer_Modeling_Methodology_for_Aerodynamic_Flows">An Interactive Boundary Layer Modeling Methodology for Aerodynamic Flows</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="165959274" href="https://independent.academia.edu/OliverOxtoby">Oliver Oxtoby</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Volume 1: Advances in Aerospace Technology; Energy Water Nexus; Globalization of Engineering; Posters, 2011</p><p class="ds-related-work--abstract ds2-5-body-sm">Purpose-The purpose of this paper is to introduce a unique technique to couple the two-integral boundary layer solutions to a generic inviscid solver in an iterative fashion. Design/methodology/approach-The boundary layer solution is obtained using the two-integral method to solve displacement thickness point by point with a local Newton method, at a fraction of the cost of a conventional mesh-based, full viscous solution. The boundary layer solution is coupled with an existing inviscid solver. Coupling occurs by moving the wall to a streamline at the computed boundary layer thickness and treating it as a slip boundary, then solving the flow again and iterating. The Goldstein singularity present when solving boundary layer equations is overcome by solving an auxiliary velocity equation along with the displacement thickness. Findings-The proposed method obtained favourable results when compared with the analytical solutions for flat and inclined plates. Further, it was applied to modelling the flow around a NACA0012 airfoil and yielded results similar to those of the widely used XFOIL code. Originality/value-A unique method is proposed for coupling of the boundary layer solution to the inviscid flow. Rather than the traditional transpiration boundary condition, mesh movement is employed to simulate the boundary layer thickness in a more physically meaningful way. Further, a new auxiliary velocity equation is presented to circumvent the Goldstein singularity. Paper type Research paper Greek letters ¢ Under-relaxation parameter £ Similarity parameter Displacement grid position ¤ * Boundary layer thickness m ¤ ** Density thickness ¤ ij Kronecker delta Difference ¥ Similarity coordinate ¡ Momentum thickness m ¡ * Kinetic energy thickness ¦ Dynamic viscosity kg.m-1 .s-1 § Density kg.m-3 ¨ Shear stress N.m-2 © Kinematic viscosity m 2 .s-1 Coordinate parallel to the boundary layer m Subscripts 0 Initial value 1,2 Variables in the x-and y-directions respectively e External flow variable f Fluid Free-stream value i, j, k Components of vector/tensor in indicial notation n Index of nodes along boundary layer w Wall Superscripts n pseudo-(iteration) time-step</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"An Interactive Boundary Layer Modeling Methodology for Aerodynamic Flows","attachmentId":82855383,"attachmentType":"pdf","work_url":"https://www.academia.edu/74851153/An_Interactive_Boundary_Layer_Modeling_Methodology_for_Aerodynamic_Flows","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74851153/An_Interactive_Boundary_Layer_Modeling_Methodology_for_Aerodynamic_Flows"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="67148019" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/67148019/Boundary_shape_control_of_the_Navier_Stokes_equations_and_applications">Boundary shape control of the Navier-Stokes equations and applications</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="211695570" href="https://kldguitar.academia.edu/LiquanMei">Liquan Mei</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Chinese Annals of Mathematics, Series B, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, the geometrical design for the blade's surface in an impeller or for the profile of an aircraft, is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations. The objective function is the sum of a global dissipative function and the power of the fluid. The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations. The Euler-Lagrange equations of the optimal control problem are derived, which are an elliptic boundary value system of fourth order, coupled with the Navier-Stokes equations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Boundary shape control of the Navier-Stokes equations and applications","attachmentId":78074909,"attachmentType":"pdf","work_url":"https://www.academia.edu/67148019/Boundary_shape_control_of_the_Navier_Stokes_equations_and_applications","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/67148019/Boundary_shape_control_of_the_Navier_Stokes_equations_and_applications"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="14123727" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14123727/Drag_Reduction_by_Improving_Laminar_Flows_past_Morphing_Configurations">Drag Reduction by Improving Laminar Flows past Morphing Configurations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33120763" href="https://etsmtl.academia.edu/RuxandraBotez">Ruxandra Botez</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In this paper, wind tunnel experiment was performed for boundary layer transition control on a morphing wing. Surface pressure fluctuations were measured using Kulite transducers at high sampling rate. A controller, linking the Kulites signals fluctuation to the smart material actuators, is incorporated to the control system, where the signals are analyzed and the transition location is detected. Several wind tunnel test runs for various Mach numbers and angles of attack were performed in the 6 × 9 ft 2 wind tunnel at the Institute for Aerospace Research at the National Research Council Canada. A rectangular finite aspect ratio wing, having a morphing airfoil cross section due to a flexible skin installed on the upper surface of the wing, was instrumented with sixteen Kulite transducers. The Mach number was varied from 0.2 to 0.3 and the angle of attack between -1 o and 2 o . Unsteady pressure signals were recorded and analyzed and a thorough comparison, in terms of mean pressure coefficients and their standard deviations, was performed against theoretical predictions using the XFoil computational fluid dynamics code. The unsteady pressure signals were analyzed through FFT spectral decomposition for detecting the Tollmien-Schlichting waves frequencies that trigger transition. In addition, infra red measurements were performed to asses the performance of the Kulite transducers in detecting the transition location and serve as an additional validation of the XFoil code in predicting the transition location .</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Drag Reduction by Improving Laminar Flows past Morphing Configurations","attachmentId":41189003,"attachmentType":"pdf","work_url":"https://www.academia.edu/14123727/Drag_Reduction_by_Improving_Laminar_Flows_past_Morphing_Configurations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14123727/Drag_Reduction_by_Improving_Laminar_Flows_past_Morphing_Configurations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="19455046" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/19455046/Aerodynamic_Design_And_Optimization_By_Means_Of_Control_Theory">Aerodynamic Design And Optimization By Means Of Control Theory</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="41263806" href="https://independent.academia.edu/FernandoMonge2">Fernando Monge</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="39730862" href="https://upc.academia.edu/SergioIdelsohn">Sergio Idelsohn</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1988</p><p class="ds-related-work--abstract ds2-5-body-sm">In numerical aerodynamic optimization, to find the search direction is the task that usually needs more computing time when the gradients of the objective function are evaluated by means of the traditional method of finite differences. In that case, the number of aerodynamic analysis is proportional to the number of design variables used for defining the geometry deformations, which can be very demanding and even prohibitive in practical situations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Aerodynamic Design And Optimization By Means Of Control Theory","attachmentId":40629910,"attachmentType":"pdf","work_url":"https://www.academia.edu/19455046/Aerodynamic_Design_And_Optimization_By_Means_Of_Control_Theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/19455046/Aerodynamic_Design_And_Optimization_By_Means_Of_Control_Theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="26279830" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/26279830/Evolution_of_an_Acoustic_Disturbance_to_Transition_in_the_Boundary_Layer_on_an_Airfoil">Evolution of an Acoustic Disturbance to Transition in the Boundary Layer on an Airfoil</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2181612" href="https://larc-nasa.academia.edu/MeelanChoudhari">Meelan Choudhari</a></div><p class="ds-related-work--abstract ds2-5-body-sm">An experiment has been conducted to examine the generation and subsequent evolution of boundary-layer disturbances on a two-dimensional airfoil up through transition to turbulent flow.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Evolution of an Acoustic Disturbance to Transition in the Boundary Layer on an Airfoil","attachmentId":46593194,"attachmentType":"pdf","work_url":"https://www.academia.edu/26279830/Evolution_of_an_Acoustic_Disturbance_to_Transition_in_the_Boundary_Layer_on_an_Airfoil","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/26279830/Evolution_of_an_Acoustic_Disturbance_to_Transition_in_the_Boundary_Layer_on_an_Airfoil"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":52023092,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":52023092,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_52023092" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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