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An analytical study was performed to define a Gust Alleviation System on a preliminary configuration of a commuter airplane. The analysis takes into account the influence of elasticity of the airplane, unsteady aerodynamic effects, mechanical nonlinearities such as backlash deadzone and control surface rate and deflection limitations. A relatively simple model shows that ride comfort can be improved by at least 50%., This article is from 'Unsteady Aerodynamics - Fundamentals and Applications of Aircraft Dynamics. Conference Proceedings of the Joint Symposium of the Fluid Dynamics and Flight Mechanics Panels Held in Goettingen, Federal Republic of Germany on 6-9 May 85,' AD-A165 045, p35-1 - 35-9.

Results of a theoretical study on the effects of unsteady aerodynamics on symmetric aircraft responses due to elevator and vertical turbulence inputs, are presented. Several linear models were developed to describe unsteady lift and downwash and delays due to horizontal tail length. Results for three example aircraft types show that calculated normal acceleration levels due to turbulence are very 'little affected by including unsteady wing lift and downwash. However, there appears to be a noticable influence on plunging acceleration and pitch rate response to elevator or vertical turbulence inputs., This article is from 'Unsteady Aerodynamics - Fundamentals and Applications of Aircraft Dynamics. Conference Proceedings of the Joint Symposium of the Fluid Dynamics and Flight Mechanics Panels Held in Goettingen, Federal Republic of Germany on 6-9 May 85,' AD-A165 045, p33-1 - 33-11.

This paper highlights recent research on two high angle-of-attack flight dynamic phenomena which are dominated by unsteady aerodynamic effects: wing rock and tumbling. Studies of wing rock induced by strong vortical flows and tumbling characteristics observed on an advanced configuration are reviewed. Results of wind tunnel experiments are summarized and the aerodynamic mechanisms involved in the phenomena are discussed., This article is from 'Unsteady Aerodynamics - Fundamentals and Applications of Aircraft Dynamics. Conference Proceedings of the Joint Symposium of the Fluid Dynamics and Flight Mechanics Panels Held in Goettingen, Federal Republic of Germany on 6-9 May 85,' AD-A165 045, p28-1 - 28-25.

This paper proposes a new representation of aerodynamic reactions in terms of the motion variables, which does not rely on assumptions of linearity. This representation is therefore indicated for extreme flight conditions where a locally linearized model is usually of questionable value. The significance within the present context of stability derivatives is discussed with the intention of pointing out their range of applicability. A wind-tunnel technique, capable of efficiently obtaining the bulk of the data required for the effective use of the above representation, is briefly described., This article is from 'Unsteady Aerodynamics - Fundamentals and Applications of Aircraft Dynamics. Conference Proceedings of the Joint Symposium of the Fluid Dynamics and Flight Mechanics Panels Held in Goettingen, Federal Republic of Germany on 6-9 May 85,' AD-A165 045, p27-1 - 27-l4.

Future air combat can be expected to differ greatly from that of the past--a result attributable to advances in enabling aircraft technologies and paced by a new generation of air-to-air weapons capabilities. Anticipated developments in the areas of structures and structural materials, control systems and the vehicle-pilot interface may be coupled with an emerging new understanding of unsteady aerodynamic behavior to provide a new level of dynamic maneuverability heretofore not thought possible. The case for the development of a 'supermaneuverable' flight capability is built on both anticipated operational need and perceived technological opportunity. The primary objectives in this are to describe the potential of this unique flight environment and discuss its underlying unsteady aerodynamic characteristics., This article is from 'Unsteady Aerodynamics - Fundamentals and Applications of Aircraft Dynamics. Conference Proceedings of the Joint Symposium of the Fluid Dynamics and Flight Mechanics Panels Held in Goettingen, Federal Republic of Germany on 6-9 May 85,' AD-A165 045, p29-1 - 29-19.

A recently developed general theory of aerodynamics is used in an investigation of non-linear unsteady flow problems involving a non-rigid lifting body. It is shown that this theory, developed on the basis of viscous flow equations, permits the important interactive fluid dynamic elements dominating the aerodynamics of non-linear unsteady flows to be identified and their contributions evaluated individually. Closed form expressions for the lift, the drag, and the power expenditure of the Weis-Fogh problem, considered as a special case of flexible lifting bodies, are presented and discussed., This article is from the Proceedings of the Workshop on Unsteady Separated Flow Held at the United States Air Force Academy on August 10-11, 1983, AD-A148 249, p137-147.

Preliminary results from an UnSTeady AiRfoil analysis in 2 dimensions have been obtained from a computer code (USTAR2) developed by the present authors. This computer code is based upon an analysis which uses a doublet panel method to model the airfoil surface, an integral unsteady boundary layer scheme to model the viscous attached flow, and discrete vortices to model the detached boundary layers which form the airfoil wake region. This model has been used successfully to predict steady lift and drag coefficients as well as pressure distributions for several airfoils with both attached and detached boundary layers. In addition, calculations have been made for a limited number of cases for both attached and detached unsteady flow situations. These calculations are compared in a cursory way with experimental data to point out some of the strengths and weaknesses of the present formulation., This article is from the Proceedings of the Workshop on Unsteady Separated Flow Held at the United States Air Force Academy on August 10-11, 1983, AD-A148 249, p152-157.

With few exceptions, aerodynamicists have historically considered unsteady flow as detrimental to performance. Two notable examples are the problems of inlet buzz and wing flutter while the performance of the pulsed combustion missiles of the 1940's is a prominent exception. In some situations unsteady flows are unavoidable, as in the case of rotating compressors and turbines. In these and other situations, it is of interest to examine the time dependence from a positive point of view. That is; if unsteadiness is deliberately introduced or amplified, are there potential performance advantages? It is the purpose of this paper to examine several recent and ongoing experiments which involve the attempt to improve performance by utilizing unsteady flow. Two areas are described. The first is the introduction of unsteadiness into a boundary layer by mechanical means. The aim is to energize the boundary layer to avoid or lessen problems resulting from separation. A second area is the unsteadiness. The time dependency can be completely fluidically produced or it can be driven by a mechanical-fluidic interface. (Author), This article is from 'A Collection of Papers in the Aerospace Sciences,' AD-A122 667.

An environmental aerodynamic test (EATS) was designed and assembled to investigate the effects of gust and turbulence on the performance of a full-scale Wortmann FX-63-137 wing. Experiments were conducted in the atmospheric boundary layer by directing the elevated wing into the prevailing wind for a range of Reynolds numbers from 80,000 to 450,000. The unsteady wind field, in essence, introduces significant and favorable effects on the aerodynamics in terms of lift overshoot, stall delay, reduction of drag at small angles of attacks, and endurance enhancement. Further analysis of the field data was conducted to investigate the unsteady aerodynamic phenomena, such as the hysteresis loops and the spectra of the aerodynamic forces and the relation to the ambient wind conditions.

Presentations made at this conference are reviewed. Topics include: airfoil designs methods and verification, airfoil calculation methods, low Reynolds number research at NASA Langley, unsteady aerodynamic characteristics, wind turbine applications, separation bubbles, experimental facilities and testing, and remotely piloted vehicles.

This report investigates the initial stage of the wake formation in linearized incompressible or compressible subsonic flows after a change of the upwash at the wing in the form of a step function in time. By a superposition of solutions of this kind all other changes of the upwash at the wing can be treated. The potential due to the above perturbation can be expressed by a circulation-free flow that satisfies the boundary condition imposed by the sudden change of upwash and the potential due to the wake vortices which leaves the boundary conditions unchanged. The latter is expressed by a superposition of the potentials due to individual vortices emanating form the trailing edge at different times and traveling downstream with the free stream velocity. The intensity of these vortices is determined by the Kutta condition, namely that at the trailing edge and at all times the upwash in the wake obtained by the combination of circulation-free flow and wake vortices be finite. In the incomprehensible flow case the analysis can be carried out in all details. In the comprehensible case the flow fields needed can be described by similarity solutions, but of a rather complex character. The feature essential for the present problem, namely the upwash singularity at the trailing edge can, however, be gleaned b a discussion in general terms so that one can determine the vortex distribution within the wake except for one constant factor. Keywords: Linearized subsonic time-dependent flow; and Unsteady aerodynamics.

Recent research progress on this multi-investigator program in unsteady seperated flows is summarized. Specific projects reviewed include: (a) oscillating airfoil dynamic stall; (b) vortex entrapment and stability analysis; and (c) natural flight lift mechanisms. Research is continued under AFOSR contract F49620-83-K-0009. (Author)

A cascade of five airfoil sections modelling the hub section of an advanced design turbine featuring a high inlet Mach number and 112 degrees of turning was evaluated at 4 steady-state conditions of varying exit Mach number and expansion ratio. The resulting steady-state airfoil surface pressures were compared to a state-of-the-art analytical prediction. A time-variant investigation was conducted at the 4 operating conditions of the steady-state experiment. Data from high response pressure transducers imbedded along the surfaces of the center airfoil was acquired by individually oscillating each airfoil of the cascade normal to its chord. From this data, the time-varying surface pressures as functions of interblade phase angle were quantified and compared with a current unsteady analysis. (Author)

Three problems which have been investigated are discussed in this report. Aerodynamic theory and computational procedures have been developed to study the aeroelastic stability of oscillating loaded airfoils in cascade with interblade phase angle. Contrary to linear theory, results show that classical flutter can occur for low speed turbine cascades operating at typical design conditions. Ground effects on fan inlet flows were investigated based on data from NASA - Lewis. The analysis showed that swirling flows are the dominant source of flow disturbances entering the fan. Finally, a study was made of three-dimensional periodic disturbances acting upon loaded airfoils in cascade. (Author)

This report gives to the user of the HP41-CV handheld programmable calculator or the IBM 3033 computer a blade element method for calculating the total power required in forward, straight and level high-speed flight for an isolated rotor. The computer programs consist of a main program which calculates the necessary dynamic parameters of the main rotor and several subroutines which calculate power required as well as maximum forward velocity, stall onset velocity, and velocity for best endurance.

A method is presented for solving the three-dimensional unsteady Euler equations on dynamic grids based on flux vector splitting. The equations are cast in curvilinear coordinates and a finite volume discretization is used for handling arbitrary geometries. The discretized equations are solved using an explicit upwind second-order predictor corrector scheme that is stable for a CFL of 2. Characteristic variable boundary conditions are developed and used for unsteady impermeable surfaces and for the far-field boundary. Dynamic-grid results are presented for an oscillating airfoil and for a store separating from a reflection plate. For the cases considered of stores separating from a reflection plate, the unsteady aerodynamic forces on the store are significantly different from forces obtained by steady-state aerodynamics with the body inclination angle changed to account for plunge velocity.

This document is the written version of a lecture presented in the Short Course on High Lift Technology at the University of Tennessee Space Institute, October 27-31, 1975., http://archive.org/details/oscillatingjetfl00plat

A method of characteristics approach is described for the computation of supersonic flow past oscillating cascades having blades of finite thickness distribution. The transonic small disturbance equation is solved for cascades with subsonic leading-edge locus. Sample calculations are presented for the inlet and passage flow and comparisons are given with calculations for flat-plate cascades and available measured pressure distributions. (Author), Prepared for: Chief of Naval Research, http://archive.org/details/methodofcharacte00voge, Supported by the Office of the Naval Research through the Naval Postgraduate School Research Foundation Program, NA

The problem of the build-up of lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchhoff's formula is applied so that the analysis is reduced, Just as in the steady state, to an investigation of sources' and doublets. Some simple applications of this method are considered, including the determination of the starting lift of a three- dimensional wing and the potential functions for some types of unsteady vortex motion.

The variation of pressure distribution is calculated for a two-dimensional supersonic airfoil either experiencing a sudden angle-of- attack change or entering a sharp-edged gust. From these pressure distributions the indicial lift functions applicable to unsteady lift problems are determined for the two cases. A close similarity is shown to exist between the calculated functions for varying free-stream Mach number and the corresponding functions in three-dimensional incompressible flow for varying aspect ratio. Results are presented which permit the determination of maximum increment in lift coefficient attained by an unrestrained airfoil during its flight through a gust. As an application of these results, the minimum altitude for safe flight through a specific gust is calculated for a particular supersonic wing of given strength and wing loading.

A tabulation is given of the 'Nonplanar Mach Box' results for unsteady generalized force coefficients for the planforms, Mach numbers, mode shapes, and frequencies recommended by AGARD. The tabulation uses the AGARD coordinate system and format. Not all the desired cases could be included because of the program's current limitation to supersonic trailing edges (leading edges can be supersonic or subsonic). The method was found to be fully workable and constitutes a valuable research and design tool. Convergence and accuracy were found to be comparable to steady-state, planar methods. The computer program is available with sample problems. (Author), See also Part 1 dated Feb 69, AD-850 647.

Reducing the impact of shipping on climate change is a must and new regulations try to enforce this. The technological development to allow for wind propulsion or wind assistance for ships are numerous and new methods need to be developed to ensure accurate performance prediction but also efficient and safe control of these ships. The interaction effects between the multiple wind propulsion units and the influence of the hull on the performance are still not well understood. The unsteady effects due to the fluctuating wind or the ship motion are seldom investigated and are also not fully understood. In this paper, we present experimental measurements of the aerodynamic performance of a 1:30 scaled model of a wind powered cargo vessel in real conditions, thus accounting for all interaction effects and unsteadiness of the wind. The results highlight the potential benefits of different trimming strategies, and also show the influence of unsteadiness on the aerodynamic coefficients and the overall performances., QC 20240909

The in-situ measurement of aerodynamic parameters on a boat evolving in natural conditions can be challenging. Nonetheless, the development of wind assistance and propulsion for cargo vessels calls for new methods to ensure the broadest possible evaluation of the aerodynamic interaction effects between the wind propulsion units and between the units and the hull. This paper proposes an experimental approach based on a scaled model of the Oceanbird concept car-carrier sailing at sea, in real conditions. A pressure measurement system was developed at KTH Royal Institute of Technology, which consists of 66 differential pressure sensors installed inside one of the four rigid wings. The capabilities and limitations of this sensor suite are explored in this article. With the implementation of specific experiments with the wings, we show that the system can detect stall and its hysteresis loop, as well as wing-wing and wing-hull interaction effects. The main limitation for the full aerodynamic characterisation of the boat comes from the lack of simultaneous measurement on all wings, which will be addressed in a second part of this paper., QC 20240909

This dissertation develops the equations of motion for the structural and aerodynamic forces and moments of a rotor blade with a trailing-edge flap using eight degrees of freedom. Lagrange's equation is applied using normal modes to find the flutter frequency and speed similar to the classic fixed-wing method developed by Smilg and Wasserman. However, rotary-wing concerns are addressed including different freestream velocities along the blade (variation of reduced frequency along the span of the rotor blade) and the influence of previously shed vortices on the aerodynamic forces and moments (Loewy's returning wake). While Loewy [Ref. 49] did not explicitly state that his 2-D theory would apply to rotor blades with trailing-edge flaps, the manner in which the theory was developed allows it to be applied in this manner. Comparisons to classic 1DOF, 2DOF and 3DOF flutter theories are made to validate this theory in the limiting cases. Flutter analyses, including g-. plots, of an example rotor blade with five degrees of freedom are performed for various rigid body flap frequencies. Classic methods of rotor blade design of ensuring freedom from flutter are to collocate the center of gravity (c.g.), elastic axis (e.a.), and aerodynamic center (a.c) at the 25% chord. With the development of rotor blades with trailing-edge flaps, it is shown that this current design practice is not valid when a trailing-edge flap is incorporated., http://archive.org/details/athreedimensiona109459855, Commander, United States Navy, Approved for public release; distribution is unlimited.

An experimental investigation of the separating boundary layer of a wing subjected to periodic turbulent disturbances was conducted. Turbulence pulses were generated by a non-thrusting spin­ning rod placed upstream of the test airfoil at the reduced frequencies of .09 and .47. Time-varying velocity measurements were made at various heights above the 70% chord location at 12 degrees angle of attack (nearly separated flow) and 22 degrees angle of attack (fully separated flow). Split-film anemometry was used to determine flow speed and direction. The flow responses were compared to the quasi-steady state of undisturbed separated flow. Variation of reduced frequency had a dramatic influence on the effects which the periodic disturbance had on the flow response. At a reduced frequency of .47 the periodic disturbance had no noticeable influence. Imposition of periodic disturbance of the same reduced frequency on attached flow near separation (12 degrees angle of attack) once again caused no apparent destabilizing effects. The lack of sensi­tivity of the separated boundary layer to the pulses generated at the higher reduced frequency of .47 apparently resulted from its inability to resolve turbulent pulses from one another. Imposition at 22 degrees angle of attack of a pulse at the reduced frequency of .09, however, first stabilized the flow, then greatly intensified the original separation before allowing the flow to return to its undisturbed separated state., http://archive.org/details/separatingbounda1094527259, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.

This paper describes the expansion and modification of an existing data acquisition system to effect extensive improvements in speed and flexibility. A microprocessor, flexible disk drive, analog to digital converter, direct memory access module, and high-speed line printer were integrated and interfaced to an IBM 360 digital computer with a high-speed data transmission line. The resultant system provided the capability of digitizing up to sixteen analog inputs simultaneously at rates in excess of 45,000 samples per second. The experimental data could be transmitted expeditiously to the IBM 360 computer for efficient manipulation. Additional benefits gained from the system were its capabilities as a remote terminal for the IBM 360 and a typewriter-quality word processor. The data acquisition and reduction system was qualified for functional performance and speed through a series of test exercises. The word processor was demonstrated in the production of this document., http://archive.org/details/highspeeddatacqu1094528263, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.

A zonal Navier-Stokes model, is installed and verified on the NASA Ames Cray X/MP-48 computer and is used to calculate the flow field about a NACA 0012 airfoil oscillating in pitch. Surface pressure distributions and integrated lift, pitching moment, and drag coefficient versus angle of attack are compared to existing experimental data for four cases and existing computational data for one case. These cases involve deep dynamic stall and fully detached flow at and below a freestream Mach number of .184. The flow field about the oscillating airfoil is investigated through the study of pressure, vorticity, local velocity and stream function. Finally, the effects of pitch rate on dynamic stall are investigated., http://archive.org/details/dynamicstallcomp1094523186, Lieutenant, United States Naval Reserve

A discrete potential element approach to subsonic numerical lifting surface theory has been developed and shown to be practical in predicting the non-steady loading on harmonically oscillating, medium to low aspect ratio wings. A unique method of including the wake effect in the wing kernel function matrix prior to the solution of the singular internal downwash equation was devised, thus greatly simplifying the velocity potential formulation. In addition, termination of the effective wake a finite distance downstream of the wing was investigated, with wing loading found to converge to within one per cent in an effective wake length of four root chords. This discrete element method has also been extended to the case of an oscillating wing, cantilevered from a cylindrical fuselage, to investigate non-planar interference effects. This interference is wing loading, while of relatively small magnitude, does exist in both pressure amplitude and phase angle distributions, and is, therefore, of importance in three-dimensional stability analysis of wing/body configurations., http://archive.org/details/adiscretepotenti1094516092, Commander, United States Navy, Approved for public release; distribution is unlimited.

Performance data from the NASA-Army OH-6A higher harmonic control (HHC) flight test program showed significant reductions in main rotor shaft torque and engine power in hover and forward flight 1. The unsteady aerodynamics with the higher harmonic control system application, including wake effects. were considered to study whether such power reductions are feasible. An airfoil oscillating in pure plunge can achieve propulsive force ( Katzmayr effect ), as in the case of birds' wings flapping in flight. Here it will be shown that this effect can be enhanced in the presence of layers of shed vorticity with the proper phasing. In addition, while it is known that an airfoil oscillating in pitch, will typically produce drag at most values of reduced frequency, it is found that the presence of another layer of shed vorticity of the proper phase, can reduce the drag on the pitching airfoil depending upon wake spacing reduced frequency, and phase. Under some conditions the added layer or layers of shed vorticity will even result in propulsive force acting on the pitching airfoil similar to the Katzmayr effect for the plunging case. It was found, for the OH- 6A helicopter,, that the measured reductions in main rotor shaft torque and engine power are feasible when evaluated with respect to the Katzmayr effect and the additional drag reduction or propulsive force obtained due to pitch and plunge oscillations with the effect of adjacent wake layers of shed vorticity, http://archive.org/details/thenalysisofwake1094526373, Lieutenant Colonel, Egyptian Air Force, Approved for public release; distribution is unlimited.

A transient linear stability analysis of the time-dependent flow around a natural laminar flow airfoil undergoing small-amplitude pitching motion is performed using the Optimally Time-Dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its evolution including the formation of a laminar separation bubble, its gradual spanwise modulation via primary global instability leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of span-wise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself., QC 20230511

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude freestream disturbances is investigated using direct numerical simulations. For turbulence intensities at the leading edge of Tu = 0.02 %, the flow is practically indistinguishable from clean inflow simulations in literature. For Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex. The non-linear simulations are complemented with a transient linear stability analysis of the time-dependent evolution of the laminar shear layer in the bursting separation bubble using a spatially localised formulation of the Optimally Time-Dependent (OTD) framework, with which the most unstable part of the instantaneous tangent space of the non-linear trajectory is tracked over time. The resulting modes reveal intermittent switching between two regimes. Rapid growth of the Kelvin--Helmholtz rolls on the separated shear layer and complicated secondary instabilities on the transitional part of the separation bubble. The appearance of the latter is linked to large spikes in the instantaneous growth rate within the linear subspace and more rapid transition in the non-linear baseflow. These intense growth spikes are well correlated with the subsequent shedding of energetic vortices from the laminar separation bubble., QC 20230511

A transient linear stability analysis of the time-dependent flow around a natural laminar flow airfoil undergoing small-amplitude pitching motion is performed using the Optimally Time-Dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its evolution including the formation of a laminar separation bubble, its gradual spanwise modulation via primary global instability leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of span-wise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself., QC 20230511

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude freestream disturbances is investigated using direct numerical simulations. For turbulence intensities at the leading edge of Tu = 0.02 %, the flow is practically indistinguishable from clean inflow simulations in literature. For Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex. The non-linear simulations are complemented with a transient linear stability analysis of the time-dependent evolution of the laminar shear layer in the bursting separation bubble using a spatially localised formulation of the Optimally Time-Dependent (OTD) framework, with which the most unstable part of the instantaneous tangent space of the non-linear trajectory is tracked over time. The resulting modes reveal intermittent switching between two regimes. Rapid growth of the Kelvin--Helmholtz rolls on the separated shear layer and complicated secondary instabilities on the transitional part of the separation bubble. The appearance of the latter is linked to large spikes in the instantaneous growth rate within the linear subspace and more rapid transition in the non-linear baseflow. These intense growth spikes are well correlated with the subsequent shedding of energetic vortices from the laminar separation bubble., QC 20230511

A transient linear stability analysis of the time-dependent flow around a natural laminar flow airfoil undergoing small-amplitude pitching motion is performed using the Optimally Time-Dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its evolution including the formation of a laminar separation bubble, its gradual spanwise modulation via primary global instability leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of span-wise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself., QC 20230511

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude freestream disturbances is investigated using direct numerical simulations. For turbulence intensities at the leading edge of Tu = 0.02 %, the flow is practically indistinguishable from clean inflow simulations in literature. For Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex. The non-linear simulations are complemented with a transient linear stability analysis of the time-dependent evolution of the laminar shear layer in the bursting separation bubble using a spatially localised formulation of the Optimally Time-Dependent (OTD) framework, with which the most unstable part of the instantaneous tangent space of the non-linear trajectory is tracked over time. The resulting modes reveal intermittent switching between two regimes. Rapid growth of the Kelvin--Helmholtz rolls on the separated shear layer and complicated secondary instabilities on the transitional part of the separation bubble. The appearance of the latter is linked to large spikes in the instantaneous growth rate within the linear subspace and more rapid transition in the non-linear baseflow. These intense growth spikes are well correlated with the subsequent shedding of energetic vortices from the laminar separation bubble., QC 20230511

A transient linear stability analysis of the time-dependent flow around a natural laminar flow airfoil undergoing small-amplitude pitching motion is performed using the Optimally Time-Dependent (OTD) framework. The most salient linear instabilities associated with the instantaneous basic state are computed and tracked over time. The resulting OTD modes reflect the variations in the basic state and can be used as predictors of its evolution including the formation of a laminar separation bubble, its gradual spanwise modulation via primary global instability leading to secondary instability and finally rapid breakdown to turbulence. The study confirms and expands upon earlier stability analyses of the same case based on the local properties of span-wise averaged velocity profiles in the bubble that predicted the onset of absolute instability soon followed by rapid breakdown of the separation bubble. The three-dimensional structure of the most unstable OTD mode is extracted which compares well with both the locally absolutely unstable mode and the evolution of the basic state itself., QC 20230511

Thin airfoil dynamic stall at moderate Reynolds numbers is typically linked to the sudden bursting of a small laminar separation bubble close to the leading edge. Given the strong sensitivity of laminar separation bubbles to external disturbances, the onset of dynamic stall on a NACA0009 airfoil section subject to different levels of low-amplitude freestream disturbances is investigated using direct numerical simulations. For turbulence intensities at the leading edge of Tu = 0.02 %, the flow is practically indistinguishable from clean inflow simulations in literature. For Tu = 0.05 %, the bursting process is found to be considerably less smooth and strong coherent vortex shedding from the laminar separation bubble is observed prior to the formation of the dynamic stall vortex. The non-linear simulations are complemented with a transient linear stability analysis of the time-dependent evolution of the laminar shear layer in the bursting separation bubble using a spatially localised formulation of the Optimally Time-Dependent (OTD) framework, with which the most unstable part of the instantaneous tangent space of the non-linear trajectory is tracked over time. The resulting modes reveal intermittent switching between two regimes. Rapid growth of the Kelvin--Helmholtz rolls on the separated shear layer and complicated secondary instabilities on the transitional part of the separation bubble. The appearance of the latter is linked to large spikes in the instantaneous growth rate within the linear subspace and more rapid transition in the non-linear baseflow. These intense growth spikes are well correlated with the subsequent shedding of energetic vortices from the laminar separation bubble., QC 20230511