aerodynamic shape optimization for natural laminar flow using a discrete adjoint approach a framework for the design of natural laminar flow airfoils is developed based on multipoint aerodynamic shape optimization capable of efficiently incorporating and exploiting laminar turbulent transition a two dimensional reynolds averaged navier stokes flow solver making use of the spalart allmaras turbulence model is extended to incorporate an iterative laminar turbulent transition prediction methodology the natural transition locations due to tollmien schlichting instabilities are predicted using a simplified en method or the compressible form of the arnal habiballah delcourt criterion the reynolds averaged navier stokes solver is subsequently used in a gradient based sequential quadratic programming shape optimization framework the transition criteria are tightly coupled into the objective and gradient evaluations the gradients are obtained using an augmented discrete adjoint formulation for nonlocal transition criteria robust design over a range of cruise flight conditions is demonstrated thro

new reductions of the kadomtsev petviashvili and two dimensional toda lattice hierarchies via symmetry constraints new types of reductions of the kadomtsev petviashvili kp hierarchy and the two dimensional toda lattice 2dtl hierarchy are considered on the basis of sato s approach within this approach these hierarchies are represented by infinite sets of equations for potentials u1 u2 u3 of pseudodifferential operators and their eigenfunctions and adjoint eigenfunctions the kp and the 2dtl hierarchies are studied under constraints of the following type n 1n nsn u1 u2 u3 x where sn are symmetries for these hierarchies n are arbitrary constants and is an arbitrary linear functional of the quantity it is shown that for the kp hierarchy these constraints give rise to hierarchies of 1 1 dimensional commuting flows for the variables u2 u3 un many known systems and several new ones are among them symmetry reductions for the 2dtl hierarchy give rise both to finite dimensional dynamical systems and 1 1 dimensional discrete systems some few results for the modified kp hierarc

a multilevel approach to single and multiobjective aerodynamic optimization an optimization platform with multilevel structure which is capable of efficiently solving design optimization problems in aerodynamics is proposed the multilevel structure relies on a two way regular exchange of information between successive search levels each level can be associated with a different evaluation software different problem parameterization and or different search tool for the minimization of the same objective function s the combination of some or all of the aforementioned strategies is possible although beyond the scope of this paper the basic optimization tool which is associated with at least one of the levels is a metamodel assisted evolutionary algorithm candidate solutions that have previously been examined are memorized and serve to train radial basis function networks operating as local surrogate evaluation models to handle multiobjective optimization problems with different search techniques at each level we hybridize an evolutionary algorithm that computes the front of pareto optimal solutions at the lower level s with a gradient based method at the upper level for the purpose of refinement through local search in aerodynamic optimization the adjoint method is used to compute the gradient of the objective function for the gradient method to apply to a front of solutions rather than a single individual an approximation of the spea 2 utility function gradient needs to be devised the multilevel platform is demonstrated on mathematical problems as well as the design of isolated and compressor cascade airfoils

feasibility study of e transition prediction in navier stokes methods for airfoils when navier stokes methods are applied in the design process for laminar airfoils the prediction of the transition location still represents an unresolved problem by the acceptence of the e n method as representing a convenient transition prediction tool the requirements for coupling e n to navier stokes methods will be demonstrated in particular the possibility to determine the laminar and turbulent viscous length scales is outlined based on the knowledge of the viscous layer thickness a mesh adaption procedure can be applied the navier stokes results produced using adapted meshes are shown to be identical to boundary layer results when the computed wall pressure from the navier stokes solution is used as input for the boundary layer calculation for the validation of the necessary steps in the coupling procedure the laminar airfoil doal3 was selected this airfoil was measured in the transonic wind tunnel braunschweig facility at the dlr german aerospace research establishment the limiting n factor for that wind tunnel was determined beforehand

periodic forcing parameters for control of incipient leading edge separation separation control by two dimensional periodic excitation is studied theoretically for nonsymmetrical flows over a parabola using a mathematical model of incompressible laminar flow with periodic perturbations this model is based on the representation of the flow as the sum of the mean and the periodic components the governing equations for both components are derived from the navier stokes equations using time averaging the momentum equations for the mean component comprise additional source terms that result from averaging the quadratic periodic terms these source terms allow the control of separation a numerical procedure has been developed to solve these equations along with equations of periodic flow and to study the influence of inflow conditions namely frequency amplitude and the station where the excitation is inserted on the mean flow using this procedure one can check if the given inflow conditions suppress the leading edge separation of the flow over a parabola

predicting stall and post stall behavior of airfoils at low mach numbers an interactive boundary layer method together with the e approach to the calculation of transition is used to predict the stall and post stall behavior of airfoils in incompressible and compressible flows at low freestream mach numbers two separate inviscid methods a panel method with compressibility corrections and a full potential method are used to compute the external velocity distribution needed in the solution of the compressible boundary layer equations the turbulence model is based on the cebeci smith algebraic eddy viscosity formulation with improvements for strong pressure gradient effects comparison of calculated results with inviscid flow computed with a panel method indicate excellent agreement with experiment for a wide range of reynolds numbers in incompressible flows comparison of calculated results obtained with inviscid flow computed with a full potential method also indicate excellent agreement with experiment for a wide range of angles of attack including stall for compressible flows at low freestream mach numbers the study also shows that even though the compressibility corrections to the panel method are adequate at small to moderate angles of attack they are not satisfactory at higher angles of attack especially near stall

classical w algebras and generalized drinfeld sokolov bi hamiltonian systems within the theory of poisson vertex algebras we describe of the generalized drinfeld sokolov hamiltonian reduction for the construction of classical mathcal w algebras within the framework of poisson vertex algebras in this context the gauge group action on the phase space is translated in terms of the exponential of a lie conformal algebra action on the space of functions following the ideas of drinfeld and sokolov we then establish under certain sufficient conditions the applicability of the lenard magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi hamiltonian equations

fully local formulation of a transition closure model for transitional flow simulations a new computational fluid dynamics compatible transition model for the natural transition and laminar separation bubble induced transition is established using two transport equations with consideration of analysis results through linear stability theory linear stability theory one transport equation is introduced to describe the growth of the laminar kinetic energy in the boundary layer in addition another transport equation of intermittency factor is built to trigger the transition by controlling the source term of turbulent kinetic energy equation finally applying the two transport equations to a shear stress transport turbulence model completes a four equation transition turbulence model comparisons of predictions using the new model with wind tunnel experiments of the schubauer and klebanoff flat plate s809 airfoil aerospatiale a airfoil and dlr f5 wing validate the predictive qualities of the new transition turbulence model

generalized multipoint inverse airfoil design in a rather general sense inverse airfoil design can be taken to mean the problem of specifying a desired set of airfoil characteristics such as the airfoil maximum thickness ratio pitching moment part of the velocity distribution or boundary layer development from thie information the corresponding airfoil shape is determined we present a method that approaches the design problem from this perspective in particular the airfoil is divided into segments along which together with the design conditions either the velocity distribution or boundary layer development may be prescribed

subgrid stabilized projection method for 2d unsteady flows at high reynolds numbers a subgrid stabilization technique is developed for solving the two dimensional incompressible navier stokes equations at high reynolds numbers the time marching algorithm is based on a well established fractional step pressure correction projection method the advection diffusion step is enriched by an implicit subgrid stabilizing term and by an explicit dissipative shock capturing term the former is calculated by means of a hierarchical finite element setting the latter is included to avoid gibbs phenomenon in the boundary layer convergence tests on prototypical two dimensional examples are reported and the method is used to simulate the viscous incompressible flows around the airfoil naca0012 at zero incidence and reynolds numbers ranging from 105 to 106

repetitive control design for mimo systems with saturating actuators this paper addresses the problem of tracking and rejection of periodic signals for linear multi input multi output systems subject to control saturation to ensure the periodic tracking rejection a modified state space repetitive control structure is considered conditions in a quasi linear matrix inequality form are proposed to simultaneously compute a stabilizing state feedback gain and an anti windup gain provided that the references and disturbances belong to a certain admissible set these gains guarantee that the trajectories of the closed loop system starting in a certain ellipsoidal set contract to the linearity region of the closed loop system where the presence of the repetitive controller ensures the periodic tracking rejection

two dimensional transonic aerodynamic design method this paper demonstrates the capabilities of a new transonic two dimensional design method based on the simultaneous solution of multiple streamtubes coupled through the position of and pressure at the streamline interfaces this allows the specification of either the airfoil shape direct analysis mode or the airfoil surface pressure distribution inverse design mode the nonlinear system of equations is formulated in a conservative manner which guarantees the correct treatment of shocks and is solved by a rapid newton solution method viscous effects can also be included through a coupled integral boundary layer analysis the first set of results shows the effect of different far field treatments demonstrating the improvement in accuracy obtained by including the second order doublet terms in addition to the usual first order vortex term the results are also compared to those obtained by specifying straight far field streamlines corresponding to solid wall wind tunnel experiments or constant far field pressure corresponding to freejet experiments to show the sensitivity to the farfield distance in the second set of results the design method is used to design a transonic airfoil with c 1 000 at a oo 0 70 it is shown that the off design performance is improved by specifying a surface pressure distribution with a very weak shock

calculation of separation bubbles using a partially parabolized navier stokes procedure a partially parabolized navier stokes solution procedure for the transitional separation bubble has been developed by coupling with the far field potential flow solution the calculation domain can be kept relatively small to minimise the computation time using the eddy viscosity turbulence model of baldwin and lomax it is shown that the procedure is capable of capturing the details of the separation bubble the results are in excellent agreement with experimental data and exhibit a marked improvement over those of existing interactive boundary layer procedures for the cases examined

solutions for the vector k constrained kp hierarchy a class of 1 1 dimensional integrable systems which are constrained from the kadomtsev petviashvili kp hierarchy is studied the bilinear equations of these integrable systems are shown first and then by using the free fermion operators their rational and soliton solutions which are closely related to the functions of the kp hierarchy are obtained the result implies that a large family of solutions of the 2 1 dimensional kp hierarchy can be obtained by solving these 1 1 dimensional integrable systems in particular the n soliton solutions of the kp hierarchy can be deduced from the soliton solutions of these 1 1 dimensional integrable systems

two dimensional unsteady leading edge separation on a pitching airfoil the initial stages of two dimension al unsteady leading edge boundary layer separation of laminar subsonic flow over a pitching naca 0012 airfoil have been studied numerically at reynolds number based on airfoil chord length rec 104 mach number mx 0 2 and nondimensional pitch rate h 0 2 computations have been performed using two separate algorithms for the compressible laminar navier stokes equations the first method denoted the structured grid algorithm utilizes a structured boundary fitted c grid and employs the implicit approximate factorization algorithm of beam and warming the second method denoted the unstructured grid algorithm utilizes an unstructured grid of triangles and employs the flux difference splitting method of roe and a discrete representation of gauss theorem for the in viscid and viscous terms respectively both algorithms are second order accurate in space and time and have been extensively validated through comparison with analytical and previous numerical results for a variety of problems the results show the emergence of a primary clockwise rotating recirculating region near the leading edge which can be traced to a pair of critical points a center and a saddle that appear within the flowfield followed by a secondary counterclockwise rotating recirculating region and a tertiary clockwise rotating recirculating region the primary and secondary recirculating regions interact with each other to give rise to the unsteady separation breakaway of the boundary layer

computation of unsteady supersonic quasi one dimensional viscous inviscid interacting internal flowfields the present steady and unsteady quasi 1d internal supersonic flowfield calculations employs a novel viscous inviscid interaction technique directly coupling and simultaneously solving the inviscid and viscous equations the coupled system is numerically solved using a two stage runge kutta scheme with first order one sided spatial differencing simple supersonic internal flow test cases are computed to demonstrate the capabilities of the computational procedure

technical communique on reachable sets for linear systems with delay and bounded peak inputs linear systems with constant coefficients and time varying delays are considered we address the problem of finding an ellipsoid that bounds the set of the states in the euclidean space that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar the system may encounter uncertainties in the matrices of its state space model and in the delay length the lyapunov razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper bound of the delay length

classical w algebras and generalized drinfeld sokolov hierarchies for minimal and short nilpotents we derive explicit formulas for brackets of the affine classical mathcal w algebras attached to the minimal and short nilpotent elements of any simple lie algebra mathfrak g this is used to compute explicitly the first non trivial pde of the corresponding integrable generalized drinfeld sokolov hierarchies it turns out that a reduction of the equation corresponding to a short nilpotent is svinolupov s equation attached to a simple jordan algebra while a reduction of the equation corresponding to a minimal nilpotent is an integrable hamiltonian equation on 2h 3 functions where h is the dual coxeter number of mathfrak g in the case when mathfrak g is mathfrak sl 2 both these equations coincide with the kdv equation in the case when mathfrak g is not of type c n we associate to the minimal nilpotent element of mathfrak g yet another generalized drinfeld sokolov hierarchy

multicomponent integrable reductions in the kadomtsev petviashvilli hierarchy new types of reductions of the kadomtsev petviashvili kp hierarchy are considered on the basis of sato s approach within this approach the kp hierarchy is represented by infinite sets of equations for potentials u2 u3 of pseudodifferential operators and their eigenfunctions and adjoint eigenfunctions the kp hierarchy was studied under constraints of the following type ni 1 i i x s x where s x are symmetries for the kp equation and i i i i are eigenfunctions with eigenvalue i it is shown that for the first three cases 2 3 4 these constraints give rise to hierarchies of 1 1 dimensional commuting flows for the variables u2 1 n 1 n bi hamiltonian structures for the new hierarchies are presented

simplified linear stability transition prediction method for separated boundary layers an existing transition prediction method for attached two dimensional incompressible boundary layers based on linear stability analysis is extended to separated two dimensional incompressible boundary layers such as those found in laminar transitional separation bubbles it is shown why the present method which tracks the growth of disturbances at many different frequencies is more accurate than the so called envelope methods for nonsimilar boundary layer developments reliance on a database of precalculated stability characteristics of known velocity profiles makes this method much faster than traditional stability calculations of similar accuracy the falkner skan self similar profiles are used for attached flow and a new very general family of profiles is used for separated flow comparisons with measured transition locations inside the bubble show good agreement over the range of chord reynolds numbers and airfoil angles of attack of interest

transition prediction for three dimensional boundary layers in computational fluid dynamics applications a method is presented for estimating the laminar turbulent transition location in three dimensional boundary layers for computational fluid dynamics cfd applications requiring numerous transition estimates with no user intervention given the reynolds number and the cp distribution the location of transition is estimated based on the attachment line state the potential for relaminarization the occurrence of laminar separation and the growth of instabilities transition caused by instability is estimated based on n factors calculated for tollmien schlichting waves and for stationary crossflow instabilities a neural network is used in place of solving the orr sommerfeld stability equation for determining the instability growth rates the current version of the method assumes incompressible flow the boundary layer flow and instabilities are calculated based on an infinite sweep strip boundary layer approximation the instability calculations also employ the parallel flow approximation

quantum reduction and representation theory of superconformal algebras abstract we study the structure and representations of a family of vertex algebras obtained from affine superalgebras by quantum reduction as an application we obtain in a unified way free field realizations and determinant formulas for all superconformal algebras

analytical approximation of two dimensional separated turbulent boundary layer velocity profiles abstract a single analytical expression is proposed to describe the velocity distribution in a two dimensional separated turbulent boundary layer on smooth impermeable adiabatic walls over the domain 0 less than or to y less than infinity the expression is an extension of one previously derived for attached flow which depends upon local values of skin friction shape factor and reynolds number based on momentum thickness boundary layer shape factor and local skin friction correlations applicable to separated flows are derived from fitting the proposed analytical expression for separated velocity profiles to available experimental data these correlations are then available for analytically describing separated velocity profiles without further fitting

viscous inviscid interaction using the navier stokes equations a numerical model for the calculation of incompressible viscous flows past airfoils and wings has been developed the approach is based on a strong viscous inviscid coupling of a boundary element method with the navier stokes equations in vorticity stream function formulation a semiadaptive or fully adaptive grid is used the interaction is achleved by iterative updating of the boundary conditions through the wall transpiration concept the navier stokes equations are discretized on a semistaggered grid space marching integration is performed starting from the stagnation streamline on two independent blocks results are presented for two different airfoils

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

convergent lmi relaxations for quadratic stabilizability and mathscr h _ infty control of takagi sugeno fuzzy systems this paper investigates the quadratic stabilizability of takagi sugeno t s fuzzy systems by means of parallel distributed state feedback compensators using finsler s lemma a new design condition assuring the existence of such a controller is formulated as a parameter dependent linear matrix inequality lmi with extra matrix variables and parameters in the unit simplex algebraic properties of the system parameters and recent results of positive polynomials are used to construct lmi relaxations that differently from most relaxations in the literature provide certificates of convergence to solve the control design problem due to the degrees of freedom obtained with the extra variables the conditions presented in this paper are an improvement over earlier results based only on polya s theorem and can be viewed as an alternative to the use of techniques based on the relaxation of quadratic forms an extension to cope with guaranteed h infin attenuation levels is also given with proof of asymptotic convergence to the global optimal controller under quadratic stability the efficiency of the proposed approach in terms of precision and computational effort is demonstrated by means of numerical comparisons with other methods from the literature

laminar separation bubble characteristics on an airfoil at low reynolds numbers an experimental investigation was conducted in order to document the structure and behavior of laminar separation bubbles at low reynolds numbers data of this type are necessary if the currently insufficient analytical and numerical models are to be improved the laminar separation bubble that forms on a naca 663 018 airfoil model was surveyed at chord reynolds numbers of 50 000 200 000 at angles of attack of 8 12 deg the effects of the various testing conditions on the separation bubble were isolated and the data were analyzed in relation to existing separation bubble correlations in order to test their low reynolds number applicability this analysis indicated that the chord reynolds number and the disturbance environment strongly influence the experimental pressure distributions these effects must be included in any analytic prediction technique applied to the low reynolds number flight regime

analysis of multi element airfoils by a vortex panel method the present vortex alone distributed vortex singularity method which uses flat panels with linearly varying vortex strength is used for the analysis of multielement airfoils this technique avoids such drawbacks of extant methods as the use of multiple singularities and the need to represent the airfoil by a large number of points the versatility of the present formulation is demonstrated by analyzing thin or cusped airfoils as well as airfoils with two three or four elements for which exact results are available as few as 20 panels are shown to suffice in the computation of pressure coefficients over a single component airfoil

classical affine w algebras associated to lie superalgebras in this paper we prove classical affine w algebras associated to lie superalgebras w superalgebras which can be constructed in two different ways via affine classical hamiltonian reductions and via taking quasi classical limits of quantum affine w superalgebras also we show that a classical finite w superalgebra can be obtained by a zhu algebra of a classical affine w superalgebra using the definition by hamiltonian reductions we find free generators of a classical w superalgebra associated to a minimal nilpotent moreover we compute generators of the classical w algebra associated to spo 2 3 and its principal nilpotent in the last part of this paper we introduce a generalization of classical affine w superalgebras called classical affine fractional w superalgebras we show these have poisson vertex algebra structures and find generators of a fractional w superalgebra associated to a minimal nilpotent

a revisit of the tonal noise of small rotors in this study asymptotic analysis of the frequency domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi rotor powered drones is conducted simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number flow speed rotation speed unsteady motion thrust and observer angle on the tonal noise the rate of noise increment with thrust or rotational speed is determined by orders of blade passing frequency harmonics and the unsteady motion the axial mean flow influence can be approximated by quadratic functions at given thrust the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive the higher tonal harmonics are significantly increased if unsteady motions although of small amplitude are existed as indicated by the defined sensitivity function emphasizing that the unsteady motions should be avoided for quiet rotor designs the scaling laws are examined by comparing with the full computations of the rotor noise using the frequency domain method the implementation of which has been validated by comparing with experiments good data collapse is obtained when the proposed scaling laws which highlights the dominant influence of the design parameters are incorporated

calculation of two dimensional turbulent boundary layers using the baldwin lomax model the algebraic turbulent eddy viscosity model of baldwin and lomax is critically evaluated for a class of twodimensional nonseparated turbulent boundary layer flows exhibiting adverse and favorable pressure gradients and boundary layer bleed the flows are computed using the twodimensional mass averaged boundary layer equations overall the results obtained using the baldwin lomax model compare favorably with the experimental data two quantities in the outer eddy viscosity formulation are examined by comparison with the eddy viscosity model of cebeci and smith contents the present capabilities for numerical simulation of highspeed turbulent flows are based on a variety of turbulence models algebraic eddy viscosity models are still among the most popular certain algebraic models require the determination of the boundary layer edge velocity and thickness which can result in large variations in the computed outer eddy viscosity due to the uncertainty in determining the boundarylayer edge 1 baldwin and lomax1 have developed a two layer algebraic eddy viscosity model in an attempt to eliminate this difficulty this model has been patterned after the model of cebeci and smith2 however it does not require the determination of the boundary layer edge the baldwin lomax turbulence model was evaluated by its originators for several cases including a shock wave turbulent boundary layer interaction on a flat plate a supersonic turbulent compression corner and a transonic airfoil 1 visbal and knight3 noted that the constants ccp and ckleb in the baldwin lomax outer formulation were dependent on flow mach number they also identified difficulties with the determination of the length scale in the outer eddy viscosity similar difficulties have been encountered by other computers 4 despite the difficulties identified with the baldwinlomax model and its increasing popularity and extensive application to two and three dimensional flows with strong viscous inviscid interaction a critical evaluation of this model for nonseparated two dimensional turbulent boundary layer flows has not been performed the present investigation seeks to contribute to the evaluation of the model by critically examining its performance for a class of turbulent boundarylayer flows baldwin and lomax determined the constants ccp and ckleb appearing in the outer formulation1 by comparison with the cebeci smith model for transonic constant pressure

essential ingredients of a method for low reynolds number airfoils a calculation method for low reynolds number flows is described and appraised in terms of comparisons between calculations and measurements it comprises interaction between solutions of inviscid and boundary layer equations and involves the e n method to determine the location of the onset of transition with further interaction to insure that upstream effects of the turbulent flow region are correctly represented

multi periodic repetitive control system a lyapunov stability analysis for mimo systems a multi input multi output mimo repetitive control problem of tracking and disturbance rejection is considered when both reference and disturbance signals are finite linear combinations of periodic but not necessarily sinusoidal signals lyapunov stability analyses under a positive real condition and a natural relaxation and exponential stability under a strict positive real condition are provided together with bounds on the induced l 2 and rms gains of the closed loop system it is shown that similar lyapunov stability results apply when the plant is a positive real state delay system extension of the analyses to a class of non linear systems is discussed and indicates a good degree of robustness in the design

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

on the abrupt turbulent reattachment downstream of leading edge laminar separation a theoretical investigation of unsteady marginal separations in a classical unsteady boundary layer is described this suggests that the nonlinear properties of such separations may be largely responsible at least initially for the central features often observed experimentally in the abrupt turbulent reattachment of eddies that follow laminar separation near the leading edges of aerofoils the theory reduces the local flow problem to the solution of a nonlinear integro partial differential equation for the unknown scaled skin friction which is also proportional to the decrement in displacement locally numerical solutions followed by linear and nonlinear analysis show that all short length small disturbances are unstable whenever reversed flow occurs but for sufficiently confined initial conditions the instabilities accumulate in such a way that a breakdown is forced after a finite time in the nonlinear breakdown a double structure arises near the point of collapse with an effective shock taking the flow abruptly from the reversed sense just upstream to the forward sense just downstream this predicted shock forms the suggested possible link with the sudden transition and turbulent reattachment of laminar eddies in practice at rounded leading edges discussions of the turbulence effects of the related phenomenon of dynamic stall of other instabilities present and of the theoretical repercussions of the work are presented also

constraints of the kadomtsev petviashvili hierarchy for the kadomtsev petviashvili kp hierarchy constructed in terms of the famous sato theory a k constraint is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates the eigenvalue problem of the k constrained system is naturally obtained from the linear system of the kp hierarchy which takes the form of kth order polynomial coupled with a first order one thus we are able to derive the correspondent lax pair recursion operator bi hamiltonian structures and conserved quantities the constraints for the bkp hierarchy are also sketched

computational fluid dynamics compatible transition modeling using an amplification factor transport equation a new laminar turbulent transition model for low turbulence external aerodynamic applications is presented that incorporates linear stability theory in a manner compatible with modern computational fluid dynamics solvers the model uses a new transport equation that describes the growth of the maximum tollmien schlichting instability amplitude in the presence of a boundary layer to avoid the need for integration paths and nonlocal operations a locally defined nondimensional pressure gradient parameter is used that serves as an estimator of the integral boundary layer properties the model has been implemented into the overflow 2 2f solver comparisons of predictions using the new model with high quality wind tunnel measurements of airfoil section characteristics confirm the predictive qualities of the model as well as its improvement over the current state of the art in computational fluid dynamics transition modeling at approximately half the computational expense

transonic aeroelastic instability searches using sampling and aerodynamic model hierarchy doi 10 2514 1 j050509 a hierarchy of flow models is exploited for transonic aeroelastic stability analysis using the kriging interpolation technique applied within the schur complement eigenvalue framework in the schur framework a modified structural eigenvalue problem describes the coupled aeroelastic system with a precomputed interaction term depending on the response frequency the interaction term representing the influence of the high dimensional computational fluid dynamics system is approximated by reconstruction based on samples that can be computed using a frequency or time domain solver the computationally cheap approximation model is developed and discussed in this paper for two degree of freedom aerofoil cases the approximation model is used for both the parametric blind search of aeroelastic instability and for updating predictions based on aerodynamic models of different fidelities

optimization of gaussian random fields many engineering systems are subject to spatially distributed uncertainty i e uncertainty that can be modeled as a random field altering the mean or covariance of this uncertainty will in general change the statistical distribution of the system outputs we present an approach for computing the sensitivity of the statistics of system outputs with respect to the parameters describing the mean and covariance of the distributed uncertainty this sensitivity information is then incorporated into a gradient based optimizer to optimize the structure of the distributed uncertainty to achieve desired output statistics this framework is applied to perform variance optimization for a model problem and to optimize the manufacturing tolerances of a gas turbine compressor blade

analysis of airfoil leading edge separation bubbles a local inviscid viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles in this analysis an inverse boundary layer finite difference analysis is solved iteratively with a cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis favorable comparisons with data indicate the overall validity of the present localized interaction approach in addition numerical tests were performed to test the sensitivity of the computed results to the mesh size limits on the cauchy integral and the location of the transition region

viscous inviscid analysis of transonic and low reynolds number airfoils a method of accurately calculating transonic and low reynolds number airfoil flows implemented in the viscous inviscid design analysis code ises is presented the euler equations are discretized on a conservative streamline grid and are strongly coupled to a two equation integral boundary layer formulation using the displacement thickness concept a transition prediction formulation of the e type is derived and incorporated into the viscous formulation the entire discrete equation set including the viscous and transition formulations is solved as a fully coupled nonlinear system by a global newton method this is a rapid and reliable method for dealing with strong viscous inviscid interactions which invariably occur in transonic and low reynolds number airfoil flows the results presented demonstrate the ability of the ises code to predict transitioning separation bubbles and their associated losses the rapid airfoil performance degradation with decreasing reynolds number is thus accurately predicted also presented is a transonic airfoil calculation involving shock induced separation showing the robustness of the global newton solution procedure good agreement with experiment is obtained further demonstrating the performance of the present integral boundary layer formulation

classical affine w algebras and the associated integrable hamiltonian hierarchies for classical lie algebras we prove that any classical affine w algebra mathcal w mathfrak g f where mathfrak g is a classical lie algebra and f is an arbitrary nilpotent element of mathfrak g carries an integrable hamiltonian hierarchy of lax type equations this is based on the theories of generalized adler type operators and of generalized quasideterminants which we develop in the paper moreover we show that under certain conditions the product of two generalized adler type operators is a lax type operator we use this fact to construct a large number of integrable hamiltonian systems recovering as a special case all kdv type hierarchies constructed by drinfeld and sokolov

dirac reduction for poisson vertex algebras we construct an analogue of dirac s reduction for an arbitrary local or non local poisson bracket in the general setup of non local poisson vertex algebras this leads to dirac s reduction of an arbitrary non local poisson structure we apply this construction to an example of a generalized drinfeld sokolov hierarchy