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GradientBased Optimum Aerodynamic Design Using Adjoint MethodsXie, Lei 02 May 2002 (has links)
Continuous adjoint methods and optimal control theory are applied to a pressurematching inverse design problem of quasi 1D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the StegerWarming fluxvectorsplitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A nonuniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressurematching inverse design is then conducted for a nozzle parameterized by a single geometric parameter.
In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the farfield boundary. A superreduced design formulation is also explored by treating the angle of attack as an additional state; superreduced gradients can be constructed either by solving adjoint equations with nonlocal boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (superreduced) gradients. / Ph. D.

2 
Multiobjective design optimization for highlift aircraft configurations supported by surrogate modelingLi, Daxin 12 1900 (has links)
Nowadays, the competition among airlines seriously depend upon the saving operating
costs, with the premise that not to degrade its services quality. Especially in the face of increasingly
scarce oil resources, reducing fleets operational fuel consumption, is an important
means to improve profits.
Aircraft fuel economy is determined by operational management strategies and application
technologies. The application of technologies mainly refers to airplane’s engine performance,
Weight efficiency and aerodynamic characteristics. A market competitive aircraft
should thoroughly consider to all of these aspects.
Transport aircraft aerodynamic performance mainly is determined by wing’s properties.
Wings that are optimized for efficient flight in cruise conditions need to be fitted with
powerful highlift devices to meet lift requirements for safe takeoff and landing. These
highlift devices have a significant impact on the total airplane performance. The aerodynamic
characteristics of the wing airfoil will have a direct impact on the aerodynamic
characteristics of the wing, and the wing’s effective cruise hand highlift configuration design
has a significant impact on the performance of transport aircraft. Therefore, optimizing
the design is a necessary airfoil design process.
Nowadays engineering analysis relies heavily on computerbased solution algorithms to investigate
the performance of an engineering system. Computational fluid dynamics (CFD)
is one of the computerbased solution methods which are more widely employed in aerospace
engineering. The computational power and time required to carry out the analysis increases
as the fidelity of the analysis increases. Aerodynamic shape optimization has become
a vital part of aircraft design in the recent years. Since the aerodynamic shape optimization
(ASO) process with CFD solution algorithms requires a huge amount of computational
power, there is always some reluctance among the aircraft researchers in employing
the ASO approach at the initial stages of the aircraft design. In order to alleviate this problem,
statistical approximation models are constructed for actual CFD algorithms. The fidelity
of these approximation models are merely based on the fidelity of data used to construct
these models. Hence it becomes indispensable to spend more computational power in order
to convene more data which are further used for constructing the approximation models.
The goal of this thesis is to present a design approach for assumed wing airfoils; it includes
the design process, multiobjective design optimization based on surrogate modelling. The
optimization design stared from a transonic singleelement singleobjective optimization
design, and then highlift configurations were two lowspeed conditions of multiobjective
optimization design, on this basis, further completed a variable camber airfoil at low speed
to highlift configuration to improve aerodynamic performance. Through this study, prove a
surrogate based model could be used in the wing airfoil optimization design.

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Řešení inverzní úlohy obtékání leteckého profilu / Solution of inverse problem for a flow around an airfoilŠimák, Jan January 2014 (has links)
Title: Solution of inverse problem for a flow around an airfoil Author: Mgr. Jan Šimák Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c., Department of Numerical Mathematics Abstract: The method described in this thesis deals with a solution of an inverse problem for a flow around an airfoil. It can be used to design an airfoil shape according to a specified velocity or pressure distribution along the chord line. The method is based on searching for a fixed point of an operator, which combines an approximate inverse and direct operator. The approximate inverse operator, derived on the basis of the thin airfoil theory, assigns a corresponding shape to the specified distribution. The resulting shape is then constructed using the mean camber line and thickness function. The direct operator determines the pressure or velocity distribution on the airfoil surface. We can apply a fast, simplified model of potential flow solved using the Fredholm integral equation, or a slower but more accurate model of RANS equations with a komega turbulence model. The method is intended for a subsonic flow.

4 
Optimization Techniques Exploiting Problem Structure: Applications to Aerodynamic DesignShenoy, Ajit R. 11 April 1997 (has links)
The research presented in this dissertation investigates the use of allatonce methods applied to aerodynamic design. Allatonce schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock discontinuities. Special treatment has to be considered for such problems and we study several approaches.
Our allatonce methods are based on the Sequential Quadratic Programming method, and are designed to exploit the structure inherent in a given problem. The first method is a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in all our applications is that careful analysis of the given problem can often lead to an efficient implementation of these allatonce methods.
Chapter 2 describes a nozzle design problem involving onedimensional transonic flow. An initial formulation as an optimal control problem allows us to solve the problem as as twopoint boundary problem which provides useful insight into the nature of the problem. Using the Reduced Hessian formulation for this problem, we find that a conventional CFD method based on shock capturing produces poor performance. The numerical difficulties caused by the presence of the shock can be alleviated by reformulating the constraints so that the shock can be treated explicitly. This amounts to using a shock fitting technique. In Chapter 3, we study variants of a simplified temperature control problem. The control problem is solved using a sparse SQP scheme. We show that for problems where the underlying infinitedimensional problem is wellposed, the optimizer performs well, whereas it fails to produce good results for problems where the underlying infinitedimensional problem is illposed. A transonic airfoil design problem is studied in Chapter 4, using the Reduced SQP formulation. We propose a scheme for performing the optimization subtasks that is based on an Euler Implicit time integration scheme. The motivation is to preserve the solutionfinding structure used in the analysis algorithm. Preliminary results obtained using this method are promising. Numerical results have been presented for all the problems described. / Ph. D.

5 
Development of a Tool for Inverse Aerodynamic Design and Optimisation of Turbomachinery Aerofoils / Utveckling av ett verktyg för invers aerodynamisk design och optimering av vingprofiler för turbomaskinerKurtulus, Berkin January 2021 (has links)
The automation of airfoil design process is an ongoing effort within the field of turbomachinery design, with significant focus on developing new reliable and consistent methods that can meet the needs of the engineers. A wide variety of approaches has been in use for inverse airfoil design process which benefit from theoretical inverse design, statistical methods, empirical discoveries and many other ways to solve the design problem. This thesis work also develops a tool in Python to be used in airfoil aerodynamic design process that is simple, fast and accurate enough for initial design of turbomachinery blades with focus on turbine airfoils used for operation in aircraft engines. To convey the decisionmaking process during development a simplified case is presented. The underlying considerations are discussed. Other available methods in the literature used for similar problems, are also evaluated and compared to demonstrate the advantages and limitations of the methods used within the tool. The inverse design problem is formulated as a multiobjective optimization problem to handle various different objectives that are relevant for aerodynamic design of turbomachinery airfoils. Test runs are made and the results are discussed to assess how robust the tool is and how the current capabilities can be modified or extended. After the development process, the tool is verified to be a suitable option for reallife design optimization tasks and can be used as a building block for a much more comprehensive tool that may be developed in the future. / Automatisering av processen för design av vingprofiler kräver fortlöpande insatser inom området turbomaskindesign, med stort fokus på att utveckla nya tillförlitliga och konsekventa metoder som kan tillgodose ingenjörernas behov. Ett stort antal olika tillvägagångssätt har provats för omvänd design av vingprofiler såsom teoretisk invers design, statistiska metoder, empiriska upptäckter och många andra sätt att lösa designproblemet. Detta avhandlingsarbete är också ett lyckat försök att utveckla ett verktyg i Python som ska användas i den aerodynamiska designprocessen; det är enkelt, snabbt och noggrant för den initiala designen av turbomaskinblad med fokus på turbinblad som för användning i flygmotorer. För att förmedla beslutsprocessen under utvecklingen presenteras ett förenklat fall. De underliggande övervägandena diskuteras. Andra tillgängliga metoder i litteraturen som används för liknande problem utvärderas och jämförs för att visa fördelarna och begränsningarna med de metoder som används i verktyget. Det omvända designproblemet formuleras som ett multiobjektivt optimeringsproblem för att hantera olika mål som är relevanta för aerodynamisk design av turbomaskiner. Testkörningar görs och resultaten diskuteras för att bedöma hur robust verktyget är och hur de nuvarande funktionerna kan modifieras eller utökas. Efter utvecklingsprocessen verifieras verktyget som ett lämpligt alternativ för verkliga designoptimeringsuppgifter och kan användas som en byggsten för ett mycket mer omfattande verktyg som kan utvecklas i framtiden.

6 
Aerodynamic optimisation of a smallscale wind turbine blade for low windspeed conditionsCencelli, Nicolette Arnalda, Von Bakstrom, T.W., Denton, T.S.A. 12 1900 (has links)
Thesis (MScEng (Department of Mechanical and Mechatronic Engineering))Stellenbosch University, 2006. / ENGLISH ABSTRACT: Wind conditions in South Africa determine the need for a smallscale wind turbine to produce useable power at windspeeds below 7m/s. In this project, a range of windspeeds, within which optimal performance o the wind turbine is expected, was selected. The optimal performance was assessed in terms of the Coefficient of Power(Cp), which rates the turbines blade's ability to extract energy form the avalible wind stream. The optimisation methods employed allowed a means of tackling the multivariable problem such that the aerodynamic characteristics of the blade were ideal throughout the wind speed range. The design problem was broken down into a twodimensional optimisaion of the airfoils used at the radial stations, and a threedimensional optimisation of the geometric features of the wind rotor. by means of blending various standard airfoil profiles, a new profile was created at each radial station. XFOIL was used for the twodimensional analysis of these airfoils. Threedimensional optimisn involved representation of the rotor as a simplified model and use of the Blade Element Momentum(BEM) method for analysis. an existimg turbine blade, on which the design specifications were modelled, was further used for comparative purposes throughout the project. The resulting blade design offers substantial improvements on the reference design. The application of optimisation methods has successfully aided the creation of a wind turbine blade with consistent peak performance over a range of design prints. / Sponsored by the Centre for Renewable and Sustainable Energy Studies, Stellenbosch University

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Site Specific Design Optimization Of A Horizontal Axis Wind Turbine Based On Minimum Cost Of EnergySagol, Ece 01 January 2010 (has links) (PDF)
This thesis introduces a design optimization methodology that is based on minimizing the Cost of Energy (COE) of a Horizontal Axis Wind Turbine (HAWT) that is to be operated at a specific wind site. In the design methodology for the calculation of the Cost of Energy, the Annual Energy Production (AEP) model to calculate the total energy generated by a unit wind turbine throughout a year and
the total cost of that turbine are used. The AEP is calculated using the Blade Element Momentum (BEM) theory for wind turbine power and the Weibull
distribution for the wind speed characteristics of selected wind sites. For the blade profile sections, either the S809 airfoil profile for all spanwise locations is used or NREL Sseries airfoil families, which have different airfoil profiles for different spanwise sections, are used,. Lift and drag coefficients of these airfoils are obtained by performing computational fluid dynamics analyses. In sample
design optimization studies, three different wind sites that have different wind speed characteristics are selected. Three scenarios are generated to present the effect of the airfoil shape as well as the turbine power. For each scenario, design optimizations of the reference wind turbines for the selected wind sites are performed the Cost of Energy and Annual Energy Production values are
compared.

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