This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at http://www.alimirjalili.com/SCA.html .

SCA: A Sine Cosine Algorithm for solving optimization problems

Salp Swarm Algorithm

Calculation procedures for viscous/inviscid analysis and mixed-inverse design of subcritical airfoils are presented. An inviscid linear-vorticity panel method with a Karman-Tsien compressiblity correction is developed for direct and mixed-inverse modes. Source distributions superimposed on the airfoil and wake permit modeling of viscous layer influence on the potential flow. A two-equation lagged dissipation integral method is used to represent the viscous layers. Both laminar and turbulent layers are treated, with an e 9-type amplification formulation determinining the transition point. The boundary layer and transition equations are solved simultaneously with the inviscid flowfield by a global Newton method. The procedure is especially suitable for rapid analysis of low Reynolds number airfoil flows with transitional separation bubbles. Surface pressure distributions and entire polars are calculated and compared with experimental data. Design procedure examples are also presented.

XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils

The purpose of the last three sections is to demonstrate by representative examples that control theory can be used to formulate computationally feasible procedures for aerodynamic design. The cost of each iteration is of the same order as two flow solutions, since the adjoint equation is of comparable complexity to the flow equation, and the remaining auxiliary equations could be solved quite inexpensively. Provided, therefore, that one can afford the cost of a moderate number of flow solutions, procedures of this type can be used to derive improved designs. The approach is quite general, not limited to particular choices of the coordinate transformation or cost function, which might in fact contain measures of other criteria of performance such as lift and drag. For the sake of simplicity certain complicating factors, such as the need to include a special term in the mapping function to generate a corner at the trailing edge, have been suppressed from the present analysis. Also it remains to explore the numerical implementation of the design procedures proposed in this paper.

/pdf/aerodynamic-design-via-control-theory-1c4pnftdq4.pdf

Aerodynamic design via control theory

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

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.

/pdf/viscous-inviscid-analysis-of-transonic-and-low-reynolds-3zmgy0hmeg.pdf

Viscous-inviscid analysis of transonic and low Reynolds number airfoils

An integrated model is developed for aerodynamic, structural, and control simulation of flexible aircraft in extreme flight situations. The structure consists of joined nonlinear beams allowing arbitrarily large deformations. The aerodynamic model is a compressible vortex/source-lattice with wind-aligned trailing vorticity. Full unsteady terms with flight dynamics are included. Model forcing is via gusts or control inputs. The overall nonlinear equation set is solved by a full Newton method. The Newton Jacobian matrix is also used for frequency-domain computations to investigate flight stability, control-response behavior, and flutter. Nonlinear performance of control laws can be examined. The numerical problem is small enough for interactive computation, allowing rapid diagnosis of local aerodynamic stall, structural failure, or control system saturation for a wide range of flight conditions. The overall approach allows quick generation of a robust multi-disciplinary preliminary design which can serve as a good basis for subsequent detailed design.

Integrated simulation model for preliminary aerodynamic, structural, and control-law design of aircraft

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.

/pdf/two-dimensional-transonic-aerodynamic-design-method-1we687ipl7.pdf

Mark Drela

Papers

XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils

Viscous-inviscid analysis of transonic and low Reynolds number airfoils

Integrated simulation model for preliminary aerodynamic, structural, and control-law design of aircraft

Two-Dimensional Transonic Aerodynamic Design Method

Newton solution of coupled viscous/inviscid multielement airfoil flows