Aerodynamics for Engineers - Research Paper Example

Aerodynamics for Engineers Abstract Increased energy costs make optimal aerodynamic design even more critical today as even small improvements in aerodynamic performance can result in significant savings in fuel costs. Energy conscious industries like transportation (aviation and ground based) are particularly affected. There have been a number of different optimization methods, some of which require geometrically parameterized models. For non-parameterized models (as it is the case often in reality where models and shapes are very complex). Shape optimization and adjoin solvers are some of the latest approaches. In our study we are focusing on generating best practices and investigating different strategies of employing the commercially available shape optimizer tool from ANSYS’CFD solver Fluent. The shape optimizer is based on a polynomial mesh- morphing algorithm. The simple case of a low speed, airfoil/flap combination is used as a case study with the objective being the lift to drag ratio. A number of different built-in optimization algorithms and the way to best employ them are investigated. CONTENTS Number Topic Pages 1 Introduction 1 2 Research Strategy Plan 2 3 Formulation 3-5 4 Result & Discussion 6-7 5 Conclusion 8-9 Bibliography 13 Introduction Computational fluid dynamics is an application of computer aided analysis for analyzing fluids and their properties. It utilizes different approaches of algorithms and fluid mechanics formulae for the same purpose. There is different software like ANSYS which supports the feature of fluid mechanics so that a fluid interaction with the surfaces and given boundary conditions can be easily simulated and predicted in the analysis phase of a design. There are different equations like Navier Equation, RANS equation and different meshing techniques like finite difference and finite volume that are used in CFD for fluid analysis. Other meshing schemes are also there like FEM and BEM but they are not used for fluid analysis (Anderson, 1995). The flow behavior in terms of velocity field for a non-turbulent, Newtonian fluid is governed by the Navier-Stokes equations. These equations are valid only for the moving flow as it describes the flow field. The Navier-Stokes equations are obtained by combining the fluid kinematics and constitutive relation into the fluid equation of motion, and eliminating some higher order tensors. Navier-stroke equation is applicable for any laminar or transient and non viscous flow passing through passage of any geometry (Tannehill, 1997). Generally; For Compressible fluid For Incompressible fluid Reynolds-averaged Navier-Stokes (RANS) equations are the oldest methodology to model turbulent flow. For the turbulent flow it introduces an additional apparent stresses called Reynolds stresses. These equations are timed-average equations but are equally valid for the flows with a time-varying mean flow. Zingg et al (2002) exclaims Computation fluid dynamics as moving towards considerably minimizing user proficiency needs. The outcomes of the RANS equations, acronym of Reynolds-averaged Navier-Stokes equations, in the arena of computational fluid dynamics (CFD) to aircraft proposal simulation & design, comprises of issues in the subsequent three areas. These are computational efficiency, human efficiency and accuracy of physical modeling. Computational Efficiency: There has to be a lessening in the computing time needed to attain suitably determined solutions. This is an imperative requirement in sleek aerodynamic and multi-purpose design customization, as a result of the drift focusing a concurrent product and process advanced manufacturing. For comprehensive incorporation into the design procedures, the time necessary for solution of the RANS equations should be limited to only some minutes, over three-dimensional simulations, which is two orders of degree quicker than capacity, a fresh improvement at the beginning of this era. Even though there is a specific benefit of parallel architectures and augmented computer processing velocity, there is a requirement for enhancement in algorithms. In design customization as well, algorithm trustworthiness has larger implication. An explicit narration of Zingg et al (2002) is articulated as “Modern design optimization an algorithm, such as adjoint methods cannot be effective if the flow solver does not converge in relevant areas of the design space”. Human Efficiency: There is a vital want for a diminution in the human endeavor and proficiency needed for computing flows over complicated configurations in view of the fact that humans are not administered by Moore’s law (Zingg et al, 2002), Kaku (1999) demonstrated that computer power increased to two times the prior one after each eighteen months, and the speedy boost in power on this level is a single and marvelous development in the account of technology. However proficiency in CFD and aerodynamics is essential for moving out with the computations, there should be a decrement in the proficiency needed in the assortment of solver and grid constraints. One more problem to be adressed is the judgment of global numerical error. Accurateness of Physical Modeling: In the course of technique for example suitable grid resolution, numerical errors can be cautiously manipulated. On the other hand, errors coming out from physical models, as well as turbulence models and calculation of laminar turbulent alteration are supplementary tricky to calculate and administer (Zingg et al, 2002). The eddy-viscosity turbulence models utilized at the moment for processing aerodynamic flows are not capable to envisage with accuracy, slight occurrence for instance Reynolds number or flap gap effects on high-lift customizations. The main finest methodology emerged to be Reynolds stress models or second moment closures. It is vital to significantly augment the speed with which similar models are included into aerodynamic flow solvers, for manufacturing utilized at this point, and to judge and direct the manufacturing of such models. Additionally manufacturing of turbulence models needs diminution of time required processing three dimensional flows; moreover there is a want for further elevated class tentative datasets which comprise all the boundary condition data required for processing. To augment the computational effectiveness of RANS solvers, two fresh algorithms are taken into account: an imprecise Newton-Krylo algorithm which minimized the time required for processing & computing in order to attain a steady state solution; and the other is an upper order spatial discretization which minimizes the grid resolution requirements for a certain point of arithmetical accuracy (Zingg et al, 2002), as a result in addition minimizing computing expense. Furthermore, objective procedures of algorithm presentation are needed. 1. Research strategy plan The plan of this research strategy is to produce an airfoil proposal design and optimization mechanism that can adapt an airfoil outer form and figure (section geometry) delivering enhanced aerodynamic performance in view of maximizing lift to drag ratio below landing and takeoff air traveling situation. Processing the airfoil optimization development can significantly squeeze manufacturing product time duration and fetch into view better designs in contrast with the traditional planned design modification methodologies. A well-organized and efficient optimization method is initiated by an amalgamation of high-fidelity business CFD utensils with numerical optimization methodologies. This organism not only presents a steady, computerized optimization device for design engineers, but furthermore significantly minimizes the expenditure and the production time for a design process. The plan will be to unite the high fidelity business CFD tools (Fluent) with mathematical optimization systems to morph high lift organization. In research plan as revealed in image listed under, we will carry out morphing (grid deformation) openly within the fluent code devoid of reconstruction of geometry and the mesh with a peripheral utensil. Direct search method algorithms for example the Simplex, Compass, and Torczon…etc. is examined. The designer can prefer one of those to use in optimization of aerodynamic shapes distinctiveness. Figure (1) research strategy plan 2. Formulation A Flow Solver The inspiring FLUENT is a computational fluid dynamics (CFD) solver. It is computer application to imitate fluid flow issues. It is founded on a finite-volume technique to resolve the principal equations for a fluid. It is a 3d method of finite difference method specially designed for fluid analysis in 3d space. First of all the given domain is distributed in to numerous finite control volumes and the concerned variable is placed into the control volumes centric. The other stage is to integrate partial differential equations of control volume. The equation obtained by the process of integration is called discretization equation. This method reformulates the prevailing equations of partial difference in a conventional approach or in algebraic approach. Fluent offers the ability to employ dissimilar physical models for example incompressible or compressible, in viscid or viscous, laminar or turbulent, steady- state or transient investigations.- In the CFD formulation too, the traditional ideas of permanence and Navier-Stake’s equations in essential outline for incompressible stream of steady viscosity were processed by the integral utilities of the Fluent 13 CFD soft application. The present work utilized two equation turbulent models. One is the attainable k-e model that processes one transfer equation to permit the turbulent kinetic energy and its debauchery rate to be autonomously identified. The attainable k-e model is chiefly appropriate for our model, as the model utilized advanced wall dealing founded on the law of the wall. K-Ε MODEL is the most common and essential method for turbulence modeling. It is also known as two equation models because it utilized two equations for the solution. In the current activity, steady-state, incompressible 2D stream flow was considered. The mathematical simulations were launched by processing the conservation equations for mass and momentum by utilizing controlled and an uncontrolled grid finite volume technique. The chronological algorithm, semi-implicit method for pressure linked equation (SIMPLE), was utilized in processing all the scalar (directionless) constraints. For the labels of the continuity and momentum equations, and as well as for the turbulence equations, the first order upwind interpolating technique was allocated so as to attain additionally precise and correct results in contrast with the experimental results. The processing boundary conditions are provided in next section. B Design Variables As revealed from figure (2), the overlap and the gap flanked by the flap and main airfoil are utilized as the design constraint. Each design variable is limited as shown in figure (3). Fig.2 reveals the parallel (overlap) and perpendicular (gap) transformation design variables in multi-element configurations. Fig.3 reveals the design variables at boundary constituency. c. Objective functions The difficulty that is assessed in present analysis is single-objective encoding dilemma. A single-objective encoding or programming dilemma can be explained as: Find X which Minimize f(X) = [f1(X)/ f2(X)] The symbols f1, f2 are drag and lift correspondingly, X is known as the design vectors. The vector of design constraints, X, principally includes factors that manipulate the shape of the airfoil. Relying on the problem of concern, supplementary design variables may comprise of the angle of attack, the parallel and perpendicular transformation design variables that administer the place of flaps in multi-element configurations as revealed in figure (2). During this activity the objective function will processed by C++ language encoding & programming and constructed on the User Defined Function (UDF) library which considers control points and angle of attack as input factors, and values of lift , drag and drag to lift ratio are output results. 3. Results and Discussion Finally in this part we demonstrate the persuancee of algorithms on assessment of L/D ratio at different angle of attack . As revealed from figure (4.21) ,all data sets point out a virtually indistinguishable lift to drag ratio numerical range at (-4 to 0) degrees angle of attack and the data carries on to be identical fairly fine at six to twenty degrees. There are little deviances ranges at angle of attack from zero to six degrees. The image beneath is revealed as the Torczon and simplex algorithms are yielding the utmost lift to drag ratio, at the same time as the compass algorithm is yielding the lowest value. Those deviations occur from the particular performance for every algorithm; the disparity between the three algorithms of the direct search method are mostly in the option of the step length and search course ; such as at compass algorithm at earliest select an initial point (x0,y0 ) for 2 dimension or ( x0,y0,z0) for 3 dimension, a preliminary step length Δ, process the objective function at preliminary point then at east ,west ,north ,south correspondingly, if among these phases of input produces to a lesser f(x ,y) for 2D,or f(x ,y ,z)for 3D there is new iteration (x1,y1) or (x1,y1.z1) as revealed in figure (4.20) . The computation phases carry on by the similar preliminary step length and search direction in anticipation of congregated optimal shape, at the same time as the step length and search direction are variables relied on objective function numerical equivalent at Torczon and simplex algorithms. As it was identified previously in description the compass algorithm has a small number of steps if related with remaining algorithms for example the simplex and Torczon algorithms. They require additional steps to move toward a lowest amount of objective as revealed. This reason the compass algorithm simple to explain, trouble-free to put into practice and may speedily move toward a solution, but may be sluggish to perceive it, if the step size is outsized. This appears evident from current work, the amount of designs approach at compass algorithm are below to relative algorithms; for instance at angle of attack zero to four degrees the maximum number of designs were thirty one & thirty to correspondingly at compass algorithm whilst at Torczon were forty & forty one at 0 and 4 degrees correspondingly and at simplex algorithm were forty & forty four for zero & four degree correspondingly. This explicates the meeting of the solution for compass algorithm is quick. Fig. 4.20 Fig. 4.21 Effect of algorithms on lift to drag ratio. As it is identified earlier the objective of present work was to enhance the numerical value of L/D ratio at landing and take-off flight situations by aerodynamic shape optimization by utilizing grid deformation . As revealed from figures (4.22-4.24), appears evident that the optimization mechanism has been victorious in attaining the objective. When the contrast between L/D ratio earlier than optimization and subsequent to optimization is considered, it is seen obviously how augmented values of L/D ratio throughout the angles of the attack differ from (-4 to 20) degrees devoid of exemption. It was the uppermost percentage of enhancement of 33.919% for the duration of angle of attack four degrees at simplex algorithm, and the minimum percentage of enhancement was 6.925% for the duration of 0 degree angle of attack at compass algorithm,as shown in appendix A. Figures (4.25-4.27) reval the final outform for airfoil after optimization manipulations. Figure 4.22 Comparion L/D ratio before and after optimization for Compass algorithm Figure 4.23 Comparion L/D ratio before and after optimization for Simplex algorithm Figure 4.24 Comparion L/D ratio before and after optimization for Torczon algorithm Figures (4.25-4.27) reveal the manipulation of diverse algorithms on ultimate shape optimization. As it is identified earlier that each algorithms has particular performance and search method therefore the compass algorithm is bounded search direction and length size, while the simplex and Torczon algorithms are unbounded length size and search direction that is appeared clearly form figures (4.26-4.27) the remaining both algorithms are produced just about the identical optimal shape. Figure 4.25The shape after optimization ( compass algorithm at 4deg) Figure 4.26 The shape after optimization( simplex algorithm at 4deg) Figure 4.27 The shape after optimization (Torczon algorithm at 4deg) COMPASS ALGORITHM FLUENT RESULTS alpha L CL D CD (L/D)after (L/D)before improvement% -4 -155.328 -0.19831 20.385 0.02602 -7.6197204 -9.36422 18.629 0 193.67516 0.247414 15.52708 0.0198238 12.4733794 10.08724 23.655 4 572.0383 0.730338 23.95354 0.03058219 23.8811591 22.33445 6.925 8 922.85634 1.178237 41.2369 0.052648 22.3793821 18.7843 19.139 12 1206.4263 1.54027 71.4266 0.09119245 16.8904344 13.231 27.658 16 1362.6852 1.73978 117.0807 0.1494804 11.6388542 10.0595 15.700 20 1412.675 1.7990488 181.91876 0.20324918 7.76541683 6.2311 24.624 SIMPLEX ALGORITHM FLUENT RESULTS alpha L CL D CD L/D)after (L/D)B improvement% -4 -141.052 -0.18 19.883 0.0253 -7.0941005 -9.36422 24.242 0 209.3865 0.267329 15.5001 0.019789 13.5087193 10.08724 33.919 4 593.6022 0.75786 24.3635 0.031105 24.3644058 22.33445 9.089 8 942.13833 1.202855 42.5575 0.0543344 22.1380093 18.7843 17.854 12 1219.0726 1.556425 70.95902 0.090595 17.1799526 13.231 29.846 16 1399.2947 1.7865207 118.31805 0.15106013 11.8265531 10.0044 18.213 20 1413.675 1.80488 182.91876 0.233537 7.72843092 6.2311 24.030 TORCZON ALGORITHM FLUENT RESULTS alpha L CL D CD L/D)after (L/D)B improvement% -4 -150.766 -0.192488 19.35581 0.024712 -7.7891858 -9.36422 16.820 0 202.4986 0.258536 15.90276 0.0203035 12.7335507 10.08724 26.234 4 578.8115 0.73898 23.36652 0.02983 24.7709757 22.33445 10.909 8 945.22 1.2067903 42.8034 0.054648 22.0828252 18.7843 17.560 12 1226.154 1.56546 73.4578 0.093785 16.691951 13.231 26.158 16 1409.3438 1.7993508 120.0749 0.153303 11.7372057 10.2303 14.730 20 1409.014 1.7989 184.38187 0.235405 7.64182509 6.2311 22.640 4. Conclusion In this optimal aerodynamic design study, a number of different analyses are performed. The report initiates with the introduction of computational fluid dynamics, where the case object is also a bit discussed along with different algorithms. Then for the problem set up we analyzed different equations that will be used by the Ansys software for the analysis of the given aerofoil optimized case. This includes three different algorithms compass, simplex and Torczon to assess and optimize the L/D ratio. The easy case of a stumpy pace, airfoil/flap amalgamation is utilized as a case study with the purpose of enhancing the lift to drag ratio. Finally through the merger of different utilized the target is achieved. Ultimately through the present work it was possible to make paramount performances with assessing dissimilar approaches of using the commercially obtainable profile optimizer tool from ANSYS’CFD solver Fluent. Bibliography Anderson, J. D. (1995). Computational Fluid Dynamics: The Basics With Applications. McGraw-Hill Science. Bertin, J. J., & Smith, M. L. (2001). Aerodynamics for Engineers. Prentice Hall. Craig, G. (2003). Introduction to Aerodynamics. Regenerative Press. Hafez, D. C. Frontiers of computational fluid dynamics. World Scientific Publishers. Kaku, M. (1999). Visions: how science will revolutionize the twenty-first century. London: Oxford University Press. . Shah, T. M. An analysis and comparison of fluid through finite element models. International Journal of Engineering and Technology . Tannehill, J. (1997). Computational Fluid mechanics and Heat Transfer. Taylor and Francis. Toro, E. F. (1999). Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag. Wesseling, P. (2001). Principles of Computational Fluid Dynamics. Springer-Verlag. Zingg, D. R. (2002). Advances in algorithms for computing aerodynamic flows. Read More