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Numerical and experimentalinvestigation of the effect of geometrymodification on the aerodynamiccharacteristics of a NACA 64(2)-415wingPRADEEPRAMESHMaster of Science ThesisStockholm, Sweden 2013
Numerical and experimental investigationof the effect of geometry modification onthe aerodynamic characteristics of aNACA 64(2)-415 wingPRADEEPRAMESHMaster’s Thesis in Scientific Computing (30 ECTS credits)Master Programme in Scientific Computing 120 creditsRoyal Institute of Technology year 2013Supervisor at KTH was Johan JanssonExaminer was Michael HankeTRITA-MAT-E 2013:11ISRN-KTH/MAT/E--13/11--SERoyal Institute of TechnologySchool of Engineering SciencesKTH SCISE-100 44 Stockholm, SwedenURL: www.kth.se/sci
AbstractThe objective of the thesis is to study the effect of geometry modifications on the aerodynamiccharacteristics of a standard airfoil (NACA series). The airfoil was chosen for a high aspect ratio andReynolds number of the range(realistic conditions for flight and naval applications).Experimental and Numerical investigation were executed in collaboration with KTH – CTL andSchlumberger. Experimental investigations were conducted at NTNU which was funded bySchlumberger. The numerical investigation was executed with the massively parallel unifiedcontinuum adaptive finite element method solver “Unicorn” and the computing resources at KTH –CTL. The numerical results are validated against the experiments and against experimental results inthe literature, and possible discrepancies analyzed and discussed based on the numerical method. Inaddition, this will help us to expand our horizon and get acquainted with the numerical methods andthe computational framework. The further scope of this thesis is to develop and implement the newmodules for the Unicorn solver suitable for the aerodynamic applications.
eometrimodifikationer på NACA-profil på dess aerodynamiska egenskaper.SammanfattningI arbetet studeras effekten av geometri-modifikationer på aerodynamiska egenskaper hos enstandard-vingprofil ur NACA-serien. Profilen valdes för en slank vinge och Reynoldstal mellan en ochtio miljoner vilket kan vara realistiskt för flygplan och marina tillämpningar. Experiment ochnumeriska beräkningar utförs i samarbete mellan KTH/CTL och Schlumberger. Experimenten utfördespå NTNU med stöd av Schlumberger. Beräkningarna gjordes med finita-element paketet "Unicorn"på KTH/CTL s datorer. Nya Unicorn-moduler för aerodynamiska beräkningar utvecklas vilket gererfarenhet av de numeriska metoderna och beräkningsmiljön. Numeriska resultat valideras motexperimenten och resultat i litteraturen, och avvikelserna för den aktuella numeriska metodenanalyseras.
AcknowledgementI would like to express my sincere gratitude to my supervisor Johan Jansson, for hiscontinuous guidance and support in all stages of the thesis. He provided me with direction,technical support and became more of a mentor and friend, than a professor.I appreciateand would also like to thank him for being an open person to ideas, for encouraging andhelping me to shape my interest and ideas.A very special thanks to Martin Howlid, Nils Halvor Heieren and Rik Wemmenhove fromSchlumberger-WOTC, Norway for the support and assistance they provided at all levels ofthe project. I recognize that this research would not have been possible without financialsupport from Schlumberger-WOTC for the Wind Tunnel Experiments.I would like to thank Per-Åge Krogstad and Tania Bracchi from the department of energy andprocess engineering at NTNU, who were involved in this project for conducting theexperiments at the Aerodynamic Laboratory.I would like to thank Johan Hoffman for the valuable inputs, support and computationalresources from Computational Technology Laboratory @ KTH. In addition, I would like tothank Michael Hanke for the administrative support and guidance.Pradeep Ramesh
Table of Contents1.Introduction . 12.Project Background . 2State of Art: . 2Working Principle: . 3Finite Element Method (FEM) . 53.NACA Airfoils . 14Nomenclature. 144.Numerical Investigation . 174.1. Governing Equations . 174.2. Boundary Conditions for the Numerical Method . 184.3. Description of the of the Numerical Method . 204.4. Software Environment . 224.5. Geometry Modelling . 244.6. Mesh Generation . 264.7. Boundary Conditions for the Computational Domain. 284.8 Solving. 284.9 Results . 285.Experimental Investigation . 345.1. Description of the Experimental Setup . 355.2. Measurements . 365.Experimental Investigation. 386.Results Comparison and Discussion . 397.Conclusions. 428.Scope for future work. 439.References . 44
List of nal Advisory Committee for AeronauticsAngle of AttackDirect Numerical SimulationReynolds-averaged Navier-StokesLarge Eddy SimulationsImplicit Large Eddy SimulationsDetached Eddy SimulationsFinite Element MethodComputational Fluid DynamicsThree Dimensional
1. IntroductionThe prime motivation for this project was realistic problems that occur in field operation atthe Schlumberger company. The main focus is to investigate and observe, how damagescontribute in performance of a wing and how to resolve these field problems. Afternumerous meetings and discussions the project idea was formulated in collaboration withSchlumberger.Numerical simulations were computed for 3D Unsteady, Incompressbile turbulent flow pasta NACA 64(2)415 wing for chord lengthfor a range ofangles of attack from low lift through stall. Two variants were considered for theinvestigation , case I - clean wing and case – II protrusion wing. The numerical investigationwas executed with the massively parallel unified continuum adaptive finite element methodsolver “Unicorn” . A stabilized finite element method is used, referred to as General Galerkin(G2), with adaptive mesh refinement with respect to the error in target output, such asaerodynamic forces.Experimental investigations have been carried out at NTNU wind tunnel laboratory incollaboration with schlumberger. Computational predictions of aerodynamic characteristicsare validated against experimental data.1
2.Project BackgroundState of Art:Today, a major computational challenge is to compute aerodynamic forces and predict stallaccurately and efficiently at realistic flight conditions [1].In the current scenario most of the simulations in the aircraft industry are based on Reynoldsaveraged Navier- Stokes equations (RANS), where time averages are computed to anaffordable cost, with the drawback of introducing turbulence models based on parametersthat have to be tuned for particular applications. Large eddy simulation (LES) [3] is analternative over Direct Numerical Simulations (DNS) and RANS.An adaptive finite element method, the General Galerkin (G2) method [4] is adopted in oursimulation method. In G2 method the residual based numerical stabilization acts as a subgridmodel similar to an Implicit LES (ILES) [3]. An adaptive mesh refinement algorithm is used,driven by a posteriori estimation of the error,chosen as the target output based on thesolution of an dual problem.According to Johan Hoffman , Johan Jansson, and Niclas Jansson [13] ”A key challenge forLES methods is the modeling of turbulent boundary layers at different angles of attack. Fullresolution of turbulent boundary layers is not feasible, due to the high cost associated withcomputational representation of all the physical scales. Instead cheaper models are used,including resolution of the boundary layer only in the wall-normal direction, wall shear stressmodels, and hybrid LES-RANS models such as DES [13–17]. For high reynolds numbers, a slipwith friction boundary condition is used [4], corresponding to a simple wall shear stressmodel of the type proposed by Schumann [18]”.We consider zero skin friction, corresponding to a free slip boundary condition, an approachthat previously has been used in [10–12].2
Working Principle:Figure 1: Overview of the WingThe wing of an aircraft is one of the critical part in aerodynamics. The wings are attached toeach side of the fuselage and are the main lifting surfaces that support the airplane in flight.Figure 2 : Working Principle of a WingThe fluid flow over and under the wing surfaces travels at different velocities producing adifference in air pressure low above the wing and high below it. The four forces acting on theairplane during the flight condition are – LIFT, DRAG, THRUST, WEIGHT. LIFT is the component of aerodynamic force perpendicular to the relative wind. DRAG is the component of aerodynamic force parallel to the relative wind. THRUST is the force produced by the engine. It is directed forward along theaxis of the engine. WEIGHT is the force directed downward from the center of mass of theairplane towards the center of the earth.3
Figure 3 : Flow around an AirfoilFigure 4 : Pressure Distribution around an AirfoilThe low pressure exerts a pulling force and the high pressure a pushing force. The liftingforce usually called lift, depends on the shape, area, the angle of attact and on the speed ofthe aircraft. The shape of the wing causes the air streaming above and below the wing totravel at different velocities. According to Bernoulli's principle, it is this difference in airvelocity that produces the difference in air pressure.In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by anairfoil, divided by the drag it creates by moving through the air. An airplane has a high L/Dratio if it produces a large amount of lift or a small amount of drag. A higher or morefavourable L/D ratio is typically one of the major goals in aircraft design.For the gliding flight of birds and airplanes with fixed wings, L/D ratio is typically between 10and 20,4
Aerodynamic Forces and CoefficientsThe force acting on the wing, perpendicular to the direction of the flow is defined as a liftforce (L). The force acting on the wing, parallel to the direction of the flow is defined as adrag force (D). The Lift and drag coefficient, thus represent global mean values in spacetime. The forces depend on number of geometric and flow parameters. Its is advantageousto work with nondimensionalized forces and moments for which most of these parametersdependencies are scaled out.The nondimensional force coefficients are given by:Lift coefficient :Drag coefficient :Where,Lift force :Drag force :Planform :Fluid Velocity :Dynamic pressure :Dimensional analysis reveals that the nondimensional coefficients depends on the angle ofattack , the Reynolds numberFor low speeds flows,, the Mach numberand on the airfoil shape.has virtually no effect and for a given airfoil shape, we have :5
Airfoil Characteritics:The fundamental parameters of airfoil characteristics are :Figure 5 : Airofoil Characteristics1. Angle of Attack2. Aspect Ratio:is the angle between the free-stream velocity and the chord.: Aspect ratio is the ratio between the span of an airfoil and its chord.Wings with larger aspect ratios generate higher lift with less drag and thus have greater flightefficiency. A high aspect ratio wing is efficient because it reduces the formation of the vortexand associated drag.3. Stall: The pressure distribution on the surface of the airfoil is dependent on the angle ofattack. The higher the angle, the greater is the perturbation to the flow, causing highervelocities and lower pressures over the upper surface. At higher angles of attack, the adversepressure gradient become too high, causing the flow to separate from the surface of theairfoil. As the angle of attack is increased, lift is also increased up to a certain angle. Beyondthis angle airflow can no longer follow the contour of the airfoil's upper surface . The regionof flow right next to the upper surface induces reverse flow and the pressure distributionover the upper surface causing a sudden loss of the lifting force. This phenomenon is termedas “Stall”. The Stall angle is the angle at which the flow separation occurs.6
Finite Element Method (FEM)The finite element method (FEM) is a computational technique used to obtain approximatesolutions of boundary value problems in engineering. FEM is used for problems withcomplicated geometries, loadings, and material properties where analytical solutions cannotbe obtained.Figure 6 : Idea of FEMBasic laws of nature are typically expressed in the form of partial differential equations(PDE), such as Navier-Stokes equations of fluid flow. The Finite element method hasemerged as a universal tool for the computational solution of PDEs with a multitude ofapplications in engineering and science. Adaptivity is an important computationaltechnology where the FEM algorithm is automatically tailored to compute a user specifiedoutput of interest to a chosen accuracy, to a minimal computational cost.Figure 7 : Finite Element Process7
In the Finite Element Method (FEM) we approximate the exact solution function “ ” as apiecewise polynomial and compute co-efficients by enforcing orthogonality (Galerkin’sMethod) [13] [14] [15].The basic steps involved in FEM are explained as below [18] :Figure 8 : Finite Element DomainPolynomial Approximation:We seek polynomial approximations “ ” to “ ”. A vector space can be constructed with aset of polynomials on a domainas basis vectors, where function addition and scalarmultiplication satisfy the requirements for a vector space.We can also define an inner product space with theTheinner product generates theJust like ininner product defined as:norm:we define orthogonality between two vectors as :8
The Cauchy-Schwartz inequality is given by:Polynomial vector spaceconsists of polynomials:One basis is the monomials:Piecewise linear polynomials:Global polynomials on the whole domainled to vector space). Only way of refining approximate solution(monomials basis:is by increasing. We insteadlook at piecewise polynomials.Partition domainnodesinto mesh:by placing. We define polynomial function on each subintervalwith lengthFigure 9 : Global basis "tent" function9
Nodal Basis:Basis function:Vector Space of continuous piecewise linear polynomials:with basis,number ofnodes in mesh.Figure 10 : Piecewise linear polynomialsPiecewise linear function:We define the residual functionfor a differential equationas :,We can thus define an equation with exact solutionas:10
Galerkin’s method:We seek a solutionin finite element vector spaceWe require the residual to be orthogonal toof the form::This form is also known as the ”Weak formulation”.For terms inwith two derivatives we perform integration by parts to move onederivative to the test function.In a nutshell the Mathematical Model Formulation for our case is described as below:Method – PDEFor a given differential equation,Function Spaceand Discrete function Space,Weak form of the PDE is given by:Numerical ApproximationThe Finite Element Method is defined by:Where Discrete Space,11
Numerical Approximation applied to Fluid flowRefer Eq. (i) in page no.23 and Eq. (ii) in page no.27Error EstimationWe follow the general framework for a posteriori error estimation based on the solution ofassociated dual problems.We use an A Posteriori Error Estimate , whereof interest.is the error andis an output functionalResidual:Primal Problem:Dual Problem:A Posteriori Error Estimate can be re-written as:Further estimates (see [4]) results in the following Error Indicator:12
Adaptive AlgorithmIn practice, the dual solution is approximated by a similar finite element method as we usefor the primal problem, linearized at the primal solution. Based on the a posteriori errorindicator we can then form adaptive algorithms for how to construct finite element meshesoptimized to approximate the functional.Starting from an initial coarse mesh, one simple such algorithm implemented in Unicorntakes the form: let k 0 then do :Adaptive mesh refinement Algorithm1. For the mesh2. Ifcompute the primal problem and the dual problem.then stop, else:3. Mark some chosen percentage of the elements with highest4. Generate the refined meshfor refinement, set k k 1, and go to 1.13
3.NACA AirfoilDuring the initial stage of our project, we had to choose a wing suitable for projectspecifications. A wing having high aspect ratio (HR 5), Reynolds number of range (Re) 10 6– 10 7, published data and geometry modifications are permitted. NTNU had two wingsprototypes at their inventory. Considering our project specifications, NTNU proposed twowing prototypes:1. “Stratford” wing, developed at NTNU and Confidential (Re 0.8M). As it was acustom wing developed at NTNU, we were not allowed to do any geometrymodifications.2. “NACA64 (2)-415” wing - high aspect ratio standard wing (Re 0.5M). We wereallowed to make the geometry modifications.The specifications of the NACA wing were in-line with our project specifications. Based onthe cost estimation, time limitations and the specifications, we decided to use the “NACA64(2)-415 wing”, for our project.NomenclatureFigure 11 : Cambered Airfoil GeometryThe figure above shows the key terms use
Experimental and Numerical investigation were executed in collaboration with KTH – CTL and Schlumberger. Experimental investigations were conducted at NTNU which was funded by Schlumberger. The numerical investigation was executed with the massively parallel unified continuum ad
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