Viscous-inviscid Interaction Method Research Articles

Validation of an engineering model for vortex generators in a viscous-inviscid interaction method for airfoil analysis

Validation of an engineering model for vortex generators in a viscous-inviscid interaction method for airfoil analysis

Local simulation of sloshing jet in a rolling tank by viscous-inviscid interaction method

In this paper, the local behavior of the jet induced by the fluid impact is studied by a new viscous-inviscid interaction (VII) method. This method is based on the inviscid Eulerian-Langrangian (IEL) scheme implemented by the boundary element method (BEM), but it places additional sources on the wetted walls to model the viscous flow within the thin boundary layer. The volume of fluid (VOF) method is also carried out to compare the numerical boundary-layer patterns. The present method not only shows good agreement with the experimental results but also remains very efficient.

Nestabilnost nelinearne panel metode sa mešovitim graničnim uslovima

A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interaction method for each station along the wing spanwise direction and Prandtle-Glauert rule for compressibility effect were used to enhance the potential results of the method. The fast turnaround time and the ability to model arbitrary geometries is the goal of the present work. Different airplanes configurations were simulated (DLR-F4, light jet, cargo and four engine commercial airplanes). The results of pressure and forces coefficients were compared with the DLR-F4 airplane. The comparisons showed a satisfying agreement with the experimental data. The method is simple and fast as compared with other singularity methods, which may be dependent as a preliminary method to design aircrafts.

The origin of patch cavitation

The initial form of partial cavitation on axisymmetric bodies in some water tunnel tests is a regular system of patches with the approximately constant azimuthal distance between them. The described numerical simulation shows that the origin of such three-dimensional system is in the relatively small non-axisymmetric regular perturbations of the inflow caused by the shapes of non-circular water tunnel cross sections (these sections were squares or hexagons). Computational prediction of cavitation inception number for patch cavitation is carried out by a viscous-inviscid interaction method that combines three-dimensional analysis of inviscid flows with quasi-two-dimensional analysis of viscous flows. Computational results are compared with the experimental data obtained in 1980s in water tunnels of Applied Physics Laboratory and David Taylor Research Center. The satisfactory agreement of computed and measured data is considered as the proof of the described explanation of the origin of patch cavitation.

Prediction of cavitation inception in slots

Cavitation inception in slots on the flat walls is analyzed in the steady flow approach using a viscous-inviscid interaction method. It was assumed that, in the accordance with known observations, cavities appear as spherical bubbles in the cores of vortices near the slot corners. Computed cavitation inception numbers are compared with published experimental results of other authors within wide ranges of inflow parameters. The comparison shows a satisfactory agreement of computations with the measured data.

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

AbstractAerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.

Improving Airfoil Drag Prediction

An improved formulation of drag estimation for thick airfoils is presented. Drag underprediction in XFOIL-like viscous–inviscid interaction methods can be quite significant for thick airfoils used in wind turbine applications (up to 30%, as seen in the present study). The improved drag formulation predicts the drag accurately for airfoils with reasonably small trailing-edge thicknesses. The derivation of drag correction is based on the difference between the actual momentum loss thickness based on freestream velocity and that based on the velocity at the edge of the boundary layer. The improved formulation is implemented in the most recent versions of XFOIL and RFOIL (an aerodynamic design and analysis method based on XFOIL, developed by a consortium of the Energy Research Centre of the Netherlands, the National Aerospace Laboratory/NLR, and the Delft University of Technology after the Energy Research Centre of the Netherlands acquired the XFOIL code; after 1996, the Energy Research Centre of the Netherlands maintained and improved the tool), and the results are compared with experimental data, results from commercial computational fluid dynamics methods like ANSYS CFX, as well as other methods like the Technical University of Denmark Aeroelastic Design Section (AED)’s EllipSys2D and the National Renewable Energy Centre (CENER)’s Wind Multiblock. The improved version of RFOIL shows good agreement with the experimental data.

Finite-volume scheme for the solution of integral boundary layer equations

An unstructured-mesh finite-volume formulation for the solution of systems of steady conservation laws on embedded surfaces is presented. The formulation is invariant to the choice of local tangential coordinate systems and is stabilized by a novel up-winding scheme applicable also to mixed-hyperbolic systems. The formulation results in a system of non-linear equations which is solved by a quasi-Newton method. While the finite volume scheme is applicable to a range of conservation laws, it is here implemented for the solution of the integral boundary layer equations, as a first step in developing a fully coupled viscous-inviscid interaction method. For validation purposes, integral boundary layer quantities computed using a minimal set of three-dimensional turbulent integral boundary layer equations are compared to experimental data and an established computer code for two-dimensional problems. The validation shows that the proposed formulation is stable, yields a well-conditioned global Jacobian, is conservative on curved surfaces and invariant to rotation as well as convergent with regard to mesh refinement.

Adaptive viscous–inviscid interaction method for analysis of airfoils in ground effect

The behavior of an airfoil in ground proximity is significantly different from out of ground. Therefore, understanding the effect of proximity to ground can help determine its aerodynamic characteristics, which are important design parameters. In this paper, an accurate viscous–inviscid interacting method is investigated as an alternative method to computing heavy Navier–Stokes solution for utilizing in the surface effect zone. The inviscid part is modeled by a 2D panel method, and the viscous part is modeled by solving the integral form of the laminar and turbulent boundary layer equations. Validation of the incompressible 2D version of the written code (so-called WIGPMBL) is carried out against experimental and other numerical codes for different airfoil geometries at various Reynolds numbers. Various aspects of aerodynamic characteristics such as pressure distribution, lift and drag coefficient, transition and separation points of symmetric and asymmetric airfoils have been validated. Consequently, the assessments have verified that the present method has good accuracy for predicting the effect of surface proximity.

Development and Validation of Computational Fluid Dynamics Models for Initial Stages of Cavitation

Various computational fluid dynamics (CFD) models employed for cavitating flows are substantially based on semi-empirical assumptions about cavitation forms and liquid flows around cavitating bodies. Therefore, the model applicability must be validated with experimental data. The stages of validation of the models are analyzed here with data on cavitating hydrofoils and axisymmetric bodies in water. Results of Reynolds-averaged Navier–Stokes (RANS), large-eddy simulation (LES), detached-eddy simulation (DES), and viscous-inviscid interaction methods are compared. The necessity of simultaneous validation of several flow parameters (as cavitation inception number and location of the appearing cavity) is pointed out. Typical uncertainties in water tunnel model test data (water quality, simplified account of wall effect) and possibilities to take them into account are also discussed. The provided comparison with experimental data manifests the impossibility to describe initial stages of cavitating flows using any single model and importance of employment of a combination of models for both the cavitation zones and the flow outside of cavities.

Aerodynamic response of an airfoil section undergoing pitch motion and trailing edge flap deflection: a comparison of simulation methods

AbstractThe study presents and compares aerodynamic simulations for an airfoil section with an adaptive trailing edge flap, which deflects following a smooth deformation shape. The simulations are carried out with three substantially different methods: a Reynolds‐averaged Navier–Stokes solver, a viscous–inviscid interaction method and an engineering dynamic stall model suitable for implementation in aeroelastic codes based on blade element momentum theory. The aerodynamic integral forces and pitching moment coefficients are first determined in steady conditions, at angles of attack spanning from attached flow to separated conditions and accounting for the effects of flap deflection; the steady results from the Navier–Stokes solver and the viscous–inviscid interaction method are used as input data for the simpler dynamic stall model. The paper characterizes then the dynamics of the unsteady forces and moments generated by the airfoil undergoing harmonic pitching motions and harmonic flap deflections. The unsteady aerodynamic coefficients exhibit significant variations over the corresponding steady‐state values. The dynamic characteristics of the unsteady response are predicted with an excellent agreement among the investigated methods at attached flow conditions, both for airfoil pitching and flap deflection. At high angles of attack, where flow separation is encountered, the methods still depict similar overall dynamics, but larger discrepancies are reported, especially for the simpler engineering method. Copyright © 2014 John Wiley & Sons, Ltd.

Boundary Layer Method for Unsteady Transonic Flow

A numerical method for determination of unsteady loads in a 2-D transonic flow, with the occurrence of a shock wave, on a pitching airfoil is demonstrated. The method implements the Euler equations for inviscid region and integral boundary layer equations for the viscous region near the airfoil. The viscous-inviscid interaction method is employed using the transpiration velocity concept on the airfoil contour. The Euler solution is calculated by using the Van Leer flux-vector splitting method on the body-fitted C-grid. The boundary layer model is calculated applying Drela’s model of integral boundary layer equations for the laminar and turbulent flow. The transition from the laminar to the turbulent flow is predicted by the en method. The viscous-inviscid interaction method is made in the direct mode. The results obtained by this method are comparable with the calculated RANS and experimental results, while time and computational costs were lower than for RANS calculations. Generally, the pressure coefficient distribution results showed good agreement with the RANS and experimental results. The method predicted the position of a shock wave to be slightly shifted towards the leading edge of the airfoil with respect to the position obtained by the RANS and experimental results. This indicates that the boundary layer model has a strong influence on the inviscid part of the flow.

Laminar Airfoil Modification Attaining Optimum Drag Reduction by Use of Airfoil Morphing

. Aerodynamic characteristics of the baseline and deformed airfoils have been investigated using a viscous–inviscid interaction method. It is shown that the leadingedge deformation is effective in reducing the drag at the offdesign angle of attack, in comparison with the baseline airfoil. The transition point has been estimated, using a numerical method based on a linear stability theory. The deformationisaneffectivemeanstomove thetransition pointaftontheairfoil,andtheextension ofthe laminar flow area results in a reduction in the drag at the offdesign angle of attack. Nomenclature Cd = drag coefficient Cl = lift coefficient Cp = pressure coefficient based on the freestream static and dynamic pressures c = airfoil chord length, m l = girth of the airfoil at the leading edge, m n = amplification factor Rx = Reynolds number based on ue and coordinate along the airfoil surface measured from the leading edge R� = Reynolds number based on ue and � Rec = Reynolds number based on the chord length t = airfoil half-thickness distribution, m U1 = freestream velocity, m=s ue = local velocity at the edge of the boundary layer, m=s x = Cartesian coordinate along the chord direction, measured from the leading edge of the baseline airfoil, m y = Cartesian coordinate perpendicular to x and measured from the leading edge, m ycamber = airfoil camber line, m Z = Cartesian coordinate parallel to x and

Intermittent Bursting of a Laminar Separation Bubble on an Airfoil

Large eddy simulation of flow around a NACA-0012 airfoil at a Reynolds number of 50,000 has been used to study the behavior of a laminar separation bubble near stall. The effects of the subgrid-scale model and explicit filtering were studied for a test case in which direct numerical simulation results were available. It was found that a method incorporating a mixed-time-scale model in addition to explicit filtering gave improved results compared with a method with filtering alone. Statistical results as well as snapshots of the flow below stall exhibit good agreement with the direct numerical simulations. For a configuration near still, the effect of the spanwise domain width was investigated by increasing the spanwise length from 20 to 50% chord. Two-point velocity correlations showed a significant improvement for the wider computational domain, in which the simulation was able to capture a low-frequency flow oscillation, in which intermittent bursting of the bubble was observed. The bubble bursting observed here is more irregular than in experiments at higher Reynolds number. The amplitude and frequency are compared with experimental results and with an unsteady viscous-inviscid interaction method which is shown to be capable of capturing unsteady behavior during stall.

Calculated Viscous and Scale Effects on Transonic Aeroelasticity

A viscous-inviscid interactive coupling method is used for the computation of unsteady transonic flows. A lagextrainment integral boundary layer method is used with a transonic small disturbance potential code to compute the transonic aeroelastic response for two wing flutter models. By varying the modeled length scale, viscous effects may be studied as the Reynolds number per reference chordlength varies. Appropriate variation of modeled frequencies and generalized masses then allows comparison of responses for varying scales or Reynolds number. Two wing planforms are studied: one a four percent thick swept wing and the other a typical business jet wing. Calculations for both wings show limit cycle oscillations at transonic speeds in the vicinity of minimum flutter speed indices.

Viscous-Inviscid Method for Airfoil Analysis and Design forAviation and Windmills

This study examines an advanced viscous-inviscid interactive method developed for the analysis and design of airfoils in two-dimensional subsonic compressible flow (Ma ∞ <0.4). Inviscid flow is solved with a panel method. The laminar boundary layer is calculated by Thwaites' method. Transition is determined by Michel's relation or the e n method. An integral solution for a turbulent boundary layer is derived from an entrainment equation. Closure conditions are obtained with empirical relations. Singularities near the separation are avoided by inverting the boundary-layer method. Inviscid and viscous flows are coupled with transpiration. The analysis method is used as a black box in the design tasks. The geometry of the starting airfoil is perturbed iteratively by transpiration until the pressure distribution converges to a predefined target This study proposes the necessary degrees of freedom in the target velocity distribution to obtain a closed airfoil. Design cases are included, which support the general applicability and accuracy of the numerical design method.

Calculation of the transonic dip of airfoils using viscous-inviscid aerodynamic interaction method

A numerical procedure for the calculation of the transonic dip of airfoils in the time domain is presented. A viscous-inviscid aerodynamic interaction method is taken to calculate the unsteady aerodynamic loads. In the present case the integral boundary layer equations are coupled with the Transonic Small Disturbance (TSD) Potential Equation. The coupling between structural motion and aerodynamic loads is carried out using State Space equation. It is solved by State Transition Matrix technique. Results are presented for NACA 64A010 and NLR 7301 airfoils with structural data from Isogai and DLR, respectively. Comparisons show good agreement with other numerical results. Certain deviations of experimental data taken from literature need more insight in the detailed test conditions.

Viscous–inviscid method for the simulation of turbulent unsteady wind turbine airfoil flow

A Viscous–inviscid interaction method is presented that allows for the simulation of unsteady airfoil flow in the context of wind turbine applications. The method couples a 2-D external unsteady potential flow to a 2-D unsteady turbulent boundary layer. The separation point on the airfoil leeward side is determined in a self-consistent way from the boundary-layer equations, and the separated flow region is modelled independently. Wake shape and motion are also determined in a self-consistent way, while an unsteady Kutta condition is implemented. The method is able to deal with attached flow and light stall situations characterised by unsteady turbulent boundary-layer separation size up to 50% of the airfoil chord length. The results of the validation campaign show that the method could be used for industrial design purposes because of its numerical robustness, reasonable accuracy, and limited computational time demands.

Viscous single and multicomponent airfoil design with genetic algorithms

An optimization procedure aimed at the design of multicomponent airfoils for high-lift applications is described. The procedure is based on a multiobjective genetic algorithm; two flow solvers have been coupled with the genetic algorithm: a viscous–inviscid interaction method, based on an Euler flow solver and an integral boundary layer routine, and a method based on a full potential flow solver. The first model is used for high-lift configurations, whereas the second is used to optimize transonic performances for cruise configurations. The applications described include both single and multiobjective design of a high-lift multicomponent airfoil, and a multipoint design where the transonic and high-lift requirements are taken into account simultaneously.

Transonic trailing-edge flow

The structure of the flowfield in the vicinity of the trailing edge of a flat plate at zero incidence in mixed transonic flow has been studied using viscous-inviscid interaction methods. The resulting nonlinear partial differential equations governing the flow were solved numerically using finite-difference methods for a range of values of a transonic similarity parameter which occurs in the mathematical formulation of the problem. Of special interest is the formula for the total drag coefficient of the plate as a function of the similarity parameter. Values of the similarity parameter have been chosen to ensure that subcritical, supercritical and mixed flow regimes are all considered.