Reduced-order modelling of the flow around a high-lift configuration with unsteady Coanda blowing

2016 ◽  
Vol 800 ◽  
pp. 72-110 ◽  
Author(s):  
Richard Semaan ◽  
Pradeep Kumar ◽  
Marco Burnazzi ◽  
Gilles Tissot ◽  
Laurent Cordier ◽  
...  
Keyword(s):  
Transient Flow ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Mean Field ◽  
Galerkin Projection ◽  
Validation Dataset ◽  
Model Parameters ◽  
High Lift ◽  
Modal Expansion ◽  
Low Dimensional

We propose a hierarchy of low-dimensional proper orthogonal decomposition (POD) models for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. The modal expansion comprises actuation modes as a lifting method for wall actuation following Graham et al. (Intl J. Numer. Meth. Engng, vol. 44 (7), 1999, pp. 945–972) and Kasnakoğlu et al. (Intl J. Control, vol. 81 (9), 2008, pp. 1475–1492). A novel element is separate actuation modes for different frequencies. The structure of the dynamic model rests on a Galerkin projection using the Navier–Stokes equations, simplifying mean-field considerations, and a stochastic term representing the background turbulence. The model parameters are identified with a data assimilation (4D-Var) method. We propose a model hierarchy from a linear oscillator explaining the suppression of vortex shedding by blowing to a fully nonlinear model resolving unactuated and actuated transients with steady and high-frequency modulation of blowing. The models’ accuracy is assessed through the mode amplitudes and an estimator for the lift coefficient. The robustness of the model is physically justified, and then observed for the training and the validation dataset.

Modelling Turbulent Flow in Deformable Highly Porous Seabed and Structures

2018 ◽  
Author(s):  
Hisham Elsafti ◽  
Hocine Oumeraci
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Stokes Equations ◽  
Pore Fluid ◽  
Navier Stokes ◽  
Model Parameters ◽  
Navier Stokes Equations ◽  
Deformable Porous Media ◽  
Physical Experiments ◽  
Fluid Coupling

In this study, the fully-coupled and fully-dynamic Biot governing equations in the open-source geotechFoam solver are extended to account for pore fluid viscous stresses. Additionally, turbulent pore fluid flow in deformable porous media is modeled by means of the conventional eddy viscosity concept without the need to resolve all turbulence scales. A new approach is presented to account for porous media resistance to flow (solid-to-fluid coupling) by means of an effective viscosity, which accounts for tortuosity, grain shape and local turbulences induced by flow through porous media. The new model is compared to an implemented extended Darcy-Forchheimer model in the Navier-Stokes equations, which accounts for laminar, transitional, turbulent and transient flow regimes. Further, to account for skeleton deformation, the porosity and other model parameters are updated with regard to strain of geomaterials. The presented model is calibrated by means of available results of physical experiments of unidirectional and oscillatory flows.

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

The dynamics of coherent structures in the wall region of a turbulent boundary layer

1988 ◽  
Vol 192 ◽  
pp. 115-173 ◽  
Author(s):  
Nadine Aubry ◽  
Philip Holmes ◽  
John L. Lumley ◽  
Emily Stone
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Outer Part ◽  
Streamwise Vortex ◽  
Decomposition Theorem ◽  
Chaotic Regime ◽  
Galerkin Projection ◽  
Wall Region ◽  
Low Dimensional

We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem (Lumley 1967, 1981). We truncate the representation to obtain low-dimensional sets of ordinary differential equations, from the Navier–Stokes equations, via Galerkin projection. The experimentally determined eigenfunctions of Herzog (1986) are used; these are in the form of streamwise rolls. Our model equations represent the dynamical behaviour of these rolls. We show that these equations exhibit intermittency, which we analyse using the methods of dynamical systems theory, as well as a chaotic regime. We argue that this behaviour captures major aspects of the ejection and bursting events associated with streamwise vortex pairs which have been observed in experimental work (Kline et al. 1967). We show that although this bursting behaviour is produced autonomously in the wall region, and the structure and duration of the bursts is determined there, the pressure signal from the outer part of the boundary layer triggers the bursts, and determines their average frequency. The analysis and conclusions drawn in this paper appear to be among the first to provide a reasonably coherent link between low-dimensional chaotic dynamics and a realistic turbulent open flow system.

Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour

1994 ◽  
Vol 258 ◽  
pp. 1-29 ◽  
Author(s):  
Mojtaba Rajaee ◽  
Sture K. F. Karlsson ◽  
Lawrence Sirovich
Keyword(s):  
Shear Flow ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Large Fraction ◽  
Galerkin Projection ◽  
Basis Set ◽  
Order System ◽  
Instability Wave ◽  
Dynamical Equations ◽  
Low Dimensional

The snapshot form of the Karhunen-Loéve (K–L) expansion has been applied to twodimensional, two-component hot-wire data from the region of a weakly pertubed free shear layer that includes the first pairing process. Low-level external perturbation was provided by a loudspeaker driven by a computer-generated signal composed of two sine waves of equal amplitude at the frequencies of the naturally developing fundamental instability wave and its first subharmonic, separated by a controllable initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-dimensional empirical eigenfunction space is obtained which describes the shear-flow coherent structures well. Galerkin projection of the Navier-Stokes equations onto this basis set of principal eigenfunction modes results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent structures associated with eigenfunctions. Finally the simulation, as obtained from the system of dynamical equations, is shown to compare reasonably well with the experiments.

REDUCED BASISA POSTERIORIERROR BOUNDS FOR THE STOKES EQUATIONS IN PARAMETRIZED DOMAINS: A PENALTY APPROACH

2011 ◽  
Vol 21 (10) ◽  
pp. 2103-2134 ◽  
Author(s):  
ANNA-LENA GERNER ◽  
KAREN VEROY
Keyword(s):  
Error Bounds ◽  
Stokes Equations ◽  
Posteriori Error ◽  
Galerkin Projection ◽  
Penalty Parameter ◽  
A Posteriori ◽  
Reduced Basis ◽  
A Posteriori Error ◽  
A Posteriori Error Bounds ◽  
Low Dimensional

We present reduced basis approximations and associated rigorous a posteriori error bounds for the Stokes equations in parametrized domains. The method, built upon the penalty formulation for saddle point problems, provides error bounds not only for the velocity but also for the pressure approximation, while simultaneously admitting affine geometric variations with relative ease. The essential ingredients are: (i) dimension reduction through Galerkin projection onto a low-dimensional reduced basis space; (ii) stable, good approximation of the pressure through supremizer-enrichment of the velocity reduced basis space; (iii) optimal and numerically stable approximations identified through an efficient greedy sampling method; (iv) certainty, through rigorous a posteriori bounds for the errors in the reduced basis approximation; and (v) efficiency, through an offline-online computational strategy. The method is applied to a flow problem in a two-dimensional channel with a (parametrized) rectangular obstacle. Numerical results show that the reduced basis approximation converges rapidly, the effectivities associated with the (inexpensive) rigorous a posteriori error bounds remain good even for reasonably small values of the penalty parameter, and that the effects of the penalty parameter are relatively benign.

Computational Investigation of the Slat Blowing Control for High-Lift Airfoil

2011 ◽  
Vol 138-139 ◽  
pp. 223-228
Author(s):  
Pei Qing Liu ◽  
Yan Xiang Cui ◽  
Liang Wang ◽  
Qiu Lin Qu
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Lower Surface ◽  
Navier Stokes ◽  
Computational Investigation ◽  
High Lift ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Computational Fluid Dynamics Cfd ◽  
A New Technique

Based on the characteristics of blowing control, a new technique was put forward to weaken slat cove separation and reduce noise. The effect of the slat blowing control on lift performance, the flow field and noise with a three-element high lift aerofoil was investigated by using the computational fluid dynamics (CFD) code of Fluent and the Reynolds-averaged Navier-Stokes equations. The blowing apertures were set on the lower surface of the slat. By using the slat blowing technique, the slat cove separation can be controlled efficiently and the lift coefficient increased. The aerodynamic performance varies with different blowing flow rates and angles of attack.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

scholarly journals COMPUTATIONAL FLUID DYNAMICS STUDY OF DUSTY AIR FLOW OVER NACA 63415 AIRFOIL FOR WIND TURBINE APPLICATIONS

2017 ◽  
Vol 79 (7-3) ◽  
Author(s):  
Iham F. Zidane ◽  
Khalid M. Saqr ◽  
Greg Swadener ◽  
Xianghong Ma ◽  
Mohamed F. Shehadeh
Keyword(s):  
Numerical Simulation ◽  
Wind Turbine ◽  
South African ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Turbine Blades ◽  
Aerodynamic Performance ◽  
Accurate Estimation ◽  
African Countries ◽  
Sand Particles

Gulf and South African countries have enormous potential for wind energy. However, the emergence of sand storms in this region postulates performance and reliability challenges on wind turbines. This study investigates the effects of debris flow on wind turbine blade performance. In this paper, two-dimensional incompressible Navier-Stokes equations and the transition SST turbulence model are used to analyze the aerodynamic performance of NACA 63415 airfoil under clean and sandy conditions. The numerical simulation of the airfoil under clean surface condition is performed at Reynolds number 460×103, and the numerical results have a good consistency with the experimental data. The Discrete Phase Model has been used to investigate the role sand particles play in the aerodynamic performance degradation. The pressure and lift coefficients of the airfoil have been computed under different sand particles flow rates. The performance of the airfoil under different angle of attacks has been studied. Results showed that the blade lift coefficient can deteriorate by 28% in conditions relevant to the Gulf and South African countries sand storms. As a result, the numerical simulation method has been verified to be economically available for accurate estimation of the sand particles effect on the wind turbine blades.

On Low-Dimensional Galerkin Modeling of Confined Twin-Jet Flow and Heat Transfer

2001 ◽  
Author(s):  
H. Gunes ◽  
K. Gocmen ◽  
L. Kavurmacioglu
Keyword(s):  
Heat Transfer ◽  
Jet Flow ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Flow And Heat Transfer ◽  
Galerkin Models ◽  
Velocity And Temperature Fields ◽  
Low Dimensional

Abstract The two-dimensional incompressible non-isothermal confined twin-jet flow has been numerically studied in the transitional flow regime by a finite volume technique. Results have been obtained for the velocity and temperature distributions close to the onset of temporal oscillations. Next, the proper orthogonal decomposition (POD) is applied to the instantaneous flow and temperature data to obtain POD-based basis functions for both velocity and temperature fields. These basis functions are capable to identify the coherent structures in the velocity and temperature fields. The low-dimensional Galerkin models of the full Navier-Stokes and energy equations are constructed by the Galerkin projection onto basis functions. Since the low-dimensional Galerkin models are much easier to analyze than the full governing equations, basic insights into important mechanisms of dynamically complex flow and heat transfer (e.g. flow instabilities) can be easily studied by these models. The numerical implications, the validity of the models and their performance characteristics are discussed.

scholarly journals Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition

2009 ◽  
Vol 629 ◽  
pp. 41-72 ◽  
Author(s):  
ALEXANDER HAY ◽  
JEFFREY T. BORGGAARD ◽  
DOMINIQUE PELLETIER
Keyword(s):  
Sensitivity Analysis ◽  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Selection Step ◽  
Low Dimensional ◽  
Proper Orthogonal

The proper orthogonal decomposition (POD) is the prevailing method for basis generation in the model reduction of fluids. A serious limitation of this method, however, is that it is empirical. In other words, this basis accurately represents the flow data used to generate it, but may not be accurate when applied ‘off-design’. Thus, the reduced-order model may lose accuracy for flow parameters (e.g. Reynolds number, initial or boundary conditions and forcing parameters) different from those used to generate the POD basis and generally does. This paper investigates the use of sensitivity analysis in the basis selection step to partially address this limitation. We examine two strategies that use the sensitivity of the POD modes with respect to the problem parameters. Numerical experiments performed on the flow past a square cylinder over a range of Reynolds numbers demonstrate the effectiveness of these strategies. The newly derived bases allow for a more accurate representation of the flows when exploring the parameter space. Expanding the POD basis built at one state with its sensitivity leads to low-dimensional dynamical systems having attractors that approximate fairly well the attractor of the full-order Navier–Stokes equations for large parameter changes.

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