Numerical Simulation of Dynamic Stall Around an Airfoil in Darrieus Motion

1999 ◽  
Vol 121 (1) ◽  
pp. 69-76 ◽  
Author(s):  
A. Allet ◽  
S. Halle´ ◽  
I. Paraschivoiu
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eddy Viscosity Model ◽  
Minimum Residual ◽  
Turbulence Effects ◽  
Numerical Solver ◽  
Naca 0015

The objective of this study is to investigate the two-dimensional unsteady flow around an airfoil undergoing a Darrieus motion in dynamic stall conditions. For this purpose, a numerical solver based on the solution of the Reynolds-averaged Navier-Stokes equations expressed in a streamfunction-vorticity formulation in a non-inertial frame of reference was developed. The governing equations are solved by the streamline upwind Petrov-Galerkin finite element method (FEM). Temporal discretization is achieved by second-order-accurate finite differences. The resulting global matrix system is linearized by the Newton method and solved by the generalized minimum residual method (GMRES) with an incomplete triangular factorization preconditioning (ILU). Turbulence effects are introduced in the solver by an eddy viscosity model. Our investigation centers on an evaluation of the algebraic Cebeci-Smith model (CSM) and the nonequilibrium Johnson-King model (JKM). In an effort to predict dynamic stall features on rotating airfoils, first we present some testing results concerning the performance of both turbulence models for the flat plate case. Then, computed flow structure together with aerodynamic coefficients for a NACA 0015 airfoil in Darrieus motion under dynamic stall conditions are presented.

Navier-Stokes Simulation of the Flow Around an Airfoil in Darrieus Motion

1994 ◽  
Vol 116 (4) ◽  
pp. 870-876 ◽  
Author(s):  
Ko-Foa Tchon ◽  
Ion Paraschivoiu
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
External Boundary ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Infinite Elements ◽  
Quadrilateral Elements ◽  
Minimum Residual ◽  
Naca 0015 ◽  
First Time

In order to study the dynamic stall phenomenon on a Darrieus wind turbine, the incompressible flow field around a moving airfoil is simulated using a noninertial stream function-vorticity formulation of the two-dimensional unsteady Navier-Stokes equations. Spatial discretization is achieved by the streamline upwind Petrov-Galerkin finite element method on a hybrid mesh composed of a structured region of quadrilateral elements in the vicinity of solid boundaries, an unstructured region of triangular elements elsewhere, and a layer of infinite elements surrounding the domain and projecting the external boundary to infinity. Temporal discretization is achieved by an implicit second order finite difference scheme. At each time step, a nonlinear algebraic system is solved by a Newton method. To accelerate computations, the generalized minimum residual method with an incomplete triangular factorization preconditioning is used to solve the linearized Newton systems. The solver is applied to simulate the flow around a NACA 0015 airfoil in Darrieus motion and the results are compared to experimental observations. To the authors’ knowledge, it is the first time that the simulation of such a motion has been performed using the Navier-Stokes equations.

Steady and Dynamic Stall Analysis of the NLR 7301 Airfoil

1999 ◽  
Author(s):  
Stefan Weber ◽  
Max F. Platzer
Keyword(s):  
Stokes Equations ◽  
Input Parameter ◽  
Hysteresis Loops ◽  
Turbulence Models ◽  
Boundary Layer Transition ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Layer Transition ◽  
Navier Stokes Equations ◽  
The One

The static and dynamic stall behavior of the supercritical NLR 7301 airfoil is analyzed with a 2D thin-layer Navier-Stokes code. The code solves the compressible Reynolds-averaged Navier-Stokes equations with an upwind biased numerical scheme in combination with the Baldwin-Lomax or the Baldwin-Barth turbulence models. The effect of boundary layer transition is incorporated using the transition length model of Gostelow et al. The transition onset location is determined with Michel’s formula or it can be specified as an input parameter. The two turbulence models yield significantly different steady-state lift coefficients at incidences greater than 8 degrees. Also, the lift hysteresis loops are strongly affected by the choice of the turbulence model. The use of the one-equation Baldwin-Barth model together with the Gostelow transition model is found to give substantially better agreement with the experimental data of McCroskey et al. than the Baldwin-Lomax model.

Effect of the turbulence models on Rushton turbine generated flow in a stirred vessel

2011 ◽  
Vol 1 (4) ◽  
Author(s):  
Wajdi Chtourou ◽  
Meriem Ammar ◽  
Zied Driss ◽  
Mohamed Abid
Keyword(s):  
Dissipation Rate ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stirred Vessel ◽  
Rushton Turbine ◽  
Numerical Predictions ◽  
Volume Method

AbstractIn this paper, we performed a comparison of four turbulence models using for numerical simulation of the hydrodynamic structure generated by a Rushton turbine in a cylindrical tank. The finite volume method was employed to solve the Navier-Stokes equations governing the transport of momentum. In this study four closure models tested were: k-ɛ standard, k-ɛ RNG, k-ɛ Realizable and RSM (Reynolds Stress Model). MRF (Multi Reference Frame) technique was used with FLUENT software package. The present work aimed to provide improved predictions of turbulent flow in a stirred vessel and in particular to assess the ability to predict the dissipation rate of turbulent kinetic energy (e) that constitutes a most stringent test of prediction capability due to the small scales at which dissipation takes place. The amplitude of local and overall dissipation rate is shown to be strongly dependent on the choice of turbulence model. The numerical predictions were compared with literature results for comparable configurations and with experimental data obtained using Particle Image Velocimetry (PIV). A very good agreement was found with regards to turbulence.

scholarly journals Viscous Flow Calculations in Turbomachinery Channels

1989 ◽  
Author(s):  
Francesco Martelli ◽  
Vittorio Michelassi
Keyword(s):  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Axisymmetric Flow ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Algebraic Expression ◽  
Two Dimensional ◽  
Approximate Factorization ◽  
Navier Stokes Equations ◽  
Flow Configurations

An implicit procedure based on the artificial compressibility formulation is presented for the numerical solution of the two-dimensional incompressible steady Navier-Stokes equations in the presence of large separated regions. Turbulence effects are accounted for by the Chien low Reynolds number form of the K-ε turbulence model and the Baldwin-Lomax algebraic expression for turbulent viscosity. The governing equations are written in conservative form and implicitly solved in fully coupled form using the approximate factorization technique. Preliminary tests were carried out in a laminar flow regime to check the accuracy and stability of the method in two-dimensional and cylindrical axisymmetric flow configurations. After testing in laminar and turbulent flow regimes and comparing the two turbulence models, the code was successfully applied to an actual gas turbine diffuser at low Mach numbers.

scholarly journals Enhanced Physics-Based Numerical Schemes for Two Classes of Turbulence Models

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Leo G. Rebholz
Keyword(s):  
Finite Element ◽  
Differential Operator ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Numerical Schemes ◽  
Discrete Laplacian ◽  
Navier Stokes Equations ◽  
Approximate Deconvolution ◽  
Finite Element Schemes

We present enhanced physics-based finite element schemes for two families of turbulence models, the models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz (2007), that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The schemes' development requires carefully chosen discrete curl, discrete Laplacian, and discrete filtering operators, in order to permit the necessary differential operator commutations.

Dynamic Stall Control by Undulatory Deformation

2013 ◽  
Vol 444-445 ◽  
pp. 299-303
Author(s):  
Lan Ge ◽  
Wen Rong Hu
Keyword(s):  
Stokes Equations ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Reynolds Average Navier Stokes ◽  
Navier Stokes Equations ◽  
Stall Angle ◽  
Stall Control ◽  
Reynolds Average ◽  
High Angles Of Attack ◽  
Better Than

Dynamic stall can delay the stall of wings and airfoils that are rapidly pitched beyond the static stall angle. A new method of active dynamic stall control by the undulatory foil was proposed in this paper. The study was based on solving unsteady Reynolds-Average Navier-Stokes equations. Comparisons of the effectiveness of pitching foils and undulatory foils on dynamic stall control in both light stall and deep stall were conducted. The undulatory foils with various controllable parameters were further discussed. The results showed that the performance of undulatory foils is much better than that of the rigid pitching foil at high angles of attack either in the light stall or in the deep stall situation.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

1997 ◽  
Vol 119 (4) ◽  
pp. 900-905 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Grid Algorithm ◽  
High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

Computational Analysis of a Inverted Double-Element Airfoil in Ground Effect

2006 ◽  
Vol 128 (6) ◽  
pp. 1172-1180 ◽  
Author(s):  
Stephen Mahon ◽  
Xin Zhang
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Near Field ◽  
Turbulence Models ◽  
Ground Effect ◽  
Wake Flow ◽  
Navier Stokes ◽  
Main Element ◽  
Ride Height ◽  
Navier Stokes Equations

The flow around an inverted double-element airfoil in ground effect was studied numerically, by solving the Reynolds averaged Navier-Stokes equations. The predictive capabilities of six turbulence models with regards to the surface pressures, wake flow field, and sectional forces were quantified. The realizable k−ε model was found to offer improved predictions of the surface pressures and wake flow field. A number of ride heights were investigated, covering various force regions. The surface pressures, sectional forces, and wake flow field were all modeled accurately and offered improvements over previous numerical investigations. The sectional forces indicated that the main element generated the majority of the downforce, whereas the flap generated the majority of the drag. The near field and far field wake development was investigated and suggestions concerning reduction of the wake thickness were offered. The main element wake was found to greatly contribute to the overall wake thickness with the contribution increasing as the ride height decreased.

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