Modelling the Flow Around Airfoils Equipped with Vortex Generators Using a Modified 2D Navier–Stokes Solver

2005 ◽  
Vol 127 (2) ◽  
pp. 223-233 ◽  
Author(s):  
I. G. Nikolaou ◽  
E. S. Politis ◽  
P. K. Chaviaropoulos
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Vortex Generators ◽  
Navier Stokes ◽  
Complex Flow ◽  
Wind Turbine Blades ◽  
Production Term

Vortex generators (VGs) are commonly used for trimming the aerodynamic and aeroelastic performance of wind turbine blades by delaying flow separation. There is therefore a need for the development of reliable, still computationally affordable, models for blade designers to use to predict and enhance the aerodynamic characteristics of airfoils equipped with VGs. Such a model is proposed in the present paper, addressing in particular near-stall and post-stall airfoil performance. Starting from the three-dimensional Navier–Stokes equations that essentially describe the complex flow around a blade/VG configuration, a spanwise averaging procedure is applied, resulting in an equivalent set of two-dimensional equations, enriched with extra source terms. These terms are modelled using elementary vortex flow theory. In turbulent flows, the production term of the turbulent kinetic energy is also augmented by the vorticity induced by the VG. The model is evaluated by studying the flow past a blade section with and without VGs. An analysis of the performance of nine alternative VG configurations is also presented to demonstrate the sensitivity of the airfoil polars to the VG geometric parameters.

Investigating Three-Dimensional and Rotational Effects on Wind Turbine Blades by Means of a Quasi-3D Navier-Stokes Solver

2000 ◽  
Vol 122 (2) ◽  
pp. 330-336 ◽  
Author(s):  
P. K. Chaviaropoulos ◽  
M. O. L. Hansen
Keyword(s):  
Wind Turbine ◽  
Stokes Equations ◽  
Twist Angle ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Wind Turbine Blades ◽  
Mean Values ◽  
Power Curves

Three-dimensional and rotational viscous effects on wind turbine blades are investigated by means of a quasi-3D Navier-Stokes model. The governing equations of the model are derived from the 3-D primitive variable Navier-Stokes equations written in cylindrical coordinates in the rotating frame of reference. The latter are integrated along the radial direction and certain assumptions are made for the mean values of the radial derivatives. The validity of these assumptions is cross-checked through fully 3-D Navier-Stokes calculations. The resulting quasi-3D model suggests that three-dimensional and rotational effects be strongly related to the local chord by radii ratio and the twist angle. The equations of the model are numerically integrated by means of a pressure correction algorithm. Both laminar and turbulent flow simulations are performed. The former is used for identifying the physical mechanism associated with the 3-D and rotational effects, while the latter for establishing semiempirical correction laws for the load coefficients, based on 2-D airfoil data. Comparing calculated and measured power curves of a stall controlled wind turbine, it is shown that the suggested correction laws may improve significantly the accuracy of the predictions. [S0098-2202(00)02702-4]

A Computational Analysis of Flow Field in Twin-Track Subway Tunnel to Improve Air Quality

2013 ◽  
Vol 319 ◽  
pp. 599-604
Author(s):  
Makhsuda Juraeva ◽  
Kyung Jin Ryu ◽  
Sang Hyun Jeong ◽  
Dong Joo Song
Keyword(s):  
Air Quality ◽  
Computational Model ◽  
Stokes Equations ◽  
Ventilation System ◽  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Subway Tunnel ◽  
Air Supply ◽  
And Performance

A computational model of existing Seoul subway tunnelwas analyzed in this research. The computational model was comprised of one natural ventilationshaft, two mechanical ventilationshafts, one mechanical airsupply, a twin-track tunnel, and a train. Understanding the flow pattern of the train-induced airflow in the tunnel was necessary to improve ventilation performance. The research objective wasto improve the air quality in the tunnel by investigating train-induced airflow in the twin-track subway tunnel numerically. The numerical analysis characterized the aerodynamic behavior and performance of the ventilation system by solving three-dimensional turbulent Reynolds-averaged Navier-Stokes equations. ANSYS CFX software was used for the computations. The ventilation and aerodynamic characteristics in the tunnel were investigated by analyzing the mass flowrateat the exits of the ventilation mechanicalshafts. As the train passed the mechanical ventilation shafts, the amount of discharged-air in the ventilationshafts decreased rapidly. The air at the exits of the ventilation shafts was gradually recovered with time, after the train passed the ventilation shafts. The developed mechanical air-supply for discharging dusty air and supplying clean airwas investigated.The computational results showed that the developed mechanical air-supplycould improve the air quality in the tunnel.

scholarly journals Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

2004 ◽  
Vol 10 (5) ◽  
pp. 373-385
Author(s):  
Steffen Kämmerer ◽  
Jürgen F. Mayer ◽  
Heinz Stetter ◽  
Meinhard Paffrath ◽  
Utz Wever ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Flow Solver ◽  
Flow Simulations ◽  
Sensitivity Equations

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades.The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution.This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are presented. Flow simulations and sensitivity calculations are presented for different test cases and parameters. The validation of the computed sensitivities is performed by means of finite differences.

Flow Characteristics in a Three-Dimensional Rectangular Channel With a Pair of Ribs Placed Symmetrically at the Channel Walls

2000 ◽  
Author(s):  
M. Singh ◽  
P. K. Panigrahi ◽  
G. Biswas
Keyword(s):  
Heat Transfer ◽  
Large Scale ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Complex Flow ◽  
Energy Equations

Abstract A numerical study of rib augmented cooling of turbine blades is reported in this paper. The time-dependent velocity field around a pair of symmetrically placed ribs on the walls of a three-dimensional rectangular channel was studied by use of a modified version of Marker-And-Cell algorithm to solve the unsteady incompressible Navier-Stokes and energy equations. The flow structures are presented with the help of instantaneous velocity vector and vorticity fields, FFT and time averaged and rms values of components of velocity. The spanwise averaged Nusselt number is found to increase at the locations of reattachment. The numerical results are compared with available numerical and experimental results. The presence of ribs leads to complex flow fields with regions of flow separation before and after the ribs. Each interruption in the flow field due to the surface mounted rib enables the velocity distribution to be more homogeneous and a new boundary layer starts developing downstream of the rib. The heat transfer is primarily enhanced due to the decrease in the thermal resistance owing to the thinner boundary layers on the interrupted surfaces. Another reason for heat transfer enhancement can be attributed to the mixing induced by large-scale structures present downstream of the separation point.

scholarly journals Numerical Investigation on Flapping Aerodynamic Performance of Dragonfly Wings in Crosswind

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Chao Wang ◽  
Rui Zhang ◽  
Chaoying Zhou ◽  
Zhenzhong Sun
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Lateral Force ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Aerodynamic Forces ◽  
Sideslip Angle ◽  
Flight Direction ◽  
Time Average ◽  
Dragonfly Wings

Numerical simulations are performed to investigate the influence of crosswind on the aerodynamic characteristics of rigid dragonfly-like flapping wings through the solution of the three-dimensional unsteady Navier-Stokes equations. The aerodynamic forces, the moments, and the flow structures of four dragonfly wings are examined when the sideslip angle ϑ between the crosswind and the flight direction varied from 0o to 90o. The stability of the dragonfly model in crosswind is analyzed. The results show that the sideslip angle ϑ has a little effect on the total time-average lift force but significant influence on the total time-average thrust force, lateral force, and three-direction torques. An increase in the sideslip angle gives rise to a larger total time-average lateral force and yaw moment. These may accelerate the lateral skewing of the dragonfly, and the increased rolling and pitching moments will further aggravate the instability of the dragonfly model. The vorticities and reattached flow on the wings move laterally to one side due to the crosswind, and the pressure on wing surfaces is no longer symmetrical and hence, the balance between the aerodynamic forces of the wings on two sides is broken. The effects of the sideslip angle ϑ on each dragonfly wing are different, e.g., ϑ has a greater effect on the aerodynamic forces of the hind wings than those of the fore wings. When sensing a crosswind, it is optimal to control the two hind wings of the bionic dragonfly-like micro aerial vehicles.

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.

Study of Losses in a Leakage Flow Through the Passage of Shrouded Turbine Blades With Swirl Velocity

2001 ◽  
Author(s):  
Yumin Xiao ◽  
R. S. Amano
Keyword(s):  
Turbine Blades ◽  
Three Dimensional ◽  
Major Effect ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Complex Flow ◽  
Local Pressure ◽  
Leakage Flow Rate ◽  
Calculation Results

In this paper the study of the flows over shrouded turbine blades with staggered-seals is presented by computing the three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations along with a compressible non-linear k-ε turbulence model. The swirl of the blade is coupled into the calculation. A multi-zone technique is used to generate the grids in the complex flow channel. The calculation results show that the leakage flow rate in the seal-channel is dominated by the pressure difference. It was also observed that the circumferential momentum transfer in the channel is very slow in the region in front of the seal tooth. The major effect of the rotating blade is the increase of local pressure distribution along the shrouded tip clearance path. However, the swirl motion of the blade tip does not significantly change the flow pattern in the axial-radial plane.

Heat Transfer in Film-Cooled Turbine Blades

1993 ◽  
Author(s):  
Vijay K. Garg ◽  
Raymond E. Gaugler
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Film Cooling ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Explicit Finite Difference ◽  
Control Volumes

In order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine blades, a three-dimensional Navier-Stokes code has been developed. An existing code (Chima and Yokota, 1990) has been modified for the purpose. The code is an explicit finite difference code with an algebraic turbulence model. The thin-layer Navier-Stokes equations are solved using a general body-fitted coordinate system. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the blade surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison with experimental data is fair. Further validation of the code is required, however, and in this respect, there is an urgent need for detailed experimental data on actual turbine blades.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

High Fidelity Simulation of Safety Relief Valve Internal Flows

2015 ◽  
Author(s):  
Yunchao Yang ◽  
Alexis Lefebvre ◽  
Ge-Cheng Zha ◽  
Qing-Feng Liu ◽  
Jun Fan ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Weno Scheme ◽  
Inlet Pressure ◽  
Navier Stokes ◽  
Implicit Time ◽  
Complex Flow ◽  
Relief Valve ◽  
Expansion Waves

This paper presents a numerical methodology and simulation for three-dimensional transonic flow in Safety Relief Valves. Simulation of safety relief valve flows is very challenging due to complex flow paths, high pressure variation, supersonic flow with shock and expansion waves, boundary layers, etc. The 3D unsteady Reynolds averaged Navier-Stokes (URANS) equations with one-equation Spalart-Allmaras turbulence model is used. A fifth order WENO scheme for the inviscid flux and a second order central differencing for the viscous terms are employed to discretize the Navier-Stokes equations. The low diffusion E-CUSP scheme used as the approximate Riemann solver suggested by Zha et al. is utilized with the WENO scheme to evaluate the inviscid fluxes. Implicit time marching method with 2nd order temporal accuracy using Gauss-Seidel line relaxation is employed to achieve a fast convergence rate. Parallel computing is implemented to save wall clock simulation time. The valve flows with air under different inlet pressures and temperatures are successfully simulated for the full geometry with all the fine leakage channels. A 3D mesh topology is generated for the complex geometry. Detailed simulations of air flow are accomplished with inlet gauge pressure 0.5MPa and 2.1MPa. The simulated air mass flow rate agrees excellently with the experimental results with an error of 0.26% for the inlet pressure of 0.5Mpa, and an error of 2.5% for the inlet pressure of 2.1MPa. The shock waves and expansion waves downstream of the orifice are very well resolved.

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