A framework for optimising aspects of rotor blades

2011 ◽  
Vol 115 (1165) ◽  
pp. 147-161 ◽  
Author(s):  
C. S. Johnson ◽  
G. N. Barakos
Keyword(s):  
Objective Function ◽  
Stokes Equations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Computational Framework ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Artificial Neural ◽  
Optimisation Methods ◽  
Selection Of

AbstractThis work presents a computational framework for the optimisation of various aspects of rotor blades. The proposed method employs CFD combined with artificial neural networks, employed as metamodels, and optimisation methods based on genetic algorithms. To demonstrate this approach, two examples have been used, one is the optimal selection of 4- and 5-digit NACA aerofoils for rotor sections and the other is the optimisation of linear blade twist for rotors in hover. For each case, an objective function was created and the meta-model was subsequently used to evaluate this objective function during the optimisation process. The obtained results agree with real world design examples and theoretical predictions. For the selected cases, the artificial neural network was found to perform adequately though the results required a substantial amount of data for training. The genetic algorithm was found to be very effective in identifying a set of near-optimal parameters. The main CPU cost was associated with the population of the database necessary for the meta-models and this task required CFD computations based on the Reynolds-averaged Navier-Stokes equations. The framework is general enough to allow for several design or optimisation tasks to be carried out and it is based on open-source code made available by the authors.

Fast forced liquid film spreading on a substrate: flow, heat transfer and phase transition

2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN
Keyword(s):  
Heat Transfer ◽  
Phase Transition ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Reynolds Numbers ◽  
Drop Impact ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
Viscous Drop

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.

Advanced Calculation Flutter Procedure Developed for Ultra-Long Last Stage Blades for Steam Turbines

2019 ◽  
Author(s):  
Vaclav Slama ◽  
Bartolomej Rudas ◽  
Ales Macalka ◽  
Jiri Ira ◽  
Antonin Zivny
Keyword(s):  
Stokes Equations ◽  
Damping Ratio ◽  
Rotor Blades ◽  
Numerical Code ◽  
Navier Stokes ◽  
Steam Turbines ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Last Stage ◽  
The Time Domain

Abstract An advanced in-house procedure, which is based on a commercial numerical code, to predict a potential danger of unstalled flutter has been developed and validated. This procedure using a one way decoupled method and a full-scale time-marching 3D viscous model in order to obtain the solution of the Unsteady Reynolds-Averaged Navier-Stokes equations in the time domain thus calculate an aerodynamic work and a damping ratio is used as an essential tool for developing ultra-long last stage rotor blades in low pressure turbine parts for modern steam turbines with a large operating range and an enhanced efficiency. An example is shown on a development of the last stage blade for high backpressures.

Numerical Simulation of Vortex Induced Vibration Using the K-ε Model

2006 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Gisele H. B. Souza ◽  
Carlos Levi
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Real Problem ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Selection Of

Numerical simulations of Vortex Induced Vibration have been failing to duplicate accurately experimental data mostly due to the complexity of the physics involved in the real problem. Therefore, a careful and comprehensive investigation on CFD algorithms is still required to indicate the most suitable numerical scheme to handle such a complicate problem. Grid generation, boundary condition implementation, and coupling between the fluid flow governing equations and body motion equation are known to have strong influence on the qualities of the numerical results. This work presents results obtained from a long-term investigation featuring different CFD methods. The investigations enabled the selection of a very effective algorithm that showed an outstanding agreement between experiment and numerical simulation of the VIV phenomenon. Good agreement is obtained in the entire range of reduced velocity covered by the experimental investigations. The successful algorithm discussed here applies the Beam and Warming implicit scheme to solve the two-dimensional slightly compressible Navier–Stokes equations with the K-ε turbulence model to simulate the turbulent flow at the wake of the cylinder.

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

scholarly journals Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations

2020 ◽  
Author(s):  
Naveed Ahmed ◽  
Gunar Matthies
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Higher Order ◽  
Navier Stokes ◽  
Optimal Error ◽  
Navier Stokes Equations ◽  
Fully Discrete ◽  
Local Projection Stabilization ◽  
Theoretical Predictions ◽  
Stable Pairs

Abstract Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier–Stokes equations. The spatial discretization based on inf–sup stable pairs of finite element spaces is stabilized using a one-level local projection stabilization method. Optimal error bounds for the velocity with constants independent of the viscosity parameter are obtained for both the semidiscrete case and the fully discrete case. Numerical results support the theoretical predictions.

Unsteady Vortices and Blade Loading in a High-Pressure Turbine

2009 ◽  
Author(s):  
Dongil Chang ◽  
Stavros Tavoularis
Keyword(s):  
High Pressure ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Blade Loading ◽  
Pressure Losses ◽  
Horseshoe Vortices

Unsteady flow in a transonic, single-stage, high-pressure, axial turbine has been investigated numerically by solving the URANS (Unsteady Reynolds-Averaged Navier-Stokes) equations with the SST (Shear Stress Transport) turbulence model. Interest has focused on the identification and effects of the quasi-stationary vane and blade horseshoe vortices, vane and blade passage vortices, vane and blade trailing edge vortices, and blade tip leakage vortices. Moreover, two types of unsteady vortices, not discussed explicitly in the previous literature, have been identified and termed “axial gap vortices” and “crown vortices”. All vortices have been clearly and distinctly identified using a modified form of the Q criterion, which is less sensitive to the set threshold than the original version. The use of pathlines and iso-contours of static pressure, axial vorticity and entropy has been further exploited to distinguish the different types of vortices from each other and to mark their senses of rotation and strengths. The influence of these vortices on the entropy distribution at the outlet has been investigated. The observed high total pressure losses in the turbine at blade midspan have been connected to the action of passage vortices. The formation and disappearance processes of unsteady vortices located in the spacing between the stator and the rotor have been time-resolved. These vortices are roughly aligned with the leading edges of the rotor blades and their existence depends on the position of the blade with respect to the upstream vanes. In addition, the present study focuses on the unsteady blade loading that influences vibratory stresses. Contours of the time-dependent surface pressure on the rotor blade have demonstrated the presence of large pressure fluctuations near the front of the blade suction sides; these pressure fluctuations have been associated with the periodic passages of shock waves originating at the vane trailing edges.

Wake Comparison of Open and Ducted Wind Turbines Using Actuator Disc Simulations

2020 ◽  
Author(s):  
Nojan Bagheri-Sadeghi ◽  
Brian T. Helenbrook ◽  
Kenneth D. Visser
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Turbulence Intensity ◽  
Stokes Equations ◽  
Rotor Blades ◽  
Energy Output ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Actuator Disc ◽  
Power And Energy

Abstract Shrouding a wind turbine inside a duct can significantly augment its power and energy output by increasing the mass flow rate through the rotor and decreasing the cut-in speed. Whether this is an advantage in a turbine array depends on the wake recovery behavior and how this compares to open wind turbines. Axisymmetric CFD simulations using the Reynolds-Averaged Navier-Stokes equations with a k–ω SST turbulence closure were used to compare the wake behavior of open and ducted wind turbines. For both cases, the rotor blades were modeled using an actuator disc. Simulations of open wind turbines revealed significant sensitivity of the wake behavior to the mean turbulence intensity at the rotor. Better agreement with experimental data for the far wake was obtained when the turbulence intensity at the rotor was comparable to values measured experimentally. It was observed that compared to an open wind turbine with similar power output, a DWT has a significantly slower wake recovery. This was attributed to the extra momentum deficit of the wake due to the drag force on the duct.

Flow instabilities between two parallel planes semi-obstructed by an easily penetrable porous medium

2011 ◽  
Vol 689 ◽  
pp. 417-433 ◽  
Author(s):  
N. Silin ◽  
J. Converti ◽  
D. Dalponte ◽  
A. Clausse
Keyword(s):  
Porous Medium ◽  
Stokes Equations ◽  
Stability Margin ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Navier Stokes Equations ◽  
Theoretical Predictions ◽  
The Stability ◽  
Cross Section Profile ◽  
Planar Flows

AbstractA study of instabilities in planar flows produced by the presence of a parallel penetrable porous obstruction is presented. The case considered is a flow between parallel plates partially obstructed by a porous medium. The most unstable perturbation modes are obtained solving numerically the eigenvalue problem derived from the linear stability analysis of the two-dimensional Navier–Stokes equations applied to the geometry of interest. The analysis leads to an extended Orr–Sommerfeld equation including a porous term. It was found that the ratios of the permeability and depth of the obstruction with respect to the free flow layer depth are the relevant parameters influencing the stability margin and the structure of the most unstable modes. To validate the conclusions of the theoretical analysis, an experiment with air flowing through a channel semi-obstructed by a regular array of cylindrical wires was performed. The critical Reynolds number, which was determined by measuring the amplitude of velocity fluctuations at the interface of the porous medium, agrees with the theoretical predictions. The dominant instability mode was characterized by the cross-section profile of the root mean square of the velocity perturbations, which matches reasonable well with the eigenfunction of the most unstable eigenvalue. Also, the wavenumber was determined by correlating the velocity measurements in two sequential locations along the channel, which compares well with the theoretical value.

Numerical Model of Liquid Film Formation and Breakup in Last Stage of a Low-Pressure Steam Turbine

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Pietro Rossi ◽  
Asad Raheem ◽  
Reza S. Abhari
Keyword(s):  
Steam Turbine ◽  
Stokes Equations ◽  
Low Pressure ◽  
Liquid Films ◽  
Operating Conditions ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Last Stage ◽  
The Impact

Formation of thin liquid films on steam turbine airfoils, particularly in last stages of low-pressure (LP) steam turbines, and their breakup into coarse droplets is of paramount importance to assess erosion of last stage rotor blades given by the impact of those droplets. An approach for this problem is presented in this paper: this includes deposition of liquid water mass and momentum, film mass and momentum conservation, trailing edge breakup and droplets Lagrangian tracking accounting for inertia and drag. The use of thickness-averaged two-dimensional (2D) equations in local body-fitted coordinates, derived from Navier–Stokes equations, makes the approach suitable for arbitrary curved blades and integration with three-dimensional (3D) computational fluid dynamics (CFD) simulations. The model is implemented in the in-house solver MULTI3, which uses Reynolds-averaged Navier–Stokes equations κ – ω model and steam tables for the steam phase and was previously modified to run on multi-GPU architecture. The method is applied to the last stage of a steam turbine in full and part load operating conditions to validate the model by comparison with time-averaged data from experiments conducted in the same conditions. Droplets impact pattern on rotor blades is also predicted and shown.

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