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.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

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.

Peristaltic Pumping

2000 ◽  
Author(s):  
M. Tadjfar ◽  
T. Yamaguchi ◽  
R. Himeno
Keyword(s):  
Pressure Wave ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Parallel Architecture ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Peristaltic Pumping

Abstract Peristaltic pumping in a cylindrical tube is simulated. The unsteady, three-dimensional, incompressible Navier-Stokes equations are solved numerically. A flow solver written for parallel architecture and capable of dealing with moving boundaries and moving grids is used. The solver uses a second-order in time and third-order upwind finite volume method for solving time-accurate incompressible flows utilizing pseudo-compressibility technique. In this study, the flow of an axisymmetric “Wine-glass” shaped, single, peristaltic wave is analyzed. The wall wave, quickly, establishes a pressure wave in the flow which pumps fluid in the tube as it moves down the tube. The pressure wave, established by the contracting geometric wall wave, grows and diffuses into the upstream and downstream direction in time due to the action of viscosity.

Numerical and scalability analysis of an unstructured Cartesian flow solver

2011 ◽  
Vol 225 (9) ◽  
pp. 2138-2148 ◽  
Author(s):  
Y H Yau ◽  
A Badarudin ◽  
P A Rubini
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Source Codes ◽  
Scalability Analysis ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Parallel Code

This article describes a systematic approach in building a flow solver for large eddy simulation (LES). Finite volume discretizations of the filtered, incompressible, Navier–Stokes equations were explained. The theory progresses to the description of the step-by-step process (mainly in increasing functionality or capability) in developing a three-dimensional, unstructured Cartesian mesh, parallel code after evaluating numerical factors, and available options carried out earlier. This was followed by a presentation of results produced from the simulations of laminar flow, related to the validation of the source codes, which indicates that the flow solver is behaving satisfactorily.

A Comprehensive Through-Flow Solver Method for Modern Turbomachinery Design

2015 ◽  
Author(s):  
Mark R. Anderson ◽  
Daryl L. Bonhaus
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Optimization Techniques ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Dimensional Solution ◽  
Loss Model ◽  
Flow Solver ◽  
Through Flow ◽  
Wide Range

Through-flow solvers have historically played a very prominent role in the design and analysis of axial turbomachinery. While three-dimensional, Full Navier-Stokes (FNS) CFD is taking an increasing larger role, quasi-3D through-flow methods are still widely used. Automated optimization techniques that search over a wide design space, involving many possible variables, are particularly suitable for the computationally efficient through-flow solver. Pressure-based methods derived from CFD solution techniques have gradually replaced older streamline curvature methods, due to their ability to capture flow across a wide range of Mach numbers, particularly the transonic and supersonic regimes. The through-flow approach allows for the solution of the three-dimensional problem with the computational efficiency of a two-dimensional solution. Since the losses are explicitly calculated through empirically based models, the need for detailed grid resolution to capture tiny flow entities (such as wakes and boundary layers) is also greatly reduced. The combined savings can result in computational costs as much as two orders of magnitude lower than full 3D CFD methods. A state-of-the-art through-flow solver has several features that are crucial in the design process. One of these is the ability to run in both a design and an analysis mode. Also important, is the ability to generate solutions where critical components are solved using 3D FNS, while others are run using a through-flow method. Other desirable features in a through-flow solver are: an advanced equation of state, injection and extraction ability, the handling of arbitrary (non-axial) shapes, and a link to a capable geometry generation engine. Through-flow solvers represent a unique mix of higher order numerical methods (increasingly CFD-based) coupled with empirically derived models (generally meanline based). The combination of these two methods in one solver creates a particularly challenging programming problem. This paper details the techniques required to effectively generate through-flow solutions. Special attention is given to an improved off-design loss model for compressors, as well as a transonic loss model needed for high-speed compressor and turbine flows. Validation with recognized test data along with corresponding 3D FNS CFD results are presented.

Numerical Simulations of Three-Dimensional Flows in a Cubic Cavity With an Oscillating Lid

1993 ◽  
Vol 115 (4) ◽  
pp. 680-686 ◽  
Author(s):  
Reima Iwatsu ◽  
Jae Min Hyun ◽  
Kunio Kuwahara
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Dependent ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Navier Stokes Equations ◽  
Sinusoidal Oscillations ◽  
Dependent Flow

Numerical studies are made of three-dimensional flow of a viscous fluid in a cubical container. The flow is driven by the top sliding wall, which executes sinusoidal oscillations. Numerical solutions are acquired by solving the time-dependent, three-dimensional incompressible Navier-Stokes equations by employing very fine meshes. Results are presented for wide ranges of two principal physical parameters, i.e., the Reynolds number, Re ≤ 2000 and the frequency parameter of the lid oscillation, ω′ ≤ 10.0. Comprehensive details of the flow structure are analyzed. Attention is focused on the three-dimensionality of the flow field. Extensive numerical flow visualizations have been performed. These yield sequential plots of the main flows as well as the secondary flow patterns. It is found that the previous two-dimensional computational results are adequate in describing the main flow characteristics in the bulk of interior when ω′ is reasonably high. For the cases of high-Re flows, however, the three-dimensional motions exhibit additional complexities especially when ω′ is low. It is asserted that, thanks to the recent development of the supercomputers, calculation of three-dimensional, time-dependent flow problems appears to be feasible at least over limited ranges of Re.

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]

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.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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