Model Validation of an Euler-Based 2D-Throughflow Approach for Multistage Axial Turbine Analysis

2020 ◽  
Author(s):  
Sebastian Föllner ◽  
Volker Amedick ◽  
Bernhard Bonhoff ◽  
Dieter Brillert ◽  
Friedrich-Karl Benra
Keyword(s):  
Analytical Solutions ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Meridional Plane ◽  
Test Case ◽  
Test Cases ◽  
Flow Solver ◽  
Axial Turbines ◽  
Development And Validation ◽  
Good Agreement

Abstract In this paper the development and validation of a new meridional throughflow solver for the analysis of multistage axial turbines is presented. The quasi-three-dimensional finite-volume solver named tFlow is based on the inviscid Euler equations. To treat transonic flows with shocks the approximate Riemann solver of Roe for the computation of the inviscid fluxes in combination with the MUSCL approach are used. In the meridional plane turbine blades are numerically modeled by introducing two volume source terms for blade blockage and blade deviation effects. In this contribution four different validation test-cases are discussed. The general fluid solver is validated by analytical solutions of the established Ringleb flow and the simulation of a two-dimensional transonic nozzle flow. In contrast to prior publications [1–3] tFlow uses a different formulation of the blockage effect which is tested using the blockage data of a general convergent-divergent nozzle. Blade deviation effects are validated by comparison with three-dimensional results obtained from the commercial flow solver CFX. The results of tFlow are consistent with the analytical solutions and in case of the blade deviation test-case in good agreement to the three-dimensional results. Compared to fully three-dimensional simulations the developed solver enables faster analyses of multistage axial turbines to evaluate the performance characteristic.

Application of a Viscous Through-Flow Model to a Modern Axial Low-Pressure Compressor

2021 ◽  
Author(s):  
Arnaud Budo ◽  
Vincent E. Terrapon ◽  
Maarten Arnst ◽  
Koen Hillewaert ◽  
Sophie Mouriaux ◽  
...  
Keyword(s):  
Flow Model ◽  
Three Dimensional ◽  
Test Case ◽  
Test Cases ◽  
Compressor Stage ◽  
Flow Solver ◽  
Closure Models ◽  
Through Flow ◽  
Time Marching ◽  
Pressure Compressor

Abstract This paper describes the evaluation of a newly developed viscous time-marching through-flow solver to two test cases to assess the applicability of the method using correlations from the literature to modern blade designs. The test cases are the classic axial compressor stage CME2 and a modern highly loaded multi-stage axial low-pressure compressor developed by Safran Aero Boosters. The through-flow solver is based on the Navier-Stokes equations and uses a pseudo-time marching method. The closure models currently include terms of major importance: the blade forces and the Reynolds stress. The results are compared to higher-fidelity results including three-dimensional RANS simulations to assess their reliability for design and off-design conditions. The main originality of this work is the evaluation of the CFD-based method in the context of a compressor with highly three-dimensional blades, as such an analysis is not commonly found in the literature. The solver gives realistic predictions of loss and deviation for the compressor stage CME2 at both design and off-design operating conditions. Regarding the second test case, the through-flow simulations based on theoretically non-adapted correlations for such a compressor are still in good agreement with RANS simulations, although the results for the 2nd test case are probably not as good as for the first. These results are a promising first step towards the use of this through-flow model for industrial design. Regarding the ongoing closure models development, suggestions to extend the loss models to a larger range of designs are discussed.

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.

Q-BOR–FDTD method for solving Schrodinger equation for rotationally symmetric nanostructures with hydrogenic impurity

2022 ◽  
Author(s):  
Arezoo Firoozi ◽  
Ahmad Mohammadi ◽  
Reza Khordad ◽  
Tahmineh Jalali
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Fdtd Method ◽  
Three Dimensional ◽  
Test Cases ◽  
Body Of Revolution ◽  
Hydrogenic Impurity ◽  
Rotationally Symmetric ◽  
Difference Time

Abstract An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

The Inertial Deposition of Fog Droplets on Steam Turbine Blades

1988 ◽  
Vol 110 (2) ◽  
pp. 155-162 ◽  
Author(s):  
J. B. Young ◽  
K. K. Yau
Keyword(s):  
Steam Turbine ◽  
Large Time ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Test Cases ◽  
Governing Equations ◽  
Three Dimensional Flow ◽  
Pressure Cylinder ◽  
Steam Turbine Blades ◽  
A New Technique

A theoretical approach for calculating the rate of deposition of fog droplets on steam turbine blades by inertial impaction is described. Deposition rates are computed by tracking a number of droplet path lines through a specified blade-to-blade vapor flowfield and identifying the limiting trajectories that just intersect the blade surface. A new technique for performing the calculations efficiently has been developed whereby the mathematical stiffness of the governing equations is removed, thus allowing the numerical integration to proceed stably with comparatively large time increments. For high accuracy, the vapor flowfield is specified by a quasi-three-dimensional flow calculation involving both meridional and blade-to-blade plane calculations. Results are presented for two representative “test cases,” namely the final stage blading of the low-pressure cylinder of a 500 MW turbine and a typical stage in a high-pressure wet steam turbine. The effect on the deposition rate of fog droplet size and blade profile geometry is investigated for both on- and off-design flowfields. Comparisons are made with the predictions of a simplified theory for inertial deposition and the effect of blade rotation in flows with high pitch angles is discussed.

An Accelerated 3D Navier–Stokes Solver for Flows in Turbomachines

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Tobias Brandvik ◽  
Graham Pullan
Keyword(s):  
Graphics Processing Units ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Scaling ◽  
Test Case ◽  
Processing Unit ◽  
Central Processing ◽  
Order Of Magnitude ◽  
Graphics Processing ◽  
Good Agreement

A new three-dimensional Navier–Stokes solver for flows in turbomachines has been developed. The new solver is based on the latest version of the Denton codes but has been implemented to run on graphics processing units (GPUs) instead of the traditional central processing unit. The change in processor enables an order-of-magnitude reduction in run-time due to the higher performance of the GPU. The scaling results for a 16 node GPU cluster are also presented, showing almost linear scaling for typical turbomachinery cases. For validation purposes, a test case consisting of a three-stage turbine with complete hub and casing leakage paths is described. Good agreement is obtained with previously published experimental results. The simulation runs in less than 10 min on a cluster with four GPUs.

An Optimum Aero-Design Process of Turbine Blades

2002 ◽  
Author(s):  
C. Xu ◽  
R. S. Amano
Keyword(s):  
Design Process ◽  
High Efficiency ◽  
Pressure Ratio ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Compressor Blade ◽  
Advanced Technology ◽  
Test Case ◽  
Blade Design

With the development of the advanced technology, the combustion temperature is raised for increased efficiencies. At the same time, the turbine and compressor pressure ratio and the mass flow rate rise; thus causing turbine and compressor blades turning and blade lengths increase. Moreover, the high efficiency requirements had made the turbine and compressor blade design difficult. A turbine airfoil has been custom designed for many years, but an optimization for the section design in a three-dimensional consideration is still a challenge. For a compressor blade design, standard section cannot meet the modern compressor requirements. Modern compressor design has not only needs a custom designed section according to flow situation, but also needs three-dimensional optimizations. Therefore, a good blade design process is critical to the turbines and compressors. A blade design of the turbomachines is one of the important steps for a good turbomachine design. A blade design process not only directly influences the overall machine efficiency but also dramatically impact the design time and cost. In this study, a blade design and optimization procedure was proposed for both turbine and compressor blade design. A compressor blade design was used as a test case. It was shown that the current design process had more advantages than conventional design methodology.

Development and Validation of a Highly Nonlinear Model for Wave Propagation Over a Variable Bathymetry

2015 ◽  
Author(s):  
Maïté Gouin ◽  
Guillaume Ducrozet ◽  
Pierre Ferrant
Keyword(s):  
Wave Propagation ◽  
Nonlinear Model ◽  
Numerical Scheme ◽  
High Order ◽  
Numerical Results ◽  
Test Case ◽  
Test Cases ◽  
Highly Nonlinear ◽  
Propagating Waves ◽  
Development And Validation

Liu and Yue [1] developed a numerical scheme for propagating waves over a variable bathymetry with a High-Order Spectral (HOS) Method. The development of this nonlinear model is detailed and validated on three different test cases. They intend to demonstrate that such a model may be applied to small bottom variations as considered in [1] but also on cases where the bottom variation may be important. In this concern, the very well documented test case of a 2D underwater bar is studied in details. Comparisons are provided with both experimental and numerical results.

Suite for Smooth Particle Hydrodynamic Code Relevant to Spherical Plasma Liner Formation and Implosion

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Kevin Schillo ◽  
Jason Cassibry ◽  
Mitchell Rodriguez ◽  
Seth Thompson
Keyword(s):  
Three Dimensional ◽  
Smooth Particle Hydrodynamic ◽  
Momentum Conservation ◽  
Plasma Jets ◽  
Test Case ◽  
Test Cases ◽  
Stage Of Development ◽  
Plasma Liner ◽  
L2 Norm ◽  
Hydrodynamic Code

Three-dimensional (3D) modeling of magneto-inertial fusion (MIF) is at a nascent stage of development. A suite of test cases relevant to plasma liner formation and implosion is presented to present the community with some exact solutions for verification of hydrocodes pertaining to MIF confinement concepts. MIF is of particular interest to fusion research, as it may lead to the development of smaller and more economical reactor designs for power and propulsion. The authors present simulated test cases using a new smoothed particle hydrodynamic (SPH) code called SPFMax. These test cases consist of a total of six problems with analytical solutions that incorporate the physics of radiation cooling, heat transfer, oblique-shock capturing, angular-momentum conservation, and viscosity effects. These physics are pertinent to plasma liner formation and implosion by merging of a spherical array of plasma jets as a candidate standoff driver for MIF. An L2 norm analysis was conducted for each test case. Each test case was found to converge to the analytical solution with increasing resolution, and the convergence rate was on the order of what has been reported by other SPH studies.

Influence of Rotation on Dynamic Stall

2013 ◽  
Vol 58 (3) ◽  
pp. 1-9 ◽  
Author(s):  
A. D. Gardner ◽  
K. Richter
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Turbulence Models ◽  
Dynamic Stall ◽  
Test Case ◽  
Test Cases ◽  
Pitching Moment ◽  
Pitching Motion ◽  
Rotating Blade ◽  
Wind Tunnel Data

A computational investigation of the effect of rotation on two-dimensional (2D) deep dynamic stall has been undertaken, showing that the effect of rotation is to reduce the severity of the pitching moment peak and cause earlier reattachment of the flow. A generic single blade rotor geometry was investigated, which had a pitching oscillation around the quarter-chord axis while in hover, causing angle-driven dynamic stall. The results at the midpoint of the blade have the same Mach number (0.31), Reynolds number (1.15 × 106), and pitching motion (α = 13° ± 7°) as a dynamic stall test case for which significant experimental wind tunnel data and 2D computations exist. The rotating blade is compared with 2D computations and computations using the same blade without rotation at Mach 0.31 and with the same pitching motion. All test cases involve geometries propagating into undisturbed flow with no downwash. The three-dimensional (3D) grid computed without rotation had lower lift at the reference section than for a 2D computation with the same geometric angle of attack time history, and the lift overshoot classically observed for Spalart–Allmaras turbulence models during 2D dynamic stall was significantly reduced in the 3D case. Rotation reduced the strength of the dynamic stall vortex, which reduced the accompanying pitching moment peak by 25%.

An Accelerated 3D Navier-Stokes Solver for Flows in Turbomachines

2009 ◽  
Author(s):  
Tobias Brandvik ◽  
Graham Pullan
Keyword(s):  
Graphics Processing Units ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Scaling ◽  
Test Case ◽  
Processing Unit ◽  
Central Processing ◽  
Order Of Magnitude ◽  
Graphics Processing ◽  
Good Agreement

A new three-dimensional Navier-Stokes solver for flows in turbomachines has been developed. The new solver is based on the latest version of the Denton codes, but has been implemented to run on Graphics Processing Units (GPUs) instead of the traditional Central Processing Unit (CPU). The change in processor enables an order-of-magnitude reduction in run-time due to the higher performance of the GPU. Scaling results for a 16 node GPU cluster are also presented, showing almost linear scaling for typical turbomachinery cases. For validation purposes, a test case consisting of a three-stage turbine with complete hub and casing leakage paths is described. Good agreement is obtained with previously published experimental results. The simulation runs in less than 10 minutes on a cluster with four GPUs.

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