scholarly journals Analysis of Transonic Turbomachinery Flows Using a 2-D Explicit Low-Reynolds k-ε Navier-Stokes Solver

1994 ◽  
Author(s):  
F. Dejean ◽  
C. Vassilopoulos ◽  
G. Slmandirakis ◽  
K. C. Giannakoglou ◽  
K. D. Papailiou
Keyword(s):  
Stokes Equations ◽  
Guide Vane ◽  
Navier Stokes ◽  
Fractional Step ◽  
Flow Conditions ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Time Marching ◽  
Low Reynolds ◽  
The Stability

An explicit, time-marching fractional-step solver for the calculation of the two-dimensional compressible Navier-Stokes equations is presented. The advantage of using a fractional-step analysis is its simplicity and the fact that greater time-steps are allowed, since the stability criterion is less strict compared to other explicit solvers. Turbulence is modeled through a low-Reynolds k-ε model, for which a novel artificial viscosity scheme is implemented, ensuring a smooth ε-distribution close to solid walls. The method is used in order to numerically investigate the flow field in three different cascades, namely a highly loaded transonic linear turbine guide vane cascade in six different flow conditions, a transonic steam turbine cascade in two different flow conditions and a low supersonic compressor cascade. Calculations are performed using both H- and C-type grids.

The Effect of Midplane Guide Vanes in a Biplane Wells Turbine

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Tapas K. Das ◽  
Abdus Samad
Keyword(s):  
Stokes Equations ◽  
Guide Vane ◽  
Flow Analysis ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Wells Turbine ◽  
Navier Stokes Equations ◽  
Guide Vanes ◽  
Ansys Cfx

Guide vanes (GVs) improve the performance of a turbine in terms of efficiency, torque, or operating range. In this work, a concept of different orientations of GVs in between a two-row biplane wells turbine (BWT) was introduced and analyzed for the performance improvement. The fluid flow was simulated numerically with a commercial software ANSYS CFX 16.1. The Reynolds-averaged Navier–Stokes equations with the k-ω turbulence closure model were solved for different designs and flow conditions. For the base model, the results from simulation and experiments are in close agreement. Among the designs considered, the configuration, where the blades are in one line (zero circumferential angle between blades of two plane) and the midplane guide vane has concave side to the leading edge of the blade, performed relatively better. However, the performance was still less compared to the base model. The reason behind the reduction in performance from the base model is attributed to the blockage of flow and the change of flow path occurring due to the presence of the midplane GVs. The flow analysis of different cases and the comparison with the base model are presented in the current study.

scholarly journals Viscous Flow Computations in Turbomachine Cascades

1990 ◽  
Author(s):  
P.-A. Chevrin ◽  
C. Vuillez
Keyword(s):  
Stokes Equations ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Different Types ◽  
Time Marching ◽  
Transonic Turbine

Accurate prediction of the flow in turbomachinery requires numerical solution of the Navier-Stokes equations. A two-dimensional Navier-Stokes solver developed at ONERA for the calculation of the flow in turbine and compressor cascades was adapted at SNECMA to run on different types of grid. The solver uses an explicit, time-marching, finite-volume technique, with a multigrid acceleration scheme. A multi-domain approach is used to handle difficulties due to the geometry of the flow. An H-C grid was used in the calculations. Two turbulence models, based on the mixing length approach, were used. The flow in a transonic compressor cascade, a subsonic and a transonic turbine cascade were computed. Comparison with experiments is presented.

scholarly journals A Unified Fractional-Step, Artificial Compressibility and Pressure-Projection Formulation for Solving the Incompressible Navier-Stokes Equations

2014 ◽  
Vol 16 (5) ◽  
pp. 1135-1180 ◽  
Author(s):  
László Könözsy ◽  
Dimitris Drikakis
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Fractional Step ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Flow Problems ◽  
Dual Time Stepping ◽  
Pressure Projection ◽  
The Stability

AbstractThis paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Graham Ashcroft ◽  
Christian Frey ◽  
Kathrin Heitkamp ◽  
Christian Weckmüller
Keyword(s):  
Stokes Equations ◽  
Temporal Integration ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Noise Generation ◽  
Academic Problems ◽  
Tonal Noise ◽  
Navier Stokes Equations ◽  
Runge Kutta ◽  
The Stability

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

scholarly journals The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wen-Juan Wang ◽  
Yan Jia
Keyword(s):  
Weak Solution ◽  
Asymptotic Stability ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Perturbed System ◽  
Regular Class ◽  
Stability Issue ◽  
The Stability

We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.

Measurement and Calculation of Nozzle Guide Vane End Wall Heat Transfer

1998 ◽  
Author(s):  
Neil W. Harvey ◽  
Martin G. Rose ◽  
John Coupland ◽  
Terry Jones
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Guide Vane ◽  
Correction Method ◽  
Navier Stokes ◽  
Design Data ◽  
Navier Stokes Equations ◽  
Wall Functions ◽  
Transfer Rates ◽  
Nozzle Guide

A 3-D steady viscous finite volume pressure correction method for the solution of the Reynolds averaged Navier-Stokes equations has been used to calculate the heat transfer rates on the end walls of a modern High Pressure Turbine first stage stator. Surface heat transfer rates have been calculated at three conditions and compared with measurements made on a model of the vane tested in annular cascade in the Isentropic Light Piston Facility at DERA, Pyestock. The NGV Mach numbers, Reynolds numbers and geometry are fully representative of engine conditions. Design condition data has previously been presented by Harvey and Jones (1990). Off-design data is presented here for the first time. In the areas of highest heat transfer the calculated heat transfer rates are shown to be within 20% of the measured values at all three conditions. Particular emphasis is placed on the use of wall functions in the calculations with which relatively coarse grids (of around 140,000 nodes) can be used to keep computational run times sufficiently low for engine design purposes.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

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