Numerical Study of the Unsteady Blade Row Interaction in a Three-Stage Low Pressure Turbine

2003 ◽  
Author(s):  
Christian Nayeri ◽  
Wolfgang Ho¨hn
Keyword(s):  
Numerical Study ◽  
Time Integration ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Implicit Time ◽  
Surface Pressure Distribution ◽  
Computational Mesh ◽  
Transition Models ◽  
Underlying Mechanisms ◽  
Turbulence Parameters

The focus of this paper is on the one hand the quantitative optimization of the unsteady numerical simulations compared to experiments, and on the other hand to gain a better insight into the underlying mechanisms when an upstream wake of a stator interacts with the flow-field of the next stator. This was achieved by optimizing the numerical turbulence parameters used in the turbulence and transition models. Using steady calculations an optimal initial solution for the unsteady calculation was found. Also, the computational mesh was refined. For the numerical computations a time accurate Reynolds averaged Navier-Stokes solver is applied. Turbulence is modeled using the Spalart-Allmaras one equation turbulence model. The integration of the governing equations in time is performed by an implicit time integration for the steady calculations, and by an implicit dual time stepping scheme for the unsteady calculations. At the inlet and outlet reflecting or non-reflecting boundary conditions are used. The quasi 3D calculations are conducted on a stream surface around midspan allowing a varying stream tube thickness. The results show that by adjusting the turbulence parameters in the turbulence and transition models, a better qualitative and quantitative agreement between experiments and numerical results can be achieved. Steady and unsteady quantities are shown, e.g. the surface pressure distribution and the wall shear stress. The unsteady simulations of two different azimuthal positions of the first and third stator reveal different evolutions of the boundary layers of the second and third stators due to the influence of the wake of the upstream stators. These differences are better captured through the above mentioned improvements, i.e. reduction of sheared cells in the computational mesh and optimization of turbulence and transition parameters in the allowable range of the models.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

Numerical Performance of Transition Models in Different Turbomachinery Flow Conditions: A Comparative Study

2000 ◽  
Author(s):  
Jiasen Hu ◽  
Torsten H. Fransson
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Numerical Study ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Flow Conditions ◽  
Transition Models ◽  
High Reynolds

A numerical study has been performed to compare the overall performance of three transition models when used with an industrial Navier-Stokes solver. The three models investigated include two experimental correlations and an integrated eN method. Twelve test cases in realistic turbomachinery flow conditions have been calculated. The study reveals that all the three models can work numerically well with an industrial Navier-Stokes code, but the prediction accuracy of the models depends on flow conditions. In general, all the three models perform comparably well to predict the transition in weak or moderate adverse pressure-gradient regions. The two correlations have the merit if the transition starts in strong favorable pressure-gradient region under high Reynolds number condition. But only the eN method works well to predict the transition controlled by strong adverse pressure gradients. The three models also demonstrate different capabilities to model the effects of turbulence intensity and Reynolds number.

scholarly journals EVALUATION OF THE POUNDING FORCES DURING EARTHQUAKE USING EXPLICIT DYNAMIC TIME INTEGRATION METHOD

2017 ◽  
Vol 13 (3) ◽  
pp. 21-39
Author(s):  
George Bogdan Nica ◽  
Andrei Gheorghe Pricopie
Keyword(s):  
Urban Areas ◽  
Integration Method ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Implicit Time ◽  
Time Integration Method ◽  
Nonlinear Viscoelastic ◽  
Weak Structure

Abstract Pounding effects during earthquake is a subject of high significance for structural engineers performing in the urban areas. In this paper, two ways to account for structural pounding are used in a MATLAB code, namely classical stereomechanics approach and nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures acted by ELCentro recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion are numerical integrated using central finite difference method, an explicit method, having the main advantage that in the displacement at the ith+1 step is calculated based on the loads from the ith step. Thus, the collision is checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. First, a comparison is done using available data in the literature. Both linear and nonlinear behavior of the structures during earthquake is further investigated. Several layout scenarios are also investigated, in which one or more weak buildings are adjacent to a stiffer building. One of the main findings in this paper is related to the behavior of a weak structure located between two stiff structures.

Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

2005 ◽  
Vol 219 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Y Mei ◽  
A Guha
Keyword(s):  
Numerical Simulation ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Flow Through

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.

An Investigation on the Synchronization Regime of a Single Cylinder in Cross-Flow Subject to Harmonic Oscillations

2007 ◽  
Author(s):  
Waldir Terra Pinto ◽  
Marcelo Arau´jo Vitola ◽  
Carlos Antoˆnio Levi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Time Integration ◽  
Cross Flow ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Harmonic Amplitude ◽  
Navier Stokes Equations ◽  
Single Cylinder ◽  
Synchronization Regime

This work presents a numerical study on the synchronization regime of a single cylinder subject to forced harmonic motion in the transverse direction of the flow. The study is carried out for a circular cylinder for Reynolds number around 500. The forced harmonic amplitude to diameter ratio is 0.22 and the forced frequency varies from 0.2 to 4.8 Hz. The Navier-Stokes equations are solved in a non-staggered grid using a sixth-order compact difference schemes to evaluate the spatial derivatives, a low-storage third-order Runge-Kutta scheme for time integration. The cylinder is represented using a feedback force methodology. The results are compared with experimental data obtained in a water tunnel. Results show clearly that synchronization phenomenon in the fundamental frequency as well as to its super and sub-harmonics.

scholarly journals Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 282 ◽  
Author(s):  
Michał Szymczyk ◽  
Marcin Nowak ◽  
Wojciech Sumelka
Keyword(s):  
Numerical Study ◽  
Dynamic Properties ◽  
Plastic Anisotropy ◽  
Time Integration ◽  
Comprehensive Analysis ◽  
Implicit Time ◽  
Integration Scheme ◽  
Viscoplastic Model ◽  
Time Integration Scheme ◽  
Non Locality

The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

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