An Implicit Algorithm for Stator-Rotor Interaction Analysis

1996 ◽  
Author(s):  
V. Michelassi ◽  
P. Adami ◽  
F. Martelli
Keyword(s):  
Interaction Analysis ◽  
Experimental Testing ◽  
Three Dimensional ◽  
Factorization Method ◽  
Steady Flows ◽  
Turbine Stage ◽  
Approximate Factorization ◽  
Time Step ◽  
Physical Time ◽  
Speed And Accuracy

A simple time-accurate algorithm is presented for the computation of the unsteady stator-rotor interaction. The algorithm is based on the scalar approximate factorization method originally developed for the computation of complex three-dimensional steady flows. The method introduces a physical time step, used to march in time, and a numerical time step to iterate in between physical time steps. The method is formulated so as to take full advantage of the implicit formulation and provide an implicit treatment of the unsteady terms. A set of preliminary tests on a turbine stage, still in the experimental testing phase, proved the speed and accuracy of the method which was able to capture the essential features of a transonic stage.

Numerical Simulation of Viscous Flow-Field in Cascade Using Thin-Layer Equations and AF Method

1999 ◽  
Author(s):  
Yumin Xiao ◽  
R. S. Amano
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Factorization Method ◽  
Computational Domain ◽  
Approximate Factorization ◽  
Calculation Results ◽  
Transonic Cascade

Abstract In this paper an implicit 3-D solver for computations of a viscous flow has been developed and the computations of the flow between blade passage are presented. This method employs an AF (Approximate Factorization) method in which four techniques are incorporated to speed up convergence to the steady-state solutions: (1) body-fitted H-grid; (2) artificial viscosity; (3) implicit residual smoothing; and (4) local time-stepping. The two-dimensional pseudo-characteristic method was used to determine the inlet and outlet boundary conditions of the computational domain and the periodic boundary conditions were used at inter-boards. The validation cases include subsonic and transonic viscous flows in C3X cascade. Results for these turbine cascade flows are presented and compared with experiments at corresponding conditions. Computed pressure distributions on blade surfaces show good agreement with the published experimental data. This method was further applied to a three-dimensional case and demonstrated the code capability for predicting the secondary flow in a 3-D transonic flow-field. From these computations it was found that the proposed method possesses superior convergence characteristics and can be extended to unsteady flow calculations. Finally, it was observed that the three-dimensional calculation results show that the secondary flow mechanism in a transonic cascade seems to be quit different from those, in a subsonic case.

scholarly journals Approximate Factorization Method Using Alternating Cell Direction Implicit Method: Comparison of Convergence Characteristics Using Basic Model Equations

2021 ◽  
Vol 48 (3) ◽  
Author(s):  
Ali Ruhs¸en C¸ ETE ◽  
Keyword(s):  
Unstructured Grids ◽  
Factorization Method ◽  
Unstructured Meshes ◽  
Implicit Method ◽  
Approximate Factorization ◽  
Time Step ◽  
Fully Implicit ◽  
Implicit Schemes ◽  
Iteration Methods ◽  
Implicit Iteration

In this paper, a fast implicit iteration scheme called the alternating cell directions implicit (ACDI) method is combined with the approximate factorization scheme. The use of fast implicit iteration methods with unstructured grids is hardly. The proposed method allows fast implicit formulations to be used in unstructured meshes, revealing the advantages of fast implicit schemes in unstructured meshes. Fast implicit schemes used in structured meshes have evolved considerably and are much more accurate and robust, and are faster than explicit schemes. It is a crucial novel development that such developed schemes can be applied to unstructured schemes. In steady incompressible potential flow, the convergence character of the scheme is compared with the Runge-Kutta order 4 (RK4), Laasonen, point Gauss–Seidel iteration, old version ACDI, and line Gauss–Seidel iteration methods. The scheme behaves like an approximation of the fully implicit method (Laasonen) up to an optimum pseudo-time-step size. This is a highly anticipated result because the approximate factorization method is an approach to a fully implicit formulation. The results of the numerical study are compared with other fast implicit methods (e.g., the point and line Gauss–Seidel methods), the RK4 method, which is an explicit scheme, and the Laasonen method, which is a fully implicit scheme. The study increased the accuracy of the ACDI method. Thus, the new ACDI method is faster in unstructured grids than other methods and can be used for any mesh construction.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals Imaging of bi-anisotropic periodic structures from electromagnetic near-field data

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Trung Truong
Keyword(s):  
Inverse Scattering ◽  
Maxwell Equations ◽  
Field Data ◽  
Periodic Structures ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Factorization Method ◽  
Unique Determination

AbstractThis paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem. We provide a rigorous justification of the factorization method which results in the unique determination and a fast imaging algorithm for the periodic scatterer. Numerical examples for imaging three-dimensional periodic structures are presented to examine the efficiency of the method.

Effect of Wake Passing on Unsteady Aerodynamic Performance in a Turbine Stage

2006 ◽  
Author(s):  
K. Yamada ◽  
K. Funazaki ◽  
K. Hiroma ◽  
M. Tsutsumi ◽  
Y. Hirano ◽  
...  
Keyword(s):  
Secondary Flow ◽  
Three Dimensional ◽  
Suction Side ◽  
Turbine Stage ◽  
Three Dimensional Flow ◽  
Unsteady Aerodynamic ◽  
Unsteady Effect ◽  
Unsteady Rans ◽  
Wake Passing ◽  
Stage Efficiency

In the present work, unsteady RANS simulations were performed to clarify several interesting features of the unsteady three-dimensional flow field in a turbine stage. The unsteady effect was investigated for two cases of axial spacing between stator and rotor, i.e. large and small axial spacing. Simulation results showed that the stator wake was convected from pressure side to suction side in the rotor. As a result, another secondary flow, which counter-rotated against the passage vortices, was periodically generated by the stator wake passing through the rotor passage. It was found that turbine stage efficiency with the small axial spacing was higher than that with the large axial spacing. This was because the stator wake in the small axial spacing case entered the rotor before mixing and induced the stronger counter-rotating vortices to suppress the passage vortices more effectively, while the wake in the large axial spacing case eventually promoted the growth of the secondary flow near the hub due to the migration of the wake towards the hub.

Ingestion Into the Upstream Wheelspace of an Axial Turbine Stage

1994 ◽  
Vol 116 (2) ◽  
pp. 327-332 ◽  
Author(s):  
T. Green ◽  
A. B. Turner
Keyword(s):  
Pressure Distribution ◽  
Static Pressure ◽  
Three Dimensional ◽  
Computer Code ◽  
Rotor Blades ◽  
Rotor Speed ◽  
Turbine Stage ◽  
Flow Rates ◽  
Static Pressure Distribution ◽  
Axial Clearance

The upstream wheelspace of an axial air turbine stage complete with nozzle guide vanes (NGVs) and rotor blades (430 mm mean diameter) has been tested with the objective of examining the combined effect of NGVs and rotor blades on the level of mainstream ingestion for different seal flow rates. A simple axial clearance seal was used with the rotor spun up to 6650 rpm by drawing air through it from atmospheric pressure with a large centrifugal compressor. The effect of rotational speed was examined for several constant mainstream flow rates by controlling the rotor speed with an air brake. The circumferential variation in hub static pressure was measured at the trailing edge of the NGVs upstream of the seal gap and was found to affect ingestion significantly. The hub static pressure distribution on the rotor blade leading edges was rotor speed dependent and could not be measured in the experiments. The Denton three-dimensional C.F.D. computer code was used to predict the smoothed time-dependent pressure field for the rotor together with the pressure distribution downstream of the NGVs. The level and distribution of mainstream ingestion, and thus the seal effectiveness, was determined from nitrous oxide gas concentration measurements and related to static pressure measurements made throughout the wheelspace. With the axial clearance rim seal close to the rotor the presence of the blades had a complex effect. Rotor blades in connection with NGVs were found to reduce mainstream ingestion seal flow rates significantly, but a small level of ingestion existed even for very high levels of seal flow rate.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

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