Assessing Viscous Body Forces for Unsteady Calculations

2002 ◽  
Author(s):  
L. Xu
Keyword(s):  
Drag Coefficient ◽  
Body Force ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Viscous Force ◽  
Local Source ◽  
Source Terms ◽  
Viscous Effects ◽  
Computational Mesh ◽  
Computational Resources

A strategy has been developed to model the three dimensional unsteady flows through turbomachines subject to non-axisymmetric flow/geometrical conditions such as low order distortions with relatively long length scale unsteadiness, by modelling the viscous effects as local source terms for a coarse computational mesh but not calculating them directly. In general full annulus multirow calculations are required for such flows but currently the computational resources are devoted to resolving detailed viscous flow very close to the walls, which in some cases is not the centre of concern. By avoiding resolving detailed viscous effects the model can accelerate the calculation by at least two orders of magnitude. The method has been illustrated to be able to resolve disturbances down to the blade passing frequency and give good estimates of overall unsteady blade forces due to blade row interactions. Obviously the correct modelling of the viscous body force as source terms in the governing equations is the key for accuracy of such calculations. Different ways of constructing/approximating the viscous body force term are discussed and their adequacy in unsteady flow calculations is assessed. It is found that in general the viscous force is relatively small compared to the total blade force, even smaller the unsteady fluctuation of the viscous force and a simple drag coefficient model is quite adequate to model both time mean and dynamic viscous effects. Whilst for the cases when separations are present variations in the drag coefficient may become large and more detailed modelling may be required.

Assessing Viscous Body Forces for Unsteady Calculations

2003 ◽  
Vol 125 (3) ◽  
pp. 425-432 ◽  
Author(s):  
L. Xu
Keyword(s):  
Drag Coefficient ◽  
Body Force ◽  
Three Dimensional ◽  
Viscous Force ◽  
Local Source ◽  
Source Terms ◽  
Viscous Effects ◽  
Computational Mesh ◽  
Blade Row ◽  
Computational Resources

A strategy has been developed to model the three-dimensional unsteady flows through turbomachines subject to nonaxisymmetric flow/geometrical conditions such as low order distortions with relatively long length-scale unsteadiness, by modeling the viscous effects as local source terms for a coarse computational mesh, but not calculating them directly. In general full annulus multi-row calculations are required for such flows, but currently the computational resources are devoted to resolving detailed viscous flow very close to the walls, which in some cases is not the center of concern. By avoiding resolving detailed viscous effects the model can accelerate the calculation by at least two orders of magnitude. The method has been illustrated to be able to resolve disturbances down to the blade passing frequency and give good estimates of overall unsteady blade forces due to blade row interactions. Obviously, the correct modeling of the viscous body force as source terms in the governing equations is the key for accuracy of such calculations. Different ways of constructing/approximating the viscous body force term are discussed and their adequacy in unsteady flow calculations is assessed. It is found that in general the viscous force is relatively small compared to the total blade force, even smaller the unsteady fluctuation of the viscous force and a simple drag coefficient model is quite adequate to model both time mean and dynamic viscous effects. However, for the cases when separations are present variations in the drag coefficient may become large and more detailed modeling may be required.

The Relative Merits of an Inviscid Euler 3-D and Quasi-3-D Analysis for the Design of Transonic Rotors

1988 ◽  
Author(s):  
D. P. Miller ◽  
A. C. Bryans
Keyword(s):  
Flow Field ◽  
Numerical Solutions ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Blade Loading ◽  
Rotor Design ◽  
Accurate Indication ◽  
Through Flow ◽  
Transonic Rotor

It is the purpose of this paper to examine the flow fields in an advanced modern transonic rotor design using both axisymmetric and three dimensional techniques. Also, to determine the deviation of the axisymmetric flow from three-dimensional flow field and whether this seriously affects the results. Inviscid Euler solvers are now widely used to analyze transonic flows through turbomachines giving a reasonably accurate indication of the flow field in blade passages. Although viscous effects are important, the inviscid analysis provides significant knowledge of the flow field which is essential to transonic design. The blade-to-blade loading and work distributions are determined quite realistically by the 3-D and quasi-3-D inviscid analyses. Through-flow and blade-to-blade inviscid solutions are presented for a highly loaded transonic rotor. Numerical solutions for various transonic rotor designs operating at peak efficiency are also compared with test data.

Research on the Improved Body-Force Method Based on Viscous Flow

2019 ◽  
Author(s):  
Zhiheng Li ◽  
Jiawei Yu ◽  
Dakui Feng ◽  
Kaijun Jiang ◽  
Yujie Zhou
Keyword(s):  
Drag Coefficient ◽  
Viscous Flow ◽  
Body Force ◽  
Lift Coefficient ◽  
Open Water ◽  
Viscous Effects ◽  
Thrust Coefficient ◽  
Force Method ◽  
Water Characteristics ◽  
Body Force Method

Abstract The virtual propeller model can achieve the rapid numerical prediction of the ship self-propulsion performance through viscous flow, which used the improved body-force method. The two-dimensional lift coefficient CL and the drag coefficient CD are very important parameters in this method, which are generally obtained by the potential flow methods and cannot incorporate viscous effects. This study will perform a fully nonlinear unsteady RANS (Reynolds Average Navier-Stokes) simulation to get the KP505 open-water characteristics and then divide its blade into several parts to get the lift coefficient CL and the drag coefficient CD on each one. Then fitting by multivariate regression method, the relationship between CL, CD and propeller parameters is obtained. The Unsteady Blade Element Theory (UBET) is coupled with RANS in house CFD code HUST-Ship (Hydrodynamic Unsteady Simulation Technology for Ship) to calculate the flow around the propeller. RANS equations are solved by the finite difference method and PISO arithmetic. have been made using structured grid with overset technology. The results show that comparing with the EFD data, the maximum differences of the result of the improved body-force method are 4.32% and 2.7% for the thrust coefficient and the torque coefficient respectively near the propeller operating point.

scholarly journals The Use of a Distributed Body Force to Simulate Viscous Effects in 3D Flow Calculations

1986 ◽  
Author(s):  
J. D. Denton
Keyword(s):  
Simple Model ◽  
Viscous Flow ◽  
Body Force ◽  
Computational Cost ◽  
Three Dimensional ◽  
Secondary Flows ◽  
The Other ◽  
Simple Extension ◽  
Viscous Effects ◽  
3D Flow

Three dimensional viscous flow calculations methods for turbomachinery are starting to become available but are not yet sufficiently well developed to be used for design purposes. Three dimensional inviscid calculations on the other hand are now well developed and are widely used for design purposes. This paper describes a method intermediate between fully viscous methods and inviscid methods. The viscous effects are approximated by a very simple model which can be tuned empirically to get the correct overall level of loss and which reproduces many of the details of real viscous flow, such as boundary layers and secondary flows. The method is a simple extension to a widely used inviscid method and enables viscous effects to be simulated with little extra computational cost compared to a 3D inviscid calculation.

Development of body force model for steady inlet distortions in high-speed multistage compressor

2016 ◽  
Vol 231 (9) ◽  
pp. 1650-1659 ◽  
Author(s):  
Jin Guo ◽  
Jun Hu
Keyword(s):  
Performance Analysis ◽  
Body Force ◽  
Three Dimensional ◽  
Aerodynamic Performance ◽  
The Body ◽  
Force Model ◽  
Source Terms ◽  
Analysis Model ◽  
Multistage Compressor ◽  
The Impact

This study aims at establishing a three-dimensional numerical model, compressor aerodynamic performance analysis model, to simulate the impact of complicated distorted flow on multistage axial flow compressor based on the body force model. The model solves the compressible three-dimensional Euler equations, which are modified to include source terms representing the effect of the blade rows. In this study, the association between blade source terms and entry Mach number together with attack angle could be established with the deviation angle model and loss model. In this paper, compressor aerodynamic performance analysis model is used to evaluate the effect of inlet circumferential total pressure distortion and swirl distortion on a five-stage high-pressure compressor. Calculated operating maps for compressor agree well with the experimental results. Meanwhile, the traveling process of inlet distortions in the multistage compressor is correctly revealed. The wide application prospect of the model can be seen in the area of inlet distortion problems.

Practical electron tomography

1995 ◽  
Vol 53 ◽  
pp. 742-743
Author(s):  
C.L. Woodcock
Keyword(s):  
Electron Tomography ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
3D Shape ◽  
Computational Resources ◽  
Shape Of Particles

Despite the potential of the technique, electron tomography has yet to be widely used by biologists. This is in part related to the rather daunting list of equipment and expertise that are required. Thanks to continuing advances in theory and instrumentation, tomography is now more feasible for the non-specialist. One barrier that has essentially disappeared is the expense of computational resources. In view of this progress, it is time to give more attention to practical issues that need to be considered when embarking on a tomographic project. The following recommendations and comments are derived from experience gained during two long-term collaborative projects.Tomographic reconstruction results in a three dimensional description of an individual EM specimen, most commonly a section, and is therefore applicable to problems in which ultrastructural details within the thickness of the specimen are obscured in single micrographs. Information that can be recovered using tomography includes the 3D shape of particles, and the arrangement and dispostion of overlapping fibrous and membranous structures.

A Three-Dimensional Viscous Transonic Inverse Design Method

2000 ◽  
Author(s):  
W. T. Tiow ◽  
M. Zangeneh
Keyword(s):  
Design Method ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Flow Equations ◽  
Flow Solution ◽  
Turbomachinery Blades ◽  
A Cell ◽  
Inverse Design Method ◽  
Euler Solver

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.

Tilting at wave beams: a new perspective on the St. Andrew’s Cross

2017 ◽  
Vol 830 ◽  
pp. 660-680 ◽  
Author(s):  
T. Kataoka ◽  
S. J. Ghaemsaidi ◽  
N. Holzenberger ◽  
T. Peacock ◽  
T. R. Akylas
Keyword(s):  
Wave Field ◽  
Finite Length ◽  
Line Source ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Resonance Phenomenon ◽  
Buoyancy Frequency ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Viscous Effects

The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified Boussinesq fluid of constant buoyancy frequency, $N$, is investigated. This variant of the widely studied horizontal configuration – where a cylinder aligned with a plane of constant gravitational potential induces four wave beams that emanate from the cylinder, forming a cross pattern known as the ‘St. Andrew’s Cross’ – brings out certain unique features of radiated internal waves from a line source tilted to the horizontal. Specifically, simple kinematic considerations reveal that for a cylinder inclined by a given angle $\unicode[STIX]{x1D719}$ to the horizontal, there is a cutoff frequency, $N\sin \unicode[STIX]{x1D719}$, below which there is no longer a radiated wave field. Furthermore, three-dimensional effects due to the finite length of the cylinder, which are minor in the horizontal configuration, become a significant factor and eventually dominate the wave field as the cutoff frequency is approached; these results are confirmed by supporting laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency as the group-velocity component perpendicular to the cylinder direction vanishes at cutoff; as a result, energy cannot be easily radiated away from the source, and nonlinear and viscous effects are likely to come into play. This scenario is examined by adapting the model for three-dimensional wave beams developed in Kataoka & Akylas (J. Fluid Mech., vol. 769, 2015, pp. 621–634) to the near-resonant wave field due to a tilted line source of large but finite length. According to this model, the combination of three-dimensional, nonlinear and viscous effects near cutoff triggers transfer of energy, through the action of Reynolds stresses, to a circulating horizontal mean flow. Experimental evidence of such an induced mean flow near cutoff is also presented.

Chebyshev multidomain pseudospectral method to solve cardiac wave equations with rotational anisotropy

2018 ◽  
Vol 09 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Jairo Rodríguez-Padilla ◽  
Daniel Olmos-Liceaga
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Finite Difference Schemes ◽  
Cardiac Models ◽  
Computational Resources ◽  
Realistic Geometries

The implementation of numerical methods to solve and study equations for cardiac wave propagation in realistic geometries is very costly, in terms of computational resources. The aim of this work is to show the improvement that can be obtained with Chebyshev polynomials-based methods over the classical finite difference schemes to obtain numerical solutions of cardiac models. To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature.

scholarly journals Semi-Inverse Design of Compressor Cascades, Including Supersonic Inflow

1990 ◽  
Author(s):  
A. Kirschner ◽  
H. Stoff
Keyword(s):  
Flow Field ◽  
Design Method ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Design Procedure ◽  
Meridional Plane ◽  
Simple Method ◽  
Blade Loading ◽  
Through Flow ◽  
Blade Element

A cascade design-method is presented which complements the meridional through-flow design procedure of turbomachines. Starting from an axisymmetric flow field and the streamline geometry in the meridional plane this simple method produces a solution for the quasi three-dimensional flow field and the blade-element geometry on corresponding stream surfaces. In addition, it provides intra-blade data on loss and turning required for a consistent design and a convenient means of optimizing blade loading. The purpose of this paper is to describe the theoretical basis of the method and to illustrate its application in the design of transonic compressors.

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