An Average-Passage Empirical Closure Model for Centrifugal Compressors

2004 ◽  
Author(s):  
Limin Gao ◽  
Guang Xi ◽  
Shangjin Wang
Keyword(s):  
Experimental Data ◽  
Empirical Model ◽  
Stokes Equations ◽  
Computational Cost ◽  
Axial Flow ◽  
Equation System ◽  
Computational Grids ◽  
Navier Stokes ◽  
Sufficient Information ◽  
Centrifugal Compressors

Applying the novel time- and passage-averaging operators, a reduced average-passage equation system is derived to remove the bodyforce and the blockage factor in Adamczyk’s average-passage equations. Like the Reynolds-averaged Navier-Stokes equations the average-passage flow model does not contain sufficient information to determine its solution. Based on the rich throughflow analysis for axial-flow turbomachinery and numerous studies for centrifugal compressors, a semi-empirical model of the deterministic stress is developed for centrifugal compressors in the present study. Finally, the empirical model coupled with the interface approach is applied to predict the time-averaged flow field in a tested centrifugal compressor stage and the results are compared with experimental data. Using the same computational grids, the computational cost with the empirical model is slightly more than that with the mixing plane model, and a good agreement was obtained between the numerical results and experimental data.

Numerical Simulation for Predicting Ship Resistance and Vertical Motions in Regular Head Waves

2019 ◽  
Author(s):  
Adham S. Bekhit ◽  
Adrian Lungu
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Numerical Results ◽  
Computational Grids ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Head Waves ◽  
Volume Method ◽  
Regular Head Waves

Abstract The present study is concerned with predicting the resistance and vertical motions of the surface combatant DTMB5512 ship model in regular head waves. A series of numerical simulations are performed for various wave lengths, heights and different ship speeds. Computations are performed by making use of the ISIS-CFD solver of the commercial software Fine™/Marine provided by NUMECA, where the discretization in space is based on finite volume method using unstructured grid. The unsteady Reynolds-Averaged Navier-Stokes equations are numerically solved while the turbulence is modeled by making use of the k-ω SST model. The free-surface is captured through an air-water interface based on the Volume of Fluid (VOF) method. Computed results are validated through direct comparisons with the experimental data provided by IIHR test cases. For the sake of numerical results verification, a grid convergence study is performed on four computational grids and a time step convergence test is also included. Validation of the numerical results shows a reasonable agreement with the experimental data.

Simulation of the Gap Resonance Between Two Rectangular Barges in Regular Waves by a Free Surface Viscous Flow Solver

2013 ◽  
Author(s):  
B. Elie ◽  
G. Reliquet ◽  
P.-E. Guillerm ◽  
O. Thilleul ◽  
P. Ferrant ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Viscous Flow ◽  
Stokes Equations ◽  
Resonance Phenomenon ◽  
Navier Stokes ◽  
Regular Waves ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Gap Resonance

This paper compares numerical and experimental results in the study of the resonance phenomenon which appears between two side-by-side fixed barges for different sea-states. Simulations were performed using SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach and results are compared with experimental data on two fixed barges with different headings and bilges. Numerical results, obtained using the SWENSE approach, are able to predict both the frequency and the magnitude of the RAO functions.

Leading Edge Film Cooling: Computations and Experiments Including Density Effects

1996 ◽  
Author(s):  
Pingfan He ◽  
Dragos Licu ◽  
Martha Salcudean ◽  
Ian S. Gartshore
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Stokes Equations ◽  
Leading Edge ◽  
Variable Density ◽  
Navier Stokes ◽  
Cooling Effectiveness ◽  
Stagnation Line ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio

The effect of varying coolant density on film cooling effectiveness for a turbine blade-model was numerically investigated and compared with experimental data. This model had a semi-circular leading edge with four rows of laterally-inclined film cooling orifices positioned symmetrically about the stagnation line. A curvilinear coordinate-based CFD code was developed and used for the numerical investigation. The code used a domain segmentation strategy in conjunction with general curvilinear grids to model the complex blade configuration. A multigrid method was used to accelerate the convergence rate. The time-averaged, variable-density, Navier-Stokes equations together with the energy or scalar equation were solved. Turbulence closure was attained by the standard k–ε model with a near-wall k model. Either air or CO2 was used as coolant in three cases of injection through single rows and alternatively staggered double raws of holes. Two different blowing rates were investigated in each case and compared with experimental data. The experimental results were obtained using a wind tunnel model, and the mass/heat analogy was used to determine the film cooling effectiveness. The higher density of the carbon dioxide coolant (approximately 1.5 times the density of air) in the isothermal mass injection experiments, was used to simulate the effects of injection of a colder air in the corresponding adiabatic heat transfer situation. Good agreement between calculated and measured film cooling effectiveness was found for low blowing ratio M ≤ 0.5 and the effect of density was not significant. At higher blowing ratio M > 1 the calculations consistently overpredict the measured values of film cooling effectiveness.

Annular Axial Flow-Induced Vibration of Cylindrical Shells by Flu¨gge’s Shell Theory

2006 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Makoto Katou
Keyword(s):  
Shell Theory ◽  
Stokes Equations ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Navier Stokes ◽  
Complex Eigenvalue ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Flowing Fluid ◽  
Narrow Passage

The unstable phenomena of thin cylindrical shells subjected to annular axial flow are investigated. In this paper, the analytical model is composed of an elastic axisymmetric shell and a rigid one which are arranged co-axially. Considering the fluid structure interaction between shells and fluid flowing through an annular narrow passage, the coupled equation of motion is derived using Flu¨gge’s shell theory and Navier-Stokes equations. The unstable phenomena of thin cylindrical shells are clarified by using the root locus based on the complex eigenvalue analysis. The numerical parameter studies on the shells with a freely supported end and a rigid one, and with both simply supported ends, are performed taking the dimensins of shells, the characteristics of flowing fluid so on as parameters. The influence of these parameters on the threshold of instability of the coupled vibration between thin cylindrical shells and annular axial flowing fluid are investigated and discussed.

scholarly journals EVALUATION OF THE APPLICABILITY OF A TURBULENT WAKE INLET BOUNDARY CONDITION

2017 ◽  
Vol 16 (2) ◽  
pp. 78
Author(s):  
P. A. Soliman ◽  
A. V. de Paula ◽  
A. P. Petry ◽  
S. V. Möller
Keyword(s):  
Stokes Equations ◽  
Transport Model ◽  
Characteristic Length ◽  
Computational Cost ◽  
The Body ◽  
Navier Stokes ◽  
Computational Time ◽  
Flow Forming ◽  
Shear Stress Transport Model ◽  
Grid Convergence Index

With the objective of reducing the computational cost of the iterative processes of aerodynamic components design, tests were carried out to study under what conditions, and with what difference, only part of the calculation domain can be solved using as input information obtained from complete simulations already solved. An experimental study of an airfoil exposed to the wake interference of an upstream airfoil at a Reynolds number of 150,000 was used to verify the solutions of the Reynolds-Averaged Navier-Stokes equations solved applying the k-ω Shear Stress Transport model for turbulence closure. A Grid Convergence Index study was performed to verify if the solution of the equations for the adopted discretization leads to results within the asymptotic range. With the physical coherence of the numerical methodology verified, comparisons between the simulations with the domain comprising the two airfoils and the domain comprising only the downstream airfoil were performed. Computational time reductions in the order of 40% are observed. The differences in the aerodynamic coefficients for the two types of simulation are presented as a function of distances non-dimensionalized by the characteristic length of the body that disturbs the flow forming the wake, showing that the difference between the two methods was inversely proportional to the distance between the two bodies. Behavior that was maintained until a point where the simulation diverges, equivalent to 25% of the characteristic length of the body that generates the wake.

scholarly journals Computation of Pressure Fields around a Two-Dimensional Circular Cylinder Using the Vortex-In-Cell and Penalization Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seung-Jae Lee ◽  
Jun-Hyeok Lee ◽  
Jung-Chun Suh
Keyword(s):  
Circular Cylinder ◽  
Solid Body ◽  
Pressure Field ◽  
Stokes Equations ◽  
Computational Cost ◽  
Fixed Time ◽  
Computational Grids ◽  
Penalty Term ◽  
Pressure Fields ◽  
Wide Range

The vorticity-velocity formulation of the Navier-Stokes equations allows purely kinematical problems to be decoupled from the pressure term, since the pressure is eliminated by applying the curl operator. The Vortex-In-Cell (VIC) method, which is based on the vorticity-velocity formulation, offers particle-mesh algorithms to numerically simulate flows past a solid body. The penalization method is used to enforce boundary conditions at a body surface with a decoupling between body boundaries and computational grids. Its main advantage is a highly efficient implementation for solid boundaries of arbitrary complexity on Cartesian grids. We present an efficient algorithm to numerically implement the vorticity-velocity-pressure formulation including a penalty term to simulate the pressure fields around a solid body. In vorticity-based methods, pressure field can be independently computed from the solution procedure for vorticity. This clearly simplifies the implementation and reduces the computational cost. Obtaining the pressure field at any fixed time represents the most challenging goal of this study. We validate the implementation by numerical simulations of an incompressible viscous flow around an impulsively started circular cylinder in a wide range of Reynolds numbers: Re=40, 550, 3000, and 9500.

Use of Experimental Data for an Efficient Description of Turbulent Flows

1990 ◽  
Vol 43 (5S) ◽  
pp. S240-S245 ◽  
Author(s):  
N. Aubry
Keyword(s):  
Experimental Data ◽  
Turbulent Flows ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Original System ◽  
Navier Stokes ◽  
Lorenz Attractor ◽  
Wall Region ◽  
Lorenz Equations ◽  
Chaotic Solution

The proper orthogonal decomposition (POD), also called Karhunen-Loe`ve expansion, which extracts ‘coherent structures’ from experimental data, is a very efficient tool for analyzing and modeling turbulent flows. It has been shown that it converges faster than any other expansion in terms of kinetic energy (Lumley 1970). First, the POD is applied to the chaotic solution of the Lorenz equations. The dynamics of the Lorenz attractor is reconstructed by only the first three POD modes. In the second part of this paper, we show how the POD can be used in turbulence modeling. The particular case studied is the wall region of a turbulent boundary layer. In this flow, the velocity field is expanded into POD modes in the normal direction and Fourier modes in the streamwise and spanwise directions. Dynamical systems are obtained by Galerkin projections of the Navier Stokes equations onto the different modes. Aubry et al. (1988) applied the technique to derive and study a ten dimensional representation which reproduced qualitatively the bursting event experimentally observed. It is shown that streamwise modes, absent in Aubry et al.’s model, participate to the bursting events. This agrees remarkably well with experimental observations. In both examples, the dynamics of the original system is very well recovered from the contribution of only a few modes.

scholarly journals Three-Dimensional Turbulent Vortex Shedding From a Surface-Mounted Square Cylinder: Predictions With Large-Eddy Simulations and URANS

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
B. A. Younis ◽  
A. Abrishamchi
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
Large Eddy

The paper reports on the prediction of the turbulent flow field around a three-dimensional, surface mounted, square-sectioned cylinder at Reynolds numbers in the range 104–105. The effects of turbulence are accounted for in two different ways: by performing large-eddy simulations (LES) with a Smagorinsky model for the subgrid-scale motions and by solving the unsteady form of the Reynolds-averaged Navier–Stokes equations (URANS) together with a turbulence model to determine the resulting Reynolds stresses. The turbulence model used is a two-equation, eddy-viscosity closure that incorporates a term designed to account for the interactions between the organized mean-flow periodicity and the random turbulent motions. Comparisons with experimental data show that the two approaches yield results that are generally comparable and in good accord with the experimental data. The main conclusion of this work is that the URANS approach, which is considerably less demanding in terms of computer resources than LES, can reliably be used for the prediction of unsteady separated flows provided that the effects of organized mean-flow unsteadiness on the turbulence are properly accounted for in the turbulence model.

A Numerical Study of the Hydrodynamics of Reversing Flows Around a Cylinder

1994 ◽  
Vol 116 (4) ◽  
pp. 202-208 ◽  
Author(s):  
K. Nakajima ◽  
Y. Kallinderis ◽  
I. Sibetheros ◽  
R. W. Miksad ◽  
K. Lambrakos
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Stokes Equations ◽  
Numerical Study ◽  
Offshore Structures ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Random Behavior ◽  
Marching Scheme

A numerical study of the nonlinear and random behavior of flow-induced forces on offshore structures and experimental verification of the results are presented. The numerical study is based on a finite-element method for the unsteady incompressible Navier-Stokes equations in two dimensions. The momentum equations combined with a pressure correction equation are solved employing fourth-order artificial dissipation with a nonstaggered grid, instead of the more commonly used staggered meshes. The solution is advanced in time with a combined explicit and implicit marching scheme. Emphasis is placed on study of reversing flows around a cylinder. Comparisons with experimental data evaluate accuracy and robustness of the method.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

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