scholarly journals On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
J.-F. Simon ◽  
J. P. Thomas ◽  
O. Léonard
Keyword(s):  
Flow Field ◽  
Flow Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Averaging ◽  
Analysis Tool ◽  
Reynolds Stresses ◽  
Present Contribution ◽  
Navier Stokes Equations ◽  
Throughflow Model

This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk’s flow model describes the 3D time-averaged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging, and a passage-to-passage averaging on the Navier–Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3D average-passage flow. The resulting set of equations is similar to the 2D axisymmetric Navier–Stokes equations, but additional terms resulting from the averages show up: blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses, and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution. The stresses and the blade forces are determined from 3D steady and unsteady databases (a low-speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier–Stokes equations. A good agreement between the throughflow solution and the averaged 3D results is obtained. These results are also compared to those obtained with a more “classical” throughflow approach based on a Navier–Stokes formulation for the endwall losses, correlations for profile losses, and a simple radial mixing model assuming turbulent diffusion.

scholarly journals On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

2008 ◽  
Author(s):  
J.-F. Simon ◽  
O. Le´onard
Keyword(s):  
Flow Field ◽  
Flow Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Averaging ◽  
Analysis Tool ◽  
Reynolds Stresses ◽  
Present Contribution ◽  
Navier Stokes Equations ◽  
Throughflow Model

This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk’s flow model describes the 3-D time-averaged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging and a passage-to-passage averaging on the Navier-Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3-D average-passage flow. The resulting set of equations is similar to the 2-D axisymmetric Navier-Stokes equations but additional terms resulting from the averages show up: blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution. The stresses and the blade forces are determined from 3-D steady and unsteady databases (a low speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier-Stokes equations. A good agreement between the throughflow solution and the averaged 3-D results is obtained. These results are also compared to those obtained with a more “classical” throughflow approach based on a Navier-Stokes formulation for the endwall losses, correlations for profile losses and a simple radial mixing model assuming turbulent diffusion.

On the Flow Fields of Inertial Impactors

1974 ◽  
Vol 96 (4) ◽  
pp. 394-400 ◽  
Author(s):  
V. A. Marple ◽  
B. Y. H. Liu ◽  
K. T. Whitby
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Water Model ◽  
Navier Stokes ◽  
Visualization Technique ◽  
Navier Stokes Equations ◽  
Theoretical Results ◽  
Plate Distance ◽  
Good Agreement

The flow field in an inertial impactor was studied experimentally with a water model by means of a flow visualization technique. The influence of such parameters as Reynolds number and jet-to-plate distance on the flow field was determined. The Navier-Stokes equations describing the laminar flow field in the impactor were solved numerically by means of a finite difference relaxation method. The theoretical results were found to be in good agreement with the empirical observations made with the water model.

Fluid flow over and through a regular bundle of rigid fibres

2016 ◽  
Vol 792 ◽  
pp. 5-35 ◽  
Author(s):  
Giuseppe A. Zampogna ◽  
Alessandro Bottaro
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Flow Field ◽  
Stokes Equations ◽  
Transversely Isotropic ◽  
Navier Stokes ◽  
Leading Order ◽  
Macroscopic Scale ◽  
Navier Stokes Equations ◽  
Homogenized Model

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model’s results to both experimental measurements and direct numerical simulations of the Navier–Stokes equations which resolve the flow also through the pores of the medium.

Simulation of Acoustic Streaming in a Resonator

2004 ◽  
Author(s):  
Bakhtier Farouk ◽  
Murat K. Aktas
Keyword(s):  
Flow Field ◽  
Standing Wave ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Acoustic Streaming ◽  
Flow Patterns ◽  
Vortical Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Streaming Flow

Formation of vortical flow structures in a rectangular enclosure due to acoustic streaming is investigated numerically. The oscillatory flow field in the enclosure is created by the vibration of a vertical side wall of the enclosure. The frequency of the wall vibration is chosen such that a standing wave forms in the enclosure. The interaction of this standing wave with the horizontal solid walls leads to the production of Rayleigh type acoustic streaming flow patterns in the enclosure. All four walls of the enclosure considered are thermally insulated. The fully compressible form of the Navier-Stokes equations is considered and an explicit time-marching algorithm is used to explicitly track the acoustic waves. Numerical solutions are obtained by employing a highly accurate flux corrected transport (FCT) algorithm for the convection terms. A time-splitting technique is used to couple the viscous and diffusion terms of the full Navier-Stokes equations. Non-uniform grid structure is employed in the computations. The simulation of the primary oscillatory flow and the secondary (steady) streaming flows in the enclosure is performed. Streaming flow patterns are obtained by time averaging the primary oscillatory flow velocity distributions. The effect of the amount of wall displacement on the formation of the oscillatory flow field and the streaming structures are studied. Computations indicate that the nonlinearity of the acoustic field increases with increasing amount of the vibration amplitude. The form and the strength of the secondary flow associated with the oscillatory flow field and viscous effects are found to be strongly correlated to the maximum displacement of the vibrating wall. Total number of acoustic streaming cells per wavelength is also determined by the strength and the level of the nonlinearity of the sound field in the resonator.

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.

Modelling of By-Pass Transition With Conditioned Navier-Stokes Equations and a K-E Model Adapted for Intermittency

1994 ◽  
Author(s):  
J. Steelant ◽  
E. Dick
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Suction Side ◽  
Navier Stokes ◽  
Intermittent Flow ◽  
Time Averaging ◽  
Bypass Transition ◽  
Navier Stokes Equations ◽  
Direct Excitation ◽  
Energy Equations

Turbomachinery flows are characterized by a very high intensity turbulent mean part. As a consequence, laminar flow in boundary layer regions undergoes transition through direct excitation of turbulence. This is the so-called bypass transition. Regions form that are intermittently laminar and turbulent. In particular in accelerating flows, as on the suction side of a turbine blade, this intermittent flow can extend over a very large part of the boundary layer. Classical turbulence modelling based on global time averaging is not valid in intermittent flows. To take correctly account of the intermittency, conditioned averages are necessary. These are averages taken during the fraction of time the flow is turbulent or laminar respectively. Starting from the Navier-Stokes equations, conditioned continuity, momentum and energy equations are derived for the laminar and turbulent parts of an intermittent flow. The turbulence is described by the classical k-ε model. The supplementary parameter introduced by the conditioned averaging is the intermittency factor. In the calculations, this factor is prescribed in an algebraic way.

CFD in the Loop: Ensemble Kalman Filtering With Underwater Mobile Sensor Networks

2014 ◽  
Author(s):  
Axel Hackbarth ◽  
Edwin Kreuzer ◽  
Thorben Schröder
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Mobile Sensor ◽  
Dynamic Simulations ◽  
Navier Stokes Equations ◽  
Time Flow ◽  
Strong Current ◽  
Predictive Controller

In marine environments, sparse in-situ measurements can be used for the estimation of the fluid dynamic field. To make best use of a mobile sensor network in an environment whose dynamics can be described by the Navier-Stokes equations, we developed a framework for data assimilation with motion-constrained underwater vehicles, that takes the physical field properties into account while sampling. Our algorithm uses an ensemble Kalman filter that propagates hundreds of slightly varied coarse fluid dynamic simulations through time. Flow and scalar measurements from the mobile sensors are integrated into all ensemble members. We implemented a model predictive controller to calculate covariance minimizing paths from the estimated flow field and motion primitives of the vehicles, which are affected by a strong current. Thereby, we were able to indirectly track dynamically changing wall temperatures through measurements of flow field variables.

Numerical Simulation of Electromagnetic Stirring Effect on Flow Pattern of Metal Melt

2011 ◽  
Vol 264-265 ◽  
pp. 1574-1579
Author(s):  
H. Namaki ◽  
S. Hossein Seyedein ◽  
M.R. Afshar Moghadam ◽  
R. Ghasemzadeh
Keyword(s):  
Flow Pattern ◽  
Maxwell Equations ◽  
Flow Model ◽  
Stokes Equations ◽  
Electromagnetic Stirring ◽  
Navier Stokes ◽  
Simultaneous Solution ◽  
Navier Stokes Equations ◽  
Stirring Effect ◽  
Good Agreement

In this study, a mathematical model was developed to simulate 2-D axisymmetric melt flow under magnetic field in a cylindrical container. The modeling of this process required the simultaneous solution of the turbulent Navier-Stokes equations together with Maxwell equations. The flow pattern in liquid bath was obtained using a two-equation κ-є turbulent flow model, which was further used to obtain the solute distribution. The governing differential equations were solved numerically using finite volume based finite difference method. The computed results, were found to be in good agreement with the measurements reported in the literature. The effect of stirring parameters on temperature homogeneity of the melt have been discussed and presented.

scholarly journals Numerical and Experimental Investigation of a Supersonic Flow Field around Solid Fuel on an Inclined Flat Plate

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Uzu-Kuei Hsu
Keyword(s):  
Flow Field ◽  
Solid Fuel ◽  
Stokes Equations ◽  
Control Volume ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Volume Method ◽  
Environmental Temperatures ◽  
Gasification Temperature

This research adopts a shock tube 16 meters long and with a 9 cm bore to create a supersonic, high-temperature, and high-pressure flowfield to observe the gasification and ignition of HTPB solid fuel under different environments. Also, full-scale 3D numerical simulation is executed to enhance the comprehension of this complex phenomenon. The CFD (Computational Fluid Dynamics) code is based on the control volume method and the pre-conditioning method for solving the Navier-Stokes equations to simulate the compressible and incompressible coupling problem. In the tests, a HTPB slab is placed in the windowed-test section. Various test conditions generate different supersonic Mach numbers and environmental temperatures. In addition, the incident angles of the HTPB slab were changed relative to the incoming shock wave. Results show that as the Mach number around the slab section exceeded 1.25, the flowfield temperature achieved 1100 K, which is higher than the HTPB gasification temperature (930 K~1090 K). Then, gasification occurred and a short-period ignition could be observed. In particular, when the slab angle was7∘, the phenomenon became more visible. This is due to the flow field temperature increase when the slab angle was at7∘.

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