Multi-Airfoil Navier–Stokes Simulations of Turbine Rotor–Stator Interaction

1990 ◽  
Vol 112 (3) ◽  
pp. 377-384 ◽  
Author(s):  
M. M. Rai ◽  
N. K. Madavan
Keyword(s):  
Experimental Data ◽  
Stokes Equations ◽  
Turbine Rotor ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Spatial Dimensions ◽  
Rotor Stator Interaction ◽  
Pitch Ratio ◽  
Experimental Ratio

An accurate numerical analysis of the flows associated with rotor–stator configurations in turbomachinery can be extremely helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier–Stokes equations in two spatial dimensions are solved on a system of patched and overlaid grids for an axial-turbine rotor–stator configuration. The governing equations are solved using a finite-difference, upwind algorithm that is set in an iterative, implicit framework. Results are presented in the form of pressure contours, time-averaged pressures, unsteady pressures, amplitudes, and phase. The numerical results are compared with experimental data and the agreement is found to be good. The results are also compared with those of an earlier study, which used only one rotor and one stator airfoil. The current study uses multiple rotor and stator airfoils and a pitch ratio that is much closer to the experimental ratio. Consequently, the results of this study are found to be closer to the experimental data.

Zero-Pressure-Gradient Turbulent Boundary Layer

1997 ◽  
Vol 50 (12) ◽  
pp. 689-729 ◽  
Author(s):  
William K. George ◽  
Luciano Castillo
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Dynamical Equations ◽  
Navier Stokes Equations ◽  
Theoretical Concepts

Of the many aspects of the long-studied field of turbulence, the zero-pressure-gradient boundary layer is probably the most investigated, and perhaps also the most reviewed. Turbulence is a fluid-dynamical phenomenon for which the dynamical equations are generally believed to be the Navier-Stokes equations, at least for a single-phase, Newtonian fluid. Despite this fact, these governing equations have been used in only the most cursory manner in the development of theories for the boundary layer, or in the validation of experimental data-bases. This article uses the Reynolds-averaged Navier-Stokes equations as the primary tool for evaluating theories and experiments for the zero-pressure-gradient turbulent boundary layer. Both classical and new theoretical ideas are reviewed, and most are found wanting. The experimental data as well is shown to have been contaminated by too much effort to confirm the classical theory and too little regard for the governing equations. Theoretical concepts and experiments are identified, however, which are consistent-both with each other and with the governing equations. This article has 77 references.

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.

scholarly journals Thermochemical Nonequilibrium in Rapidly Expanding Flows of High-Temperature Air

1997 ◽  
Vol 52 (4) ◽  
pp. 358-368 ◽  
Author(s):  
Michio Nishida ◽  
Masashi Matsumotob
Keyword(s):  
High Temperature ◽  
Vibrational Energy ◽  
Stokes Equations ◽  
Computational Study ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Free Jet

Abstract • This paper describes a computational study of the thermal and chemical nonequilibrium occuring in a rapidly expanding flow of high-temperature air transported as a free jet from an orifice into low-density stationary air. Translational, rotational, vibrational and electron temperatures are treated separately, and in particular the vibrational temperatures are individually treated; a multi-vibrational temperature model is adopted. The governing equations are axisymmetric Navier-Stokes equations coupled with species vibrational energy, electron energy and species mass conservation equations. These equations are numerically solved, using the second order upwind TVD scheme of the Harten-Yee type. The calculations were carried out for two different orifice temperatures and also two different orifice diameters to investigate the effects of such parameters on the structure of a nonequilibrium free jet.

Numerical Investigation of Blade Flutter at or Near Stall in Axial Flow Turbomachines

2001 ◽  
Author(s):  
Wolfgang Höhn
Keyword(s):  
Viscous Flow ◽  
Stokes Equations ◽  
Separated Flow ◽  
Parallel Computer ◽  
Navier Stokes ◽  
Computational Domain ◽  
Compressor Cascade ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Blade Flutter

During the design of the compressor and turbine stages of today’s aeroengines, aerodynamically induced vibrations become increasingly important since higher blade load and better efficiency are desired. In this paper the development of a method based on the unsteady, compressible Navier-Stokes equations in two dimensions is described in order to study the physics of flutter for unsteady viscous flow around cascaded vibrating blades at stall. The governing equations are solved by a finite difference technique in boundary fitted coordinates. The numerical scheme uses the Advection Upstream Splitting Method to discretize the convective terms and central differences discretizing the viscous terms of the fully non-linear Navier-Stokes equations on a moving H-type mesh. The unsteady governing equations are explicitly and implicitly marched in time in a time-accurate way using a four stage Runge-Kutta scheme on a parallel computer or an implicit scheme of the Beam-Warming type on a single processor. Turbulence is modelled using the Baldwin-Lomax turbulence model. The blade flutter phenomenon is simulated by imposing a harmonic motion on the blade, which consists of harmonic body translation in two directions and a rotation, allowing an interblade phase angle between neighboring blades. Non-reflecting boundary conditions are used for the unsteady analysis at inlet and outlet of the computational domain. The computations are performed on multiple blade passages in order to account for nonlinear effects. A subsonic massively stalled unsteady flow case in a compressor cascade is studied. The results, compared with experiments and the predictions of other researchers, show reasonable agreement for inviscid and viscous flow cases for the investigated flow situations with respect to the Steady and unsteady pressure distribution on the blade in separated flow areas as well as the aeroelastic damping. The results show the applicability of the scheme for stalled flow around cascaded blades. As expected the viscous and inviscid computations show different results in regions where viscous effects are important, i.e. in separated flow areas. In particular, different predictions for inviscid and viscous flow for the aerodynamic damping for the investigated flow cases are found.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

The space-time CE/SE method for the Navier-Stokes equations in three spatial dimensions

2000 ◽  
Author(s):  
Zeng-Chan Zhang ◽  
S. Yu ◽  
Xiao-Yen Wang ◽  
Sin-Chung Chang ◽  
Philip Jorgenson
Keyword(s):  
Stokes Equations ◽  
Space Time ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Spatial Dimensions

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.

Numerical Study of Oscillatory Flow Past Four Cylinders in Square Arrangement for Pitch Ratio Equal to 4

2011 ◽  
Author(s):  
P. Anagnostopoulos ◽  
Ch. Dikarou ◽  
S. A. Seitanis
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Central Line ◽  
Circular Cylinders ◽  
Navier Stokes ◽  
Constant Frequency ◽  
Navier Stokes Equations ◽  
Symmetry Of The Solution ◽  
Pitch Ratio ◽  
Two Sides

The results of a numerical study of the viscous oscillating flow around four circular cylinders are presented herein, for a constant frequency parameter, β, equal to 50, and Keulegan-Carpenter numbers, KC, ranging between 0.2 and 10. The cylinders were placed on the vertices of a square, whose two sides were perpendicular and two parallel to the oncoming flow, for a pitch ratio, P/D, equal to 4. The finite-element method was employed for the solution of the Navier-Stokes equations, in the formulation where the stream function and the vorticity are the field variables. The streamlines and the vorticity contours generated from the solution were used for the flow visualization. When the Keulegan-Carpenter number is lower than 4, the flow remains symmetrical with respect to the horizontal axis of symmetry of the solution domain and periodic at consecutive cycles. As KC increases to 4 the flow becomes aperiodic in different cycles, although symmetry with respect to the horizontal central line of the domain is preserved. For KC equal to 5 asymmetries appear intermittently in the flow, which are eventually amplified as KC increases still further. These asymmetries, in association with the aperiodicity at different cycles, lead to an almost chaotic configuration, as KC grows larger. For characteristic cases the flow pattern and the traces of the hydrodynamic forces are presented. In addition, the mean and r.m.s. values of the in-line and transverse forces and the hydrodynamic coefficients of the inline force were evaluated for the entire range of Keulegan-Carpenter numbers examined.

scholarly journals Investigating the Effect of the Closure in Partially-Averaged Navier–Stokes Equations

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Filipe S. Pereira ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Coherent Structures ◽  
Stokes Equations ◽  
The Other ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Auxiliary Functions ◽  
Modeling Accuracy

The importance of the turbulence closure to the modeling accuracy of the partially-averaged Navier–Stokes equations (PANS) is investigated in prediction of the flow around a circular cylinder at Reynolds number of 3900. A series of PANS calculations at various degrees of physical resolution is conducted using three Reynolds-averaged Navier–Stokes equations (RANS)-based closures: the standard, shear-stress transport (SST), and turbulent/nonturbulent (TNT) k–ω models. The latter is proposed in this work. The results illustrate the dependence of PANS on the closure. At coarse physical resolutions, a narrower range of scales is resolved so that the influence of the closure on the simulations accuracy increases significantly. Among all closures, PANS–TNT achieves the lowest comparison errors. The reduced sensitivity of this closure to freestream turbulence quantities and the absence of auxiliary functions from its governing equations are certainly contributing to this result. It is demonstrated that the use of partial turbulence quantities in such auxiliary functions calibrated for total turbulent (RANS) quantities affects their behavior. On the other hand, the successive increase of physical resolution reduces the relevance of the closure, causing the convergence of the three models toward the same solution. This outcome is achieved once the physical resolution and closure guarantee the precise replication of the spatial development of the key coherent structures of the flow.

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