Calculation of Wake-Induced Unsteady Flow in a Turbine Cascade

1993 ◽  
Vol 115 (4) ◽  
pp. 675-686 ◽  
Author(s):  
N.-H. Cho ◽  
X. Liu ◽  
W. Rodi ◽  
B. Scho¨nung
Keyword(s):  
Unsteady Flow ◽  
Flow Behavior ◽  
Unsteady Motion ◽  
Equation Model ◽  
Wall Region ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Flow Equations ◽  
Numerical Predictions ◽  
Wake Passing

Numerical predictions are reported for two-dimensional unsteady flow in a linear turbine cascade, where the unsteadiness is caused by passing wakes generated by the preceding row of blades. In particular, an experiment is simulated in which the passing wakes were generated by cylinders moving on a rotating squirrel cage. Blade-to-blade calculations were carried out by solving the unsteady two dimensional flow equations with an accurate finite-volume procedure, thereby resolving the periodic unsteady motion. The effects of stochastic turbulent fluctuations are simulated with a two-layer turbulence model, in which the standard k–ε model is applied in the bulk of the flow and a one-equation model in the near-wall region. This involves also a transition model based on an empirical formula from Abu-Ghannam and Shaw (1980), which was adapted for the unsteady situation by applying it in a Lagrangian way, following fluid parcels in the boundary layer under disturbed and undisturbed free streams on their travel downstream. The calculations are compared with experiments for various wake-passing frequencies. On the whole, the complex unsteady flow behavior is simulated realistically, including the moving forward of transition when the wake-passing frequency increases, but not all details can be reproduced.

Calculation of Wake-Induced Unsteady Flow in a Turbine Cascade

1992 ◽  
Author(s):  
N.-H. Cho ◽  
X. Liu ◽  
W. Rodi ◽  
B. Schönung
Keyword(s):  
Unsteady Flow ◽  
Unsteady Motion ◽  
Equation Model ◽  
Wall Region ◽  
Turbine Cascade ◽  
Flow Equations ◽  
Squirrel Cage ◽  
Numerical Predictions ◽  
2D Flow ◽  
Wake Passing

Numerical predictions are reported of two-dimensional unsteady flow in a linear turbine cascade, where the unsteadiness is caused by passing wakes generated by the preceding row of blades. In particular, an experiment is simulated in which the passing wakes were generated by cylinders moving on a rotating squirrel cage. Blade-to-blade calculations were carried out by solving the unsteady 2D flow equations with an accurate finite-volume procedure, thereby resolving the periodic unsteady motion. The effects of stochastic turbulent fluctuations are simulated with a two-layer turbulence model, in which the standard k-ε model is applied in the bulk of the flow and a one-equation model in the near-wall region. This involves also a transition model based on an empirical formula due to Abu-Ghannam and Shaw (1980), which was adapted for the unsteady situation by applying it in a Lagrangean way, following fluid parcels in the boundary layer underneath disturbed and undisturbed free stream on their travel downstream. The calculations are compared with experiments for various wake-passing frequencies. On the whole, the complex unsteady flow behaviour is simulated realistically, including the moving forward of transition when the wake-passing frequency increases, but not all details can be reproduced.

Three-Dimensional Non-Reflecting Boundary Condition for Linearized Flow Solvers

2010 ◽  
Author(s):  
Paul J. Petrie-Repar
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Equations ◽  
Flow Simulations ◽  
Unsteady Aerodynamic ◽  
2D And 3D

A three-dimensional (3D) non-reflecting boundary condition for linearized flow solvers is presented. The unsteady aerodynamic modes at the inlet and outlet (far-field) are numerically determined by solving an eigen problem for the semi-discretized flow equations on a two-dimensional mesh. Unlike previous methods the shape of the far-field can be general and the non-uniformity of the steady flow across the far-field is considered. The calculated unsteady modes are used to decompose the unsteady flow at the far-field into modes. The direction of each mode is determined, and incoming modes are prescribed and outgoing modes are extrapolated. The results of 2D and 3D inviscid linearised flow simulations using the new boundary condition are presented.

Unsteady Flow in Oscillating Turbine Cascades: Part 2—Computational Study

1998 ◽  
Vol 120 (2) ◽  
pp. 269-275 ◽  
Author(s):  
L. He
Keyword(s):  
Unsteady Flow ◽  
Flow Separation ◽  
Computational Study ◽  
Flow Behavior ◽  
Numerical Test ◽  
Computational Method ◽  
Influence Coefficient ◽  
Turbine Cascade ◽  
Influence Coefficient Method ◽  
Coefficient Method

Unsteady flow around a linear oscillating turbine cascade has been experimentally and computationally studied, aimed at understanding the bubble type of flow separation and examining the predictive ability of a computational method. It was also intended to check the validity of the linear assumption under an unsteady viscous flow condition. Part 2 of the paper presents a computational study of the experimental turbine cascade that was discussed in Part 1. Numerical calculations were carried out for this case using an unsteady Navier–Stokes solver. The Baldwin–Lomax mixing length model was adopted for turbulence closure. The boundary layers on blade surfaces were either assumed to be fully turbulent or transitional with the unsteady transition subject to a quasi-steady laminar separation bubble model. The comparison between the computations and the experiment was generally quite satisfactory, except in the regions with the flow separation. It was shown that the behavior of the short bubble on the suction surface could be reasonably accounted for by using the quasi-steady bubble transition model. The calculation also showed that there was a more apparent mesh dependence of the results in the regions of flow separation. Two different kinds of numerical test were carried out to check the linearity of the unsteady flow and therefore the validity of the influence coefficient method. First, calculations using the same configurations as in the experiment were performed with different oscillating amplitudes. Second, calculations were performed with a tuned cascade model and the results were compared with those using the influence coefficient method. The present work showed that the nonlinear effect was quite small, even though for the most severe case in which the separated flow region covered about 60 percent of blade pressure surface with a large movement of the reattachment point. It seemed to suggest that the linear assumption about the unsteady flow behavior should be adequately acceptable for situations with bubble-type flow separation similar to the present case.

scholarly journals Integrable unsteady motion with an application to ocean eddies

1998 ◽  
Vol 5 (3) ◽  
pp. 145-151
Author(s):  
A. D. Kirwan, Jr. ◽  
B. L. Lipphardt, Jr.
Keyword(s):  
Potential Vorticity ◽  
Particle Motion ◽  
Gulf Stream ◽  
Incompressible Flows ◽  
Unsteady Motion ◽  
Ring System ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ocean Eddies ◽  
Multilayered Systems

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

scholarly journals Effects of Periodic Wake Passing Upon Aerodynamic Loss of a Turbine Cascade: Part I — Measurements of Wake-Affected Cascade Loss by Use of a Pneumatic Probe

1999 ◽  
Author(s):  
Ken-ichi Funazaki ◽  
Nobuaki Tetsuka ◽  
Tadashi Tanuma
Keyword(s):  
Turbine Cascade ◽  
Flow Angle ◽  
Linear Cascade ◽  
Local Loss ◽  
Aerodynamic Loss ◽  
Free Stream Turbulence ◽  
Pressure Distributions ◽  
Wake Turbulence ◽  
Wake Passing ◽  
Profile Loss

This paper reports on an experimental investigation of aerodynamic loss of a low-speed linear turbine cascade which is subjected to periodic wakes shed from moving bars of the wake generator. In this case, parameters related to the wake, such as wake passing frequency (wake Strouhal number) or wake turbulence characteristics, are varied to see how these wake-related parameters affect the local loss distribution or mass-averaged loss coefficient of the turbine cascade. Free-stream turbulence intensity is changed by use of a turbulence grid. In Part I of this paper a focus is placed on the measurements by use of a pneumatic five-hole yawmeter, which provides time-averaged stagnation pressure distributions downstream of the moving bars as well as of the turbine cascade. Spanwise distributions of wake-affected exit flow angle are also measured. From this study it is found that the wake passing greatly affects not only the profile loss but secondary loss of the linear cascade. Noticeable change in exit flow angle is also identified.

Calculation of two-dimensional dispersion in a gas in unsteady flow in a porous medium

1983 ◽  
Vol 17 (5) ◽  
pp. 704-710
Author(s):  
E. G. Basanskii ◽  
V. M. Kolobashkin ◽  
N. A. Kudryashov
Keyword(s):  
Porous Medium ◽  
Unsteady Flow ◽  
Two Dimensional

On the criteria for reverse transition in a two-dimensional boundary layer flow

1969 ◽  
Vol 35 (2) ◽  
pp. 225-241 ◽  
Author(s):  
M. A. Badri Narayanan ◽  
V. Ramjee
Keyword(s):  
Longitudinal Velocity ◽  
Outer Region ◽  
Transition Process ◽  
Velocity Profiles ◽  
Wall Region ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Reverse Transition ◽  
Turbulence Decay

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

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