scholarly journals A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery

1993 ◽  
Author(s):  
Kenneth C. Hall ◽  
William S. Clark ◽  
Christopher B. Lorence
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Computational Method ◽  
Shock Capturing ◽  
Flow Conditions ◽  
Mean Flow ◽  
Transonic Flows ◽  
Linearized Euler Equations ◽  
Volume Equations

A computational method for efficiently predicting unsteady transonic flows in two- and three-dimensional cascades is presented. The unsteady flow is modelled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax-Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.

scholarly journals A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery

1994 ◽  
Vol 116 (3) ◽  
pp. 477-488 ◽  
Author(s):  
K. C. Hall ◽  
W. S. Clark ◽  
C. B. Lorence
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Computational Method ◽  
Shock Capturing ◽  
Flow Conditions ◽  
Mean Flow ◽  
Transonic Flows ◽  
Linearized Euler Equations ◽  
Volume Equations

A computational method for efficiently predicting unsteady transonic flows in two-and three-dimensional cascades is presented. The unsteady flow is modeled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax–Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.

The influence of mean shear on Alfvén-internal wave propagation

1976 ◽  
Vol 15 (2) ◽  
pp. 197-222
Author(s):  
R. J. Hartman
Keyword(s):  
Three Dimensional ◽  
Dimensional System ◽  
Linear Wave ◽  
Mean Flow ◽  
Wave Processes ◽  
Initial Value ◽  
Initial Wave ◽  
Wave Phenomena ◽  
Three Dimensional System

This paper uses the general solution of the linearized initial-value problem for an unbounded, exponentially-stratified, perfectly-conducting Couette flow in the presence of a uniform magnetic field to study the development of localized wave-type perturbations to the basic flow. The two-dimensional problem is shown to be stable for all hydrodynamic Richardson numbers JH, positive and negative, and wave packets in this flow are shown to approach, asymptotically, a level in the fluid (the ‘isolation level’) which is a smooth, continuous, function of JH that is well defined for JH < 0 as well as JH > 0. This system exhibits a rich complement of wave phenomena and a variety of mechanisms for the transport of mean flow kinetic and potential energy, via linear wave processes, between widely-separated regions of fluid; this in addition to the usual mechanisms for the absorption of the initial wave energy itself. The appropriate three-dimensional system is discussed, and the role of nonlinearities on the development of localized disturbances is considered.

scholarly journals Dynamics of Orographically Triggered Banded Convection in Sheared Moist Orographic Flows

2007 ◽  
Vol 64 (10) ◽  
pp. 3542-3561 ◽  
Author(s):  
Oliver Fuhrer ◽  
Christoph Schär
Keyword(s):  
Small Amplitude ◽  
Three Dimensional ◽  
Horizontal Resolution ◽  
Small Scale ◽  
Mean Flow ◽  
Topographic Roughness ◽  
Wide Range ◽  
Orographic Convection ◽  
Wind Profiles

Abstract Shallow orographic convection embedded in an unstable cap cloud can organize into convective bands. Previous research has highlighted the important role of small-amplitude topographic variations in triggering and organizing banded convection. Here, the underlying dynamical mechanisms are systematically investigated by conducting three-dimensional simulations of moist flows past a two-dimensional mountain ridge using a cloud-resolving numerical model. Most simulations address a sheared environment to account for the observed wind profiles. Results confirm that small-amplitude topographic variations can enhance the development of embedded convection and anchor quasi-stationary convective bands to a fixed location in space. The resulting precipitation patterns exhibit tremendous spatial variability, since regions receiving heavy rainfall can be only kilometers away from regions receiving little or no rain. In addition, the presence of banded convection has important repercussions on the area-mean precipitation amounts. For the experimental setup here, the gravity wave response to small-amplitude topographic variations close to the upstream edge of the cap cloud (which is forced by the larger-scale topography) is found to be the dominant triggering mechanism. Small-scale variations in the underlying topography are found to force the location and spacing of convective bands over a wide range of scales. Further, a self-sufficient mode of unsteady banded convection is investigated that does not dependent on external perturbations and is able to propagate against the mean flow. Finally, the sensitivity of model simulations of banded convection with respect to horizontal computational resolution is investigated. Consistent with predictions from a linear stability analysis, convective bands of increasingly smaller scales are favored as the horizontal resolution is increased. However, small-amplitude topographic roughness is found to trigger banded convection and to control the spacing and location of the resulting bands. Thereby, the robustness of numerical simulations with respect to an increase in horizontal resolution is increased in the presence of topographic variations.

scholarly journals Experimental and Computational Study of the Unsteady Flow in a 1.5 Stage Axial Turbine With Emphasis on the Secondary Flow in the Second Stator

1998 ◽  
Author(s):  
Ralf E. Walraevens ◽  
Heinz E. Gallus ◽  
Alexander R. Jung ◽  
Jürgen F. Mayer ◽  
Heinz Stetter
Keyword(s):  
Unsteady Flow ◽  
Secondary Flow ◽  
Computational Study ◽  
Three Dimensional ◽  
Cross Flow ◽  
Axial Flow ◽  
Time Dependent ◽  
Flow Structures ◽  
Mean Flow ◽  
Dependent Flow

A study of the unsteady flow in an axial flow turbine stage with a second stator blade row is presented. The low aspect ratio blades give way to a highly three-dimensional flow which is dominated by secondary flow structures. Detailed steady and unsteady measurements throughout the machine and unsteady flow simulations which include all blade rows have been carried out. The presented results focus on the second stator flow. Secondary flow structures and their origins are identified and tracked on their way through the passage. The results of the time-dependent secondary velocity vectors as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts throughout the domain of the second stator. At each location the experimental and numerical results are compared and discussed. A good overall agreement in the time-dependent flow behaviour as well as in the secondary flow structures is stated.

On the interaction of an internal wavepacket with its induced mean flow and the role of streaming

2018 ◽  
Vol 838 ◽  
Author(s):  
Boyu Fan ◽  
T. Kataoka ◽  
T. R. Akylas
Keyword(s):  
Nonlinear Interaction ◽  
Laboratory Experiments ◽  
Modulation Instability ◽  
Three Dimensional ◽  
Mean Flow ◽  
Interaction Dynamics ◽  
Dimensional Gravity ◽  
Combined Action ◽  
Beam Bending

The coupled nonlinear interaction of three-dimensional gravity–inertia internal wavepackets, in the form of beams with nearly monochromatic profile, with their induced mean flow is discussed. Unlike general three-dimensional wavepackets, such modulated nearly monochromatic beams are not susceptible to modulation instability from their inviscid, purely modulation-induced mean flow. However, streaming – the induced mean flow associated with the production of mean potential vorticity via the combined action of dissipation and nonlinearity – can cause cross-beam bending, transverse broadening and increased along-beam decay of the beam profile, in qualitative agreement with earlier laboratory experiments. For wavepackets with general three-dimensional modulations, by contrast, streaming does arise, but plays a less prominent role in the interaction dynamics.

Non-Equilibrium Relaxing Gas Flow Behind Three Dimensional Unsteady Curved Shock Wave

1980 ◽  
Vol 35 (11) ◽  
pp. 1166-1170
Author(s):  
V. D. Sharma ◽  
Radhe Shyam
Keyword(s):  
Shock Wave ◽  
Unsteady Flow ◽  
Gas Flow ◽  
Three Dimensional ◽  
Flow Conditions ◽  
Shock Surface ◽  
Flow Parameters ◽  
Upstream Flow ◽  
Relaxing Gas ◽  
Non Equilibrium

Abstract A shock wave is assumed to exist in a three-dimensional unsteady flow of a relaxing gas. The variation of flow parameters at any point behind the shock surface is determined in terms of the shock geometry and the upstream flow conditions. The expressions for the vorticity and the curvature of a streak line at the rear of the shock surface are also determined in terms of the known quantities.

Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 2—Computational Results

1993 ◽  
Vol 115 (1) ◽  
pp. 101-109 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Unsteady Flow ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Computational Results ◽  
Flow Conditions ◽  
Viscous Effects ◽  
Blade Flutter ◽  
Coupled Solution

A quasi-three-dimensional inviscid-viscous coupled approached has been developed for unsteady flows around oscillating blades, as described in Part 1. To validate this method, calculations for several steady and unsteady flow cases with strong inviscid-viscous interactions are performed, and the results are compared with the corresponding experiments. Calculated results for unsteady flows around a biconvex cascade and a fan tip section highlight the necessity of including viscous effects in predictions of turbomachinery blade flutter at transonic flow conditions.

scholarly journals Zonal Flow Regime Changes in a GCM and in a Simple Quasigeostrophic Model: The Role of Stratospheric Dynamics

2009 ◽  
Vol 66 (5) ◽  
pp. 1366-1383 ◽  
Author(s):  
Isabella Bordi ◽  
Klaus Fraedrich ◽  
Michael Ghil ◽  
Alfonso Sutera
Keyword(s):  
General Circulation ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Vertical Wind Shear ◽  
Circulation Model ◽  
Zonal Flow ◽  
Heat Fluxes ◽  
Mean Flow ◽  
Single Wave

Abstract The atmospheric general circulation is characterized by both single- and double-jet patterns. The double-jet structure of the zonal mean zonal wind is analyzed in Southern Hemisphere observations for the two calendar months of November and April. The observed features are studied further in an idealized quasigeostrophic and a simplified general circulation model (GCM). Results suggest that capturing the bimodality of the zonal mean flow requires the parameterization of momentum and heat fluxes associated with baroclinic instability of the three-dimensional fields. The role of eddy heat fluxes in generating the observed double-jet pattern is ascertained by using an analytical Eady model with stratospheric easterlies, in which a single wave disturbance interacts with the mean flow. In this model, the dual jets are generated by the zonal mean flow correction. Sensitivity of the results to the tropospheric vertical wind shear (or, equivalently, the meridional temperature gradient in the basic state’s troposphere) is also studied in the Eady model and compared to related experiments using the simplified GCM.

Numerical Solutions for Unsteady Subsonic Vortical Flows Around Loaded Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 810-816 ◽  
Author(s):  
J. Fang ◽  
H. M. Atassi
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Frequency Range ◽  
Mean Flow ◽  
Vortical Flows ◽  
Unsteady Aerodynamic ◽  
Reduced Frequency ◽  
The Mean

A frequency domain linearized unsteady aerodynamic analysis is presented for three-dimensional unsteady vortical flows around a cascade of loaded airfoils. The analysis fully accounts for the distortion of the impinging vortical disturbances by the mean flow. The entire unsteady flow field is calculated in response to upstream three-dimensional harmonic disturbances. Numerical results are presented for two standard cascade configurations representing turbine and compressor bladings for a reduced frequency range from 0.1 to 5. Results show that the upstream gust conditions and blade sweep strongly affect the unsteady blade response.

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