An Asymptotic Analysis of Mixing Loss

1995 ◽  
Vol 117 (3) ◽  
pp. 367-374 ◽  
Author(s):  
G. Fritsch ◽  
M. B. Giles
Keyword(s):  
Asymptotic Analysis ◽  
Compressible Flow ◽  
Control Volume ◽  
Physical Significance ◽  
Pressure Waves ◽  
Two Dimensional ◽  
Asymptotic Approach ◽  
Transonic Turbine ◽  
Steady Simulation ◽  
Interface Mixing

The objective of this paper is to establish, in a rigorous mathematical manner, a link between the dissipation of unsteadiness in a two-dimensional compressible flow and the resulting mixing loss. A novel asymptotic approach and a control-volume argument are central to the analysis. It represents the first work clearly identifying the separate contributions to the mixing loss from simultaneous linear disturbances, i.e., from unsteady entropy, vorticity, and pressure waves. The results of the analysis have important implications for numerical simulations of turbomachinery flows; the mixing loss at the stator/rotor interface in steady simulations and numerical smoothing are discussed in depth. For a transonic turbine, the entropy rise through the stage is compared for a steady and an unsteady viscous simulation. The larger interface mixing loss in the steady simulation is pointed out and its physical significance is discussed. The asymptotic approach is then applied to the first detailed analysis of interface mixing loss. Contributions from different wave types and wavelengths are quantified and discussed.

scholarly journals An Asymptotic Analysis of Mixing Loss

1993 ◽  
Author(s):  
Gerd Fritsch ◽  
Michael B. Giles
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Compressible Flow ◽  
Control Volume ◽  
Physical Significance ◽  
Pressure Waves ◽  
Asymptotic Approach ◽  
Transonic Turbine ◽  
Steady Simulation ◽  
Interface Mixing

The objective of this paper is to establish, in a rigorous mathematical manner, a link between the dissipation of unsteadiness in a 2D compressible flow and the resulting mixing loss. A novel asymptotic approach and a control-volume argument are central to the analysis. It represents the first work clearly identifying the separate contributions to the mixing loss from simultaneous linear disturbances, i.e. from unsteady entropy, vorticity, and pressure waves. The results of the analysis have important implications for numerical simulations of turbomachinery flows; the mixing loss at the stator/rotor interface in steady simulations and numerical smoothing are discussed in depth. For a transonic turbine, the entropy rise through the stage is compared for a steady and an unsteady viscous simulation. The large interface mixing loss in the steady simulation is pointed out and its physical significance is discussed. The asymptotic approach is then applied to the first detailed analysis of interface mixing loss. Contributions from different wave types and wavelengths are quantified and discussed.

Nonlinear dynamics of a two dimensional airfoil with freeplay in an inviscid compressible flow

2000 ◽  
Vol 4 (2) ◽  
pp. 125-133 ◽  
Author(s):  
Zoran Dimitrijević ◽  
Guy Daniel Mortchéléwicz ◽  
Fabrice Poirion
Keyword(s):  
Nonlinear Dynamics ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Inviscid Compressible Flow

An obstacle problem for elliptic membrane shells

2018 ◽  
Vol 24 (5) ◽  
pp. 1503-1529 ◽  
Author(s):  
Philippe G. Ciarlet ◽  
Cristinel Mardare ◽  
Paolo Piersanti
Keyword(s):  
Vector Field ◽  
Asymptotic Analysis ◽  
Obstacle Problem ◽  
Displacement Vector ◽  
Middle Surface ◽  
Two Dimensional ◽  
Displacement Vector Field ◽  
Membrane Shells ◽  
Signorini Condition ◽  
Confinement Condition

Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement condition expressing that all the points of the admissible deformed configurations remain in a given half-space. To this end, we embed the shell into a family of linearly elastic elliptic membrane shells, all sharing the same middle surface [Formula: see text], where [Formula: see text] is a domain in [Formula: see text] and [Formula: see text] is a smooth enough immersion, all subjected to this confinement condition, and whose thickness [Formula: see text] is considered as a “small” parameter approaching zero. We then identify, and justify by means of a rigorous asymptotic analysis as [Formula: see text] approaches zero, the corresponding “limit” two-dimensional variational problem. This problem takes the form of a set of variational inequalities posed over a convex subset of the space [Formula: see text]. The confinement condition considered here considerably departs from the Signorini condition usually considered in the existing literature, where only the “lower face” of the shell is required to remain above the “horizontal” plane. Such a confinement condition renders the asymptotic analysis substantially more difficult, however, as the constraint now bears on a vector field, the displacement vector field of the reference configuration, instead of on only a single component of this field.

The Aerodynamics of Trailing-Edge-Cooled Transonic Turbine Blades: Part 2 — Theoretical and Computational Approach

1997 ◽  
Author(s):  
Mathias Deckers ◽  
John D. Denton
Keyword(s):  
Transonic Flow ◽  
Theoretical Study ◽  
Computational Study ◽  
Control Volume ◽  
Turbine Blades ◽  
Computational Approach ◽  
Trailing Edge ◽  
Time Marching ◽  
Transonic Turbine ◽  
Volume Method

A theoretical and computational study into the aerodynamics of trailing-edge-cooled transonic turbine blades is described in this part of the paper. The theoretical study shows that, for unstaggered blades with coolant ejection, the base pressure and overall loss can be determined exactly by a simple control volume analysis. This theory suggests that a thick, cooled trailing edge with a wide slot can be more efficient than a thin, solid trailing edge. An existing time-marching finite volume method is adapted to calculate the transonic flow with trailing edge coolant ejection on a structured, quasi-orthogonal mesh. Good overall agreement between the present method, inviscid and viscous, and experimental evidence is obtained.

scholarly journals Asymptotic analysis of a two--dimensional coupled problem for compressible viscous flows

2003 ◽  
Vol 10 (1-2) ◽  
pp. 137-163
Author(s):  
Cristian A. Coclici ◽  
Jörg Heiermann ◽  
Gh. Moroşanu ◽  
W. Wendland
Keyword(s):  
Asymptotic Analysis ◽  
Viscous Flows ◽  
Two Dimensional ◽  
Coupled Problem ◽  
Compressible Viscous Flows

scholarly journals Resonance Vibration of Mistuned Bladed Discs in Stationary Operations

1997 ◽  
Author(s):  
Romuald Rządkowski
Keyword(s):  
Numerical Model ◽  
Compressible Flow ◽  
Two Dimensional ◽  
Rotating System ◽  
Response Level ◽  
Stationary Response ◽  
The Real ◽  
Disc Model ◽  
Real Geometry ◽  
Airfoil Blades

A numerical model for the calculation of resonance stationary response of mistuned bladed disc is presented. The bladed disc model includes all important effects on a rotating system of the real geometry. The excitation forces were calculated by a code on the basis of two-dimensional compressible flow (to M < 0.8) for thin airfoil blades. The calculations presented in this paper show that centrifugal stress, and the values of excitation forces, play an important role in considering the influence of mistuning on the response level.

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