Measurement of Nonsteady Forces in Three Turbine Stage Geometries Using the Hydraulic Analogy

1978 ◽  
Vol 100 (4) ◽  
pp. 525-532 ◽  
Author(s):  
N. F. Rieger ◽  
A. L. Wicks
Keyword(s):  
Free Surface ◽  
Gas Flow ◽  
Two Dimensional ◽  
Turbine Stage ◽  
Summary Table ◽  
Rotating Blade ◽  
Blade Row ◽  
Gasdynamic Flow ◽  
Flow Through ◽  
Hydraulic Analogy

Experimental results for the nonsteady forces and nonsteady torques acting at the e.g. of an instrumented moving turbine blade have been obtained. Three different turbine stage geometries have been tested in this manner. The data described was obtained using a rotating model turbine stage consisting of a row of stationary inlet nozzles and a rotating blade row. The hydraulic analogy was used to stimulate the two-dimensional gasdynamic flow through the three stage geometries in turn. The free-surface horizontal flow of water across the rotating water table then represents the gas flow through the stage. Results for the nonsteady forces and torques in the tangential, axial, and torsional directions are presented as dimensionless force ratios or dimensionless torque ratios in each instance. Charts of results are presented for various stage pressure ratios, for practical ranges of stage velocity ratios. Typical results and observed trends are discussed in detail, and a summary table of observed nonsteady excitation values is presented.

Calculations of Cooled Turbine Efficiency

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
J. H. Horlock ◽  
Leonardo Torbidoni
Keyword(s):  
Film Cooling ◽  
Gas Flow ◽  
Coolant Flow ◽  
The Other ◽  
Turbine Stage ◽  
Isentropic Expansion ◽  
Turbine Efficiency ◽  
Flow Through ◽  
Definition Of ◽  
Industrial Gas Turbine

The efficiency of a cooled turbine stage has been discussed in the literature. All proposed definitions compare the actual power output with an ideal output, which has to be determined; but usually, one of two definitions has been used by turbine designers. In the first, the so-called Hartsel efficiency, the mainstream gas flow, and the various coolant flows to rotor and stator are assumed to expand separately and isentropically to the backpressure. In the second, it is assumed that these flows mix at constant (mainstream) gas pressure before expanding isentropically (sometimes, the rotor coolant flow is ignored in this definition). More recently, it has been suggested that a thermodynamically sounder definition is one in which the gas and coolant flows mix reversibly and adiabatically before isentropic expansion to the backpressure. In the current paper, these three efficiencies are compared, for a typical stage—the first cooled stage of a multistage industrial gas turbine. It is shown that all the efficiencies fall more or less linearly with increase of the fractional (total) coolant flow. It is also shown that the new definition of efficiency gives values considerably lower than the other two efficiencies, which are more widely used at present. Finally, the various irreversibilities associated with the flow through a cooled turbine are calculated. Although all these irreversibilities increase with the fractional coolant flow, it is shown that the “thermal” irreversibility associated with film cooling is higher than the other irreversibilities at large fractional coolant flow.

A Numerical Modelling of Stator-Rotor Interaction in a Turbine Stage With Oscillating Blades

2002 ◽  
Author(s):  
V. I. Gnesin ◽  
L. V. Kolodyazhnaya ◽  
R. Rzadkowski
Keyword(s):  
Gas Flow ◽  
Mutual Influence ◽  
Structural Equations ◽  
Rotor Blades ◽  
Turbine Stage ◽  
Aerodynamic Forces ◽  
Time Step ◽  
Outer Flow ◽  
Flow Through ◽  
Flow Nonuniformity

In real flows nonstationary phenomena connected with the circumferential non-uniformity of the main flow and those caused by oscillations of blades are observed only jointly. An understanding of the physics of the mutual interaction between gas flow and oscillating blades, and the development of predictive capabilities is essential for improved overall efficiency, durability and reliability. In the study presented the algorithm proposed involves the coupled solution of 3D unsteady flow through a turbine stage and dynamic problem for rotor blades motion by action of aerodynamic forces without separating of outer and inner flow fluctuations. The partially integrated method involves the solution of the fluid and structural equations separately, but information is exchanged at each time step, so that solution from one domain is used as boundary condition for the other domain. 3D transonic gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite-volume difference scheme of Godunov-Kolgan. The structure analysis uses the modal approach and 3D finite element model of a blade. The blade moving is assumed to be constituted as a linear combination of the first natural modes of blade oscillations with the modal coefficients depending on time. There has been performed the calculation for the last stage of the steam turbine. The numerical results for unsteady aerodynamic forces due to stator-rotor interaction are compared with results obtained with taking into account the blades oscillations. It has investigated the mutual influence of both outer flow nonuniformity and blades oscillations. It has shown that amplitude-frequency spectrum of blade oscillations contains the high frequency harmonics, corresponding to rotor moving past one stator blade pitch, and low frequency harmonics caused by blade oscillations and flow nonuniformity downstream from the blade row. Moreover, the spectrum involves the harmonics which are not multiple to the rotation frequency.

The Unsteady Response of a Blade Row From Measurements of the Time-Mean Total Pressure

1973 ◽  
Author(s):  
R. E. Henderson
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Total Pressure ◽  
Theoretical Data ◽  
Two Dimensional ◽  
Interference Effects ◽  
Experimental Procedure ◽  
Rotating Blade ◽  
Reduced Frequency ◽  
Blade Row

An experimental procedure is described which permits the unsteady response of a rotating blade row to spatial variations in its inlet flow to be determined from measurements of the time-mean total pressure. This procedure has been employed to determine the unsteady circulation of a non-lifting rotor as a function of reduced frequency for two values of space-chord ratio. Comparisons of these experimental data are made with a recent theoretical analysis of the indirect or design problem of unsteady lift in a moving two-dimensional cascade. Both the experimental and theoretical data are shown to exhibit the same trends with variations in space-chord ratio and reduced frequency. These results demonstrate that the unsteady blade interference effects are significant, and that the representation of the unsteady response of a turbomachine blade row as an isolated airfoil is not valid for reduced frequencies less than 1.2.

Numerical analysis of rarefied gas flow through two-dimensional nozzles

1995 ◽  
Vol 11 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Chan-Hong Chung ◽  
Kenneth J. De Witt ◽  
Duen-Ren Jeng ◽  
Theo G. Keith
Keyword(s):  
Numerical Analysis ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Two Dimensional ◽  
Rarefied Gas Flow ◽  
Flow Through

2-D CFD Model for Free Surface River Flow with Tilt Rigid Leave of Submerged Vegetation

2012 ◽  
Vol 212-213 ◽  
pp. 332-335 ◽  
Author(s):  
Yan Hong Li ◽  
Li Quan Xie
Keyword(s):  
Free Surface ◽  
Velocity Profile ◽  
River Flow ◽  
Longitudinal Velocity ◽  
Submerged Vegetation ◽  
Two Dimensional ◽  
Cfd Model ◽  
Cross Sectional ◽  
Vertical Velocity Profile ◽  
Flow Through

Keywords: river flow; two-dimensional CFD model; velocity profile; submerged vegetation leave Abstract. River flow with submerged foliage vegetation in straight and rectangular cross-sectional channel is numerically simulated through a vertical two-dimensional CFD model. Tilt thin strips are assigned in river flow to mimic the configuration of vegetation leave. The free surface line and the vertical profiles of longitudinal velocity are presented. The vertical velocity profile differs from the well acknowledged logarithmic or semi-logarithmic law. The submerged leave canopy resist the flow through it and pilots the flow upward over it, resulting in a decreased velocity within the canopy and an increased velocity above the canopy. The velocity profiles within the leave canopy are impacted by the configurations of the leave.

3D Unsteady Forces of the Transonic Flow Through a Turbine Stage With Vibrating Blades

2002 ◽  
Author(s):  
Romuald Rza˛dkowski ◽  
Vitaly Gnesin
Keyword(s):  
Transonic Flow ◽  
Gas Flow ◽  
Element Model ◽  
Ideal Gas ◽  
Rotor Blades ◽  
Turbine Stage ◽  
Unsteady Forces ◽  
Outer Flow ◽  
Natural Modes ◽  
Flow Through

Numerical calculations of the 3D transonic flow of an ideal gas through turbomachinery blade rows moving relatively one to another with taking into account the blades oscillations is presented. The approach is based on the solution of the coupled aerodynamic-structure problem for the 3D flow through the turbine stage in which fluid and dynamic equations are integrated simultaneously in time, thus providing the correct formulation of a coupled problem, as the blades oscillations and loads, acting on the blades, are a part of solution. An ideal gas flow through the mutually moving stator and rotor blades with periodicity on the whole annulus is described by the unsteady Euler conservation equations, which are integrated using the explicit monotonous finite-volume difference scheme of Godunov-Kolgan and moving hybrid H-H grid. The structure analysis uses the modal approach and 3D finite element model of a blade. The blade motion is assumed to be constituted as a linear combination of the first natural modes of blade oscillations with the modal coefficients depending on time. The algorithm proposed allows to calculate turbine stages with an arbitrary pitch ratio of stator and rotor blades, taking into account the blade oscillations by action of unsteady loads caused both outer flow nonuniformity and blades motion. There has been performed the calculation for the stage of the turbine with rotor blades of 0.765 m. The numerical results for unsteady aerodynamic forces due to stator-rotor interaction are compared with results obtained with taking into account the blades oscillations.

Three-Dimensional Lifting-Surface Theory for an Annular Blade Row

1979 ◽  
Author(s):  
G. F. Homicz ◽  
J. A. Lordi
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Computer Time ◽  
Two Dimensional ◽  
Blade Loading ◽  
Surface Theory ◽  
Lifting Surface ◽  
Strip Theory ◽  
Blade Row ◽  
Flow Through

A lifting-surface analysis is presented for the steady, three-dimensional, compressible flow through an annular blade row. A kernel-function procedure is used to solve the linearized integral equation which relates the unknown blade loading to a specified camber line. The unknown loading is expanded in a finite series of prescribed loading functions which allows the required integrations to be performed analytically, leading to a great savings in computer time. Numerical results are reported for a range of solidities and hub-to-tip ratios; comparisons are made with both two-dimensional strip theory and other three-dimensional results.

Pore geometry in woven fiber structures: 0°/90° plain-weave cloth layup preform

1998 ◽  
Vol 13 (5) ◽  
pp. 1209-1217 ◽  
Author(s):  
S-B. Lee ◽  
S. R. Stock ◽  
M. D. Butts ◽  
T. L. Starr ◽  
T. M. Breunig ◽  
...  
Keyword(s):  
Gas Flow ◽  
Three Dimensional ◽  
Pore Geometry ◽  
Two Dimensional ◽  
Transverse Distribution ◽  
One Dimensional ◽  
X Ray ◽  
Woven Structures ◽  
Flow Through

Composite preform fiber architectures range from the very simple to the complex, and the extremes are typified by parallel continuous fibers and complicated three-dimensional woven structures. Subsequent processing of these preforms to produce dense composites may depend critically on the geometry of the interfiber porosity. The goal of this study is to fully characterize the structure of a 0°/90° cloth layup preform using x-ray tomographic microscopy (XTM). This characterization includes the measurement of intercloth channel widths and their variability, the transverse distribution of through-cloth holes, and the distribution of preform porosity. The structure of the intercloth porosity depends critically on the magnitude and direction of the offset between adjacent cloth layers. The structures observed include two-dimensional networks of open pipes linking adjacent holes, arrays of parallel one-dimensional pipes linking holes, and relatively closed channels exhibiting little structure, and these different structures would appear to offer very different resistances to gas flow through the preform. These measurements, and future measurements for different fiber architectures, will yield improved understanding of the role of preform structure on processing.

Choking Effects in the Blade Rows of Turbomachines

1980 ◽  
Vol 22 (4) ◽  
pp. 161-173 ◽  
Author(s):  
J. H. Horlock
Keyword(s):  
Shear Flows ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Entry And Exit ◽  
Transonic Compressor ◽  
Dimensional Flow ◽  
Blade Row ◽  
Two Dimensional Flow ◽  
Flow Through

Three-dimensional flows through cascades of blades are studied, the blading being fully choked internally. Initially the two-dimensional flow through a ‘zero stagger, zero camber’ blade row, with subsonic entry and exit flow, is described. The radial flows are produced by radial variations in throat area, or by a variety of entry shear flows. Subsequently, the analysis is developed to describe similar fully choked flows through staggered blade rows, particularly the first rotating row of a transonic compressor.

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