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.

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.

Part II. Research on the Performance of a Type of Internally Air-cooled Turbine Blade

1953 ◽  
Vol 167 (1) ◽  
pp. 351-370 ◽  
Author(s):  
D. G. Ainley
Keyword(s):  
Gas Flow ◽  
Thermal Stresses ◽  
Turbine Blades ◽  
Small Diameter ◽  
Rotor Blades ◽  
Air Cooling ◽  
Gas Temperature ◽  
Flow Through ◽  
Cooling Air ◽  
Practical Feasibility

A comprehensive series of tests have been made on an experimental single-stage turbine to determine the cooling characteristics and the overall stage performance of a set of air-cooled turbine blades. These blades, which are described fully in Part I of this paper had, internally, a multiplicity of passages of small diameter along which cool air was passed through the whole length of the blade. Analysis of the, test data indicated that, when a quantity of cooling air amounting to 2 per cent, by weight, of the total gas-flow through the turbine is fed to the row of rotor blades, an increase in gas temperature of about 270 deg. C. (518 deg. F.) should be permissible above the maximum allowable value for a row of uncooled blades made from the same material. The degree of cooling achieved throughout each blade was far from uniform and large thermal stresses must result. It appears, however, that the consequences of this are not highly detrimental to the performance of the present type of blading, it being demonstrated that the main effect of the induced thermal stress is apparently to transfer the major tensile stresses to the cooler (and hence stronger) regions of the blade. The results obtained from the present investigations do not represent a limit to the potentialities of internal air-cooling, but form merely a first exploratory step. At the same time the practical feasibility of air cooling is made apparent, and advances up to the present are undoubtedly encouraging.

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.

scholarly journals СНИЖЕНИЕ ВИБРОНАПРЯЖЕННОСТИ ПОПАРНО БАНДАЖИРОВАННЫХ РАБОЧИХ ЛОПАТОК ТУРБИНЫ

2020 ◽  
pp. 52-58
Author(s):  
Юрий Петрович Кухтин ◽  
Руслан Юрьевич Шакало
Keyword(s):  
Film Cooling ◽  
Gas Flow ◽  
Stokes Equations ◽  
Operating Conditions ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Turbine Stage ◽  
Turbine Engine ◽  
Exciting Forces ◽  
Working Blades

To reduce the vibration stresses arising in the working blades of turbines during resonant excitations caused by the frequency of passage of the blades of the nozzle apparatus, it is necessary to control the level of aerodynamic exciting forces. One of the ways to reduce dynamic stresses in rotor blades under operating conditions close to resonant, in addition to structural damping, maybe to reduce external exciting forces. To weaken the intensity of the exciting forces, it is possible to use a nozzle apparatus with multi-step gratings, as well as with non-radially mounted blades of the nozzle apparatus.This article presents the results of numerical calculations of exciting aerodynamic forces, as well as the results of experimental measurements of stresses arising in pairwise bandaged working blades with a frequency zCA ⋅ fn, where fn – is the rotor speed, zCA – is the number of nozzle blades. The object of research was the high-pressure turbine stage of a gas turbine engine. Two variants of a turbine stage were investigated: with the initial geometry of the nozzle apparatus having the same geometric neck area in each interscapular channel and with the geometry of the nozzle apparatus obtained by alternating two types of sectors with a reduced and initial throat area.The presented results are obtained on the basis of numerical simulation of a viscous unsteady gas flow in a transonic turbine stage using the SUnFlow home code, which implements a numerical solution of the Reynolds-averaged Navier-Stokes equations. Discontinuity of a torrent running on rotor blades is aggravated with heat drops between an ardent flow core and cold jets from film cooling of a blade and escapes on clock surfaces. Therefore, at simulation have been allowed all blowngs cooling air and drain on junctions of shelves the impeller.As a result of the replacement of the nozzle apparatus with a constant passage area by a nozzle apparatus with a variable area, a decrease in aerodynamic driving force by 12.5 % was obtained. The experimentally measured stresses arising in a pairwise bandaged blade under the action of this force decreased on average by 26 %.

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.

Aeroelastic Analysis of Last Stage LP Steam Turbine Rotor Blades With Exhaust Hood for Various Non-Nominal Regimes

2018 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Vitaly Gnesin ◽  
Lubov Kolodyazhnaya ◽  
Ryszard Szczepanik
Keyword(s):  
Pressure Distribution ◽  
Steam Turbine ◽  
Gas Flow ◽  
Element Model ◽  
Turbine Rotor ◽  
Ideal Gas ◽  
Rotor Blades ◽  
Exhaust Hood ◽  
Flow Through ◽  
Last Stage

Presented here are the numerical calculations of the 3D transonic flow of an ideal gas through an LP steam turbine last stage with exhaust hood, taking into account blade oscillations. The approach is based on a solution to the coupled aerodynamic-structure problem for 3D flow through a turbine stage using the partially integrated method. The blade oscillations and loads acting on the blades are a part of the solution. An ideal gas flow through the stator and moving rotor blades with periodicity on the whole annulus is described by unsteady Euler conservation equations, integrated with the Godunov-Kolgan explicit monotonous finite-volume difference scheme and a moving hybrid H-H rotor blade grid. The structural analysis uses the modal approach and a 3D finite element model of a blade. The proposed algorithm allows for the calculation of turbine stages with an arbitrary pitch ratio of stator and rotor blades, taking into account unsteady-load induced blade oscillations. The pressure distribution behind the rotor blades was non-uniform on account of the exhaust hood. As a result of the fluid-structure interaction and exhaust hood induced nonsymmetrical pressure distribution behind the rotor blades, the first blade mode was no longer bending but bending-torsion.

Effect of Stator Clocking on the 3D Aeroelastic Characteristics of Compressor Rotor Blades

2008 ◽  
Author(s):  
Romuald Rza˛dkowski ◽  
Vitally Gnesin ◽  
Luba Kolodyazhnaya
Keyword(s):  
Gas Flow ◽  
Element Model ◽  
Ideal Gas ◽  
Rotor Blades ◽  
Compressor Stage ◽  
Compressor Rotor ◽  
Natural Modes ◽  
Structure Problem ◽  
Flow Through ◽  
Volume Difference

Presented here are numerical calculations of the 3D transonic flow of an ideal gas through a three-row compressor stage including the clocking effects. 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 the solution. An ideal gas flow through the mutually moving stators and rotor blades with periodicity on the entire annulus is described using unsteady Euler conservation equations, integrated using the Godunov-Kolgan explicit monotonous finite-volume difference scheme and a moving hybrid H-H grid. The structure analysis uses the modal approach and a 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. A calculation has been performed for the compressor stage with 0.106 m long rotor blades. The aeroelastic characteristics are obtained for different positions of the upstream stator.

Numerical Prediction of Fluid-Elastic Instability in Normal Triangular Tube Bundles With Multiple Flexible Circular Cylinders

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Hamed Houri Jafari ◽  
Behzad Ghadiri Dehkordi
Keyword(s):  
Tube Bundle ◽  
Equations Of Motion ◽  
Cross Flow ◽  
Structural Equations ◽  
Circular Cylinders ◽  
Staggered Grid ◽  
Elastic Instability ◽  
Time Step ◽  
Tube Bundles ◽  
Flow Through

Prediction of fluid-elastic instability onset is a great matter of importance in designing cross-flow heat exchangers from the perspective of vibration. In the present paper, the threshold of fluid-elastic instability has been numerically predicted by the simulation of incompressible, unsteady, and turbulent cross flow through a tube bundle in a normal triangular arrangement. In the tube bundle under study, there were single or multiple flexible cylinders surrounded by rigid tubes. A finite volume solver based on a Cartesian-staggered grid was implemented. In addition, the ghost-cell method in conjunction with the great-source-term technique was employed in order to directly enforce the no-slip condition on the cylinders' boundaries. Interactions between the fluid and the structures were considered in a fully coupled manner by means of intermittence solution of the flow field and structural equations of motion in each time step of the numerical modeling algorithm. The accuracy of the solver was validated by simulation of the flow over both a rigid and a flexible circular cylinder. The results were in good agreement with the experiments reported in the literatures. Eventually, the flow through seven different flexible tube bundles was simulated. The fluid-elastic instability was predicted and analyzed by presenting the structural responses, trajectory of flexible cylinders, and critical reduced velocities.

Calculations of Cooled Turbine Efficiency

2006 ◽  
Author(s):  
J. H. Horlock ◽  
Leonardo Torbidoni
Keyword(s):  
Film Cooling ◽  
Gas Flow ◽  
Back Pressure ◽  
Coolant Flow ◽  
The Other ◽  
Turbine Stage ◽  
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 back pressure. 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 back pressure. 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.

INVESTIGATION OF THE TIME OF GAS FLOW THROUGH A HOLE IN LONG PIPELINES UNDER HIGH PRESSURE

2020 ◽  
Vol 58 (1) ◽  
pp. 30-43
Author(s):  
N.D. Yakimov ◽  
◽  
A.I. Khafizova ◽  
N.D. Chichirova ◽  
O.S. Dmitrieva ◽  
...  
Keyword(s):  
High Pressure ◽  
Gas Flow ◽  
Flow Through
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