Three-dimensional dynamic inflow below the rotor disk based on the finite-state method

2016 ◽  
Vol 22 (16) ◽  
pp. 3491-3503
Author(s):  
Zhongyang Fei ◽  
Yang Zhang
Keyword(s):  
Three Dimensional ◽  
Finite State ◽  
Rotor Disk ◽  
State Method

Finite state induced flow models. II - Three-dimensional rotor disk

1995 ◽  
Vol 32 (2) ◽  
pp. 323-333 ◽  
Author(s):  
David A. Peters ◽  
Cheng Jian He
Keyword(s):  
Three Dimensional ◽  
Flow Models ◽  
Finite State ◽  
Rotor Disk ◽  
Induced Flow

scholarly journals Influence of Rim Seal Geometry on Hot Gas Ingestion Into the Upstream Cavity of an Axial Turbine Stage

1999 ◽  
Author(s):  
Dieter Bohn ◽  
Bernd Rudzinski ◽  
Norbert Sürken ◽  
Wolfgang Gärtner
Keyword(s):  
Mach Number ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Main Flow ◽  
Rotor Blades ◽  
Flow Rates ◽  
Hot Gas ◽  
Carbon Dioxide Gas ◽  
Industrial Gas Turbines ◽  
Rotor Disk

The ingestion of hot gas at the rim seal of a turbine has been investigated for a complete stage with nozzle guide vanes and rotor blades for two types of geometry: 1. the simple axial gap between a flat rotor disk and a flat stator disk, commonly used for industrial gas turbines and 2. an axial lip of the rim seal on the stator combined with a flat rotor disk, often found in aero engine applications. The clearance of the axial gap has been varied for the second type. The efficiency of the rim seal has been examined for different seal flow rates, rotational Reynolds numbers and Mach numbers in the main flow. For the determination of the sealing effectiveness carbon dioxide gas concentration measurements have been carried out in the wheelspace. The distribution of the static pressure in the vicinity of the seal and inside the wheelspace has been measured by means of pressure taps at the stator disk. It is shown that the external flow Mach number in the main flow has a significant effect on the sealing efficiency. As Mach number increases sealing efficiency goes down. The rotational Reynolds number has a distinct effect on the rim seal efficiency depending on the examined configuration. Even for high seal flow rates the ingestion of hot gas can not be fully avoided. The experimental results were the motivation for a three-dimensional CFD approach neglecting the influence of the rotor blades. The results give further insight into aerodynamic features of the ingestion phenomenon.

scholarly journals A Finite State Method in the Performance Evaluation of the Bernoulli Serial Production Lines

2020 ◽  
Vol 10 (18) ◽  
pp. 6602
Author(s):  
Neven Hadžić ◽  
Viktor Ložar ◽  
Filip Abdulaj
Keyword(s):  
Large Scale ◽  
Performance Measure ◽  
Production Lines ◽  
Stationary Probability Distribution ◽  
Transition Systems ◽  
Serial Production ◽  
Work In Process ◽  
Finite State ◽  
State Method ◽  
Serial Production Lines

Research on the performance measure evaluation of Bernoulli serial production lines is presented in this paper. Important aspects of the modeling and analysis using transition systems within the Markovian framework are addressed, including analytical and approximation methods. The “dimensionality curse” problems of the large scale and dense transition systems in the production system engineering field are pointed out as one of the main research and development obstacles. In that respect, a new analytically-based finite state method is presented based on the proportionality property of the stationary probability distribution across the systems’ state space. Simple and differentiable expressions for the performance measures including the production rate, the work-in-process, and the probabilities of machine blockage and starvation are formulated. A finite state method’s accuracy and applicability are successfully validated by comparing the obtained results against the rigorous analytical solution.

Coupling of a State-Space Inflow to Nonlinear Blade Equations and Extraction of Generalized Aerodynamic Force Mode Shapes

1993 ◽  
Vol 46 (11S) ◽  
pp. S295-S304 ◽  
Author(s):  
Donizeti de Andrade ◽  
David A. Peters
Keyword(s):  
Aerodynamic Force ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Mode Shapes ◽  
State Equations ◽  
Force Mode ◽  
Rotor Disk ◽  
Induced Flow ◽  
Wake Model

The aeroelastic stability of helicopter rotors in hovering flight has been investigated by a set of generalized dynamic wake equations and hybrid equations of motion for an elastic blade cantilevered in bending and having a torsional root spring to model pitch-link flexibility. The generalized dynamic wake model employed is based on an induced flow distribution expanded in a set of harmonic and radial shape functions, including undetermined time dependent coefficients as aerodynamic states. The flow is described by a system of first-order, ordinary differential equations in time, for which the pressure distribution at the rotor disk is expressed as a summation of the discrete loadings on each blade, accounting simultaneously for a finite number of blades and overall rotor effects. The present methodology leads to a standard eigenanalysis for the associated dynamics, for which the partitioned coefficient matrices depend on the numerical solution of the blade equilibrium and inflow steady-state equations. Numerical results for a two-bladed, stiff-inplane hingeless rotor with torsionally soft blades show the importance of unsteady, three-dimensional aerodynamics in predicting associated generalized aerodynamic force mode shapes.

The double molybdate Na9Sc(MoO4)6refined from powder XRD data

2013 ◽  
Vol 69 (11) ◽  
pp. 1301-1303 ◽  
Author(s):  
Aleksandra A. Savina ◽  
Vladimir A. Morozov ◽  
Olga M. Basovich ◽  
Elena G. Khaikina ◽  
Bogdan I. Lazoryak
Keyword(s):  
Solid State ◽  
Three Dimensional ◽  
Basic Structure ◽  
Powder Xrd ◽  
The Other ◽  
Double Molybdate ◽  
Solid State Method ◽  
State Method

Na9Sc(MoO4)6{nonasodium scandium hexakis[tetraoxidomolybdate(II)]} was synthesised by a solid-state method. The basic structure units are polyhedral clusters composed of an ScO6octahedron and three NaO6octahedra sharing total edges. The clusters are connected by sharing vertices with bridging MoO4tetrahedra, forming a three-dimensional framework where the cavities are occupied by the other two crystallographically independent Na atoms.

scholarly journals Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1461
Author(s):  
Viktor Ložar ◽  
Neven Hadžić ◽  
Tihomir Opetuk ◽  
Vedran Slapničar
Keyword(s):  
Performance Measures ◽  
Analytical Approach ◽  
Manufacturing Industry ◽  
Production Systems ◽  
Numerical Approach ◽  
Production Lines ◽  
State Behavior ◽  
Finite State ◽  
State Method ◽  
Numerical Approaches

The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely, the analytical approach, the finite state method, the aggregation procedure, and numerical modeling. The accuracy of the performance measures determined using the semi-analytical methods and the numerical approach was validated using numerous theoretical examples and the results obtained using the analytical model. All of the considered methods demonstrated relevant reliability, regardless of the different theoretical backgrounds.

scholarly journals Rietveld refinement of the langbeinite-type phosphate K2Ni0.5Hf1.5(PO4)3

2020 ◽  
Vol 76 (10) ◽  
pp. 1634-1637
Author(s):  
Liang Zhou ◽  
Denys S. Butenko ◽  
Ivan V. Ogorodnyk ◽  
Nickolai I. Klyui ◽  
Igor V. Zatovsky
Keyword(s):  
Solid State ◽  
Rietveld Refinement ◽  
Title Compound ◽  
Three Dimensional ◽  
Solid State Method ◽  
Coordination Numbers ◽  
Rotation Axes ◽  
State Method

Polycrystalline potassium nickel(II) hafnium(IV) tris(orthophosphate), a langbeinite-type phosphate, was synthesized by a solid-state method. The three-dimensional framework of the title compound is built up from two types of [MO6] octahedra [the M sites are occupied by Hf:Ni in ratios of 0.754 (8):0.246 (8) and 0.746 (8):0.254 (8), respectively] and [PO4] tetrahedra are connected via O vertices. The K+ cations are located in two positions within large cavities of the framework, having coordination numbers of 9 and 12. The Hf, Ni and K sites lie on threefold rotation axes, while the P and O atoms are situated in general positions.

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