Rotordynamic characterization of tilting-pad bearings with eight pads in vertical rotors

2021 ◽  
pp. 1-20
Author(s):  
David J Rondon ◽  
Gudeta Berhanu Benti ◽  
Jan-Olov Aidanpää ◽  
Rolf Gustavsson
Keyword(s):  
Stokes Equations ◽  
Forced Response ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Mean Values ◽  
Stationary Coordinate System ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
Stiffness And Damping

Abstract It has been documented that stiffness and damping for a four-pad bearing are dependent not only the magnitude of the load but also on the position of the rotor in the bearing. However, 8-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explore the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier-Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with 8-pad bearings can be simplified which allow more effective simulations and dynamic analysis.

Computational Characterization of Passive Fluid Mixing in Microfluidics

Volume 3 ◽  
2004 ◽  
Author(s):  
Erik D. Svensson
Keyword(s):  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Fluid Mixing ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Systems ◽  
Sensitive Dependence ◽  
Microfluidic Mixers

In this work we computationally characterize fluid mixing in a number of passive microfluidic mixers. Generally, in order to systematically study and characterize mixing in realistic fluid systems we (1) compute the fluid flow in the systems by solving the stationary three-dimensional Navier-Stokes equations or Stokes equations with a finite element method, and (2) compute various measures indicating the degree of mixing based on concepts from dynamical systems theory, i.e., the sensitive dependence on initial conditions and mixing variance.

Characterization of coherent vortical structures in a supersonic turbulent boundary layer

2008 ◽  
Vol 613 ◽  
pp. 205-231 ◽  
Author(s):  
SERGIO PIROZZOLI ◽  
MATTEO BERNARDINI ◽  
FRANCESCO GRASSO
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Stokes Equations ◽  
Supersonic Boundary Layer ◽  
Navier Stokes ◽  
Hairpin Vortices ◽  
Length Scales ◽  
Navier Stokes Equations ◽  
Vortical Structures

A spatially developing supersonic boundary layer at Mach 2 is analysed by means of direct numerical simulation of the compressible Navier--Stokes equations, with the objective of quantitatively characterizing the coherent vortical structures. The study shows structural similarities with the incompressible case. In particular, the inner layer is mainly populated by quasi-streamwise vortices, while in the outer layer we observe a large variety of structures, including hairpin vortices and hairpin packets. The characteristic properties of the educed structures are found to be nearly uniform throughout the outer layer, and to be weakly affected by the local vortex orientation. In the outer layer, typical core radii vary in the range of 5–6 dissipative length scales, and the associated circulation is approximately constant, and of the order of 180 wall units. The statistical properties of the vortical structures in the outer layer are similar to those of an ensemble of non-interacting closed-loop vortices with a nearly planar head inclined at an angle of approximately 20° with respect to the wall, and with an overall size of approximately 30 dissipative length scales.

Characterization of the Behavior of Confined Laminar Round Jets

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
D. Tyler Landfried ◽  
Anirban Jana ◽  
Mark Kimber
Keyword(s):  
Stokes Equations ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Half Width ◽  
Navier Stokes ◽  
Centerline Velocity ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Round Jets

In this work, the Navier–Stokes equations are solved for a laminar, round jet in a large confinement. The flow is characterized as a function of the enclosure-to-jet diameter ratio, in the range 40–100, and the Reynolds numbers at jet inlet in the range 32–65. Results for jet decay and half width suggest that near the jet inlet the flow is identical to a free jet but eventually deviates away from the jet inlet. We develop a set of correlations including the jet centerline velocity and the jet half width, and features of the transition regions in the flow field.

Unsteady Forcing vs. Efficiency: The Effect of Clocking on a Transonic Industrial Compressor

2013 ◽  
Author(s):  
Florian Fruth ◽  
Damian M. Vogt ◽  
Ronnie Bladh ◽  
Torsten H. Fransson
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Forced Response ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Design Changes ◽  
Transient Simulations ◽  
Stator Blade ◽  
The Impact

A numerical investigation on the impact of clocking on the efficiency and the aerodynamic forcing of the first 1.5 stages of an industrial transonic compressor was conducted. Using unsteady 3D Navier-Stokes equations, seven clocking positions were calculated and analyzed. Efficiency changes due to clocking were up to 0.125%, whereas modal excitation changes up to 31.7%. However, no direct correlation between the parameters of efficiency, stimulus and modal excitation was found as reported by others. It was found that potential forced response risks can be reduced by clocking, resulting only in minor efficiency penalties. Assuming almost sinusoidal behavior of efficiency and stimulus changes, as found in this investigation, both parameters can be set into correlation by using an ellipse interpolation. Direct impact of design changes on efficiency and stimulus through clocking can be deducted from that graph and quick estimations about extrema be made using only 5–6 transient simulations. Results however also stress the importance of considering modal excitation when optimizing for aerodynamic forcing, for which the ellipse interpolation is not necessarily possible. Highest efficiency is achieved with the IGV wake impinging on the stator blade leading edge at mid-span. It was found however that this alone is not a sufficient criteria in case of inclined wakes, as wake impingement at different span positions leads to different efficiencies.

The Theory of Molecular Dispersion in Flowing Fluids: An Analytic Solution of the Navier-Stokes Equations

2008 ◽  
Author(s):  
William Todd
Keyword(s):  
Reynolds Number ◽  
Free Energy ◽  
Analytic Solution ◽  
Stokes Equations ◽  
Fluid Model ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Energy Calculation ◽  
Navier Stokes Equations

This development is a description of the transport of mass, energy and momentum in flowing viscous fluids at the molecular level; and results in: • A thermostatistical link between Reynolds’ number and momentum and free energy, • A wave characterization of the behavior of flowing fluids using the forces of attraction between molecules as a basis, • Calculation of the velocity components in flowing fluids for all Reynolds’ numbers greater than 535; thus defining a mathematical theory of turbulence, • An analytic solution of the Navier-Stokes equations for incompressible fluids in 3-dimensions. The following steps lead to the solution: • Definition of the fluid Model, • A re-characterization of Reynolds’ number in terms of momentum and free energy, • Calculation of the shear and circulatory components of velocity, • Transformation of the Navier-Stokes equations into the curvilinear coordinates of the intermolecular force waves, • Using the transformed equations to calculate the velocity components and Pressure-wave front resulting from the current, • Corroboration of the theoretical results with: a) wave fronts as manifest in the behavior of sails in uniform flow, b) boundary layer definition/behavior compared to theoretical and empirical developments of Schlichting and others, and c) empirical results for forces measured in the OCEANIC/DeepStar high Re beam-tow tests.

Turbine forced response prediction using an integrated non-linear analysis

2000 ◽  
Vol 214 (1) ◽  
pp. 45-60 ◽  
Author(s):  
A I Sayma ◽  
M Vahdati ◽  
M Imregun
Keyword(s):  
Stokes Equations ◽  
Prediction Method ◽  
Response Prediction ◽  
Forced Response ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Engine Order ◽  
Lp Turbine ◽  
Nozzle Guide

The forced response due to flow defects caused by the upstream blade rows is predicted for two turbines: intermediate pressure (IP) and low pressure (LP). The prediction method is based on an advanced numerical tool where the compressible viscous flow field is modelled by solving Favre-averaged Navier-Stokes equations with the Baldwin and Barth turbulence model. The flow solution is coupled to a modal model of the structure and information is exchanged every time step between the fluid and the structural domains. The hybrid unstructured mesh is moved at each time step to follow the structural motion using a spring analogy. For the IP turbine, the method was used to rank two different designs of nozzle guide vanes. For the LP turbine, special emphasis was placed on predicting vibration amplitudes due to high and low engine order excitations. Predictions and measurements were found to be in good agreement for both turbines. Due to insufficient experimental data, it was difficult to assess the accuracy of the low engine order computations, although it was shown that the model was capable of undertaking such a task.

Symmetry-invariant conservation laws of partial differential equations

2017 ◽  
Vol 29 (1) ◽  
pp. 78-117 ◽  
Author(s):  
STEPHEN C. ANCO ◽  
ABDUL H. KARA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Stokes Equations ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Partial Differential ◽  
Navier Stokes Equations ◽  
General Method

A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, theb-family of peakon equations, and the Navier–Stokes equations for compressible, viscous fluids in two dimensions.

Multibladerow Forced Response Modeling in Axial-Flow Core Compressors

2005 ◽  
Vol 129 (2) ◽  
pp. 412-420 ◽  
Author(s):  
M. Vahdati ◽  
A. I. Sayma ◽  
M. Imregun ◽  
G. Simpson
Keyword(s):  
Structural Model ◽  
Stokes Equations ◽  
Axial Flow ◽  
Forced Response ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Engine Order ◽  
Grid Points ◽  
Response Modeling

This paper describes the formulation and application of an advanced numerical model for the simulation of blade-passing and low-engine order forced response in turbomachinery core compressors. The Reynolds averaged Navier–Stokes equations are used to represent the flow in a nonlinear time-accurate fashion on unstructured meshes of mixed elements. The structural model is based on a standard finite-element representation. The fluid mesh is moved at each time step according to the structural motion so that changes in blade aerodynamic damping and flow unsteadiness can be accommodated automatically. A whole-annulus 5-bladerow forced response calculation, where three upstream and one downstream bladerows were considered in addition to the rotor bladerow of interest, was undertaken using over 20 million grid points. The results showed not only some potential shortcomings of equivalent 2-bladerow computations for the determination of the main blade-passing forced response, but also revealed the potential importance of low engine-order harmonics. Such harmonics, due to stator blade number differences, or arising from common symmetric sectors, can only be taken into account by including all stator bladerows of interest. The low engine-order excitation that could arise from a blocked passage was investigated next. It was shown that high vibration response could arise in such cases.

scholarly journals CFD study of the thermal transfer of a non-Newtonian fluid within a tank mechanically stirred by an anchor-shaped impeller

2018 ◽  
Vol 180 ◽  
pp. 02089
Author(s):  
L. Rahmani ◽  
O. Seghier ◽  
A. Benmoussa ◽  
B. Draoui
Keyword(s):  
Newtonian Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thermal Fields ◽  
Thermal Transfer ◽  
Finite Volume Discretization ◽  
Mobile Anchor ◽  
Anchor Agitator

The most of operations of chemical, biochemical or petrochemical industries are carried out in tanks or in reactors which are mechanically-controlled. The optimum mode of operation of these devices requires a finalized knowledge of the thermo-hydrodynamic behavior induced by the agitator. In the present work, the characterization of the incompressible hydrodynamic and thermal fields of a non-Newtonian fluid (Bingham) in a flat, non-baffled cylindrical vessel fitted with anchor agitator was undertaken by numerical simulation, using the CFD code Fluent (6.3.26) based on the finite volume discretization method of the energy equation and the Navier-Stokes equations which are formulated in (U.V.P) variables. We have summarized this simulated system by comparing of the consumed power and the Nusselt number for this type of mobile (Anchor agitator).

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