Flow and Stress Induced Cavitation in a Journal Bearing With Axial Throughput

2001 ◽  
Vol 123 (4) ◽  
pp. 742-754 ◽  
Author(s):  
A. Pereira ◽  
G. McGrath ◽  
D. D. Joseph
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Journal Bearing ◽  
Maximum Tensile Stress ◽  
Navier Stokes ◽  
Relative Pressure ◽  
Navier Stokes Equation ◽  
Open Region ◽  
The Difference ◽  
The Stability

The problem of predicting flow between rotating eccentric cylinders with axial throughput is studied. The system models a device used to test the stability of emulsions against changes in drop size distribution. The analysis looks for the major variation in flow properties which could put an emulsion at risk due to coalescence or breakage and finds the most likely candidate in the pressure gradient defined as the ratio of the difference between the maximum and minimum pressure to the arc length between the difference. The axial throughput is modeled by flow driven by a constant pressure gradient. The flow is calculated from the Navier-Stokes equation using the code SIMPLER (Patankar 1980). The effects of inertia at values typical for the device are studied. Several eccentricities and different rotational speeds are computed to sample the changes in flow and stress parameters in the idealized device for typical conditions. The numerical analysis is validated against the lubrication approximation in the low Reynolds number case. Conditions for stress induced cavitation are evaluated. The flow is completely determined by a Reynolds number, an eccentricity ratio and a dimensionless pressure gradient and all computed results are either presented or can be easily expressed in terms of these dimensionless parameters. The effect of inertia is to shift the eddy or re-circulation zone which develops in the more open region of the gap toward the region of low relative pressure; the zero of the relative pressure migrates away from the center and the distribution breaks the skew symmetry of the Stokes flow solution. The state of stress in the journal bearing is analyzed and a cavitation criterion based on the maximum tensile stress is compared with the traditional criterion based on pressure.

scholarly journals Study of the instability of the Poiseuille flow using a thermodynamic formalism

2015 ◽  
Vol 112 (31) ◽  
pp. 9518-9523 ◽  
Author(s):  
Jianchun Wang ◽  
Qianxiao Li ◽  
Weinan E
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Critical Reynolds Number ◽  
Thermodynamic Formalism ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Action Function ◽  
Continuous Transition ◽  
Wide Range ◽  
The Stability

The stability of the plane Poiseuille flow is analyzed using a thermodynamic formalism by considering the deterministic Navier–Stokes equation with Gaussian random initial data. A unique critical Reynolds number, Rec≈2,332, at which the probability of observing puffs in the solution changes from 0 to 1, is numerically demonstrated to exist in the thermodynamic limit and is found to be independent of the noise amplitude. Using the puff density as the macrostate variable, the free energy of such a system is computed and analyzed. The puff density approaches zero as the critical Reynolds number is approached from above, signaling a continuous transition despite the fact that the bifurcation is subcritical for a finite-sized system. An action function is found for the probability of observing puffs in a small subregion of the flow, and this action function depends only on the Reynolds number. The strategy used here should be applicable to a wide range of other problems exhibiting subcritical instabilities.

Whirl Stability of Herringbone-Grooved Gas-Lubricated Journal Bearing

2014 ◽  
Author(s):  
Katsuhisa Fujita
Keyword(s):  
High Speed ◽  
Journal Bearing ◽  
Time History ◽  
Navier Stokes ◽  
Response Analysis ◽  
Complex Eigenvalue ◽  
Navier Stokes Equation ◽  
Transient Time ◽  
Whirling Motion ◽  
The Stability

A herringbone-grooved gas-lubricated journal bearing can rotate silently at high speed with low friction, and moreover it can be small-sized. In this paper, the equation of motion of a herringbone-grooved gas-lubricated journal bearing is derived using the gas force which can be obtained by applying the Navier-Stokes equation to the grooved and the ridged parts of a journal. The stability analysis is performed by using the analysis method by Routh-Hurwitz, the root locus of complex eigenvalue analysis, and the transient time history response analysis. The physical meanings of the stability charts which have not been explained sufficiently in the conventional studies are clarified by considering the forward whirling motion and the backward whirling motion, and the more reasonable stability charts are proposed. In addition, it is reported that the present analysis results show a good agreement with the already reported experimental results. Furthermore, the parametric studies as for the specification of gas-lubricated bearing are performed, and it is shown that the stability charts are affected by the change of specifications intricately.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Numerical Simulation of High Reynolds Number Flow Structure in a Lid-Driven Cavity Using MRT-LES

2014 ◽  
Vol 554 ◽  
pp. 665-669
Author(s):  
Leila Jahanshaloo ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Technique ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Reynolds Number Flow ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical and fluid mechanics problems. In this paper multi-relaxation lattice Boltzmann model (MRT) coupled with a Large Eddy Simulation (LES) and the equation are applied for driven cavity flow at different Reynolds number (1000-10000) and the results are compared with the previous published papers which solve the Navier stokes equation directly. The comparisons between the simulated results show that the lattice Boltzmann method has the capacity to solve the complex flows with reasonable accuracy and reliability. Keywords: Two-dimensional flows, Lattice Boltzmann method, Turbulent flow, MRT, LES.

scholarly journals Comparison and analysis of calculation of Bridge backwater based on Mike21 hydrodynamic model

2021 ◽  
Vol 233 ◽  
pp. 03043
Author(s):  
Jiang Chuan Liu ◽  
Zhu Qiu Hu ◽  
Mao Yuan Zhu
Keyword(s):  
Theoretical Basis ◽  
Impact Analysis ◽  
Navier Stokes ◽  
Efficiency Coefficient ◽  
Navier Stokes Equation ◽  
The Real ◽  
Comparison And Analysis ◽  
Simulation Results ◽  
The Difference ◽  
Local Water

The construction of bridges and other structures across the river will affect the flood discharge capacity and local water potential of the river.Based on navier-Stokes equation of MIKE21FM hydrodynamic module, this paper carries out two-dimensional numerical simulation of part of Shixi River. By optimizing the grid near the piers to reduce the difference brought by the terrain generalized grid of the real river, it simulates and analyzes the length of the curve of yong-high and Yong-water under different flood frequencies,the Nash-Sutcliffe efficiency coefficient and relative error analysis are used to verify the rationality of the results. The simulation results can accurately reflect the real changes of river water level, It provides a theoretical basis for flood impact analysis.

Stability of Horizontal Boundary Layers

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Mathematical Proof ◽  
Vertical Component ◽  
Ekman Layer ◽  
Numerical Results ◽  
Energy Estimates ◽  
Navier Stokes ◽  
The 1960S ◽  
The Stability

Let us now detail the stability properties of an Ekman layer introduced in Part I, page 11. First we will recall how to compute the critical Reynolds number. Then we will describe briefly what happens at larger Reynolds numbers. The first step in the study of the stability of the Ekman layer is to consider the linear stability of a pure Ekman spiral of the form where U∞ is the velocity away from the layer and ζ is the rescaled vertical component ζ = x3/√εν. The corresponding Reynolds number is Let us consider the Navier–Stokes–Coriolis equations, linearized around uE The problem is now to study the (linear) stability of the 0 solution of the system (LNSCε). If u=0 is stable we say that uE is linearly stable, if not we say that it is linearly unstable. Numerical results show that u=0 is stable if and only if Re<Rec where Rec can be evaluated numerically. Up to now there is no mathematical proof of this fact, and it is only possible to prove that 0 is linearly stable for Re<Re1 and unstable for Re>Re2 with Re1<Rec<Re2, Re1 being obtained by energy estimates and Re2 by a perturbative analysis of the case Re=∞. We would like to emphasize that the numerical results are very reliable and can be considered as definitive results, since as we will see below, the stability analysis can be reduced to the study of a system of ordinary differential equations posed on the half-space, with boundary conditions on both ends, a system which can be studied arbitrarily precisely, even on desktop computers (first computations were done in the 1960s by Lilly).

Numerical Performance of Transition Models in Different Turbomachinery Flow Conditions: A Comparative Study

2000 ◽  
Author(s):  
Jiasen Hu ◽  
Torsten H. Fransson
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Numerical Study ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Flow Conditions ◽  
Transition Models ◽  
High Reynolds

A numerical study has been performed to compare the overall performance of three transition models when used with an industrial Navier-Stokes solver. The three models investigated include two experimental correlations and an integrated eN method. Twelve test cases in realistic turbomachinery flow conditions have been calculated. The study reveals that all the three models can work numerically well with an industrial Navier-Stokes code, but the prediction accuracy of the models depends on flow conditions. In general, all the three models perform comparably well to predict the transition in weak or moderate adverse pressure-gradient regions. The two correlations have the merit if the transition starts in strong favorable pressure-gradient region under high Reynolds number condition. But only the eN method works well to predict the transition controlled by strong adverse pressure gradients. The three models also demonstrate different capabilities to model the effects of turbulence intensity and Reynolds number.

Viscous drag and energy transfer of pulsatile flow in large arteries

1962 ◽  
Vol 202 (4) ◽  
pp. 661-663 ◽  
Author(s):  
Robert L. Evans ◽  
Eugene F. Bernstein ◽  
Darrel L. Lary
Keyword(s):  
Energy Transfer ◽  
Pressure Gradient ◽  
Pulsatile Flow ◽  
Simultaneous Measurement ◽  
Pulse Wave ◽  
Navier Stokes ◽  
Viscous Drag ◽  
Navier Stokes Equation ◽  
Early Results ◽  
Almost All

Early results of simultaneous measurement of pressure gradient and flow in the thoracic aorta of the dog during systole are used in calculations of viscous drag and energy transfer of actual pulsatile flow. Viscous drag is large when the flow is small, and small when the flow is large, so that almost all the energy of the pulse wave is transmitted along the vessel. The amplitude of the viscous drag is a much greater fraction of the amplitude of the pressure gradient than is predicted by the Navier-Stokes equation, which is only theoretical and may assume an unrealistic form of viscous drag during pulsatile flow.

scholarly journals Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation

2013 ◽  
Vol 729 ◽  
pp. 285-308 ◽  
Author(s):  
Maciej J. Balajewicz ◽  
Earl H. Dowell ◽  
Bernd R. Noack
Keyword(s):  
Reynolds Number ◽  
Galerkin Method ◽  
Stokes Equation ◽  
High Reynolds Number ◽  
Transient Flow ◽  
Navier Stokes ◽  
Power Balance ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
High Reynolds

AbstractWe generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds equations, can be achieved in straightforward variation of the presented results.

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