The Magnetohydrodynamic (MHD) Effects on the Performance of a Hydrostatic Thrust Bearing With Hybrid Raleigh Step

2010 ◽  
Author(s):  
Frank E. Horvat ◽  
Minel J. Braun
Keyword(s):  
Reynolds Number ◽  
Thrust Bearing ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Angular Speed ◽  
Navier Stokes ◽  
Operational Parameters ◽  
Navier Stokes Equations ◽  
Pressure Profiles ◽  
Ansys Cfx

This paper studies the numerical development of flow patterns and pressure profiles inside a hybrid Rayleigh step thrust bearing (HRSB) where the working magnetohydrodynamic (MHD) fluid is subject to an imposed magnetic field. This hybrid type bearing stems from integrating two classical component: the modified Rayleigh step (variable depth) and the hydrostatic feed entering at the center of the circular thrust bearing. The parameters used in this study consist of one geometric parameter, the Rayleigh step aspect ratio (depth to length ratio) and two dimensionless operational parameters, (i) the Reynolds number based on the hydrostatic fluid jet velocity entering the restrictor (Rejet) and the Reynolds number based on the smooth upper plate angular speed (Replate). The numerical results are obtained using the commercially available package ANSYS (CFX) [4], which utilizes the full three-dimensional Navier-Stokes equations for the steady-state incompressible MHD fluid with constant properties. Results to be presented will will contain both vector and pressure fields within the Rayleigh step profile and on the smooth lands.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Variation of Hydraulic Performance by Impeller Trimming of a Mixed-Flow Pump

2015 ◽  
Author(s):  
Hyeonmo Yang ◽  
Sung Kim ◽  
Kyoung-Yong Lee ◽  
Young-Seok Choi ◽  
Jin-Hyuk Kim
Keyword(s):  
Numerical Analysis ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Total Efficiency ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Ansys Cfx ◽  
Total Head ◽  
Flow Pump

One of the best examples of wasted energy is the selection of oversized pumps versus the rated conditions. Oversized pumps are forced to operate at reduced flows, far from their highest efficiency point. An unnecessarily large impeller will produce more flow than required, wasting energy. In the industrial field, trimming the impeller diameter is used more than changing the rotation speed to reduce the head of a pump. In this paper, the impeller trimming method of a mixed-flow pump is defined, and the variation in pump performance by reduction of the impeller diameter was predicted based on computational fluid dynamics. The impeller was trimmed to the same meridional ratio of the hub and shroud, and was compared in five cases. Numerical analysis was performed, including the inlet and outlet pipes in configurations of the mixed-flow pump to be tested. The commercial CFD code, ANSYS CFX-14.5, was used for the numerical analysis, and a three-dimensional Reynolds-averaged Navier-Stokes equations with a shear stress transport turbulence model were used to analyze incompressible turbulence flow. The performance parameters for evaluating the trimmed pump impellers were defined as the total efficiency and total head at the designed flow rate. The numerical and experimental results for the trimmed pump impellers were compared and discussed in this work.

Finite-Reynolds-Number Effects in Steady, Three-Dimensional Airway Reopening

2006 ◽  
Vol 128 (4) ◽  
pp. 573-578 ◽  
Author(s):  
Andrew L. Hazel ◽  
Matthias Heil
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Elastic Tube ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Airway Reopening ◽  
Reynolds Number Effects ◽  
Steady Propagation

Motivated by the physiological problem of pulmonary airway reopening, we study the steady propagation of an air finger into a buckled elastic tube, initially filled with viscous fluid. The system is modeled using geometrically non-linear, Kirchhoff-Love shell theory, coupled to the free-surface Navier-Stokes equations. The resulting three-dimensional, fluid-structure-interaction problem is solved numerically by a fully coupled finite element method. Our study focuses on the effects of fluid inertia, which has been neglected in most previous studies. The importance of inertial forces is characterized by the ratio of the Reynolds and capillary numbers, Re∕Ca, a material parameter. Fluid inertia has a significant effect on the system’s behavior, even at relatively small values of Re∕Ca. In particular, compared to the case of zero Reynolds number, fluid inertia causes a significant increase in the pressure required to drive the air finger at a given speed.

Numerical Simulation of a Pouring Flow From a Beverage Can

2019 ◽  
Author(s):  
Yu Nishio ◽  
Keiji Niwa ◽  
Takanobu Ogawa
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Angular Speed ◽  
Experimental Result ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Result ◽  
Liquid Flows ◽  
Good Agreement

Abstract Motion of liquid pouring from a beverage can is numerically studied. A liquid is poured from a can which is rotated at a prescribed angular speed. The flow is simulated by solving the unsteady three-dimensional Navier-Stokes equations. An experiment under the same condition is also carried out to validate the computational result. The result shows that, when the can is tipped, the liquid flows over the lid of the can and is once obstructed by the rim of the lid. The numerical result is in good agreement with the experimental result. The effect of condensation formed on a can surface is also considered. The effect of condensation is taken into account by adjusting a contact angle. The liquid pouring from a can trickles down along the can body. The computation reproduces these experimental observations.

scholarly journals Estimating intermittency in three-dimensional Navier–Stokes turbulence

2009 ◽  
Vol 625 ◽  
pp. 125-133 ◽  
Author(s):  
J. D. GIBBON
Keyword(s):  
Reynolds Number ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Space Time ◽  
Navier Stokes ◽  
Local Velocity ◽  
Vortex Sheets ◽  
Navier Stokes Equations ◽  
Local Number

The issue of why computational resolution in Navier–Stokes turbulence is hard to achieve is addressed. Under the assumption that the three-dimensional Navier–Stokes equations have a global attractor it is nevertheless shown that solutions can potentially behave differently in two distinct regions of space–time $\mathbb{S}$± where $\mathbb{S}$− is comprised of a union of disjoint space–time ‘anomalies’. If $\mathbb{S}$− is non-empty it is dominated by large values of |∇ω|, which is consistent with the formation of vortex sheets or tightly coiled filaments. The local number of degrees of freedom ± needed to resolve the regions in $\mathbb{S}$± satisfies $\mathcal{N}^{\pm}(\bx,\,t)\lessgtr 3\sqrt{2}\,\mathcal{R}_{u}^{3},$, where u = uL/ν is a Reynolds number dependent on the local velocity field u(x, t).

Numerical Study on the Flow Characteristics of the Francis Turbine With Various Blade Profiles

2013 ◽  
Author(s):  
J.-H. Jeon ◽  
S.-S. Byeon ◽  
Y.-J. Kim
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Francis Turbine ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Ansys Cfx ◽  
Commercial Code ◽  
Sst Turbulence Model

The Francis turbine is a kind of reaction turbines, which means that the potential energy of water converted to rotational kinetic energy. In this study, the flow characteristics have been investigated numerically in a Francis turbine on the 15 MW hydropower generation with various blade profiles (NACA 65 and NACA 16 series) and discharge angles (14°, 15°, 17°, and 18°), using the commercial code, ANSYS CFX. The k-ω SST turbulence model is employed in the Reynolds averaged Navier-Stokes equations. The computing domain includes the spiral casing, guide vanes, and draft tube, which are discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The results showed that the change of blade profiles and discharge angles significantly influenced the performance of the Francis turbine.

scholarly journals Exact coherent structures at extreme Reynolds number

2016 ◽  
Vol 794 ◽  
pp. 1-4 ◽  
Author(s):  
G. P. Chini
Keyword(s):  
Reynolds Number ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations ◽  
Wall Flows ◽  
Tollmien Schlichting ◽  
Turbulent Wall

Exact coherent structures (ECS), unstable three-dimensional solutions of the Navier–Stokes equations, play a fundamental role in transitional and turbulent wall flows. Dempsey et al. (J. Fluid Mech., vol. 791, 2016, pp. 97–121) demonstrate that at large Reynolds number reduced equations can be derived that simplify the computation and facilitate mechanistic understanding of these solutions. Their analysis shows that ECS in plane Poiseuille flow can be sustained by a novel inner–outer interaction between oblique near-wall Tollmien–Schlichting waves and interior streamwise vortices.

scholarly journals A Closed-Form Analytical Solution to the Complete Three-Dimensional Unsteady Compressible Navier-Stokes Equations

2021 ◽  
Author(s):  
Taofiq Amoloye
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Potential Theory ◽  
Stream Function ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Consistent Solution

Abstract The three main approaches in fluid dynamics are actual experiments, numerical simulations, and theoretical solutions. Numerical simulations and theoretical solutions are based on the continuity equation and Navier-Stokes equations (NSE) that govern experimental observations of fluid dynamics.Theoretical solutions can offer huge advantages over numerical solutions and experiments in the understanding of fluid flows and design. These advantages are in terms of cost and time consumption. However, theoretical solutions have been limited by the prized NSE problem that seeks a physically consistent solution than what classical potential theory (CPT) offers. Therefore, the current author refined CPT. He introduced refined potential theory (RPT) that provides a viscous potential/stream function as a physically consistent solution to the NSE problem. This function captures observable unsteady flow features including separation, wake, vortex shedding, compressibility, turbulence, and Reynolds-number-dependence. It appropriately combines the properties of a three-dimensional potential function that satisfy the inertia terms of NSE and the features of a stream function that satisfy the continuity equation, the viscous vorticity equation, and the viscous terms of NSE. RPT has been verified and validated against experimental and numerical results of incompressible unsteady sub-critical Reynolds number flows on stationary finite circular cylinder, sphere, and spheroid.

Vortex Breakdown in a Cylindrical Enclosure With a Rotating Lid

2005 ◽  
Author(s):  
Majid Molki ◽  
Ismail Hakan Olcay
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Cylindrical Wall ◽  
Navier Stokes Equations ◽  
Number Comparison ◽  
Computational Research

A computational research was conducted to explore the nature of the flow in a cylindrical enclosure with a rotating lid. The aspect ratio (AR) of the cylinder used in this research was maintained at 1.5 and 2.5, and the Reynolds number (Re) ranged from 990 to 2200. The three-dimensional Navier-Stokes equations were solved by the finite volume technique. Mesh adaptation was used to improve the quality of the mesh and computations. The results for (AR, Re) = (1.5, 1290) and (2.5, 2200) indicated the existence of one and two vortex breakdown bubbles along the axis of the cylinder, respectively. The results also showed that fluid spirals downward along the cylindrical wall and moves slowly inward towards the axis. This spiral motion was intensified at higher values of the Reynolds number. Comparison with experimental data indicated an excellent agreement. The vortex breakdown and the flow patterns predicted by this work are consistent with those reported in the existing literature.

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