scholarly journals Viscoacoustic squeeze-film force on a rigid disk undergoing small axial oscillations

2021 ◽  
Vol 933 ◽  
Author(s):  
S. Ramanarayanan ◽  
W. Coenen ◽  
A.L. Sánchez
Keyword(s):  
Stokes Equations ◽  
Circular Disk ◽  
Radial Pressure ◽  
Stokes Number ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Edge Region ◽  
Governing Parameter ◽  
Viscous Forces ◽  
Critical Separation

This paper investigates the air flow induced by a rigid circular disk or piston vibrating harmonically along its axis of symmetry in the immediate vicinity of a parallel surface. Previous attempts to characterize these so-called ‘squeeze-film’ systems largely relied on simplifications afforded by neglecting either fluid acceleration or viscous forces inside the thin enclosed gas layer. The present viscoacoustic analysis employs the asymptotic limit of small vibration amplitudes to investigate the flow by systematic reduction of the Navier–Stokes equations in two distinct flow regions, namely, the inner gaseous film where streamlines are nearly parallel to the confining walls and the near-edge region of non-slender flow that features gas exchange with the surrounding stagnant atmosphere. The flow in the gaseous film depends on the relevant Stokes number, defined as the ratio of the characteristic viscous time across the film to the characteristic oscillation time, and on a compressibility parameter, defined as the square of the ratio of the acoustic time for radial pressure equilibration to the oscillation time. A Strouhal number based on the local residence time emerges as an additional governing parameter for the near-edge region, which is incompressible at leading order. The method of matched asymptotic expansions is used to describe the solution in both regions, across which the time-averaged pressure exhibits comparable variations that give opposing contributions to the resulting time-averaged force experienced by the disk or piston. A diagram structured with the Stokes number and compressibility parameter as coordinates reveals that this steady squeeze-film force, typically repulsive for small values of the Stokes number, alternates to attraction across a critical separation contour in the parametric domain that exists for all Strouhal numbers. This analysis provides, for the first time, a unifying viscoacoustic theory of axisymmetric squeeze films, which yields a reduced parametric description for the time-averaged repulsion/attraction force that is potentially useful in applications including non-contact fluid bearings and robot locomotion.

Inertial effect on gas squeeze film for large radius disc excited by standing waves with complex modal shapes

2019 ◽  
Vol 33 (24) ◽  
pp. 1950282 ◽  
Author(s):  
Yi Qiang Fan ◽  
M. Miyatake ◽  
S. Kawada ◽  
Bin Wei ◽  
S. Yoshimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Standing Waves ◽  
Inertial Effect ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Large Radius ◽  
Navier Stokes Equations ◽  
Sinusoidal Functions

In order to investigate the gas inertial effect on bearing capacity of acoustic levitation on condition of complex exciting shapes, a new kind of numerical model including inertial effect in cylindrical coordinates was proposed. The inertial terms in Navier–Stokes equations are packaged to derive modified Reynolds equations. The amplitudes of standing waves were tested by distance probe in experiment and film thickness equation were reconstructed by sum of the sinusoidal functions. The theoretical and experimental results implied that the inertial effect is strongly related to the exciting modal shapes. It is concluded that the proposal of modified Reynolds equation can provide more optimized numerical solutions to solve the problems about the deviation between theoretical and experimental data.

scholarly journals Effect of the Radial Pressure Gradient on the Secondary Flow Generated in an Annular Turbine Cascade

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hesham M. El-Batsh
Keyword(s):  
Pressure Gradient ◽  
Secondary Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Radial Pressure ◽  
Navier Stokes ◽  
Pressure Probe ◽  
Passage Vortex ◽  
Flow Loss ◽  
Radial Pressure Gradient

This paper introduces an investigation of the effect of radial pressure gradient on the secondary flow generated in turbine cascades. Laboratory measurements were performed using an annular sector cascade which allowed the investigation using relatively small number of blades. The flow was measured upstream and downstream of the cascade using a calibrated five-hole pressure probe. The three-dimensional Reynolds Averaged Navier Stokes equations were solved to understand flow physics. Turbulence was modeled using eddy-viscosity assumption and the two-equation Shear Stress Transport (SST)k-ωmodel. The results obtained through this study showed that the secondary flow is significantly affected by the pressure gradient along blade span. The experimental measurements and the numerical calculations predicted passage vortex near blade hub which had larger and stronger values than that predicted near blade tip. The loss distribution revealed that secondary flow loss was concentrated near blade hub. It is recommended that attempts of reducing secondary flow in annular cascade should put emphasis on the passage vortex near the hub.

scholarly journals Effect of Inlet Temperature Non-Uniformity on High-Pressure Turbine Performance

2010 ◽  
Author(s):  
Craig I. Smith ◽  
Dongil Chang ◽  
Stavros Tavoularis
Keyword(s):  
High Pressure ◽  
Heat Load ◽  
Stokes Equations ◽  
Computation Time ◽  
Radial Pressure ◽  
Navier Stokes ◽  
Inlet Temperature ◽  
High Pressure Turbine ◽  
Navier Stokes Equations ◽  
Hot Streak

The temperature of the flow entering a high-pressure turbine stage is inherently non-uniform, as it is produced by several discrete, azimuthally-distributed combustors. In general, however, industrial simulations assume inlet temperature uniformity to simplify the preparation process and reduce computation time. The effects of a non-uniform inlet field on the performance of a commercial, transonic, single-stage, high-pressure, axial turbine with a curved inlet duct have been investigated numerically by performing URANS (Unsteady Reynolds-Averaged Navier-Stokes equations) simulations with the SST (Shear Stress Transport) turbulence model. By adjusting the alignment of the experimentally-based inlet temperature field with respect to the stator vanes, two clocking configurations were generated: an aligned case, in which each hot streak impinged on a vane and a misaligned case, in which each hot streak passed between two vanes. In the aligned configuration, the hot streaks produced higher time-averaged heat load on the vanes and lower heat load on the blades. As the aligned hot streaks impinged on the stator vanes, they also spread spanwise due to the actions of the casing passage vortices and the radial pressure gradient; this resulted in a stream entering the rotor with relatively low temperature variations. The misaligned hot streaks were convected undisturbed past the relatively cool vane section. Relatively high time-averaged enthalpy values were found to occur on the pressure side of the blades in the misaligned configuration. The non-uniformity of the time-averaged enthalpy on the blade surfaces was lower in the aligned configuration. The flow exiting the rotor section was much less non-uniform in the aligned case, but differences in calculated efficiency were not significant.

Squeeze Film Flow Analysis Using Moving Particle Semi-Implicit Calculation

2012 ◽  
Author(s):  
Nobuyuki Hirooka ◽  
Elon J. Terrell
Keyword(s):  
Stokes Equations ◽  
Flow Analysis ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Original Form ◽  
Particle Interactions ◽  
Navier Stokes Equations ◽  
Mps Method ◽  
Moving Particle ◽  
Film Flows

We have presented an application of the modified Moving Particle Semi-implicit (MPS) method for squeeze film flows. In addition to calculating the flow field of a squeeze film using the full Navier-Stokes equations, this method has the advantage of being meshless, which gives it the capability of analyzing dynamic and/or highly transient squeeze films by discretizing the domain as a series of particles and numerically analyzing inter-particle interactions. Although past literature has indicated the MPS method in its original form to be unstable in terms of its calculation of pressure, a modified algorithm was implemented to provide agreement between the numerical results and the analytical solutions.

Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure

2017 ◽  
Vol 822 ◽  
pp. 717-761 ◽  
Author(s):  
M. Vlachomitrou ◽  
N. Pelekasis
Keyword(s):  
Stokes Equations ◽  
Step Change ◽  
Basis Functions ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Compressive Stresses ◽  
Post Buckling ◽  
Flow Domain

A numerical method is developed to study the dynamic behaviour of an encapsulated bubble when the viscous forces of the surrounding liquid are accounted for. The continuity and Navier–Stokes equations are solved for the liquid, whereas the coating is described as a viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed for the spatial discretization of the flow domain surrounding the bubble, with the standard staggered grid arrangement that uses biquadratic and bilinear Lagrangian basis functions for the velocity and pressure in the liquid, respectively, coupled with a superparametric scheme with $B$-cubic splines as basis functions pertaining to the location of the interface. The spine method and the elliptic mesh generation technique are used for updating the mesh points in the interior of the flow domain as the shape of the interface evolves with time, with the latter being distinctly superior in capturing severely distorted shapes. The stabilizing effect of the liquid viscosity is demonstrated, as it alters the amplitude of the disturbance for which a bubble deforms and/or collapses. For a step change in the far-field pressure the dynamic evolution of the microbubble is captured until a static equilibrium is achieved. Static shapes that are significantly compressed are captured in the post-buckling regime, leading to symmetric or asymmetric shapes, depending on the relative dilatation to bending stiffness ratio. As the external overpressure increases, shapes corresponding to all the solution families that were captured evolve to exhibit contact as the two poles approach each other. Shell viscosity prevents jet formation by relaxing compressive stresses and bending moments around the indentation generated at the poles due to shell buckling. This behaviour is conjectured to be the inception process leading to static shapes with contact regions.

Dynamic and Stability Response of a Cylindrical Shell Subjected to Viscous Annular Flow and Thermal Load

2016 ◽  
Vol 16 (10) ◽  
pp. 1550072 ◽  
Author(s):  
W.-B. Ning ◽  
D.-Z. Wang
Keyword(s):  
Cylindrical Shell ◽  
Thermal Load ◽  
Annular Flow ◽  
Stokes Equations ◽  
Contour Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Critical Flow Velocity ◽  
Fluid Forces ◽  
Viscous Forces

This paper presents an analytical approach for investigating the dynamics and stability of an outer cylindrical shell conveying viscous fluid (i.e. water) in the annulus between the inner shell-type body and the outer shell with thermal load. The steady viscous forces that induce prestress on the shells are determined based on the time–mean Navier–Stokes equations. The shell motions are described by Flügge’s shell equations incorporating the prestress arising from the viscous effect. The shell-vibration-induced fluid forces are described by means of the potential flow theory, and the thermal loads are determined by the thermoelastic theory. The analytical model is conducted by the zero-level contour method with the aid of the weighted residual technology. The present study shows that the effect of viscosity in the annular flow renders the system more unstable. Moreover, the thermal load tends to reduce the critical flow velocity pronouncedly, for which there exists a critical temperature rise.

Turbulent Flows

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Turbulent Flows ◽  
High Speed ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
River Channels ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Thermally Driven ◽  
Flow Phenomena

Many geological flows involve turbulence, wherein the velocity field involves complex, fluctuating motions superimposed on a mean motion. Flows in natural river channels are virtually always turbulent. Magma flow in dikes and sills, and lava flows, can be turbulent. Atmospheric flows involving eolian transport are turbulent. The complex, convective overturning of fluid in a magma chamber or geyser is a form of turbulence. Thus, a description of the basic qualities of these complex flows is essential for understanding many geological flow phenomena. Turbulent flows generally are associated with large Reynolds numbers. Recall from Chapter 5 that the Reynolds number Re is a measure of the ratio of inertial to viscous forces acting on a fluid element, . . . Re = ρUL/μ . . . . . . (14.1) . . . where the characteristic velocity U and length L are defined in terms of the particular flow system. Thus, turbulence is typically associated, for given fluid density ρ and viscosity μ, with high-speed flows (although we must be careful in applying this generality to thermally driven convective motions; see Chapter 16). A simple, visual illustration of this occurs when smoke rises from a cigar within otherwise calm, surrounding air. The smoke acts as a flow tracer. Smoke molecules at the cigar tip start from rest, since they are initially attached to the cigar. Upward fluid motion, as traced by the smoke, initially is of low speed, and viscous forces have a relatively important influence on its behavior. The flow is laminar; smoke streaklines are smooth and locally parallel. But as the flow accelerates upward, it typically reaches a point where viscous forces are no longer sufficient to damp out destabilizing effects of growing inertial forces, and the flow becomes turbulent, manifest as whirling, swirling fluid motions (see Tolkien [1937]). Throughout this chapter we will consider only incompressible Newtonian fluids. Unfortunately, the complexity of turbulent fluid motions precludes directly using the Navier–Stokes equations to describe them. Instead, we will adopt a procedure whereby the Navier–Stokes equations are recast in terms of temporally averaged or spatially averaged values of velocity and pressure, and fluctuations about these averages.

Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass Coupled to Internal, External and Annular Flow

2002 ◽  
Author(s):  
M. Amabili ◽  
R. Garziera
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Computer Code ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Added Masses ◽  
Circular Cylindrical Shells ◽  
Lumped Masses

The effect of steady viscous forces on vibrations of shell with internal and annular flow has been considered by using the time-mean Navier-Stokes equations. The model developed by Amabili & Garziera (2000), capable of simulating shells with non-uniform boundary conditions, added masses and partial elastic bed, has been extended to include non-uniform prestress. The effect of steady viscous forces has been added to the inviscid flow formulation considered by Amabili & Garziera (2002). The computer code DIVA has been developed by using the model developed in the present study. It has been validated by comparison with available results for shells with uniform constraints and has been used to study shells with non-uniform constraints and added lumped masses.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 1. Velocity and acceleration distributions

2010 ◽  
Vol 646 ◽  
pp. 59-90 ◽  
Author(s):  
PARTHA S. GOSWAMI ◽  
V. KUMARAN
Keyword(s):  
Particle Velocity ◽  
Stokes Equations ◽  
Hard Spheres ◽  
Flow Direction ◽  
Fluid Velocity ◽  
Gaussian White Noise ◽  
Stokes Number ◽  
Navier Stokes ◽  
Velocity Fluctuations ◽  
Non Gaussian

The effect of fluid velocity fluctuations on the dynamics of the particles in a turbulent gas–solid suspension is analysed in the low-Reynolds-number and high Stokes number limits, where the particle relaxation time is long compared with the correlation time for the fluid velocity fluctuations, and the drag force on the particles due to the fluid can be expressed by the modified Stokes law. The direct numerical simulation procedure is used for solving the Navier–Stokes equations for the fluid, the particles are modelled as hard spheres which undergo elastic collisions and a one-way coupling algorithm is used where the force exerted by the fluid on the particles is incorporated, but not the reverse force exerted by the particles on the fluid. The particle mean and root-mean-square (RMS) fluctuating velocities, as well as the probability distribution function for the particle velocity fluctuations and the distribution of acceleration of the particles in the central region of the Couette (where the velocity profile is linear and the RMS velocities are nearly constant), are examined. It is found that the distribution of particle velocities is very different from a Gaussian, especially in the spanwise and wall-normal directions. However, the distribution of the acceleration fluctuation on the particles is found to be close to a Gaussian, though the distribution is highly anisotropic and there is a correlation between the fluctuations in the flow and gradient directions. The non-Gaussian nature of the particle velocity fluctuations is found to be due to inter-particle collisions induced by the large particle velocity fluctuations in the flow direction. It is also found that the acceleration distribution on the particles is in very good agreement with the distribution that is calculated from the velocity fluctuations in the fluid, using the Stokes drag law, indicating that there is very little correlation between the fluid velocity fluctuations and the particle velocity fluctuations in the presence of one-way coupling. All of these results indicate that the effect of the turbulent fluid velocity fluctuations can be accurately represented by an anisotropic Gaussian white noise.

On the Dynamics and Stability of Cylindrical Shells Conveying Inviscid or Viscous Fluid in Internal or Annular Flow

1991 ◽  
Vol 113 (3) ◽  
pp. 409-417 ◽  
Author(s):  
A. El Chebair ◽  
A. K. Misra
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Dynamical Behavior ◽  
Internal Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Forces ◽  
Viscous Forces ◽  
The Fourier Transform ◽  
The Stability

This paper investigates theoretically for the first time the dynamical behavior and stability of a simply supported shell located coaxially in a rigid cylindrical conduit. The fluid flow is incompressible and the fluid forces consist of two parts: (i) steady viscous forces which represent the effects of upstream pressurization of the flow; (ii) unsteady forces which could be inviscid or viscous. The inviscid forces were derived by linearized potential flow theory, while the viscous ones were derived by means of the Navier-Stokes equations. Shell motion is described by the modified Flu¨gge’s shell equations. The Fourier transform technique is employed to formulate the problem. First, the system is subjected only to the unsteady inviscid forces. It is found that increasing either the internal or the annular flow velocity induces buckling, followed by coupled mode flutter. When both steady viscous and unsteady inviscid forces are applied, for internal flow, the system becomes stabilized; while for annular flow, the system loses stability at much lower velocities. Second, the system is only subjected to the unsteady viscous forces. Calculations are only performed for the internal flow case. The results are compared to those of inviscid theory. It is found that the effects of unsteady viscous forces on the stability of the system are very close to those of unsteady inviscid forces.

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