The Stokes-flow drag on prolate and oblate spheroids during axial translatory accelerations

1972 ◽  
Vol 52 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Robert Y. S. Lai ◽  
Lyle F. Mockros
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Equations Of Motion ◽  
Mass Effect ◽  
Added Mass ◽  
Fluid Forces ◽  
Fluid Resistance ◽  
Oblate Spheroids ◽  
History Of ◽  
Flow Drag

Stokes's linearized equations of motion are used to calculate the flow field generated by a spheroid executing axial translatory oscillations in an infinite, otherwise still, incompressible, viscous fluid. The flow field, expressed in terms of spheroidal wave functions of order one, is used to develop general expressions for the drag on oscillating prolate and oblate spheroids. Formulae for the approximate drag, useful in making calculations, are obtained for small values of an oscillation parameter. These formulae reduce to the Stokes result in the limit when the spheroid becomes a sphere and the steady-state drag for a spheroid as the frequency of oscillation becomes zero. The fluid forces on spheroids of various shapes are compared graphically. The approximate formulae for the drag are integrated over all frequencies to obtain formulae for the drag on spheroids executing general axial translatory accelerations. The fluid resistance on the spheroid is expressed as the sum of an added mass effect, a steady-state drag and an effect due to the history of the motion. A table of added mass, viscous and history coefficients is given.

scholarly journals The formation of vortices from a surface of discontinuity

1931 ◽  
Vol 134 (823) ◽  
pp. 170-192 ◽  
Keyword(s):  
Steady State ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Small Oscillations ◽  
Approximate Form ◽  
History Of ◽  
State Increase ◽  
Liquid Surfaces

Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

Hydrodynamics of scallop locomotion: unsteady fluid forces on clapping shells

1996 ◽  
Vol 317 ◽  
pp. 73-90 ◽  
Author(s):  
J.-Y. Cheng ◽  
M. E. DeMont
Keyword(s):  
Flow Model ◽  
Boundary Surface ◽  
Mass Effect ◽  
Added Mass ◽  
Time Dependent ◽  
Fluid Forces ◽  
Aquatic Locomotion ◽  
Unsteady Fluid ◽  
Opening And Closing ◽  
Potential Flow Model

A potential flow model has been formulated for scallop swimming. Under the smalldisturbance approximation, the problem of the unsteady flow past the wing-like configuration of a scallop is separated into two linear sub-problems: the steady lifting problem and the unsteady symmetric thickness problem. The latter is associated with the expansion and contraction of the boundary surface of the scallop due to the shell opening and closing. A quasi-two-dimensional analytical solution of the thickness problem was obtained to give the time-dependent fluid forces acting on the outer surfaces of the shells. In addition to the added-mass effect, which has been widely accepted in the hydrodynamics of aquatic locomotion, there are two other mechanisms in the fluid reaction: flow-induced pseudo-elasticity and pseudo-viscosity. The pseudoelasticity provides a force proportional to the gape angle displacement, and will assist shell opening but resist shell closing. The pseudo-viscosity force is proportional to the angular velocity of the gape, and benefits both shell opening and closing. Their roles are discussed through comparison with those of shell inertia, hinge ligament elasticity and hinge damping. At 10 °C the hinge damping in the scallop was found to be almost compensated by the flow pseudo-viscosity. The unsteady fluid reaction may have a significant effect on the operation of the dynamic swimming system of scallops.

Steady-State Response of a Flexibly Mounted Stator Mechanical Face Seal Subject to Dynamic Forcing of a Flexible Rotor

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Philip Varney ◽  
Itzhak Green
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
External Input ◽  
Face Seal ◽  
Flexible Rotor ◽  
State Equations ◽  
Fluid Forces ◽  
Flexible Rotors ◽  
Successful Design ◽  
Constitutive Components

Mechanical face seals are constitutive components of much larger turbomachines and require consideration of the system dynamics for successful design. The dynamic interplay between the seal and rotor is intensified by recent trends toward reduced clearances, higher speeds, and more flexible rotors. Here, the “rotor” consists of the flexible shaft and the rotating seal seat. The objective here is to, for the first time, determine how the rotor affects the seal performance and vice versa. Thresholds can then be established beyond which the rotor influences the seal but not vice versa (i.e., the rotordynamics can be sent to the seal analysis as an exogenous input). To this end, a model of a flexibly mounted stator face seal is provided including the coupled dynamics of the flexible rotor. The model accounts for axial and angular deflections of the rotor and seal. Coupled rotordynamics are modeled using a lumped-parameter approach including static and dynamic rotor angular misalignments. For expediency, linearized expressions for fluid forces are used, and the resulting steady-state equations of motion are solved analytically to investigate how rotor inertia, speed, and angular misalignment influence the coupled seal dynamics. Importantly, results from the study reveal that in some operating regimes, neglecting the rotordynamics implies healthy seal operation when instead intermittent rub exists between the faces. This work also shows that when the rotor inertia is much larger than the seal inertia, the rotordynamics can be solved separately and used in the seal model as an external input.

Fluid Added Mass Effect in the Modal Response of a Pump-Turbine Impeller

2009 ◽  
Author(s):  
Eduard Egusquiza ◽  
Carme Valero ◽  
Quanwei Liang ◽  
Miguel Coussirat ◽  
Ulrich Seidel
Keyword(s):  
Natural Frequencies ◽  
Experimental Tests ◽  
Mass Effect ◽  
Added Mass ◽  
Mode Shapes ◽  
Pump Turbine ◽  
Modal Response ◽  
Surrounding Fluid ◽  
Turbine Impeller ◽  
Good Agreement

In this paper, the reduction in the natural frequencies of a pump-turbine impeller prototype when submerged in water has been investigated. The impeller, with a diameter of 2.870m belongs to a pump-turbine unit with a power of around 100MW. To analyze the influence of the added mass, both experimental tests and numerical simulations have been carried out. The experiment has been performed in air and in water. From the frequency response functions the modal characteristics such as natural frequencies and mode shapes have been obtained. A numerical simulation using FEM (Finite Elements Model) was done using the same boundary conditions as in the experiment (impeller in air and surrounded by a mass of water). The modal behaviour has also been calculated. The numerical results were compared with the available experimental results. The comparison shows a good agreement in the natural frequency values both in air and in water. The reduction in frequency due to the added mass effect of surrounding fluid has been calculated. The physics of this phenomenon due to the fluid structure interaction has been investigated from the analysis of the mode-shapes.

A Double Birkhoff Wake Oscillator for the Modeling of Vortex-Induced Vibration

2011 ◽  
Author(s):  
R. H. M. Ogink
Keyword(s):  
Free Vibration ◽  
Added Mass ◽  
Mass Force ◽  
Near Wake ◽  
Vibration Measurements ◽  
Vortex Induced Vibration ◽  
Fluid Forces ◽  
Wake Oscillator ◽  
Model Equations ◽  
Far Wake

A double Birkhoff wake oscillator for the modeling of vortex-induced vibration is presented in which the oscillating variables are assumed to be associated with the boundary layer/near wake and the far wake. The fluid forces are assumed to consist of a potential added mass force and a force due to vortex shedding. In the limit of vanishing incoming flow velocity, the model equations reduce to a form similar to the Morison equation. The results of the double wake oscillator have been compared with forced vibration measurements and free vibration measurements over a range of mass and damping ratios. The model is capable of describing the most important trends in both the forced and free vibration experiments. Specifically, the double wake oscillator is able to model both the upper and lower branch of free vibration.

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

A System for Individualized Dosing of Intravenous Aminophylline Using a Programmable Calculator

PEDIATRICS ◽  
1984 ◽  
Vol 73 (1) ◽  
pp. 64-67
Author(s):  
J. Chris Mitsuoka ◽  
Richard J. Fleck
Keyword(s):  
Steady State ◽  
Serum Sample ◽  
Drug Exposure ◽  
Plasma Concentrations ◽  
Dose Administration ◽  
Programmable Calculator ◽  
Concentration Determination ◽  
A Value ◽  
Individualized Dosing ◽  
History Of

A program that calculates a value of clearance for an individual patient prior to reaching steady state in the early stages of aminophylline therapy is presented. The program is written for the Texas Instruments TI-59 programmable calculator and may be used with or without the PC-100C printer. The program can provide clinically useful information concerning projected plasma concentrations prior to reaching steady state with an accurate history of the dose administration and serum concentration determination. If the patient has not received xanthene therapy prior to admission, only one serum sample is required. If there has been prior drug exposure, a second serum sample is required. An iterative technique, which would be impractical to use without calculator assistance, is employed to make these determinations.

Effect of Material and Geometric Parameters on the Steady-State Belt Stresses and Belt Slip for Flat Belt-Drives

2015 ◽  
Author(s):  
Cagkan Yildiz ◽  
Tamer M. Wasfy ◽  
Hatem M. Wasfy ◽  
Jeanne M. Peters
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Flexible Multibody Dynamics ◽  
Friction Model ◽  
Rigid Bodies ◽  
Geometric Parameters ◽  
Rubber Matrix ◽  
Axial Stiffness ◽  
Belt Drive

In order to accurately predict the fatigue life and wear life of a belt, the various stresses that the belt is subjected to and the belt slip over the pulleys must be accurately calculated. In this paper, the effect of material and geometric parameters on the steady-state stresses (including normal, tangential and axial stresses), average belt slip for a flat belt, and belt-drive energy efficiency is studied using a high-fidelity flexible multibody dynamics model of the belt-drive. The belt’s rubber matrix is modeled using three-dimensional brick elements and the belt’s reinforcements are modeled using one dimensional truss elements. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure. The material parameters studied are the belt-pulley friction coefficient and the belt axial stiffness and damping. The geometric parameters studied are the belt thickness and the pulleys’ centers distance.

CFD Leakage Predictions of Unworn and Worn Labyrinth Seals With and Without Tooth Axial Offset

2017 ◽  
Author(s):  
Hasham H. Chougule ◽  
Alexander Mirzamoghadam
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Numerical Modeling ◽  
Steady State ◽  
Flow Field ◽  
Labyrinth Seals ◽  
Small Clearance ◽  
Total Leakage ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Deflection

The objective of this study is to develop a Computational Fluid Dynamics (CFD) based methodology for analyzing and predicting leakage of worn or rub-intended labyrinth seals during operation. The simulations include intended tooth axial offset and numerical modeling of the flow field. The purpose is to predict total leakage through the seal when an axial tooth offset is provided after the intended/unintended rub. Results indicate that as expected, the leakage for the in-line worn land case (i.e. tooth under rub) is higher compared to unworn. Furthermore, the intended rotor/teeth forward axial offset/shift with respect to the rubbed land reduces the seal leakage. The overall leakage of a rubbed seal with axial tooth offset is observed to be considerably reduced, and it can become even less than a small clearance seal designed not to rub. The reduced leakage during steady state is due to a targeted smaller running gap because of tooth offset under the intended/worn land groove shape, higher blockages, higher turbulence and flow deflection as compared to worn seal model without axial tooth offset.

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