On the Effective Viscosity Expression for Modeling Squeeze-Film Damping at Low Pressure

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Maria F. Pantano ◽  
Leonardo Pagnotta ◽  
Salvatore Nigro
Keyword(s):  
Experimental Data ◽  
Stokes Equation ◽  
Effective Viscosity ◽  
Optimization Procedure ◽  
Low Pressure ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equation ◽  
Squeeze Film Damping

While at high pressure, the classical Navier–Stokes equation is suitable for modeling squeeze-film damping, at low pressure, it needs some modification in order to consider fluid rarefaction. According to a common approach, fluid rarefaction can be included in this equation by substituting the standard fluid viscosity with a fictitious quantity, known as effective viscosity, for which different formulations were proposed. In order to identify which expression works better, the results obtained when either formulation is implemented inside the Navier–Stokes equation (that is then solved by both analytical and numerical means) are compared with already available experimental data. At the end, a novel expression is discussed, derived from a computer-assessed optimization procedure.

A Novel Expression for the Effective Viscosity to Model Squeeze-Film Damping at Low Pressure

2013 ◽  
Vol 390 ◽  
pp. 76-80 ◽  
Author(s):  
Maria F. Pantano ◽  
Salvatore Nigro ◽  
Franco Furgiuele ◽  
Leonardo Pagnotta
Keyword(s):  
Experimental Data ◽  
Effective Viscosity ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
The Novel ◽  
Mems Devices ◽  
Navier Stokes Equation ◽  
Experimental Procedure ◽  
Squeeze Film Damping

The Navier-Stokes equation is currentlyconsidered for modelling of squeeze-film damping in MEMS devices, also when the fluid flow associated to it is rarefied.In order to include rarefaction effects in such equation, a common approach consists of replacing the ordinary fluid viscosity with a scaled quantity, known as effective viscosity.The literature offers different expressions for the effective viscosity as a function of the Knudsen number (Kn). Such expressions were shown to work well whenKn<1, but theyresulted to be lessaccurate in case ofKn>1. In this paper a new expression is proposed to evaluate the effective viscosity for 1<Kn<40with increased reliability. Such anexpression was derivedfrom an optimized numerical-experimental procedure,developed in MATLAB® environment, using a finite element code and experimental data extracted from the literature. A comparison is finally reported and discussed between the results, in terms of damping coefficient, obtained considering previously reported effective viscosity expressions and the novel one,with reference to different squeeze film damping layouts, for which experimental data are already available.

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.

MODELING THE SEPARATION PROCESS IN A HYDROCYCLONE

2020 ◽  
Author(s):  
Сергей Ильдусович Валеев ◽  
Владимир Александрович Савчук
Keyword(s):  
Stokes Equation ◽  
Effective Viscosity ◽  
Numerical Study ◽  
Separation Process ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Light Impurities

На основе уравнения Навье-Стокса проведено численное исследование эффективной вязкости в цилиндрическом гидроциклоне для разделения эмульсий с малым содержанием легких примесей. Установлено, что эффективная вязкость в гидроциклоне возрастает с увеличением разгрузочного соотношения. On the basis of the Navier-Stokes equation, a numerical study of the effective viscosity in a cylindrical hydrocyclone for the separation of emulsions with a low content of light impurities is carried out. It was found that the effective viscosity in a hydrocyclone increases with an increase in the unloading ratio.

Numerical Modeling of a Static Cavitation Module

2016 ◽  
Vol 817 ◽  
pp. 64-69
Author(s):  
Tatiana Vitenko ◽  
Paweł Droździel ◽  
Nazar Horodysky
Keyword(s):  
Experimental Data ◽  
Numerical Modeling ◽  
Numerical Modelling ◽  
Stokes Equation ◽  
Liquid State ◽  
Software Package ◽  
Navier Stokes ◽  
State Equations ◽  
Navier Stokes Equation ◽  
Good Agreement

This paper presents the results of numerical modelling of cavitation flows in a hydrodynamic module. The simulation was performed using the SolidWorks software package. The computations were made based on the Navier-Stokes equation combined with liquid state equations and empirical dependencies which define liquid parameters. The numerical results are in good agreement with experimental data.

scholarly journals Laminar Flow Velocity and Temperature Distributions Between Coaxial Rotating Disks of Finite Radius

1988 ◽  
Author(s):  
D. T. Orletsky ◽  
J. F. Louis
Keyword(s):  
Experimental Data ◽  
Temperature Distribution ◽  
Laminar Flow ◽  
Aspect Ratio ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Large Aspect Ratio ◽  
Rotating Disks ◽  
Finite Radius ◽  
Navier Stokes Equation

Predictions of the laminar flow and temperature distribution between coaxial rotating disks of finite radius have been obtained using a computer model solving the Navier-Stokes equation for a laminar fluid of constant properties. To do this, a stream vorticity model in the r-z plane is used in the solution of the Navier-Stokes equation. The velocity fields were obtained for both shrouded and unshrouded disks with or without radial throughflow for either co-rotating or counter-rotating disks. Velocity profiles predicted by this model were compared to experimental data, to a similarity solution and to a large aspect ratio model. The results obtained by this model closely matched the experimental data, and the large aspect ratio solution for the cases considered. The uncoupled energy equation was then solved using the calculated velocity distribution for the temperature distribution between the disks. This was done for two cases: i) two isothermal disks, and ii) one isothermal disk and one adiabatic disk.

Three-Dimensional Calculation of Bubble Growth and Drop Ejection in a Bubble Jet Printer

1992 ◽  
Vol 114 (4) ◽  
pp. 638-641 ◽  
Author(s):  
A. Asai
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Stokes Equation ◽  
Bubble Growth ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Bubble Behavior ◽  
Navier Stokes Equation ◽  
Bubble Pressure ◽  
First Time

The three-dimensional Navier-Stokes equation for the motion of ink both inside and outside the nozzle of a bubble jet printer is numerically solved, for the first time, to predict the bubble behavior and the drop ejection. The results of calculation for three types of ink agreed well with experimental data. The effect of initial bubble pressure, viscosity and surface tension on the volume and the velocity of the drop is numerically investigated. The three-dimensional calculation is very useful to the design of bubble jet printers because it saves a lot of time and cost to make and evaluate prototypes.

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