Prediction of Liquid and Gas Leak Rates in Packed Stuffing Boxes

2019 ◽  
Author(s):  
Ali Salah Omar Aweimer ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Axial Stress ◽  
Slip Flow ◽  
Experimental Tests ◽  
Theoretical Models ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Packing Rings

Abstract The prediction of gas and liquid leak rate through packed stuffing boxes subjected to gas flow is a subject of very few studies in the literature. For better prediction of leakage, the change of porosity with length due to the non-uniform axial stress must be accounted for. There are few theoretical models on the prediction of leak rates in packing rings with capillary models. However, a model that incorporates the change of the capillary area with stress gives a better prediction. In this paper, the first slip flow model is used to predict gas and liquid flow considering the straight capillaries and capillaries having an area dependent on the axial stress in the packing rings. An approach that uses an analytical-computational methodology based on the number and the size of pores obtained experimentally is adopted to predict gas and liquid leak rates in uniform and non-uniform compressed yarned packings. The Navier-Stokes equations associated with slip boundary condition at the wall are used to predict leakage. Experimental tests with helium, argon, nitrogen and air for gazes and water and kerosene for liquids will be used to validate the models. The porosity parameters characterization will be conducted experimentally with helium at a reference gas at different gland stresses and pressures.

Liquid Leak Predictions in Micro- and Nanoporous Gaskets

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Experimental Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through

In recent years, quite few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However, a very limited work is done on liquid leak rates through gaskets. The slip flow model is used to predict liquid flow through porous gaskets based on measurements of gas flow at different pressures. In fact, an extrapolation of the porosity parameter approach (Grine, L., and Bouzid, A., 2009, “Correlation of Gaseous Mass Leak Rates Through Micro and Nano-Porous Gaskets,” ASME Paper No. PVP2009-77205) used to correlate leak rates between different gases is used to predict liquid leak rates. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid micro- and nanoflows in the slip flow regime through gaskets is presented. The formulation is based on the Navier–Stokes equations associated with slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under various experimental conditions of fluid media, pressure, and gasket stress were conducted on a special gasket test rig. Gaseous and liquid leaks are measured and comparisons with the analytical predictions are made.

A Friction Factor Correlation for Gas Flow in Parallel Plate Microchannels by Considering Combined Effects of Compressibility and Rarefaction

2008 ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Friction Factor ◽  
Velocity Gradient ◽  
Parallel Plate ◽  
Gas Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Combined Effects ◽  
Slip Boundary

The effects of compressibility and rarefaction for gas flow in microchannels have been extensively studied separately. However, these two effects are always combined for gas flow in microchannels. In this paper, the two-dimensional compressible Navier-Stokes equations are solved for gas flow in parallel plate channels with a slip boundary condition to study the combined effects of compressibility and rarefaction on the friction factor. The numerical methodology is based on the control volume finite difference scheme. It is found that the effect of compressibility increases the velocity gradient near the wall which then increases the friction factor. On the other hand, increasing the velocity gradient near the wall leads to a much larger slip velocity and implies a stronger rarefaction effect and a corresponding decrease in the friction factor. These two opposite effects make the effect of compressibility on friction factor for slip flow weaker than that for no-slip compressible flow. A correlation among fRe, Kn and Ma is presented. The correlation is validated with available experimental and analytical results.

Liquid Leak Predictions in Micro and Nano-Porous Gaskets

2010 ◽  
Author(s):  
Lotfi Grine ◽  
Abdel-Hakim Bouzid
Keyword(s):  
Stokes Equations ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Gas Leak ◽  
Flow Through ◽  
Parameter Approach ◽  
Experimental And Theoretical Studies

In recent years, few experimental and theoretical studies have been conducted to predict gas leak rate through gaskets. However a very limited work is done on liquid leak rates through gaskets. A new method based on a slip flow model to predict liquid flow through nano-porous gaskets is presented. A recent study [1] had shown that the leakage prediction based on the porosity parameter approach was successful in predicting gaseous leaks and an extrapolation of the latter to liquid leaks is the purpose of this study. In the present article, an analytical-computational methodology based on the number and pore size to predict liquid nanoflow in the slip flow regime through gaskets is presented. The formulation is based on the Navier-Stokes equations associated to slip boundary condition at the wall. The mass leak rates through a gasket considered as a porous media under variable experimentally conditions of (fluid media, pressure, and gasket stress) were conducted on a test bench. Gaseous and liquid leaks are measured and comparisons are made with the analytical predictions.

Experimental and Numerical Studies on Gas Flow Through Silicon Microchannels

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
K. Srinivasan ◽  
P. M. V. Subbarao ◽  
S. R. Kale
Keyword(s):  
Boundary Condition ◽  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Flow Characteristics ◽  
Slip Boundary Condition ◽  
Second Order ◽  
Navier Stokes ◽  
Slip Boundary ◽  
Aspect Ratios

The present work investigates the extension of Navier–Stokes equations from slip-to-transition regimes with higher-order slip boundary condition. To achieve this, a slip model based on the second-order slip boundary condition was derived and a special procedure was developed to simulate slip models using FLUENT®. The boundary profile for both top and bottom walls was solved for each pressure ratio by the customized user-defined function and then passed to the FLUENT® solver. The flow characteristics in microchannels of various aspect ratios (a = H/W = 0.002, 0.01, and 0.1) by generating accurate and high-resolution experimental data along with the computational validation was studied. For that, microchannel system was fabricated in silicon wafers with controlled surface structure and each system has several identical microchannels of same dimensions in parallel and the processed wafer was bonded with a plane wafer. The increased flow rate reduced uncertainty substantially. The experiments were performed up to maximum outlet Knudsen number of 1.01 with nitrogen and the second-order slip coefficients were found to be C1 = 1.119–1.288 (TMAC = 0.944–0.874) and C2 = 0.34.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

scholarly journals Flow of a viscous compressible fluid produced in a circular tube by an impulsive point source

2011 ◽  
Vol 668 ◽  
pp. 100-112 ◽  
Author(s):  
B. U. FELDERHOF ◽  
G. OOMS
Keyword(s):  
Compressible Fluid ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Sudden Impulse

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. An efficient numerical scheme has been developed for the calculation of flow velocity and pressure disturbance as a function of position and time.

Numerical Analysis of Rarefaction and Compressibility Effects in Bent Microchannels

2010 ◽  
Author(s):  
O. Rovenskaya ◽  
G. Croce
Keyword(s):  
Gas Flow ◽  
Flow Characteristics ◽  
Wall Slip ◽  
Outer Wall ◽  
Slip Boundary Condition ◽  
Central Line ◽  
Navier Stokes ◽  
Strong Impact ◽  
First Order ◽  
Slip Boundary

Numerical investigation of a gas flow through microchannels with a sharp, 90 degrees bend is carried out using Navier-Stokes (N-S) equations with the classical Maxwell first-order slip boundary condition, including the tangential gradient effect due to the wall curvature, and Smoluchowski first order temperature jump definition. The details of the flow structure near the corner are analyzed, investigating the competing effects of rarefaction and compressibility on the channel performances. The flow characteristics in terms of velocity profiles, slip velocity distribution along inner and outer wall, pressure, average Mach number along central line of the channel have been presented. The results showed that impact of the bend on the channel performances is smaller at high rarefaction levels. The behaviour of pressure and velocity away from the bend is similar to that of a straight microchannel; however, the asymmetry in the flow at the bend, with high velocities and high velocity gradients on its inner side, has a strong impact on wall slip velocities. The presence of a recirculation is detected on both the inner and outer walls of the corner for larger Reynolds. However, rarefaction may delay the onset of recirculation. It is also observed that the mass flux through a bend microchannel can even be slightly larger than that through a straight microchannel of the same length and subjected to the same pressure difference.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

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