An algebraic expansion of the potential theory for predicting dynamic stability limit of in-line cylinder arrangement under single-phase fluid cross-flow

2017 ◽  
Vol 72 ◽  
pp. 80-95 ◽  
Author(s):  
Mustapha Benaouicha ◽  
Franck Baj ◽  
Elisabeth Longatte
Keyword(s):  
Potential Theory ◽  
Dynamic Stability ◽  
Single Phase ◽  
Cross Flow ◽  
Stability Limit ◽  
Phase Fluid

Single-Phase Fluid Flow in a Stratified Porous Medium With Crossflow(includes associated paper 12946 )

1984 ◽  
Vol 24 (01) ◽  
pp. 97-106 ◽  
Author(s):  
Gao Cheng-Tai
Keyword(s):  
Differential Equations ◽  
Single Phase ◽  
Cross Flow ◽  
Vertical Direction ◽  
Multilayer System ◽  
Low Permeability ◽  
Wall Model ◽  
Vertical Resistance ◽  
Vertical Permeability ◽  
Phase Fluid

Abstract A new model is presented for a stratified reservoir. The model is used to study the influence of cross flow on pressure transient well tests and other single-phase flow problems. The reasons for single-phase cross flow in multilayer reservoirs are discussed. Solutions for linear and radial incompressible flow in a stratified reservoir with cross flow are presented; effects of reservoir parameters and cross flow on pressure are studied, and acriterion for considering cross flow between layers is suggested. Introduction Real reservoirs normally consist of many layers with different permeabilities. Frequently, thin low-permeabilitysilts or shales separate the layers. For simplicity, such reservoirs often are treated as a single uniform layer or asseveral independent layers. In reality, these layers influence each other through cross flow and cannot be treated so simply. In the early 1960's, several papers addressed the behavior and influence of single-phase fluid cross flow in multilayer reservoirs. These papers studied the unsteady flow behavior to explain transient well test results obtained in multilayer reservoirs with cross flow. From these papers it is clear that rigorous mathematical treatment of the single-phase cross flow problem in two-layer reservoirs is quite difficult-even under the highly idealized assumptions that each layer is homogeneous, that no low-permeability shale is between the layers, and so on. The problem is even more difficult if the reservoir has more than two layers. So, the problems really need to be simplified. A simplified model, called "semipermeable wall model," is suggested here to approximate the actual multilayer reservoir. In this model we ignore the pressure variation in the vertical direction in the differential equations and avoid the need for boundary conditions between layers, so the problem is greatly simplified mathematically. The purposes of this work areto establish fundamental equations for the semipermeable wall model,to discuss why single-phase cross flow occurs, andto study the flow in a multilayer system with cross flow to determine when to treat the multilayer system as a single uniform layer or as many independent layers and when neither of these simplifications applies. This paper gives some exact solutions for simple multilayer flow cases with cross flow. These examples are used to give a clear picture of the flow in a multilayer reservoir and to give criteria for deciding when we can treat the multilayer system as a single layer or as many independent layers. Semipermeable Wall Model and Fundamental Differential Equations. Reservoirs generally have horizontal dimensions much greater than their thickness between impermeable rocks at the top and bottom. If there is no low-permeability shale within a layer, the change of pressure is generally very small in the vertical direction. The pressure at the midway point in the vertical direction of the layer is a good representation of the average pressure in the layer. The vertical equilibrium (VE) concept is used widely in the petroleum literature. VE in each layer means that the vertical pressure drop is zero at all times and positions in each layer, so the pressure will be the same for all the points on any vertical line in each layer. Assuming VE implies perfect vertical communication, which is equivalent to assuming infinite vertical permeability. VE will be a good assumption for layers with effective length-to-thickness ratio of 10 or more. Since the pressure change is very small in the vertical direction in any layer, we can concentrate the vertical resistance to flow at the walls between the layers, and let the vertical resistance be zero within layers. Because the wall has concentrated vertical resistance, it is no longer an ordinary interface between layers. The pressures on opposite sides of the wall will differ by a finite amount. The resistances of the walls between layers should be taken such that they are equivalent to the actual vertical resistance of the reservoir. These imaginary walls, called "semipermeable walls," are a remedy for the assumption of infinite vertical permeability within layers. Five assumptions are used in the semipermeable wall model.The reservoir pore space is filled with a slightly compressible single-phase fluid.The reservoir is homogeneous in vertical direction in each layer.The thickness of each layer is constant.The reservoir consists of n layers. In each layer, the horizontal permeability is finite, but the vertical permeability is infinite.Gravity force is negligible. Fluid flowing through each semipermeable wall is assumed proportional to the local pressure difference across the wall and inversely proportional to viscosity of the fluid. Consider a two-layer model (see Fig. 1A). SPEJ P. 97^

Large Eddy Simulation of Fluid-Elastic Instability in Square Normal Cylinder Array

2015 ◽  
Author(s):  
Vilas Shinde ◽  
Elisabeth Longatte ◽  
Franck Baj
Keyword(s):  
Single Phase ◽  
Cross Flow ◽  
Normal Direction ◽  
Cylinder Surface ◽  
Elastic Instability ◽  
Eddy Simulation ◽  
Cylinder Array ◽  
Moving Cylinder ◽  
Large Eddy ◽  
Phase Fluid

Large Eddy Simulations (LES) are performed at low Reynolds number (2000 upto 6000) to investigate the dynamic fluid-elastic instability in square normal cylinder array for a single-phase fluid cross flow. The fluid-elastic instability is dominant in flow normal direction, at least for all water-flow experiments (Price et al. [18]). The instability appears even in the case of single moving cylinder in an otherwise fixed-cylinder arrangement resulting in the same critical velocity (Khalifa et al. [1]). Therefore, in the present work only a central cylinder out of 20 cylinders is allowed to vibrate in flow normal direction. The square normal (90°) array has 5 rows and 3 columns of cylinders with 2 additional side columns of half wall-mounted cylinders. The numerical configuration is a replica of the experimental setup except for the length of cylinders, which is 4 diameters (4D) in numerical setup against about 8D in the experiment facility. The single-phase fluid is water. The standard Smagorinsky turbulence model is used for the sub-grid scale eddy viscosity modeling. The numerical results are analysed and compared with the experimental results, for a range of flow velocities in the vicinity of the instability. Moreover, instantaneous pressure and fluid-force profiles on the cylinder surface are extracted from the LES calculations in order to better understand the dynamic fluid-elastic instability.

Waves in poroelastic solid saturated by a single-phase fluid

2016 ◽  
pp. 1-31
Author(s):  
Juan Enrique Santos ◽  
Patricia Mercedes Gauzellino
Keyword(s):  
Single Phase ◽  
Phase Fluid

On the Dynamic Stability of Fluid-Conveying Pipes

1973 ◽  
Vol 40 (1) ◽  
pp. 48-52 ◽  
Author(s):  
D. S. Weaver ◽  
T. E. Unny
Keyword(s):  
Potential Theory ◽  
Dynamic Stability ◽  
Thin Shell ◽  
Critical Flow ◽  
Thin Shells ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Limiting Case ◽  
Beam Mode ◽  
Fluid Conveying Pipes

This paper presents a general analysis of the dynamic stability of a finite-length, fluid-conveying pipe. The Flu¨gge-Kempner equation is used in conjunction with classical potential theory so that circumferential modes as well as the usual beam modes may be considered. The cylinders are found to become unstable statically at first but flutter is predicted for higher velocities. The critical flow velocities for short, thin shells are associated with a number of circumferential waves. This number reduces for thicker and longer shells until the instability is in a beam mode. When the limiting case of a long thin shell is taken, it is found to agree with previous results obtained using a simpler beam approach.

A Numerical Algorithm for Single Phase Fluid Flow in Elastic Porous Media

2007 ◽  
pp. 80-92 ◽  
Author(s):  
Hongsen Chen ◽  
Richard E. Ewing ◽  
Stephen L. Lyons ◽  
Guan Qin ◽  
Tong Sun ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Algorithm ◽  
Single Phase ◽  
Phase Fluid

Single phase fluid-stator heat transfer in a rotor–stator spinning disc reactor

2014 ◽  
Vol 119 ◽  
pp. 88-98 ◽  
Author(s):  
M.M. de Beer ◽  
L. Pezzi Martins Loane ◽  
J.T.F. Keurentjes ◽  
J.C. Schouten ◽  
J. van der Schaaf
Keyword(s):  
Heat Transfer ◽  
Single Phase ◽  
Phase Fluid ◽  
Spinning Disc

Laminar Flow Forced Convection Heat Transfer Behavior of Phase Change Material Fluid in Microchannels With Staggered Pins

2010 ◽  
Author(s):  
Satyanarayana Kondle ◽  
Jorge L. Alvarado ◽  
Charles Marsh ◽  
Gurunarayana Ravi
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Phase Change ◽  
Single Phase ◽  
Convection Heat Transfer ◽  
Heat Removal ◽  
High Heat ◽  
High Heat Flux ◽  
Small Areas ◽  
Phase Fluid

Microchannels have been extensively studied for electronic cooling applications ever since they were found to be effective in removing high heat flux from small areas. Many configurations of microchannels have been studied and compared for their effectiveness in heat removal. However, there is little data available in the literature on the use of pins in microchannels. Staggered pins in microchannels have higher heat removal characteristics because of the continuous breaking and formation of the boundary layer, but they also exhibit higher pressure drop because pins act as flow obstructions. This paper presents numerical results of two characteristic staggered pins (square and circular) in microchannels. The heat transfer performance of a single phase fluid in microchannels with staggered pins, and the corresponding pressure drop characteristics are also presented. An effective specific heat capacity model was used to account for the phase change process of PCM fluid. Comparison of heat transfer characteristics of single phase fluid and PCM fluid are made for two pins geometries for three different Reynolds numbers. Circular pins were found to be more effective in terms of heat transfer by exhibiting higher Nusselt number. Circular pin microchannels were also found to have lower pressure drop compared to the square pin microchannels.

Analysis of two-phase ejectors with Fabri choking

2002 ◽  
Vol 216 (5) ◽  
pp. 607-621 ◽  
Author(s):  
W E Lear ◽  
G M Parker ◽  
S A Sherif
Keyword(s):  
Single Phase ◽  
Phase Region ◽  
Working Fluid ◽  
Two Phase ◽  
Cross Sectional ◽  
Flow Phenomena ◽  
Mass Flowrate ◽  
Inlet Conditions ◽  
R 134A ◽  
Phase Fluid

A one-dimensional mathematical model was developed using the equations governing the flow and thermodynamics within a jet pump with a mixing region of constant cross-sectional area. The analysis is capable of handling two-phase flows and the resulting flow phenomena such as condensation shocks and the Fabri limit on the secondary mass flowrate. This work presents a technique for quickly achieving first-approximation solutions for two-phase ejectors. The thermodynamic state of the working fluid, R-134a for this analysis, is determined at key locations within the ejector. From these results, performance parameters are calculated and presented for varying inlet conditions. The Fabri limit was found to limit the operational regime of the two-phase ejector because, in the two-phase region, the speed of sound may be orders of magnitude smaller than in a single-phase fluid.

Improved Correlations for Counting the Effect of Natural Convection on Laminar Flow of Nanofluids

2013 ◽  
Author(s):  
Si-pu Guo ◽  
Zhao-zan Feng ◽  
Ze-cong Fang ◽  
Wei Li ◽  
Jin-liang Xu ◽  
...  
Keyword(s):  
Experimental Data ◽  
Natural Convection ◽  
Laminar Flow ◽  
Prandtl Number ◽  
Single Phase ◽  
Colloidal Suspensions ◽  
Horizontal Tube ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Phase Fluid

Nanofluids are colloidal suspensions of nano-scale particles in water, or other base fluids. In this paper, the effect of natural convection on laminar flow of nanofluids in a horizontal tube has been addressed. The obtained experimental data could not be reconciled with existing correlations over a wide range of Prandtl number under laminar mixed convection. Three improved correlations have been derived by using single-phase fluid approach. These correlations fit our data to within ± 10 % and also agree with the data in literature quite well. Such results verify that nanofluids can be treated as a homogeneous mixture with effective thermophysical properties. Utimately, the new correlations have grasped the essence of natural convection and can reduce to both normal forced convection and pure natural convection equations at limiting cases.

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