Flow Transition in Finned Tubes

International Journal of Multiphase Flow, 1977

In this book we look at deriving the governing equations of fluid flow using conservation of energy techniques on a differential element undergoing shear stress or viscous forces as it moves along a pipe and we use the expression for friction coefficient for laminar flow to derive the equations.We also derive other friction factors to explain experimental observations. We also derive the equations that work for Torricelli flow and there conditions. We derive the turbulent flow equations too. We derive the general equation for all regimes laminar, transition and turbulent flow. The Reynolds number is also derived and the conditions for which it acts are derived and modified to fit experimental observations

Rheology Series, 1999

Book Publisher International (a part of SCIENCEDOMAIN International), 2021

An 8, OOO-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 Jl8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 BID at various gas-liquid ratios from 105 to 9,433 scflbbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gasliquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scflbbl. These deviations are believed to be rna inly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.1 As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gasliquid ratios and flow rates. Definite changing

Proceedings of EPTT 2016,10th ABCM Spring School on Transition and Turbulence, ABCM, 2016

The flow in pipes for non-Newtonian fluids is considered using a truncated series relating the shear stresses whit the radial velocity gradient. This approximation is used as an alternative way for the quantification of velocity profiles, and a lower order theoretical solution for the velocity is presented. It is observed that the calculated profiles allow approximations to pseudoplastic and to dilatant behaviors, approaching the Newtonian (parabolic) profile from the “inner side” or the “outer side”, respectively. This suggest that power series may be used to quantify aspects of non-Newtonian fluids. In the sequence, the possibility of turbulent flows in pipes was considered, and a qualitative view of the velocity profiles and the turbulent shear stresses is then presented here. This study was conducted theoretically, aiming the obtainance of solutions that allow verifying mathematical possibilities and impossibilities (such as discontinuities). The results suggest further numerical studies to evidence the possibilities of this kind of approximation.

In this chapter, however, a method of expressing the loss using an average flow velocity is stated. Studies will be made on how to express losses caused by a change in the cross sectional area of a pipe, a pipe bend and a valve, in addition to the frictional loss of a pipe. Consider a case where fluid runs from a tank into a pipe whose entrance section is fully rounded. At the entrance, the velocity distribution is roughly uniform while the pressure head is lower by V 2 /2g. As shown in below Figure ,the section from the entrance to just where the boundary layer develops to the tube centre is called the inlet or entrance region, whose length is called the inlet or entrance length. For steady flow at a known flow rate, these regions exhibit the following: Laminar flow:A local velocity constant with time, but which varies spatially due to viscous shear and geometry. Turbulent flow: A local velocity which has a constant mean value but also has a statistically random fluctuating component due to turbulence in the flow. Typical plots of velocity time histories for laminar flow, turbulent flow, and the region of transition between the two are shown below .

International Journal of Thermal Sciences, 2017

The geometry considered in the present work (serpentine pipe) is a sequence of U-bends of alternate curvature. It is characterized by pipe diameter, d ¼ 2a and bend diameter, D ¼ 2c. The repeated curvature inversion forces the secondary flow pattern, typical of all flows in curved ducts, to switch between two mirror-like configurations. This causes (i) pressure drop and heat or mass transfer characteristics much different from those occurring either in a straight pipe or in a constant-curvature pipe, and (ii) an early loss of stability of the base steady-state flow. In the present work, four values of the curvature d ¼ a/c (0.2, 0.3, 0.4 and 0.5) were considered. For each value of d, the friction velocity Reynolds number Re t ¼ u t a/n was made to vary in steps between 10 and 50. Fully developed flow was simulated using a three-dimensional, time-dependent finite volume method and computational grids with a number of nodes ranging from~1.8 to~4.6 Â 10 6 , according to the curvature. The computational domain included two consecutive and opposite bends and thus coincided with the minimum spatially repetitive unit. Heat transfer was also simulated for uniform wall heat flux conditions and a Prandtl number of 1. A complex scenario of transitions was predicted, leading from the base steady-state, top-down symmetric flow to turbulence through intermediate regimes which included steady-state asymmetric and time-periodic flows. For all curvatures, at the highest value of Re t investigated (50) the flow was turbulent and exhibited top-down symmetric time averages.

SPE Annual Technical Conference and Exhibition, 1988

Thinpapa wasprepared forpreaantation at the Wrd Annual TeohnicdConference andExhibition of the Scelefyof Petroleum Enginwrsheldin Houalon, TX, October 2-5, 1SS8. Thk paperwaseetected forpresentation by qn SPE Program Committee following reviewof Information contained Inaneb8treot submlfred bythe q ulhor(8). Centenfs of thopaper,es presented, havenolbeenreviewed bytheSccIetyof Petroleum Engheeraandare aublecr tocorrection bythe author(e). Themateriel, espresented, doesnd noceeeerily reflect anypoeitbnoftheSocIefy ofPetroleum Englneere, Itsolfkers,ormembers. Papers z pf.aantedat SP%tmellngeare subject10 publication revkwby Editorlel Committees of theSoolefy of PekokumEngineers. .?armkeion to copyla reefrktw toqn ebalreof of notnwretrren3)0 wcida.Illustrations maynotbe wpied, Theabstract should oontein omwpkuous ecknmtodgrnant of wherearslbywhom thepepsrb presented. WritePublkationa Manager, SPE,P.O.SoxS22S2S, Rkherdeon, TX7S0SNS2S.Telex,730SSS SPEDAL from the well is transformed into a volumetric If uingle phase flow of a slightly compressible liquid is assumed, then Eq. 1 could be sim-References and illustrations at end of paper. pli.fiedto Eq, 2. .-Izl F A[Ap]

Journal of Fluids and Structures, 1990

Aqueous flow through thick-walled silicone rubber tubes held open at both ends and externally pressurized is investigated for tubes of four different lengths, each at three levels of downstream flow resistance. The tubes are compared at operating points spanning all the observed types of dynamic behaviour, where an operating point is set by adjusting driving pressure head and external pressure. It is found that longer tubes display relatively more oscillatory operating points, while shorter tubes display more divergently unstable operating points. The observed self-excited oscillations can be divided into well-separated bands of low, intermediate and high frequency, within each of which the frequency generally increases gradually with flow-rate and external pressure. In addition, in the region at high external pressure where turbulent noise dominates, isolated operating points display very-high-frequency repetitive oscillations of small amplitude. The border between the noise-dominated region and the region below, independently of whether the latter is oscillatory or divergent, displays complex behaviour. This includes aberrantly highfrequency oscillation which is sometimes superimposed on a particular phase of a low-frequency oscillation, and the behaviour depends on whether the external pressure has previously been higher or lower. Whereas the regions of low, intermediate and high frequency oscillations are arranged such that in general higher flow-rates and external pressures cause transitions to higher-frequency bands, these aberrant 'border oscillations' yield very high frequencies at low flow-rate and external pressure. The minimum frequency of oscillation decreases in longer tubes, but the dependence is far weaker than if end-to-end wave propagation were the period-setting mechanism. Longer tubes appear predisposed to more widespread low-frequency modes, although high frequencies can be excited with sufficient flow-rate and external pressure. Few low-frequency operating points are found with short tubes. As downstream resistance is decreased, steady flow gives way to divergent operating points which in turn become oscillatory. Possible mechanisms for all these behaviours are discussed.

Applied Mathematics and Computation, 2007

In this paper, the steady flow of blood through tapered tube has been analyzed assuming blood as (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for pressure drop, wall shear stress and resistance to flow have been obtained. The effects of tapering of the tube and the non-Newtonian nature of the fluid on pressure drop, wall shear stress and resistance to flow are discussed. For all fluids, the pressure drop increases with increasing angle of taper from 0.5°to 1°for a given value of yield stress h and tapered tube Reynolds number Re w. The resistance to flow as well as the wall shear stress increase with increasing yield stress for Herschel-Bulkley fluid and also for Casson's fluid when the other parameters held constant. Both for Herschel-Bulkley fluid and Casson's fluid, the wall shear stress as well as the resistance to flow increase with increasing axial distance for a given tapered tube Reynolds number Re w , angle of taper w and yield stress h.