Experimental correlations on critical Reynolds numbers and friction factor in tubes with wire-coil inserts in laminar, transitional and low turbulent flow regimes

2018 ◽  
Vol 91 ◽  
pp. 64-79 ◽  
Author(s):  
J. Pérez-García ◽  
A. García ◽  
R. Herrero-Martín ◽  
J.P. Solano
Keyword(s):  
Turbulent Flow ◽  
Friction Factor ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Critical Reynolds Numbers ◽  
Wire Coil

Numerical and Experimental Analysis of Turbulent Flow in Corrugated Pipes

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
Henrique Stel ◽  
Rigoberto E. M. Morales ◽  
Admilson T. Franco ◽  
Silvio L. M. Junqueira ◽  
Raul H. Erthal ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Velocity Magnitude ◽  
Geometric Configurations ◽  
Corrugated Surfaces ◽  
Friction Factors

This article describes a numerical and experimental investigation of turbulent flow in pipes with periodic “d-type” corrugations. Four geometric configurations of d-type corrugated surfaces with different groove heights and lengths are evaluated, and calculations for Reynolds numbers ranging from 5000 to 100,000 are performed. The numerical analysis is carried out using computational fluid dynamics, and two turbulence models are considered: the two-equation, low-Reynolds-number Chen–Kim k-ε turbulence model, for which several flow properties such as friction factor, Reynolds stress, and turbulence kinetic energy are computed, and the algebraic LVEL model, used only to compute the friction factors and a velocity magnitude profile for comparison. An experimental loop is designed to perform pressure-drop measurements of turbulent water flow in corrugated pipes for the different geometric configurations. Pressure-drop values are correlated with the friction factor to validate the numerical results. These show that, in general, the magnitudes of all the flow quantities analyzed increase near the corrugated wall and that this increase tends to be more significant for higher Reynolds numbers as well as for larger grooves. According to previous studies, these results may be related to enhanced momentum transfer between the groove and core flow as the Reynolds number and groove length increase. Numerical friction factors for both the Chen–Kim k-ε and LVEL turbulence models show good agreement with the experimental measurements.

The stability of a stratified fluid

1967 ◽  
Vol 29 (2) ◽  
pp. 233-240
Author(s):  
J. B. Hinwood
Keyword(s):  
Turbulent Flow ◽  
Froude Number ◽  
Reynolds Numbers ◽  
Stratified Fluid ◽  
Stratified Flows ◽  
Rectangular Duct ◽  
Interfacial Waves ◽  
Homogeneous Flow ◽  
Critical Reynolds Numbers ◽  
The Stability

For the flow of a stably-stratified fluid in the inlet region of a rectangular duct, it is shown experimentally that the upper and lower critical Reynolds numbers are functions of the interfacial Froude number F, and that if F is large they are lower than for a homogeneous flow. In stratified flows the disturbances leading to turbulent flow sometimes arise at the interface and lead to interfacial waves, whose wavelength at breaking is equal to the conduit depth.

Flow Through Porous Media of Packed Spheres Saturated With Water

1994 ◽  
Vol 116 (1) ◽  
pp. 164-170 ◽  
Author(s):  
Ifiyenia Kececioglu ◽  
Yuxiang Jiang
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Flow Regimes ◽  
Reynolds Numbers ◽  
Column Height ◽  
Small Range ◽  
Dimensionless Pressure ◽  
Medium Permeability ◽  
Limited Applicability

The existing literature on the flow of fluids through porous packed beds gives very limited quantitative information on the criteria employed in marking the applicability of the different flow regimes. It is the objective of this paper to provide experimental evidence for determining the demarcation criteria during the flow of water through a bed of randomly packed spherical beads. Two different sizes of glass beads, 3 mm and 6 mm, were employed as the porous matrix through which water flowed at rates varying from 5.07 × 10−6 m3/s to 4920 × 10−6 m3/s. Our dimensionless pressure drop data showed less variation when the characteristic length of the porous medium was taken to be proportional to the square root of the permeability over the porosity and not the bead diameter. Curves of properly nondimensionalized pressure drop (P’K/μv) plotted against the actual flow Reynolds number based on the porous medium permeability (RˆeK) provided the following information. It was found that Darcy’s law has very limited applicability and is valid for a small range of Reynolds numbers (0.06<RˆeK<0.12). This leads to a pre-Darcy flow that is valid for a much broader range of Reynolds numbers than expected (RˆeK<0.06). Alternatively, the range of validity of the post-Darcy laminar Forchheimer flow is also found to be of much more limited applicability (0.34<RˆeK<2.30) than previous studies (Fand et al., 1987) have indicated (0.57<RˆeK Fand et al. <9.00). Transition to turbulence takes place earlier than expected and turbulent flow prevails from then on (RˆeK>3.40). The dimensionless pressure drop in both the Forchheimer and turbulent flow regimes can be modeled by an appropriately nondimensionalized Ergun’s equation (Carman, 1937), i.e., a first-order inertia term correction is sufficient in both flow regimes. However, the magnitude of the correction coefficients in the Forchheimer regime differs significantly from that in the turbulent flow regime (AˆF=1.00, BˆF=0.70, BˆT=1.90, BˆT=0.22). Again, this differs from previous findings (Fand et al., 1987). The effect of the angle of inclination of the porous medium with respect to the horizontal on the transition mechanisms was also experimentally investigated. No changes other than the correction in the pressure drop due to the static liquid column height were observed.

Hysteresis Curve in Reproduction of Reynolds’ Color-Band Experiments

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Hidesada Kanda ◽  
Takayuki Yanagiya
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Reynolds Numbers ◽  
Clear Relationship ◽  
Hysteresis Curve ◽  
Pipe Flows ◽  
Critical Reynolds Numbers ◽  
Extended Analysis ◽  
First Time

This article describes the reproduction and extended analysis of Reynolds’ color-band experiment. Reynolds found two critical Reynolds numbers (Rc) in pipe flows: Rc1 of 12,830 from laminar to turbulent flow and Rc2 of 2030 from turbulent to laminar flow. Since no clear relationship has been established between them, we studied how the entrance shape affects Rc. Thus, for the first time, a hysteresis graph can be drawn by connecting the two curves of Rc1 and Rc2 such that the two Rc values lie on separate branches of the hysteresis plot.

scholarly journals Fluid friction between rotating cylinders I—Torque measurements

1936 ◽  
Vol 157 (892) ◽  
pp. 546-564 ◽  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Centrifugal Force ◽  
Outer Cylinder ◽  
Reynolds Numbers ◽  
Stream Line ◽  
Rotating Cylinders ◽  
Torque Measurements ◽  
Critical Reynolds Numbers ◽  
The Stability

The stability of fluid contained between concentric rotating cylinders has been investigated and it has been shown that, when only the inner cylinder rotates, the flow becomes unstable when a certain Reynolds number of the flow is exceeded. When the outer cylinder only is rotated, the flow is stable so far as disturbances of the type produced in the former case are concerned, but provided the Reynolds number of the flow exceeds a certain value, turbulence sets in. The object of the present experiments was partly to measure the torque reaction between two cylinders in the two cases in order to find the effect of centrifugal force on the turbulence, and partly to find the critical Reynolds numbers for the transition from stream-line to turbulent flow. The apparatus is shown diagrammatically in fig. 1.

scholarly journals Three-dimensional numerical investigation of turbulent flow and heat transfer inside a horizontal semi-circular cross-sectioned duct

2014 ◽  
Vol 18 (4) ◽  
pp. 1145-1158 ◽  
Author(s):  
Kamil Arslan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Forced Flow ◽  
Flow And Heat Transfer ◽  
Darcy Friction Factor

In this study, steady-state turbulent forced flow and heat transfer in a horizontal smooth semi-circular cross-sectioned duct was numerically investigated. The study was carried out in the turbulent flow condition where Reynolds numbers range from 1?104 to 5.5?104. Flow is hydrodynamically and thermally developing (simultaneously developing flow) under uniform surface heat flux with uniform peripheral wall heat flux (H2) boundary condition on the duct?s wall. A commercial CFD program, Ansys Fluent 12.1, with different turbulent models was used to carry out the numerical study. Different suitable turbulence models for fully turbulent flow (k-? Standard, k-? Realizable, k-? RNG, k-? Standard and k-? SST) were used in this study. The results have shown that as the Reynolds number increases Nusselt number increases but Darcy friction factor decreases. Based on the present numerical solutions, new engineering correlations were presented for the average Nusselt number and average Darcy friction factor. The numerical results for different turbulence models were compared with each other and similar experimental investigations carried out in the literature. It is obtained that, k-? Standard, k-? Realizable and k-? RNG turbulence models are the most suitable turbulence models for this investigation. Isovel contours of velocity magnitude and temperature distribution for different Reynolds numbers, turbulence models and axial stations in the duct were presented graphically. Also, local heat transfer coefficient and local Darcy friction factor as function of dimensionless position along the duct were obtained in this investigation.

Heat transfer at low temperatures between tube walls and gases in turbulent flow

1947 ◽  
Vol 191 (1024) ◽  
pp. 6-21 ◽  
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Low Temperatures ◽  
Reynolds Numbers ◽  
Internal Diameter ◽  
Fluid Temperature ◽  
External Diameter ◽  
Bulk Fluid

An apparatus was designed on the counter-flow system to study heat transfer between tube walls and gases at low temperatures in a region in which careful measurements had not previously been made. Oxygen, nitrogen and carbon dioxide were used, covering a temperature range from + 45° to –167° C, pressures up to 11 atm., and Reynolds numbers from 3000 to 60,000. Results were correlated by the use of dimensionless groups and a general equation ob­tained, independent of the nature of the gas and applicable over the whole range of experi­ments. With Reynolds numbers evaluated at mean film temperatures, the coefficient in the equation was found to be 5% lower than that obtained from measurements made at normal and high temperatures. This is regarded as justifying the extension of the ordinary equation to low-temperature regions. Determinations on friction accompanying heat transfer with gases in turbulent flow at low temperatures showed that the effect of heat transfer on the friction factor was small. Nomenclature C constant in Sutherland equation. D diameter of tube; equivalent diameter of annulus, i. e. internal diameter of outer tube minus external diameter of inner tube. F frictional force per lb. of fluid. L length of tube. T absolute temperature, ° K. V linear velocity of gas, as calculated from mass flow per unit time per unit of cross sectional area, divided by the mean density of the fluid. c specific heat of fluid at constant pressure. f friction factor, or coefficient of proportionality in pressure drop equation. g acceleration due to gravity. h coefficient of heat transfer between fluid and surface. k thermal conductivity of fluid. r, s constants (used as exponents). α, β constants. ϕ(x) function of x . μ absolute viscosity of fluid. ρ absolute density of fluid. Δp pressure drop in pipe. Subscripts a refers to annulus. i refers to inner tube. f refers to properties evaluated at film temperatures. Film temperature is taken as the arithmetic mean of the bulk fluid temperature and the tube-wall temperature.

Turbulent Flow in D-Type Corrugated Pipes: Flow Pattern and Friction Factor

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
H. Stel ◽  
A. T. Franco ◽  
S. L. M. Junqueira ◽  
R. H. Erthal ◽  
R. Mendes ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Flow Pattern ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Important Change ◽  
Groove Width ◽  
Simple Method ◽  
Pressure Drag ◽  
Aspect Ratios

Turbulent flow in d-type corrugated pipes of various aspect ratios has been numerically investigated in terms of flow pattern and friction factor, for Reynolds numbers ranging from 5000 to 100,000. The present numerical model was verified by comparing the friction factor with experimental and numerical results from the literature. The numerical analysis suggested that d-type behavior exists for groove aspect ratios up to w/k = (groove width/rib height) = 2 independent of the pitch. However, for a ratio of w/k = 3 an important change in the flow pattern occurs so that the pressure drag exerted by the groove walls becomes important. It is shown that the friction factor is independent of the groove height as long as the flow is similar to a flow in a d-type corrugated pipe. Moreover, the friction factor curve for d-type pipes shows a logarithmic behavior as function of the Reynolds number, so that a simple method can be used to derive an expression for the friction factor as a function of the Reynolds number and the relative groove width only. The results may be useful to engineering projects that require a better prediction of the friction factor in d-type corrugated pipes.

Alternate Scales for Turbulent Flow in Transitional Rough Pipes: Universal Log Laws

2006 ◽  
Vol 129 (1) ◽  
pp. 80-90 ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Friction Velocity ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Momentum Theory ◽  
The Mean ◽  
Pipe Roughness

In transitional rough pipes, the present work deals with alternate four new scales, the inner wall transitional roughness variable ζ=Z+∕ϕ, associated with a particular roughness level, defined by roughness scale ϕ connected with roughness function ▵U+, the roughness friction Reynolds number Rϕ (based on roughness friction velocity), and roughness Reynolds number Reϕ (based on roughness average velocity) where the mean turbulent flow, little above the roughness sublayer, does not depend on pipes transitional roughness. In these alternate variables, a two layer mean momentum theory is analyzed by the method of matched asymptotic expansions for large Reynolds numbers. The matching of the velocity profile and friction factor by Izakson-Millikan-Kolmogorov hypothesis gives universal log laws that are explicitly independent of pipe roughness. The data of the velocity profile and friction factor on transitional rough pipes provide strong support to universal log laws, having the same constants as for smooth walls. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional-type roughness, monotonic Colebrook-Moody roughness, etc. In traditional variables, the roughness scale, velocity profile, and friction factor prediction for inflectional pipes roughness are supported very well by experimental data.

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