Eccentric Annular Channels Research Articles

Conjugate Natural Convection: A Study of Optimum Fluid Flow and Heat Transfer in Eccentric Annular Channels

Laminar natural convection-conduction heat transfer in vertically positioned annular channels with inherent eccentricity is investigated for optimum solid-fluid thermal conductivity ratio and optimum cylinder walls thicknesses allowing maximum induced fluid flow rate and heat transfer under varying geometry parameters, i.e., annulus eccentricity and radius ratio. A finite-difference technique is employed to solve the coupled momentum and energy equations for the cylindrical annulus walls and the annular fluid with Prandtl number 0.7. As part of the results, fluctuations in the induced fluid flow rate and heat transfer in the eccentric annular channel due to the conjugate effect, governed by the ratios of the solid and fluid thermal conductivities and thicknesses of outer and inner circular cylinder walls, are obtained for the boundary conditions of one wall heated isothermally and the other kept adiabatic. Commonly encountered ratios of the solid and fluid thermal conductivities and cylinder walls thicknesses are utilized in the present analysis. Results reveal that the optimum conductivity ratio and cylinder walls thicknesses increase nonlinearly with eccentricity and radius ratio. Such results can be very useful in effectively designing the heat transfer equipment for optimum performance.

Further experiments and analysis on flow instability in eccentric annular channels

Abstract

Flow instability in weakly eccentric annuli

A temporal linear stability analysis of laminar flow in weakly eccentric annular channels has been performed. It has been shown that, even for eccentricities ε and Reynolds numbers that were much smaller than those considered in previous studies, flow instability occurred in the form of travelling waves having characteristics that are very different from those of Tollmien-Schlichting waves and which were triggered at mid-gap by an inviscid mechanism that is associated with the presence of inflection points in azimuthal profiles of the base velocity. The critical stability conditions have been determined for 0 ≤ ε ≤ 0.1 and for diameter ratios 0 < γ < 1. The critical Reynolds number Rec decreased with increasing γ for 0 < γ ≲ 0.13, reached a minimum at γ ≈ 0.13, and increased with further increase in γ. The lowest observed Rec was 529 and occurred for ε = 0.1 and γ ≈ 0.13. As ε → 0, Rec ∝ ε−2. The critical wave number and the critical frequency of the disturbances decreased with increasing γ and approached zero as γ → 1, whilst their ratio was nearly constant in the range of parameters considered in this study. The most unstable regions were found to be at roughly mid-gap on the two flanks of the annulus, and the phase speed of the disturbances was close to the base flow velocity at these regions.

Experimental and numerical study on forced convection heat transport in eccentric annular channels

In the process of drilling, the tubing-casing annulus are easily to be eccentric. Heat transport phenomenon occurring in such tubes and annulus can be complex, and this paper investigates forced convection in a vertical eccentric annulus with different radius ratios and eccentricity (normalized by the radius difference). Physical experiments and numerical simulation have been conducted with constant inner tube inlet temperature and flow rate of hot water. Results show that with the increase of radius ratios, the convection heat transport coefficient increases. For a radius ratio of 1.875, the heat transport coefficient increases as the eccentricity increases when the Re > 2000 and it decreases when the Re < 2000. For a radius ratio of 2.25 and Re < 1500, the influence of eccentricity is trivial, but for Re > 1500, the increase of eccentricity strengthens the heat convection. For a radius ratio of 3.06, the heat transport coefficient increases as the eccentricity increases. An empirical correlation for Nusselt number is derived as a function of Reynolds number, Prandtl number and eccentricity.

Numerical Simulations of Natural Convective Heat Transfer in Vertical Concentric and Eccentric Annular Channels

Natural convective heat transfer in a concentric and a highly eccentric, vertical, open ended, annular channel has been investigated numerically. The inner to outer diameter ratio was 0.61, and the height to hydraulic diameter ratio was 18:1. Three heating modes were considered, all having uniform heat flux applied to one or both of the two walls, while the unheated wall was kept adiabatic. The wall temperature distribution, mass flow rate, and midchannel Nusselt number for the case with both walls heated were found to be in excellent agreement with available experimental results. For the same heating conditions, the heat transfer rate in the concentric annular channel was found to be greater than that in the highly eccentric channel, while the mass flow rate was higher in the eccentric channel. A novel finding for the eccentric channel was that the location of maximum velocity was intermediate between the narrow and wide gaps. Another novel observation, which was attributed to radiation effects, was that the fluid temperature in the wide gap region was lower than that of an adiabatic wall. The paper contains additional observations that would be of interest to designers of systems containing annular channels.

An Experimental Study of Forced Heat Convection in Concentric and Eccentric Annular Channels

An experimental study of the effect of eccentricity on forced convective heat transfer was conducted for upward flows in vertical, open-ended annular channels with a diameter ratio of 0.61, a length to outer diameter ratio of 18:1, and both internal surfaces heated uniformly. Flows with Reynolds numbers Re = 5450, 10,000, and 27,500 and eccentricities varying from 0 to 0.9 were examined. These results are deemed to be mostly in the forced convection regime with some possible overlap with the mixed convection regime at the lowest Reynolds number considered. This work complements our previous work on natural and mixed convection using the same facility. The effect of eccentricity was not significant at lower eccentricities, but, in highly eccentric cases, the wall temperature in the narrow gap was much higher than in the wide gap and the average heat transfer coefficient was as low as one-fifth of the concentric value. For Re &gt; 10,000, the average Nusselt number for the concentric case was nearly four times higher than the value predicted by the Dittus–Boelter correlation.

Experimental investigation of flow development and gap vortex street in an eccentric annular channel. Part 2. Effects of inlet conditions, diameter ratio, eccentricity and Reynolds number

The development and structure of flows in eccentric annular channels and their dependence on inlet conditions, inner-to-outer diameter ratio $d/D$, eccentricity $e=2{\rm\Delta}y/(D-d)$, where ${\rm\Delta}y$ is the distance between the axes of the inner and outer cylinders, and Reynolds number $\mathit{Re}$, based on the hydraulic diameter and the bulk velocity, were studied experimentally, with focus on the phenomena of gap instability and the resulting vortex street. Experimental conditions covered a Reynolds number range between 0 and 19 000, an eccentricity range from 0 to 0.9 and inner-to-outer diameter ratios equal to 0.25, 0.50 and 0.75. Much of the discussion is based on measurements in the middle of the narrow annular gap, where the phenomena of interest could be observed most vividly. In the range $\mathit{Re}&lt;10\,000$, the Strouhal number, the normalized mid-gap axial flow velocity and the normalized axial and cross-flow fluctuations at mid-gap were found to increase with increasing $\mathit{Re}$ and to depend strongly on inlet conditions. At higher Reynolds numbers, however, these parameters reached asymptotic values that were less sensitive to inlet conditions. We constructed a map for the various stages of periodic motions versus eccentricity and Reynolds number and found that for $e&lt;0.5$ or $\mathit{Re}&lt;1100$ the flow was unconditionally stable, as far as gap instability is concerned. For $e\leqslant 0.5$, transition to turbulence occurred at $\mathit{Re}\approx 6000$, whereas, for $0.6\leqslant e\leqslant 0.9$, the critical Reynolds number for the formation of periodic motions was found to increase with eccentricity from 1100 for $e=0.6$ to 3800 for $e=0.9$.

Experimental investigation of flow development and gap vortex street in an eccentric annular channel. Part 1. Overview of the flow structure

AbstractFlow visualization, laser Doppler velocimetry and planar and stereoscopic particle image velocimetry were used to investigate the isothermal velocity field along an eccentric annular channel with a diameter ratio of 0.5 and an eccentricity of 0.8 for a Reynolds number of 7300. Observation of the flow development has identified three distinct regions: the entrance region, the fluctuation-growth (FG) region and the rapid-mixing (RM) region. Weak quasi-periodic velocity fluctuations were first detected in the downstream part of the entrance region, and grew into very strong ones, reaching peak-to-peak amplitudes in the narrow gap that were nearly 60 % of the bulk velocity. Two mixing layers were identified on either side of the gap, which generated a street of counter rotating vortices and thorough large-scale mixing of the fluid in the channel.

Heat transfer in CO2 at supercritical pressures in an eccentric annular channel

An experimental investigation of a supercritical heat transfer in an eccentric annular channel was performed using a supercritical heat transfer test facility, SPHINX, at the Korea Atomic Energy Research Institute (KAERI). The eccentric channel was built by placing a 9.5mm outer diameter heater rod in a 12.5mm inner diameter tube with an eccentricity of 0.33. The narrowest gap was 1mm, and the widest gap was 2mm. The rod was heated indirectly by an imbedded Nickel Chrome heating wire made of NCHW1. Three simple spacers were installed to see their effect, if any, on the heat transfer. The mass fluxes were 400 and 1200kg/m2s, and the heat flux was varied between 30 and 150kW/m2 such that the pseudo-critical point was located within the test section as long as possible. When this was not the case, several tests with stepwise increased inlet temperatures were performed so that at least one of them included the pseudo-critical point. The tests were performed at two different pressures of 7.75 and 8.12MPa to check the pressure effect. The influence of the gap size was clearly seen with the eccentric channel, if not significant. The wall temperatures along the narrowest gap were higher than those along the widest gap as expected, while it was reversed at the end part of the test section. The test results for the eccentric channel were not much different from those for the concentric channel of a similar gap size. As we have seen from the plain tube test, the diameter effect on the heat transfer was also not significant in this test. On the contrary, the effect of the spacer as a turbulence generator was noticeable, particularly at the thermocouples, which were 10mm downstream from the trailing edge of the first spacer.

An Experimental Study of Mixed Convection in Vertical, Open-Ended, Concentric and Eccentric Annular Channels

The effect of eccentricity on heat transfer in upward flow in a vertical, open-ended, annular channel with a diameter ratio of 0.61, an aspect ratio of 18:1, and both internal surfaces heated uniformly has been investigated experimentally. Results have been reported for eccentricities ranging from the concentric case to the near-contact case and three inlet bulk Reynolds numbers, equal approximately to 1500, 2800, and 5700. This work complements our recently reported experimental results on natural convection in the same facility. The present results are deemed to be largely in the mixed convection regime with some overlap with the forced convection regime and likely to include cases with laminar, transitional, and turbulent flows in at least a part of the test section. Small eccentricity had an essentially negligible effect on the overall heat transfer rate, but high eccentricity reduced the average heat transfer rate by up to 60%. High eccentricity also resulted in wall temperatures in the narrow gap region that were much higher than those in the open channel. The concentric-case Nusselt number was higher than the Dittus–Boelter prediction, whereas the highly eccentric-case Nusselt number was significantly lower than that.

A method for describing and calculating critical heat fluxes in annular channels in a wide range of parameters

The paper presents a method for describing and calculating critical heat fluxes during flow of boiling water in concentric and eccentric annular channels heated on one and two sides for different ratios of heat fluxes on opposite walls and for different ratios of annular channel radiuses and eccentricities.

An Experimental Study of Natural Convection in Vertical, Open-Ended, Concentric, and Eccentric Annular Channels

The effects of eccentricity on the natural convection heat transfer from a vertical open-ended cylindrical annulus with diameter ratio of 1.63 and aspect ratio of 18:1 have been investigated experimentally. Within the range of present conditions, and with the possible exclusion of the highest eccentricities, it was found that the flow was thermally fully developed in a considerable section of the apparatus, as indicated by the linear variation of wall temperature with height. This made it possible to estimate the mass flow rate from the wall temperature gradient in the mid-section of the annulus, and use it to calculate the bulk Reynolds number, which was found to be weakly sensitive to eccentricity for a constant wall heat flux and to increase with increased wall heat flux. With the exception of the very low eccentricity range in which it was insensitive to eccentricity, the overall heat transfer rate diminished monotonically with increasing eccentricity. Plots of the local azimuthal variation of the Nusselt number showed that, at low eccentricities, the heat transfer rate increased near the wider gap but decreased near the narrower gap. The average Nusselt number was found to decrease measurably with increasing eccentricity and to increase slightly with increasing heat flux within the examined range. In contrast, the Grashof number was found to be much more sensitive to changes in heat flux and only had a weak dependence on eccentricity.

Gap instability of laminar flows in eccentric annular channels

Flow visualization has demonstrated that the critical Reynolds number for flow instability in the narrow gap of an annular channel with a diameter ratio of about 0.28 increases with increasing eccentricity e in the range 0.5 < e < 0.8. The critical Reynolds numbers in the wide gap at all eccentricities and in the narrow gap for 0 < e < 0.5 seem to be insensitive to eccentricity. These observations and comparison of the frequencies of transverse flow oscillations at different Reynolds numbers and different eccentricities demonstrate that at least two distinct instability mechanisms are present in annular flows. The one of particular interest in this work arises in narrow gaps and is attributed to the instability of the two shear layers forming on either side of the gap. Linear stability analysis demonstrated that the basic flow in concentric annuli is stable for the considered diameter ratio and range of Reynolds numbers. In contrast, the basic flow in eccentric annuli has an azimuthal variation that contains two inflection points, thus being potentially linearly unstable.

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry

Recently, it has been observed that simple geometry characterized by a low level of symmetry present interesting peculiarities in the process of transition from laminar Poiseuille flow to turbulent flow. Examples of this type of geometry are eccentric channels and, more generally, parallel channels containing a narrow gap. In the present work, a global linear stability analysis for the flow in this class of geometry has been performed. The problem is discretized through spectral collocation and the eigenvalue problem has been solved with the Arnoldi-method based algorithms and the QZ algorithm. Since no numerical studies of this type have yet been performed to address the issue of transition in this geometry, the codes have been validated toward results obtained in simplified geometries (e.g., concentric annular channel and square channel). The eigenvalue spectra of the Poiseuille flow in eccentric channels and a U-shaped channel have then been computed and analyzed for a wide range of geometric parameters. After comparison with spectra typical of channel flow and pipe flow it is shown that an additional linear mechanism of instability is present, related to the spanwise variation of the laminar velocity profile.

Anisotropic Turbulence and Coherent Structures in Eccentric Annular Channels

Eccentric annular pipe flows represent an ideal model for investigating inhomogeneous turbulent shear flows, where conditions of turbulence production and transport vary significantly within the cross-section. Moreover recent works have proven that in geometries characterized by the presence of a narrow gap, large-scale coherent structures are present. The eccentric annular channel represents, in the opinion of the present authors, the prototype of these geometries. The aim of the present work is to verify the capability of a numerical methodology to fully reproduce the main features of the flow field in this geometry, to verify and characterize the presence of large-scale coherent structures, to examine their behavior at different Reynolds numbers and eccentricities and to analyze the anisotropy associated to these structures. The numerical approach is based upon LES, boundary fitted coordinates and a fractional step algorithm. A dynamic Sub Grid Scale (SGS) model suited for this numerical environment has been implemented and tested. An additional interest of this work is therefore in the approach employed itself, considering it as a step into the development of an effective LES methodology for flows in complex channel geometries. Agreement with previous experimental and DNS results has been found good overall for the streamwise velocity, shear stress and the rms of the velocity components. The instantaneous flow field presented large-scale coherent structures in the streamwise direction at low Reynolds numbers, while these are absent or less dominant at higher Reynolds and low eccentricity. After Reynolds averaging is performed over a long integration time the existence of secondary flows in the cross session is proven. Their shape is found to be constant over the Reynolds range surveyed, and dependent on the geometric parameters. The effect of secondary flows on anisotropy is studied over an extensive Reynolds range through invariant analysis. Additional insight on the mechanics of turbulence in this geometry is obtained.

Geometry effects on conjugate natural convection heat transfer in vertical eccentric annuli

PurposeTo explore the effect of the annulus geometrical parameters on the induced flow rate and the heat transfer under the conjugate (combined conduction and free convection) thermal boundary conditions with one cylinder heated isothermally while the other cylinder is kept at the inlet fluid temperature.Design/methodology/approachA finite‐difference algorithm has been developed to solve the bipolar boundary‐layer equations for the conjugate laminar free convection heat transfer in vertical eccentric annuli.FindingsNumerical results are presented for a fluid of Prandtl number, Pr=0.7 in eccentric annuli. The geometry parameters of NR2 and E (the fluid‐annulus radius ratio and the eccentricity, respectively) have considerable effects on the results.Practical implicationsApplications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.Originality/valueThe paper presents results that are not available in the literature for the problem of conjugate laminar free convection in open‐ended vertical eccentric annular channels. Geometry effects having been investigated by considering fluid annuli having radii ratios NR2=0.1 and 0.3, 0.5 and 0.7 and four values of the eccentricity E=0.1, 0.3, 0.5 and 0.7. Moreover, practical ranges of the solid‐fluid conductivity ratio (KR) and the wall thicknesses that are commonly available in pipe standards have been investigated. Such results are very much needed for design purposes of heat transfer equipment.

Maximum possible induced flow rates in open‐ended vertical eccentric annuli with uniform heat flux

PurposeObtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature). Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature).Design/methodology/approachThe fully‐developed laminar free convection momentum equation has been solved numerically using an analytical solution of the governing energy equation.FindingsResults are presented to show the effect of the annulus radius ratio and the dimensionless eccentricity on the induced flow rate, the total heat absorbed by the fluid, and the fully developed Nusselt numbers on the two boundaries of the annulus for a fluid of Prandtl number 0.7.Practical implicationsApplications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.Originality/valueThe paper presents a solution that is not available in the literature for the problem of fully developed free convection in open‐ended vertical eccentric annular channels under thermal boundary conditions of the fourth kind. Also presents the maximum possible induced flow rates, the total heat absorbed by the fluid, and the Nusselt numbers on the two boundaries of the annulus. The effects of N and E (the radius ratio and eccentricity, respectively) on these results are presented. Such results are very much needed for design purposes of heat transfer equipment.

Developing mixed convection in vertical eccentric annuli

This paper deals with the problem of combined (forced–free) convection in vertical eccentric annuli with simultaneously developing hydrodynamic and thermal boundary layers. A bipolar model has been developed and a numerical algorithm for solving this model is outlined. Results, not available in the literature, are presented for the developing velocity profiles, axial variation of pressure, full development length, and heat transfer parameters under thermal boundary conditions of having one of the annulus boundaries at a constant temperature while the other boundary is insulated. Both aiding and opposing free convection have been considered and possibilities of flow reversal occurrence have also been checked. After a distance from the channel entrance and provided that the value of Gr/Re is sufficiently large, aiding free convection can develop to overcome the fluid friction and the eccentric annular channel eventually works as a diffuser. The value of Gr/Re for which a vertical eccentric annular channel can work as a diffuser decreases as the eccentricity increases. The axial distance from the entrance at which the channel starts to work as a diffuser decreases as Gr/Re increases.

Characteristics of laminar viscous shear-thinning fluid flows in eccentric annular channels

Laminar fully developed flows of time-independent viscous shear-thinning fluids in straight eccentric annuli are considered. The fluid rheology is modeled by the power-law constitutive equation, which is representative of many industrial process liquids. The annulus models flow channels in process heat exchangers, extruders, and drilling wells, among others. The flow cross-section geometry is mapped into a unit circle by means of a coordinate transformation, and the governing momentum equation is solved by finite-difference techniques using second-order accurate discretization. Numerical solutions for a wide variation of annuli radius ratio (0.2 ≤ r ∗ ≤ 0.8) , inner core eccentricity (0 ≤ ε ∗ ≤ 0.8) , and shear index (1 ≥n ≥ 0.2) , are presented. Both fluid rheology and annuli eccentricity are seen to have a strong influence on the flow behavior. The eccentricity causes the flow to stagnate in the narrow gap with higher peak velocities in wide gap, and large azimuthal variations in the velocity field. The fluid pseudoplasticity gives rise to even greater flow maldistribution around the annulus, with non-uniform velocity fields, wall shear-stress distribution, and friction factor characteristics.

Heat and mass transfer for turbulent flow of chemically reacting gas in eccentric annular channels

An algorithm is proposed for calculating the velocity, temperature, and concentration fields under conditions of cooling of a cylindrical heat-releasing rod, placed off-center in a circular casing pipe, by a longitudinal flow of chemically reacting gas [N2O4].