Effect of natural convection on stability of flow in a vertical pipe

Scheele, George F.; Hanratty, Thomas J.

doi:10.1017/s0022112062001226

Cited by 99 publications

(47 citation statements)

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“…A following brief review is emphasised on the flow reversal phenomenon and the flow instability in a vertical tube. For such configuration, the pioneers works by Hanratty and colleagues in the early sixties [3,4] have clearly shown that the non-isothermal flow appears to be highly unstable and may undergo its transition from a steady laminar state to an unstable one at rather low Reynolds number. The unstable flow structure, which was not turbulent, has shown, in fact, the 'new equilibrium' state that consisted of large scale, regular and periodic fluid motions.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Nguyen

Maı̈ga

Landry

et al. 2004

International Journal of Thermal Sciences

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Section: Introductionmentioning

confidence: 99%

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Nguyen

Maı̈ga

Landry

et al. 2004

International Journal of Thermal Sciences

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“…The critical ratio increases with increasing a from 15.9 at CI = 0.25 to 99.1 at CY = 1.50. For ratio values larger than the critical, flow separation and instability have been observed experimentally for Newtonian liquids (12) and would be expected to occur also for non-Newtonian liquids. It appears that for downflow as well as upflow, the limiting stable N G J N R~ value is lower for pseudoplastic than for dilatant fluids.…”

Section: Numerical Resultsmentioning

confidence: 83%

Natural convection distorted non‐Newtonian flow in a vertical pipe

DeYoung

Scheele

1970

AIChE Journal

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The equations of motion and energy are solved numerically for fully developed laminar flow of a power law fluid in a vertical pipe with constant heat flux at the wall. Density is assumed to be the only temperature dependent physical property of the fluid. Temperature profiles, velocity profiles, and Nusselt numbers are presented as functions of the power law exponent and the ratio of the Grashof number divided by the Reynolds number.The prediction of the rate of heat transfer to or from a laminar flowing non-Newtonian liquid in a smooth circular pipe is complicated by the variation of fluid physical properties with temperature. This variation will cause a distortion in the isothermal velocity profile which in turn affects the temperature field and the rate of heat transfer. Numerous studies which confirm the lack of agreement between experimental heat transfer coefficients and those predicted by constant property analyses are summarized by Metzner (7) and Skelland (16). Large profile distortions can even cause an otherwise laminar flow to become turbulent ( 11 ).Several variable property analyses exist, all of which consider a temperature dependent consistency and assume that natural convection effects are negligible (7,16). Many non-Newtonian liquids are so highly viscous that such an assumption is valid. However, there is experimental evidence for less viscous non-Newtonian liquids that natural convection effects may influence heat transfer rates significantly (8, 10). In fact, Metzner (7) estimates from available data that "the maximum effects due to natural convection, temperature dependence of rheological properties and non-Newtonian properties are 300 %, 43 % and 3076, respectively." Furthermore, the heat transfer induced flow instabilities observed at low Reynolds numbers most likely are caused by profile distortions resulting primarily from natural convection (11 ) . Empirical heat transfer correlations which account for natural convection effects, such as those for flow in horizontal tubes (8, l o ) , may be satisfactory for design purposes, but they give no information about the velocity distribution and hence the stability of such flows.In spite of the demonstrated importance of natural convection effects, no analysis exists for non-Newtonian fluids with a temperature dependent density. Any complete analScott H. DeYoung is with Amoco Chemicals Corp., Whiting, Indiana.Page 712 ysis should include both temperature varying viscosity and density, but the complexity is such that a constant viscosity analysis should be a useful preliminary step in understanding the role of natural convection. To be of value the analysis should not only predict the magnitude of the convection effect on heat transfer coefficients but should also present velocity profiles suitable for comparing hydrodynamic stability theory predictions with experimental transition results.Constant wall flux heat transfer in vertical pipes is ideally suited to such a study when the density is the only temperature dependent fluid property because...

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“…Koppel and Smith (14) have shown the fallacy of the second assumption by proving that it leads to the conclusion that velocity profiles can be calculated without recourse to the momentum equation, and the calculated profiles are independent of the gravity field. This assertion conflicts with the experimental results of Hanratty, Rosen, and Kabel ( 4 ) , and Scheele and Hanratty (17). Thus, a radial velocity component must exist.…”

Section: Literature Surveymentioning

confidence: 80%

Uniform flux heat transfer to a gas in laminar forced convection in a circular tube

Bergman¹,

Koppel²

1966

AIChE Journal

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Heat transfer from a circular tube to a contained gas in laminar forced convection was studied dimensionally and experimentally. The boundary condition of uniform heat flux was physically achieved, and the experiments were conducted in a statistically designed pattern. The dimensional analysis, based upon the principle of corresponding states, and more general than any hitherto proposed, indicated four independent variables in this experiment. Of these, only bulk velocity showed a statistically significant effect in the region studied: a reduction in heat transfer coefficient with decreasing bulk velocity. No existing theories could explain this effect. LITERATURE SURVEYroblem of laminar flow heat transfer to a gas in a circu P ar tube with a prescribed wall heat flux has been a subject of recent theoretical and experimental inquiiy. Much of the discrepancy between theory and measurements in these studies arises from the inability to assess properly the role of variable physical properties in heat transfer. For the idealized case of constant fluid properties, the problem has been solved by Sellars et al. (18) and Siege1 et al. (19). For a gas with variable physical properties, several theoretical solutions have been promulgated. Deissler ( 3 ) examined the problem of fully developed laminar flow of a gas with uniform wall heat flux (UHF). Viscosity and theimal conductivity were taken as being proportional to a power of temperature, while density was assumed to vary inversely with temperature. The two major assumptions made by Deissler were: the velocity at any radial distance does not depend on axial distance along the tube, and the radial equation of motion can be ignored and the radial velocity component is zero. The first assumption is correct only for no density change in the axial direction, and so is valid only for extremely low rates of heating. Koppel and Smith (14) have shown the fallacy of the second assumption by proving that it leads to the conclusion that velocity profiles can be calculated without recourse to the momentum equation, and the calculated profiles are independent of the gravity field. This assertion conflicts with the experimental results of Hanratty, Rosen, and Kabel ( 4 ) , and Scheele and Hanratty (17). Thus, a radial velocity component must exist. Koppel and Smith (14) considered the laminar flow UHF problem for the entire thermal regime and solved the continuity equation and energy equation for variable specific heat and thermal conductivity, assuming a zero radial velocity. Their numerical results were for supercritical carbon dioxide, Davenport and Leppert ( 2 ) considered the effect of a radial velocity component on heat transfer and Auid flow by postulating that the radial convective heat flux was equaI to the negative product of the radial conductive heat flux, and a function of radial distance. Expressed mathematically, this means that Page 648A.1.Ch.E.The function R ( r ) must lie between zero and one. If R ( r ) were unity, this would imply that no energy was being tra...

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Effect of natural convection on stability of flow in a vertical pipe

Cited by 99 publications

References 1 publication

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Natural convection distorted non‐Newtonian flow in a vertical pipe

Uniform flux heat transfer to a gas in laminar forced convection in a circular tube

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