Numerical treatment of fully developed laminar flow in helically coiled tubes
TL;DR: In this paper, the axial and secondary velocities of helically coiled tubes are calculated for both circular and elliptical cross sections. But only closely wrapped helices, that is, helices with modest pitch, are considered.
Abstract: Laminar flow in helically coiled tubes is treated numerically. Fully developed axial and secondary velocities are calculated for both circular and elliptical cross sections. Only closely wrapped helices, that is, helices with modest pitch, are considered. Ten solutions with Deans numbers up to 200 have good accuracy. Two additional solutions with Deans numbers up to 280 are approximate.
Citations
More filters
TL;DR: The potential industrial applications of curved tubes for single and two-phase flow are reviewed within the context of physics of flow, trends in the development of technology, and its laboratory to industrial-scale commercialization.
Abstract: The potential industrial applications of curved tubes for single- and two-phase flow are reviewed within the context of physics of flow, trends in the development of technology, and its laboratory to industrial-scale commercialization. Comparison of the performance of curved tube configurations demonstrates its edge over the conventional motionless mixers, heat exchangers, and reactors. Alongside, their respective advantages and limitations are also highlighted. Further, a compendium of the available correlations for single- and two-phase friction factor and heat- and mass-transfer coefficient in curved tubes has also been presented. Key issues regarding the design parameters governing the performance of the curved tubes for mixing and heat- and mass-transfer that impact the research, development, and scale-up or scale-down of such devices are also analyzed. Emerging trends for the development of a new class of curved tubes, namely, inverters and serpentine and chaotic devices are also presented.
285 citations
01 Oct 2007
TL;DR: In this paper, a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems is provided, providing a comprehensive review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid 2-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-
Abstract: Providing a comprehensive introduction to the fundamentals and applications of flow and heat transfer in conventional and miniature systems, this fully enhanced and updated edition covers all the topics essential for graduate courses on two-phase flow, boiling, and condensation. Beginning with a concise review of single-phase flow fundamentals and interfacial phenomena, detailed and clear discussion is provided on a range of topics, including two-phase hydrodynamics and flow regimes, mathematical modeling of gas-liquid two-phase flows, pool and flow boiling, flow and boiling in mini and microchannels, external and internal-flow condensation with and without noncondensables, condensation in small flow passages, and two-phase choked flow. Numerous solved examples and end-of-chapter problems that include many common design problems likely to be encountered by students, make this an essential text for graduate students. With up-to-date detail on the most recent research trends and practical applications, it is also an ideal reference for professionals and researchers in mechanical, nuclear, and chemical engineering.
270 citations
TL;DR: A non-orthogonal helical co-ordinate system is introduced and it is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40.
Abstract: A non-orthogonal helical co-ordinate system is introduced to study the effect of curvature and torsion on the flow in a helical pipe. It is found that both curvature and torsion induce non-negligible effects when the Reynolds number is less than about 40. When the Reynolds number is of order unity, torsion induces a secondary flow consisting of one single recirculating cell while curvature causes an increased flow rate. These effects are quite different from the two recirculating cells and decreased flow rate at high Reynolds numbers.
192 citations
TL;DR: In this article, a point successive-overrelaxation method was used to solve the thermal energy equation in curved tubes of circular cross section, where the curvature ratio was considered as an additional parameter.
180 citations
TL;DR: In this paper, a general correlating equation has been developed for all Prandtl and Dean numbers by joining the theoretical Nusselt number for a straight tube and a theoretical asymptote for the regime of creeping secondary flow.
Abstract: A general correlating equation has been developed for all Prandtl and Dean numbers. This expression was constructed by joining the theoretical Nusselt number for a straight tube, a theoretical asymptote for the regime of creeping secondary flow, a semi-theoretical expression for the boundary layer regime and an asymptotic value of Nu for the intervening regime of flow.The arbitrary coefficients and exponents in the model were evaluated using experimental and numerically computed values. Slightly differing sets of coefficients are required for uniform wall temperature and longitudinally uniform heating with uniform peripheral wall temperature. All prior theoretical results were for toroidal flow (zero pitch). A numerical solution was developed for helical flow (finite pitch). These results confirm the validity of neglecting pitch for tightly wound coils but suggest a generalization of the correlating equation for large pitch.
168 citations