Article pubs.acs.org/IECR
Flow Characteristics of Power-Law Fluids in Coiled Flow Inverter Jogender Singh, Vikrant Verma, and K. D. P. Nigam* Chemical Engineering Department, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India ABSTRACT: A novel device coiled flow inverter (CFI) has shown great potential as a heat exchanger and inline mixer.1−3 The device offers negligible thermal and concentration gradient in the radial direction. CFI may find potential applications in food industry for different processes such as pasteurization and sterilization, due to its ideal characteristic. Therefore, in the present study, the hydrodynamic of single and two-phase non-Newtonian fluid flow in CFI have been investigated experimentally and numerically. The experiments have been performed in three different CFI geometries. The aqueous solution of carboxymethyl cellulose (CMC) of three different concentrations has been used as a working fluid. The single-phase Reynolds number ranged from 100 to 10000, while the two-phase liquid and gas Reynolds numbers ranged from 100 to 10000 and 100 to 8500, respectively. The various flow patterns for two-phase non-Newtonian fluid flow in CFI have been observed during experimental investigation. The effects of the gas and liquid flow rates, curvature ratio and concentration of non-Newtonian fluid on frictional pressure drop have been investigated. The correlation for the friction factor in CFI has been developed for single and two-phase air non-Newtonian fluid flow under laminar condition. The development of velocity fields has been demonstrated for single and two-phase non-Newtonian fluid flow in CFI. The contours of the volume fraction are plotted at different axial length and after each 90° bend. The contour plots bring about an understanding of flow inversion and flow distribution of pseudoplastic fluids after each 90° bend in CFI.
1. INTRODUCTION
industry for pasteurization and sterilization processes, as it provides higher mixing and heat transfer. The present study experimentally explores the flow characteristics of single-phase aqueous solution of CMC and two-phase air−aqueous solution of CMC in CFI under laminar flow conditions. The flow patterns, average hold-up of the individual phase, and the frictional pressure gradient in three different geometries of CFI were investigated to understand the complex flow behavior of non-Newtonian fluids in complex geometries. The fluid flow developments for single- and two-phase nonNewtonian fluids were also demonstrated by numerical simulations. The numerically computed results were found in close agreement with experimental results. The influence of the fluid properties such as concentration of non-Newtonian fluid, flow rates of the gas and non-Newtonian fluid, on flow phenomena has been investigated. The effect of the design parameter of the geometry has been also investigated.
The non-Newtonian fluids have vast areas of application from plastics, dye-stuffs, and pharmaceuticals to foods. In food processing, uniformity of temperature is essential to ensure the quality and microbial safety of liquid foods. Continuous ultrahigh temperature (UHT) sterilizers are widely used in food industry for sterilization of liquid foods ranging from fruit juices to sauces and custards, owing to their improved thermal treatment. The continuous sterilizers provide several advantages over the conventional batch sterilizers, for example, higher heat transfer due to forced convection and lower temperature gradients inside the tube, which favors the liquid food quality. However, UHTsterilization induces a nonuniform heat treatment for viscous products.4 The broad residence time distribution of UHTsterilization results in fluid elements with different thermal histories, which results in nonuniformity of product quality. Coiled flow inverter (CFI) configuration is a novel design, which shows potential for the intensification of heat transfer and mixing process. The geometrical configuration of CFI consists of 90° bends in a helical coil, with equal arm length before and after the bend. The flow generated in this device continuously changes direction due to change in the direction of centrifugal force caused by bending of helical coil. The plane of vortex formation rotates with the change in the direction of centrifugal force by same angle. A sharp 90° bend in CFI increases mixing between the fluid elements of different age groups, which provides a uniform temperature condition within CFI. The single-phase fluid flow study conducted on laboratory scale shows significant narrowing of residence time distribution in CFI.5 The heat transfer study conducted at pilot plant scale shows that the Nusselt number was enhanced up to 30% in CFI, as compared to helical coil of identical design parameters under laminar flow condition.6 Hence, CFI can play an important role in the food © 2012 American Chemical Society
2. LITERATURE REVIEW The continuous flow device's specially curved tube has got special attention of the researchers for the processing of nonNewtonian fluids, as the result of several advantages, such as enhanced mixing, higher heat transfer performance, and compactness.7 Literature review shows that most of the studies emphasize the flow of Newtonian fluids or two-phase gas Newtonian fluids. A few studies have been reported for nonNewtonian fluid flow in complex geometries. The behavior of Special Issue: L. T. Fan Festschrift Received: Revised: Accepted: Published: 207
March July 5, July 6, July 6,
2, 2012 2012 2012 2012
dx.doi.org/10.1021/ie300516w | Ind. Eng. Chem. Res. 2013, 52, 207−221
Industrial & Engineering Chemistry Research
Article
Table 1. Numerical Studies of Single-Phase Power-Law Fluid Flow in Helical Coil range of parameter
author Mashelkar and Devarajan10 Hsu and Patnaker12 Kewase and young13 Rathna et al.16 Takami et al.17 Nigam et al.18
theoretical method boundary layer approach
curvature ratio (λ)
power-law index (n)
Dean number (NDe)
10−100
0.5−1.5
>50
0.5−1.25
1−100
Theory is applicable of higher value of Dean number. applicable for large range of curvature ratio
numerical finite difference technique
remark
integral momentum boundary layer approach
10−100
0.5−1.0
>100
applicable for both laminar and turbulent flow
analytical method solution is obtained up to first order term boundary layer approach numerical time marching method
20−100
0.5−1.5
1−20
10−100
0.5−1.5
1−1000
Analytical perturbation method solution is found up to second order term
10−100
0.5−1.5
1−30
Reported that flow rate is independent of curvature ratio. Relations fc and NDe can be expressed with a single curve dependent on n. Flow rate is found as a function of curvature ratio, Reynolds number, and power-law index.
Table 2. Experimental Studies of Single-Phase Power-Law Fluid Flow in Helical Coil range of parameter author Rajasekharan et al.8 Gupta and Mishra9 Mashelkar and devarajan10 Mujawar and Raja Rao11 Takami et al.17 Mishra and Gupta19
working fluid
curvature ratio (λ)
power-law index (n)
Dean number (NDe)
30−100
0.8−1.0
10−2000
fc/fs = 1.25(NDe)0.3
correlations
CMS of 0.5 and 1% sodium silicate CMC 0.6−2.1% CMC, PE, PAA, kaolan suspension SA, SCMC 0.5−1.0%
30−40 10−100
0.77−0.85 0.7−1.0
1−10000 70−400
fc/fs = 1 + 0.026(NDe)0.675 fc = (9.069 − 9.438n + 4.374n2)(λ)−0.5NDe(−0.768+0.122n)
10−100
0.7−1.0
1−1000
not available
PAA, PEO, CMC CMC, SCMC
30−150 30−150
0.6−1.0 0.7−1.0
1−1000 1−100000
not available fc/fs = 1 + 0.033(log NDe)0.4
thermal entrance region of coiled circular tubes was investigated numerically.14 It was observed that the Nusselt number increases with increase in the value of flow behavior index (n) for a given value of Prandtl and Dean number. The thermal entrance length was observed to be shortened for dilatant fluids as compared to pseudoplastic fluids. The effect of centrifugal force on the hydrodynamics of non-Newtonian fluid flow in coiled tube was also investigated by employing the integral momentum method invoking boundary layer approximation.15 The central assumption in this approach hinges on the fact that secondary flow field consist an inner inviscid core and a thin boundary layer adjacent to the wall for large values of the Dean number. Tables 1 and 2 show the numerical and experimental studies of non-Newtonian fluid flow in curved tube reported in the literature. Two-phase gas−non-Newtonian liquid flow through curved geometries is more complex in nature. In curved tube, the higher density fluid, that is, liquid, flows toward the wall from center of curvature subjected to larger centrifugal force, while the gas flows toward the center of the curvature. This process is a continuous function of coiled geometry. The flow behavior of air−CMC mixtures in helical coils was studied for two different curvature ratios, 10.76 and 19.8.20 Three types of flow patterns, namely, slug, wavy, and annular were proposed. However, it was observed that no data on the entrance length to stabilize the flow pattern was provided in the literature. It is reported in literature that in the gas−non-Newtonian liquid two-phase flow the frictional pressure drop could be successfully correlated by the Lockhart− Martinelli method.15,21 The flow patterns, hold-up, and pressure drop were also studied for cocurrent upward and downward flow of air−water in coiled tubes.22 The flow patterns in coiled tubes were observed similar to the flow patterns in inclined tubes reported by Spedding et al.23
mildly non-Newtonian aqueous carboxymethyl cellulose solutions in coiled tubes was studied with the curvature ratio (λ) varying from 10 to 27.8 The separate correlations of friction factors for laminar, transition, and turbulent flow regimes were proposed. However, it is not clear what criterion was used to outline the flow regimes. A similar study was reported for pressure drop measurements for the laminar flow of mildly shear thinning polymer solutions in two coils of curvature ratios of 13 and 25.9 An empirical correlation of friction factor as a function of the Dean number was proposed in terms of the excess pressure drop in helical coil, as compared to the straight tube. The pressure drop in helical coils was found to be higher than that of the straight tube due to the effect of curvature. A new correlation of fc was proposed for the single phase non-Newtonian fluid flow in curved tube under laminar flow conditions.10 The hydrodynamics of dilute aqueous polymeric solutions of sodium alginate (SA) and sodium carboxymethyl cellulose (SCMC) in helical coil was investigated in the concentration range 0.3−1.0% (w/w).11 The predicted values of friction factors were found to be satisfactorily in agreement with the Mashelkar and Devarajan’s10 correlation, whereas the correlation of Gupta and Mishra9 gives 20−30% higher values of friction factors. The heat transfer and flow characteristics of non-Newtonian fluid (n = 0.5 and 0.75) flow in a curved tube of constant curvature ratio (λ = 10) was also investigated under laminar flow conditions. It was reported that the friction factor increases with increase in the value of Dean number and the power-law index. The new correlations of friction factor and Nusselt number for the flow of non-Newtonian fluid in coiled tubes were reported.13 The computed values of Nusselt number and friction factor were found in reasonably good agreement with the experimental results. Laminar convection of non-Newtonian fluids in the 208
dx.doi.org/10.1021/ie300516w | Ind. Eng. Chem. Res. 2013, 52, 207−221
Industrial & Engineering Chemistry Research
( Dd )
0.721 ± 0.076
0.440−42.03 × 10−5 3.334−15.003 × 10−5 0.6−0.9 11−27 Biswas and Das25
0.757 ± 0.025 −1.437 ± 0.059 −0.348 ± 0.017 NRe,SL Npl proposed. ftplc = 0.40NRe, SG
gc d
0.44−42.03× 10−5 0.6−0.9 0.04−0.09 Biswas and Das24
3.33−15.00 × 10−5
Effects of the gas flow rate, liquid flow rate, concentrations of SCMC, and coil diameter on the liquid hold-up have been examined. A new correlation for two-phase friction factor in helical coil has been
2 ρSG VSG
(ΔP /ΔL)TP = (ΔP /ΔL)SG + C(n)(C L)q
A new correlation for two-phase pressure gradient was developed.
