Article Highlights
* Performance of a Komax static mixer was determined for non-Newtonian fluid streams
* Pressure drop studies were carried out for different flow rates with different concentrations
* The results of the experimental runs for the designed elements were presented
* Complete mixing is achieved with pressure losses of 75% for the designed element
* Pressure losses for the designed element are less than that of conventional static mixers
Abstract
Mixing is the degree of homogeneity of two or more phases and it plays a vital role in the quality of the final product, it is conventionally carried out by mechanical agitators or by static mixers. Static mixers are a series of geometric mixing elements fixed within a pipe, which use the energy of the flow stream to create mixing between two or more fluids or to inject metered liquid into a continuous process. The objective of this work is to predict hydrodynamic aspects of the static mixer designed. The mixing performance of a Komax static mixer has been determined for the blending of non-Newtonian fluid streams with identical or different rheology by using experimental study. The energy needed for mixing comes from the force created by the liquid due to turbulence and the geometry of the static mixer. Pressure drop in the static mixer depends strongly on the geometric arrangement of the inserts, properties of fluids to be mixed and flow conditions. Hence, pressure drop studies are carried out for different flow rates of fluids with different concentrations of two non-Newtonian fluids. Starch and xanthan gum solutions are used as working fluids, it is observed from the experimental results that the pressure drop per unit length increases as the fluid flow rate increases, and the nature of fluid flow varies with the velocity of the fluids.
Keywords: pressure drop studies, mixing performance, non-Newtonian fluid blending, fluid rheology, static mixer.
Mešanje utiče na stepen homogenosti dve Hi više faza i igra vitalnu ulogu u kvalitetu konačnog proizvoda. Konvencionalno se vrši mehaničkim mešaiicama Hi statičkim mešačima. Statički mešači su niz geometrijskih elemenata za mešanje pričvršćeni u cevi, koji koriste energiju strujanja za mešanje dve iii više tečnosti ili ubrizgavanje odmerene količine tečnosti u kontinuaini proces. Cilj ovog rada je da predvidi hidrodinamičke parametre projektovanog statičkog miksera, istražene su performanse statičkog mešača Komax za mešanje nenjutnovskih tečnosti sa identičnom iii drugačijom reoiogijom. Energija potrebna za mešanje potiče od sile koju tečnost stvara zbog turbulencije i geometrije statičkog mešača. Pad pritiska u statičkom mešaiču jako zavisi od geometrijskog rasporeda umetaka, svojstava fluida koji se mešaju i usiova protoka. Zbog toga je istražen pad pritiska za različite protoka tečnosti sa različitim udeiima dve nenjutnovske tečnosti. Kao radne tečnosti, koršćeni su rastvori skroba i ksantana. Iz eksperimentalnih rezultata se zapaža da se pad pritiska po jedinici dužine povećava sa povećanjem protoka fluida, pri čemu priroda strujanja fluida varira u zavisnosti od njegove brzine.
Ključne reči: pad pritiska, efekat mešanja, mešanje nenjutnovskih tečnosti, reoiogija fluida, statički mešač.
(ProQuest: ... denotes formulae omitted.)
Mixing is a vital unit operation that ensures the homogeneity of phases by converting a heterogeneous mixture to a homogeneous mass by dissolution, dispersion, and diffusion. It enables the transfer of heat and mass across one or more streams or phases and influences the operating time, safety and quality of the product and process [1]. Most of the industrial processes employ mixing in one form or another. However, those industries which employ processing of jams, inks, polymers and other viscous fluids result in mixing operations under laminar flow conditions in order to homogenize the product. In laminar flow conditions, the level of mixing is low which results in nonhomogeneities in composition [1,2]. Mixing in food industries encounters many challenges in maintaining the homogeneity, consistency and enhancement of the texture of final products as they are processed under laminar conditions.
A static mixer is a device designed incorporating motionless elements in a tubular arrangement which may enable the flow of fluids in various directions based on the design in order to provide continuous mixing of fluids. The metallic elements cause intermaterial contact due to fluid splitting and recombining, and thus enhance mixing in systems ranging from simple blending operations to chemical reactions and heat transfer [3]. Further, in static mixers, the flow is split into layers which are rearranged and forced to flow in radial direction. The first ever static mixer designed was a single element mixer [4].
Static mixers have numerous advantages compared to those of the conventional mixers. They are cost-effective and consume less power. The absence of moving parts makes it easier for maintaining them. The compact design makes a static mixer easy to install and it occupies less floor space. The mixing elements are either self-cleaning or disposable, thus preventing erosion or scale formation [5]. There is a wide range of static mixers like Komax, Kenics, SMX, etc. that are commercially available. Very few researches have highlighted the performance of static mixers [6,7]. Recent studies have compared the performance of all the commercially available static mixers with pressure drop and length as criteria [8].
Kenics and Multiflux mixers were initially developed to mix fluids under laminar conditions [9]. Static mixers have evolved over the years offering a wide variety of applications in almost all chemical process industries that involve mixing of chemical reactants, heating and cooling, scrubbing, stripping and water treatment. Inline mixers provide quality processing of edible products that are viscous in nature. They can be used in industries that process jams, oils, juices, chocolates, beverages and dairy products [10]. Recent application of static mixers was as catalyst support for heterogeneous photocatalysis [11]. The studies on static mixer applications for non-Newtonian fluids are fewer. Some such studies have shown that these fluids have better mixing quality than Newtonian fluids [12]. Shear-thinning fluids get deformed readily, as the shear-thinning viscosity enhances mixing. For low elasticity fluids, mixing is enhanced till shearthinning effects appear [13]. The first study on the hydrodynamic aspects of non-Newtonian fluids has been done recently at low primary flow rates for costeffective mixing [14]. So, this paper focuses on the experimental study of hydrodynamic aspects of mixing non-Newtonian fluids for a Komax static mixer.
MATERIALS AND METHODS
Experimental setup
The experimental study on the mixing of nonNewtonian fluids is carried out in a continuous flow setup, as depicted in Figure 1. The experimental setup consists of two gear pumps each of 5 L/min capacity to pump the solutions. Starch and xanthan gum are used as working fluids. Electrical resistance tomography depicts the effect of xanthan gum solution rheology on the quality of mixing in the chaotic SMX static mixer, showing that the xanthan gum solution at higher concentration results in a more homogenous mixing, as given in literature [15].
Six Komax static elements with opposite twists are interlocked with each other in series and are placed in the pipe of a specified dimension. Fluid flow is determined using flow sensors and pressure is measured at the inlet and outlet of the static element setup using pressure transducers. Pressure across the pipe section is displayed in the Arduino board, which converts and records the signals from the pressure transducers into analog signals. A mesh is placed at a distance of 8 cm from the inlet of the pipe to prevent the formation of a dead zone. The specification of the static mixer setup is provided in Table 1. The static mixer designed is shown in Figure 2.
Experimental procedure
The starch and xanthan solutions of specific concentrations are pumped to a static mixer setup using rotary gear pumps powered by motors. The specification of the rotary gear pump is provided in Table 2. The flow sensor detects the flow rate of process fluids and its specifications are provided in Table 3. The process fluid enters the mixer pipe through the inlet nozzle. The fluids split and are recombined inside the pipe by mixing elements. Further, the inlet and outlet pressure are determined using the pressure transducers P1 and P2, respectively. The specifications of the pressure transducers are provided in Table 4. Likewise, the intensity of the mixing is determined by collecting samples from several ports located along the length of the pipe. The mixed fluid, thus obtained, drains to the outlet tank through the outlet nozzle. The experiments are repeated by varying the flow rates and the concentration of process fluids in order to study the mixing performance of static mixer.
Power requirement
The energy consumed by a static mixer can be determined using the following equation:
... (1)
The energy is supplied by the pump used to create the flow of the fluid through the mixer for homogenization of two or more liquids. Static mixers reduce standard deviation or coefficient of variance. The reduction of variance is the product of shear rate and time, and variance is equal to UDX. Early investigations into the performance of static mixers have focused on the pressure drop across the mixer with various fluids. It is found that at low Reynolds numbers, there is an increase in pressure drop as fluid elasticity increases [16,17]. Depending on the flow rate and liquid viscosity, the pressure drop varies. In laminar flow conditions, the performance varies widely for different mixers and mixing efficiency does not necessarily follow Sauter mean drop diameter, but pressure drop needs to be considered. For a Kenics mixer, APmixer is about 6 times that of an empty pipe in laminar flow, and for a Sulzer SMX mixer it is 64 times higher. The pressure drop in a static mixer depends strongly on the geometric arrangement of the inserts. It is simply defined in relation to the pressure drop AP in an empty tube given by Darcy's equation:
... (2)
... (3)
K depends on the mixer type and its value can be obtained from the manufacturer's literature.
Energy and efficiency of mixing
Mixing efficiency is accomplished by controlled vortex structures generated by the patented low- profile tab geometry. This provides uniform blending while limiting the mixer length to less than half of the pipe diameter. Complete mixing is achieved with pressure losses of 75% which are less than that of conventional static mixers [18]. An understanding of the energy requirement of a static mixer is necessary with respect both to the establishing of installed pressure drop and flow rate requirement. The empirical relation for friction factor is as follows [19]:
... (4)
... (5)
The two dimensionless groups are based on the empty pipe diameter (Dt), including the value of V, which is a superficial velocity. In principle, it is required only for the value of APto be measured at one value of V to define the product fNRe for any static mixer, but a range of measurements can give useful information regarding the slight volubility of fNRe and the upper limit of the laminar flow regime in terms of NRe. In more recent studies, a simple method has been used where the pressure drop characteristics are described as a ratio of mixer pressure drop and empty pipe pressure drop for the same flow rate and diameter (Harnby).
The mixer pressure drop ratio is commonly measured by the design factor K, (Z-factor) which is defined as follows [20]:
... (6)
... (7)
As both fNRe and NRe are constant for any mixer or pipe in the laminar regime, it follows that Zis also constant. Further, the relationship among various parameters is very simple to determine:
... (8)
It is suggested that the product of the pressure drop ratio (Z) and the value of L/D would provide a useful quantitative estimate of mixer efficiency given in Eq. (8). This is less ambitious than the ratio values used in previous comparative tests, and provides a basis for the comparison of data from various sources.
RESULTS AND DISCUSSION
Rheological properties
The rheological behavior of the process fluids like xanthan gum and starch is determined by plotting shear stress as a function of shear rate for varying compositions. The starch and xanthan solutions are prepared by first dissolving the appropriate amount of starch and xanthan into deionized water warmed to about 40 °C to make a solution with a concentration of varying weight percentages. Rheological measurements are carried out using a Brookfield DV-III ultra programmable rheometer. Both starch and xanthan-based fluids show a slight shear-thinning for low shear rates. Figure 3 shows the consolidated graph depicting the rheological behavior of process fluids at the concentrations of: /) 2 and 3% starch solution, and i) 0.1 and 0.2% xanthan gum solution.
The shear-thinning behavior of process fluids has been depicted by plotting the viscosity as a function of shear rate. Viscosity is reported as function of shear rate for starch and xanthan solutions at different concentrations. Figure 4 shows the decrease in viscosity as the shear rate increases.
Pressure drop observations
The pressure drop is found using pressure transducers placed at the inlet and outlet of the static mixer pipe. Pressure drop for different flow rates of starch and xanthan at varying concentrations across the empty tube and mixer tube with elements are investigated and the readings are noted. The pressure drop is calculated using Eqs. (2) and (3). Plotting pressure drop against set flow rate and measured using a flow sensor shows the variation of the former. An increase in pressure drop is observed with the increase in flow rate. The results remain the same when the experiments are carried out by varying flow rates. For a turbulent flow system, the greater value of pressure drop shows better mixing in a static mixer system. The variation of pressure drop with respect to flow rate is shown in Figure 5.
Effect of friction factor and Reynolds number on mixing efficiency
Mixing efficiency is determined by plotting the ZK) factor as a function of the Reynolds number. The friction factor is calculated using Eq. (4) while Z-factor is calculated using Eq. (7). Figure 6 depicts the variation of the friction factor as a function of the Reynolds number. As fluid flows through the mixer tube, pressure drop across the tube occurs with frictional forces on the fluid. The friction factor, ffor static mixers, is high at laminar regime and decreases gradually, almost to constant value with the increase in the Reynolds number, which ensures turbulence. The friction factor in Komax mixers varies with twist angle, thickness, and length of the static element. At turbulent flow conditions, the number of mixing elements decreases with flow velocity approaching constant values for high Reynolds numbers. The mixing efficiency is high under laminar flow conditions as well, but gets reduced as the flow begins to approach turbulent conditions. It is obvious that under a turbulent regime, as velocity increases, the pressure increases as this is proportional to the square of velocity.
Effect of pressure drop ratios, Z factor, on mixing efficiency
Pressure drop ratios, Z for a static mixer depend on the design of the mixer and the Reynolds number. Figure 7 shows the variation of the Z-factor with respect to the Reynolds number. The development zone provided in the static mixer ensures the negligible backmixing. The mixing efficiency of a static mixer is the product of pressure drop ratios and the mixing length required to achieve a specified CoV of 0.05. In order to assess the accuracy of the experiment, the Z-factor results are compared with the lite- rature. From literature, measured pressure drop ratio, Zfor Komax mixer, is found to be 25 for a L/Dt ratio in the range of 29-38 and as per the investigation it is found to be around 23 for a L/Dt ratio of 8.4. The available experimental data shows variability due to slight difference in measurement locations. Mixer selection is best based on mixing efficiency, design with low pressure drop and shorter length. The investigation shows that this designed mixer with a comparatively less L/Dt ratio is a better design for the selected fluid system.
CONCLUSION
In this present study, a static mixer (Komax) is designed, fabricated and tested in a pipeline for inline mixing. From experimental result, it is found that the pressure drop per unit length increases with the increase in flow rate, and for a turbulent flow system, better mixing is achieved for higher values of the pressure drop. Rheological behavior of various fluids is studied for the absolute viscosity of the process fluid. The increase in velocity is twofold for turbulent flow and it is directly proportional to velocity for laminar flow. The friction factor decreases with the increase in the Reynolds number, and a sharp decrease is observed for the laminar region. In further study, CFD modeling for the flow profile of static mixing system has to be done and compared with the experimental run.
Nomenclature
Q Flow rate (m3/s)
P Pressure drop (N/m2)
f Friction factor
L Length of the static mixing element (m)
Dt Inner diameter of the static mixer tube (m)
p Density of the fluid (kg/m3)
V Velocity of the fluid (m/s)
m Viscosity of the fluid (kg/m s)
P minor Pressure drop ratios for static mixer
P empty pipe Pressure drop in static mixer (N/m2)
P emty Pressure drop in empty pipe (N/m2)
f Darcy's friction factor for fluid in static mixer
f Darcy's friction factor for fluid in empty pipe
Npe Reynolds number
e Mixing efficiency of the static mixer
Dimensionless numbers
Reynolds Number, ...
Correspondence: D. Revathi, Faculty of Chemical Engineering, Kongu Engineering College, Erode, Tamil Nadu, India.
E-mail: [email protected]
Paper received: 17 October, 2019
Paper revised: 27 January, 2020
Paper accepted: 28 February, 2020
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Abstract
Mešanje utiče na stepen homogenosti dve Hi više faza i igra vitalnu ulogu u kvalitetu konačnog proizvoda. Konvencionalno se vrši mehaničkim mešaiicama Hi statičkim mešačima. Statički mešači su niz geometrijskih elemenata za mešanje pričvršćeni u cevi, koji koriste energiju strujanja za mešanje dve iii više tečnosti ili ubrizgavanje odmerene količine tečnosti u kontinuaini proces. Cilj ovog rada je da predvidi hidrodinamičke parametre projektovanog statičkog miksera, istražene su performanse statičkog mešača Komax za mešanje nenjutnovskih tečnosti sa identičnom iii drugačijom reoiogijom. Energija potrebna za mešanje potiče od sile koju tečnost stvara zbog turbulencije i geometrije statičkog mešača. Pad pritiska u statičkom mešaiču jako zavisi od geometrijskog rasporeda umetaka, svojstava fluida koji se mešaju i usiova protoka. Zbog toga je istražen pad pritiska za različite protoka tečnosti sa različitim udeiima dve nenjutnovske tečnosti. Kao radne tečnosti, koršćeni su rastvori skroba i ksantana. Iz eksperimentalnih rezultata se zapaža da se pad pritiska po jedinici dužine povećava sa povećanjem protoka fluida, pri čemu priroda strujanja fluida varira u zavisnosti od njegove brzine.