energies

Article Effect of Impeller Design on Power Characteristics and Newtonian Fluids Mixing Efficiency in a Mechanically Agitated Vessel at Low Reynolds Numbers

Marek Jaszczur 1,* , Anna Młynarczykowska 2 and Luana Demurtas 3

1 Faculty of Energy and Fuels, AGH University of Science and Technology, 30059 Krakow, Poland 2 Faculty Mining and Geoengineering, AGH University of Science and Technology, 30059 Krakow, Poland; [email protected] 3 Department of Ingegneria Civile, Ambientale e Architettura, University of Cagliari, 09123 Calgari, Italy; [email protected] * Correspondence: [email protected]; Tel.: +48-12-6172657



Received: 30 November 2019; Accepted: 29 January 2020; Published: 3 February 2020


Abstract: The mixing process is a widespread phenomenon, which plays an essential role among a large number of industrial processes. The effectiveness of mixing depends on the state of mixed phases, temperature, viscosity and density of liquids, mutual solubility of mixed fluids, type of stirrer, and, what is the most critical property, the shape of the impeller. In the present research, the objective was to investigate the Newtonian fluids flow motion as well as all essential parameters for the mechanically agitated vessel with a new impeller type. The velocity field, the power number, and the pumping capacity values were determined using computer simulation and experimental measurements. The basis for the assessment of the intensity degree and the efficiency of mixing had to do with the analysis of the distribution of velocity vectors and the power number. An experimental and numerical study was carried out for various stirred process parameters and for fluids whose viscosity ranged from low to very high in order to determine optimal conditions for the mixing process.

Keywords: fluid mixing; agitated vessel; stirred tank; impeller

1. Introduction Stirred vessels are widely used in a large number of chemical and engineering processes. They also play an essential role in the food industry, bioprocessing, wastewater treatment, and mineral processing to accomplish homogenization, heat transfer, gas dispersion, solid suspension, etc. [1]. They play an important role in selected processes as prevention of sediment aggregation, gas dispersion in liquids, the formation of suspensions and slow-sedimenting mixtures. In the number of analyses, researchers achieved a certain degree of awareness on the basic development and mechanism of fluid mixing, above all, on the single-phase flow. Nevertheless, there is still insufficient information on the fluid behavior particularly in unbaffled single-impeller stirred vessels which are highly important in the pharmaceutical and cosmetics industry, which require the highest standard of cleanliness, or in shear-sensitive cultures that need an appropriate gas intake [2]. Independent of an industrial process, the main goal has always been to find the most efficient and nondestructive method of mixing which consumes as low amounts of power as possible. For that reason, a large number of research studies have been performed to obtain various shapes for the impellers that could achieve a high-quality mixture usually with low axial velocity, low shear stress, and low internal heat generation, which are crucial issues for vitamins, enzymes, and for food production. Undeniably,

Energies 2020, 13, 640; doi:10.3390/en13030640 www.mdpi.com/journal/energies Energies 2020, 13, 640 2 of 19 substantial progress has been made in reference to energy consumption by the mixing systems that can be still minimized by modifying the shape of the single impeller. That becomes particularly important nowadays when energy consumption and environmental care become a critical issue and may determine the economic success of the investment. In multi-impeller systems, one recently preferred which utilizes a single impeller, the shape is also a crucial issue because it consists of a series of single impellers. The shape of the single impeller is a primary issue on the basis that more advanced systems can be developed. In a research study performed by T. Su et al. [3] the power consumption, the fluid phenomenon, hydrodynamics of the flow, and the mixing process using the Rushton-type impellers were compared. The analyses showed an 18% decrease in power owing to the modification of the Rushton turbine shape, which also managed to enhance the local fluid velocity and obtain higher turbulence intensity around the optimized impeller. F. Scargiali et al. [4] analyzed the impact of the Reynolds and Froude numbers on the power consumption characteristics in the case of unbaffled stirred tanks. The authors concluded that the primary factor that impacts power consumption and the mixing intensity is the shape of the impeller. Hence, many analyses have been performed in order to find the optimal shape of the impellers suitable for a wide range of processes. T. Kumaresan and J.B. Joshi [5] investigated the impact of impeller geometry on the fluid flow pattern and mixing time for preselected sets of axial impellers (pitched blade turbines and hydrofoils). The authors observed that the shape with a blade twist decreased the power number and flow numbers and that, for a down-flow impeller, the jet stream leaving the impeller strongly interacted with the stirred vessel and generated high-energy dissipation below the impeller. On the other hand for the up-flow impeller, the jet stream leaving the impeller interacted with the free surface and generated significantly lower energy dissipation. In another work, M. Basavarajappa et al. [6] analyzed turbulent fluid flow characteristics in laboratory-scale stirred vessels characterized by different geometries using Computational Fluid Dynamics (CFD) simulations and comparing the Rushton turbine with the flotation impeller. H. Ameur et al. [7] performed a three-dimensional numerical analysis to investigate the effects of blade diameter and blade curvature as well as the blade number and Reynolds number on power consumption. The authors concluded that the curvature of the blades had the most significant impact on power reduction and the efficiency of the mixing process. The energy consumption for an agitated vessel equipped with a pitched blade turbine and the performance impellers was the object of a detailed study in [8,9]. Due to their high-efficiency, the most high-speed turbine-type impellers are often used in industrial processes. Such a solution produces a radial-axial or radial-fluid motion. One of the well-known constructions is a Rushton turbine. However, due to the hopper formation for high rotational speed, quite often two to four baffles need to be used, which separate stirring areas. The stirred vessel geometry and the turbine shape and position of the blades or the number of turbines have been found to play an essential role in energy consumption and mixing intensity [10]. In the literature, only a small number of numerical and experimental studies deal with laminar mixing as a promising alternative to the more destructive turbulent mixing which also consumes more power [11]. For this type of flow regime, energy consumption can also be significantly decreased by modifying the shape of the impeller. In different studies, Ferrari and Rossi [12] and Rossi et al. [13] analyzed the mixing performance in a quasi-turbulent flow via the measurements of power input and output in the fluid. In the past, a mechanically agitated vessel design was limited to the mere empirical experiment, as a result of a deficiency reliable computational fluid dynamics models and the inadequacy of computer resources. At present, computer technology and advanced single-phase, multi-phase, or dispersion-phase models enable researchers to rely in the majority of cases on a numerical analysis in order to predict the hydrodynamics of more and more complex systems, replacing at the same time the number of the time-consuming and expensive experiments during the prototyping phase. On the other hand, due to the continuous increase in the complexity of the flow phenomenon, an experimental analysis is still required [14] as the final step of the analysis or of the optimization process. Energies 2020, 13, 640 3 of 19

Many researchers have made assessments of different turbulent models to the study mixing phenomena in stirred vessels. A. Delafosse et al. [15] performed a research study in the flow behavior during mixing between two adjacent compartments using CFD modelling. The results showed that the numerical model was capable of reproducing with reasonable accuracy the spatial distribution of concentrations during the mixing process, without any adjustable parameters. The analyses presented by H. Singh et al. [16] compared different turbulence models, including k–ε, exhibiting the accuracy of prediction for the mean axial and tangential velocities. Results obtained close to the impeller were very accurate but the numerical solution failed to predict the decay of the mean radial velocity away from the impeller. The authors noticed that the k–ε model predicted the random and periodic components of the kinetic energy of fluctuating motion poorly in the vicinity of the impeller. The k–ε model has also been compared to the RSTM (Reynolds Stress Turbulent Model) and LES (Large Eddy Simulation) in the work of B.N. Murthy et al. [17]. They found that the standard k–ε model under predicted the turbulent kinetic energy profile in the impeller region and failed to simulate the mean flow associated with the strong swirl. Current research studies have indicated the advantageous characteristics of stirred vessels with more than one impeller. Recent analyses have shown that the use of systems with many impellers can solve many technical mixing-related problems. Multiple-impeller systems require less energy per volume [18]. The typical stirred vessels with a single-impeller are often criticized because they generate non-uniform shear distribution, which is recognized as harmful, especially for the pharmaceutical and the cosmetics industry. The flow field in multiple-impeller systems is similar to that generated by the single-impeller systems, only when the distance between the impellers is larger than the diameter of the impeller. The required power of systems with multiple impellers is also dependent on the impeller clearance and for the distance of the impellers which is greater than one impeller diameter, the required power can be evaluated by a superposition of individual solutions [19]. However, for shorter distances, the power consumption is much smaller about 30–50% in reference to superposition. In [20] authors investigated the flow field and the power consumption in reference to the coaxial impeller (a double inner mixer with four-pitched-blade turbine and a Rushton turbine) in transitional to laminar flow regimes. The results show that the outer frame had a very small impact on the required power while the inner impeller behaved differently and had a large influence on the power required by the outer frame. In reference to the single rotation mode, the outer frame required a significant increase of power in the counter-rotation mode and a decrease of power in the co-rotation mode. The authors conclude that the co-rotation mode should be preferred because it generated a similar flow field but required much lower power. An interesting investigation of the mixing intensification with two coaxial mixers including an anchor was conducted in [21]. The mixing quality obtained for various configurations was assessed for the transitional to laminar flow regime in the co-rotating mode using experimental measurement and a computational fluid dynamic. The authors evaluated the functional correlation for the mixing efficiency in reference to complex configurations. Scale-up in laminar to transient flow regimes in the case of multi-impeller system has been conducted in [22]. A unique methodology of scale-up applied in reference to an industrial mixing vessel was proposed. One presented an approach that can be very helpful in reference to the process of scaling in situations when the hydrodynamic becomes essential. In review paper [23], the authors showed that the current analyses concentrated on the effect of the multiple-impeller combinations on the required power, mixing time, flow pattern, and mass transfer but there was still a need for future research on multiple-impeller systems in the aspects related to the different impellers geometries, numerical studies on the power and flow field, or studies on solid suspensions. In [24], the authors analyzed horizontal velocity fields in stirred vessels with helical coils using the particle image velocimetry method. They found that the flow pattern generated by the Rushton turbine was dominated by tangential flow structures and the cross-flow structures through cylindrical coils were not observed. The influence of various internal heat exchanger (heating plugs, helical pipe coils, pipe Energies 2020, 13, 640 4 of 19 registers) and stirred tank bottom geometries (flat, torispherical, hemispherical) on the velocity field and the kinetic energy of turbulence in agitated vessels were investigated [25] using stereo—Particle Image Velocimetry (PIV) experimental measurements. The research studies show advantages as well as disadvantages of various setup configurations which have a significant impact on the fluid flow and heat transport. The investigation of potentials in efficiency optimization for stirred vessels in laboratory-scale configuration is presented in [26]. The model was analyzed using PIV and LIF (laser-induced fluorescence) methods which give a good validation basis for CFD. In a large number of investigations, a particular effort was made in reference to the impeller geometry as well as the vessel shape. As a result, several new types for the impeller design and the vessel were proposed in the past. Astonishingly enough, the unbaffled vessel regarded in the past as less effective in reference to the baffled one recently turned out to be more effective. A new investigation has shown that unbaffled vessel but one equipped with an appropriately designed impeller can be an excellent alternative to the baffled vessel [27–29]. Recent analyses estimated that optimized impeller-vessel configuration without baffles for a complete mixture homogenization requires significantly lower energy [1,30]. This demonstrates the significant and unexplored potential of unbaffled vessels. Besides that, vessels with baffles are not recommended in applications where substantially a shear can significantly affect the quality of the product, for example, in reference to the production of drugs, creams, vitamins, and enzymes [31]. For that application, proper impeller design is a critical issue. In the literature, there is neither sufficient information on the optimal impeller design, particularly for unbaffled vessels, nor information concerning fluid phenomena in such vessels. However, for every industrial process the main goal is to find a nondestructive way of mixing which properly homogenizes the product, maintaining high product quality and using as low amounts of electrical power as possible. Thus, there is still a need for more research studies on the applications of impeller systems and on new novel geometries which ensures high-quality and effective mixing. Depending on what the mixing process has to carry out, it is appropriate to select different geometrical configurations. That is particularly crucial for unbaffled vessels, a solution which has been recommended recently for many applications. However, at present, there is a poor choice of impellers suitable for unbaffled vessels or various situations as well as operating conditions. In order to save time, materials, and environment, companies (pharmaceutical, chemical, and cosmetics) are interested in liquids mixing directly in tanks where liquids are transported. They search for impeller type to be suitable to (cylindrical and rectangular) vessels with a flat bottom and no baffles. For this reason, the present studies aimed to propose and analyze a novel impeller shape that has good efficiency and low power consumption for wide viscosity ranges. The developed impellers are suitable for a large variety of emulsions which are able to yield high-quality products. The present paper focused on mixing efficiency using the power number, capacity number, mean axial velocity, and mean radial velocity. An effect of impeller design on power characteristics and mixing efficiency for the Newtonian fluids at the low Reynolds number conditions in a mechanically agitated vessel was analyzed using the computational fluid dynamic and experimental measurement.

2. The Experimental Setup and Methodology The mechanically agitated vessel configuration is presented in Figure1, and the dimensions that were used are shown in Table1. As a working fluid in experimental and numerical analysis depending on the case, 100% glycerol (ρ = 1261.1 kg/m3, µ = 1.4101 Pa s), 30% propylene glycol solution, · and distilled water were used at the temperature 20 ◦C(+/ 0.2 ◦C). The distance between the impeller − 1 and the bottom of the stirred vessel h was, in this case, a dependent parameter and was equal to 4 H, 1 1 2 / 3 H, 2 H, and / 3 H of the fluid initial high H. Energies 2020, 13, x FOR PEER REVIEW 5 of 20

The stirred tank that was studied had smooth walls and no baffled pilots. The impeller was equipped with a six-bladed Rushton turbine (for case A) or with the three arms novel impellers (for cases B and C). The Novel impellers were a rescaled copy of the real impeller developed by the authorsEnergies 2020 for, 13the, 640 industry. The analyzed scale-down impellers were created using a 3D printer and5 had of 19 smooth plastic walls whose thickness was 2.0 mm.

D

Torque meter

Hc

H b a

d h z Torque meter table Tt r (a) (b)

FigureFigure 1. 1. SchematicSchematic diagram diagram of of the the experimental experimental setup setup wi withth a a Rushton Rushton turbine turbine and and an an agitated agitated vessel vessel ((a)) and and a a photo photo of of the experimental setup ( b).

Table 1. Dimensions of the stirred tank and the Rushton turbine. Table 1. Dimensions of the stirred tank and the Rushton turbine.

H, Hc H, Hc h h D, dD, d a a b c b c Symbol Symbol mm mm mm mm mmmm mmmm mm mmmm mm 1 1 1 2 H, / 3¼H H, , 1H/3 ,H,/ 3½H H, 2/3 H 170170 DimensionDimension 170, 300 170,4 300 2 12 1215 2 15 2 42, 57, 85,42, 11357, 85, 113 85 85

The stirred tank was installed on the specially designed table equipped with calibrated torque H H D meterThe FSA-2denotes (AXIS, max the fluid2 N∙m) level enabling while thec ismeasurement the total tank of heightthe vessel and causedis the by tank the analyzed diameter. d a b c, impellerThe impeller torque diameter with the is precision denoted of as 0.001. Additional N∙m and the geometrical sampling dimensionsfrequency of are 1000, Hz., Anheight, additional width, a b torqueand thickness meter (with for Rushton the precision turbine of blades 0.002and N∙m)and was installedare height in and a fully width controlled of the Novel-1 Hei-TORQUE impeller d d l Precisioncross-section 100 and electrical1 and motor2 refer towith the a diameter digital atover thehead entrance stirrer. and A exit monitoring to the Novel-0 system impeller ensured while a consistentis the impeller rotational length speed (see Figure independent2 and Table of2 inst forantaneous dimensions). fluid viscosity and the impeller shape duringThe measurements. stirred tank that was studied had smooth walls and no baffled pilots. The impeller was equippedTo evaluate with a the six-bladed mixing properties, Rushton turbine the velocity (for case field, A) as or well with as the the three pumping arms capacity, novel impellers the particle (for imagecases B velocimetry and C). The Novel(PIV) impellersmethod, was were used. a rescaled In order copy to of theminimize real impeller optical developed distortion by during the authors PIV measurement,for the industry. a cylindrical The analyzed stirred scale-down vessel (made impellers of 4-mm-thick were created plexiglass) using a 3D was printer installed and had inside smooth the squareplastic wallsvessels whose (made thickness of 3-mm-thick was 2.0 high-quality mm. glass) filled with water. This successfully reduced the unwantedThe stirred distortion tank was in installed the experiments on the specially and ensured designed after table conducting equipped 2D withcalibration calibrated procedure torque meter FSA-2 (AXIS, max 2 N m) enabling the measurement of the vessel caused by the analyzed high-quality seed double-images· for post-processing. impeller torque with the precision of 0.001 N m and the sampling frequency of 1000 Hz. An additional The instantaneous velocity in the axial ·and radial directions were measured in the tank (filled torque meter (with the precision of 0.002 N m) was installed in a fully controlled Hei-TORQUE Precision under no agitation conditions) with a fluid· at high H = D (in total about 5 L). It should be noticed that, due100 electricalto the rotation, motor with fluid a digitallevel close overhead to the stirrer. cylinder A monitoring wall increased. system Howe ensuredver, a all consistent the experiments rotational whosespeed independentresults are presented of instantaneous in this work fluid were viscosity cond anducted the for impeller a subcritical shape duringflow regime measurements. to avoid air To evaluate the mixing properties, the velocity field, as well as the pumping capacity, the particle image velocimetry (PIV) method, was used. In order to minimize optical distortion during PIV measurement, a cylindrical stirred vessel (made of 4-mm-thick plexiglass) was installed inside the square vessels (made of 3-mm-thick high-quality glass) filled with water. This successfully reduced Energies 2020, 13, 640 6 of 19 the unwanted distortion in the experiments and ensured after conducting 2D calibration procedure high-quality seed double-images for post-processing. Energies 2020, 13, x FOR PEER REVIEW 7 of 20

(a) (b)

H H b d1

a d2 d h d h

z D D r

l l

FigureFigure 2. The geometry2. The geometry of stirred of tank stirred with (tanka) Novel-1 with ( impellera) Novel-1 (squire impeller type) and(squire (b) Novel-0type) and impeller (b) Novel-0 (roundimpeller type). The (round top figure type). is The the top side figure view andis the the side bottom view oneand isthe the bottom top view. one is the top view.

Table 2.TableDimensions 2. Dimensions of the stirredof the stirred tank and tank Novel and impellers.Novel impellers.

H, D H, Dh h d d a/d1a/d1 b/db2/ d2 l l Impeller Type Impeller Type mm mmmm mm mm mmmm mm mmmm mm mm Novel-1 220Novel-1 22080 80 130 130 4040 30 3038 38 1 1 1 2 H, /220H , H, / 1 H3 2 3 85 Novel-0220Novel-0 4 3 2 ¼ H, 3 / H, ½ H,85 / H 1515 18 1840 40 The steady state of flow behavior inside the stirred tank can be described by governing equations Thefor instantaneousmass and momentum velocity conservation. in the axial andThe continuity radial directions equation, were for measureda 3D analysis, in the is as tank follows: (filled under no agitation conditions) with a fluid at high H = D (in total about 5 L). It should be noticed 𝜕𝑢 𝜕𝑢 𝜕𝑢 that, due to the rotation, fluid level close to the cylinder+ wall+ increased.=0 However, all the experiments (4) 𝜕𝑥 𝜕𝑥 𝜕𝑥 whose results are presented in this work were conducted for a subcritical flow regime to avoid air suckingFor from momentum the area conservation, above the free assumi surface.ng Asincompressible shown in the fluid, literature, the Navier–Stokes a large number equations of even are small given by: air bubbles may significantly influence PIV measurement as well as fluid properties. 𝐷𝑢 𝜕𝑢 𝜕𝑢 𝜕𝑢 𝜕𝑢 The seed particles (the diameter of glass hollow spheres was below 1 µm, ρ = 1020 kg/m3) were 𝜌 = +𝜇 + + , 𝑖 = 1,2,3 (5) illuminated with a double-pulse𝐷𝑡 Nd: YAG𝜕𝑥 laser of∂𝑥 the energy∂𝑥 of about∂𝑥 30 mJ per pulse. A vertical laser sheet (height, 200 mm; thickness, about 1 mm) was located in the center of the vessel directly where 𝑢 is the velocity component, respectively, in the 𝑖, 𝑗, and 𝑘 directions. The set of Equations illuminating the rotor shaft and completely shadowing the left-hand part of the tank. At present (4) and (5) is averaged using the Reynolds decomposition which allows separating mean and configuration, one CCD camera (La Vision) with a resolution of 2048 2048 pixels equipped with a fluctuating components of an instantaneous quantity. The Equations× (6) and (7) are, indeed, the 50-mm/1.2 lens was used. Laser light reflected from seed particles was acquired by the CCD camera, corresponding turbulence equations: installed perpendicularly to the plane of the light sheet. To determine the distribution of the velocity vectors, seed particles were registered by the CCD𝜕𝜌 camera𝜕𝜌𝑢 on two different and consecutive frames. + =0 (6) 𝜕𝑡 𝜕𝑥

Energies 2020, 13, 640 7 of 19

The measuring PIV system was subjected to testing and calibration procedures under fluid flow condition in order to evaluate the minimum number of acquired images required to ensure accurate statistics, as well as the optimal size of the interrogation window for the cross-correlation application. In each measurement, 100 frames were acquired with the CCD camera at a frequency of 5 Hz, which yielded the duration of a single measurement equal to 20 s. This duration and the number of frames were sufficient for an analysis at a low Reynolds number (Re = 10–1000) presented here. The time step ∆t between double frames varied depending on Reynolds number ranging from 500 up to 20,000 µs. During the calculations, the interrogation windows size that exhibited satisfying results varied from 32 32 pixels to 64 64 pixels and with an overlapping 25%. To analyze the time series of frames × × and to evaluate the velocity vector components, the Davis software ver. 8.0 with PIV/LIF module was used. In the mixing system analysis, there were two important criteria numbers: Power number Np and Reynolds number Re defined and calculated according to the following equations:

P Nd2ρ NP = ; Re = (1) ρN3d5 µ where ρ is the density (kg/m3), µ is the viscosity (kg/m s), N is the number of rotations per second (rot/s), · d is the maximum diameter of the impeller rotor (m), and P is the power (W) required to rotate the impeller with a specific rotational speed. It depends on the torque τ, and can be evaluated as follows:

P = 2π N τ (2) · · where τ is the torque (N m). · The third important parameter is the pumping capacity Q. It can be calculated for different Reynolds numbers through a cylindrical (vertical) surface with a specified radius r or through the horizontal surface at heights z. In the present configuration, the pumping capacity was evaluated through a horizontal surface (axial pumping capacity Qz) and for the height z = 0.01 m. Axial pumping capacity Qz can be obtained from PIV measurement by integrating the mean axial velocity over the whole horizontal positions, i.e., from r1 = 0 m to r2 = 0.085 m.

Z r2 Qz = uz dS (3) r1 | |

It is also common to normalize this parameter with rotational speed and the impeller diameter, i.e., N d3 yielding one of the global flow characteristics. · 3. Numerical Modelling The mechanically agitated vessel configuration is presented in Figure2a,b, and the dimensions used are shown in Table2. For presented results, water was used as a working fluid with a viscosity at a selected temperature. For numerical analyses, the distance between the impeller and the bottom of the tank h was equal to 80 mm. The steady state of flow behavior inside the stirred tank can be described by governing equations for mass and momentum conservation. The continuity equation, for a 3D analysis, is as follows:

∂u ∂u ∂u 1 + 2 + 3 = 0 (4) ∂xi ∂xj ∂xk

For momentum conservation, assuming incompressible fluid, the Navier–Stokes equations are given by:    2 2 2  Dui ∂ui ∂ ui ∂ ui ∂ ui  ρ = + µ + + , i = 1, 2, 3 (5) Dt ∂x  2 2 2  ∂xi ∂xj ∂xk Energies 2020, 13, 640 8 of 19 Energies 2020, 13, x FOR PEER REVIEW 8 of 20 where u is the velocity component, respectively, in the i, j, and k directions. The set of Equations (4) i 𝜕𝜌𝑢 𝜕𝜌𝑢 𝑢 and (5) is averaged using the+ Reynolds decomposition which allows separating mean and fluctuating components of an instantaneous𝜕𝑡 𝜕𝑥 quantity. The Equations (6) and (7) are, indeed, the corresponding turbulence equations: 𝜕𝑝 𝜕 𝜕𝑢 𝜕𝑢 2 𝜕𝑢 (7) =− ∂ρ+ ∂(ρu𝜇i) + − 𝛿 𝜕𝑥 +𝜕𝑥 =𝜕𝑥0 𝜕𝑥 3 𝜕𝑥 (6) 𝜕 ∂t ∂x   ∂ ρu u + −𝜌𝑢" 𝑢 !#   ∂(ρui) i j ∂𝜕𝑥p ∂ ∂ui ∂uj 2 ∂uk ∂ + = + + + 0 0 µ δij ρui uj (7) ∂t ∂xj −∂xi ∂xj ∂xj ∂xi − 3 ∂xk ∂xj − This procedure generated additional unknowns that needed to be solved and required the turbulenceThis procedure model flow generated problem additional closure. The unknowns last term that in neededEquation to (7) be is solved a second-order and required tensor, the turbulencederivative with model respect flow to problem xj, it defines closure. the turbulence The last term effect, in and Equation it is known (7) is aas second-orderthe Reynolds tensor,stress. derivativeTo determine with the respect value to ofx j,the it definesReynolds the stress turbulence we used effect, the and k-ε it model, is known which as the has Reynolds the following stress. Toequation: determine the value of the Reynolds stress we used the k-ε model, which has the following equation:   " ! # 𝜕 𝜌𝑘∂(ρk) 𝜕𝜌𝑘𝑢∂ ρkuj 𝜕∂ µ𝜇t ∂k𝜕𝑘 + + == µ𝜇++ +G+𝐺k ρε−𝜌𝜀 (8)(8) 𝜕𝑡 ∂t 𝜕𝑥∂xj 𝜕𝑥∂xj σ𝜎k ∂x𝜕𝑥j −

𝜕𝜌𝜀 𝜕𝜌𝜀𝑢  𝜕 " 𝜇 𝜕𝜀# 𝜀 ∂(ρε) ∂ ρε uj  µ  2 + = ∂𝜇+ t ∂ε +𝜌𝑐𝑠 −𝜌𝑐ε (9) 𝜕𝑡 +𝜕𝑥 =𝜕𝑥 µ + 𝜎 𝜕𝑥 + ρc1sε ρc2 (9) ∂t ∂xj ∂xj σε ∂xj − k + √𝑘+vε √𝑣𝜀 h η i p where 𝑐 = 𝑚𝑎𝑥 0.43 ,𝜂 =𝑠k ,𝑠 =2𝑠𝑠 and where 𝐺 is the generation of kinetic energy of where c1 = max 0.43 η+5 , η = s ε, s = 2sijsij and where Gk is the generation of kinetic energy of turbulence k𝑘due due to to mean meanvelocity velocity gradientsgradients and µ𝜇trepresents represents the the turbulent turbulent viscosity.viscosity. TheThe constant values typically used in k-ε model are c𝑐1ε ==1.441.44, ,c 2𝑐==1.91.9, σ, k𝜎= =11, and, andσε 𝜎= =1.21.2. . The set of Equations (6)–(9) consists of 6 equations that need to be discretized discretized and solved in order to obtainobtain aa solution solution for for the the velocities velocities and and pressure. pressu Ansysre. Ansys Fluent Fluent was used was asused a flow as solver.a flow Tosolver. produce To aproduce reliable a modelreliable to model study to the study flow the generated flow generated by the novelby the impellers,novel impellers, the simulation the simulation results results were comparedwere compared with the with results the results presented presented in the literature in the literature for the Rushton for the turbineRushton (RT). turbine For the(RT). validation For the analysis,validation the analysis, same as the in literature,same as in flow literature, and boundary flow and conditions boundary were conditions used: Water were as used: a working Water fluidas a withworking a viscosity fluid with of µ a= viscosity0.001003 of kg μ/(m = 0.001003s) and a densitykg/(m∙s) of andρ = a998.2 density kg/m of3. ρ The = 998.2 vessel kg/m diameter3. The wasvesselD · =diameter27 cm, andwas equal D = 27 to cm, the and height equalH ( Dto =theH ).height The impeller H (D = H was). The installed impeller centrally, was installed and a rotorcentrally, diameter and wasa rotor 9.3 diameter cm. The impellerwas 9.3 speedcm. The was impeller considered speed as was a parameter considered and as the a parameter Reynolds numberand the calculatedReynolds fromnumber Equation calculated (1) was infrom the rangeEquation from Re(1)= 1–100,000.Computationwas in the range algridfrom was Re tested = for1–100,000. various resolutions,Computationalgridwastestedforvarious and the final resolution was resolutions, the middle resolutionandthe final which resolution consisted ofwas 190,000 the controlmiddle volumesresolution (Figure which3 consisted). of 190,000 control volumes (Figure 3).

(a) (b)

Figure 3. Mesh of the computationalcomputational domain for ComputationalComputational Fluid Dynamics (CFD) simulation global view (a) and inside the domaindomain ((b).).

Energies 2020, 13, x FOR PEER REVIEW 9 of 20

4. Results and Discussion

4.1. CFD Modelling The main goal for every industrial process related to the mixing is to find the most efficient way Energies 2020, 13, 640 9 of 19 of mixing using as low power as possible and, at the same, maintaining the high quality of the product. Power required by the impeller is related to the power number Np. Figure 4 shows the power 4.number Results N andp, calculated Discussion for various Reynolds numbers in reference to the Rushton turbine and a new impeller (Novel-1). The results were also compared with the experimental data for the Rushton 4.1.turbine CFD available Modelling in the literature [10]. One can infer from this figure that the prediction for the RushtonThe mainturbine goal is compatible for every industrial with CFD processnumerical related results. to theThe mixing power isnumber to find N thep and most Reynolds efficient Re waynumber of mixing were calculated using as low according power asto possibleEquation and, (1). at the same, maintaining the high quality of the product.In reference Power required to laminar, by the transient, impeller isand related turbul to theent powerflow regimes, number Nonep. Figuremay discern4 shows that the powerpower numbernumberN Npp, at calculated low Reynolds for various numbers Reynolds depended numbers on the inReynolds reference number to the and Rushton for the turbine Novel-1 and impeller a new impellerwas about (Novel-1). 6–10 times The lower results than were for also the compared Rushton with turbine. the experimental The power number data for theNp for Rushton the turbulent turbine availableflow regime in the remained literature constant. [10]. One The can power infer fromdecrease this figurefor Novel-1 that the impeller prediction was forsignificant the Rushton and turbineapplied isto compatible both laminar with and CFD turbulent numerical flow results.regimes. The power number Np and Reynolds Re number were calculated according to Equation (1).

1000 CFD Lit. Data CFD Baffled RT CFD Novel-1 Impeller 100 CFD Unbaffled RT p N 10

1

0 1 10 500 10000 40000 Re Figure 4. A comparison of power number Np of CFD predictions with literature data [10]. Figure 4. A comparison of power number Np of CFD predictions with literature data [10]. In reference to laminar, transient, and turbulent flow regimes, one may discern that power number The lower power number Np for Novel-1 impeller denotes that the turbine required less energy. Np at low Reynolds numbers depended on the Reynolds number and for the Novel-1 impeller was However, this parameter was not related to fluid mixing phenomena and the above-mentioned about 6–10 times lower than for the Rushton turbine. The power number Np for the turbulent flow information is important but not sufficient to describe a new impeller as a device that represents regime remained constant. The power decrease for Novel-1 impeller was significant and applied to higher efficiency. For that reason, it is worthwhile to keep track of the pumping capacity Q parameter both laminar and turbulent flow regimes. (see Equation (3)) which was directly related to the fluid motion and mixing phenomena. Figure 5 The lower power number Np for Novel-1 impeller denotes that the turbine required less energy. shows the normalized (by the factor Nd3) radial pumping capacity Qr for different Reynolds number However, this parameter was not related to fluid mixing phenomena and the above-mentioned through a cylindrical surface with a radius of 0.05 m. As can be seen, the Novel-1 impeller yielded information is important but not sufficient to describe a new impeller as a device that represents higher for a low Reynolds number, which was very promoted due to nondestructive mixing, a much higher efficiency. For that reason, it is worthwhile to keep track of the pumping capacity Q parameter (see value (up to 2.3 times) than for the Rushton turbine. However, for a Reynolds number above 750 Equation (3)) which was directly related to the fluid motion and mixing phenomena. Figure5 shows (above the range important for 3very high viscous fluids mixing) evaluated pumping capacity Qr was the normalized (by the factor Nd ) radial pumping capacity Qr for different Reynolds number through lower for Novel-1 impeller than for the Rushton turbine. a cylindrical surface with a radius of 0.05 m. As can be seen, the Novel-1 impeller yielded for a low Reynolds number, which was very promoted due to nondestructive mixing, a much higher value (up to 2.3 times) than for the Rushton turbine. However, for a Reynolds number above 750 (above the range important for very high viscous fluids mixing) evaluated pumping capacity Qr was lower for Novel-1 impeller than for the Rushton turbine.

Energies 2020, 13, 640 10 of 19 Energies 2020, 13, x FOR PEER REVIEW 10 of 20

30 CFD Novel Impeller 25 CFD Unbaffled RT

20 3 /Nd

r 15 Q

10

5

0 1 10 500 10000 40000 Re

Figure 5. Normalized radial pumping capacity in the function of the Reynolds number. Figure 5. Normalized radial pumping capacity in the function of the Reynolds number. After exceeding the value of Re = 500, the dynamics of the increase in the amount of yield pumping After exceeding the value of Re = 500, the dynamics of the increase in the amount of yield capacitypumping decreased. capacity For decreased. the Novel-1 For the impeller, Novel-1 there impe wasller, there a strong was relationshipa strong relationship between between Reynolds numberReynoldsRe and number power Re number and powerNp ,number and thus Np, and with thus the with impeller the impeller pumping pumping capacity capacity such such that that with increasingwith Reynoldsincreasing numberReynoldsRe numberdecreased Re decreased the power the number power numberNp and therebyNp and thereby the impeller the impeller pumping capacitypumping increased capacity up toincreased the limit up value to the equallimit value to Re equal= 500. to Re Further = 500. Further increase increase of Re caused of Re caused a gradual a reductiongradual in the reduction value ofin pumpingthe value of capacity. pumping capacity. FigureFigure6 presents 6 presents the mixing the mixing e ffi efficiencyciency calculated calculated asas aa ratioratio between the the normalized normalized pumping pumping capacitycapacity and the and power the power number number for for the the Rushton Rushton turbine turbine andand Novel-1 impeller. impeller. One One can can infer infer from from this figure a very high efficiency for the Novel-1 impeller for all fluid flow regimes analyzed in this this figure a very high efficiency for the Novel-1 impeller for all fluid flow regimes analyzed in this work. The mixing efficiency for Novel-1 impeller increased very fast with the Reynolds number and work. The mixing efficiency for Novel-1 impeller increased very fast with the Reynolds number and for a higher value it remained constant. The high efficiency was related with the jet stream leaving for a higherthe impeller value which it remained strongly constant. interacted Thewith highthe ta enkffi andciency generated was related a high withenergy the dissipation jet stream next leaving to the impellerand below which the stronglynew impeller interacted (compare with with the Figure tank 8) and. This generated showed that a high the energyNovel-1 dissipation impeller can next be to and belowconsidered the new a very impeller promising (compare device withfor mixing Figure for 8). low This as well showed as for thathigh theReynolds Novel-1 numbers. impeller can be Energies 2020, 13, x FOR PEER REVIEW 11 of 20 consideredFigure a very 7 promisingshows the velocity device forvectors mixing for Novel-1 for low impeller as well asat rotational for high Reynoldsspeed N = numbers.200 rpm (Re = 28,692) in an x–y cross-section plane for the distance z = 7 cm from the vessel bottom and in y–z cross- section plane for φ25 = 0° and 180°. One may obtain from this figure a high-velocity magnitude in the internal part of the channel type blades of the impeller.CFD Novel-1 impeller CFD Unbaffled Rushton Turbine 20

15

E, % E, 10

5

0 5 10 50 500 5000 10000 28692 40000 65000 Re

Figure 6. FigureThe 6. The efficiency efficiency comparison comparison for for Rushton Rushton turbineturbine and Novel-1 Novel-1 impeller impeller as asa function a function of of ReynoldsReynolds number. number.

Velocity Velocity magnitude 0.24 magnitude z

0 -0.11 0 0.11 y

(a) (b)

Figure 7. The velocity vectors in x–y (a) and y–z (b) cross-section plane for rotational speed at Re = 28,692.

In Figure 8 the velocity vectors from the particle image velocimetry experimental measurements in the y–z cross-section plane for φ = 0° and two rotational speeds, N = 200 (Re = 28,692) and 400 rpm (Re = 57,384) are presented for the Rushton turbine and the Novel-1 impeller. One may be observed as a high axial motion as well as a high radial one created by the Novel-1 impeller. In Figure 8d a clear fluid “ejection” out the rotor zone towards the tank walls is seen. This is consistent with the numerical predictions and shows a very high mixing potential for the novel impeller. In reference to the fluid motion presented in Figure 8d, much lower velocities are observed in Figure 8b for Rushton turbine at the same Reynolds number. Apart from flow motion in the case of the Rushton turbine, the fluid was divided into two large co-rotating zones, one above and one below the impeller. Unfortunately, the fluid above and below impeller were not mixed with each other properly, which was the significant drawback of this configuration. This phenomenon was also seen at a lower rotational speed of 200 rpm (at Re = 28,692) presented in Figure 8a. One can infer from Figure 8c,d that the Novel-1 impeller was free from this drawback and fluid mixing occurred in the whole domain.

Energies 2020, 13, x FOR PEER REVIEW 11 of 20

25 CFD Novel-1 impeller CFD Unbaffled Rushton Turbine 20

15

E, % E, 10

5

Energies 2020, 13, 640 11 of 19 0 5 10 50 500 5000 10000 28692 40000 65000 Figure7 shows the velocity vectors for Novel-1Re impeller at rotational speed N = 200 rpm (Re = 28,692) in an x–y cross-section plane for the distance z = 7 cm from the vessel bottom and in y–z cross-sectionFigure 6. plane The efficiency for ϕ = 0 ◦comparisonand 180◦. Onefor Rushton may obtain turbine from and this Novel-1 figure aimpeller high-velocity as a function magnitude of in the internalReynolds part number. of the channel type blades of the impeller.

Velocity Velocity magnitude 0.24 magnitude z

0 -0.11 0 0.11 y

(a) (b)

Figure 7.7. TheThe velocityvelocity vectors vectors in inx– yx–(ay) ( anda) andy–z y(b–z) cross-section(b) cross-section plane plane for rotational for rotational speed atspeedRe = at28,692. Re = 28,692. In Figure8 the velocity vectors from the particle image velocimetry experimental measurements in theIny –Figurez cross-section 8 the velocity plane vectors for ϕ = from0◦ and the two partic rotationalle image speeds, velocimetryN = 200 experimental (Re = 28,692) measurements and 400 rpm (inRe the= 57,384) y–z cross-section are presented plane for for the φ Rushton = 0° and turbine two rotational and the Novel-1speeds, N impeller. = 200 (Re One = 28,692) may be and observed 400 rpm as a(Re high = 57,384) axial motionare presented as well for as the a high Rushton radial turbine one created and the by Novel-1 the Novel-1 impeller. impeller. One Inmay Figure be observed8d a clear as fluida high “ejection” axial motion out theas well rotor as zone a high towards radial the one tank created walls by is seen.the Novel-1 This is consistentimpeller. In with Figure the numerical8d a clear predictionsfluid “ejection” and out shows the rotor a very zone high towards mixing the potential tank walls for theis seen. novel This impeller. is consistent In reference with the to numerical the fluid motionpredictions presented and shows in Figure a very8d, high much mixing lower potential velocities for are the observed novel impeller. in Figure 8Inb forreference Rushton to turbinethe fluid atmotion the same presented Reynolds in Figure number. 8d, much Apart lower from velocities flow motion are inobserved the case in of Figure the Rushton 8b for Rushton turbine, turbine the fluid at wasthe same divided Reynolds into two number. large co-rotatingApart from zones, flow motion one above in the and case one ofbelow the Rushton the impeller. turbine, Unfortunately, the fluid was thedivided fluid into above two and large below co-rotating impeller werezones, not one mixed abov withe and each one other below properly, the impelle whichr. Unfortunately, was the significant the drawbackfluid above of and this below configuration. impellerThis were phenomenon not mixed with was each also seenother at properly, a lower rotational which was speed the ofsignificant 200 rpm

(atdrawbackEnergiesRe = 202028,692) of, 13 this, x FOR presented configuration. PEER REVIEW in Figure This 8 phenomenona. One can infer was from also Figureseen at8 ac,d lower that rotational the Novel-1 speed impeller of 12200 of was rpm 20 free(at Re from = 28,692) this drawback presented and in Figure fluid mixing 8a. One occurred can infer in from the whole Figure domain. 8c,d that the Novel-1 impeller was free from this drawback and fluid mixing occurred in the whole domain. 0.24 0.24 0.24 0.24 (a) (b) (c) (d)

z z z z

0 0 0 0 0 0 0 0 y 0.125 y 0.125 0 y 0.125 y 0.125

Figure 8. The velocity field from experimental measurement at Re = 28,692 (a,c) and at Re = 57,384 (Figureb,d) for 8. the The Rushton velocity turbine field from (a,b) experimental and the Novel-1 measurement impeller (c at,d ).Re = 28,692 (a,c) and at Re = 57,384 (b,d) for the Rushton turbine (a,b) and the Novel-1 impeller (c,d).

4.2. The Efficiency of Mixing Process The impeller which was analyzed in this work was equipped with a six-bladed Rushton turbine (case A) or the three-blade Novel impeller referred to as Novel-0 (case C). This innovative impeller was a rescaled copy of a new impeller type proposed for the industry. Laboratory tests were carried out for the mechanically agitated vessel, in reference to the configuration presented in Figure 1. The dimensions which were used are shown in Table 2. The series of measurements were performed for various distances of the impeller from the bottom of the tank h and at a different rotational speed. The rotors for this analysis were placed at the heights of h equal to ¼ H, 1/3 H, and ½ H of the fluid initial high H. The impact of the vertical position of the impeller in the tank on the mixing efficiency was assessed. It was possible to compare the operation of Novel-0 impeller with reference to the Rushton turbine treated here as a reference impeller. For the mixing efficiency analysis, all essential criteria numbers were evaluated: The power number Np, the Reynolds number Re, as well as the pumping capacity Q (or normalized pumping capacity) and finally the mixing efficiency E. The pumping capacity for the presented configuration was calculated for different Reynolds numbers through a horizontal surface (axial pumping capacity Qz) and for the height h equal to 1 cm above the vessel bottom. Pumping capacity was evaluated using the velocity obtained from the PIV measurement by integrating the mean axial velocity over the whole horizontal plane, i.e., from axis r1 = 0 m up to vessel wall r2 = 0.085 m. From the point of view of the industry, the most important parameter for assessing the mixing process is the power required by the impeller to generate fluid motion. This parameter was evaluated based on direct torque measurements. The power number and the normalized pumping capacity Qz for the analyzed impellers are shown in Figures 9 and 10. The mean axial pumping capacity Qz through a horizontal surface located 1 cm above vessel bottom and dimensionalized by the N∙d3 increased significantly with the Reynolds number. Values obtained from experimental measurements for the Novel-0 impeller were substantially higher in reference to the Rushton turbine. For the Reynolds number equal to 100, the difference was as high as one order of magnitude and increased with rotational speed. Therefore, the Novel-0 impeller for analogical rotational speed resulted in a remarkably higher flow motion which significantly enhanced the mixing process. That is the essential impeller advantage which is particularly important for the mixing process realization, for example, during the production of pharmaceuticals, where a technological process cannot be destructive or take a long time and rotational speed has to be low.

Energies 2020, 13, 640 12 of 19

4.2. The Efficiency of Mixing Process The impeller which was analyzed in this work was equipped with a six-bladed Rushton turbine (case A) or the three-blade Novel impeller referred to as Novel-0 (case C). This innovative impeller was a rescaled copy of a new impeller type proposed for the industry. Laboratory tests were carried out for the mechanically agitated vessel, in reference to the configuration presented in Figure1. The dimensions which were used are shown in Table2. The series of measurements were performed for various distances of the impeller from the bottom of the tank h and at a different rotational speed. The rotors for this analysis were placed at the heights 1 1 1 of h equal to 4 H, / 3 H, and 2 H of the fluid initial high H. The impact of the vertical position of the impeller in the tank on the mixing efficiency was assessed. It was possible to compare the operation of Novel-0 impeller with reference to the Rushton turbine treated here as a reference impeller. For the mixing efficiency analysis, all essential criteria numbers were evaluated: The power number Np, the Reynolds number Re, as well as the pumping capacity Q (or normalized pumping capacity) and finally the mixing efficiency E. The pumping capacity for the presented configuration was calculated for different Reynolds numbers through a horizontal surface (axial pumping capacity Qz) and for the height h equal to 1 cm above the vessel bottom. Pumping capacity was evaluated using the velocity obtained from the PIV measurement by integrating the mean axial velocity over the whole horizontal plane, i.e., from axis r1 = 0 m up to vessel wall r2 = 0.085 m. From the point of view of the industry, the most important parameter for assessing the mixing process is the power required by the impeller to generate fluid motion. This parameter was evaluated based on direct torque measurements. The power number and the normalized pumping capacity Qz for the analyzed impellers are shown in Figures9 and 10. The mean axial pumping capacity Qz through a horizontal surface located 1 cm above vessel bottom and dimensionalized by the N d3 increased significantly with the Reynolds · number. Values obtained from experimental measurements for the Novel-0 impeller were substantially higher in reference to the Rushton turbine. For the Reynolds number equal to 100, the difference was as high as one order of magnitude and increased with rotational speed. Therefore, the Novel-0 impeller for analogical rotational speed resulted in a remarkably higher flow motion which significantly enhanced the mixing process. That is the essential impeller advantage which is particularly important for the mixing process realization, for example, during the production of pharmaceuticals, where a Energies 2020, 13, x FOR PEER REVIEW 13 of 20 technological process cannot be destructive or take a long time and rotational speed has to be low.

1.4 RushtonTurbine 1.2 Novel-0 impeller

1 h=1/3H

3 0.8 /Nd z

Q 0.6

0.4

0.2

0 0 20 40 60 80 100 120 140 Re

Figure 9. Normalized pumping capacity Qz evaluated from experimental measurements as a function Figure 9. Normalized pumping capacity1 Qz evaluated from experimental measurements as a function of the Reynolds number and for h = / 3 H. of the Reynolds number and for h = 1/3 H.

8 Ruston Turbine 7 Novel-0 impeller 6 h=1/3H 5 p

N 4

3

2

1

0 0 50Re 100 150

Figure 10. The power number Np obtained from experimental measurement as a function of the

Reynolds number and for h = 1/3 H.

Another important parameter which was directly related to the power required by the mixing process was the power number Np. In Figure 10 this parameter is shown as a function of the Reynolds number. Results are presented for the Rushton turbine and the Novel-0 impeller at a constant distance above the vessel bottom equal to 1/3 H (57 mm). For other distances associated with impeller very similar results were obtained (in the trend of volatility). Based on experimental data, it was clearly seen that the power number Np depended on the Reynolds number. For a higher Reynolds number, a lower power number was observed. The power number Np for both impellers Novel-0 and Rushton turbine showed a very similar value. Although the required power was very similar, the flow motion generated by the impellers was very different. This effect was observed for all impeller distances from the bottom of the tank that were analyzed in this work. When the power consumption required to mix the fluid decreased, at the same time the internal heat generation decreased and the mixing

Energies 2020, 13, x FOR PEER REVIEW 13 of 20

1.4 RushtonTurbine 1.2 Novel-0 impeller

1 h=1/3H

3 0.8 /Nd z

Q 0.6

0.4

0.2

0 0 20 40 60 80 100 120 140 Re

Figure 9. Normalized pumping capacity Qz evaluated from experimental measurements as a function Energies 2020, 13, 640 13 of 19 of the Reynolds number and for h = 1/3 H.

8 Ruston Turbine 7 Novel-0 impeller 6 h=1/3H 5 p

N 4

3

2

1

0 0 50Re 100 150

Figure 10. The power number N obtained from experimental measurement as a function of the Figure 10. The power number pNp obtained from experimental measurement as a function of the 1 ReynoldsReynolds number number and and for hfor= h /=3 1H/3 H. .

AnotherAnother important important parameter parameter which which was was directly directly related to to the the power power required required by bythe themixing mixing processprocess was the was power the power number numberNp .N Inp. In Figure Figure 10 10 this this parameterparameter is is shown shown as as a function a function of the of theReynolds Reynolds number.number. Results Results are presented are presented for for the th Rushtone Rushton turbine turbine andand the Novel-0 Novel-0 im impellerpeller at a at constant a constant distance distance above the vessel bottom equal 1to 1/3 H (57 mm). For other distances associated with impeller very above the vessel bottom equal to / 3 H (57 mm). For other distances associated with impeller very similarsimilar results results were were obtained obtained (in (in the the trend trend of of volatility). volatility). Based on on experimental experimental data, data, it was it was clearly clearly seen that the power number Np depended on the Reynolds number. For a higher Reynolds number, seen that the power number Np depended on the Reynolds number. For a higher Reynolds number, a lower power number was observed. The power number Np for both impellers Novel-0 and Rushton a lower power number was observed. The power number N for both impellers Novel-0 and Rushton turbine showed a very similar value. Although the required ppower was very similar, the flow motion turbinegenerated showed by a verythe impellers similar was value. very Although different. This the requiredeffect was power observed was for very all impeller similar, distances the flow from motion generatedthe bottom by the of impellers the tank wasthat were very analyzed different. in This this ework.ffectwas When observed the power for consumption all impeller distancesrequired to from the bottommix the of fluid the tank decreased, that were at the analyzed same time in this the work.internal When heat thegeneration power consumptiondecreased and required the mixing to mix the fluid decreased, at the same time the internal heat generation decreased and the mixing system required a smaller electrical motor, smaller gears, shaft, etc. All of these items minimize investment cost and operating cost. 3 The ratio of the Qr/N d to Np, i.e., nondimensional pumping capacity to the nondimensional · power, can be considered as a mixing efficiency parameter E. This ratio for the Novel-0 impeller and for the Rushton turbine is presented in Figures 11 and 12, respectively, as a function of the Reynolds number and for various impeller distances from the bottom of the vessel. It can be seen that the mixing efficiency strongly depended on the Reynolds number and impeller distance h from the tank bottom. For selected configurations, an almost 10-times greater efficiency for the Novel-0 impeller in reference to the Rushton turbine was observed. In Figures 11 and 12, the points represent the experimental data, while the individual lines represent a model fitting to all experimental results. For both the Rushton turbine and the Novel-0, impeller nonlinear semi-exponential functions were proposed as a best-fitting function. The empirical equation for mixing efficiency evaluation for Rushton turbine as a function of Reynolds number Re and normalized distance h/H between impeller and vessel bottom can be presented as follows:

1.15 E(Re, h) = 0.08 Re (h/H)− (10) · · where H is the initial fluid height (under no agitation conditions) and h is the distance between impeller and tank bottom. Coefficient of correlation R2 for the Equation (10) is equal to 0.887. Energies 2020, 13, x FOR PEER REVIEW 14 of 20

system required a smaller electrical motor, smaller gears, shaft, etc. All of these items minimize investment cost and operating cost. The ratio of the Qr/N∙d3 to Np, i.e., nondimensional pumping capacity to the nondimensional power, can be considered as a mixing efficiency parameter E. This ratio for the Novel-0 impeller and for the Rushton turbine is presented in Figures 11 and 12, respectively, as a function of the Reynolds number and for various impeller distances from the bottom of the vessel. It can be seen that the mixing efficiency strongly depended on the Reynolds number and impeller distance h from the tank bottom. For selected configurations, an almost 10-times greater efficiency for the Novel-0 impeller in reference to the Rushton turbine was observed. In Figures 11 and 12, the points represent the experimental data, while the individual lines represent a model fitting to all experimental results. For both the Rushton turbine and the Novel-0, impeller nonlinear semi-exponential functions were proposed as a best-fitting function. The empirical equation for mixing efficiency evaluation for Rushton turbine as a function of Reynolds number Re and normalized distance h/H between impeller and vessel bottom can be presented as follows:

𝐸𝑅𝑒, ℎ =0.08∙𝑅𝑒∙ℎ/𝐻. (10) where H is the initial fluid height (under no agitation conditions) and h is the distance between impeller and tank bottom. Coefficient of correlation R2 for the Equation (10) is equal to 0.887. A similar empirical equation for the mixing efficiency has been proposed for the Novel-0 impeller in the form as follows: 𝐸𝑅𝑒, ℎ = 0.0048 ∙ 𝑅𝑒 ∙ ℎ/𝐻.. (11)

The coefficient of correlation R2 for the Equation (11) is equal to 0.89. Equations (10) and (11) allow us to calculate mixing efficiency at any impeller height. One may discern that there is, for specified Reynolds number, an optimal impeller height which ensures the highest efficiency. Increasing impeller distance above or below this value results in mixing efficiency decrease. It can be observed that installing each of the impellers at a height equal to 2/3 H and 1/2 H caused similar and relatively low mixing efficiency. The most significant differences can be seen for impellers positions of 1/3 H and 1/4 H, respectively. At that range, dynamic increase in the value of E was observed with the increase of Re. One should notice that the highest mixing efficiency which was observed in reference to the Rushton turbine and in reference to the Novel-0 impeller was 6.1% and 59.0%, respectively, which demonstrated a huge potential as far as the improvement of the mixing process Energiesas2020 well, 13 as, 640the reduction of the energy consumption and operating cost are concerned. 14 of 19

70 Novel-0 impeller 60 h=1/4H h=1/3H 50 h=1/2H h=2/3H 40

E, [%] E, 30

20

10

0 Energies 2020, 13, x FOR PEER REVIEW 15 of 20 1 21 41 61 81 101 121 141 161 Figure 11. The mixing efficiency evaluated from experiRemental measurement for the Novel-0 impeller Figureand 11. differentThe mixing distances effi fromciency the evaluated tank bottom. from experimental measurement for the Novel-0 impeller and different distances from the tank bottom.

7 Rushton Turbine

6 h=1/4H h=1/3H 5 h=1/2H h=2/3H e247 4

3 E, [%] E,

2

1

0 0 20 40 60 80 100 120 140 Re

Figure 12. The mixing efficiency evaluated from experimental measurement for the Rushton turbine Figure 12. The mixing efficiency evaluated from experimental measurement for the Rushton turbine and diandfferent different distances distances from from the the tank tank bottom. bottom.

4.3.A similar The Power empirical Number equation in Relation for to the Impeller mixing Geometry efficiency has been proposed for the Novel-0 impeller in the form as follows: In order to evaluate the characteristic of impellers, a much1.65 larger Reynolds number range had E(Re, h) = 0.0048 Re (h/H)− . (11) to be implemented. In this section, an analysis of the· experiments· similar to those described above wasThe coeperformedfficient ofbut correlation this time forR2 forReynolds the Equation numbers (11) whose is equal value to 0.89.was Equationsup to 100,000 (10) and and using (11) allow us todifferent calculate fluids mixing (100% effi ciencyglycerol, at 30% any impellerpropylene height. glycol Onesolution, may and discern distilled that water) there is,all for in specifiedthe Reynoldssubcritical number, regime. an optimalThe results impeller obtained height from whichthe experimental ensures the measurement highest effi forciency. the Rushton Increasing turbine impeller and the Novel-0 impeller are presented in Figures 13 and 14. distance above or below this value results in mixing efficiency decrease. It can be observed that 2 1 installing each of the impellers at a height equal to /3 H and /2 H caused similar and relatively low 1 1 mixing efficiency. The14 most significant differences can be seen for impellers positions of /3 H and /4 H, respectively. At that range, dynamic increase in the value ofRushtonE was turbine observed with the increase of Re. One should notice that12 the highest mixing efficiency which was observed in reference to the Rushton turbine and in reference to the Novel-0 impeller was 6.1% and 59.0%, respectively, which demonstrated 10 a huge potential as far as the improvement of the mixing process as well as the reduction of the energy

consumption and operatingp 8 cost are concerned. N

6

4

2

0 1 10 100 1000 10,000 100,000 1 10 100 1000 10000 100000 Re

Energies 2020, 13, x FOR PEER REVIEW 15 of 20

Figure 11. The mixing efficiency evaluated from experimental measurement for the Novel-0 impeller and different distances from the tank bottom.

7 Rushton Turbine

6 h=1/4H h=1/3H 5 h=1/2H h=2/3H e247 4

3 E, [%] E,

2

1

0 0 20 40 60 80 100 120 140 Re

Energies 2020,Figure13, 640 12. The mixing efficiency evaluated from experimental measurement for the Rushton turbine 15 of 19 and different distances from the tank bottom.

4.3. The4.3. Power The Power Number Number in Relation in Relation to theto the Impeller Impeller Geometry Geometry In orderIn order to evaluate to evaluate thecharacteristic the characteristic of impellers,of impellers, a mucha much larger larger Reynolds Reynolds numbernumber range range had had to be implemented.to be implemented. In this section,In this section, an analysis an analysis of the of experiments the experiments similar similar to thoseto those described described above above was performedwas performed but this time but forthis Reynoldstime for Reynolds numbers nu whosembers valuewhose was value up was to 100,000up to 100,000 and using and using different fluids (100%different glycerol, fluids (100% 30% propylene glycerol, 30% glycol propylene solution, glycol and distilledsolution, water) and distilled all in the water) subcritical all in regime.the The resultssubcritical obtained regime. from The theresults experimental obtained from measurement the experimental for measurement the Rushton for turbine the Rushton and the turbine Novel-0 and the Novel-0 impeller are presented in Figures 13 and 14. impeller are presented in Figures 13 and 14.

14 Rushton turbine 12

10

p 8 N

6

4

2

0 1 10 100 1000 10,000 100,000 Energies 2020, 13, x FOR PEER1 REVIEW 10 100 1000 10000 100000 16 of 20 Re Figure 13. The power number Np evaluated from experimental measurements as a function of the FigureReynolds 13. The number power for number the RushtonNp evaluated turbine. from experimental measurements as a function of the Reynolds number for the Rushton turbine.

60 Novel-0 impeller 50

40 p

N 30

20

10

0 11 10 10 100 100 1000 1000 10,000 10000 100,000 100000 Re

Figure 14. The power number Np evaluated from experimental measurements as a function of the Reynolds number for the Novel-0 impeller. Figure 14. The power number Np evaluated from experimental measurements as a function of the It is knownReynolds from number the for literature the Novel-0 that impeller. the setting angle of the Rushton turbine blades (here considered as a reference device) has a significant impact on the power number as well as the efficiency of the It is known from the literature that the setting angle of the Rushton turbine blades (here mixingconsidered process. as The a reference highest device) resistance has (and,a significant therefore, impact power on the consumption) power number occurred as well foras the angled bladesefficiency (90 degrees), of the mixing and the process. lowest The for highest angles resi ofstance 45 and (and, 30 therefore, degrees [power8]. This consumption) tendency wasoccurred not even changedfor angled by the blades presence (90 degrees), of baffles and inside the thelowest vessel, for angles although of 45 the and authors 30 degrees measured [8]. This for tendency small valueswas of the Reynoldsnot even changed number by and the classical presence positioning of baffles insi ofde the the Rushton vessel, although turbine bladesthe authors (90 degrees),measured thatfor the small values of the Reynolds number and classical positioning of the Rushton turbine blades (90 degrees), that the presence of baffles did not significantly affect the efficiency of mixing. Based on the experimental results for the Novel-0 impeller, it can be seen that for Re values above 1500 the “blade” angle of the impeller did not influence the value of the power number. Figure 15 shows that rotating the Novel impeller “blades” caused a decrease in the power number value, both when the blades were facing the top of the tank as well as when they were directed to the bottom of the tank.

Energies 2020, 13, 640 16 of 19 presence of baffles did not significantly affect the efficiency of mixing. Based on the experimental results for the Novel-0 impeller, it can be seen that for Re values above 1500 the “blade” angle of the impeller did not influence the value of the power number. Figure 15 shows that rotating the Novel impeller “blades” caused a decrease in the power number value, both when the blades were facing the top ofEnergies the tank2020, 13 as, x wellFOR PEER as when REVIEW they were directed to the bottom of the tank. 17 of 20

25 Novel-0, Novel-0,-15 20 Novel-0,+15

15 p N

10

5

0 1 1 10 10 100 100 1000 1000 10,000 10000 100,000 100000 Re

Figure 15. The power number Np from experimental measurements as a function of the Reynolds Figure 15. The power number Np from experimental measurements as a function of the Reynolds number for various angles of novel impeller “blades”. number for various angles of novel impeller “blades”.

It shouldIt should be be noted noted that, that, according according toto calculationscalculations from from the the experiment experiment measurements, measurements, rotating rotating the blades of the Novel impeller by an angle of +/ 15 degrees (bottom of the vessel) reduced power the blades of the Novel impeller by an angle of +/−−15 degrees (bottom of the vessel) reduced power consumption,consumption, i.e., i.e., lower lower impeller impeller resistance resistance was observed observed for for Reynolds Reynolds number number below below 1000. 1000.

5. Conclusions5. Conclusions TheThe mixing mixing process process plays plays an an essentialessential role amon amongg a alarge large number number of chemical of chemical and andindustrial industrial processes.processes. The The eff effectivenessectiveness ofof mixing depends depends on onmany many parameters, parameters, but the but most the critical most one critical is the one is the impellerimpeller shape. shape. This This is isalso also important important in mult in multiple-impelleriple-impeller systems. systems. Independent Independent of system ofand system andoperation, operation, the the main main goal goal has always has always been to been find tothe find most the efficient most way effi cientof mixing way that of mixingcould achieve that could a high-quality mixture usually with low axial velocity and low heat generation (which is a crucial achieve a high-quality mixture usually with low axial velocity and low heat generation (which is issue for vitamins and enzymes and in cosmetics and food production) and using as low power as a crucialpossible. issue Undeniably, for vitamins the andenergy enzymes consumption and in duri cosmeticsng the andmixing food process production) can be andsignificantly using as low powerminimized as possible. improving Undeniably, the shape the of energy the impeller. consumption When the during power the required mixing to process carry out can the be process significantly minimizeddecreased, improving at the same the time shape the internal of the impeller.heat generation When decreased the power and required the mixing to system carry outrequired the process a decreased,smaller atelectrical the same motor, time smaller the internal gears, shaft, heat generationetc. All of these decreased items minimi and theze investment mixing system cost and required a smalleroperating electrical cost. motor, smaller gears, shaft, etc. All of these items minimize investment cost and operatingUsing cost. a new impeller shape presented in this work, it is possible to significantly reduce the powerUsing consumption a new impeller while shape maintaining presented at inthe this same work, time it a is similar possible or better to significantly level of mixing. reduce It thewas power found that power number for the reference Rushton turbine was much higher in comparison to consumption while maintaining at the same time a similar or better level of mixing. It was found optimized Novel impellers. The results evaluated from experimental measurements and numerical that power number for the reference Rushton turbine was much higher in comparison to optimized calculations showed that at least 6–10 times lower energy consumption can be obtained. The new Novelgeometry impellers. of the The impeller results that evaluated is currently from being experimental developed measurementsis a promising alternative and numerical to the calculationsclassic showedrotating that disc at least or other 6–10 timesblades- lower and nonblades-based energy consumption impeller can types. be obtained. With this The solution, new geometry it is also of the impellerpossible that to is reduce currently the power being developednumber Np for is a a promising low as well alternative a high Reynolds to the number, classic rotating i.e., for laminar disc or other blades-or turbulent and nonblades-based flow regime. After impeller exceeding types. the With Reynolds this solution, number it(about is also Re possible= 1000), which to reduce is critical the power numberfor theNp phenomena,for a low as a turbulent well a high regime Reynolds occurred number, and stabilization i.e., for laminar of the power or turbulent number was flow observed. regime. After exceedingThe the calculated Reynolds mean number axial pumping (about Re capacity= 1000), Qz through which isa horizontal critical for surface the phenomena, located 1 cm aabove turbulent regimethe occurredbottom of andthe vessel stabilization was significantly of the power higher number for Novel-0 wasobserved. impeller in reference to the Rushton turbine. For the Reynolds number whose value was about 100, the difference was as high as one order of magnitude and it increased further with rotational speed. Those are the essential impeller advantages particularly for the realization of the mixing process during the production of

Energies 2020, 13, 640 17 of 19

The calculated mean axial pumping capacity Qz through a horizontal surface located 1 cm above the bottom of the vessel was significantly higher for Novel-0 impeller in reference to the Rushton turbine. For the Reynolds number whose value was about 100, the difference was as high as one order of magnitude and it increased further with rotational speed. Those are the essential impeller advantages particularly for the realization of the mixing process during the production of pharmaceuticals or cosmetics, where a technological process cannot be destructive, where it can take a very long time, and when the rotational speed cannot be very high. 3 The ratio Qr/N d to the Np, i.e., nondimensional pumping capacity to the nondimensional power, · can be considered a mixing efficiency parameter E. This ratio for selected cases presented here was 10 times higher for novel impeller than for the Rushton turbine. However, results that were provided showed also that the mixing efficiency was significantly influenced by the distance between the impeller and the vessel bottom and, generally speaking, the impeller-to-fluid configuration. It means that impeller shape should be optimized in parallel with vessel shape or at least for predetermined geometrical configuration of the vessel.

Author Contributions: Conceptualization and measurements, M.J. and A.M.; methodology and software, M.J. and L.D.; supervision, M.J.; writing original draft and review and editing, M.J. and A.M. All authors have read and agreed to the published version of the manuscript. Funding: The present work was supported by the Polish Ministry of Science (Grant MNiSW/2019/162/DIR). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

H Water height in the tank, m Hc Tank total height, m h Height of the impeller, m D Diameter of the tank, m d Diameter of the impeller, m a Height of the impeller section, m b Width of the impeller section, m c Thickness for Rushton turbine blades, m l Length of the impeller, m d1, d2 Diameter at inlet, outlet in Novel-0 impeller, m w Width of the impeller, m ν Velocity components, m/s p Pressure, kg/(m s2) · P Np Power number = ρN3D5 P Power, W N Impeller rotational speed, rps ρ Fluid density, kg/m3 µ Fluid viscosity, kg/(m s) · τ Torque, N m ·

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