Performance of Closed Loop Venturi Aspirated Aeration System: Experimental Study and Numerical Analysis with Discrete Bubble Model

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Article Performance of Closed Loop Venturi Aspirated Aeration System: Experimental Study and Numerical Analysis with Discrete Bubble Model

Roohany Mahmud * , Mustafa Erguvan and David W. MacPhee Department of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL 35487, USA; [email protected] (M.E.); [email protected] (D.W.M.) * Correspondence: [email protected]; Tel.: +1-205-861-7531

Received: 29 April 2020; Accepted: 5 June 2020; Published: 7 June 2020

Abstract: In wastewater treatment plants, aeration plays a significant role as it encourages aerobic respiration of microbes, which are necessary to break down carbonaceous matter in the waste stream. This process can account for the majority of energy use in wastewater treatment plants. The aeration process is also necessary in odor control in lagoons and in the aquaculture industry. Generally, the aeration process is accomplished with compressors or blowers which can be of low efficiency due to ideal gas laws. This study introduces the idea of increasing aeration efficiency by looping water from a reservoir through a piping network which includes a venturi aspirator at its inlet. For this purpose, an experimental study has been conducted in a laboratory setup with a pump which pulls water from a tank, passes it through a Venturi aspirator and a helical piping network intended to increase bubble residence time, before depositing it back into the bulk fluid tank. This same process is modeled computationally, using a discrete bubble method (DBM), with good agreement with experiments. The overall purpose here is to determine the optimal configurations for standard aeration efficiency (SAE) and the standard oxygen transfer rate (SOTR). A parametric study has been implemented using the DBM based on different hydraulic and flow parameters. The model is also used to predict the SAE of a hypothetical aeration system. Results indicate that it is possible to achieve SAE values in the range of surface aerators or submersed jet aerators using the proposed aeration system with less complex components, thereby decreasing overall costs.

Keywords: venturi aerator; dissolved oxygen; standard aeration eﬃciency

1. Introduction The ecological quality of a water system depends on the availability of the dissolved oxygen (DO) in the system. Although water molecules contain an oxygen atom, this is not readily available to cellular life for respiration. In fact, it is a measure of the amount of diatomic oxygen (O2) freely available in the water. Therefore, the dissolved oxygen level in the water is an important indicator of water quality as aquatic organisms and fish live on the dissolved oxygen in the water. If the dissolved oxygen level is too low, the aquatic life may not survive and the system may have odor problems as well. Additionally, excessive dissolved nitrogen can be harmful to fish and zooplankton. Naturally, oxygen enters the stream from the atmosphere where groundwater discharges into the stream. Therefore, rapidly moving water contains more dissolved oxygen than stagnant water. Bacteria in water depending on this dissolved oxygen consume organic matter. As the DO level decreases due to temperature variation throughout the day or in different seasonal periods, the organic matter can grow to excessive levels and create undesirable bacterial growth. Entraining air bubbles can help oxygen enter the water. As a result, many physical processes have been used in industrial and environmental water streams to aerate liquid by the entrainment of air bubbles.

Water 2020, 12, 1637; doi:10.3390/w12061637 www.mdpi.com/journal/water Water 2020, 12, 1637 2 of 22

Water aeration is commonly being use to improve DO concentration in lakes and rivers and to increase water quality [1,2]. Aeration is the process of adding air into a water stream in the form of small bubbles and allowing them to rise through the water column. The efficiency of aeration depends on the amount of surface contact between the air and water which is controlled mainly by the size of the air bubble. Aeration helps increase the dissolved oxygen level when there is a deficiency in the system. Different hydraulic structures can be introduced to improve dissolved oxygen levels by creating turbulent conditions where small air bubbles are carried into the water stream. It has been stated [3] that about 4% of national energy consumption is consumed by wastewater treatment plants. Energy used in aeration processes in wastewater plants amount to over 60% of total energy consumption of the overall plant [4]. Many different types of aerators are used for a variety of diverse needs and processes. Fine pore aerator systems are today most often available in municipal wastewater aeration in developed countries, due to their advantageous aeration efficiency (mass of oxygen transferred per unit of energy required). This type of aeration device is placed at the bottom of aeration tanks/ponds with limiting water depths of 13 to 16 feet. To overcome this high water column pressure, high energy compressed air is injected through the pores which translates into high energy consumption and higher costs. Fine-pore diffusers have two major disadvantages: (a) clogging if not cleaned regularly; (b) decrease in oxygen transfer efficiency caused by dissolved surfactants. Other water aeration devices are surface aerators or coarse bubble generators. Older water treatment plants and many industrial treatment plants are still equipped with these motor-driven propellers or surface aerators. These surface aerators require larger motors in the range of 25 hp–300 hp to operate and facilities may utilize multiple aerators simultaneously. They aerate water by agitating surface wastewater in order to infuse oxygen. Higher energy consumption of surface aerators makes them less attractive. Moreover, they have many moving parts which require significant downtime of the plant and maintenance costs [5,6]. The venturi tube has widely been used in measuring flow rate in pipelines, pressurization systems in internal combustion engines, in natural gas transmission, industrial waste gas cleaning, and in dust cleaning [7,8]. Lately, venturi aeration has received increasing attention, and can be regarded as an effective technique to increase air entrainment and oxygen content in water bodies for hydraulic and environmental engineering. In the venturi aeration process, the gas is introduced in the fluid stream when a minimal amount of differential pressure exists between the inlet and the outlet sides of the venturi tube; a vacuum (air suction) occurs at suction holes (throat) of the venturi tube. However, it is also possible to apply a forced gas supply through the throat which limits the gas dispersion efficiency at high gas flow rates [9]. Venturi-type bubble generators have several advantages: (a) simple structure, (b) easy to install, (c) no internal moving parts, and (d) less maintenance. They require less power than competing technologies, which make them a more attractive economic alternative for enhancing gas–liquid mass transfer [10,11]. By using a venturi tube as an aeration device, it is possible to increase the concentration of dissolved oxygen in the water to promote the growth of aquatic life and plants. Venturi aeration systems have recently been applied to fish farming [12] and to agriculture production [13,14]. Since venturi aerators are able to produce large number of fine bubbles, they can have a significant impact in waste water treatment plants as well [15,16]. Aeration efficiency is defined as the ratio of the amount of oxygen transfer to the power consumed. The effectiveness of any aeration system is measured by this parameter. Recently, studies on conduit flow aeration efficiency have been performed [17] considering gate Froude number, gate opening, and conduit length. Bunea [18] investigates bubble column standard aeration efficiency using a metal perforated plate aerator and tries to optimize based arrangement aerator apertures and aperture diameters. There have been several studies performed by Baylar [19–21] investigating aeration efficiency of venturi tube flow considering the effect of the Reynolds number, air inlet diameter, location of the air inlet, air injection rates, and the angle of the Venturi tube. Water 2020, 12, 1637 3 of 22

The goal of this study is to explore the effect of different parameters in venturi aeration systems to find an optimized system that will have higher standard aeration efficiency (SAE). An analytical model is developed based on the discrete bubble model premise. One of the objectives of this study Water 2020, 12, x FOR PEER REVIEW 3 of 23 is to investigate whether this analytical model can be applied to model the oxygen transfer for an accompanyingmodel is developed experiment. based Withon the model discrete validation, bubble model the DBM premise. technique One of isthe then objectives used toof determinethis study the effectsis to of investigate pipe diameter, whether pipe this length analytical and number model ofcan aerators be applied on resultingto model SAE.the oxygen This paper transfer is completely for an uniqueaccompanying in that it is experiment. the first study With conductedmodel validation, to consider the DBM the technique possibility is then of an used accompanying to determine “closedthe loopeffects tube” of to pipe increase diameter, bubble pipe residence length timeand andnumber hence, of aerators aeration on effi resultingciency, when SAE. compared This paper to is other venturicompletely aeration unique systems. in that it is the first study conducted to consider the possibility of an accompanying “closed loop tube” to increase bubble residence time and hence, aeration efficiency, 2. Cleanwhen Watercompared Tests to other venturi aeration systems. To compare different aeration systems and configurations, the clean water testing procedure 2. Clean Water Tests described in ASCE 2007 [22] is followed. This reference describes the procedure to calculate the To compare different aeration systems and configurations, the clean water testing procedure standard oxygen transfer efficiency (SOTE, %), the standard oxygen transfer rate (SOTR, kgO2/h), and described in ASCE 2007 [22] is followed. This reference describes the procedure to calculate the the standard aeration efficiency (SAE, kgO2/kWh). To calculate the SAE, the power measurement standard oxygen transfer efficiency (SOTE, %), the standard oxygen transfer rate (SOTR, kgO2/h), and is important and can be expressed in different ways. Generally, power measured directly from the the standard aeration efficiency (SAE, kgO2/kWh). To calculate the SAE, the power measurement is electrical cabinet is usually desirable as it includes blower, coupling, gearbox, and motor inefficiencies. important and can be expressed in different ways. Generally, power measured directly from the To measureelectrical SAE, cabinet the standardis usually conditions desirable areas 20it ◦Cincludes temperature, blower, zero coupling, DO, mean gearbox, atmospheric and motor pressure, andinefficiencies. zero impact To of watermeasure salinity SAE, orthe other standard contaminants conditions (e.g.,are 20α °Cfactor temperature,= 1.0, β factorzero DO,= 1.0). mean Clean wateratmospheric test results pressure, can be usedand zero as a impact warranty of water of performance salinity or other between contaminants different (e.g., systems. α factor = 1.0, β factor = 1.0). Clean water test results can be used as a warranty of performance between different 3. Experimentalsystems. Procedure Before starting each experiment (see Figure1), a large aeration tank was filled with water. 3. Experimental Procedure The aeration tank maximum capacity is 300 gallons. The height of the tank is 6.75 ft with 2.92 ft in diameter.Before The starting tank each is filled experiment with 250 (see gallons Figure of1), tap a large water aeration and the tank height was filled of the with water water. level The from theaeration bottom oftank the maximum tank is approximatelycapacity is 300 gallons. 5 ft. In The industrial height of boiler the tank systems, is 6.75 it ft is with very 2.92 common ft in to diameter. The tank is filled with 250 gallons of tap water and the height of the water level from the use anhydrous sodium sulfite (Na2SO3) in the presence of a catalyst (CoCl2) to scavenge DO in bottom of the tank is approximately 5 ft. In industrial boiler systems, it is very common to use water [23]. Sodium Sulfite (Na2SO3) was added to the water which produced Sodium Sulfate Na2SO4. anhydrous sodium sulfite (Na2SO3) in the presence of a catalyst (CoCl2) to scavenge DO in water [23]. The following Equation shows the chemical reaction achieving oxygen scavenging: Sodium Sulfite (𝑁𝑎𝑆𝑂 ) was added to the water which produced Sodium Sulfate 𝑁𝑎𝑆𝑂 . The following Equation shows the chemical reaction achieving oxygen scavenging: 2Na SO + O 2Na SO , (1) 2 3 2 → 2 4 2𝑁𝑎𝑆𝑂 +𝑂 →2𝑁𝑎𝑆𝑂, (1)

Figure 1. Schematic of Current Experimental Setup. Figure 1. Schematic of Current Experimental Setup.

Water 2020, 12, 1637 4 of 22

According to Equation (1), the amount of Na2SO3 required can be determined by knowing the water volumeWater 2020 in, 12 the, x FOR system, PEER REVIEW the present DO concentration, and the required level of DO concentration.4 of 23 CoCl2 was used to increase the reaction speed and the suggested amount was 0.1% of Na2SO3 by According to Equation (1), the amount of Na2SO3 required can be determined by knowing the weight [water23,24 ].volume Theoretically, in the system, 7.88 mg the/L ofpresent Sodium DO Sulﬁteconcentration, is required and tothe scavenge required 1level mg/ Lof of DO dissolved oxygenationconcentration. concentrations. CoCl2 was used to increase the reaction speed and the suggested amount was 0.1% of TheNa aeration2SO3 by weight system [23,24]. testing Theoretically, has two steps: 7.88 mg/L (1) deoxygenate of Sodium Sulfite the is testing required water to scavenge and then 1 mg/L (2) reaerate the waterof dissolved while recording oxygenation the concentrations. DO concentration. For this purpose, two Vernier optical DO probes (Model Number:The aeration ODO-BTA) system testing are used has totwo measure steps: (1) thedeoxygenate instantaneous the testing dissolved water and oxygen then (2) concentrationsreaerate the water while recording the DO concentration. For this purpose, two Vernier optical DO probes in the aeration(Model Number: tank at ODO-BTA) two suspended are used to heights. measure th Thee instantaneous Vernier DO dissolved probe oxygen comes concentrations with its own data acquisitionin the system aeration where tank dataat two are suspended collected heights. at a frequency The Vernier of 1 DO Hz. probe The DOcomes probe with has its theown capability data of self-calibrationacquisition based system on where atmospheric data are collected pressure at anda frequency temperature. of 1 Hz. The DO probe has the capability A smallof self-calibration scale experimental based on atmo systemspheric was pressure built to and see temperature. the performance of the venturi injectors with a coiled pipe ofA small varied scale lengths. experimental The systemsystem was is shown built to insee Figure the performance2. The list of ofthe equipment venturi injectors required with to do a coiled pipe of varied lengths. The system is shown in Figure 2. The list of equipment required to do the test is listed in Table1. The setup with a single venturi injector is shown in Figure1. The list of the test is listed in Table 1. The setup with a single venturi injector is shown in Figure 1. The list of equipmentequipment required required to do to the do testthe test is listedis listed in in Table Table1 1..

FigureFigure 2. Experimental 2. Experimental Setup Setup at the the University University of Alabama. of Alabama.

TableTable 1. List1. List of of experimental experimental equipment. equipment.

EquipmentEquipment Quantity Quantity ½ hp Centrifugal Pump 1 1/2 hp Centrifugal Pump 1 PEX Pipe (1 in. Dia) 20 ft. PEX Pipe (1 in. Dia) 20 ft. Mazzei [25] Venturi Injectors (1 in. Dia) 1 Mazzei [25] Venturi Injectors (1 in. Dia) 1 Digital Pressure Gauge 2 Digital Pressure Gauge 2 Digital Flow Meter 2 Digital Flow Meter 2 Aeration Tank Size (300 Gallons) 1 Aeration Tank Size (300 Gallons) 1 Ball Valve 6 Ball Valve 6 Optical DOOptical Probe DO Probe 2 2 TemperatureTemperature Sensor Sensor 1 1

The pumps and aeration tanks are on at floor level in the aeration testing lab of The University Theof pumpsAlabama. and During aeration tests, tanksthe aeration are on tank at flooris closed level and in therefore, the aeration surface testing oxygen lab enrichment of The University is of Alabama.neglected. During The system tests, creates the aeration a positive tank pressure is closed head in and the therefore,pump’s suction surface side. The oxygen pump enrichment is self- is neglected.priming The and system has its creates own six-gallon a positive pressurized pressure tank head attached in theto it. pump’s The suction suction side water side. flow The rate pump is self-priming and has its own six-gallon pressurized tank attached to it. The suction side water flow rate is controlled with a ball valve. The discharge side of the pump is attached to the flowmeter and pressure gauge to measure the flow rate and pressure in the discharge side of the pump. Instead of Water 2020, 12, 1637 5 of 22 adding the venturi injector directly to the main line, it has been added to the side line and whenever the operation venturi injector is required, the mainline valve is shut and the side line valve is opened. From the discharge side of the injector, the coiled, cross-linked polyethylene (PEX) pipe is attached. Since the PEX pipe is coiled and can be kept hanging over the wall with a mounting, it does not hold much space and the length of the coiled pipe is also variable. Finally, the coiled pipe discharges over the aeration tank, making the outlet thermodynamic pressure to be atmospheric pressure. The pressurized water, when traveling through the convergence part of the injector, experiences a pressure drop to below atmospheric pressure due to the venture effect in the throat, which results in the suction of air through the venturi suction port and a large number of small air bubbles are produced. The suction diameter of the venturi injector is 0.75 inches. Three individual tests have been conducted with the experimental setup shown in Figure2. In the first two experiments, the pressure differential between the injector inlet to the outlet is varied from 6.6 psi to 12.4 psi. In the last experiment, the flow rate of the moving fluid was varied with a ball valve from 1.26 cfm to 1.13 cfm along with a reduction in the injector inlet pressure. In all experiments, two oxygen probes are used in different depths of the tank to observe the dissolved oxygen level. The oxygen probes are able to collect one sample of data per second. The variation of dissolved oxygen data from the two probes was insignificant, confirming that the water in the aeration tank had been well mixed. Since, in all cases, the pressure differential between the injector inlet and outlet has been varied, the suction air through the injector hole is also different in each case. Table2 lists the important experimental parameters that varied throughout the tests.

Table 2. Diﬀerent physical parameters.

Experimental Value Parameter Dimensions Test-1 Test-2 Test-3 Pipe length ft 20 20 20 Pipe diameter inch 1 1 1 Venturi injectors – 1 1 1 Injector inlet pressure psi 17.8 17.8 14.05 Injector outlet pressure psi 5.4 11.2 4.1 Air ﬂow rate SCFM 0.302 0.142 0.2183 Water ﬂow rate CFM 1.26 1.26 1.13 Aerated water volume Gallons 250 250 250 Temperature ◦C 25 25 25 Reynolds Number (Water) 33,493 33,493 30,037 Reynolds Number (Mixture) 1,234,100 1,434,400 1,172,600

4. Theory This section provides an overview of the theory that is being used in calculating aeration eﬃciency for the experimental setup. Moreover, this section discusses the fundamentals behind the discrete bubble modeling and the algorithm developed for numerical analysis.

4.1. Two Film Theory Mass transfer in multiphase flow (gas–liquid–solid) processes is a significant phenomenon occurring in chemical, petrochemical, and biological engineering problems. The transport of species among phases is accomplished by two means: diffusion (physical) and chemical reactions. There are several parameters that govern this mass transfer process, for example, system pressure, temperature, concentration gradients, reaction kinetics, conductance of mass transfer, and activation energy. There are different theories available for dealing with mass transfer among the phases, for example, two-film theory, penetration theory, and the surface renewal theory. Among them, the two-film theory developed by Lewis and Whitman [26] is one of the oldest for gas transfer to a particular liquid. The theory assumes that there exists a stagnant gas and a stagnant liquid film with thickness (δ) which are separated by an interface. The thin films are covered by gas bulk and liquid bulk on their Water 2020, 12, 1637Water 2020, 12, x FOR PEER REVIEW 6 of 23 6 of 22

film theory developed by Lewis and Whitman [26] is one of the oldest for gas transfer to a particular liquid. The theory assumes that there exists a stagnant gas and a stagnant liquid film with thickness respective sides.(δ) which To dissolveare separated a gasby an molecule interface. The into thin the films liquid, are covered it has by to gas pass bulk theseand liquid four bulk distinct on regions. The reversedtheir path respective applies sides. for aTo gas dissolve molecule a gas molecule leaving into the the liquid. liquid, Theit has assumptions to pass these four made distinct in this theory are: (1) linearregions. concentration The reversed profile path applies in stagnant for a gas molecule films, leaving (2) mass the liquid. transfer The throughassumptions the made films in occurs as this theory are: (1) linear concentration profile in stagnant films, (2) mass transfer through the films steady-stateoccurs conditions, as steady-state (3) instantaneous conditions, (3) instantaneous equilibrium, equilibrium, and (4) and dilute (4) dilute solutions solutions and and Henry’s Henry’s Law is applicable. TheLaw theoryis applicable. states The that theory the states boundary that the bounda (or thery (or interface) the interface) of gas–liquidof gas–liquid phases is two is two distinct films. Figuredistinct3 shows films. an Figure illustrative 3 shows an diagram illustrative for diagram the two-film for the two-film theory. theory.

Figure 3. Two Film theory (absorption of gas molecule). Figure 3. Two Film theory (absorption of gas molecule).

4.2. Experimental4.2. Experimental Results Evaluation Results Evaluation Technique Technique Bubble aerationBubble is aeration a mass is a transfer mass transfer process. process. The The ra ratete of of gas gas transfer transfer is generally is generally proportional proportional to to the differencethe between difference thebetween existing the existing concentration concentration and and the equilibrium equilibrium concentration concentration of the gas ofin the the gas in the solution. This rate of gas transfer is basically governed by the liquid phase mass transfer coefficient, solution. This𝐾 rate. However, of gas it is transfer non-trivial is to basically determine the governed interfacialby area the for liquidmass transfer phase (𝐴) mass per unit transfer volume coefficient, KL. However,(V it) experimentally. is non-trivial In tothat determine case, the overall the mass interfacial transfer coefficient area for mass𝐾𝑎 is used transfer without (A obtainingt) per unit volume the factors 𝐾 and ( ). In short, the overall mass transfer coefficient is written as follows: (V) experimentally. In that case, the overall mass transfer coefficient KLa is used without obtaining the At ( ) 𝐴 factors KL and V . In short, the overall mass transfer𝐾 𝑎=𝐾 × coe fficient is written as follows: (2) 𝑉

−1 In Equation (2), 𝐾𝑎 is an overall volumetric oxygenA tmass transfer coefficient in clean water, h , K a = K V is water volume in the tank, m3 and 𝐴 Lis an interfacialL area of mass transfer, m2. Moreover,𝑎= (2) × V 2 3 is interfacial area per unit volume m /m . To determine the oxygen transfer coefficient 𝐾𝑎 non- steady methods were employed [26]. According to two-film theory and Fick’s law [27–29], the non- 1 In Equation (2), KLa is an overall volumetric oxygen mass transfer coefficient in clean water, h− , steady oxygen transfer di3fferential equation is: 2 At V is water volume in the tank, m and At is an interfacial area of mass transfer, m . Moreover, a = is 𝑑𝐶 V 2 3 =𝐾𝑎×(𝐶 −𝐶) (3) interfacial area per unit volume m /m . To determine𝑑𝑡 the oxygen transfer coefficient KLa non-steady methods were employedAfter integration, [26]. Equation According (3) becomes, to two-film theory and Fick’s law [27–29], the non-steady oxygen transfer differential equation is: 𝐶 =𝐶 −(𝐶 −𝐶)𝑒 (4)

where, 𝐶 is the saturation concentrationdC of oxygen under test conditions, 𝐶 is the concentration of oxygen at time, 𝑡=0 and 𝐶 is oxygen= concentrationKLa (Cs at timeCt) 𝑡. If the initial concentration in the (3) dt × − liquid is 𝐶 =0, then Equation (4) becomes:

After integration, Equation (3) becomes,𝐶 =𝐶(1 − 𝑒 ) (5)

KLat Ct = Cs (Cs C )e− (4) − − 0 where, Cs is the saturation concentration of oxygen under test conditions, C0 is the concentration of oxygen at time, t = 0 and Ct is oxygen concentration at time t. If the initial concentration in the liquid is C0 = 0, then Equation (4) becomes:

KLat Ct = Cs(1 e− ) (5) −

Finally, the total mass transfer coeﬃcient KLa with respect to the total volume of liquid in the system can be calculated in the following way [30]:

ln (C Ct) = KLa t (6) S − × Water 2020, 12, 1637 7 of 22

1 Here, KLa is the mass transfer coeﬃcient of the system measured in (h− ) at water temperature T. Applying non-linear regression analysis of the logarithmic function of concentration deﬁcit (Cs Ct) − with aeration time t, it is possible to determine KLa. KLa is then converted to a standard reference temperature of 20 ◦C (KLa20) followed by Equation (6):

(T 20) KLa20 = KLa/θ − (7)

In Equation (7), T represents the water temperature (◦C) and θ is the temperature correction factor which stands for 1.024 for pure water. For any aeration system to compare with the existing system, it is very important to discuss the standard oxygen transfer rate (SOTR). The SOTR is defined as the mass of oxygen transferred to the water volume per unit time when zero initial dissolved oxygen and standard conditions are considered (i.e., water temperature at 20 ◦C and pressure at 1 atm). SOTR is therefore defined as follows: SOTR = KLa (Cs C ) V (8) 20 × − 0 × The efficiency of the aeration system is determined by computing standard aeration efficiency, which is stated as rate of oxygen transfer per unit power input and expressed in the following way:

SOTR SAE = (9) Pin

In this Equation, Pin stands for the total power drawn from the outlet of the compressor or pump. It is expressed in Kg O2/kWh or lbs O2/hp-h.

4.3. Discrete Bubble Model (Analytical Technique) The analytical model used here is a discrete bubble model. The discrete bubble model was first used in literature [31] in the phenomena of plug flow through a tank of well-mixed water. Bubbles affect the flow significantly when they are experiencing large pressure gradients and velocity variations. This model tracks every bubble motion as discrete entities and also the bubble deformation due to mass transfer across the bubble surface. The main characteristics of this model are listed below: 1. The model is based on the Euler-Euler (E-E) approach. 2. This model is capable of solving homogeneous multiphase flow. 3. This E-E model employs the volume averaged mass and momentum conservation equation to describe time dependent motion of both phases. 4. The bubble number contained in a computational cell is represented by a volume fraction. 5. The bubble size information is obtained by incorporating population balance equations with break-up and coalesce of bubbles as well as growth or shrinkage of bubbles due to mass transfer across the bubble surface. This model is being extensively used in modeling gas–liquid dispersed flow in bubble column reactors to investigate complex phenomena like hydrodynamics, mass transfer, and chemical reactions [32–34]. The benefit of using the Euler-Euler approach is that the number of bubbles is not limited and storage requirement and computational power demand are not dependent on bubble numbers. However, this approach comes with diffusion errors and is sensitive to bubble diameter. The distribution of bubble diameters is either estimated by population balance along with coalescence and break up events [35] or directly obtained from the experiment [36,37]. DBM is applied successfully in airlift aerators [38,39], bubble plume [40], and diffused bubble and wastewater ozonation systems [41,42]. In this present paper, the bubble and fluid is considered as a continuous interpenetrating fluid which gives the opportunity to use the DBM method to predict the rate of oxygen transfer during bubble aeration. The bubbles are considered spherical in shape, which simplifies the forces exerted on the bubbles. In DBM studies, no turbulence of continuous phase is considered. The specific interface area is significant since the mass transfer among the two phases is dependent on Water 2020, 12, 1637 8 of 22 it. In fact, the bubble size distribution is time-dependent, as processes like bubble coalesce and break up affect this phenomenon. Consequently, this affects the interface area and mass transfer. In this study, the size of the bubble is a function of the pressure gradient and mass transfer only, and the effects of bubbles coalescing and breaking up is overlooked. The bubbles are assumed to be moving with the fluid with an average mixture velocity. For each experiment, the number of bubbles in the pipe at any given time is assumed to be invariable considering that no input of the system has been changed. The bubbles are simply experiencing pressure forces inside the pipe which varies along the pipe length. Surface tension and liquid head pressure is negligible in this case. For simplifying the model, it is assumed that bubble break-up and coalescing are not occurring. The flow is incompressible with the volume-average mixture properties (e.g., viscosity, density) being used. The distribution of the bubble size is represented by a single Sauter mean diameter [43]. The water and air temperature are assumed to be equal and constant. The mass transfer flux across the surface of a bubble is:

J = KL(Cs C) (10) − where, KL is liquid side mass transfer coeﬃcient, CS is equilibrium concentration at the gas/water interface, C is bulk aqueous-phase concentration, and J is mass transfer ﬂux. The gas side mass transfer resistance has been neglected. The equilibrium concentration can be expressed as: Cs = HPi (11) where, H is Henry’s constant and Pi is partial pressure of the gas. With this, Equation (10) can be written as follows:

J = KL(HP C) (12) i − 3 1 1 Henry’s constant (H) (mol.m− .bar− ) and mass transfer coeﬃcient (ms− ) are determined in the following way [44]: 2 4 2 Ho = 2.125 5.021 10− T + 5.77 10− T (T in C) (13) − × × 2 4 2 Ho = 2.125 5.021 10− T + 5.77 10− T (T in C) (14) − × × and 4 KL = 0.6r, r < 6.67 10 m (15) × − 4 4 KL = 4 10− , r 6.67 10 m (16) × ≥ × − The rate of mass transfer across the surface area of the bubble of radius (r) can be obtained from the mass transfer ﬂux Equation:

dm 2 = J A = KL(HP C) 4πr (17) dt × i − ×

The discrete bubble is moving with the water with mixture velocity vm. At any time, the velocity of the bubble inside the pipe along the horizontal axis can be related by the following equation:

dx = v (18) dt m Since the bulk aqueous-phase concentration does not change signiﬁcantly during the travel of bubbles inside the pipe, the pseudo-steady state assumption may be considered. From this equation, it is possible to determine the mass transfer of gaseous species per bubble per unit length of pipe:

dm 4πr2 = KL(HPi C) (19) dx − − vb Water 2020, 12, 1637 9 of 22

The number of bubbles in the pipe at any instant is constant. This number of bubbles is calculated by knowing the volumetric flow of air through the venturi injector, Q0 and the initial bubble volume, V0.

Q N = 0 (20) V0

Multiplying the mass transfer equation for a single bubble with the total number of bubbles (N) will give the total mass transfer per unit length at per unit time.

dm 4πr2 N = KL(HPi C) × (21) dx − − vb

The above equation is a one-dimensional ordinary differential equation. On the right hand side, the variables are H, which is function of temperature only and KL, which is a function of bubble radius. Bubble radius will change with the change in pressure inside the pipe and also with the mass transfer of oxygen and nitrogen gas across the bubble and liquid interface. As said before, the ideal gas law is used in this case to measure the change of bubble radius with time. In this experiment, a coiled pipe is used to transfer water from the source to the aeration tank. To include the effect of the coiled pipe in the calculation, the friction loss of this type of pipe is being calculated using the Mishra and Gupta correction factor with Blasius correlations [45]. The friction factor for curved or helically coiled tubes, taking into consideration the equivalent curve radius, RC, is as follows: r 1 DP f = 0.316Re− 4 + 0.0075 (22) 2RC " # H 2 R = R 1 + ( ) (23) C 2πR where, DP, R, H, and Re represent pipe diameter, curve radius, helicoidal pitch, and Reynolds Number respectively. In the current analysis, the two phase flow is modeled as the homogeneous flow model which is the simplest technique for analyzing multiphase flows. In the homogeneous model, both liquid and gas phases move at the same velocity (slip ratio = 1). It is also known as the zero slip model. The homogeneous model considers the two-phase flow as a single-phase flow having the average fluid properties in which the properties depend upon the mixture quality. For this purpose, one parameter which is known as mass quality is defined as follows:

Q χ = 1 ( air ) (24) − Qwater

3 where, Qwater and Qair stand for volumetric flow rate of water (m /s) and volumetric flow rate of air (m3/s) respectively. The definition of two phase viscosity (µm) based on the mass averaged value of the reciprocals of the gas viscosity (µg) and liquid viscosity (µl) is defined as follows:

1 χ 1 χ − µm = ( + − ) (25) µg µl

The mixture density (ρm) also obtained in the mass averaged process of gas density (ρg) and liquid density (ρl) is calculated as follows:

1 χ 1 χ − ρm = ( + − ) (26) ρg ρl Water 2020, 12, 1637 10 of 22

The velocity and the Reynolds number of the mixture is calculated in the following way:

vm = (Qair + Qwater)/Apipe (27)

The Reynolds number of the mixture can be found in this way:

ρmvmDp Rem = (28) µm

Water 2020, 12, x FOR PEER REVIEW π 2 2 10 of 23 where, Apipe is pipe area which is equal to 4 Dp (m ). Finally,The the Reynolds frictional number head of loss the (mixturehf) across can thebe found length in this of theway: coiled pipe (l) is calculated by using mixture density, velocity, and Reynolds number which is written as follows: 𝜌𝑣𝐷 𝑅𝑒 = (28) 𝜇 l 1 2 2 where, 𝐴 is pipe area which is equalh f to= f𝐷( (m) ).ρ mvm (29) Dp 2 Finally, the frictional head loss (hf) across the length of the coiled pipe (l) is calculated by using Gordiychukmixture density, [46] havevelocity, performed and Reynolds an number experiment which tois written calculate as follows: the Sauter mean diameter of the 𝑙 1 bubble (d ) generated in venturi-type bubble generators. They have derived the relation to determine 32 ℎ = 𝑓( ) 𝜌𝑣 (29) the Sauter mean diameter as a function of water𝐷 ﬂow2 rate, air ﬂow rate, and air inlet diameter. The relation isGordiychuk given in [46] the followinghave performed way an (see experiment Table 2 ofto calculate [46] for the ML-BGS Sauter algorithm):mean diameter of the bubble ( 𝑑 ) generated in venturi-type bubble generators. They have derived the relation to determine the Sauter mean diameter as a function of water flow rate, air flow rate, and air inlet d32 1.4767 0.7566 0.5110 diameter. The relation is given in= the1215.9 followingRe wayw− (see TableRe air2 of [46] forα ML-BGS− algorithm): (30) dinlet,(suction) × × × 𝑑 . . . = 1215.9 × 𝑅𝑒 ×𝑅𝑒 ×𝛼 (30) In this relation, α stands𝑑,() for air to water fraction. Rew and Reair are Reynolds number for water and air respectively.In this relation, The Reynolds 𝛼 stands numberfor air to ofwater air isfraction. evaluated 𝑅𝑒 basedand 𝑅𝑒 on suctionare Reynolds diameter number (d inletfor ,(suction)), suction velocity,water and and air airrespectively. density. OnThe theReynolds other hand,number for of water,air is evaluated Reynolds based number on suction is calculated diameter based on pipe diameter,(𝑑,() water), velocitysuction velocity, and water and air density. density. On the other hand, for water, Reynolds number is Nowcalculated that all based necessary on pipe equations diameter, water to calculate velocity and mass water transfer density. in the discrete bubble model have Now that all necessary equations to calculate mass transfer in the discrete bubble model have been documented,been documented, an overview an overview of the of the algorithm algorithm structurestructure used used for for this this model model is shown is shown in Figure in 4: Figure 4:

Figure 4. Representation of the Discrete Bubble Model algorithm. Figure 4. Representation of the Discrete Bubble Model algorithm.

5. Discussion

Water 2020, 12, 1637 11 of 22

5. Discussion

InWater this 2020 section,, 12, x FOR three PEERdi REVIEWfferent experimental results are shown. These results are compared11 of 23 with the results obtained from the discrete bubble model to determine the model efficiency in predicting the oxygen transferIn this esection,fficiency three of different the discussed experimental system. results In are the shown. end, theThese discrete results are bubble compared model with is used to the results obtained from the discrete bubble model to determine the model efficiency in predicting predict a proposed aeration system for an aquaculture farm to obtain an SAE over 1.5. The following the oxygen transfer efficiency of the discussed system. In the end, the discrete bubble model is used sectionto is predict divided a inproposed three subsections: aeration system the firstfor an subsection aquaculture will farm validate to obtain the analyticalan SAE over model, 1.5. The the second sectionfollowing discusses section the e isff ectsdivided of di inff erentthree subsections: parameters the on first oxygen subsection transfer will evalidatefficiency the using analytical the discrete bubblemodel, model, the and second the section third will discusses cover the a proposedeffects of different aeration parameters system suitableon oxygen for transfer aquaculture. efficiency using the discrete bubble model, and the third will cover a proposed aeration system suitable for 5.1. Validationaquaculture. of the Numerical Model

In5.1. all Validation experiments, of the Numerical the air Model suction through the venturi hole was natural. The air suction is dependentIn on all pressure experiments, diff erentialthe air suction and water through flow the rates venturi for hole a specific was natural. injector. The Mazzei air suction documented is the airdependent suction rate on throughpressure differential the injector and hole water for flow diff rateserent for scenarios a specific ininjector. their Mazzei product documented catalogue for the specificthe injector air suction model. rate Sincethrough then, the injector the pressure hole for di difffferenterentials scenarios and water in their flow product rate catalogue conditions forfor the different experimentsspecific in injector this study model. are Since close then, to what the pressure is mentioned differentials in the and product water catalogue, flow rate conditions the air suction for rate is not measureddifferent but experiments rather is in directly this study used are from close the to wh catalogue.at is mentioned This also in the gives product the independencecatalogue, the air of testing suction rate is not measured but rather is directly used from the catalogue. This also gives the different scenarios in numerical studies as it subsides the requirement of measuring suction flow rate. independence of testing different scenarios in numerical studies as it subsides the requirement of While doingmeasuring numerical suction analysis,flow rate. inWhile each doing case, numerical the water analysis, flow rate in iseach known case, the and water the code flow israte also is capable of calculatingknown and the the injector code is inlet also pressure capable of head calculating from di thefferent injector hydraulic inlet pressure parameters. head from As different a result of this, varietieshydraulic of pressure parameters. of diff Aserentials a result of can this, be varieties tested alongof pressure with of di differentialsfferent water can be flow tested conditions. along with Thedifferent analytical water resultsflow conditions. were obtained using the same physical parameters as the experiments. Data from theThe twoanalytical probes results are were averaged obtained over using the the time same period. physical Figure parameters5 shows as the experiments. average dissolved Data from the two probes are averaged over the time period. Figure 5 shows the average dissolved oxygenoxygen vs. time vs. time results results for for three three di differentfferent experiments.experiments. The The analytical analytical results results obtained obtained through through discretediscrete bubble bubble models models for for each each case case are are plotted plotted in in the the same same graph graph to show to show their conformity their conformity with the with the experimentalexperimental results. results.

(a) (b)

(c)

FigureFigure 5. Dissolved 5. Dissolved Oxygen Oxygen (mg (mg/L)/L) versus Time Time (min) (min) for three for threetest conditions test conditions defined in deﬁned Table 2: ( ina) Table2: Test-1; (b) Test-2; (c) Test-3. (a) Test-1; (b) Test-2; (c) Test-3.

Figure5 shows the increase in dissolved oxygen in the aeration tank with time. From the experimental results, it can be observed that the ﬁrst test reaches saturation more quickly than the other WaterWater2020 2020, 12,, 12 1637, x FOR PEER REVIEW 12 12of 23 of 22

Figure 5 shows the increase in dissolved oxygen in the aeration tank with time. From the two.experimental The second results, test takes it can the be longest observed time that to reach the first saturation. test reaches This saturati is due toon the more fact quickly that in thethan second the test,other less two. air is The drawn second into test the takes aerator. the Thelongest analytical time to resultsreach saturation. are reasonably This is able due to to predict the fact the that measured in the DO.second In most test, cases, less air the is analyticaldrawn into model the aerator. results The fall analytical within 10–15% results are of thereasonably measured able data, to predict although the it underestimatesmeasured DO. the In results.most cases, In the the beginninganalytical model of the test,results the fall analytical within 10–15% results of divert the measured mostly from data, the experimentalalthough it underestimates results, but with the time results. the measuredIn the beginn anding predicted of the test, values the analytic startedal toresults conform divert more mostly with eachfrom other. the Thisexperimental difference results, in predicted but with results time withthe measured measured and values predicted could values happen started for several to conform reasons. Onemore of the with main each factors other. is This the degreedifference of variabilityin predicted of theresults bubble with size measured in real measurementvalues could happen compared for to theseveral analytical reasons. model. One In theof analyticalthe main factors model, allis the bubbles degree are of considered variability spherical of the bubble in shape size which in real is not truemeasurement in real phenomena. compared Bubble to the radius analytical also model. changes In due the toanalytical coalesce model, and breakage. all bubbles Moreover, are considered the effect of turbulentspherical in mixing shape insidewhich theis not pipe true after in real the injectorphenomena. is not Bubble included radius in thealso model. changes The due velocity to coalesce of the bubbleand breakage. and water Moreover, is assumed the to effect be the of same turbulent with having mixing a inside mixture the velocity pipe after which the might injector be is another not included in the model. The velocity of the bubble and water is assumed to be the same with having source of error. This average velocity is added in the model without considering the time-dependent a mixture velocity which might be another source of error. This average velocity is added in the model velocity change due to the turbulent flow inside the pipe. without considering the time-dependent velocity change due to the turbulent flow inside the pipe. Based on KLa, the standard aeration efficiency (SAE) and the standard oxygen transfer rate (SOTR) Based on 𝐾𝑎, the standard aeration efficiency (SAE) and the standard oxygen transfer rate are determined. All values of KLa, SOTR and SAE are presented in Table3 for both the experiment (SOTR) are determined. All values of 𝐾𝑎, SOTR and SAE are presented in Table 3 for both the andexperiment analytical and results. analytical By comparing results. By the comparin experimentalg the results,experimental the highest results, SAE the was highest achieved SAE forwas the thirdachieved test, while for the the third maximum test, while oxygen the maximum transfer rate oxygen was transfer observed rate for was test-1. observed This is for also test-1. valid This for is the analyticalalso valid results. for the analytical results.

TableTable 3. 3.Performance Performance ofof aerationaeration experiments.

PercentagePercentage DiDifferenceﬀerence Experimental Value (EV) Analytical Value (AV) Experimental Value (EV) Analytical Value (AV) 𝑬𝑽| EV AV − 𝑨𝑽 100|% Tests EV− × 𝟏𝟎𝟎 % Tests 𝑬𝑽 × KLa SOTR SAE KLa SOTR SAE KLa SOTR SAE KLa SOTR SAE KLa SOTR SAE KLa SOTR SAE (h 1) (lbsO2/h) (lbsO2/hp-h) (h 1) (lbsO2/h) (lbsO2/hp-h) (%) (%) (%) (h− −1) (lbsO2/h) (lbsO2/hp-h) −(h−1) (lbsO2/h) (lbsO2/hp-h) (%) (%) (%) Test-1Test-1 4.034.03 0.0680.068 0.56 0.56 3.38 3.38 0.0590.059 0.49 0.49 16 13 13 13 13 Test-2Test-2 2.872.87 0.0500.050 0.42 0.42 2.55 2.55 0.0440.044 0.37 0.37 11 12 12 12 12 Test-3Test-3 3.203.20 0.0540.054 0.63 0.63 2.81 2.81 0.0470.047 0.55 0.55 12 13 13 12 12

AccordingAccording to to Equation Equation (6), (6), a a semisemi log-basedlog-based graph is is plotted plotted with with respect respect toto time time in inFigure Figure 6. 6. The slope of the curve represents the oxygen transfer coefficient (𝐾𝑎) of the aerator module which is The slope of the curve represents the oxygen transfer coefficient (KLa) of the aerator module which an important parameter in determining the efficiency of the aerator. Oxygen transfer coefficient is an important parameter in determining the efficiency of the aerator. Oxygen transfer coefficient expresses the relationship between the rate of mass transfer and the concentration deficit which is the expresses the relationship between the rate of mass transfer and the concentration deficit which is the driving force to dissolve oxygen in the water. In this case, the 𝐾𝑎 values obtained through driving force to dissolve oxygen in the water. In this case, the K a values obtained through experiment experiment under standard conditions for test-1, test-2, and test-3L are 0.067 min−1, 0.048 min−1, and under standard conditions for test-1, test-2, and test-3 are 0.067 min 1, 0.048 min 1, and 0.053 min 1 0.053 min−1 respectively. The highest oxygen transfer coefficient is −achieved through− test-1. In the − respectively. The highest oxygen transfer coefficient is achieved through test-1. In the analytical model, analytical model, a similar log deficit plot is generated to determine the 𝐾𝑎. The analytical model 1 a similar log deficit plot−1 is generated−1 to determine− the1 KLa. The analytical model KLa are 0.056 min , 𝐾𝑎 are −0.056 min , 0.042 min , and 0.047 min for test-1,-2, and -3 respectively. In all− cases, the− 1 1 K a 0.042analytical min− , andmodel 0.047 𝐾𝑎 min is −lessfor than test-1,-2, the experimental and -3 respectively. 𝐾𝑎 values In all and cases, the the difference analytical in model them areL is lessbetween than the 10–16%. experimental KLa values and the difference in them are between 10–16%.

(a) (b)

Figure 6. Cont.

Water 2020, 12, x FOR PEER REVIEW 13 of 23 WaterWater2020 2020, 12,, 12 1637, x FOR PEER REVIEW 13 13of 23 of 22

(c) (c) Figure 6. Determination of oxygen transfer coefficient for three test conditions defined in Table 2: (a) FigureFigure 6. 6.Determination Determination ofof oxygen transfer transfer coefficient coeﬃcient for for three three test test conditions conditions defined deﬁned in Table in Table 2: (a)2 : Test-1; (b) Test-2; (c) Test-3. (a) Test-1; ( (bb)) Test-2; Test-2; ( (cc)) Test-3. Test-3.

5.2.5.2. Parametric Parametric Parametric Study Study Here,Here, the the effects eff effectsects of of didifferent differentfferent hydraulic hydraulic andand flowflowflow parametersparameters have have been been tested tested with with the the discrete discrete bubblebubble model. model. This This This study study study gives gives gives an an an insight insight into into which which parameters areare affectingaffecting affecting the the oxygen oxygen transfer transfer coefficientcoecoefficientfficient (K𝐾 L(𝐾𝑎)a),𝑎), SOTRSOTR, SOTR and and SAE, SAE, and and will will help help find findfind an anan optimumoptimum inputinput input for for for future, future, future, larger-scale larger-scale larger-scale systems systems systems for foraeration aeration purposes. purposes. In In In all all all cases, cases, cases, test-1 test-1 test-1 conditions conditions conditions are are usedused while while varyingvarying varying test-1 test-1 test-1 parameters parameters parameters are are used used to investigate to investigate eeffectsff effectsects on on aeration aeration eefficiency ffiefficiencyciency inin in varyingvarying varying these thesethese parameters.parameters.

5.2.1.5.2.1. Effect Eff Effectect of ofPipe Pipe Length Length OneOne ofof theofthe the main main main purposes purposes purposes of of thisof this this study study study was waswas to determine toto determine the e thefftheect effecteffect of coiled of of coiled coiled pipe lengthpipe pipe length inlength oxygen in in oxygentransferoxygen transfer effi transferciency. efficiency. efficiency. The coiled The The pipe coiled coiled will pipe pipe start will will after start start the afterafter injector the injector and will and and hang will will hang over hang theover over aeration the the aeration aeration basin. Accordingbasin.basin. According According to [47], to in to the[47], [47], helical in in the the tube, helical helical bubbles tube, tube, dispersedbubbles bubbles disperseddispersed mostly around mostlymostly the aroundaround center the the of center the center coil of andof the the acoil drag coil and a drag reduction was observed on the bubble surface. In the analytical model, the same inputs andreduction a drag was reduction observed was on observed the bubble on surface. the bubble In the surface. analytical In the model, analytical the same model, inputs the are same used inputs from are used from test-1 with only a change in the pipe length. aretest-1 used with from only test-1 a change with inonly the a pipechange length. in the pipe length. In Figure 7a, the DO concentration profile versus time is plotted to show the effect of pipe length. In Figure 77a,a, thethe DODO concentrationconcentration profileprofile versusversus timetime isis plottedplotted toto show the eeffectffect of of pipe pipe length. length. The profile conforms to a general non-steady aeration curve where the rate of change in dissolved The profileprofile conforms to a general non-steady aerationaeration curve where the rate of change in dissolved oxygen levels decrease with time. This is due to a reduction in saturation deficit level with time. It oxygencan be levelslevels observed decreasedecrease that, with with an time. time. increase This This isin is duepipe due to length to a reductiona reduction, the system in saturationin takes saturation less deficittime deficit tolevel reach level with the with saturation time. time. It can It canbelevel. observed be observed Since, that, with that, with an with anincrease an increase increase in pipe in in pipe length,pipe length, length bubbles the, the system aresystem taking takes takes a lessmuch less time time longer to to reachreach retention thethe saturation time to level.transfer Since,Since, oxygen withwith an withan increase increase water, in the in pipe oxygenpipe length, length, transfer bubbles bu ratebbles are is takingalsoare increased.taking a much a much longerMoreover, longer retention the retentionbubbles time to remain transfertime to transferoxygenin the withoxygen center water, andwith thethus water, oxygen less the likely oxygen transfer to collide transfer rate iswithalso rate the increased.is alsopipe increased.surface. Moreover, This Moreover, helps the bubbles them the bubblestoremain maintain remain in a the incenter thespherical andcenter thusshape and less forthus likely a longerless to likely collide period to withofcollide time the andwith pipe increases the surface. pipe the Thissurface. overall helps This mass them helps transfer to maintainthem rate. to Thismaintain a spherical mass a sphericalshapetransfer for shape a rate longer increase for period a longer comes of timeperiod with and a ofsmall increases time increase and the increases overallin the friction massthe overall transfer head lossmass rate. which transfer This causes mass rate. transferless This pump mass rate transferincreasepower rate comesrise. increase In with effect, acomes smallthe overall with increase a oxygenation small in the increase friction transfer in headthe efficiency friction loss which headincreases. causesloss whichHowever, less pumpcauses this power lesspositive pump rise. powerIn eeffectffect, rise. of the pipe In overall effect,length oxygenation theincrease overall dampens oxygenation transfer after effi certaiciency transfern intervals increases. efficiency (in However,this in case,creases. from this However, 80 positive ft. to 100 ethisff ft.)ect positive of pipe effectlength of increase pipe length dampens increase after dampens certain intervals after certai (inn this intervals case, from (in this 80 ft.case, to 100from ft.) 80 ft. to 100 ft.)

(a) (b)

Figure 7. Cont.

Water 2020, 12, 1637 14 of 22 Water 2020, 12, x FOR PEER REVIEW 14 of 23

−11 FigureFigure 7.7. EEffectﬀect ofof pipepipe lengthlength on:on: ((aa)) DissolvedDissolved (mg (mg/L)/L) oxygen oxygen vs. vs. time time (min); (min); ( b(b) )K KLaLa(h (h− );); ((cc)) SOTRSOTR (lbs(lbs OO22//h);h); ((dd)) SAESAE (lbs(lbs OO22//hp-h).hp-h).

K𝐾La𝑎,, SOTR,SOTR, and and SAE SAE are are plotted plotted in thein the graph graph from from Figure Figure7b–d 7b–d with respectwith respect to pipe to length. pipe length. In every In case,every the case, linear the linear trend trend line is line obtained is obtained which which passes pass throughes through most most of the of values.the values. If the If the pipe pipe length length is doubled,is doubled, the the SOTR SOTR is is also also increased increased by by a factora factor of of 1.4. 1.4. For For a a 100 100 ft. ft. section sectionof ofpipe, pipe, thethe oxygenationoxygenation eefficiencyﬃciency isis 2.62.6 timestimes betterbetter thanthan thethe 2020 ft.ft. pipe.pipe. Values ofof K𝐾La𝑎,, SOTR, SOTR, and and SAE SAE are are listed listed in in Table Table4. 4.

Table 4.4. Performance ofof didifferentﬀerent aerationaeration conditionsconditions obtainedobtained fromfrom thethe analyticalanalytical model.model.

AnalyticalAnalytical ValueValue ParameterParameter ValuesValues −1 1 KLa K(hLa)(h − ) SOTRSOTR (lbsO (lbsO2/h)2 /h) SAE (lbsO(lbsO2/2hp-h)/hp-h) 2020 ft. ft. 3.38 3.38 0.06 0.06 0.49 0.49 4040 ft. ft. 5.24 5.24 0.09 0.09 0.77 0.77 PipePipe Length Length 6060 ft. ft. 7.21 7.21 0.13 0.13 1.05 1.05 8080 ft. ft. 8.20 8.20 0.14 0.14 1.20 1.20 100 ft. 9.97 0.17 1.46 100 ft. 9.97 0.17 1.46 1 1in. in. 3.38 3.38 0.06 0.06 0.49 0.49 2 in 9.65 0.17 1.41 Pipe Diameter 2 in 9.65 0.17 1.41 Pipe Diameter 3 in. 12.60 0.22 1.84 3 4in. in. 12.60 15.94 0.22 0.28 2.33 1.84 0.24 in. cfm 15.94 2.34 0.28 0.04 0.34 2.33 0.20.4 cfm cfm 2.34 4.75 0.04 0.08 0.69 0.34 Airflow Rate 0.40.6 cfm cfm 4.75 7.77 0.08 0.14 1.14 0.69 Airflow Rate 0.60.8 cfm cfm 7.77 9.62 0.14 0.17 1.41 1.14 0.81.26 cfm cfm 9.62 3.87 0.17 0.07 0.57 1.41 2.52 cfm 2.52 0.04 0.18 Water flow Rate 1.26 cfm 3.87 0.07 0.57 3.78 cfm 2.40 0.04 0.12 2.52 cfm 2.52 0.04 0.18 Water flow Rate 5.04 cfm 1.57 0.03 0.06 3.78 cfm 2.40 0.04 0.12 5.04 cfm 1.57 0.03 0.06 5.2.2. Effect of Pipe Diameter 5.2.2.In Effect the current of Pipe research,Diameter only 1-inch diameter pipe is being used for all experiments. However, one-inch pipe usually has a higher frictional loss and thus affects the SAE in a negative way. In Figure8, In the current research, only 1-inch diameter pipe is being used for all experiments. However, effects of diameter change in dissolved oxygen rate and in efficiency are shown. one-inch pipe usually has a higher frictional loss and thus affects the SAE in a negative way. In Figure 8, effects of diameter change in dissolved oxygen rate and in efficiency are shown.

WaterWater2020 2020,,12 12,, 1637x FOR PEER REVIEW 1515 ofof 2223

(a) (b)

1 FigureFigure 8.8. EEffectﬀect ofof pipepipe diameterdiameter on:on: ((aa)) DissolvedDissolved (mg (mg/L)/L) oxygen oxygen vs. vs. time time (min); (min); ( b(b))K KLaLa(h (h−−1);); ((cc)) SOTRSOTR (lbs(lbs OO22//h);h); ((dd)) SAESAE (lbs(lbs OO22//hp-h).hp-h).

FromFrom FigureFigure8 8,, it it is is evident evident that that the the dissolved dissolved oxygenoxygen levellevel risesrises withwith timetime inin thethe aerationaeration tank.tank. TheThe DODO level rises rapidly at at first, first, then then this this rate rate of of increase increase decreases decreases as as it itge getsts close close to tosaturation. saturation. It Itfollows follows that that increasing increasing the the diameter diameter helps helps the the system system reach reach the the saturation saturation more more quickly. quickly. This This can can be beattributed attributed to tothe the fact fact that that increasing increasing the the pipe pipe diameter diameter decreases decreases the the mixture velocity.velocity. In realreal phenomena,phenomena, therethere exists exists a a slip slip velocity velocity due due to to the the density density diff differenceerence between between two two phase phase flow. flow. The The gas bubblesgas bubbles do not do exactly not exactly travel travel with thewith liquid the liquid [48]. Additionally, [48]. Additionally, in smaller in smaller diameter diameter pipe more pipe bubbles more tendbubbles to travel tend towardsto travel thetowards pipe wall.the pipe Oxygen wall. transfers Oxygen totransfers the water to throughthe water di throughffusion. Todiffusion. overcome To theovercome resistance the inresistance gas–water in gas–water interface, bubbles interface, need bubbl suffiescient need time. sufficient Since time. the water Since velocitythe water decreases velocity withdecreases the diameter with the increase, diameter the increase, gas bubbles the gas get bubbles more time get for more mass time transfer for mass to overcome transfer theto overcome diffusion resistance.the diffusion This resistance. positive eThisffect positive can also effect be observable can also be while observable determining while thedetermining oxygenation thecoe oxygenationfficient as it increases with the diameter increase. In Figure8b,c, K a, and are plotted against the diameter and coefficient as it increases with the diameter increase. In FigureL 8b, c, 𝐾𝑎, and are plotted against the arediameter fitted withand are a trend fitted line. with This a trend trend line. line equationThis trend is line a simple equation mathematical is a simple model mathematical of the relationship model of betweenthe relationship the diameter between with the oxygenation diameter coewithffi cientoxygenation and SOTR. coefficient SAE also and attains SOTR. higher SAE values also attains as the systemhigher values is able as to the transfer system oxygen is able faster to transfer without oxygen changing faster the without operating changing condition the operating of the pump. condition of the pump. 5.2.3. Effect of Gas Flow Rate 5.2.3.This Effect section of Gas will Flow discuss Rate the effect of increasing the suction gas flow rate while keeping the motive flow rateThis andsection the linewill pressure discuss constant.the effect Inof this increasing case, the the test-1 suction condition gas flow is used rate only while in changing keeping thethe gasmotive suction flow rate. rate and the line pressure constant. In this case, the test-1 condition is used only in changingIt can the be gas observed suction from rate. Figure 9 that in all cases of simulation, gas suction flow rates increase significantlyIt can be the observed impact from of dissolved Figure 9 oxygen that in level.all cases With of thesimulation, increase gas in gas suction flow rate,flow therates dissolved increase oxygensignificantly attains the the impact saturation of dissolved concentration oxygen more level. rapidly. With the Gas increase flow rate in basicallygas flow increasesrate, the dissolved the mass qualityoxygen inattains Equation the saturation (24). This concentration positive impact more can rapidly. be explained Gas flow in tworate ways:basically firstly, increases an increase the mass in gasquality flow in rate Equation generally (24). creates This positive more turbulence impact can inbe the explained liquid interface. in two ways: At thisfirstly, point, an increase mass transfer in gas flow rate generally creates more turbulence in the liquid interface. At this point, mass transfer is

Water 2020, 12, 1637 16 of 22 Water 2020, 12, x FOR PEER REVIEW 16 of 23 is governed by the disturbance and rate of restoration of the liquid ﬁlm. This is described by the governed by the disturbance and rate of restoration of the liquid film. This is described by the Danckwertz surface rejuvenation theory [49]: Danckwertz surface rejuvenation theory [49]: p KL𝐾= = D𝐷Lr𝑟 (31)(31)

where, 𝐾 is the liquid film coefficient discussed in Equation (10), 𝐷 is the diffusion coefficient of where, KL is the liquid film coefficient discussed in Equation (10), DL is the diffusion coefficient of oxygen (m22·h−11) and 𝑟 is the rate of restoration of liquid the film (h−11). Since an increase in gas flow oxygen (m h− ) and r is the rate of restoration of liquid the film (h− ). Since an increase in gas flow rate increases· the r value in Equation (31), 𝐾 also increases. This positive effect of 𝐾 also increases rate increases the r value in Equation (31), KL also increases. This positive effect of KL also increases the oxygenthe oxygen transfer transfer coeffi coefficientcient and and SOTR. SOTR.

(a) (b)

−11 FigureFigure 9.9. EEffectﬀect ofof gasgas ﬂowflow raterate on:on: ((aa)) DissolvedDissolved (mg(mg/L)/L) oxygen oxygen vs. vs.time time (min); (min); ( b(b))K KLLaa(h (h− );); ((cc)) SOTRSOTR (lbs(lbs OO22//h);h); (d)) SAESAE (lbs(lbs OO22/hp-h)./hp-h).

Secondly,Secondly, a a rise rise in in the the gas gas ﬂow flow rate rate also also increases increases the number the number of bubbles of bubbles at any time.at any This time. increase This inincrease gas bubbles in gas raises bubbles the total raises available the total interfacial available area interfacial to the surrounding area to the medium surrounding for diﬀusion medium [50– 52for].

Indiffusion short, this [50–52]. creates In favorable short, this conditions creates favorable for KLa and conditions SOTR. In thisfor discussion,𝐾𝑎 and SOTR. SAE alsoIn this increases discussion, since noSAE flow also parameters increases since have no been flow changed. parameters However, have be inen real changed. life this However, might not bein real true life as thethis increase might not in pressurebe true as di thefferential increase and in motivepressure flow differential rate is required and mo totive increase flow rate the is suction required gas to flow increase rate forthe existing suction venturi.gas flow Anotherrate for existing way that venturi. a gas suction Another increase way that is possible a gas suction is if a newincrease and is improved possible venturiis if a new aerator and wasimproved available. venturi This aerator is currently was otheravailable. promising This is research currently in theother field promising of venturi research aeration. in the field of venturi aeration. 5.2.4. Effect of Liquid Flow Rate 5.2.4.In Effect this section,of Liquid the Flow discussion Rate is made on the effect of liquid flow rate in overall performance of theIn aeration this section, system. the discussion This effect is foundmade on ignoring the effect other of liquid changes flow associated rate in overall withliquid performance flow rate of changethe aeration like pressure system. headThis decreaseseffect is found in pump. ignoring The rest other of thechanges other associated conditions with of this liquid simulation flow rate are samechange as like in test-1. pressure head decreases in pump. The rest of the other conditions of this simulation are sameIn as Figure in test-1. 10a, it can be seen that a liquid flow rate increase has adverse effects on the dissolve oxygenIn riseFigure with 10a, time. it can As thebe seen liquid that flow a liquid rate increases, flow rate the increase system has takes adverse more time effects to reach on the saturation. dissolve Onoxygen the otherrise with hand, time. no observable As the liqu trendid flow has been rate seenincreases, for the the oxygen system transfer takes coe morefficient time and to SOTR.reach saturation. On the other hand, no observable trend has been seen for the oxygen transfer coefficient

and SOTR. Both the 𝐾𝑎 and the SOTR plots against the liquid flow rate have a downward slope

Water 2020, 12, 1637 17 of 22

Water 2020, 12, x FOR PEER REVIEW 17 of 23

Both the KLa and the SOTR plots against the liquid flow rate have a downward slope which shows the which shows the performance degradation of the system with the flow rate. The reasons should be performance degradation of the system with the flow rate. The reasons should be opposite those of the opposite those of the gas flow rate discussion. One factor is that the increasing liquid flow rate gas flow rate discussion. One factor is that the increasing liquid flow rate decreases the average gas decreases the average gas mass fraction at any time. Therefore, less interfacial area is available for mass fraction at any time. Therefore, less interfacial area is available for mass transfer through diffusion. mass transfer through diffusion. Additionally, a higher liquid flow rate decreases the bubble contact Additionally, a higher liquid flow rate decreases the bubble contact time. All of these parameters also time. All of these parameters also affect the aeration efficiency of the system negatively. affect the aeration efficiency of the system negatively.

(a) (b)

1 Figure 10. EEffectffect of liquidliquid raterate on:on: ((aa)) DissolvedDissolved (mg(mg/L)/L) oxygenoxygenvs. vs. timetime(min); (min); ( b(b))K KLLaa(h (h−−1); (c) SOTR (lbs(lbs OO22/h);/h); (d) SAE (lbs O2/hp-h)./hp-h). 5.3. Proposed System 5.3. Proposed System Based on all the previous analysis done in this research, a new system is proposed with the aim to reachreach anan SAESAE ofof overover 1.5.1.5. The proposed system is is considered for for an assumed real-life real-life problem. problem. Therefore, the size size of of the the system system is ismuch much larger larger than than the the system system tested. tested. The Theproblem problem considered considered here hereis that is the that proposed the proposed system system needs needs to aerate to aerate an aq anuaculture aquaculture (catfish) (catfish) pond pond the size the of size two of acres. two acres. The Theaverage average depth depth of the of system the system is four is feet. four This feet. gi Thisves approximately gives approximately 26,042 26,042gallons gallons of water of to water aerate. to aerate.This analysis This analysis is still done is still based done on based the assumption on the assumption of clean of water. clean water.In the previous In the previous section, section, it was itobserved was observed that diameter that diameter and airflow and airflow rate increa rate increasese have havethe maximum the maximum impact impact on increasing on increasing the theefficiency efficiency of the of theaeration aeration system. system. However, However, the the ai airflowrflow rate rate increase increase comes comes with with higher higher pressure didifferentialsfferentials and motive flowflow which in turnturn negativelynegatively impacts the SAE. In that case,case, pipe length increase playsplays aa betterbetter role,role, sincesince frictionalfrictional headhead lossloss isis muchmuch lessless throughthrough PVCPVC oror PEXPEX pipe.pipe. A pump size of 5 hphp isis chosenchosen inin thisthis casecase afterafter calculatingcalculating the total head developed by the system. Finally, Finally, multiple simulations have been done in the analyticalanalytical model to determine the optimum system to aerate this catfishcatfish pond. The input parameters that are found to be useful to get an SAE over 1.5 are given in Table5 5.. FigureFigure 11 11a,ba,b representrepresent thethe dissolveddissolved oxygenoxygen levellevel andand loglog deficitdeficit concentrationconcentration ofof oxygen with respect to timetime inin thethe catfishcatfish pondpond forfor thethe proposedproposed setupsetup respectively.respectively.

Water 2020, 12, x FOR PEER REVIEW 18 of 23

Table 5. Different physical parameters for the proposed system.

Parameter Dimensions Input Value Pipe length ft. 250 Pipe diameter inch 4

Water 2020, 12, 1637 Venturi injectors – 1 18 of 22 Injector inlet pressure psi 15 Injector outlet pressure psi 5 Table 5. DiAirfferent flow physicalrate parameters SCFM for the proposed 7 system. ParameterWater flow rate Dimensions CFM 31 Input Value Aerated water volume Gallons 26,041 Pipe length ft. 250 Pipe diameterTemperature inch °C 25 4 Venturi injectors – 1 The Mazzei InjectorInjector has inlet a catalogue pressure of their different psi venturi injectors 15 with the best possible air suction rates at differentInjector pressure outlet pressure differentials and mo psitive flow rates. From 5there, a four-inch injector was chosen which is capableAir flow of rateproducing an airflow SCFM rate of 7 scfm at the pressure 7 differentials and Water flow rate CFM 31 water flow rates describedAerated waterin Table volume 5. According to Gallonsthese input values, the 26,041 analytical model gives an −1 2 oxygen transfer coefficientTemperature of 0.045 min , an SOTR of ◦4.38C lbs O /hr, and an 25 SAE of 1.8.

(a) (b)

FigureFigure 11. 11.Proposed Proposed System: System: ((aa)) DissolvedDissolved (mg (mg/L)/L) oxygen oxygen vs. vs. timetime (min);(min);( (bb)) DeterminationDetermination of of oxygen oxygen transfertransfer coe coefficient.ﬃcient.

TheThe Mazzei possible Injector setup of has the a catalogueproposed ofsystem: their different venturi injectors with the best possible air suction rates at different pressure differentials and motive flow rates. From there, a four-inch injector 1. The proposed system will be a closed loop system where a pump will be set up on the ground. was chosen which is capable of producing an airflow rate of 7 scfm at the pressure differentials and The water intake of the pump will be at the bottom of the catfish pond. water flow rates described in Table5. According to these input values, the analytical model gives an 2. The water will reach the main discharge line located on the ground. There will be a pressure oxygen transfer coefficient of 0.045 min 1, an SOTR of 4.38 lbs O /hr, and an SAE of 1.8. gauge to measure the pressure of −the upcoming fluid before2 it enters into the injector. The possible setup of the proposed system: 3. A pressure reducing valve will be attached to the proposed system in the discharge side of the 1. Theinjector proposed to maintain system the will desired be a closed pressure loop diff systemerential. where Therefore, a pump willmaximum be set upair onsuction the ground. can be Theachieved. water intake of the pump will be at the bottom of the catfish pond. 2.4. TheThe watercoiled willpipe reach will start the mainon the discharge discharge line side located of injector on theandground. will hang There in from will the be ground. a pressure The gaugepressurized to measure water the will pressure be evacuated of the upcomingfrom the pond fluid on before top surface. it enters into the injector. 3.5. AFinally, pressure the water reducing from valve the discharge will be attached side will to be the ejected proposed into the system catfish in pond the with discharge high velocity. side of theA schematic injector to of maintain the proposed the desired system pressure is shown di inff erential.Figure 12. Therefore, maximum air suction can be achieved. 4. The coiled pipe will start on the discharge side of injector and will hang in from the ground. The pressurized water will be evacuated from the pond on top surface. 5. Finally, the water from the discharge side will be ejected into the catfish pond with high velocity. A schematic of the proposed system is shown in Figure 12.

In Table6, e fficiency ranges for various types of aeration equipment obtained from [53] are listed. However, SAE values in Table6 can be used only as a reference; exact values are equipment and application specific. In this present study, only one aerator is considered. Since multiple aerators attached in parallel form can cause more air to be injected into water, this type of setup can also be used to increase the efficiency of the overall aeration system [54,55]. Future studies could focus on the effect of multiple parallel aerators on aeration efficiency. Water 2020, 12, 1637 19 of 22 Water 2020, 12, x FOR PEER REVIEW 19 of 23

Figure 12. A schematic of the proposed system with one aerator. Figure 12. A schematic of the proposed system with one aerator. Table 6. Efficiency of different aeration systems. In Table 6, efficiency ranges for various types of aeration equipment obtained from [53] are listed. However, SAE values in TypeTable 6 can be used only as a reference; SAE (lbs exact O2/hp-h) values are equipment and application Closedspecific. Loop In this Venturi present Aspirated study, Aeration only one aerator is considered. 1.8 Since multiple aerators attached in parallel formLow-Speed can cause Surface more Aerators air to be injected into water, this 2.5–3.4 type of setup can also be High-Speed Surface Aerators 1.8–2.3 used to increase the efficiency of the overall aeration system [54,55]. Future studies could focus on Submersed Jet Aerators 1.6–2.3 the effect of multiple parallelFine Bubble aerators Diffusers, on aeration Disks efficiency. 3–10 High Density Low Flux (HDLF) Fine Bubble Diffuser 5–13 Table 6. Efficiency of different aeration systems.

6. Conclusions Type SAE (lbs O2/hp-h) In this study, a novelClosed closed Loop loopVenturi aeration Aspirated system Aeration is proposed, consisting 1.8 of a venturi air injector and a coiled pipe coupledLow-Speed with a pump. Surface Several Aerators conclusions have been made 2.5–3.4 from this study which are summarized below: High-Speed Surface Aerators 1.8–2.3 Submersed Jet Aerators 1.6–2.3 1. The experimental studyFine of Bubble the current Diffusers, closed Disks loop venturi aspirated aeration 3–10 system achieved an SOTR inHigh the range Density of 0.050–0.068 Low Flux lbs(HDLF) O2/h Fine and anBubble SAE inDiffuser the range of 0.42–0.63 5–13 lbs O2/hp-h. With the analytical study, SOTR is found to be similar for this system and is 0.047–0.059 lbs O2/h and 6. ConclusionsSAE in the range of 0.37–0.55 lbs O2/hp-h. In all cases, the difference between experimental and analytical results are within 15%. The analytical model underestimates the experimental values, In this study, a novel closed loop aeration system is proposed, consisting of a venturi air injector likely because it cannot account for turbulent mixing, bubble breakup, and bubble coalescing. and a coiled pipe coupled with a pump. Several conclusions have been made from this study which 2. The hydraulic parameters considered herein are the pipe diameter and pipe length. Both are summarized below: significantly impact the system’s aeration efficiency. Increasing the pipe length by a factor of 1. fiveThe increasesexperimental the SAE study by of 2.5 the times. current For closed pipe diameter loop venturi increase, aspirated the eff ectaera istion more system evident, achieved since increasingan SOTR in the the diameter range of by 0.050–0.068 4 times increases lbs O2 the/h and SAE an by SAE 4.1 times. in the The range linear of 0.42–0.63 trend line lbs is obtained O2/hp-h. withWith athe simple analytical mathematical study, SOTR relationship is found to between be similar SAE for against this system the pipe and is length 0.047–0.059 and diameter. lbs O2/h and SAE in the range of 0.37–0.55 lbs O2/hp-h. In all cases, the difference between experimental and analytical results are within 15%. The analytical model underestimates the experimental

Water 2020, 12, 1637 20 of 22

The probable cause for this positive influence is that pipe length increases the bubble contact time with water. Moreover, the bubbles do not migrate towards the pipe wall and try to follow the centerline by avoiding coalesce and breakup. The diameter increase has a similar impact since it reduces the water flow rate and also reduces the frictional head loss. Thereby, it increases the system’s efficiency. The flow parameters that are considered here are: gas flow rate and water flow rate. Gas flow rate seems to play an important role in the system’s efficiency. It is observed that increasing the gas flow rate by 75% increases the SAE by almost 76%. The trend line of SAE versus gas flow rate also shows a linear relationship. The gas flow rate increases the amount of bubbles or gas volume fractions in the continuous medium of water flow at any instant. This results in a higher interfacial area for mass transfer. However, liquid flow rate increase impacts the system in a negative way. It does not give enough time for bubble contact and also reduces the gas volume fraction in the continuous media. There is no observable trend line found between SAE versus liquid flow rate. 3. A system is proposed to optimize SAE based on the limited experimental information in this study. This proposed system is intended for aquaculture (e.g., catfish farm). The proposed system requires a 5-hp pump with 250 feet of 4-inch diameter coiled pipe. A 4-inch diameter venturi injector is chosen which can aspirate 7 scfm of air at 10 psi pressure differential with a water flow rate of 230 gpm. The system has an SOTR of 4.38 lbs O2/h and an SAE of 1.8.

Author Contributions: Conceptualization, D.W.M. and R.M.; methodology, D.W.M. and R.M.; validation, R.M.; formal analysis, R.M.; investigation, R.M. and M.E.; resources, R.M. and M.E.; data curation, R.M.; writing—original draft preparation R.M.; writing, R.M.; review and editing, D.W.M.; visualization, R.M.; supervision, D.W.M.; project administration, D.W.M.; funding acquisition, D.W.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to acknowledge the support from the Department of Energy’s Industrial Assessment Center’s Awards for Excellence in Applied Energy Engineering Research. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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