Aquacultural Engineering 31 (2004) 83–98 Design of high efficiency surface aerators Part 1. Development of new rotors for surface aerators Beatriz Cancino a,∗ , Pedro Roth b , Manfred Reuß c a Department of Food Engineering, Universidad Católica de Valparaı́so, Waddington 716, Valparaı́so, Chile Mechanical Department, Universidad Técnica Federico Santa Marı́a, P.O. Box 110V, Valparaı́so, Chile c ZAE Bayern, Domagkstr. 11, D-80807 Muenchen, Germany b Received 1 April 2003; accepted 14 March 2004 Abstract The main objective of this work was the design of a high efficiency centrifugal surface aerator for fishponds. The proposed system has been designed to be used with photovoltaic panels as an energy supply. The work is presented in three papers, of which this is the first part. The objective was reached through a theoretical design of the rotor using the traditional mass transfer equations and the mechanical approach using the superficial similarities of aerators to axial flow pumps. A total of 23 different rotor configurations were tested. The configurations were defined by the type of propeller, the inlet and exit angles of the blades and the rotor’s immersion percentage. Dimensional analyses was used to find the equations that describes the aerator’s behavior. © 2004 Elsevier B.V. All rights reserved. Keywords: Surface aerator design; Surface aerator efficiency 1. Introduction Aeration systems have been studied with different methods of analysis, which can be classified by: • Theoretical, using the mass transfer equations and computational methods that involve turbulence theory, and • Experimental, which is based on tests made in the laboratory or in the field. ∗ Corresponding author. Tel.: +56-32-274226; fax: +56-32-274205. E-mail address: beatriz.cancino@ucv.cl (B. Cancino). 0144-8609/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.aquaeng.2004.03.002 84 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 The practical applications of aeration give other points of view for the classification, such as: • aeration for waste water treatment (residential and industrial); • gas transfer in the chemical industry; • aeration in aquaculture. Both classifications are superimposed; that is, the use of oxygen in the water is related to the analysis of the phenomena. For example, compressors and diffused gas bubble systems are equipment traditionally used in the chemical industry. Because of this, the first studies (Higbie, 1935; Danckwerts, 1955; Harriot, 1962) analyzed the mass transfer equation, the size of the nozzle and the size of the bubbles. With the development of computers, these investigations turned—in great part—to the analysis of turbulence and modeling (Perlmutter, 1961; Calderbank and Moo-Young, 1961). The concept of eddies and the question about the eddy’s size became more interesting as modeling became easier (Calderbank and Moo-Young, 1961; Hinze, 1959; Ferziger, 1983). However, the treatment of the aeration phenomena in water treatment and aquaculture has been different. The focus here has been the aeration efficiency (AE). The research efforts have been directed towards the optimization of the AE, which contains the global mass transfer coefficient (kL a). Several aquaculture works can be found in this direction: Boyd and Watten (1989), Busch et al. (1974), Colt (2000, 2000a), Colt and Tchobanoglous (1981), Petrille and Boyd (1984). The centrifugal surface aerator along with the paddle wheel surface aerator are widely used. The centrifugal surface aerator had been traditionally used in wastewater treatment (ASCE, 1997; Stukenberg et al., 1977; Wagner, 1997). Nestmann (1984) designed and optimized equipment that could be classified within this group but it is different from the traditional aerators because it uses a rotor design with a spiral staircase channel forming an inverted truncated cone. The needs of the aquaculture industry, however, are different than those of the waste water treatment industry. In aquaculture applications, the dissolved oxygen concentration must be much higher than in waste water treatment (Colt and Tchobanoglous, 1981; Colt, 2000a). Boyd and Watten (1989) summarized the importance of the dissolved oxygen concentration in aquaculture. They have shown that most warm water species can tolerate concentrations as low as 2–3 mg/l of dissolved oxygen, and many cold water species can tolerate 4 or 5 mg/l. The problem is that aquatic organisms eat and grow better and are healthier when the dissolved oxygen concentration is at or near saturation. Colt and Tchobanoglous (1981) have shown similar conclusions for fish that are important in aquaculture (rainbow trout, salmon, channel catfish, and Malaysian shrimp). The centrifugal surface aerator used in aquaculture is constructed with individual rotor blades. However, research about the design of this equipment has not yet been reported. Questions such as best number of blades used in the design, the necessary number of blades, the shape of the blades, the relevant geometric parameters involved in the mass transfer—which are interesting to study in order to determine the aeration efficiency (kg O2 /kWh)—have not yet been determined. This works tries to answer these questions and is specially focused in the optimization of the aeration efficiency so that the photovoltaic energy may be used in the fishpond systems. B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 85 The rotor, which controls the aeration, is the main component of the aerator. Because of this, the objective is to design a rotor or to find the best aerator configuration for the optimization of the aeration efficiency. 2. Gas transfer According to Pöpel (1984), the surface aerator oxygenates because: 1. The aerator hits the air in the water with its propellers or blades. 2. The aerator stirs the water and creates droplets and films of water in the air. 3. The droplets and masses of water that fall again on the surface of the liquid bring air with them. 4. The aerator produces currents that drag bubbles of water to the bottom of the tank. 5. The water surface is in constant movement, renovating itself continuously. Aeration is the mass transfer phenomena between air and water, of which the variation of the oxygen concentration in the water, as a function of time, is given by (Treybal, 1980): dC = kL a(Cs − C) dt (1) where C is the oxygen concentration in water (mg/l); Cs the saturated oxygen concentration (mg/l); kL a the overall mass transfer coefficient (h−1 ); t the time (h). In the water–air systems, the liquid phase places the most resistance to the mass transfer, therefore the mass transfer phenomena is controlled by the liquid phase and the overall mass transfer coefficient (kL a) can be calculated using the movement of the oxygen in the water (Treybal, 1980). In order to compare the coefficients for different temperatures, the following equations can be used (Boyd, 1986; Pöpel, 1985): CsT = 2234.34(T + 45.93)−1.31403 kL aTr = kL aT 1.024(T −Tr) (2) (3) where Tr is the reference temperature (◦ C); T the water temperature for the test (◦ C); CsT the saturated oxygen concentration at temperature T (mg/l); kL aTr the overall mass transfer coefficient at the reference temperature (h−1 ); kL aT the overall mass transfer coefficient at the water’s temperature for the test (h−1 ). In order to allow comparisons of different units, the aeration performance is reported at a standard temperature: Germany uses 10 ◦ C and USA uses 20 ◦ C (Wagner, 1997; ASCE Standard, 1992). Using the German standard: OTR10 = kL a10 Cs10 where OTR10 is the oxygen transfer rate at 10 ◦ C and 1 atm (g/m3 /h). From Eq. (2), we obtain Cs10 = 11.29 mg/l and Cs20 = 9.09 mg/l. (4) 86 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 The equation for the aeration efficiency at 10 ◦ C is: AE10 = OTR10 V P (5) where P is the power of the motor (W); V the volume of water tank (m3 ) (Pöpel, 1984); AE10 the aeration efficiency at 10 ◦ C (kg O2 /kWh). To design a high efficiency surface aerator it is necessary to identify the parameters that are relevant to the oxygen transfer phenomena and to investigate the best way to optimize the AE value. This means that the value of kL a must be increased and that the power consumption must be kept the same level or diminished. As a first approach the kL a value is given by (Treybal, 1980): kL a = kL × a (6) where kL is the transfer rate of oxygen from the air to the water (m/s); a the specific area through which the oxygen transfer occurs (m−1 ). In the previous equation, as well as with the following equations, kL a is given in s−1 . Nevertheless, through a change in units the value is obtained in hours, maintaining the meaning of the equations. In surface aerators (Pöpel, 1984; Zlokarnik, 1991; Wagner, 1997), the variable a is defined by: a= A V (7) where A is the air–water contact area (m2 ); V the water volume splashed (m3 ). According to Pöpel (1984), in a surface aerator it corresponds to the tank volume. According to Eqs. (4) and (5), in order to achieve lower power consumption it is necessary to increase the value of kL a so that the value of AE may increase. According to Higbie (1935), kL is given by:
D (8) kL = 2 πtk where tk is the average time of air–water interface (s) and 1/tk represents the interface renovation speed (s−1 ). In a surface aerator (Pöpel, 1984) te = tk (9) where te is the contact time of the droplets with the air (s); D the oxygen diffusion in water (m2 /s). The contact time, or exposure, between the droplet or jet of water increases as the height of the splashed water increases. This behavior corresponds to a parabolic movement where:
8H (10) te = g where g is the gravitational acceleration (m/s2 ); H the height of splashed water (m). B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 87 This analysis indicates that the value of kL a can be increased changing the set-up of the equipment. These modifications result in an increment of the water surface area, which is the mass transfer area. In this way, the increment of water surface area can be carried out increasing the amount of water splashed. Another possibility could be to increase the dispersion of the water splashed, turning the jet into smaller sized droplets. In order to optimize AE, it is necessary to maximize the Q/P rate, which is defined as the flow of water splashed by the aerator (Q) per unit of aerator power (P). Propellers for the surface aerator were chosen using this criterion. These rotors were able to splash the largest amounts of water with minimum power consumption at a distance in which the contact time, te from Eq. (10), was enough to produce the oxygen transfer but not so large as to make the value of kL drop. 3. Design of the rotor Using the mechanical approach, the centrifugal aerator was thought of as an axial flow pump without prerotation. Prerotation is the movement that captures the liquid so that it enters the impeller passages with a minimum disturbance. Prerotation can be implemented in pumps with a suction device as the suction nozzle and suction pipe design. However, to simplify the calculation, the design methodology will consider an axial flow pump without prerotation. The direction of flow of the liquid depends on the impeller vane’s entrance angle, the capacity going through and the peripheral velocity (Stepanoff, 1993). Each of these parameters is used to design the rotor. It was estimated that the maximum power used by the prototype was 250 W. The rotor named “Kinetic 3” was obtained with this method. axis of rotor D0 Dm Dh exit angle b blade hb inlet angle direction ofrotation b Dh Dm D0 hb : : : : blade length diameter of center average diameter outer diameter blade heigh Fig. 1. Drawing of the rotor with inlet and exit angle. 88 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 φ φ ßc φ θ2 2 θ1 ß2 φ ß1 distance between two blades R direction of rotation Fig. 2. Drawing of the angles of a blade for axial flow. Fig. 1 shows a general schematic of the rotor with the inlet and exit angles of the blade. The inlet angle is the first angle to have contact with the water when the rotor turns. The exit angle is the blade’s angle that gives the direction to the splashed water. The axial pumps have two principals parts: the impeller, or rotor, which forces the liquid into a rotary motion by impelling action and the pump casing which directs the liquid to the impeller and leads it away at a higher pressure. The impeller vanes and impeller side walls form the impeller channels (Stepanoff, 1993). The theory used for the analysis of the axial flow pump is based on the movement of the liquid when it is flowing between the channels. In the aerator we can considerer that the rotor and the spaces between the blades are the channels where the liquid acquires the velocity and the exit angle. Fig. 2 shows the angles of a blade in an axial flow pump. In an axial flow pump, the liquid approaches the impeller axially and the forward component of velocity is obtained from the impeller, which is parallel to the shaft axis. This is the effect that is desired for the centrifugal surface aerator. Following the axial flow pump theory of Stepanoff (1993), it is necessary to use the following equation for the external forces acting on the water flowing through two blades (see Fig. 3): T = dm (r2 cu2 − r1 cu1 ) dt (11) u = πDn (12) c1 w1 cm1 w2 c2 ß1 α1 cu1 u1 wu1 entrance velocity triangle α2 cm2 c u2 ß2 w u2 u2 discharge velocity triangle Fig. 3. Euler’s velocity triangle. B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 89 cu2 = c2 cos α2 (13) cu1 = c1 cos α1 (14) where T is the momentum of the water flowing through two blades (J); m the water mass between two blades (kg); t the time (s); u the peripheral velocity (m/s); n the revolutions per minute (s−1 ); D the diameter of the circle in which the fluid at the perimeter of the blade moves (m); c the absolute velocity of flow. This is equal to the vectorial sum of the relative velocity and the peripheral velocity of the impeller (aerator blades) (m/s); r the radio of the circle in which the fluid at the perimeter of the blade moves (m); w the relative velocity of flow. Subscript 1 refers to the liquid that enters the aerator and subscript 2 to the liquid discharged. The velocity depends on the inlet and exit angles. Using Eq. (11) in the velocity analysis, the flow water and the dynamic head, we obtain Euler’s equation: Hp = 1 (u2 cu2 − u1 cu1 ) g (15) where Hp is the theoretical head (m). The power applied to the liquid by the impeller (aerator blades) can be estimated by: P = Tω = Qρ (u2 cu2 − u1 cu1 ) (16) where P is the theoretical power (W); Q the flow of water (m/s); ρ the water density (kg/m3 ); ω the angular velocity of the impeller (s−1 ). Assuming that there is no loss of head between the impeller and the point where the total dynamic head is measured, all of this power is available at the output of an idealized pump. In our case, we can suppose this is the power output of an idealized aerator. In the axial flow pump theory described by Stepanoff (1993), the analysis incorporates the velocity calculated using the angles of the blades (inlet and exit angles). Theses are named “Euler’s velocity triangles” and are shown in Fig. 3. With this, it is possible to calculate the head in Eq. (15), named Euler’s head (He ). Euler’s head is considerably higher than the input head. Euler’s equation (Eq. (15)), with the water flowing in an axial direction (without the tangential velocity component) reduces to: u2 cu2 Hp = (17) g Using the Euler’s velocity triangle (see Fig. 2), cm2 cu2 = u2 − wu2 = u2 − tan β2 (18) we can obtain the following equation for He : He = u2 2 u2 cm2 − g g tan β2 (19) 90 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 In Eq. (19), cm2 is proportional to Q, and Q is equal to the product between cm2 and the area normal to cm2 . In axial flow pumps the angle β2 is less than 90◦ . Therefore, He diminishes when the pump’s flow (Q) increases. It is common for β2 to be between 30◦ and 15◦ . Without considering the efficiency, the mechanical power is equal to the power used for the flow of water. Therefore, multiplying Eq. (19) by Q gives the theoretical power. If we use the pump’s constant, K, substituting Q with Kcm2 in Eq. (19), we obtain: u2 cm2 u2 cm2 Ptheoretical = 2 − K g g tan β2 (20) Stepanoff (1993) described different parameters in the theory of axial flow pumps. One of these constants is the velocity factor, Ku . These parameters are calculated to permit the design of new pumps and are based on experimental tests. u2 (21) Ku = √ 2gHe with Ku and Eq. (12), it is possible to calculate the diameter of the rotor. Another parameter used in this work, cited by Stepanoff, is the head coefficient, given by: ψ= He gHe = 2 2 2 2 π n D u2 /g (22) Table 1 shows the steps used for calculating the design parameters of the rotor. Steps 1–3 are based on previous tests—made by the same researchers—with commercial surface aerators (Cancino, 2001). The number of paddles was chosen according to Stepanoff’s work on axial flow pumps. The exit angle (β2 ) was selected between the typical angles used for axial pumps (Stepanoff). The value of D in the previous equations correspond to rotor’s Table 1 Summary of the criteria and results in the design of the rotor (Cancino, 2001) Design steps Results 1. Height of thrown water 2. Flow of water thrown by aerator 3. n 4. ns (specific speed) 5. Amount of paddles 6. Exit angle β2 7. Exit angle for the tests 8. Approximate speed constant, Ku (Stepanoff, 1993) 9. Approximate value of Dr 10. Correct of value Dr 11. Head coefficient ψ (Stepanoff, 1993) 12. Ku 13. Inlet angle β1 and velocities (by drawing Euler’s velocity triangle) 14. P/k ratio: theoretical power/constant power of the pump 0.5 m 0.009 m3 /s 1500 rpm 12,360 3 27.5◦ > β2 > 15◦ β2 = 25◦ Ku ≈ 2.2 Dr = 0.09 m Dr = 0.094 m ψ = 0.098 Ku = 2.26 β1 ≈ 11◦ P ≈ 291 W B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 91 Table 2 Summary of rotors studied Type of rotor Inlet angle (i), exit angle (o) Flat 1 i = o (tested angles: 30◦ , 45◦ , 60◦ , 70◦ ) Width and length of paddle (mm) Number of paddles Total diameter (mm) 20, 70 3 166 Flat 2 i = o (tested angles: 70◦ ) 20, 50 3 126 Flat 3 i = o (tested angles: 30◦ , 45◦ , 60◦ , 70◦ ) 35, 35 3 92 Flat 4 i = o (tested angles: 30◦ , 30◦ , 45◦ , 45◦ , 60◦ , 60◦ , 70◦ ) 35, 50 3 120 o= 36◦ – 3 90 o= 74◦ i= 21◦ ; German 2 i= 24◦ ; – 3 87 Conrad i = 25◦ ; o = 12◦ – 3 104 Kinetic 1 i = 21◦ ; o = 35◦ German 1 Kinetic 2 Kinetic 3 i= 26◦ ; i= 11◦ ; – 4 118 o= 42◦ – 4 117 o= 25◦ 35, 35 3 94 (±) diameter (Dr ). The value of Ku was taken from Stepanoff using the previous steps. Step 9 is calculated using Eqs. (11) and (12) and step 8. The final size of Dr (step 10) was measured when the rotor was built. With the real size of Dr , the values of Ku and ψ were calculated using Eq. (21) and (22) (steps 11 and 12). The inlet angle β1 (step 12) was calculated using the drawing of Euler’s triangle for this rotor. Finally, the rate P/k of the rotor was calculated using Euler’s triangle and Eq. (20). housing motor support water level hprof shaft float θ dimension in mm Fig. 4. Drawing of the prototype used for the aeration tests. hprof is the distance measured between surface of water to end of blade, or immersion depth. 92 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 Fig. 5. Picture of the prototype used for the aeration tests. top view 2 22 R8 2 c 12 Ø6 b a side view Details of the blade Fig. 6. General schematic diagram for flat rotors. Table 3 Measurements of lengths described in Fig. 6 for each flat rotor studied Rotor a (mm) b (mm) c (mm) Flat 1 Flat 2 Flat 3 Flat 4 8 8 3 3 70 50 35 50 20 20 35 35 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 Fig. 7. German 1 propeller. 93 94 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 4. Rotors tests In this work, 10 different types of rotors were tested: Flat 1, Flat 2, Flat 3, Flat 4, German 1, German 2, Conrad, Kinetic 1, Kinetic 2, and Kinetic 3. All the dimensions shown in the figures are in millimeters. The characteristics of the rotor are shown in Table 2. Fig. 4 shows a picture of the apparatus used for the tests and Fig. 5 shows a drawing of the apparatus with the dimensions of each Fig. 8. German 2 propeller. B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 Fig. 9. Conrad propeller. Top view Side view Fig. 10. Kinetic 1 type rotor, β1 = 21◦ . 95 96 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 component. The apparatus has a support and plastic housing for the electrical motor. It is maintained on top of the water with help of floaters. The rotor is installed at the end of the shaft. The distance between the rotor and the water level, related to the power used by the aerator, is modifiable. Flat rotors have the inlet angle equal to the exit angle. Fig. 6 shows a schematic of a flat rotor. The difference between flat rotors is the length of the blade, shown in Table 3. Variations in the angle of each one of the blades cause the differences observed in Table 2, in the column where the “tested angles” appear. The angle is adjusted using a screw available for this, as shown in Fig. 6. In the oxygen tests, four angles were used for each flat rotor: 30◦ , 45◦ , 60◦ , and 70◦ . The choice of the angle was based on previous unpublished work made by the authors. In that study tests were made with exit angles the same or lower (25◦ ) than which were calculated in the previous section using the mechanical approach. That study showed that the lower angles yielded a very low flow of water and the same amount of power. In those experiments with the lower angles it was not possible to get reliable results. The second criterion for the selection of those angles was based on the design of commercial centrifugal surface aerators. These aerators have the inlet and exit angles shown Top view Side view Fig. 11. Kinetic 2 type rotor, β1 = 26◦ . B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 97 in the specifications presented in Table 2, these rotors will be referred to as German 1 and German 2. In German 1 the exit angle is 36◦ and in German 2 it is 74◦ . Therefore, there is no similar criterion used in the design of these commercial aerators. German 1 and German 2 are scaled versions of rotors from commercial aerators. The scale was geometric, maintaining the inlet and exit angles. Figs. 7 and 8 shows pictures of the German 1 and German 2 rotors, respectively. The Conrad rotor is a rotor designed supposing a shift propeller. This design, shown in Fig. 9, was chosen as another possibility in order to compare rotors. The Kinetic 1 rotor was designed considering the German 1 rotor. The inlet angles are the same, and the exit angles are very similar in both models. The differences are the shape, the number of blades and the diameter. Fig. 10 shows a drawing of Kinetic 1. The Kinetic 2 rotor was thought of as a rotor design with inlet and exit angles different from the others but with the same shape and number of blades as Kinetic 1. Fig. 11 shows a drawing of Kinetic 2. The Kinetic 3 rotor was designed based on the steps shown in the previous section and its characteristics are resumed in Table 1. Fig. 12 shows a picture of this rotor. Fig. 12. Kinetic 3 type rotor. 98 B. Cancino et al. / Aquacultural Engineering 31 (2004) 83–98 Acknowledgements Thanks to GIARA (German–Israel Agricultural Research Agreement for the benefit of the third world) for financing a previous part of the investigation; to DAAD (Deutsche Akademischer Austausch Dienst); to the Dirección de Investigación y Postgrado of the Universidad Federico Santa Marı́a in Chile, for grating the funds for this research. References ASCE Standard, 1992. Measurement of Oxygen Transfer in Clean Water, second ed. The American Society of Civil Engineers. ASCE Standard, 1997. Standard Guidelines for In-Process Oxygen Transfer Testing. The American Society of Civil Engineers, ASCE 18–96, New York. Boyd, C., 1986. A method for testing aerators for fish tanks. Prog. Fish-Cult. 48, 68–70. Boyd, C., Watten, B., 1989. Aeration systems in aquaculture. CRC Critical Reviews in Aquatic Science, vol. 1 (3). CRC Press, pp. 425–472. Busch, C.D., Koon, J.L., Allison, R., 1974. 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