12T W.L<I5w IF NEEDED 15W≤L·2W Figure 19. Suggested bailes for square and rectangular tanks 5.0 FLUID SHEAR RATES Figure 20 illustrates flow pattern in the laminar flow region from a radial flat blade turbine. By using a velocity probe, the parabolic velocity distribution coming off the blades of the impeller is shown in Fig. 21. By taking the slope of the curve at any point, the shear rate may be calculated at that point. The maximum shear rate around the impeller periphery as well as the average shear rate around the impeller may also be calculated Animportant conceptis that one must multiply the fluid shear rate from the impeller by the viscosity of the fluid to get the fluid shear stress that actually carries out the process of mixing and dispersion Fluid shear stress= u(fluid shear rate) Even in low viscosity fluids, by going from l cp to 10 cp there will be 10 times the shear stress of the process operating from the fluid shear rate of the
Agitation 203 I I -.&.- I W 1. k IF NEEDED L-1.5WS L= 2w -4 Figure 19. Suggested bafles for square and rectangular tanks. 5.0 FLUID SHEAR RATES Figure 20 illustrates flow pattern in the laminar flow region from a radial flat blade turbine. By using a velocity probe, the parabolic velocity distribution coming off the blades of the impeller is shown in Fig. 2 1. By taking the slope of the curve at any point, the shear rate may be calculated at that point. The maximum shear rate around the impeller periphery as well as the average shear rate around the impeller may also be calculated. An important concept is that one must multiply the fluid shear rate from the impeller by the viscosity of the fluid to get the fluid shear stress that actually carries out the process of mixing and dispersion. Fluid shear stress = p(fluid shear rate) Even in low viscosity fluids, by going from 1 cp to 10 cp there will be 10 times the shear stress of the process operating from the fluid shear rate of the impeller
204 Fermentation and Biochemical Engineering handbook Figure 20. Photograph of radial flow impeller in a baffled tankin the laminar region, made by passing a thin plane of light through the center of the tank. △Y △V SHEAR RATE=△V △Y Figure 21. Typical velocity pattern coming from the blades of a radial flow turbine showing calculation of the shear rate△Z/△Y
204 Fermentation and Biochemical Engineering Handbook Figure 20. Photograph of radial flow impeller in a baffled tank in the laminar region, made by passing a thin plane of light through the center of the tank. f:iY M- ~y SHEAR RATE ~ Figure 21. Typical velocitypattem corning from the bladesofaradial flow turbine showing calculation of the shear rate ~V/~Y
Agitation 205 Figure 22 shows the flow pattern when thereis sufficient power andlow enough viscosity for turbulence to form. Now a velocity probe must be used that can pick up the high frequency response of these turbulent flow patterns and a chart as shown in Fig 23 is typical. The shear rate between the small scale velocity fluctuations is called microscale shear rate, while the shea rates between the average velocity at this point are called the macroscale rates. These macroscale shear rates still have the same general form and are determined the same way as shown in Fig. 21 graph of flow patterns in a mixing tank passing a thin plane of light through the center of the tank. TME.sEc。ND5 Schematic, typical velocity fluctuation pattern obtained from high frequency velocity probe placed at a point in the mixing vesse
Agitation 205 Figure 22 shows the flow pattern when there is sufficient power and low enough viscosity for turbulence to fonn. Now a velocity probe must be used that can pick up the high frequency response of these turbulent flow patterns, and a chart as shown in Fig. 23 is typical. The shear rate between the small scale velocity fluctuations is called microscale shear rate, while the shear rates between the average velocity at this point are called the macroscale rates. These macroscale shear rates still have the same general fonn and are determined the same way as shown in Fig. 21. Figure 22. Photograph of flow patterns in a mixing tank in the turbulent region, made by passing a thin plane of light through the center of the tank. 0 ..z =» 0 -u 2 >- ... ~ "' u « 0 ... ...A. I > ::: ... -to """-~~.-~-..~- 0 20 40 60 80 loo 120 140 TIME. SECONDS U = 0 + u' X x Figure 23. Schematic, typical velocity fluctuation pattern obtained from high frequency velocity probe placed at a point in the mixing vessel
206 Fermentation and Biochemical Engineering Handbook Table 2 describes four different macroscale shear rates of importance remixing tank. The parameter for the microscale shear rate at a point is the ot mean square velocity fluctuation at that point, RMS Table 2. Average Point Velocity Max imp. zone shear rate Ave imp. zone shear rate Ave, tank zone shear rate Min, tank zone shear rate RMS velocity fluctuations y(u') 5.1 Particles The consideration macro- and microscale relationships in a mixing vessel leads to helpful concepts. Particles that are greater 1,000 microns in size are affected primarily by the shear rate between the average velocities in the process and are an essential part of the overall flow throughout the tank and determine the rate at which flow and velocity distribute throughout the tank, and is a measure of the visual the tank in terms of surface action, blending or particle suspensions The other situation is on the microscale particles. They are particles less than 100 microns and they see largely the energy dissipation which occurs through the mechanism of viscous shear rates and shear stresses and ultimately the scale at which all energy is transformed into heat The macroscale environment is effected by every geometric variable and dimension and is a key parameter for successful scaleup of any process, whether microscale mixing is involved or not. This has some unfortunate consequences on scaleup since geometric similarity causes many other parameters to change in unusual ways, which may be either beneficial or
206 Fermentation and Biochemical Engineering Handbook Table 2 describes four different macroscale shear rates of importance in a mixing tank. The parameter for the microscale shear rate at a point is the root mean square velocity fluctuation at that point, RMS. Table 2. Average Point Velocity Max. imp. zone shear rate Ave. imp. zone shear rate Ave. tank zone shear rate Min. tank zone shear rate 5.1 Particles The consideration of the macro- and microscale relationships in a mixing vessel leads to several helpful concepts. Particles that are greater 1,000 microns in size are affected primarily by the shear rate between the average velocities in the process and are an essential part of the overall flow throughout the tank and determine the rate at which flow and velocity distribute throughout the tank, and is a measure of the visual appearance of the tank in terms of surface action, blending or particle suspensions. The other situation is on the microscale particles. They are particles less than 100 microns and they see largely the energy dissipation which occurs through the mechanism of viscous shear rates and shear stresses and ultimately the scale at which all energy is transformed into heat. The macroscale environment is effected by every geometric variable and dimension and is a key parameter for successful scaleup of any process, whether microscale mixing is involved or not. This has some unfortunate consequences on scaleup since geometric similarity causes many other parameters to change in unusual ways, which may be either beneficial or
Agitation 207 detrimental, but are quite different than exist in a smaller pilot plant unit. On the other hand, the microscale mixing condition is primarily a function of power per unit volume and the result is dissipation of that energy down through the microscale and onto the level of the smallest eddies that can be identified as belonging to the mixing flow patterm. an analysis of the energy dissipation can be made in obtaining the kinetic energy of turbulence by putting the resultant velocity from the laser velocimeter through a spectrum analyzer. Figure 24a shows the breakdown of the energy as a function of frequency for the velocities themselves. Figure 24b shows a similar spectrum analysis of the energy dissipation based on velocity squared and Fig. 24c shows a spectrum analyzer result from the product of two orthogonal velocities, VR and Vz' which is called the Reynolds stress(a function of An estimation method of solving complex equations for turbulent flow uses a method called the K-E technique which allows the solution of the Navier-Stokes equation in the turbulent region 5.2 Impeller Power Consumption Figure 25 shows a typical Reynolds number-Power number curve for different impellers. The important thing about this curve is that it holds true whether the desired process job is being done or not. Power equations have three independent variables along with fluid properties: power, speed and diameter. There are only two independent choices for process considerations For gas-liquid operations there is another relationship called the K factor which relates theeffect of gas rate on power level. Figure 26 illustrates a typical K factor plot which can be used for estimation. Actual calculation of K factor in a particular case involves very specific combinations of mixer variables, tank variables, and fluid properties, as well as the gas rate being used Commonly, a physical picture of gas dispersion is used to describe the degree of mixing required in an aerobic fermenter. This can be helpful on occasion, but often gives a different perspective on the effect of power, speed and diameter on mass transfer steps. To illustrate the difference between physical dispersion and mass transfer, Fig. 27 illustrates a measurement made in one experiment where the height of a geyser coming off the top of the tank was measured as a function of power for various impellers. Reducing the geyser height to zero gives a uniform visual dispersion of gas across the surface of the tank. Figure 28 shows the actual data and indicates that the 8-inch impeller was more effective than the 6-inch impeller in this particular tank
Agitation 20 7 detrimental, but are quite different than exist in a smaller pilot plant unit. On the other hand, the microscale mixing condition is primarily a function of power per unit volume and the result is dissipation of that energy down through the microscale and onto the level of the smallest eddies that can be identified as belonging to the mixing flow pattern. An analysis of the energy dissipation can be made in obtaining the kinetic energy of turbulence by putting the resultant velocity from the laser velocimeter through a spectrum analyzer. Figure 24a shows the breakdown of the energy as a function of frequency for the velocities themselves. Figure 24b shows a similar spectrum analysis of the energy dissipation based on velocity squared and Fig. 24c shows a spectrum analyzer result from the product of two orthogonal velocities, V, and Vz9 which is called the Reynolds stress (a function of momentum), An estimation method of solving complex equations for turbulent flow uses a method called the K-E technique which allows the solution of the Navier-Stokes equation in the turbulent region. 5.2 Impeller Power Consumption Figure 25 shows a typical Reynolds number-Power number curve for different impellers. The important thing about this curve is that it holds true whether the desired process job is being done or not. Power equations have three independent variables along with fluid properties: power, speed and diameter. There are only two independent choices for process considerations. For gas-liquid operations there is another relationship called the K factor which relates the effect ofgas rate on power level. Figure 26 illustrates a typical K factor plot which can be used for estimation. Actual calculation of K factor in a particular case involves very specific combinations of mixer variables, tank variables, and fluid properties, as well as the gas rate being used. Commonly, a physical picture of gas dispersion is used to describe the degree of mixing required in an aerobic fermenter. This can be helpful on occasion, but often gives a different perspective on the effect of power, speed and diameter on mass transfer steps. To illustrate the difference between physical dispersion and mass transfer, Fig. 27 illustrates a measurement made in one experiment where the height of a geyser coming off the top of the tank was measured as a function of power for various impellers. Reducing the geyser height to zero gives a uniform visual dispersion of gas across the surfBce ofthe tank. Figure 28 shows the actual data and indicates that the 8-inch impeller was more effective than the 6-inch impeller in this particular tank
208 Fermentation and Biochemical Engineering Handbook VZ& VR SPECTRUMS FOR 15.9 IN. A200(PBT) A SEc 30 37 FT/SEC N·2.0R POWER SPECTRUM VZ& 2 FOR 15 IN. R100(RUSHTON TURBINE) T 2/ SEc2.12 HZ 77 FT2/SEC :8 23儿L87=4 REYNOLDS STRESS X FOR 15.9 IN. A200(PBT) 8.00Hz VZI VR ,073F ( dB 儿L87·4 Figure 24. Typical spectrum analysis of the velocity as a function of (a) velocity frequency fluctuation, (b) the frequency of the fluctuations using the square of the velocity to give the ergy dissipation, and(c) the product of two orthogonal vele the frequency the fluctuations. The product of two orthogonal velocities is related to the momentum in the fluid stream
208 Fermentation and Biochemical Engineering Handbook vz (dB) VZ & VR SPECTRUMS FOR 15.9 IN. A200 (PBT) - - 70 10 L - 30 (dB) -50 - 70 VR 0 4 10 15 20 HZ N - 2.0 RPS C - 16 IN. ZC - 12.8 IN. RC = 5.6 IN. RUN 23 JUL 87-4 POWER SPECTRUM VZ2& VR2 FOR 15 IN. R 100 ( RUSHTON TURBINE 1 0 - 20 -40 - -60 I I I I 1 N = 2.0 RPS C = 16.0 IN ZC 16.75 IN: RC = 9.00 M. REYNOLDS STRESS VZ xVR FOR 15.9 IN. A200 (PBT) I \ 8.00 HZ -10 1 ,073 FT2ISEC2 i' -70 0 5 10 15 20 HZ N - 2.0 RPS (4 C 8 16 IN ZC 12.8 IN RC - 5.6 IN RUN 23 JUL 87-4 Figure 24. Typical spectrum analysis of the velocity as a function of (a) velocity frequency fluctuation, (b) the frequency of the fluctuations using the square of the velocity to give the energy dissipation, and (c) the product of two orthogonal velocities versus the frequency of the fluctuations. The product of two orthogonal velocities is related to the momentum in the fluid stream
10 FLAT BLADE TURBINE BAFFLED TANK CURVED BLADE TURBINE· BAFFLED TANK 1.0 PROPELLER SQUARE PITCH BAFFLED OR OFF-CENTER 102 D2 N D IMPELLER DIAMETER μL。 UID VISCOS|Y N IMPELLER ROTATIONAL SPEED P POWER P LIQUID DENSITY 9 GRAVITY CONSTANT Figure 25. Power number/Reynolds number curve for the power consumption of impellers CENTERL INLET SUPERFICIAL GAS VELOCITY, FEET PER SECOND gure 26. Typical curve of K factor, power drawn with gas on versus power drawn with gas off, for various superficial gas velocities
Agitation 209 - IIIII 1 Ill I IIII I I III I I Ill I 1 lj - - - - - FLAT BLADE TURBINE- - - - BAFFLED TANK 1 - CURVED BLADE - TURBINE - BAFFLED TANK - .. I I - - - - - - - BAFFLED OR OFF- CENTER I IIIII 1111 I I Ill I I Ill I I Ill I I I - 100 10 1 .o 0.1 DZ Np t.' D IMPELLER DIAMETER LlOUlD VISCOSITY N IMPELLER ROTATIONAL SPEED p LlOUlD DENSITY P POWER g GRAVITY CONSTANT Figure 25. Power number/Reynolds number curve for the power consumption of impellers. Figure 26. Typical curve of K factor, power drawn with gas on versus power drawn with gas off, for various superficial gas velocities
210 Fermentation and Biochemical Engineering Handbook MAX GEYSER HEIGHT L」 Figure 27. Schematic of geyser height T=30"E=30 Figure 28. Plot illustrating measurement of geyser height
21 0 Fermentation and Biochemical Engineering Handbook Figure 27. Schematic of geyser height. 3.0 2.5 2.0 a W ln ln Q W vj -I q a 1.5 0.5 I I 1 1 I I I 0125456 GEYSER HEIGHT, INCHES Figure 28. Plot illustrating measurement of geyser height
Agitation 211 Also, the 8-inch impeller with standard blades was more effective than the 8-inch impeller with narrow blades. These results all indicate that in this range of impeller-size-to-tank-size ratio, pumping capacity is more impor tant than fluid shear rate for this particular criterion of physical dispersion Looking now at some actual published mass transfer rates, Fig. 29 shows the results of some experiments reported previously and Figs. 30 through 33 show some additional experiments reported which give further clarification to Fig. 29 In Fig. 29, the ratio of mixer horsepower to gas expansion horsepower is shown with the optimum D/Trange from a mass transfer standpoint in air- water systems. At the left of Fig. 29, it can be seen that large D/Tratios are moreeffective than small D/Tratios. This is in an area where the mixer power level is equal to or perhaps less than the gas expansion power level. Moving to the right, in the center range it is seen that the optimum D/ratios are on the order of 0. 1 to 0. 2. This corresponds to an area where the mixer power level is two to ten times higher than the expansion power in the gas stream Thus shear rate is more important than pumping capacity in this range, which is a very practical range for many types of gas-liquid contacting operations, including aerobic mass transfer in fermentation FERMENTATION ≤0.3 o0.2 wuz WASTE TREA TING 000 RATIO ARBITRARY UNITS GAS RATE Figure 29. Effect of horsepower-to-gas rate ratio at optimum DT
Agitation 21 I Also, the 8-inch impeller with standard blades was more effective than the 8-inch impeller with narrow blades. These results all indicate that in this range of impeller-size-to-tank-size ratio, pumping capacity is more important than fluid shear rate for this particular criterion of physical dispersion. Looking now at some actual published mass transfer rates, Fig. 29 shows the results of some experiments reported previously and Figs. 30 through 33 show some additional experiments reported which give firther clarification to Fig. 29. In Fig. 29, the ratio ofmixer horsepower to gas expansion horsepower is shown with the optimum D/Trange from a mass transfer standpoint in airwater systems. At the left of Fig. 29, it can be seen that large DIT ratios are more effective than small D/Tratios. This is in an area where the mixer power level is equal to or perhaps less than the gas expansion power level. Moving to the right, in the center range it is seen that the optimum D/T ratios are on the order of 0.1 to 0.2. This corresponds to an area where the mixer power level is two to ten times higher than the expansion power in the gas stream. Thus shear rate is more important than pumping capacity in this range, which is a very practical range for many types of gas-liquid contacting operations, including aerobic mass transfer in fermentation. 10 100 1000 RATIO, "' '' ARBITRARY UNITS GAS RATE Figure 29. Effect of horsepower-to-gas rate ratio at optimum DIT
212 Fermentation and Biochemical Engineering Handbook CENTER INLET F=. 02 FT/SEC HP/IOOO GALS. GASSED igure 30. Effect of sparge ring diameter on mass transfer performance of a flat blade turbine, based on gassed horsepower at gas velocity F=0.02 fUsed T|8"2= 6 FBT C=6 CENTER INLET 04 F=. 04 FT/SEC 02 HP/IOOO GALS. GASSED Figure 31. Effect of horsepower and impeller diameter on mass transfer coefficient at O
212 Fermentation and Biochemical Engineering Handbook .04 6 I I- .02' 5 c y+ o= .01 008 ia' dZ II d Y * .004 - . T= 18" L= 18" 6FBT C=6" CENTER INLET I1 1 1 a, .8 1.0 2.0 4.0 8.0 IO .002 ' .4 HP/IOOO GALS. GASSED Figure 30. Effect of sparge ring diameter on mass transfer performance of a flat blade turbine, based on gassed horsepower at gas velocity F = 0.02 ft/sec. T= 18" z= 18" 6 FBT C=6" CENTER INLET F=.04 FT/SEC Figure 31. Effect ofhorsepower and impeller diameter onmass transfer coefficient at 0.04 Wsec gas velocity