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