CENTRIFUGATION EQUIPMENT
DESIGN De Laval's " K Q value" spelled out. the continuous
disk
Design factors with
centrifuge as a case in point
by FRANK E. SULLIVAN and RICHARD A. ERIKSON, The De Laval Separator co., Poughkeepsie, N . Y.
SEPARATION
of immiscible liquids and insoluble particles has been occurring in nature since the beginning of the universe. However, the application of centrifugal force to aid separation is of more recent times. Flowers (7) describes centrifugal force as the force which is produced by any moving mass that is compelled to depart from the rectilinear path which it tends to follow, the force being exerted away from the center of curvature of its path. Further, he states, a centrifuge is a machine designed to subject material, held in it or being passed through it, to centrifugal force. With the advent of missiles and astronauts, these terms-once only for the scientist-are now common newspaper topics. There are numerous types of machines to produce centrifugal force on materials. This article will be confined to the development and design of the continuous disk centrifuge.
Typical Centrifuge The modern, high-capacity disk centrifuge will be used to illustrate centrifuge design. The unit as shown is a hermetic separator (74). T h e feed material enters at the bottom through a carbonto-ceramic face seal to a built-in feed pump. T h e feed pump mounted on the spindle forces the material through the hollow rotating spindle and upward into the centrifugal bowl. The lightand heavy-phase liquids are separated and discharged under pressure through
434
separate seals into pipes which carry the liquids to further processing or storage. T h e outlet seals, also of carbon-toceramic, are designed, normally, for the 100- to 150-p.s.i. range; however, for special applications, balanced seals may be employed for higher pressures. The bowl for the continuous disk centrifuge shown is forged from high strength corrosion resistant 329 stainless steel. The bowl of 24-inch diameter contains approximately 130 disks, each 18 inches in diameter, with a total bowl weight of 1300 pounds. The disks are significantly smaller in diameter than the bowl shell in order to provide an adequate sediment-holding space for heavy solids which do not discharge with the heavy-phase liquid. An important design feature in a disk bowl is that sediment may completely fill the space between the outer edge of the disk and the bowl shell without affecting the separation capacity or efficiency. The bowl operating a t 4500 r.p.m. is driven through worm gearing by a direct-connected, 1760-r.p.m. specially controlled torque motor. The same basic bowl may be modified for certain problems in that the bowl may be driven by a solid spindle. I n this case, the feed material will enter through a top entering feed tube leading to the center of the bowl. T h e separated liquids leave the bowl through either a double-paring device (75) or a single-paring device for the light phase with a gravity ring for the heavy phase. The term paring device is used to indicate a centripetal pump whereby the rotor blade is stationary, and the liquid revolves with the bowl.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Gustaf De Laval designed and built the first operable, continuously discharging centrifuge for separating t w o immiscible liquids. This rather basic unit (shown above) was first disclosed in an English patent in 1878 and a corresponding U. S. patent in 1881 ( 4 ) . It consisted of a hollow b o w l rotating a t moderate speeds with the light phase liquid discharging over a fixed dam while the heavy phose discharged through a tube. This unit was capable
Clarifying Efficiency
The separating efficiency of a centrifuge depends on the design of the centrifugal bowl. The science of internal bowl construction has developed over the years, especially in more recent times, because of the newer laboratory tools available. Particle sedimentation rates have been studied and described. A recent article by Bergner ( 2 ) describes the effect of particle size distribution on centrifugal separation. A basic equation relating the geometry of the bowl, number of disks, speed, and sedimentation rate has been in use for many years. One form of this relationship was published by Ambler (7) :
Q
2 x Ap = 27P
D 2w2 cot @(Rz3- Rl3)(n) (1)
Where Q is the rate of flow of liquid through the bowl, R1 and Rz are the inner and outer radius of the disk, e is the conical half angle of the disk with the perpendicular, and n is the number of flow spaces between the disks in the stack. Other authors have published equations of similar nature (70, 73, 76, 77, 79).
Empirical data show that t h e exponents of t h e disk radius a n d the speed may v a r y slightly for various liquid-liquid a n d liquid-solid systems. From test data accumulated over a long period of time, the basic equation as shown i n Equation I may b e rewritten to form a practical means of evaluating centrifugal performance. H e r e the radii a r e i n centimeters.
either higher or lower capacity centrif u g e s - o n the same or similar material. These equations a r e useful to relate capacities on bowls of t h e same general configuration. For example, data obtained on a straight-sided disk bowl a r e not always reliable on a nozzletype disk bowl. However, data obtained on a straight-sided bowl a r e reliable for other sized straight-sided disk bowls, a n d t h e same would hold t r u e from one nozzle bowl to another.
RI’.’~)(n) (2)
Bowl Stresses Of the many stresses involved i n the
This simplified version of t h e equation may now b e applied to the practical design of centrifuges. Experience gained over t h e past 75 years has resulted i n reliable data w h e r e b y K values could b e established for various materials both i n liquid-liquid a n d liquid-solid separation. T h e only practical method of determining a useful constant or K is b y operating a disk bowl of known geometry on a definite material separation (2). With this information, it is t h e n possible to evaluate mathematically a n d design
high-speed rotating centrifuge bowl, only tangential stresses in a freely rotating ring will be considered. Those having the same outer and inner radius as the bowl shell to be calculated. Those exposed to an inside hydraulic pressure. This tangential stress is highest a t the inside of the bowl shell and is termed normal stress in the bowl wall. A centrifugal bowl with a section shown as the freely rotating ring is illustrated on page 437.
Development of the Continuous Disk Centrifuge of separating milk a t the rate of 300 pounds p e r hour. To overcome bowl balancing problems and a t the same time develop higher centrifugal forces, a long tubular bowl o f rather small
HEA
3
diameter was built which rotated on a horizontal axis (5). O n e of the next advances was the tubular bowl running on a vertical axis. O n e version, shown a t left, was patented in the U. S. in 1890 (6). A major advance in increasing efficiency was contributed by Von Bechtolsheim (78) with the advent of partitions in the bowl, b e t t e r known in today’s terminology as disks. A
drawing from a patent granted in the U. S. in 1890 i s illustrated (center). By comparison with the present-day centrifuges, these early versions locked capacity and efficiency; however, they opened up a n e w field o f technology. A modern, high-capacity disk centrifuge (shown above) i s capable of efficienily separating liquids a t flow rates as high as 300 g.p.m.
VOL. 53, NO. 6
JUNE 1961
435
Table I For confinuous disk centrifuge the calculated stresses in the bowl shell, calculated according to Equations 3, 4, 5, vary with specific gravity of liquids
Self Stress, P.S.I. 23,100 23,100 23,100
SBecific - . Gravity of. Liauid 1.0 1.30 1.50 Hvdraulic Stress. P.S.I.
15,000 19,500 22,500
The total stress in the bowl shell wall is the sum of that due to the wall material, that due to the sludge bed, and that due to the liquid. Flowers (7) illustrates these principles and outlines several basic equations. More accurate stress calculations may be obtained when Poisson’s ratio-also termed the contraction module-is considered ( 7 1 ) . All stress is the result of cenrrifugal force and is a combination of the self stress and hydraulic stress. These may be calculated by: ST
= SS $. S H
(31
r2
- ri
T1
38,100 42,600 45,600
and pressure, and extreme corrosiveness I n addition to the bowl shell waI1. other points of high stress must be carefully calculated. One of these is the bowl lock ring. There is a bending moment caused by the hydraulic p e s sure against the b o ~ dtop, in addition to the self stress. New metals require very exhaustive testing. Even though stresses are calculated in advance, overspeed testing of prototype units is often necessar). A common procedure is to run the centrifuge bowl at 25 to 10070 overspeed, depending on the metal, to test for any creeping and fatigue of the metal. Fatigue is especially common in 30Cseries stainless steels. This may be done by automatically starting. running u p to speed, and stopping the centrifuge
Metallurgy
The designer must have a complete knowledge of the physical characteristics of the various available metals which may be used for centrifugal construction. Table I1 lists a few of the common metals along with their physical characteristics. The tensile strengths are given here. T h e values shokvn are the minimum values for the various metals which are acceptable for centrifugal design. Experience shows that the average tensile strength of test bar samples submitted for experimental evaluation may be considerably higher than a test bar sample cut from the acrual bowl shell forging. To allow a suitable safety factor, these values have been set for properly heat-treated or annealed materials. Corrosion Resistance
The early centrifugal bowls were constructed of carbon manganese sreel. T o impart a degree of corrosion resistance, these were tin coated or a t times lined with a layer of lead u p to 1 mm. in thickness.
(5)
By reference to Table 11, Physical Properties of Metals, the yield strength a t minimum value for 329 stainless steel is 65,000 p.s.i. The normal allowable designing stress for average operating conditions is 42,500 p.s.i. which permits an adequate safety factor. Table I shows that the total stresses a t specific gravity of 1.3 are 42,600 p.s.i. and hence are a t the maximum allowable point. When a liquid has a specific gravity of 1.5, the total stresses exceed this limit. The bowl speed must therefore be reduced to reduce the total stresses to within the allowable range. A classical example of overstressing a centrifuge may occur when mercur>- is separated from water in a standard centrifuge operating a t normal speed. From the ratios of density of mercury to water, the hydraulic stress is found to be 204,000 p.s.i. When combined with the self stress, the total stress on the bowl shell would be 227,000 p.s.i. Obviously, a few changes in operating conditions must be made. For this reason, centrifugal manufacturers usually state the maximum allowable density and further request that their representatives be consulted before operating the centrifuge a t other than design conditions-such as high density liquid, high temperatures
436
Total Stress. P.S.I.
bowl for as many as 10,000 times and then testinp for stress fatigue. This may be followed by cutting sections from the shell for metallurgical tests ( 3 ) .
Table II These values of physical properties of metals have been found safe for Centrifugal design. The tensile strengths given here are considerably lower than those commonly found in reference handbooks
INDUSTRIAL AND ENGINEERING CHEMISTRY
Metals 1308 Steel 131 B Steel 4340 Steel 41 30 Steel 20 302 SS 304 31 6 31 6L 329 41 6 43 1 Monel
K Monel Hastelloy C Titanium 120 Alloy
Yield Strength, P.S.I.
Tensile Strength, P.S.I.
40,000 60,000 80,000 60,000 32,000 32,000 32,000 35,000 32,000 65,000 40,000 60,000 35,000 80,000 50,000 55,000
80,000 85,000 100,000 88,000 70,000 75,000 75,000 70,000 70,000 90,000 80,000 85,000 70,000 130,000 100,000 75,000
Elongation 2 Inches, % 20 20 20 25 40 35 35 40 40
20 15 20 20 25 25 22
I
As the metallurgical technology of stainless steels developed-along with the commercial production by the Krupp Industries-research work was carried out on stainless steels suitable for centrifugal bowls. Because of high stresses in centrifugals, new methods for testing were required. Materials which were satisfactory in regard to corrosion under normal conditions would corrode severely when subjected to high stress. This lead to an intensive study of stress corrosion (72). Stress corrosion is corrosim which occurs under stress and usually results in the development of fine cracks emanating from the point of corrosion. Intergranular stress corrosion occurs more rapidly in metals which are not in their properly heat treated condition. It would appear that, in two-phase alloys not properly annealed, harder phases are surrounded by softer phases, and under centrifugal forces the harder phases have less plastic deformation. This residual stress results in intergranular corrosion and subsequent metal failure. Before using some of the more exotic stainless metals, stress corrosion tests are made. During testing, the metal test panels are subjected to 80,000 p.s.i. in a dilute salt solution while a direct current of 1 ma. is applied ( 3 ) . A test bar which will withstand 200 days under these conditions would be considered a suitable metal for centrifugal use.
-r, r 2
-
This schematic o f a centrifuge bowl shows how to calculate tangential stresses in a freely rotating ring
Bowl Stability
For purposes of balancing a bowl and also smooth running operation, a centrifuge bowl must have a good stability. Stability is the ratio of the polar moment of inertia to the equatorial moment of inertia. A thin circular plate whose thickness approaches zero has the maximum stability and a ratio apprcaching 2. The moment of inertia, I, about each axis is determined by the method of torsion pendulum. The bowl is hung by a wire and rotated slightly i n harmonic motion.
I,
=
(;y
Where I, is the polar moment of inertia (with respect to the axis of rotation), T is time in minutes for 100 complete cycles of the bowl, and C is a constant for a specific wire. The equatorial moment of inertiamoment of inertia with respect to an axis a t right angles to the axis of rotation and through the center of gravity-is determined in the same manner except that the bowl is suspended on an axis a t right angles to its rotation. From the knowledge of the moment of inertia, the other
necessary constants may be calculated, such as radius of gyration K, kinetic energy, E K , and WK2. This last expression, also known as WR2, is commonly used by motor manufacturers to calculate the starting torque necessary to bring the bowl u p to speed in a definite time (8). Power Requirements
The frictional losses during running are largely windage losses; a minor portion are due to the friction of the bearings and the worm gearing drive. Several methods have been published for calculating windage losses. A recent article on this subject includes a nomograph by H a m m (9). The bearing and gear losses are best found by experimental testing whereby losses on similar centrifuges may be extrapolated. For this particular centrifuge, operating a t 4500 r.p.m., the total frictional losses were 9 hP. T h e power consumed by the liquid passing through the centrifuge varies with the throughput capacity, type of
discharge. and use of inlet or outlet pumps. The centrifuge can be visualized as a pump in which the liquid fed into the bowl must be continuously accelerated u p to the linear velocity of the largest diameter part of the bowl through which it passes. If slippage does not occur the energy imparted to the liquid a t the largest diameter part of the bowl is partially recoverable on its return toward the centerline before its discharge. The power consumption caused by the liquid is due to the frictional losses inside the bowl and the final kinetic energy imparted to the liquid as it leaves the revolving bowl. The kinetic energy in the liquid as it leaves the bowl depends on the discharge diameter and the type of discharge design. The power consumption is the lowest in the hermetic design. I n this design, the liquid is fed through the hollow spindle under pressure and discharges a t the top of the bowl by means of centrally located axial seals. The angular velocity of the liquid discharge is very low. The power consumption of the liquid passing through this particular centrifuge in VOL. 53, NO. 6
JUNE 1961
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hermetic execution is never more than 5 hp. I n this particular centrifuge, at a capacity of 300 g.p.m., the liquid is in the bowl for only 2 seconds. During that time, the liquid must accelerate from zero angular velocity u p to 240 m.p.h. and then decelerate down to the discharge velocity of 10 to 15 m.p.h. T h e internal design of the centrifuge is very important with proper consideration to flow passages in order to reduce friction losses. T h e total power consumption is composed of 9 hp. for frictional losses and 5 hp. for the liquid losses, making a total of 14 hp. A 15-hp. motor would be suitable for the running load ; however, the drive is complicated by high inertia of the centrifuge bowl during starting and must be considered. The energy required to bring the bowl u p to speed depends on the amount of inertia and the speed of the bowl. T h e energy may be expressed as:
EK =
2x2 I,
(N/60)*
(7)
I n practice forrotatingparts, the inertia load is usually represented by W R 2 ( 8 ) . For this centrifuge, the weight, W’, of the bowl is 1300 pounds and the radius of gyration, R, is 0.68 feet giving a WR2 of 602 lb. ft.2. At its operating speed of 4500 r.p.m., the amount of energy is the same as if the bowl were traveling in a straight line a t 220 m.p.h. T h e problem is to bring this weight up to speed without burning out the 15-hp. motor. Several methods may be used to accelerate the bowl to its operating speed. Of these, only slip clutches and special motors will be considered. Using either method first involves determination of the total WR2requirement a t the drive shaft speed. I n this centrifuge. the horizontal drive shaft runs a t the speed of the motor or 1760 r.p.m. I t is therefore necessary to convert the TVR2 of the bowl to its equivalent n7R2 a t the motor shaft speed using the equation: Equivalent U R2 = WRg (~V/i\’m)~ (8) ‘IVhere ,V is the speed of bowl (4500 r.p.m.) and X m is the speed of drive (1760 r.p.m.). For this bowl, the equivalent M7R2 a t the motor shaft is 4000 lb. ft.2. I n addition to the centrifuge bowl, there are other items which must be considered such as the centrifuge spindle, the horizontal shaft, and clutch drum. These items amount to a WR2 of 300 lb. ft.2. T h e total M’R2 required is 4300 lb. ft.2. The torque produced by the motor and transmitted to the centrifuge drive through the clutch is partially dissipated by the frictional losses. The available torque for acceleration of the bowl is equal to the torque of the drive less the frictional torque. For calculation of frictional losses during acceleration, it
438
may be assumed that the losses vary directly as the speed. When using a slip clutch, it is important to recognize that the energy used to overcome the WR2and frictional demands of the system are the same as the energy converted to heat. T h e heat developed by this particular slip clutch during starting is sufficient to raise the temperature of the 90-pound clutch drum over 400” F. T o help dissipate this heat a fan is attached to the motor shaft to circulate air around the clutch. T h e type of clutch commonly used for centrifugal drives is a dry, trailing-weight friction clutch in which the weights are attached to the motor shaft and press against the inside of a heavy d r u m on the drive shaft of the centrifuge. This type produces a constant torque. By sizing the weights proper1)- this torque can be set a t 10% to 20% above the rated torque output of the motor. Thus the motor will instantly come u p to nearly full speed while the centrifuge bowl starts to rotate very slowly. When the centrifuge is at operating speed, no slippage will occur as long as the load on the centrifuge does not exceed the rating of the motor. Using a 15-hp. standard motor and suitable friction clutches, this centrifuge will reach full speed in 8 to 9 minutes. T h e starting time can be estimated by the equation shown by Harper ( 8 ) . (9) Where t is time in seconds, WR2 is the W R 2 a t motor shaft (lb. ft.”, AT is the speed of drive shaft (r.p.m.), and T is the available torque in lb. ft. (This is the average clutch torque less the frictional torque.) For greater accuracy this formula can be calculated in increments using A N for N and using the true values of net torque. A slip clutch does require some maintenance in the form of replacement of the clutch pads. Also the heat developed does not make it suitable for hazardous location. I n these cases the clutch is eliminated by using a special motor. When using a special motor, it is necessary to work closely with the motor manufacturers. The informdtion required for motor design is the value of the demand TVR2as well as the frictional values. I n addition, it is necessary to set an upper limit on the torque developed by the motor. The purpose of the motor torque limit is to prevent excessive torque while accelerating the bowl, which could cause rapid wear on the worm gear drive. Using these values the motor manufacturers can set the problem on a computer and design a motor with sufficient mass to absorb the heat generated in the starting period.
INDUSTRIAL AND ENGINEERING CHEMISTRY
T h e special controlled torque motor developed for this particular centrifuge was a 15-hp. motor i n what is usually a 40-hp. frame. I t is also possible to use motors with special windings such as Star-Delta or wound rotor types. Nomenclature
D
diameter of the limit particle (Equation 1) p = absolute viscosity of liquid g = acceleration in the gravitational field, 981 cm./sec.2 K , R = radius of gyration I, = polar moment of inertia, kg. cm. sec.2 11 = equatorial moment of inertia, kg. c m . set.* X = Poisson’s ratio: 0.3 for steel N = speed,r.p.m. w = angular velocity in radians per sec. = ~ X / 3 0 70 = discharge radius of liquid r1 = inner radius of bowl shell wall. cm. r2 = outer radius of bowl shell wall, cm . = inner radius of sludge level, cm. r3 pm = density of metal, k g . / ~ m . ~ pS = density of sludge, k g . / ~ m . ~ pl = density of liquid, k g . / ~ m . ~ Ss = tangential self stress, kg./cm. S , = tangential hydraulic stress, kg./ cm.2 ST = total tangential stress in shell wall, kg./cm.2 TV = weight of bowl, Ib. =
Literature Cited
(1) Ambler, C. M., Chem. Eng. Prozr. 48, 150 (1952). ( 2 ) Bergner: N. E.: Trans. Inst. Chem. Enqrs. (London) 35, 181 (1957). (3) Chem. Week, 83 (July 1958). (4) . , De Laval, G.. U. S. Patent 247.804 (Oct. 4, 1881). (5) 16id.. 372.788 (Nov. 8, 1887). (6) De Lavai, G. ’(to Aktiebolaget Separator), U. S. Patent 445,066 (Jan. 20, 1891). (7) Flowers, A. E., in “Chemical Engineers’ Handbook,” 2nd ed., p. 1808-49, McGraw-Hill, New York, 1941. (8) Harper, J. W., Prod. Eng. (1934). (9) Hamm, H. W., Design News (Jan. 15, 1961). (IO) Jury, S. H., Locke, W. L., A.I.Ch.E. Journal 3, 480 (1957). (11). Kimball, Barr, in “Mechanical Engineers Handbook,” Kent, Ed., 11 ed., p. 11-24, M‘iley, New York, 1946. (12) Merget. A. E., Chem. Processing 21, 122 (July 1958). (13) Polrovskv, “Separation of Yeast,” Moscow, 1956. (14) Sullivan, F. E.. Chem. Eny. Progr. 52, 83 (1956). (15) Ibid., 5 5 , 96 (1959). (16) Trawinski, H., Chem.-Inq. Tech. 2 6 , 189 (1954). (17) Trawinski. H.. .4chema Bericht. (1 8) Von Bechtolsheim, C. (to Aktiebolaget Separator), U. S. Patent 432,719 (July 22, 1890). (19) Wilsmann, W., Fette u. Seifen 5 5 , No. 10. 710 (1953).
RECEIVED for review March 13, 1961 ACCEPTED March 13, 1961 Division of Industrial and Engineering Chemistry, 139th Meeting, ACS, St. Louis, Mo., March 1961.
