THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING FLUID FLOW AT A SCRAPED HEAT TRANSFER SURFACE Paul F. Youngdahl January, 1961 IP-487

PREFACE The problems encountered in designing a heat exchanger for very viscous fluids became evident during the work of the writer at Mechanical Handling, Systems Inco A unit was needed that would adjust fluid temperatures continuously, have low pressure drops, occupy a small space, and have modest power requirements. A scraped-surface heat exchanger at least partially fulfilled most of the demands, but no information was available in the literature to serve as a basis for design, although the principle dates back to the old-fashioned, hand-cranked ice cream freezer. This investigation was made to establish some of the factors which determine the mechanical design of a scraped-surface heat exchanger handling viscous fluids. The writer wishes to express his appreciation to the members of his Doctoral Committee for their interest and advice, and to the mechanics in the Fluids' Laboratory for their help in constructing the experimental apparatus. Particular thanks are due to the Chairman of the Committee Professor Glen V. Edmonson and to Doctor Gordon Jo Van Wylen for their encouragement and assistance. The generous gift of "Ucon" fluid by the Carbide and Carbon Chemicals Company is gratefully acknowledged, and many thanks go to the Industry Program of the College of Engineering for their part in the final preparation of this dissertation. The assistance of Doctor F. H. Westervelt in the computer phases of this work is much appreciated. ii

Finally, the writer wants to express his gratitude to his wife and his family for their understanding during the years when this work was accomplished. The time it has required was taken from that which would have been spent with themo iii

TABLE OF CONTENTS PREFACE... oo o~ e o...o o o... o oe. o.o. oo.o. o. LIST OF TABLES..00000000000000000000000.. LIST OF FIGURES............................ NOMENCLATURE o o o..... o. o o. o o CHAPTER o. o 0 o o. o e * o o o. o o o 0 o o o o o o a. o a o e e a o o o o e o e o o o o o o o o o e o o e. o o. o e o o... 4 o o o e o e o. e o o...... o o... o o I INTRODUCTION... o o..... o o.. o. o... o. o.............. o o o o o Objectives..... o o.. o,. o o,.. o. o o o.o o o o. o. o o. o o. o. o o Description of process..o................oo.oo.oooooo Prior Work o.. o....... o. o........o... o o o o o o II DESCRIPTION OF APPARATUS AND EXPERIMENTAL PROCEDURE. o... Rotor-Stator Assembly......... o.o........o... Heat Transfer Stator............ o................ o Rotor and Blades.......o.......,oo o..ooo o.....o o.... Drive-Speed and Torque Measuring..... o......... o.o.o Primary Fluid Circulating System.o......... o. o o. Heat-Transfer Fluid Circulating System......o.......o The Primary Fluid.......o.............,o oo.... o Experimental Procedure and Technique............ III RESULTS Visual Observations o... oooo...o. o o..... o. o o... Torque Measurementso....oo..oooooo.....o..o..oooooo oo Heat Transfer Measurements..o....o...........o...... Discussion.......o o o o... o o o o... o o o o o IV CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORKo... o... o APPENDIX o o..o o............o o o o o o o o o...o o BIBLIOGRAPHYo o o o... o....o o o o o o.. o o o..o o o o o o o o o....o o. o o o o Page ii v vi viii 1 1 2 5 9 9 14 16 16 21 25 27 30 33 39 45 56 64 67 77 iv

LIST OF TABLES Table Page I Torque Measurement Data.......................... 68 II Mechanical Effects Data - 2 and 4 Type A Blades....... 73 III Mechanical Effects Data - Smooth Rotor......,...0..... 74 IV Heat Transfer Data - 2 and 4 Type A Blades o.........o. 74 V Heat Transfer Data Smooth Rotor..........,............ 76 v

LIST OF FIGURES Figure Page 1 Schematic Representation of Temperature Distribution through One Scraping Cycle in a Heating Application..... 4 2 Rotor-Stator Assembly with Glass Tube. o.......oo.. o o 10 3 Dimensional Factor vso Active Rotor Length.... o o o o 12 4 Heat Transfer Tubeo..oo.. o..o o................. o 15 5 Rotor and Blade Assemblyo.....oo...........oo. o o.... 17 6 Scraping Blades and Attachmentso...................... o 18 7 Drive Arrangement.ooo..o........... o o o...........o 19 8 Strain Transducer for Torque Measurement.............. 22 9 Strain Gage Dynamometer Calibrationo. o.. o oo... o.o. 23 10 Primary Fluid Circulating System...........o..00........ 24 11 Heat-Transfer Fluid Circulating System.....o........ 26 12 Viscosity of Ucon-Water Solutions at 75~Fo...oo......... 29 13 Approximate Velocity Profile of Fluid in Annulus with Type A Blade....... o o..o ooo....o.....o oo. o....... 35 14 Relative Motion of Fluid with Respect to Type A Blade and Rotoro o. oo.o oo...000o000000000o..o.oo000000ooo 35 15 Streamlines in Fluid Showing Blade End Effects with Type A Blade o.....o.oo..oooooooo.. oooo........oooo 36 16 Approximate Velocity Profile of Fluid in Annulus with Type B Blade,o.o...oo...0 o...... o0....o0o...... 38 17 Relative Motion of Fluid with Respect to Type B Blade and Rotor....o....oo...o................o.......00 38 18 Temperature Profile with Only Mechanical Effects.....o.. 47 19 Temperature Profile - Heating plus Mechanical Effectsoo. 48 20 Temperature Profile - Cooling plus Mechanical Effectso.. 49 vi

LIST OF FIGURES (CONT'D) Figure Page 21 Plot of Significant Groups for Mechanical Input of Rotor and Blades o.. o o o o o o o o o o o o o o o o 52 22 Plot of Significant Groups for Mechanical Input with Smooth Rotor..o...o.....o........................ 53 23 Plot of Dimensionless Heat Transfer Groups...o...... o 57 24 Plot of Dimensionless Heat Transfer Groups - No Blades o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 58 vii

NOMENCLATURE B number of scraper blades Cp specific heat - Btu/lb; ~F d Ri - Ri Feet Fd apparatus dimensional factor - (/2 2) l/Ri2 - l/R2 h heat transfer film coefficient at scraped surface - Btu/hr; ft; ~F k thermal conductivity - Btu/hr; ft2; ~F/ft i axial length - feet n rotor speed - rps n? rotor speed - rpm NTa Taylor number, d —i RiV v NTacr critical Taylor number for transition from laminar flow to vortex flow d/2 lo r _ 48,70(2 + i) 1 007lI62 0.00056 Lo^o571(1 - 0-652 R^ (1.o652 j Ri radius of rotor - feet Ro radius of stator bore - feet S frequency of scraping surface - i/hours t temperature - ~F Atnet temperature change of fluid due to heat;transfer.:at. the scraped surface - F Atmech temperature rise of fluid due to mechanical effects - ~F T torque - lbs (mass) ft2/sec2 T' torque - inch pounds V speed of blade at scraped surface ft/hr W axial fluid flow rate lbs/hr viii

NOMENCLATURE (CONT'D) 1 iviscosity lb/hr; ft jp tviscosity - centipoises v kinematic viscosity - ft2/hr p density - lbs/ft3 Ii angular velocity of rotor - 1/hr ix

CHAPTER I INTRODUCTION This is an investigation of some of the factors which determine the mechanical design of scraped-surface heat exchangers handling viscous fluids. The fluid to be heated or cooled flows axially in an annular space between a stationary outer cylinder and a powered concentric rotor. The inner wall of the outer cylinder is the heat transfer surface which is scraped periodically by blades attached to the rotor. In this study, fluid viscosities are restricted to the 2,000 to 20,000 centipoise range, and the axial fluid flow rates are low. Properly designed and applied, scraped-surface heat exchangers can be used economically in continuous processes to effect close control of the temperatures of products or reactants. Conventional batch heating or cooling of viscous materials, such as resins and prepolymers, in agitated vessels is slow, consumes much power, and requires large-size, expensive equipment. Although scraped-surface heat exchangers have been used in industry, the literature provides no basis for adequate mechanical or thermal design. Objectives The objectives of the laboratory observations, measurements, and analysis of this work using an experimental apparatus are as follows: 1. To determine the nature of the motion of the fluid in the passage between the rotor and the stator. Visual observations are made to reveal the action of the scraping blades on the fluid, and to show changes in this -1

-2 action with variations in the type of blade, the number of blades, the viscosity of the fluid, and the speed of the rotoro 2. To determine the energy required to power the rotor. It is necessary to know the power demands in order to design the drive system. Much of the motive power is put into the fluid, and this energy imposes an additional load on the heat exchanger in cooling applicationso Rotor torque requirements are measured as functions of speed, number of blades, and fluid viscosity. 3. To determine the order-of-magnitude heat transfer coefficients when the heat transfer surface is periodically scraped. Approximate heat transfer coefficients are determined to show the effects of the speed of rotation and the number of blades on heat transfer rateso Description of Process The experimental apparatus, described later, is typical of the components and arrangement of a commercial scraped-surface heat exchangero The purpose of this section is to describe the nature of the fluid flow and heat transfer at an element of the scraped surface. Within the fluid viscosity and flow rate limitations of this investigation, criteria indicate that both axial and rotational flows are primarily laminaro The prevailing mode of heat transfer between the surface and the fluid is conduction until the surface is scraped and the film is mixed with the bulk fluid. As long as flow is laminar, the axial velocity of the fluid does little to influence heat transfer coefficientso

-3 A stepwise description of the process is as follows: 1o Bulk fluid is presented to the heat transfer surfaceo The full temperature gradient between the surface and the fluid is across the interface so that a relatively rapid transfer of energy occurso The temperature distribution in a heating application is shown in Figure la 2. The fluid next to the surface quickly approaches the surface temperature, and the temperature difference shifts to within the fluid. The energy transfer continues, but at a decreasing rate because the temperature difference occurs over a film of increasing thicknesso The rate of heat transfer is limited by the thermal conductivity of the fluid which is generally low for viscous and resinous materialso The temperature distribution in a heating application is shown in Figure lbo 3~ When a scraper passes over the surface, it removes the thin film that has been heated or cooledo This film is mixed with the bulk fluido The new temperature distribution is shown in Figure 1co 4. New bulk fluid, which has some slight change in temperature due to the mixing of the heated or cooled film, is presented to the heat transfer surface, and the process repeats

Scraper No. 2 Wall - Corresponding to Stationary Outer Cylinder No. 1 Scraper No. 2 Heating Medium Heating Medium Heating Medium Cold Material Cold Material ran E< (X Initial Temperature of Cold Material Distance from Distance from Scraped Surface Scraped Surface a) Initial contact of new cold material with surface b) Just before first scraper passes surface c) Just after first scraper passes surface Figure 1. Schematic Representation of Temperature Distribution through One Scraping Cycle in a Heating Application.

-5 Good scraper blades will completely remove the heated or cooled film from the surface, and will thoroughly mix it with the bulk fluid so that the maximum temperature differential can be maintained at the interface between the heat transfer surface and the fluid in contact with it, Prior Work The published literature reveals little concerning the design and performance of scraped-surface heat exchangers handling viscous fluids The behavior of fluids between rotating concentric smooth cylinders has been. the subject of considerable theoretical analysis and experimental work, and heat transfer rates in such systems have been explored under a variety of conditions. In the design analysis of this experimental apparatus, the fundamentals developed for smooth rotors are used to establish the mode of fluid flow for the no blade limiting conditiono The classical mathematical and experimental work of G. I. Taylor(15) provides a means for evaluating the stability of fluid flow in an annular space between concentric, rotating, smooth cylinderso Goldstein(4) expanded on Taylor's work to include the effects of axial flow of the fluid in the annular spaceo A mathematical approach was used to develop an equation for calculating the angular velocity for which flow just becomes unstable for a given axial Reynolds membero He shows that under laminar flow conditions the axial and rotational flow characteristics are independent of each other, and that the torque required for a given rotational speed is independent of the axial-flow

-6 velocity. The torque requirements of a smooth rotor system can be calculated from the Reiner and Riwlin equation for the rotational viscometer as in Greents(5) discussion of the forces and stresses in various classes of fluids. Gazley(3) investigated heat transfer with rotational and axial flow between concentric cylinders as in the gap between the rotor and the stator in rotating electrical machineryo He used a Reynolds number based on the peripheral speed of the rotor to establish modes of flow, and concludes that steady-state heat transfer across an annular gap for laminar flow is accomplished by pure conductiono Kaye and Elgar(8) investigated modes of flow for adiabatic and diabatic flow of air in annuli with an inner rotating smooth cylinder and an outer stationary cylindero They established a new dimensionless group called the Taylor number which is used with an axial Reynolds number to establish four modes of fluid flow, ioe O laminar flow, turbulent flow, laminar flow plus vortices, and turbulent flow plus vorticeso The heat transfer aspects of their work shows the Nusselt number remains constant in the laminar-flow regimeo Bjorkland and Kays(l) used air in the annulus of a system of concentric rotating cylinders to show that heat transfer rates indicate three regimes of flow, ioeO, (a) laminar flow with heat transfer by conduction, (b) vortex flow which, increases the heat transfer rate, and (c) distorted vortex flowo Equations are presented to calculate a ratio of actual. Nusselt number to a conduction Nusselt number in terms of the Taylor number and dimensions of the apparatuso Jacob and Rees(7) developed equations for heat transfer coefficients for systems of smooth rotating cylinders where both axial and rotational flows are laminaro

-7 In a water-to-water scraped-surface heat exchanger, Houlton(6) evaluated overall heat transfer coefficients experimentallyo Rotor speeds and axial fluid flow rates were both high so that the mode of flow without blades would have been other than laminaro He developed no equations for calculating film coefficients at the scraped surface, and he did not determine the power requirementso Kool(l0) made a mathematical analysis of the heat transfer coefficient of a scraped-surface heat exchanger handling viscous fluidso The theoretical equation which he developed assumes that all of the fluid is scraped from the surface with each pass of a blade, and that the heated or cooled scraped film is mixed completely with the bulk fluido He illustrates how a residual thin film on the scraped. surface will decrease the heat transfer coefficient, and he notes that incomplete mixing after scraping, as is obtained in practice, will cause a further lowering of an actual coefficient. In one of his earlier papers, Skelland(ll) used dimensional analysis to develop an equation from experimental data for calculating heat transfer rates in a scraped-surface heat exchangero Later papers recommend changes to this equation because of probable errors. Kern(9) indicates that Skelland's equation, even if correct, would be misapplied in the case of pure laminar flow, and that the viscous core of fluid between the scrapers and the rotor body in is laminar flow rotationally as well as axiallyo Skelland, Oliver, and Tooke(14) arranged the variables affecting heat transfer rates in a scraped-surface heat exchanger into dimensionless groups, and by experiment, they evaluated the constants and

-8 exponents to give equations for calculating film coefficientso Two equations were presented, one for the case of cooling viscous liquids, and, one for the case of cooling thin, mobile liquidso There are considerable discrepancies between the results of this work and that of Skelland,(l2) and explanations are given to show why the later work is more nearly correcto In the only published work regarding power requirements of scraped-surface heat exchangers, Skelland and Leung(l3) arranged the significant variables into dimensionless groups, and by experiment, established a coefficient and exponents for a Reynolds number and for the number of scraping blades groupo Two different equations for making the same calculation are presented, and the necessity of doing additional work to establish accurate values is emphasizedo The above references are cited here to indicate their scope and content, but detailed comments and comparisons are made in later sections where the application is directo

CHAPTER II DESCRIPTION OF APPARATUS AND EXPERIMENTAL PROCEDURE The basic unit in the experimental apparatus is the rotorstator assemblyo It consists of a driven rotor within a stationary concentric tube, The rotor is solid aluminum with fittings for attaching 0 to 4 axial blades which scrape the inside surface of the outer cylinder. This stationary outer cylinder is a precision-bored glass tube for making the visual studies and torque measurementso A composite tube made of a water-jacketed steel section between two glass ends is used for making the heat transfer observationso A four-speed, rotary, floating drive is arranged to measure torque demands through a strain gage transducer. The rotor speed. is measured on the input side of a 10 to 1 fixed ratio gear reducer. The working fluids are water solutions of "Ucon"* 75-H-90,000 covering the full viscosity range of 2,000 to 20,000 centipoises. The circulating systems for the primary fluid. and the heat transfer fluid complete the equipment, Rotor-Stator Assembly The arrangement and principal dimensions of the rotor-stator assembly with the glass tube are shown in Figure 2. The viscous fluid. is admitted at the bottom of the apparatus, through four 3/4 inch standard pipe connections, into a distribution plenum., and. flows axially, through the annulus, to the top. The collecting pan directs the fluid, * Trademark, Carbide and Carbon Chemicals Company -9

-10 BUSHING RETAINER 8 DISTRIBUTION PLATE Figure 2. kotor-Stator Assembly with Glass Tube.

-11 as it overflows, to the open channel which drains into the weigh tanko The bore of the glass tube and the diameter of the rotor are within + 0O002 inches of the nominal dimensions shown on the drawing, including out-of-round tolerances. In the assembly of the rotor and stator, concentricity is held to within a tolerance of 0O003 incheso All axial dimensions are correct to + 00005 incheso The level of the fluid in the system must be considered when the experimental data are calculatedo This level changes as a function of flow rate, viscosity, and rotor speed, and the effective diameter of the outer member changes with the levelo The Reiner and Riwlin equation for smooth rotors can be applied because the blades do not extend, into the area of changing fluid level and stator diametero With a rotating inner member and stationary outer member, this equation is T = 41ji_ -- (1) T - 1 1 Ri2 Ro2 For convenience in making later calculations, it can be simplified by substituting constants and grouping termso All terms relQting to the dimensions of the apparatus are included in the expression Fd = dimensional factor = (2) 1 1 Ri2 Ro2 which varies with the length of the rotor which is exposed to the fluid, This dimensional factor is plotted against the active rotor length in Figure 3. Introducing conversion factors and. substituting (2), Equation (1) becomes T'= lo909 x 10-7 lin'Fd (3)

216 215 214 - w 213 z z 2123 — _. 292 --- --- --- --- --- -— __ —- --- -- _- -.0 2 I _ _ _ _ I _ 211 210 0 as/.'o 208 207 -- 206 -------------- 17.9 18.0 18.1. 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19.0 19.1 19.2 19.3 19.4 ACTIVE ROTOR LENGTH INCHES Figure 3. Dimensional Factor versus Active Rotor Length.

-13 where T' = rotor driving torque in inch pounds (force)'I = fluid viscosity in centipoises n' = rotor speed in rpm Fd = dimensional factor in inches3o The Reiner and Riwlin equation, and thus Equation (3), assumes the rotational flow of the fluid. to be laminaro Taylor(l5) established the criteria for determining when instability in rotational flow just starts. Using the notation of Bjorklund and Kays,(l) a dimensionless Taylor number is defined, Ri n~ d. (4 NTa = i (4) and the critical Taylor number is 48.70(2 + ) 1/2 NTacr (5) TaC = L0571(1-0o652 ) + (o 00056 Ri. 1-o652 di When the Taylor number is less than the critical Taylor number, rotational flow is laminar. Goldstein(4) and Kaye and Elgar(8) show that the additional of an axial component either does not affect rotational flow or may make it slightly more stableo For a dimensionally similar smooth rotor apparatus, the critical Taylor number is 47.2. Assuming the minimum fluid viscosity of 2,000 centipoises and the maximum rotor speed of 170 rpm, the Taylor number is 2077. Although the addition of blades to the rotor may change the magnitude of the Taylor number slightly, rotational flow can be clearly classified as laminaro

Heat Transfer Stator For heat transfer measurements, the stationary cylinder is modified to include a water-jacketed steel surface which is scraped by the rotor blades. Figure 4 shows the arrangement and dimensions of the heat transfer tube. The total scraped area is O0858 ft2. Thermocouple numbers 5 and 6 are inserted into small drilled holes at each. end of the steel heat-transfer tube The bead. is brought to the surface and then peened flush with the surfaceo The thermocouple leads are secured by potting with epoxy resin~ Other thermocouples are used to measure temperatures as follows: Thermocouple No. Location and Temperature Measured 1 Primary fluid inlet temperature in inlet plenum. 2 Same as No. 1. except on opposite side of plenum. 3 & 4 Primary fluid outlet temperature in fluid film near bottom of open channel to weigh tank. 5 & 6 Heat transfer surface temperature as noted in Figure 4 7 Heating or cooling water inlet temperature in inlet plenumo 8 Heating or cooling water outlet temperature in outlet plenumo All thermocouples were calibrated at the ice point, steam point, and. decomposition temperature of sodium sulphate decahydrate (90o270F)o

-1i - SIX TIE RODS /-1/4" DIA. PRIMARY FLUID OUTLET (I) cr 0 I -J Cl) z Ip, U) -j a \ PRIMARY FLUID INLET Figure 4. Heat Transfer Tube.

-16 Rotor and Blades The rotor body is solid aluminum, 20 inches long and 3~997 inches in diametero Drilled, tapped, and, counterbored holes for holding blade attachments are located as shown in Figure 5o The brass endfittings were fitted before the final turning of the rotor outside diameter to insure concentricity. When one or more blades are not used, the attaching holes are plugged with "Allen-Head" screws and putty to make a smooth surfaceo The two types of blades and the detail of the blade attachment are shown in Figure 6. The springs in the blade attaching fittings were selected to have the minimum force to just cause the blades to contact the surface without adding mechanical drag to the system. The type A blade spans the entire annular space between the rotor and. statoro Type B blade is designed to scrape the entire heat transfer surface, but maximum clearance is maintained for fluid flow between the scraping blade and the rotor bodyo Drive-Speed and Torque Measuring The rotor is driven by an electric motor through a V-belt and. pair of 4-step pulleys to a countershafto A V-belt and pulleys connect the countershaft to the input of a worm-type gear reducer which connects directly to the rotor power fitting. The general arrangement is shown in Figure 7~ The significant design feature of the drive is the mounting arrangement so tat th all elements in the power train are free to turn, as an assembly, about the main power shaft centerlineo A plate bolted to

- 17 TYPE A 1 0 0 0 o o or - |-'"- POWER FITTING PILOT AND BOLT WITH 3- 3/8" BOLTS, / / / / / ~/ ALUMINUM ROTOR a ce/y/A/' /// A BODY TYPE B BLADE DRILLED, TAPPED, ~/ ///a/ ~COUNTER BORED HOLE FOR FITTINGS BRASS FITTING FOR THRUST AND RADIAL LOADS Figure 5. Rotor and Blade Assembly.

-18 BLADES TYPE A TYPE B r _L-. BOTH BLADES 1/8" THICK -10 CD 0.456" 0.460"' I8 8 0.456" 0.460" THREAD 3/8 - 16 Nl 1/16" f roll pin, tight in blade. Attachment has 1/8" i hole so blade can float I 1''- I' ell"'r~~~~~~~~~~i;r Spring holds blade on scraped surface Figure 6. Scraping Blades and Attachments.

-19 ci CL I I I I I STRAIN GAGE UNIT' MOTOR DRIVE SUPPORT BEARING Figure 7. Drive Arrangement.

-20 the top of the worm-gear reducer holds the motor and countershaft, and is machined to receive the inner race of the top drive-support bearingo A second plate is bolted to the bottom of the reducer, and is machined, to receive the outer race of the lower drive-support bearingo The other race of each, bearing is fitted to respective upper and. lower plates, bolted to the rigid, main-support frame. The bearings are an aircraft type and quality with no seals or retainerso The radial and axial capacities are well over the load imposedo The tachometer generator is driven from the reducer input shaft through a cogged "timing" belt and pulley arrangement. The timing belt drive is a 1-to-l ratio, so indicated speed is exactly 10 times true rotor speed because of the lO-to-l ratio of the reducer. The tachometer generator is bolted to the reducer, so it too becomes a part of the rotating assembly. The drive machinery, mounted on the bearings, is restrained from rotating by a torque arm attached to the reducero The force developed at the end. of the arm is measured with a combination of a straingage instrumented, cantilever beam and a pan-balance and weights. The effective length of the torque arm is.12,024" (+ 0.002"). The torque arm has a point-bearing on the strain beam., and at the knife-edge, cords are attached which lead over bearings to support weight pans. Two pans are used so the weights on each are opposingo The one acts in the direction to impose a load on the strain beam, and is used for calibration. The balance pan and weights act in the opposite direction so that their effect is additive to the strain indicator readingo The total force exerted by the torque arm is the sum of the weights on the balance pan and the force on the strain transducero

-21 The instrumented strain transducer is shown in Figure 80 Once mounted and clamped in place, it was calibrated, and then was not moved or loosenedo The calibration curve shown as Figure 9, was obtained by placing dead weights, in 1/8 pound increments, on the calibration pan described aboveo The calibration was accomplished with the motor and all floating drive machinery running, but the coupling to the rotor disconnected. The gage factor adjustment on the SR-4 indicator was used to reset the zero point to a dial reading of 480 before each run. Frequent checks throughout the experimental work showed that linearity and. calibration was maintained. The accuracy of the system is such that it can be read to + OoOl poundso The greatest probable error because of needle swing, damping, friction, etc,, is + 0005 poundso Primary Fluid Circulating System The primary fluid circulating system, shown in Figure 10, is designed to provide intermittent flow through the test apparatus0 A 30 gallon pressure tank is filled with the fluid of the viscosity desired for a particular run and blanketed with air at a controlled pressureo The fluid is forced through a delivery line, into a pipe manifold, through four hoses, to the bottom plenum of the rotor and. stator assemblyo It flows upward in the annular space between the rotor and the stator, and as it overflows the stator tube, it is collected in an attached pan with one side openo The open side of the pan connects to a sheet metal channel that permits the fluid to flow by gravity into the weigh tank on a platform scale0 The discharge of the weigh tank is kept

-22 - FORCE APPLIED WIRING DIAGRAM 4 - SR4 STRAIN GAGES 0 R4 R3 0 (Letters refer to wire connections en SR4 indicator) THIS END CLAMPED TIGHTLY Figure 8. Strain Transducer for Torque Measurement.

2.0 - 1.6 1.4 a J ac i. 0.8 I- 2z 0.6 — 0 Io 0.4 20.2 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825 850 875 900 475 500 525 550 575 600 625 650 675 700 725 750 775 800 825 850 875 900 SR - 4 INDICATOR READING Figure 9. Strain Gage Dynamometer Calibration. I w

AIR SUPPLY I Figure 10. Primary Fluid Circulating System.

-25 closed until the end of the run, and the scale is periodically balanced to indicate flow rateso At the end of a run, the fluid collected in the weigh tank is pumped back into the pressure tank, and the cycle repeatso The inset in Figure 10 shows the method used to introduce air bubbles or a dye into the main fluid for making some of the visual studieso Food coloring is mixed with a small amount of the test fluid of the viscosity being used, and is placed in a pressure-feed grease cupo The discharge of the grease cup is connected to a hypodermic needle which is inserted into one of the hoses attached to the rotor-stator assemblyo A turn of the screw feed will introduce one or more drops of a colored fluid with approximately the same viscosity as the primary fluid.. An air connection to the same hypodermic needle permits air bubbles to be introduced in a similar mannero Heat-Transfer Fluid Circulating System A schematic diagram of the system for circulating hot and cold water in the jacket of the heat transfer tube is shown in Figure 11o A supply manifold and a return manifold each have three connections for rubber hoses which attach to corresponding fittings on the heat transfer tube. The water flows in the bottom and out the top of the annular jacket surrounding the steel cylinder that has its inside surface scraped by the bladeso In heating runs, the water is circulated with a positive displacement pump at a rate of about 4 gpmo The 1000 watt heater has a self-contained thermostat that controls the temperature on an on-off basis0 A reservoir, fabricated from large-size pipe, holds the heater and feeds

Heat Transfer Tube with Internal Scraped Surface Return Hoses Supply Hoses t Connected to Domestic Cold Water Supply Supply Manifold Return Manifold To Water Reservoir and Heater 1000 Watt - Electric Bayonet Heater with Self Contained Thermostat Pump Figure 11. Heat-Transfer Fluid Circulating System.

-27 the inlet of the pumpo The water leaving the jacket returns to the reservoir, through the return manifold, by gravity. A by-pass recirculation line is provided for start-upo In cooling runs, the hot water connections are shut off from the manifolds, and domestic cold water feeds the supply manifoldo The spent cooling water is directed to drain when it leaves the return manifoldo The Primary Fluid After an investigation of several water-mixed and water-soluble materials, Ucon 75-H-90,000 was selected as the working fluid. The characteristics which are desired and which determined the choice are: a. the complete viscosity range of 2,000 to 20,000 centipoises can be obtained by mixing different amounts of water with the base fluid, bo the fluid and its water solutions are stable and they will maintain the same viscosity over the entire test period. c, the rheological classification of the fluid and its solutions is Newtonian, do the fluid presents no health hazard in its useo Other materials which were investigated for use include water solutions of cellulose gums and a high molecular weight polymer of ethylene oxide. The viscosity of the latter (Polyox* WSR301) shows a marked * Trademark - Union Carbide Chemicals Company

-28 dependence on shear rate, and was rejected for this reason. The ropy consistency or stringiness of the water solutions of the Polyox resin would probably be objectionable, Water solutions of sodium carboxymethylcellulose (CMC) were considered because of the small percentages of CMC required, to attain the desired viscosities. Although the measured viscosities of the solutions were somewhat responsive to shear rates, the effect was not marked. Beaker samples of the proposed solutions appeared quite stable, but full scale quantities showed a considerable loss of viscosity during storageo The change in viscosity was attributed to biochemical action even though a preservative (sodium benzoate) was addedo The properties of Ucon 75-H-90,000 and its water solutions were determined by measurement and from information supplied by the manufacturer's catalog (Union Carbide Chemicals Company), It is classified as an unrefined polyalkylene glycol-type fluid containing 0.07% of an alkaline material calculated as potassium hydroxide. A blackening and slight etching of the aluminum rotor is the only noted effect of the fluid on the equipmento A Brookfield Model LVF Synchro-Lectric Viscometer with four spindles and four speeds is used to measure viscosities. During each run, a viscosity determination was made at several different shear-rates at the temperature of useo From these accumulated data, temperatureviscosity curves were drawn and the viscosity of various concentrations is determined at 75~Fo A plot of the viscosity of water solutions of Ucon 75-H-90,000 is shown in Figure 12o This curve is presented for

c- N I ( 3X X o X X o.- ~%, ~. Qo,,,o, SOLUTION VISCOSITY, CENTIPOISE ~b C ~ -4 co la 0UI 0" J 0 0F) N ul N in ( 04 04 04 04 X1 X 01 X x xx.,,. m o0 o x oo o, 0 0 55o 0004 HOq (D IU) o Ca CD 0 1C.D 0 0 cI C0 Ca dol r 0 Z -- C 0 0 z I r Z 0 I, 0 o 0 o 0 0) 0 0 o - L i i im iii I-J

-30 for reference only, because the actual observed viscosities for each run are used in all calculations Other fluid properties of interest in the heat transfer phases are specific heat and thermal conductivityo Using the data of Curme and Johnston(2) for aqueous solutions of glycols, the equations from the International Critical Tables, and the manufacturer's data the following values are obtained: Solution Viscosity Percent Thermal Conductivity Specific Heat at 75~F - Centipoises Ucon Btu/hr; ft2; ~F/ft Btu/lb; OF 10,700 77o5 0.131 0o62 15,100 83o0 0ol21 Oo59 Experimental Procedure and Technique The experimental work can be divided into three phases as follows: lo visual observations, 2 torque measurements, 3. heat transfer determinationso During any one of these phases, the following factors can be varied: 1o rotor speed - Four belt positions on the step-cone pulleys give approximate rotor speeds of 32, 60, 95, and 150 rpm. The actual rotor speed is influenced by belt slip and motor response under loado The rotor speed is measured several times during each run. 20 fluid viscosity - Four basic solutions have been prepared to cover the full viscosity range with nominal

values of 2,000, 8,000, 14,000, and 20,000 centipoises. The actual solution viscosity is influenced by its temperature (ambient) at the time of the runo The exact fluid viscosity is measured several times during each runo 3o scraper blades - The scraper blades constitute a variable in the following two ways: a, number of blades - The rotor is operated with 0, 1, 2, or 4 bladeso bo blade design - Both type A and type B blades, described above are radial and spring-loadedo The design difference is basic in the blade action on the core material next to the rotoro Torque measurements were made with all combinations of all of the above variables, but the full scope of variables was not explored in the heat transfer phases. It was convenient to observe the significant changes in the action of the rotor and blades on the fluid during the torque measurement set-up. Before any observations or readings were taken, the system was operated long enough to attain steady-state conditions. For the visual parts, the prepared dye of the same viscosity as the fluid was forced into the inlet stream. The motion of the dye streak could be readily followed at the lower rotor speeds, and the general flow pattern could be established even at the top speed. The pressure gradient from the leading face of one blade to the following face of another blade was determined by operating the tube partially filled with fluid and measuring the difference in fluid heighto

-32 For each given rotor speed, type of blade, number of blades, and fluid viscosity combination, a series of torque measurements were made. In preparation, the fluid was pumped into the pressure tank, the air pressure regulator was adjusted for the desired flow rate, and the weigh tank drain valve was closedo The fluid flow was started, the rotor was turned on, the system was operated until steady-state was assured, and the following readings were taken: ao Room temperatureo b. Fluid level below the top of the rotoro Co Rotor speed. do Fluid flow rate - (by measuring the time interval for an incremental weight of fluid to flow into the weigh tank)o eo Drive force on dynamometero At the same time, a fluid sample was collected as it ran into the weigh tank, and the fluid viscosity and temperature were measuredo The same preparations and start-up procedure was followed for the heat transfer measurementso When the recording potentiometer showed steady-state, the following readings were taken: a. Room temperature. b. Rotor speed. c. Fluid flow rate - (as above) do Potentiometer reading in millivolts for each of the thermocouples, progressing from couple number 1 through number 8. The same procedure as above was followed in determining the fluid viscosityo

CHAPTER III RESULTS The results of the experimental work show that type A..blades produce the scraping and mixing effects that are necessary to obtain the optimum heat transfer rateso The rotor speed, the fluid viscosity, and the number of blades all influence the rotor driving torque requirementso A torque equation to show the relationship of the variables is derived from the measurementso The improvement in heat transfer rates with scraping is evaluated. The detailed results of the three phases are discussed separatelyo Visual Observations The first visual observations were made with no blades on the rotoro They confirmed the design calculations for smooth concentric cylinders that both rotational and. axial flows are laminar within the defined limits of rotor speed and viscosityo Two type A blades were installed on the rotor, and the fluid motion was observed for the entire series of rotor speed and fluid viscosity combinationso In all cases, the fluid responded to the blade action in substantially the same wayo An approximate absolute velocity profile of the fluid in the annulus with type A blades is shown in Figure 13~ That fluid right next to the stator surface remains at rest, and that fluid right next to the rotor surface moves at rotor speedo The dotted line indicates the fluid velocity distribution if no blades were on the rotoro Superimposed on this pattern is another motion caused by the pumping action of the blades. The resultant profile shows that -33

within the annular space the maximum fluid velocity is higher than the rotor speedo It is estimated that this maximum velocity is about 1o5 times rotor speedo Because the quantity of fluid between two blades remains a constant and some of the fluid moves faster than the rotor, it follows that some of the fluid has a relative motion opposite to the direction of rotation of the rotoro The relative motion of the fluid with respect to the blade is shown in Figure 14o It is this action that produces the mixing effect that is required to realize the potential heat transfer rates in a scraped-surface exchangero As the scraper removes the heated or cooled film at the stator surface, it causes this material to flow toward the rotor surface and move at the higher velocity. On the opposite side of the blade, the fluid that was near the rotor surface is directed to the stator surfaceo Thus, after each time a scraping blade passes, fluid at the bulk temperature is presented to the heat transfer surface and the temperature gradient at the interface is a maximum. The action described. above and illustrated in Figures 13 and 14 is substantially the same with 1, 2, or 4 type A blades installed on the rotoro The ends of the blades are not covered, shielded, or baffled so the fluid is free to respond to the blade pressureso Figure 15 illustrates the motion of the fluid at the top end of the blades. Because the fluid essentially bypasses the blade and escapes from between two blades, the circumferential flow pattern described above is disturbed. The fact that there is a low pressure area at the blade trailing edge is evident in the flow streamlines, and in addition, any air bubbles in the fluid will accumulate into an air pocket at this trailing edge near the

-35 Figure 13. Approximate Velocity Profile of Fluid in Annulus with Type A Blade. Figure 14. Relative Motion of Fluid with Respect to Type A Blade and Rotor.

-36 STATOR TOP ROTOR END OF A BLADES ANNULUS IS OF FLUID DIRECTION OF BLADE ROTATION Figure 15. Streamlines in Fluid Showing Blade End Effects with Type A Blade.

-37 top of the bladeo The end effects are less apparent as the number of blades increase from 1 to 40 A further measure of the pressure gradient between the trailing edge of one blade and the leading edge of another was possible by operating the unit partially full of fluid. Under these conditions, the fluid level is responsive to the blade pressureo The difference between the fluid level at the leading edge of one blade and the fluid level at the trailing edge of the next blade was measured as follows: Fluid Rotor Difference in Viscosity Speed. Fluid Level Centipoises rpm Inches 6900 32. 15.25 2000 32. 7 79 2000 60o 12,00 At higher speeds and higher viscosities, the fluid would overflow the -top of a blade, meaning that the pressure gradient was greater than 1.6-5/8 inches. When type B blades were installed on the rotor, the fluid motion was changed considerablyo As is illustrated in Figure 16, the velocity profile approaches that of fluid in an annulus between smooth, concentric, rotating cylinders. The relative motion of the fluid with respect to a blade is shown in Figure 17. Although the blade scrapes the fluid from the stator, or heat transfer surface, this fluid which has been heated or cooled is not mixed with the remaining bulk fluido The streamlines are compressed and the velocity of fluid is increased when a blade passes, but there is substantially no mixing. That fluid

-38 Figure 16. Approximate Velocity Profile of Fluid in Annulus with Type B Blade. Figure 17. Relative Motion of Fluid with Respect to Type B Blade and Rotor.

-39 which was right next to the scraped surface returns to that surface, and the remainder of the fluid is undisturbed. Axial flow does nothing to improve the mixing, because these streamlines also stay in their same relative position. Thus the type B blade does not fulfill one of the basic requirements, that the heated or cooled scraped film be mixed with the bulk fluid and new bulk fluid be presented to the heat transfer surface Torque Measurements The complete results of the torque measurement studies are given in Table I in the Appendix. The fluid viscosity, column E, is the average of several measurements made at different shear rates on a single sample collected from the fluid flowing out of the annuluso The active rotor length, column H, is the height of the fluid on the rotor determined by subtracting the exposed length of the rotor from the total rotor length, For each given combination of blades, rotor speed, and fluid viscosity, the fluid level was adjusted to the bottom of the rotor, and the torque was measured. This "friction" torque is that torque required to turn the rotor because of the following factors: a. bottom bearing friction, b blade drag on the scraped surface, co fluid action of the bottom end of the rotoro For each run shown in Table I, the friction torque is subtracted from the total torque reading to give the observed torque, column I. Because the blades are only 16-5/8 inches long, the torque readings for all runs

are reduced to the equivalent torque for a rotor 16-5/8 inches longo Using the modified Reiner and Riwlin equation, Equation (3), and the rotor dimensional factor from Figure 3, the torque requirements for a smooth rotor with length in excess of 16-5/8 inches are calculated. This calculated torque is subtracted from the observed torque (column I) to give the adjusted torque of column J. Because of the large number of observations and the interdependence of the variables, an attempt was made to fit a single equation to the data, making use of a digital computer. Westervelt s(16) stepwise regression program with simple learning was used to obtain the equation. The input data were the number of blades (column B), the fluid viscosity (column E), the rotor speed (column G), and. the adjusted torque (column J). Only those data for the type A blade were used. It was requested that torque be expressed as a function of speed., viscosity, and number of blades. The computer determined coefficients and evaluated the sum of terms of power functions of the variables and derived the following equation on its pass number 5 after 15 steps: T 5 3.61 n''I + 8066 n'.'B1/2 - 0..l n'1'B3 - 1o05 n'- 1/4111/5B-6 + 4.15 n4Bl/2 - 5304 J 3B4 - 2.80 n'4 1/2Bl/3 - 0.024 n'- 1/4 - 1/5B6 _ 7 88 x 109 v5B5 + 1.41 n 1/3B3 + 0.43 n - 1/4 V- 1/4B (6) Scaling factors in the above equation are Speed x 10-2 (rpm) Viscosity x 10-3 (centipoises) B as observed (number of blades) T' as observed (inch pounds)

-41 With the computer, the predicted torque was calculated from the equation and compared with each data point. This was done to evaluate the deviation of the individual data points from the fitted curveo Runs 25 through 32 had a small absolute deviation but a percentage deviation of up to 50% in some cases. In these runs, the friction torque was almost twice the value of the adjusted torque, so a slight error in observations could easily reflect the deviation notedo The computer indicated that run number 153 had the largest deviation (37.0 inch pounds, 33.1%). Upon reference to the original observation sheets, it was noted that there was considerable entrained air in the viscosity sample, and that the viscosity reading was probably in error. The computed torque for run number 173 was 12.08 inch pounds high (4.8%), but again, there was reason to question the viscosity reading because there had been some mixing of solutions during a change over, and the sample may not have been representativeo Errors for run 281 (2~56 inch pounds, 16.6%) and run 282 (.93 inch pounds, 6.7%) were also high, but the original observation sheets showed that the readings were changing during the runs and that the system was not operating in steady-state. The fitted curve (including the runs discussed above) had an absolute standard error of 4070 inch pounds, and a coefficient of determination of 0.998, showing that it was an accurate representation of the data. The large number and unconventional form of the terms of Equation (6) make an analysis with respect to physical occurrences very difficulto However, when B = 0 (smooth rotor), the equation reduces to Tv = 3o61 ne'a

-42 Introducing the scaling factors, and dividing both sides by nlpi, it becomes T' 361 x 10-5 (7) nap where T' - torque in inch pounds n' = rpm W = viscosity in centipoises If the dimensional factor for a smooth rotor 16-5/8 inches long (19o52 in3) is introduced into Equation (3), it is T' = 3.66 x 10-5 (8) nItL Thus there is excellent agreement between the theoretical equation for a smooth rotor and that portion of Equation (6) which applies to a smooth rotor, indicating that both the data and the curve fitting technique are valid. A more conventional method of analysis of these data can be made with a dimensional analysis study, again using a digital computer to determine the coefficients and the exponents of the dimensionless groupso The following are considered to be significant variables: ML2 Torque =T - (2 M Viscosity = i - M L0 Noo of blades = B - dimensionless Speed of blade at scraped.surface = V - Radial clearance between rotor and stator = d - L

-43 Density of fluid p M L3 Length of active rotor = 2 - L Axial velocity is not included as a variable because the work of Goldstein(4) and others show that within the laminar flow range, axial and rotational flows are independent. These can be arranged in dimensionless groups as T 1 ( = ( )a(B)b(-)c (9) d3pV2 pVd d From the analysis of the visual observations, it is evident that the torque is a function of two factors, i.eo (1) that torque required to turn a smooth rotor, and (2) that torque required to turn the rotor because of the blade effectso In order to separate these effects, Equation (9) is written T Y1(t-X )al(,)cl + Y2( )a2(B)b( c2 d3pV2 pVd d pVd d Substituting V = 2j.ROn -T- ~Y- ( L )al( )cl + Y2( ( )a2(B)b(_ )c2 4d3pt2Ro2n2 2tRonpd d 2jiRond d since - is constant for this apparatus, there is no opportunity to evalud ate C1 or C2, so let c1 1 (i C1 4 j t 2 and c2 4"2 Y2() 2 Tc Y2

then T 2 T ~ Y'( + 2( --— )a(B)b (10) d3pR02n2 Ronpd Ronpd From this, the computer program was written to evaluate the best coefficients and exponents in the least squares sense based on the equation Tnv = 1(L')al+ (C2() B (B1) n'2 nn nV The values obtained were U1 = 3.24 x 10-5 e2 = 1L01 x 10-4 a1 = 1.0 a2 = loO b = 0o46 Introducing the proper numerical conversion factors, this solution is written into Equation (10) as T = 2o41 x 104( ) + 751 x 104( _ )(B)0046 (12) d3pR02n2 Ronpd Ronpd all in consistent units. The questionable data were not included in this calculationo Tg To indicate the spread of the data, Tv- was calculated and compared with corresponding observed valueso With but few exceptions, the calculated values are well within + 10% of the observed readingso For a smooth rotor, Equation (11) can be written nV n or TV = 3o24 x 10-5 (13) nV

-45 This compares with the theoretical Equation (8)o It is noted that agreement is not as good as with the equation derived by the stepwise regression method for the zero blade conditiono The visual studies showed that type B blades would not give the mixing effect required to achieve maximum heat transfer rates, so the torque measurements with type B blades were not extensiveo An analysis of the data in runs 309 through 354 yields the equation T - 808 wE.i (14) l/R.2 - 1/Ro2 The torque calculated with this equation is in excellent agreement with the observed adjusted torque. However, it should be emphazized that the effect of the number-of blades was not investigated, and this equation is based on only 2 type B bladeso Heat Transfer Measurements The heat transfer measurements were made to demonstrate the improvement in heat transfer rates that results when properly designed scraping blades are added to a smooth rotor operating within a concentric heat transfer cylinder. Two independent thermal effects are noted in the heat transfer run, as follows: ao the energy added to the fluid by the mechanical effects of the rotating rotor and blade system, b. the energy added to or removed from the fluid because of heat transmission at the heat transfer surface (scraped surface) The way the temperature of the fluid responds to these thermal effects is different for various conditionso The temperature profile of

the fluid as it passes through the apparatus illustrates its response characteristics for the following three conditions: ao Energy is added to the fluid because of mechanical effects alone. Figure 18 shows this as a linear temperature increase of the fluid as it passes through the apparatus in the annulus with the rotor and blade system rotating. It is recognized that end effects, blade length, and other factors cause the profile to be other than a straight line, but the assumption is approximately correct because the influence of these factors is smallo b. During heating, energy is tranferred from the scraped surface to the fluid and. at the same time, energy is added to the fluid because of the mechanical effectso Figure 19 shows the fluid temperature profile in relation to the heat transfer surface temperature~ The components which contribute to the total temperature rise of the fluid are broken down and detailed on, the drawingo Co During cooling, energy is tranferred from the fluid to the scraped surface, and, at the same time, energy is added to the fluid because of the mechanical effectso Figure 20 shows the fluid temperature profile in relation to the heat transfer surface temperature for these conditionso As above, the components which contribute to the fluid temperature change are detailedo The location of the significant thermocouples is also noted on these drawingso Points 1 and 2 are in the fluid just as it enters the

-4 7 TEM FLUI I P. 384 ID OUTLE D I a) n bu L 0 0 Ji tj r I - I -- LF I. 4 I. FLUID 6 5 INCREASING TEMPERATURE a = total fluid temperature rise - due only to input of mechanical effects Figure l8. Temperature Profile with Only Mechanical Effects.

-48 4H^ Zs /i l l l l HEAT TRANSFER ST E \P a L3 1 WALL _/h - _J 0 J oSURFACE = 0 - 0 I F= I N 2 TEMP _ rd ~ uWALL... INLE XITEMP5 TEMERAUR <I <~ x ^WALL' a - total fluid temperature rise b - fluid temp. rise due to mech. effects before heating zone c - fluid temp. rise due to mech. effects in heating zone d - total fluid temp. rise in heating zone e - fluid temp. rise due to heat transfer at surface f - fluid temp. rise due to mech. effects after heating zone g - outlet temp. difference - wall to fluid h - inlet temp. difference - wall to fluid -J / TEMP I AND 2 ________.FLUID _/ INCREASING TEMPERATURE a - total fluid temperature Profile Heating plus Mechanical b - fluid temp. rise due to mech. effects before heating zone c - fluid temp. rise due to mech. effects in heating zone d - total fluid temp. rise in heating zone e - fluid temp. rise due to heat transfer at surface f - fluid temp. rise due to mech. effects after heating zone g - outlet temp. difference - wall to fluid h - inlet temp. difference - wall to fluid Figure 19. Temperature Profile - Heating plus Mechanical Effects.

-49e d~ f TEMR 3 AND 4- FLUID OUTLET 0)~~ 3) <1: 0 - 0 tL Q U. c4 TEMP. 6 Id z WAlL r oF WALL t _I_ Ih ~ ~- inlt tmp.diferece wal t flI I- I TM. 5 TEMP. _,____ __ o 0 TEMP. I AND 2 INCREASING TEMPERATURE a - total fluid temperature rise b - fluid temp.rise due to mech. effects before cooling zone c - fluid temp. rise due to mech. effects in cooling zone d - total fluid temp change in cooling zone e - fluid temp. change due to heat transfer at surface f - fluid temp.rise due to mech. effects after cooling zone g - outlet temp. difference - wall to fluid h - inlet temp. difference - wall to fluid Figure 20. Temperature Profile - Cooling plus Mechanical Effects.

-50 annulus, and points 3 and 4 are in the fluid just as it leaves the annuluso Points 5 and 6 are at the wall of the scraped surface, but at a distance from the entrance and exit ends of the heat transfer portion of the stator. In this location, tube end effects (conduction to insulating spacers) will not influence the readingo If it is assumed that the temperature gradient is linear along the length of the scraped surface, then the temperature of this surface at entrance and, exit can be calculated by extrapolation of the temperature profile line through points 5 and 60 To evaluate a coefficient of heat transfer at the scraped surface, it is necessary to separate the mechanical effects from the purely heat transfer effects. In order to measure the mechanical effects, two series of runs were made with no heat transfer~ Table II in the Appendix is a summary of these data for the rotor with 2 and 4 type A blades with two solutions made with 77.5% and 83.0% Ucono Table III in the Appendix is a summary of the data for the other series for a smooth rotor with a solution made with 83o0% Ucono To correlate these data, a dimensional analysis of the mechanical effects alone is made, It is assumed that the energy input to the fluid is a function of the following~ Energy into fluid = f(p, V, p, d, i) also Energy input to fluid = W C At mech where W = Axial flow rate - lbs/hr Cp = Specific heat - Btu/lb; ~F Amech= Temperature rise (a, Figure 18) -

-51 These variables can be arranged in dimensionless groups as [WCp Atmech]gcJ -= 0( )a()b V3p d2 Vdp d Substituting V = 2jRon This becomes [WCp Atmech]gcJ ( )a( (2 iRon)3pd2 2 TRonp d For the apparatus used in these studies, the physical dimensions do not change. Grouping all constants, the equation can be written as WCp Atmech = l(ta. (15) n13 n? These quantities are tabulated in Table II and III with the data, and are plotted in Figures 21 and 22. It is not necessary to determine the numerical values of the exponents and coefficients, because the curves are used directly in later calculations. It is evident from the temperature profiles, shown in Figures 19 and 20, that a heat transfer coefficient must be calculated from only that temperature change of the fluid which occurs because of heat transfer at the scraped surface. This is represented by the temperature change "e" on Figures 19 and 20, and the symbol Atnet. It is calculated by subtracting the temperature rise due to mechanical effects from the total temperature change of the fluid. On Figures 19 and 20 this can be represented by Atnet - e = a-b-c-f where the letters are defined on the figures.

T OG- -.___ —600 goo —-- -- 700 I l l 600 -- 250 -- 2400 30.0 250 a 200.... II Z 3 UJ 0 -- 0 150 100 90 80 70 60 50 40 30 25 20 10: L - | |~~~zr 1 1 I << L T /01*/ I) j!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I - I I I II. I IIJ I ro R).4 2x106 3x10 4x(10 6x10' S8lO I3 -3 -3 -3 -3 -3 -2 2x10 3x10 4x10 6x10 8xl0 10 W Cp tmech BTU ~T 2 MIN Figure 21. Plot of Significant Groups for Mechanical Input of Rotor and Blades.

-53 1000 900 800 700 600 500 400 U) w I-. z w Co z u) LC U -4' 300 250 200 150 100 90 80 / 70 - 60 50 -4 I0 -4 -4 -4 2xI0 310 4xl10 -4 -4 -5 6x 10 8x10 10 W Cp tmech n3 NS el 2, BTU ~ MIN. Figure 22. Plot of Significant Groups for Mechanical Input with Smooth Rotor.

-54 For each run, the temperature rise due to the mechanical effects, Atmech, is determined from Figures 21 and 22o The ratio n-1 is used to find Wtmech; e2 WCp Atmech on the graph, and Atmech calculated from this valueo n'3 It is recognized that the mechanical effects were measured under approximately adiabatic conditions, and then were used with heat transfer measurements. Small temperature differences in the fluid were maintained so that this approximation had little influence on the resultso It is also necessary to know the temperature difference between the exit and entrance ends of the scraped. surface and the fluido The temperatures at the ends of the scraped surface ( x and y - Figures 1.9 and. 20) are calculated by graphically extrapolating wall temperatures 5 and 6 to the ends of the tube, assuming linear distributiono The temperature of the fluid at w (Figures 19 and 20) is calculated by adding (5/18) (Atmech) to the fluid inlet temperature (average of 1 and 2)e The temperature of the fluid at z (Figures 19 and 20) is calculated by subtracting (5/18) (Atmech) from the fluid outlet temperature (average of 3 and 4). Then temperature differences g and h (Figures 19 and 20) can be used to calculate the log mean temperature difference, Table IV is a summary of the heat transfer data and the calculated heat transfer coefficient for the apparatus with 2 and 4 type A blades attached to the rotoro Table V contains similar data for a smooth rotoro The analysis of these data is simplified with an equation derived by dimensional analysis For the condition with type A blades, it is assumed that h = f(Cp, k, p, V, B, Ro, [, d)

-55 where h = film coefficient at scraped surface, Btu/hr; ft2; ~F Cp specific heat of fluid, Btu/lb; ~F k = thermal conductivity of fluid., Btu/lb; ft2; ~F/ft p = density of fluid, lbs/ft3 V = speed of blade at scraped surface, ft/hr B = number of blades Ro = radius of stator bore, feet. = viscosity of fluid, lb/hr; ft d = annular gap, ft These variables can be arranged in dimensionless groups to give the equation hd = _ (C_)a (VdP)b(d)c (B)d k k p. Ro If the blade thickness is neglected, the annular passage between two blades 2 ThR can be considered to have a length factor -- The last two groups can be combined as ( dB ) which is a (d) factor Now the Nusselt number is proportional to the product of a Prandtl number, a Reynolds number, and a (d) ratio. These are usually combined into a Graetz number for laminar flow. Making this combination and substituting V 2tRon the equation become s hd (CP d2p nB a _ = a (cP.'k k Substituting nB - s, the correlating equation is hd (Cp d2p s) (16) k k

-56 These calculated groups are tabulated in Table IV with the data, and plotted in Figure 23, The measured temperatures are to the nearest 0.1 ~F, but small differences in the readings make large changes in the heat transfer coefficiento All of the readings taken during a run are included to show the spread. The average value of h is used to calculate -h Although there is considerable spread, the slope of the curve, and thus the exponent of cpsd2 and thus the exponent of - is clearly evidento As the frequency of scraping the surface decreases, the film coefficient approaches the cocpsd2 efficient for a smooth rotor. For conditions where the group --- exceeds 3000, the correlating equation is hd CpPsd2 062 (17) - = 0.104 (- )06 (17) In a similar manner, the data for a smooth rotor is calculated and tabulated in Table V and plotted in Figure 24. The correlating equation is hd = 100 (Cppnd )0.03 (18) k k where n = rotor speed in rev/hr replacing s in Equation (17) Discussion If the heated or cooled fluid film is scraped from the heat transfer surface and then returned to the surface, it is obvious that the full advantages of the scraped surface heat exchanger cannot be realized. With very visious fluids, such as used in this work, both rotational and axial flows are laminar and are very stableo As visually observed, a

40 35 30 25 20 18 16 14 12 10 8 6 4 BLADE EFFECTDIMINISHES -I - I- II SLOPE 0.62 I I. 1-> V l: \ I I - 0 HEATING -4 TYPE A BLADES El COOLING-4 TYPE A BLADES A HEATING -2 TYPE A BLADES X COOLING-2 TYPE A BLADES L 11XJ~~~~~~~~~~~~ I -ki I 2,- 2x1o0 3x103 4xo10 6x103 8x10 104 cpsd k 2xl04 Figure 23. Plot of Dimensionless Heat Transfer Groups.

30 25 20 19 16 14 12 10 9 8 7 6 5 4 3 2 I I 200 300 400 600 800 1000 cpnd2 k 2000 3000 4000 6000 9000 Figure 24. Plot of Dimensionless Heat Transfer Groups - No Blades.

-59 disturbing element such as the type B blade did not change the mode of flow, even though its scraping action is effective. It is necessary that the blade produce forced mixing as well as scrape the surfaceo The type A blade accomplishes these objectives. The pressure difference between the leading and trailing edges of the blades is caused by the shear effects in the fluid and by the turning around of the scraped film. This pressure difference "pumps" the fluid within the space between blades where the fluid is trapped. At each end of the closed passage (at the blade faces) the pumped fluid must turn 180, and mixing is assured. It should be recognized that this mixing is still not completeo There is material right next to the rotor face which may never get to the heat transfer surface. The springs in the blade mounting attachments exert enough force to move the blades to their outward position. This force is not enough to scrape the surface completely dry, because the Ucon fluid is a lubricant, and its film is tenacious. It is estimated that this film is 00003" to 0010" thick, and acts as a lubricant. The presence of this very low velocity fluid does influence the heat transfer film coefficiento The motion of the fluid with the type A blade is especially significant. There is no known reference in the literature to a blade that completely spans the annuluso Kern(9) recognized that an application of Skellandls(l2) equations to fluids in laminar flow would be in error because of the core of unmixed fluid next to the rotoro In industrial practice, the blades can be mounted in many ways so that they span the annular gap and give the degree of scraping pressure

-6o desired. One possible arrangement is a blade hinged at the rotor so that the action of the fluid holds the blade edge on the heat transfer surfaceo An apparent reason for knowing the power requirements is to design the driving machineryo Equally important is the influence of the power input on the net heat transfer effecto For economical reasons it is desireable to keep the power demand as low as possible, consistent with heat transfer performanceo In addition, most of the mechanical energy input is added to the fluid, and. becomes an additional load on the heat transfer surface in cooling applicationso The conclusion is that the heat exchanger should be designed to require the least power in relation to the maximum heat transfer rate The equations developed in this work show how speed of rotation and the number of blades affect power demand and the heat transfer rateo Since power is proportional to the product of torque and speed, from Equation (12) it can be shown that power CCn2(l + B0~46) and from Equation (17) h c (n)0o62 (B)0062 From these equations it is apparent that the addition. of more blades causes the heat transfer coefficient to increase at a faster rate than the power requirements. Increasing speed causes the power to increase faster than the heat transfer coefficient. For a given heat transfer coefficient, physical dimensions, fluid, and frequency of scraping, the best arrangement is the largest practical number of blades operating at the lowest speedo In the only literature dealing with power consumption of a scrapedsurface heat exchanger, Skelland and Leung(l3) have made a dimensional

-61 analysis of the problem and evaluated the exponents and coefficients experimentally. Their data are not consistent, so they suggest two possible equations and indicate the need for additional worko Except for the fact that they did not consider the annular gap a significant parameter, the dimensionless groups are the same as in this worko An explanation for the poor correlation of their data can be found in an analysis of the mode of rotational fluid flowo The blades on their rotor did not span the annular gap, so there is some-fluid next to the rotor that is not in the path of the blade. If a Taylor number and a critical Taylor number are calculated for a dimensionally similar smooth rotor apparatus and fluid conditions, it can be shown that for some runs the Taylor number is less than critical, and for some greatero For the one condition, there will be no Taylor vortices, and. the core fluid will remain in laminar flow rotationally, and will not be mixed with. the heated or cooled film. For the other condition, the Taylor vortices do occur and the core fluid is mixedo In spite of the inconsistencies described above, the exponent applied to the number of blades is in reasonable agreemento They did not consider the zero blade condition, and determined the exponent on the number of blades to be 059 or Oo64. If all other parameters which influence torque are considered constant, Equation (12) can be written T constant (0o321 + B0o46) A comparison is made in the following table:

-62 Number of Blades B0O59 B0o64 (0.321 + B0o46) 2 1.51 1L56 1.70 3 lo91 2.02 1.98 4 2.27 2.43 2.21 The purpose of making the heat transfer measurements in this work was to demonstrate that the heat transfer film coefficient is increased when scraping blades are added to the rotor. A comparison of Figures 23 and 24 clearly shows the effect. The same comments relative to the mode of rotational flow which were made about the above work of Skelland and Leung(15) apply to that of Skelland, Oliver, and Tooke.(14) Again, in spite of the differences in modes of flow, the effect of the frequency of scraping the surface on the film coefficienct was determined to be of the same order. Assuming all other parameters to be constant, Skelland, Oliver and Tooke found h GC constant n0.62 B053 It was found in this work (Figure 24) that h OC constant n0o62 BO.62 The mathematical derivation of Kool(10) was made for an apparatus operating under substantially the same conditions as in this work. He assumes perfect scraping and perfect mixing in setting up a heat balance within the annulus. His solution is given as -1/2 2 2Sjt + expS erfcS - 1 s h S2 - 2Si1/2 - expS2erfcS + 1 where hs = film coefficient at the scraped surface h.' = film coefficient at jacket fluid surface

-63 S = (h -I1 pp) t = time between each scrape When S has a value of 02 to 30, hs = 1.24 h' S-1o03 From this equation, the effect of the frequency of scraping can be expressed as h GC S~o52 which compares with h CC S0o62 determined in this worko If the film coefficients are calculated using Kool's equation for conditions existing in the experimental work, they are 3 to 4 times higher than those determined experimentallyo Kool shows that a residual film of 0,2 mm to 005 mm can cause all of this difference, As noted above, the residual film in these experiments could approach this thicknesso It is known that the condition of perfect mixing is not attained. Kool also shows the adding scrapers to a smooth rotor will increase the film coefficient by 2 to 4 times

CHAPTER IV CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER WORK A basis for the design of a scraped-surface heat exchanger for viscous fluids with viscosities in the range of 2,000 to 20,000 centipoises has been determinedo Specific conclusions from the labroatory observations and measurements of this work are as follows: lo The required scraping and mixing action will be produced by solid blades attached. to the rotor. These blades should span the entire annular gap between the rotor and the stator, so that a complete block to rotational fluid flow occurs at each scraper. The action of this type of scraping blade on the fluid is substantially the same for 1 through 4 blades. 2o Scrapers which are essentially rods will not mix the scraped film with the bulk fluid, and will leave an undisturbed core of fluid next to the rotoro 3o The torque requirements, and thus the power demand, can be calculated from either Equation (6) or (12)o Equation (12) is simpler to use and. provides almost as good correlationo It is 3 T2 = 2 41x ) + 75 x 104-( 75 x 1 )(B)0~46 d3pRo n Ronpd Ronpd 4o The heat transfer film coefficient at the scraped surface shows a significant improvement with the addition of scrapers -64

-65 to the smooth rotor. The degree of improvement that can be expected can be calculated by comparing the film coefficient calculated from Equation (18) for a smooth rotor with that calculated from Equation (17) for a rotor with blades. These equations are hd 10.0 (cpd2)0~03 (18) k k hd = 0.104 (cpsd2)O.62 (17) k k Much additional work needs to be done, because there is very little material in the literature on either the design or the performance of scraped-surface heat exchangers, particularly units for viscous fluids, The following specific recommendations are made: 1. The Taylor number should be used to calculate the mode of rotational fluid flow for a dimensionally similar system with a smooth rotor. Data taken in future work can be classified and properly correlated when the mode of flow is defined. 2. Within the fluid viscosity range of 2,000 to 20,000 centipoises, this work should be extended to higher rotor speeds and more blades. 3. The effects of dimensional changes should be investigated within the limits of commercially practical units. Although the cross sectional area of the annulus must be large enough to avoid a prohibitive axial pressure drop, the influence of the width of the annular gap would be of

-66 interest. The inside diameter of the stator should be as large as possible to obtain maximum heat transfer area per unit length, consistent with a linear scraping speed that will not result in excessive wear. 4. The scraping efficiency of blades should be investigated. The scraped-surface heat exchanger has a wide field of use where other types of heat exchangers are not effective or economicalo In atuomatic and continuous processes, the accurate control of the temperature of viscous components is a necessity. Another application for this type of unit is as an agitated, controlled-temperature chemical reactor. Components can be introduced along the axial length as the base fluid flows through. The heat-transfer jacket can be zoned to provide different temperatures along the length. The scraped-surface heat exchanger is a versatile mechanical device for use by the chemical process industries. Its industrial application will expand with increased knowledge of design and performance.

APPENDIX -67

-68 TABLE I TORQUE MEASUREMENT DATA A B C D E F G H I J Axial Fluid Rotor Active Adjusted Fluid Observed Run No. of Blade Flow Viscosity Speed Rotor Torque No. Blades Type ibs/min Centipoises rpm Length Torque Inch-lbs W OF n' Inches Inch-lbs T 1 0 -- 4.39 2,133 76.6 164.9 18.733 12.746 11.47 2 0 -- 4.39 2,087 76.8 165.6 18.733 12.866 11.57 3 -- 4.39 2,129 76.6 165.7 18.733 12.866 11.57 4 0 -- 4.39 2,126 76.6 166.0 18.733 13.127 11.80 5 0 -- 4.44 2,127 76.6 98.5 18.900 9.018 8.06 6 -- 4.44 2,129 76.6 99.0 18.900 9.018 8.06 7 -- 4.44 2,120 76.8 98.9 18.900 9.018 8.06 8 0 -- 4.44 2,072 76.8 99.0 18.900 9.018 8.06 9 0 -- 4.45 1,929 77.7 58.5 18.857 6.252 5.60 10 0 -- 4.45 1,993 77.6 58.5 18.857 6.132 5.49 11 0 -- 4.45 1,999 77.5 58.5 18.857 6.012 5.39 12 0 -- 4.45 2,039 77.4 58.6 18.857 5.891 5.27 13 0 -- 4.50 2,131 76.8 32.0 19.012 3.257 2,91 14 0 -- 4.50 2,074 76.8 32.0 19.012 3.127 2.79 15 0 - 4.50 2,066 77.0 32.0 19.012 3.127 2.79 16 0 - 4.50 2,055 76.8 32.0 19.012 3.257 2.91 17 0 - 3.96 1,262 73.9'164.0 18.704 7.936 7.14 18 0 3.96 1,238 73.9 165.5 18.704 7.816 7.03 19 0 3.96 1,238 73.9 165.9 18.704 7.816 7.03 20 0 - 3.96 1,235 73.9 166.6 18.704 7.816 7.03 21 0 3.79 1,153 73.8 98.6 18.819 4.930 4.42 22 0 3.79 1,220 74.1 98.8 18.819 5.050 4.53 23 0 - 3.79 1,240 73.4 99.0 18.819 4.930 4.42 24 0 3.79 1,243 73.5 98.9 18.819 5.170 4.64 25 0 - 3.83 1,368 74.5 58.6 18.900 2.525 2.26 26 0 3.83 1,262 74.4 58.9 18.900 2.525 2.26 27 0 - 3.83 1,243 74.3 58.6 18.900 2.525 2.26 28 0 3.83 1,235 74.2 58.6 18.900 2.766 2.48 29 0 - 4.06 1,289 74.0 32.0 18.894 1.202 1.08 30 0 - 4.06 1,251 74.0 32.0 18.894 0.962 0.86 31 0 4.06 1,241 73.8 32.0 18.894 0.962 0.86 32 0 4.06 1,226 73.9 32.0 18.894 0.962 0.86 33 0 - 2.04 14,853 77.9 157.9 18.845 87.534 78.50 34 0 2.04 15,153 78.5 158.6 18.845 85.370 76.52 35 0 -- 2.04 14,400 79.3 159.0 18.845 85.250 76.50 36 0 -- 2.04 13,613 79.8 159.1 18.845 84.288 75.60 37 0 2.00 14,280 76.4 96.7 19.013 59.759 53.25 38 0 2.00 15,233 76.2 97.1 19.013 58.677 52.30 39 0 2.00 15,303 76.7 97.3 19.013 58.316 51.95 4 0 - 2.00 15,107 76.5 97.4 19.013 58.076 51.80 41 0 2.21 16,490 74.5 58.3 19.080 34.629 30.83 42 0 - 2.21 16,327 75.0 58.3 19.080 34.509 30.72 43 0 2.21 15,940 75.4 58.3 19.080 34.629 30.83 44 0 2.21 16,327 75.0 58.2 19.080 34.629 30.83 45 0 - 2.10 15,653 73.9 31.8 19-159 19.599 17.42 46 0 2.10 16,448 74.0 32.0 19.159 18.998 16.89 47 0 2.10 16,907 74.0 31.9 19.159 18.758 16.68 48 0 -- 2.10 16,807 74.2 31.8 19.159 18.637 16.58 49 2 A 4.19 1,993 78.3 161.3 18.834 66.853 65.51 50 2 A 4.19 2,107 78.2 162.1 18.834 66.372 64.95 51 2 A 4.19 2,128 78.2 162.0 18.834 66.613 65.17 52 2 A 4.19 2,109 78.2 162.5 18.834 66.853 65.41 53 2 A 4.32 2,167 77.9 98.1 18.904 43.386 42.37 54 2 A 4.32 2,176 77.7 98.4 1.8.904 43.888 42.97 55 2 A 4.32 2,121 77.8 98.5 18.904 43.647 42.75 56 2 A 4.32 2,113 77.8 98.4 18.904 43.286 42.40 57 2 A 4.24 2,189 77.3 56.6 18.983 25.611 25.07 58 2 A 4.24 2,155 77.4 56.5 18.983 25.972 25.43 59 2 A 4.24 2,155 77.5 56.5 18.983 25.852 25.31 60 2 A 4.24 2,190 77.5 56.5 18.983 25.611 25.07 61 2. A 4.25 2,181 77.2 31.9 18.983 13.707 13.40 62 2 A 4.25 2,173 77.3 32.0 18.983 13.948 13.64 63 2 A 4.25 2,161 77.3 32.0 18.983 13.948 13.65

-69-'TAlI, I (cont i nied) A B C D E F f1 I J Axial Fluid Rotor Active Adjusted Run No. of Blade Flow Viscosity T Speed Rotor Oserve Torque No. Blades Type lbs/min Centipoises rpm Length orque Inch-ts W O~ n Inches Inch-lbs T 64 2 A 65 2 A 66 2 A 67 2 A 68 2 A 69 2 A 70 2 A 71 2 A 72 2 A 73 2 A 74 2 A 75 2 A 76 2 A 77 2 A 78 2 A 79 2 A 80 2 A 81 2 A 82 2 A 83 2 A 84 2 A 85 2 A 86 2 A 87 2 A 88 2 A 89 2 A 90 2 A 91 2 A 92 2 A 93 2 A 94 2 A 95 2 A 96 2 A 97 2 A 98 2 A 99 2 A 100 2 A 101 2 A 102 2 A 103 2 A 104 2 A 105 2 A 106 2 A 107 2 A 108 2 A 109 2 A 110 2 A 111 2 A 112 2 A 113 2 A 114 2 A 115 2 A 116 2 A 117 2 A 18 2 A 119 2 A 120 2 A 121 2 A 122 2 A 123 2 A 1.24 2 A 125 2 A 126 2 A 127 2 A 128 2 A 129 2 A 130 2 A 13] 2 A 132 2 A 4.25 4.29 4.29 4.29 4.29 9.52 9.52 9.52 9.52 9.58 9.58 9.58 9.58 4.36 4.36 4.36 4.36 4.33 4.33 4.33 4.33 9.75 9.75 9.75 9.75 9.97 9.97 9.97 9.97 4.64 4.64 4.64 4.64 2.89 2.89 2.89 2.89 4.36 4.36 4.36 4.36 4.46 4.46 4.46 4.46 2.93 2.93 2.93 2.93 2.99 2.99 2.99 2.99 4.77 4.77 4.77 4.77 4.95 4.95 4.95 4.95 3.35 3.35 3.35 3.35 2.87 2.87 2.87 2.87 2,157 1,974 2,047 2,091 2,112 2,139 2,112 2,117 2,115 2,149 2,143 2,118 2,118 2,160 2,149 2,128 2,117 2,118 2,112 2,068 2,077 2,127 2,072 2,075 2,0o4 2,101 2,077 2,039 2,018 2,035 2,008 2,007 1,995 8,398 8,643 8,478 8,030 8,178 8,323 8,160 8,183 8,178 8,118 8,023 7,905 7,870 8,125 8,010 7,865 7,528 7,533 7,513 7,560 7,545 7,745 7,548 7,495 7,135 7,275 7,183 7,003 6,653 6,940 6,790 6,345 12,053 L2,920 13,0(7f 12,620 77.3 32.0 18.983 13.707 13.41 78.6 31.8 18.983 15.751 15.47 78.3 31.9 18.983 15.511 15.22 78.4 31.8 18.983 15.632 15.34 78.3 31.8 18.983 15.511 15.22 78.4 31.8 19.075 15.511 15.20 78.3 31.7 19.075 15.632 15.33 78.2 31.9 19.075 15.511 15.21 78.3 31.8 19.075 15.511 15.21 78.1 57.8 19.075 28.136 27.58 78.1 58.0 19.075 27.535 26.98 78.3 58.0 19.075 27.776 27.25 78.2 58.1 19.075 27.535 26.99 77.9 58.1 18.971 27.415 26.86 78.2 58.1 18.971 27.776 27.23 78.1 58.1 18.971 27.535 27.00 78.3 58.1 18.871 27.295 26.75 78.5 97.3 18.942 44.730 43.83 78.3 97.5 18.942 44.730 43.84 78.5 97.6 18.942 44.128 43.26 78.4 97.6 18.942 43.046 42.17 78.2 97.8 19.008 43.166 42.25 78.4 97.9 19.008 43.046 42.12 78.3 97.9 19.008 42.565 41.65 78.6 98.1 19.008 42.084 41.19 79.2 159.6 18.922 67.454 65.99 79.0 161.0 18.922 67.214 65.75 79.1 161.5 18.922 66.973 65.53 79.2 161.9 18.922 66.613 65.19 80.1 160.9 18.871 65.636 64.26 80.2 162.0 18.871 64.070 62.68 80.4 162.5 18.871 64.341 62.96 80.6 162.4 18.871 64.672 63.29 75.4 31.6 19.123 48.577 47.38 75.0 31.6 19.123 48.577 47.35 75.1 31.6 19.123 48.577 47.37 75.3 31.6 19.123 48.336 47.21 75.5 31.6 19.160 48.697 47.52 75.6 31.6 19.160 47.374 46.17 75.9 31.5 19.160 47.855 46.68 75.6 31.6 19.160 47.855 46.69 75.9 57.0 19.145 83.567 81.45 76.0 57.1 19.145 82.004 79.89 76.2 57.0 19.145 81.403 79.32 76.2 57.1 19.145 83.207 81.15 76.6 57.1 19.068 82.004 79.97 77.0 57.1 19.068 80.922 78.85 77.3 57.1 19.068 80.207 78.14 77.1 57.1 19.068 81.283 79.27 77.6 94.0 19.010 122.164 119.01 77.8 94.3 19.010 120.240 117.08 78.1 94.6 19.010 119.769 116.60 79.0 94.3 19.010 122.164 119.01 78.2 94.5 19.069 121.563 118.38 78.4 94.6 19.069 120.020 116.73 78.5 94.9 19.069 119.639 116.44 78.8 95.0 19.069 118.436 115.24 80.7 145.5 19.026 164.729 160.o8 81.0 145.1 19.026 161.482 156.83 81.1 145.7 19.026 160.039 155.34 81.5 145.9 19.026 160.280 155.68 81.8 146.5 18.961 156.192 151.94 83.5 146.5 18.961 155.711 151.29 81.1 ]47.L 18.961 153.907 149.49 rf3.9 147.6 18.961 152.104 148.00 74.(, 31.4 19.]61 76.462 74.76 74.4 31.4 19.161 75.150 73.32 74.3 31.2 1.9.1 61 75.150 73.33 74.4 31.1 19. 16 73.346 71.58

-70 TABLE I (continued) A B C D E F C H I J Axial Fluid F d Rotor Active Adjusted Run No. of Blade Flow Viscosity 1 Speed Rotor Tbserved Torque No. Blades Type lbs/min Centipoises rpm Length Toue Inch-lbs I OFi n, Inches Inch-lbs n' Inches T' 133 2 A 2.70 134 2 A 2.70 135 2 A 2.70 136 2 A 2.70 137 2 A 2.65 138 2 A 2.65 139 2 A 2.65 140 2 A 2.65 141 2 A 3.66 142 2 A 3.66 143 2 A 3.66 144 2 A 3.66 145 2 A 3.78 146 2 A 3.78 147 2 A 3.78 148 2 A 3.78 149 2 A 3.88 150 2 A 3.88 151 2 A 3.88 152 2 A 3.88 153 2 A 1.58 154 2 A 1.58 155 2 A 1.58 156 2 A 1.58 157 2 A 1.59 158 2 A 1.59 159 2 A 1.59 160 2 A 1.59 161 2 A 1.59 162 2 A 1.68 163 2 A 1.68 164 2 A 1.68 165 2 A 2.46 166 2 A 2.46 167 2 A 2.46 168 2 A 2.46 169 2 A 2.51 170 2 A 2.51 171 2 A 2.51 172 2 A 2.51 173 2 A 2.53 174 2 A 2.53 175 2 A 2.53 176 2 A 2.53 177 A 1.61 178 A 1.61 179 1 A 1.61 180 L A 1.61 181 1 A 1.64 182 1 A 1.64 183 1 A 1.64 184 1 A 1.64 185 A 1.62 186 1 A 1.62 187 1 A 1.62 188 A 1.62 189 0 - 2.48 19 0 - 2.48 191 0 -- 2.48 192 0 -- 2.48 193 0 -- 2.36 194 0 -- 2.36 195 0 - 2.36 196 0 -- 2.36 197 0 -- 2.21 198 0 -- 2.21 199 0 -- 2.21 200 0 -- 2.21 201 0 -- 2.28 202 0 -- 2.28 203 0 - 2.28 204 0 -- 2.28 13,073 13,497 13,257 13,177 12, ]60 12,500 12,247 12,180 11,287 12,267 11,917 12,233 12,490 12,910 12,387 12,120 11,923 12,097 12,140 11,553 17,877 19,443 19.477 19,610 19.533 19,247 18,890 19,370 18.400 17,810 17,650 17,890 19,853 19,477 19,183 19,273 19,107 19,387 19,040 18,947 17,840 18,607 18.007 17,330 19,710 20,650 20.925 20,500 20,650 20,725 20,825 20,650 20,900 20,900 20,900 20,775 14.123 14,423 13,920 13,777 13,930 13,933 14,107 13,847 14,727 14,683 14,180 14,153 14,047 12,963 12,893 12,880 74.5 74.7 75.0 75.2 75.6 76.8 77.1 77.0 76.3 76.1 76.0 76.3 76.8 76.6 77.2 77.1 78.1 78.5 78.4 78.8 78.6 78.4 78.5 78.4 79.2 80.0 80.4 80.4 80.6 32.5 83.6 82.5 79.8 79.7 80.0 79.9 80.3 80.2 80.3 80.3 81.5 81.3 81.5 83.8 77.3 77.3 77.5 77.5 77.8 77.7 77.8 77.9 77.7 77.8 77.8 77.8 79.7 79.8 80.0 80.0 80.2 80.0 79.9 79.8 78.5 78.8 78.9 78.9 80.6 81.5 82.4 82.4 55.6 19.115 122.284 119.01 55.6 19.115 123.848 120.45 55.6 19.115 124.569 121.24 55.6 19.115 125.170 121.87 90.2 19.063 186.612 181.67 90.6 19.063 187.334 182.23 90.9 19.063 184.328 179.33 90.7 19.063 186.011 181.11 31.2 19.210 75.751 74.14 31.1 19.210 73.347 71.59 31.2 19.210 72.385 70.68 31.1 19.210 72.866 71.11 55.5 19.170 128.898 125.75 55.6 19.170 129.860 126.56 55.6 19.170 123.487 120.34 55.6 19.170 125.651 122.58 89.0 19.138 181.924 177.12 89.5 19.138 175.070 170.15 90.0 19.138 177.835 172.89 90.5 19.138 171.102 166.35 31.0 19.156 114.348 111.80 31.0 19.156 113.627 110.88 31.0 19.156 113.627 110.88 31.0 19.156 115.791 113.04 59.4 19.112 190.460 185.31 59.5 19.112 187.694 182.54 59.8 19.112 186.251 181.15 59.5 19.112 190.700 185.50 86.4 19.076 257.313 250.16 87.8 19.076 253.947 246.92 87.8 19.076 252.744 245.79 87.8 19.076 254.428 247.38 31.0 19.187 113.627 110.83 31.1 19.187 111.823 109.07 31.0 19.187 111.823 109.12 31.0 19.187 111.463 108.71 54.2 19.158 182.404 177.75 54.2 19.158 181.322 176.62 54.3 19.158 179.638 174.99 54.2 19.158 179.879 175.33 84.5 19.115 257.193 250.39 86.2 19.115 256.712 249.41 87.1 19.115 252.624 245.57 86.9 19.115 250.340 243.54 31.0 18.933 79.979 77.33 31.0 18.933 79.979 77.18 31.0 18.933 78.896 76.05 31.0 18.933 77.813 75.04 54.6 18.456 134.447 130.15 54.5 18.456 135.409 131.16 54.2 18.456 135.289 131.04 54.2 18.456 135.890 131.69 83.0 17.67 210.439 206.44 83.0 17.67 207.794 203.79 82.9 17.67 213.926 209.93 82.7 17.67 214.046 210.15 32.0 19.150 16.472 14.63 32.0 19.150 16.593 14.74 32.0 19.150 16.472 14.63 32.0 19.150 16.472 14.63 56.1 19.111 29.819 26.58 56.7 19.111 29.819 26.58 56.5 19.111 30.180 26.85 56.6 19.111 29.940 26.65 97.1 19.043 53.266 47.45 97.1 19.043 52.885 47.10 97.5 19.043 52.304 46.60 97.6 19.043 52.304 46.60 158.3 18.900 80.921 72.43 159.5 18.900 79.698'71.40 160.1 18.900 78.997 70.70 160.5 18.900 78.637 70.45

-71 TABLE I (continued) A B C D E i F, H I J Axial Fluid Rotor Active Adjusted Observed Run No. of Blade Flow Viscosity Tep. Speed Rotor Torque No. Blades Type bs/min Centipoises rpm Length o Inch-bs W I'n' Inches T' 205 0 -- 1.57 16,287 80.5 152.5 18.930 105.691 94.40 206 0 -- 1.57 16,160 81.3 154.7 18.930 107.133 95.80 207 0 -- 1.57 16,080 82.1 155.3 18.930 108.817 97.10 208 0 -- 1.57 15,827 83.0 156.4 18.930 108.937 97.25 209 0 - 1.57 15,373 83.7 159.9 18.930 107.133 95.80 210 0 -- 1.55 16,820 80.9 97.4 19.038 63.968 57.00 211 0 -- 1.55 16,867 80.9 97.2 19.069 66.372 59.05 212 0 - 1.55 16,880 81.0 97.4 19.069 65.771 58.55 213 0 -- 1.55 16,897 81.3 97.6 19.045 64.449 57.40 214 0 -- 1.64 16,847 80.9 58.0 19.120 39.800 35.42 215 0 --.64 16,783 80.9 58.0o 19.120 39.439 35.12 216 0 -- 1.64 16,810 81.o 58.0 19.120 39.559 35.20 217 0 -- 1.64 16,610 81.3 58.0 19.120 39.199 34.88 218 0 -- 1.73 16,863 80.9 32.0 19.191 21.884 19.47 219 0 -- 1.73 17,287 80.8 32.0 19.168 22.124 19.67 220 0 -- 1.73 16,903 80.9 31.9 19.208 23.086 20.53 221 0 -- 1.73 16,953 81.0 32.0 19.208 22.605 20.07 222 0 -- 1.66 16,127 82.0 145.3 18.919 103.045 92.15 223 0 -- 1.66 15,850 84.0 155.2 18.919 102.564 91.65 224 0 -- 1.66 15,610 84.7 156.3 18.919 102.204 91.50 225 0 -- 1.66 15,107 85.4 157.2 18.919 101.242 90.55 226 0 -- 3.86 5,14o0 83.1 160.5 18.960 36.673 32.75 227 0 - 3.86 5,095 82.9 162.4 i8.915 39.198 35.07 228 0 -- 3.86 5,080 83.2 163.2 18.915 41.362 36.95 229 0 -- 3.86 5,110 83.3 163.5 18.915 42.685 38.20 230 0 -- 3.86 163.6 18.915 43.647 231 0 -- 3.86 163.9 18.915 43.767 232 0 -- 3.72 5,335 82.6 161.4 18.860 36.673 32.85 233 0 -- 3.72 5,255 82.8 162.7 18.860 34.629 31.05 234 0 - 3.72 5,210 82.7 163.4 18.860 33.426 29.95 235 0 -- 3.72 5,180 82.9 164.4 18.860 33.186 29.75 236 0 -- 3.91 5,200 82.3 98.7 19.000 24.890 22.22 237 0 -- 3.91 5,235 82.8 98.9 19.000 27.295 24.35 238 0 -- 3.91 5,250 83.0 98.7 19.000 27.655 24.68 239 0 -- 3.91 5,190 82.8 98.7 19.000 28.257 25.21 240 0 - 3.91 98.5 19.000 28.978 241 0 -- 3.92 5,365 82.2 58.7 19.075 13.226 11.79 242 0 -- 3.92 5,560 82.4 58.6 19.075 14.308 12.73 243 0 -- 3.92 5,330 82.4 58.7 19.075 14.068 12.51 244 0 - 3.92 5,345 82.4 58.6 19.075 13.707 12.22 245 0 -- 3.69 5,460 82.2 32.0 19.144 8.176 7.27 246 0 -- 3.69 5,415 82.1 32.0 19.100 8.296 7.38 247 0 -- 3.69 5,360 82.1 32.0 19.100 7.936 7.06 248 0 -- 3.69 5,44o0 82.1 32.0 19.100 7.455 6.64 249 0 -- 3.13 5,735 78.3 159.5 18.864 40.160 35.60 250 0 -- 3.13 5,790 78.9 162.1 18.864 38.717 34.68 251 0 -- 3.13 5,840 78.8 162.9 18.864 38.356 34.38 252 0 -- 3.13 5,800 78.8 163.5 18.864 38.236 34.25 253 0 -- 3.10 6,825 78.2 32.0 19.118 7.936 7.06 254 0 - 3.10 6,410 78.3 32.0 19.118 7.936 7.06 255 0 - 3.10 6,300 78.3 32.0 19.118 7.936 7.06 256 0 -- 3.10 6,225 78.3 32.0 19.118 7.936 7.06 257 0 3.13 6,460 78.3 58.6 19.076 14.669 13.06 258 0 -- 3.13 6,410 78.5 58.6 19.076 14.549 12.96 259 0 - 3.13 6,390 78.3 58.6 19.076 14.549 12.96 260 0 -- 3.13 6,325 78.4 58.6 19.076 14.549 12.96 261 0 -- 3.12 6,450 78.7 98.4 18.975 24.770 22.08 262 0 -- 3.12 6,380 78.7 98.4 18.975 24.529 21.88 263 -- 3.12 6,305 78.8 98.6 18.075 24.650 22.00 264 0 -- 3.12 6,240 78.7 98.6 18.975 24.409 21.79 265 1 A 2.49 8,510 75.6 137.5 18.332 134.909 130.66 266 1 A 2.49 8,750 75.7 136.5 18.332 132.024 127.67 267 1 A 2.49 8,670 75.7 137.0 18.332 132.144 127.89 268 1 A 2.49 8,690 75.7 135.0 18.332 132.384 128.18 269 1 A 2.49 8.655 74.9 91.5 18.489 103.407 100.39 270 1 A 2.49 8,720 74.8 91.1 18.489 99.920 96.92 27 1 A 2.49 8,690 75.0 91.1 18.489 103.152 100.12 272 1 A 2.49 8,670 75.1 91.1 18.489 103.286 100.29 273 1 A 2.47 9,190 74.5 56.2 18.542 63.968 61.99 274 1 A 2.47 9,100 74.6 56.3 18.542 63.126 61.13 275 1 A 2.47 8,730 74.7 56.2 18.542 63.246 61.35 276 1 A 2.47 8,870 74.8 56.2 18.542 63.246 61.27

-72 TABLE I (continued) A B C D E F G H I J Axial Fluid F Rotor Active Observed Adjusted Run No. of Blade Flow Viscosity T Speed Rotor Torque No. Blades Type lbs/min Centipoises p rpm Length Inch-orquebs Inch-lbs WB' I F n' Inches T' 277 1 A 2.40 7,710 75.1 31.4 18.690 29.819 28.84 278 1 A 2.40 8,450 74.8 31.4 18.690 32.623 31.53 279 1 A 2.40 8,610 74.7 31.3 18.690 33.o66 31.97 280 1 A 2.40 8,895 74.7 31.3 18.690 32.942 31.81 281 1 A 2.80 3,391 74.7 31.6 18.674 15.873 15.43 282 1 A 2.80 3,408 74.0 31.6 18.674 14.309 13.87 283 1 A 2.80 3,115 73.8 31-7 18.674 12.386 11.99 284 1 A 2.80 3,153 73.8 31.6 18.674 11.303 10.89 285 1 A 2.64 3,385 73.8 57.1 18.541 29.099 28.35 286 1 A 2.64 3,378 73.6 57.1 18.541 30.783 30.03 287 1 A 2.64 3,481 73.7 57.' 18.541 30.788 30.01 288 1 A 2.64 3,465 73.7 57.1 18.541 31.023 30.26 289 1 A 2.61 3,531 73.8 95.0 18.557 43.899 42.60 290 1 A 2.61 3,487 73.8 94.5 18.557 44.981 43.71 291 1 A 2.61 3,483 74.0 94.4 18.557 44.500 43.21 292 1 A 2.61 3,522 73.9 94.6 18.557 45.702 44.41 293 1 A 2.62 3,622 73.9 151.2 18.418 66.744 64.69 294 1 A 2.62 3,531 74.0 152.4 18.418 63.017 61.02 295 I A 2.62 3,559 74.0 150.9 18.418 63.378 61.39 296 1 A 2.62 3,541 74.1 152.9 18.418 64.460 62.44 297 1 A 2.63 14,417 75.1 87.5 18.779 148.016 142.72 298 1 A 2.63 15,100 74.8 87.1 18.779 148.497 143.05 299 1 A 2.63 14,907 75.1 86.9 18.779 149.338 144.04 300 1 A 2.63 14,860 75.1 86.3 18.779 152.585 147.39 301 1 A 2.60 14,087 74.7 55.3 18.850 97.996 94.75 302 1 A 2.60 14,353 74.8 55.2 18.850 94.870 91.54 303 1 A 2.60 14,527 74.8 55.3 18.850 98.357 94.99 304 1 A 2.60 14,427 75.0 55.3 18.850 98.357 95.01 305 1 A 2.57 11,977 75.2 31.1 18.850 54.108 52.54 306 1 A 2.57 13,537 74.8 31.1 18.850 55.550 53.77 307 1 A 2.57 13,683 74.8 31.1 18.850 55.310 53.51 308 1 A 2.57 14,227 74.6 31.1 18.850 55.550 53.67 309 2 B 2.39 11,957 77.3 91.6 19.077 104.369 99.42 310 2 B 2.39 13,120 77.1 91.5 19.077 105.451 100.15 311 2 B 2.39 13,640 77.1 92.6 19.077 105.451 99.65 312 2 B 2.40 13,147 77.9 142.8 19.014 149.218 140.82 313 2 B 2.40 12,890 78.3 144.1 19.014 142.124 133.87 314 2 B 2.40 12,697 80.6 144.6 19.014 139.839 131.64 315 2 B 2.34 14,733 77.5 57.0 19.129 65.290 61.49 316 2 B 2.34 14,823 76.3 57.1 19.129 63.126 59.31 317 2 B 2.34 14,473 76.8 57.0 19.129 62.284 58.56 318 2 B 2.59 14,580 76.5 31.6 19.190 34.750 32.64 319 2 B 2.59 14,593 76.6 31.5 19.190 34.630 32.53 320 2 B 2.59 14,400 76.1 31.5 19.190 35.712 33.66 321 2 B 2.59 15,017 76.3 31.5 19.190 36.073 33.90 322 2 B 1.90 4,545 75.5 151.6 18.866 69.979 67.08 323 2 B 1.90 4,915 76.1 155.1 18.866 69.979 66.78 324 2 B 1.90 4,790 76.6 156.1 18.866 69.258 66.14 325 2 B 2.08 5,165 76.4 96.3 18.947 43.166 41.00 326 2 B 2.08 4,930 75.8 96.4 18.947 42.084 40.02 327 2 B 2.08 4,965 75.6 96.4 18.047 41.483 39.38 328 2 B 2.14 5,000 75.2 57.8 19.006 25,371 24.10 329 2 B 2.14 4,990 75.0 57-9 19.006 24.890 23.61 330 2 B 2.14 5,000 74.9 57.9 19.006 24.409 23.15 331 2 B 2.06 5,050 74.8 31.6 19.033 13.587 12.88 332 2 B 2.06 5,230 74.5 31.6 19.033 13.828 13.10 333 2 B 2.06 5,130 74.3 31.6 19.033 13.707 12.99 334 2 B 3.74 9,570 76.2 31.3 19.207 27.896 26.52 335 2 B 3.74 10,017 76.0 31.5 19.207 28.016 26.55 336 2 B 3.74 9,703 76.2 31.5 19.207 27.535 26.13 337 2 B 3.83 9,635 76.6 56.9 19.139 49.419 46.92 338 2 B 3.83 9,643 76.5 56.9 19 39 48.457 45.96 339 2 B 3.83 9,735 76.8 57.0 1. 9 48.697 46.15 340 2 B 3.92 9,298 77.4 94.2 19 069 75.391 71.49 341 2 B 3.92 9,470 78.0 94.4 1~.069 75.872 71.87 342 2 B 3.92 8,143 78.2 94.5 19.069 74.308 70.46 343 2 B 4.05 8,763 79.3 151.2 18.968 109.178 103.33 344 2 B 4.05 8,728 80.1 152.5 18.968 105.691 99.74 345 2 B 4.05 8,570 80.5 152.7 18.968 105.451 99.70 346 2 B 2.54 18,587 77.5 31.0 19.236 50.501 47.48 347 2 B 2.54 19,033 78.0 31.2 19.236 49.779 47.04 348 2 B 2.54 18,517 77.8 31.2 19.236 49.418 46.76

-73 TABLE I (continued) A B C D E F i H I J Axial Fluid Rotor Active Obs d Adjusted Run No. of Blade Flow Viscosity Speed Rotor ser Torque No. Blades Type lbs/min Centipoises rpm Length rque Inch-lbs C t' OF n' Inch-lbs W H ~ ~n' Inches T' 349 2 B 2.58 19,040 78.0 55.6 19.163 91.262 86.46 350 2 B 2.58 19,777 78.0 55.6 19.163 91.142 86.09 351 2 B 2.58 18,660 79.1 55.7 19.163 88.737 84.04 352 2 B 2.64 18,267 79.2 88.7 19.100 141.643 134.24 353 2 B 2.64 19,140 79.0 88.4 19.100 141.763 134.11 354 2 B 2.64 18,723 78.5 88.0 19.100 143.326 135.88 355 4 A 2.35 17,987 77.8 30.6 19.237 133.827 131.26 356 4 A 2.35 19,720 77.7 30.5 19.237 134.308 131.52 357 4 A 2.35 19,723 77.4 30.6 19.237 131.903 129.11 358 4 A 2.39 19,260 78.9 54.5 19.169 217.394 212.64 359 4 A 2.39 20,250 78.5 54.4 19.160 217.875 212.83 360 4 A 2.39 19,890 78.5 54.4 19.169 216.312 211.36 361 4 A 2.46 18,960 78.9 84.0 19.100 286.172 278.92 362 4 A 2.46 19,173 78.9 84.7 19.100 287.614 280.3]. 363 4 A 2.46 19,100 79.4 85.6 19.100 285.811 278.41 364 4 A 4.55 5,220 75.6 31.1 19.108 45.802 45.08 365 4 A 4.55 4,925 75.1 31.1 19.108 41.363 40.67 366 4 A 4.55 4,860 75.6 81.2 19.108 4o.641 39.96 367 4 A 4.44 5,000 75.7 56.9 19.064 70.340 69.04 368 4 A 4.44 4,940 75.9 56.9 19.064 69.859 68.62 369 4 A 4.44 4,890 75.8 56.9 19.064 70.821 69.58 370 4 A 4.40 4,870 76.2 91.3 19.032 111.102 109.12 371 4 A 4.40 4,840 76.5 94.1 19.032 109.900 107.85 372 4 A 4.40 4,900 76.2 93.9 10.032 111.342 109.28 373 4 A 3.62 8,360 72.4 31.1 19.200 73.467 72.27 374 4 A 3.62 8,680 72.4 31.1 19.200 73.467 72.23 375 4 A 3.62 8,915 72.2 31.0 19.200 75.270 73.99 376 4 A 3.76 9,170 73.0 55.9 19.143 125.531 123.20 377 4 A 3.76 9,070 72.8 56.0 19.143 123.247 120.97 378 4 A 3.76 9,070 72.5 56.0 19.143 122.645 120.36 379 4 A 3.81 8,790 73.5 90.4 19.100 188.295 184.70 380 4 A 3.81 8,810 73.3 90.6 19.100 186.612 183.01 381 4 A 3.81 8,795 73.4 90.6 19.100 187.454 183.85 382 4 A 2.96 16,073 72.7 30.6 19.216 114.108 111.85 383 4 A 2.96 16,633 73.1 30.6 19.216 111.823 109.49 384 4 A 2.96 16,700 72.9 30.7 19.216 112.304 109.93 385 4 A 3.15 15,443 74.3 54.9 19.175 188.416 184.54 386 4 A 3.15 16,030 74.2 55.0 19.175 183.847 179.85 387 4 A 3.15 15,787 74.1 55.0 19.175 183.606 179.66 388 4 A 3.33 14,220 76.1 86.1 19.125 268.856 263.31 389 4 A 3.33 15,333 75.8 86.3 19.125 266.452 260.45 390 4 A 3.33 14,633 76.0 86.5 19.125 266.692 260.99 TABLE II MECHANICAL EFFECTS DATA - 2 AND 4 TYPE A BLADES A B C D E F G H I J No. of Axial Flow Fluid Rotor FLid Line Data Sheet Type A Solution Rate - W Viscosity Speed Fui W Cp At No. No. Bades % Ucon Centipoises rpm Temp. Rise - n'3 Blades lbs/hr., t- F n L 1T 4 83.0 137 12,910 30.8 1.6 419 0.00443 2 6T 4 83.0 197 13,372 30.9 1.0 432 0.00394 3 7T 4 83.0 208 14,374 55.6 2.7 258 0.00193 4 8T 4 83.0 210 12,792 89.6 6.1 143 0.00105 5 15T 4 83.0 192 13,580 30.7 1.1 442 0.00430 6 18T 4 77.5 222 11,500 31.0 0.7 371 0.00323 7 19T 4 77.5 232 10,900 56.1 2.0 194 0.00163 8 20T 4 77.5 237 10,100 91.8 4.2 110 0.00080 9 29T 2 77.5 237 9,400 31.2 0.6 301 0.00290 10 30T 2 77.5 246 9,049 56.9 1.3 159 0.00108 11 31T 2 77.5 253 8,652 94.2 2.0 92 9.00054 12 40T 2 83.0 212 12,319 31.0 0.9 398 0.00378 13 41T 2 83.0 225 12,414 51.3 2.1 242 0.00206;4 42T 2 83.0 237 11,755 91.9 4.5 128 0.00081

-74 TABLE III MECIANICAL EFFECTS DATA - SMOOTH ROTOR A B C D E F G H I J Fluid Rotor Axial Flow F luid Line Data Sheet No. of Solution l ow Viscosity Speed R r is' W Cp At No. No. Blades % Ucon Rate - Centipo.s rise pm n n3 Ibs/hr.' n' t -OF 1 56T 0 83% 193 16,100 31.4 0.3 513 0.00110 2 57T 0 83% 199 15,534 57.5 0.8 270 0.00049 3 58% 0 83% 204 14,829 96.4 1.9 154 0.00026 4 59T 0 83% 212 13,759 158.6 4.2 87 0.0013 TABLE IV HEAT TRANSFER DATA - 2 AND 4 TYPE A BLADES A B C D E F G H I J K L Observed Rotor hd Ror vAxial Temp. Net Temp LMTD Heat hd 4 Blades on Rotor - Heating Fluid Line Sheet Viscosity Speed Solution Ra Rs Ml Tras- Sheet Rate ~U,,, Mech F to er No. Centipoises rpm c r At Fluid Coeff No. nt lbs /h At net Btu/hr;ft2;oF 4 Blades on Rotor - Heating Fluid 1 2T 13,659 30.9 148 2 3 4 5 9T 12,215 56.3 234 6 7 8 11T 10,367 89.4 207 9 10 11 16T 13,107 31.0 207 12 13 14 21T 8,455 31.1 253 15 16 17 25T 9,035 56.3 219 18 19 20 27T 8,078 92.9 225 21 22 83 % 1.5 1.8 4.6 2.1 5.3 2.0 4.5 2.2 5.4 83 % 2.3 2.5 4.5 2.3 5.8 2.1 4.9 83 % 4.6 6.6 12.0 6.8 12.3 6.9 11.6 83 % 1.0 4.8 14.6 5.0 14.4 5.0 14.1 77.5% 0.4 3.5 13.5 3.7 12.9 3.8 13.1 77.5% 3.1 6.3 12.0 6.3 12.3 5.8 12.7 77.5% 3.1 7.3 9.7 6.9 9.2 6.7 9.7 39.8 40.3 45.2 41.4 89.4 63.8 69.0 78.2 78.6 84.7 46.8 49.4 50.4 47.4 52.4 53.0 83.0 81.0 72.2 130.8 121.9 121.0 3,520 13.6 6,410 24.2 10,180 26.3 3,530 15.8 3,440 15.3 6,230 23.7 10,250 37.6 4 Blades on Rotor - Cooling Fluid 23 4T 18,817 30.6 149 83.0% 2.2 -12.2 21.3 24 -12.9 20.6 25 -13.1 20.6 26 14T 16,839 86.7 211 83.0% 8.0 -13.1 16.9 27 -13.7 16.3 28 -13.7 17.0 29 23T 12,215 30.9 229 77.5% 0.8 -7.8 21.4 30 -7.8 21.7 31 -7.6 22.2 32 26T 12,907 55.8 237 77.5% 2.2 -10.2 21.5 33 -10.7 20.8 -10.9 20.7 35 28T 12,352 90.6 248 77.5% 4.6 -11.8 19.4 36 -1.1.9 19.7 37 -12.1 19.6 58.6 64.1 65.7 112.3 122.0 117.0 60.3 59.4 56.6 81.2 88.1 90.2 109.0 108.2 110.7 3,480 20.5 9,860 38.2 3,420 17.6 6,170 26.1 10,020 33.0

-75 TABLE IV (continued) A B C D E F G H I J K L Axial Temp. LMTD Heat LineObserved Rotor Flow Rise Net Temp. Wall Trans- d2 hd Line Viscosity Speed Solution Rise Cp p2 No. Sheet Centipoises rpm % Ucon teh Fluid Coeff. No., n.' W A c. Atnet OF h (avg. h) 2 BlaAeotor -mecht. Btu/hr;ft2;OF 2 Blades on Rotor - Heating Fluid 38 32T 39 41 36T 42 43 44 43T 45 46 47 47T 48 49 50 53T 51 52 53 55T 54 55 56 34T 57 58 59 37T 60 61 62 39T 63 64 65 45T 66 67 68 48T 69 70 71 50T 72 73 8,527 9,254 11,288 11,659 12,492 11,775 10,822 11,097 10,584 14,157 14,123 13,454 31.3 263 77.5% 0.4 2.1 10.9 2.3 10.2 2.5 11.1 57.0 235 31.2 256 56.7 228 56.7 224 93.0 229 31.1 256 56.6 242 92.8 249 31.1 255 55.9 246 89.8 253 77.5 % 83.0% 83.0% 83.0% 83.0% 2 Blades on 77.5% 77.5% 77.5% 83.0% 83.0% 83.0% 1.5 2.4 2.6 2.5 0.7 2.7 2.7 2.5 2.2 3.1 2.6 2.4 2.5 5.5 5.4 5.3 5.2 3.9 4.3 4.0 Rotor - Cooling Fluid 0.6 -5.7 -6.1 -6.0 1.9 -5.5 -5.9 -5.9 3.9 -6.0 -6.5 -6.4 0.9 -5.4 -6.2 -6.4 2.6 -6.6 -6.9 -7.1 5.2 -8.1 -8.3 -8.3 14.0 13.2 14.l 11.8 11.4 11.8 14.5 15.6 15.9 13.2 14.0 13.9 12.9 12.7 12.6 30.4 29.5 29.5 23.6 23.3 23.2 21.7 21.5 21.4 30.4 29.7 30.1 28.7 28.3 28.2 30.9 31.1 31.0 36.6 42.9 42.8 29.1 33.4 30.1 40.3 41.7 37.3 33.5 26.1 23.7 64.2 59.4 58.7 47.6 53.3 50.0 34.7 38.2 37.6 40.7 44.3 44.5 49.7 54.4 53.8 31.1 36.6 37.3 38.9 41.2 42.6 45.6 46.4 46.6 1,740 12.3 3,140 9.3 1,770 13.0 3,230 9.1 3,230 19.9 5,290 16.4 1,720 11.1 3,130 13.0 5,120 16.0 1,770 11.4 3,180 13.4 5,110 15.1

TABLE V HEAT TRANSFER DATA - SMOOTH ROTOR A B C D E F G H I J K L Observed Rotor Axial Temp. Net Temp LMTHeat Data Flow Rise Wall Trans - Sheet Rate % Ucon Mech. OF to fer p k No. Centipoises rpm Uon k No. lbs/hr F Fluid Coeff. k n W tmeh net OF Btu/hr;ft2;OF (Avg. h) tmech. h Heating Fluid 1 62T 13,210 57.8 218 83.0% 0.6 0.7 19.1 57.1',650 13.5 2 0.7 20.2 54.0 3 70T 0.7 19.6 55.7 4 0.3 19.4 22.4 5 0.3 20.2 21.5 6 0.5 19.0 38.2 7 64T 12,989 97.1 223 83.0% 1.5 0.5 19.8 38.7 2,770 13.4 8 0.5 19.9 38.5 9 0.6 20.0 46.0 10 66T 12,150 160.4 224 83.0% 3.4 0.4 17.1 36.0 4,560 11.7 11 0.3 17.7 27.0 12 0.5 17.3 45.0 13 68T 12,139 31.3 208 83.0% 0.2 0.7 19.9 50.3 892 14.7 14 0.5 20.0 35.9 15 0.7 20.5 48.8 Cooling Fluid 16 63T 14,419 57.9 228 83.0% 0.6 -0.5 26.0 30.2 L,640 12.5 17 -0.6 25.9 36.3 18 -0.8 25.8 48.7 19 65T 13,749 97.1 223 83.0% 1.5 -0.6 27.0 34.7 2,770 12.6 20 -0.7 26.9 40.6 21 -0.7 26.9 40.6 22 67T 12,948 159.9 246 83.0%o 3.4 -0.5 29.1 29.1 4,550 14.4 23 -0.9 29.4 51.7 24 -0.9 29.6 51.4 25 69T 14,530 31.3 214 83.0% 0.2 -0.1 24.6 6.0 892 9.7 26 -0.5 24.8 29.7 27 -0.5 24.7 29.8

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-7816. Westervelt, F. Ho A Study of Automatic System Simulation Programming and the Analysis of the Behavior of Physical Systems Using an Internally Stored Program Computero PhDo Thesis at The University of Michigan, Ann Arbor, Michigan, October 1960o