THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING PRESSURE GRADIENTS ASSOCIATED WITH NON-ADIABATIC TWO-PHASE FLOW V. Lemi Ulugol January, 1961 IP-490

ACKNOWLEDGMENT The author wishes to express his gratitude to Dr. John A. Clark, Professor-in-charge of the Heat Transfer and Thermodynamics Laboratory, for his continual encouragement and guidance throughout the course of the present investigation. The author also expresses his appreciation to Professor Gordon J. Van Wylen, Chairman of the Mechanical Engineering Department, for his interest and the cooperation received from the Department in the allocation of the equipment, instruments and space. The financial assistance of the University of Michigan Research Institute is also gratefully acknowledged, The cooperation of Mr. Waldemar Salva, Laboratory technician and of the other laboratory personnel is highly appreciated. The assistance of Mrs. Norlene Martin and the cooperatipn of the Industry Program of the College of Engineering in the preparation of the manuscript also is highly appreciated. The appointment held during the period of this research and supported by the International Cooperation Administration under the Visiting Research Scientists Program administered by the National Academy of Sciences of the United States of America, is gratefully acknowledged. ii

TABLE OF CONTENTS Page ACKNOWIEDGMENTS................................ * * o * *. * * ii LIST OF FIGURES..................................... iv NCMENCLATUBRE................................ vi SUMMARY.................................................. iii I INTRODUCTION........................... 1 A. Statement of the Problem.......................... 1 B. Present Work............................. 3 II EXPERIMENTAL APPARATUS AND INSTRUMENTATION.......... 5 A. General Description of the Equipment............. 5 B Instrumentation................................. 7 1. Measurement of the Flow Rate........... 7 2. Flow Rate Recording....................... 8 3. Measurement of the Electrical Power Input to the Test Section............................ 9 4. Measurement of the Temperatures............... 10 5. Static Pressure Measurements.................. 11 C. Experimental Procedure......................... 12 D. Data Reduction Method........................... 12 III EXPERIMENTAL RESULTS............................ 15 A. Flow Steadiness......................... 15 B. Adiabatic Pressure Drop................. 15 C. Non-Adiabatic Pressure Drop..................... 16 D. Comparison of the Non-Adiabatic Pressure Drop Results with that of Previous Workers............ 20 E. Wall Temperatures............................ 2 F. Photographic Study of the Outlet Mixture........ 25 BIBLIOGRAPHY............................................. 58 iii

LIST OF FIGURES Figure Page 1 Schematic Diagram of the Equipment..................... 27 2 Over-all View of the Equipment.......................... 28 3 Close-up of the Instruments............................ 29 4 Detail of the Test Section............................. 30 5 Calibration Curve for the 0.218 in. Diameter Orifice... 31 6 Calibration Curve for the 0.312 in. Diameter Orifice... 32 7 Calibration Curve for the Turbine Type Flowmeter....... 33 8 Flowmeter Output Voltage (Peak-to-Peak) versus Flow Rate............ *............................ 34 9 Electrical Circuit for the Measurement and Recording of the Flow Rate by Means of the Flowmeters............ 35 10 Voltage-Divider Network for the Test Section Voltage Drop Measurement 3........................... 36 11 The Pressure Tap and Manometer Connections............... 37 12 Friction Factor versus Reynolds Number for Adiabatic Runs,.......* *.**.....*.. *......................... 58 13 Pressure Prifiles and Steam Quality Curves for a Series of Non-Adiabatic Runs........................... 39 14 Plot of R versus X for G = 1.38 x 105 lb/hr ft2........ 40 15 Plot of R versus X for G = 2.76 x 105 lb/hr ft2...... 41 16 Plot of R versus X for G = 4.14 x 105 lb/hr ft2 42 17 Comparison of the Experimental Results with the Steam-Water System Flow Pattern Chart for 14.7 psia (chart taken from reference 16)....................... 43 18 Comparison of the R-X curves in the Liquid-Dispersed Region............................................... F 44 19 Plot of R[10-5G]0.25 versus X in the Liquid-Dispersed Region................................................. 45 iv

LIST OF FIGURES CONT'D Figure Page 20 Plot of R[0O-5G]'0'1 versus X in the Liquid-Dispersed Region.... *..,........................ 46 21 Comparison of the Measured Pressure Drop with the Predictions of the Martinelli-Nelson Correlation...... 47 22 Comparison of the Measured and Predicted Pressure Drops Along the Test Section..................... 48 23 Coefficient m versus Steam Quality.................. 49 -.4 1.47 24 Coefficients m and n versus 10 - x. G.... 50 25 Inner Wall Temperatures for G = 1.38 x 105 lb/hr ft2, ti = 205~F, q/A = 0 - 2 x 105 BTU/hr ft2..... 51 =i-n- ft............... 51 26 Inner Wall Temperatures for G = 2.76 x 105 lb/hr ft2, tin 205~F,q/A = 10 - 2 x 105 BTU/hr ft.......... 52 27 Inner Wall Temperatures for G = 4.14 x 105 lb/hr ft.2 ti 205~F,q/A = 10 - 2 x 105 BTU/hr ft2........... 53 28 - 34 Photographs of Unsteady Stratified Slug Flow Patterns at the Test Section Outlet............................. 54 - 55 28 - 32. G = 1.38 x 105 lb/hr ft, xe = 5.5% 33 - 34 G = 2.76 x 105 lb/hr ft2, x = 2.5% 35 - 37 Photographs of Annular Flow Patterns at the Test Section Outlet...................................... 56 2 35. G = 1.8 x 105 lb/hr ft, x = 14% 36. G = 2.76 x 105 lb/hr ft2, xe = 5.3% 37. G = 4.14 x 105 lb/hr ft2^ x = 4 38 - 39 Photographs of Fog (or Liquid-dispersed Flow Patterns at the Test Section Outlet....................... o 57 38. G = 1.38 x 105 lb/hr ft2, xe = 29 G = 138 x 105 lb/hr ft2 xe = 47% V

NOMENCLATURE A D E f G m. n NRe P VdlJXp AP, Ah q q/A _(dP/dl)TP R r T AT U V W Heat transfer area, sq. ft. Diameter, in. Voltage, volts Friction factor Mass velocity, lb/hr ft2 Enthalpy, Btu/lb Current, Amps Thermal conductivity Btu/hr ft degF. Length of the test section, in. Distance from test section inlet, in. Coefficients in equation (14) Reynolds number Pressure (lb/sq in or in.-wat ) Pressure drop Pressure gradient for two-phase flow Pressure gradient for liquid flow Heat Input, Btu/hr Heat flux, Btu/hr sq ft Pressure gradient ratio Radius, in, Temperature, deg F Temperature difference, deg F Velocity, ft/sec Specific volume, ft3/lb Flow rate (lb/hr or gpm) vi

x Steam quality [p Dynamic viscosity (cp) X Dimensionless parameter defined by Equation (7) Subscripts ACT Actual flow FOG Fog flow SEP Separated flow g Steam 1 Saturated liquid in Inlet o Inside w Outside ts Test section TP Two-phase vii

SUMMARY Pressure drop and wall temperature data have been obtained during forced-circulation boiling of water in an electrically heated horizontal tube at substantially atmospheric pressure. The test section was a 0.750 in O.D. by 0.620 in. I.D. stainless steel tube. The heat generation was accomplished by passing the electric current through the test section. Local pressure gradients were determined for a range of mass flow rates and steam qualities using heat flux values up to 225,000 Btu/hr ft2. Two different heat transfer and flow regions, designated as "nucleate boiling region" and "liquid-dispersed region" were distinguished. The value of the steam quality corresponding to the suggested transition point between these regions was found to be almost inversely proportional to the mass velocity. An empirical equation for the pressure gradients in the liquid dispersed region is given as a function of the steam quality. Some local wall temperature measurements are presented. The high-speed still pictures of the steam-water mixture at the outlet of the test section also are presented. viii

I. INTRODUCTION Ao Statement of the Problem During the last two or three decades considerable research has been devoted to the problem of the co-current flow of gas-liquid or vapor-liquid systems in tubes. Such flow systems are encountered in many branches of industry, such as petroleum production and refining, steam generation, refrigeration etc. Recent growing interest in single-component two-phase nonadiabatic systems results from their association with the heat removal from the nuclear reactors and rocket motors. Since the relative mass flow rates in steady flow of both phases are a function of the position along the tube, this type of flow is the most difficult to investigate experimentally and to analyze. The main problems involved include the flow stability, the pressure drop characteristics, the vapor-liquid distribution and holdup, the heat transfer rates and burnout or the maximum heat flux. Owing to the relative complexity of the problem, very little progress has been made toward understanding the processes involved in progressive vaporization of a fluid along a tube. One of the main difficulties is that several flow patterns of widely different geometry may exist depending upon the position of the confining conduit and the interplay of the relevant forces, such as gravitational, intraphase and interphase forces. The descriptions of the two-phase flow patterns are available in the literature (1,2,3,4)*. The behavior of the system is closely associated with the type of flow pattern which occurs. Consequently, for an analysis of boiling inside tubes, it is of primary importance to study the variation of the point or local conditions along -1

the tube, including the pressure, the axial pressure gradient, the wall temperature, the fluid temperature and the liquid and vapor holdup. The information gathered through experimental investigations directed at a study of the above conditions will be helpful in framing appropriate physical models and thus will make possible a sound analytical approach to the several aspects of the problem. Not until quite recently have studies of the local conditions during boiling inside tubes been published, Dengler (5) in 1952 and Dengler and Addoms (6) in 1956 presented data for local pressure gradients and local film heat transfer coefficients for vaporization of water in a vertical tube at low pressures and over the entire steam quality range of 0 to 100 percent. Querrieri and Talty (7) published a study of heat transfer to a number of organic liquids boiling in two single tube natural circulation vertical evaporators. Jakob, Leppert and Reynolds (8) presented pressure drop data during forced circulation boiling of water in an electrically heated horizontal tube at operating pressures between 30 and 200 psia. Empirical- correlations were given for the over-all static pressure drop and the local pressure gradient as a function of the weight fraction evaporated and the absolute system pressure. Mumm (9) investigated the heat transfer characteristics of the system described in reference (8). * Numbers in parentheses refer to the bibliography at the end.

McNelly and Coulson (10) in a study of the performance of the climbing film evaporators, confirmed the successive change of the flow conditions along the tube and distinguished between three different mechanisms of heat transfer as taking place in the evaporator. Bennett, Collier, Pratt and Thornton (11) have published the local heat transfer and pressure drop data for a vertical steamwater flow in an annulus at approximately atmospheric pressure. B. Present Work In view of the foregoing, an experimental investigation of the local conditions of pressure and temperature was undertaken using a steam-water system at substantially atmospheric pressure. Water which was preheated to approximately the saturation condition was introduced into an electrically heated test section. This consisted of a horizontal stainless steel tube (0.750 in O.D., 0,620 in. I.D., 50 inches long) and the heat generation was accomplished by passing the electric current through the test section itself, This tube simulates systems having internal heat generation in the walls such as heterogeneous nuclear reactor coolant channels, The over-all pressure drop, the local pressure gradients, and the local wall temperatures at the lower and upper portions of the tube were determined for a range of mass flow rates and steam qualities, using heat flux up to 225,000 BTU/hr-ft 2 Mass velocity was varied from 1.38 x 105 lb/hr ft2 to 4.14 x 105 lb/hr ft2 and the maximum weight fraction evaporated was about 50%. A photographic study of the steam-water mixture at the outlet of the test section also was included. Photographs were taken with a 4 in. x 5 in. camera

used with a strobe-light unito Also motion pictures of the outcoming mixture were taken with a 16mm camera at a speed of 300 frames/second.

II. EXPERIMENTAL APPARATUS AND INSTRUMENTATION For the purpose of the present study, the equipment which is described below was designed, built, and used in the Heat Transfer and Thermodynamics Laboratory of the Mechanical Engineering Department. A. General Description of the Equipment A schematic diagram and an over-all view of the equipment are shown in Figures 1 and 2. Figure 3 shows a close-up of the instruments. A once-through system was used because of its relative simplicity with the Ann Arbor City water as the water supply. During the preliminary runs water was taken direct from the Laboratory lines but the pressure fluctuations proved to be unsatisfactory. The subsequent use of a centrifugal pump has permitted the maintenance of steady inlet conditions for the system. The water which was pumped from a water tank passed through an ion exchanger and two filters which were incorporated to prevent the contamination of the test section surface. A pressure regulating valve was used in conjunction with a needle valve for flow adjustments. The flow rate was measured by both a calibrated orifice and by a turbine type flowmeter. Preheating was accomplished by a series of immersion type electric heaters placed in 2~ in. brass pipes, having a total rating of 40 KW. By means of several on-off switches and a 3KVA Variac the pre-heating capacity could be adjusted continuously in the range of 0-40KW. Air bleeding cocks were provided at the highest points of the pre-heater connections. A second flowmeter was placed immediately upstream of the test section for monitoring the fluctuations in the flow. The test section was insulated electrically from the rest of the equipment. -5

The tube used as the test section was a 0.750 in O.D. by 0.620 in. I.D., type 304, seamless stainless steel tube. The total length of the tube was 7 feet, with an unheated hydrodynamic starting length having an L/D of 45, and a heated length of 50 inches. The internal heat generation was accomplished by passing the electric current through the test section itself. For this purpose current leads were attached to the copper lugs silver soldered at each end of the test section. Power was supplied from a 50 KW, 25V D.C., 2000 A germanium rectifier unit. This power was subject to remote manual and automatic control and regulation. The bulk temperature of water entering the test section was measured by means of a pre-calibrated 30-gage copper-constantan thernocouple which was immersed in the water stream. The details of the test section are shown in Figure 4. Ten pressure taps spaced 5 inches apart were located along the test section and two other pressure taps were provided before and after the test section. Each pressure tap consisted of one inch length of 1/8 in OD. by 1/16 in. I.D. stainless steel tubing, silver-soldered to the test section. A 1/32 inch radial hole was drilled through the wall of the test section at each pressure tap location. The pressure taps were connected, by means of Tygon tubing, to a 13-tube common-reservoir type manometer, which premitted the measurement of the pressure drop as well as the pressure at the inlet of the test section. One horizontal and one vertical thermocouple probe were placed in four cross-sections at 10, 25, 40 and 49 inches from the inlet of the test section, for the measurement of the fluid temperatures.

-7 The position of each thermocouple in the tube was controlled by a micrometer adjustment system. For the measurement of the outside tube wall temperatures, twenty thermocouples were placed at the top and bottom of the tube at several stations. From the measured outside wall temperatures, inside wall temperatures were calculated considering the radial temperature difference across the wall of the resistance heated tube. A drain tank was used to receive the discharge from the test section and a spray of water was provided for reducing the amount of steam escaping to the atmosphere. Since the test section outlet was open to the atmosphere, the discharging steam-water mixture could be visually observed. All pipework and valve material was either stainless steel or brass. The part of the equipment extending from the preheater inlet to the test section outlet was thoroughly insulated with 2^ in. thick fiberglass blanket insulation. B. Instrumentation 1. Measurement of the Flow Rate An orifice and a turbine type flowmeter were used for the measurement of the flow rate. a. Orifice Two orifice plates of 0.218 ino and 0.312 in diameters were used for the range of flow rate studied. Each orifice had been previously calibrated by means of a weigh tank, and the calibration was checked at regular intervals. No deviation from the original calibration was detected. The calibration curves for both orifices are shown

-8 in Figures 5 and 6. As seen from these curves, the orifice diameters used made it possible to have a differential pressure range which could be read with good accuracy. A 100-inch inverted-U-type manometer was used for measuring the differential pressure across the orifice. An adjustable air pressure was applied at the top of the water columns. The pressure on the upstream side of the orifice was also applied to a reservoir-type mercury manometer open to the atmosphere. The indication of this manometer reflected the constancy of the flow through the equipment b. Flowmeter A Waugh turbine type flowmeter (Model No. FL-8S) was used. This flowmeter measures the fluid flow by determining the fluid velocity in a passage containing a freely spinning turbine wheel. The passage of the fluid results in the rotation of the turbine wheel at a speed proportional to the flowrateo As the turbine rotates, electrical pulses are generated in the externally mounted coil assembly. The frequency of the generated pulses is directly proportional to the flow:rate. The calibration curve for this flowmeter is shown in Figure 7. After proper pre-amplification the output of the flowmeter was fed to a Model 522B Hewlett-Packard Electronic counter. In all cases the flow rate values measured with the orifice and the flowmeter were essentially the same. And it is believed that the mass flow rates are correct within + I%. 2. Flow rate Recording In addition to the readings of the electronic counter, a record of the flow rate as a function of time was considered desirable from the standpoint of a better analysis of the system performance.

Besides measuring the frequency of the pulses generated by the flowmeter as an indication of the flow rate, the voltage of these pulses was used to obtain such a record. Figure 8 shows a plot of the peak-to-peak voltage of the pulses, as measured with an oscilloscope and a voltage calibrator, versus the flow rate. It is seen that' this voltage is also proportional to the flow rate within close approximation. Consequently a simple rectifying circuit was incorporated in order to obtain a DC, voltage which would be proportional to the flow rate, And this D.Co voltage was fed to one channel of a direct recording multiple channel Visicorder oscillographo This flowmeter was placed at the inlet side of the equipment. A second flowmeter of the same type was placed just before the test section. This location was considered to be more suitable for evaluating fluctuations in the flow, since it offered a much smaller damping for any possible flow oscillation occurring in the test section, A diagram of the electrical circuit used for the measurement and recording of the flow rate with these flowmeter is given in Figure 9. 30 Measurement of the Electrical Power Input to the Test Section, The power dissipated in the test section was determined by measuring the voltage drop across the test section and the current passing through ito For the test section voltage drop measurement voltage taps were taken directly from the ends of the test section and a voltagedivider network was used as illustrated in Figure 10o The voltagedivider network consisted of a 50 K2 and a 25 2 precision wire wound resistor in series. The voltage drop across the 252 re sistOr was

measured with a Leeds & Northrup Model 8662 portable precision potentiometer. The voltage drop across the test section is then Et E1 (Rl R2) The electric current was determined from the measured voltage drop across a 25 x 10 fQ calibrated shunt which was in series with the test section. The same portable precision potentiometer was used for this measurement. 4, Measurement of the temperatures a. Fluid Temperatures For the measurement of the test section inlet temperature and of the fluid temperatures in the test section, pre-calibrated 30gage copper-constantan thermocouples were used. Previous use of the iron-constantan thermocouples had not been satisfactory owing to the rapid corrosion of the bare thermocouple tips, The emf of these thermocouples were read with a LeedsNorthrup portable precision potentiometer. In addition, provisions had been made for feeding them to a multiple-channel direct recording Minneapolis-Honeywell Model 1012 "Visicorder" oscillograph which would make it possible to have simultaneous time recordings, of the fluid temperatures. b. Wall Temperatures The outside wall temperatures were measured by precalibrated 30-gage iron-constantan thermocouples which were attached to the outside tube surface. These thermocouples were insulated from the tube wall by a thin sheet of mica of 0.0015 in, thick and held to the tube

surface by high temperature glass electrical tape and asbestos cord, In order to keep the thermal errors from axial conduction to a minimum each thermocouple was wrapped around the tube one quarter turn before it was led out through the insulation, In addition to reading the emf of these thermocouples with a portable precision potentiometer, a 20-point (adjustable zero, adjustable range) Leeds-Northrup Speedomax temperature recorder was used to obtain chart recordings, 5. Static Pressure Measurements For measurement of the static pressure along the test section, a 13-tube 60-inch common-reservoir type manometer was used. The pressure taps were connected to the manometer tubes, by Tygon tubing, as shown in Figure 11. The pressure at the first pressure tap was applied to the manometer reservoir and to the tube no. 12 (starting from the left side) and was used as a reference pressure for all pressure readings. Thus, the height of the indicating liquid in any one tube above the indicating liquid level in the tube no, 12 corresponded to the pressure drop between the first and the considered pressure tapso The last manometer tube was left open to the atmosphere so that it would indicate the gage pressure at the first pressure tap. Mercury and an indicating liquid having a specific gravity of 1.75 were used in the manometer, for different pressure drop rangesa The manometer used was a photo-manometer with translucent scales and built-in backlighting which could permit photographing the manometer columns. However, in view of the steadiness of the flow and of the pressure values observed during the experiments, a recourse to photography was unnecessary,

-12 C. Experimental Procedure At the beginning of each run, a constant flow rate was set by means of the flow control valve, the preheater power was turned on and the pre-heating capacity was adjusted to obtain the desired test section inlet temperature. Then the power was applied to the test section, and a re-adjustment was made on the flow rate to maintain it at the originally set value. Steady state conditions were established, for each run and held for a period of one hour before recording the data. During this one hour period four sets of flow rate, pressure and temperature readings were taken for checking the uniformity and steadiness of the flow. Re-runs were made periodically to check the reproducibility of the experimental results. D. Data Reduction Method 1. In the reduction of the recorded experimental results, the following assumptions were made: -Thermodynamic equilibrium between the phases exists at each point along the tube. -The generation ofelectrical heat in the tube wall is uniform, and the thermal conductivity and electrical resistivity properties of the tube material are constant radially and axially along the length of the tubeo (Maximum tube wall A was 60 F) -Vapor formation starts at the point where the fluid enthalpy becomes equal to the local saturated liquid enthalpyo -Steam quality (mass fraction evaporated) is calculated by a heat balance,

-13 2o Using these assumptions, the following is a description of the data reduction procedure: -From the pressure drop measurements the pressure profile along the test section is determinedo -Fluid enthalpy (hin) at the test section inlet is known from the measured inlet temperature (Tin)o -From the measured test section voltage drop (E ) and the ts current (I), the electrical power input to the test section is known. The heat loss from the test section is estimated as 1% of the total heat input, The heat transfer area (A) is defined by the inside surface of the test sectionr Therefore the heat flux (q/A) may be computed as follows: 0.99x3 413 Ets I q/A =0 99X 3 t Bt u/hr. ft2 (2) where A = J D L A = 0o.62 50 = 0.676 sq. ft; 12 12 consequently q/A = 5 Ets I Btu/hr ft2 (3 -From the known heat input (q) to the test section, the increase of the fluid enthalpy per unit length along the test section is knowno Therefore at any point along the test section, the enthalpy of the two-phase mixture cal be calculated as, htp = bin + - I Btu/lb (4) -Point steam qualities are calculated as X % htph x 100 (5) hlg

where hi and hlg are the saturated liquid and the evaporation enthalpies corresponding to the pressure to the pressure at the point in consideration. -From the measured outside wall temperatures (Tw), inside wall temperatures (To) are calculated considering the radial temperature difference across the wall of the resistance heated tube. The differential equation governing the temperature distribution in an electrically heated circular tube with temperature-dependent properties of thermal conductivity and electrical resistivity was originally solved by Kreith and Summerfield (12). An interesting solution from the standpoint of a hand calculation was presented by Clark (13) for the case of temperature-dependent properties and with outward heat flow. For the present case of inward heat flow using the same procedure and assuming constant properties for the wall material a similar and simplified form was derived. This equation is, =" o - A I - 2 Ln w " 2 2 ( Tw -To r [ r2 Ln(6) rw -r0

III. EXPERIMENTAL RESULTS The experimental work reported herein was limited to the following range of variables: 1. System: 0.750 in. OoD., 0,620 in. IoD. horizontal tube 2. Mass velocity, G = 1.38 x 105 - 4.14 x 105 lb/hr ft corresponding to inlet velocity, Uin = 0.64 - lo92 ft/sec 3. Test section inlet temperature, Tin = 205F corresponding to inlet Reynolds number, NRe = 10 - 3 x 10 4. Heat flux, q/A = up to 2.25 x 105 BTU/hr ft2 5. Bulk steam quality (mass fraction), x: up to 50.5% 6. Pressure, P = substantially atmospheric pressure A, Flow Steadiness Except the runs with low exit qualities the flow through the test section was found to be essentially steady, as indicated by the turbine type flowmeter. The lower limit of the steady flow range corresponded to an exit quality of about 7% for the minimum mass velocity used which was 1.38 x 105 lb/hr-ft2, and to smaller qualities with increasing flow rateso The unsteady flow condition consisted mainly in a pulsating stratified flow with alternate slugs of liquid and vapor. Pictures were taken for both the steady and unsteady flow conditions and are presented in the section dealing with the photographic study of the outlet mixture, B, Adiabatic Pressure Drop For the purpose of comparing the adiabatic pressure drop -15

-16 characteristics of the test section with the smooth tube friction data, a series of pressure drop measurements was made without heat input to the test section. Figure 12 shows a plot of the experimentally determined liquid friction factor versus Reynolds number. The solid line represents the smooth tube data available in the literature. A close agreement was observed between the smooth tube data and the experimental points, as shown, indicating that there was hydrodynamic smoothness. Co Non-Adiabatic Pressure Drop Several series of runs with different flow rates and heat flux values were made for non-adiabatic pressure drop measurements. Under non-adiabatic conditions, the pressure drop is the result of the frictional forces and of the rate of increase of momentum of the mixture. During all the pressure drop measurements, the thermocouple probes for the fluid temperature measurement were not placed in the test section. From these pressure drop measurements the pressure profiles along the test section were obtainedo Figure 13 shows typical pressure profiles for a series of runs made with constant flow rate, constant inlet temperature, and with different heat flux. On the same figure, curves representing the local bulk steam qualities also are given, From the pressure profiles, the axial pressure gradients dP for two-phase flow, (d-) were calculated for each tap position dlTP along the boiling length of the test section~ For comparing the pressure gradients obtained for different flow rates, the pressure gradients for the case of the adiabatic all-liquid flow at the

-17 saturation condition were introduced. The ratio of the non-adiabatic pressure gradient to the adiabatic pressure gradient, R = (dP/dl)TP, (dP/dl)^^ was used in the presentation of the results. This pressure gradient ratio was plotted as a function of a dimensionless parameter X which was first introduced by Martinelli and co-workers (4,14,15). The parameter X is defined as 1 n V 2-n. 2-n i. x =() ((L) (-1) (7) Vg fig X Here n is the exponent of the Reynolds number in the friction factor equation. From the adiabatic pressure drop data n was found to be 0.25. Therefore, 0.5n 0.143 X = (V) (V-) (1-l) (8) Vg JLg X Figures 14, 15 and 16 show the plots of the pressure gradient ratio versus the parameter X for three different flow rates, For each flow rate several runs corresponding to different heat flux values are represented. A common feature is observed on these plots. That is, the curves corresponding to different heat flux values merge into a single curve below a certain X value, Also, this particular X value increases with an increase in the flow rate. Expressed from the standpoint of steam quality, which is the main variable in the parameter X, it may be said that above a certain quality the pressure gradient ratio, R, for a constant flow rate can be represented by a single curve and is independent of the heat flux. The quality corresponding to this merging point decreases as the flow rate is increased, For the cases illustrated, the merging points correspond to steam qualities of 20%, 10%, and 6% for

mass velocities of 1.38 x 10, 2.76 x 105 and 4,14 x 105 lb/hr ft2 respectively. It is noted that an almost exact inverse ratio prevails between these corresponding X and G values. It is also observed that before merging, the curves corresponding to increasing heat flux, also corresponded to increasing pressure gradient ratios. These observations and the study of the still and motion pictures of the outlet mixture led to the following postulates: The merging of the pressure gradient ratio curves is the result of a change occurring in the flow and heat transfer mechanisms. Nucleat boiling and forced convection are two primary processes which control the heat transfer and the pressure drop characteristics of the system. For the low steam qualities and low mass flow rates nucleate boiling process seems to be dominant. Since for a constant flow rate a higher heat flux would correspond to a more vigorous boiling and a higher degree of turbulence, a higher pressure gradient ratio should be expected. In this region the flow pattern may be assumed to be more or less annular, composed of a steam core and of a liquid film on the walls which is thick enough to support bubble growth. Above a certain range of the steam quality, the increased velocity of the two-phase mixture becomes sufficient to suppress the nucleate boiling process. In this region the liquid droplets are more or less homogeneously dispersed in the high-velocity steam phase. And the system characteristics are governed by the forced convective process. This flow pattern corresponds to what has been termed in the literature as fog, homogeneous or liquid-dispersed flowo Although the actual flow pattern is not yet clearly defined, it is generally thought that a very

-19 rapid exchange of liquid droplets between the walls and the main stream is responsible for the transfer of heat. In a recent paper, Goldmann and co-workers (16) proposed that the liquid transport to the walls is accomplished by eddy diffusion of droplets. This change in the flow mechanism and the accompanying disappearance of the liquid film and of the nucleate boiling on the walls is suggested as the explanation of the observed merging of different heat flux curves in Figures 14, 15 and 16o As a result of the foregoing, the region in which the pressure gradient ratio curves are separated might be called "nucleate boiling region" and the region corresponding to the merging of these curves might be called "liquid-dispersed region". Similar conclusions and the distinction between heat transfer mechanisms were forwarded by some previous workers (6,11) from the standpoint of the local heat transfer coefficients in non-adiabatic two-phase flow systems. The following comparison is made as a further remark in connection with the merging points of the pressure gradient ratio curves, which are interpreted as the transition points toward a liquid-dispersed flow pattern. Figure 17 showing a flow pattern chart for a steam-water system at atmospheric pressure is taken from the reference (16). For the sake of clarity only the curves corresponding to the atmospheric pressure are reproduced from the original chart which also included similar curves for 800 psia and 1500 psia pressures. The mass velocities and the steam qualities at the merging points corresponding eto Figures 14, 15 and 16 are marked on this chart. Even not considering the fact that

-20 the boundaries between flow patterns shown as lines in the chart are in reality diffuse bands, the favorable comparison is interestingo The liquid-dispersed region pressure gradient ratio curves of Figures 14, 15, and 16 are compared with each other in Figure 18o A slight effect of the mass velocity on the ratio R is noticed. The ratio R increases with increase in mass velocity for the same X value, Within the range of mass velocities studied, this effect can be expressed as, R~ [G]0~25 (9) Consequently a correction in this form was applied to the curves in Figure 18. Figure 19 shows that when plotted as R[lO5G]-O025 versus X the liquid dispersed region data can be represented by a single curve for all the flow rate and heat flux range studied, Since the main variable in the parameter X was the steam quality, x, a plot of the ratio R versus x in the liquid dispersed region also was tried. Here again a slight mass velocity effect was observedo With a resulting correction Figure 20 shows a plot of the R[10-5G]-0 1 values versus x. It is seen that all the data may be represented within +15%, by the expression -5 -0ol 4 1,32 R[10 G] = 0437 x 10 X (10) D. Comparison of the Non-Adiabatic Pressure Drop Results with that of Previous Workers a) Reference (8) reports an investigation on the forced circulation boiling of water in an electrically heated horizontal tube at operating pressures of 30-200 psia. The following empirical correlation was presented for the variation of the pressure gradient ratio as a function

-21 of mass fraction evaporated and absolute system pressure, R -0.795 x 105 xl93-0037 log + 6 (11) plo04 Here R was obtained by averaging the values corresponding to different flow rates. Although the lowest system pressure studied was 30 psia, this relationship would be reduced to the following form, for the case of P = 14.7 psia, R - 0.485 x 104 x150 + 6 (12) It is of similar form with the expression (10) given above as representing the liquid-dispersed region data of the present worke In Reference (8) the Equation (11) was presented to cover all the experimental data. However it should be pointed out that, since the mass velocity range studied was 3.9 x 105 to 12.9 x 105 lb/hr ft2, the liquid-dispersed region was probably reached for much smaller qualities than in the present work and most of the data belonged to this regiono In this respect it is interesting to note the author's remark that higher pressure gradient values were obtained during a few runs made with shorter boiling lengths and consequently with lower exit qualities. b) Martinelli and Nelson(15) proposed a method for the calculation of pressure drop during forced-circulation boiling of water in horizontal tubes. The method was an extension to steam-water mixtures of the correlations based mostly upon, the isothermal two-phase two-component data. The over-all pressure drop measurements of the present work have been compared with the pressure drop values predicted by this method. For

-22 this purpose, some of the original curves given in Reference (15) were re-plotted in a manner to permit more accurate readings for the pressure and quality values studied. In order to obtain a greater number of points for this comparison, the pressure drop between the incipient boiling point and each pressure tap was taken as corresponding to an independent runo The pressure value used in the calculations was taken equal to the average of the measured pressures in that part of the test section used in the comparison. Figure 21 shows this comparison. It is seen that in all cases, the measured pressure drop values fall within the values predicted for separated and fog flow models. For a small pressure drop (low flow rates and low qualities), the separated flow predictions are in better agreement with the measured values, while the fog flow predictions largely overestimate the pressure drop. As the pressure drop increases a trend is observed toward, an improved agreement between the fog flow predictions and the measured values. Another comparison between the measured and predicted pressure drop is shown in Figure 22. In this figure, the measured pressure drop between the incipient boiling point and the successive pressure taps along the test section for a particular run is shown together with the predicted curves corresponding to fog flow and separated flow. A curve representing the calculated local steam qualities also is includedO It is seen that with increasing quality the measured pressure drop characteristic follows a transitional form from that of a separated flow mechanism to that represented by a fog flow mechanism. Similar plots were repeated for each run

-23 and on all these plots the same tendency of the measured pressure drop curve was observed, This observation led to the concept of correlating the actual pressure drop curve using a linear combination of the separated and fog flow pressure drop characteristics in the following manner: PACT - m LPSEP + n LPFOG (14) In which it is assumed that m + n =1 (15) since this is the trend at the limits of large and small qualities. From these two equations, ^m = FOG - LPACT (16) PFOG - PSEP PACT - LPSEP (17) APFOG - APSEP Consequently m and n values were calculated for several runs and plotted versus steam quality. Figure 23 shows the plot of the coefficient m for three different mass velocities. The points belonging to each mass velocity could be represented by a separate curve. Then it was tried to combine these three separate curves into a single curve by a change of the co-ordinates. Figure 24 is the result of such a modification, and the m values for all the mass velocities were grouped together and represented by a single curve within a certain scatter of data, when plotted versus the product 10-4 X147 G. E. Wall Temperatures For measuring the outside tube wall temperatures, twenty thermocouples were placed at the top and bottom of the test section at several

-24 stations. During the preliminary measurements some differences and changes had been observed, between the top and bottom temperatures under certain conditions. And for a better interpretation of the temperature measurements, a test section which would have no pressure taps or thermocouple probe attachments seemed to be more desirable from the standpoint of the heat generation uniformity. Consequently, such a test section of the same general dimensions as the original one was built using the same tubing material. And the wall temperature measurements were carried out on this test section. The location of the wall thermocouples are indicated in the Figures 25, 26, and 27. The temperature drop across the tube wall was calculated using the Equation (6), for determining the inside wall temperatures. The data of Dickinson and Welch(l7) was used for the thermal conductivity of AISI type 304 stainless steel. Figures 25, 26, and 27 show the inner wall temperatures for three series of runs made with different mass velocities, constant inlet temperature and increasing heat flux. The exit qualities corresponding to each run also are specified. If Figure 25 which belongs to the lowest mass velocity, the first run is an adiabatic run with water at 205 Fo The purpose of this run was to check the uniformity of the thermocouple readings. In the two following runs corresponding to exit qualities of 2% and 5%, the upper wall temperatures were found to be consistently lower than the lower wall temperatures. The difference was about 10-12 ~Fo The photographic study of the outlet mixture showed an unsteady, pulsating, stratified flow pattern for these conditions (see Figures 28, 29, 30, 31, 32). Lower

-25 temperatures observed at the upper portion of the test section are attributed to a more effective transfer of heat between the upper wall and the high-velocity steam phase (including the entrained water) which is moving in the upper portion of the tube cross-section. As the heat flux is further increased during the following runs, it is observed that the difference between the upper and lower wall temperatures disappears, and for most of the locations both temperatures become essentially the same. This is in agreement with the observed more symmetrical flow patterns as the heat flux increases. (Figure 35-39). The same general remarks can be made about Figure 26. However, in the first two runs with low heat flux the temperature difference between upper and lower portions was smaller than in the first series of runs. During the runs made with the highest mass velocity studied and shown in Figure 27, no similar temperature difference between the upper and lower portions of the tube wall was found. F. Photographic Study of the Outlet Mixture Since the outlet of the test section was open to the atmosphere a photographic study of the outcoming steam-water mixture was conducted. Still pictures were taken with a 4 in. x 5 in. Speedgraphic camera which was used with a strobelight unit of 0.5 millisecond duration. Super panchro press type film was used with an F18 aperture. Motion pictures were also taken with a medium speed Fast-Air 16mm camera at a speed of 300 frames/second, using tri-x negative film. Some of the still pictures are shown in Figures 28-39.

-26 Figures 28, 29, 30, 31, and 32 were taken under the same experimental conditions which were G = 1.38 x 105 lb/hr ft2, tin = 205 F, q/A = 25000 BTU/hr ft2, xe = 5.5%. As seen by the pictures, the flow was unsteady, and consisted mainly in a pulsating stratified flow with alternate slugs of liquid and vapor. Figures 33-34 correspond to a similar flow condition with a different mass velocity. Figures 35, 36, and 37 correspond to annular flow patterns. Essentially this pattern consists of a core of vapor which may contain some water in the form of droplets, and of a liquid film on the tube walls. Figures 38 and 39 are typical photographs corresponding to high steam qualities and to a liquid-dispersed flow pattern. The mixture is in the form of a more or less homogeneous dispersion of water droplets in the steam phase.

FILTER I REDUCING VALVE ORIFICE PICKUP tON EXCHANGER Figure 1. Schematic Diagram of the Equipment.

t9021 p4,{ $ -4:.. 0't 4):1 04 f'o t 0A Q)j 4.1 *t 4 O 81 t;t 4A PrAc

-29 On; i i: i:i::i B" Q U)3 If 0, ai) 11 0) 10 Q ci a) Go r-4 ~f-L PC, ~::::: iii:i:i:ii~::; i iii:iii:!~'.l! i:E v i'SSF::? 20:::i:: t;: i::::i:::E: \:cE E ~i i.i.,ii iv i... t::!: i: iA.:.:,:E..... i:00: Ei:::,E: C,i: ~i1i~!i iE;:.i R'!:.:.::.::i i::::i:::pi::::::SR:::.U:a:-; - i:::::;;;:::,:i i:-:::::: I::-::: I

POWER CONNECTION INLET THERMOCOUPLE CONNECTION h Figure 4. Detail of the Test Section.

FLow Rate'W (Ubh.) L" N (1n uo 0) 0 Un 0 0 u* oh tl 00 O N 0 r-7 _. 1 CS 1 0 o o( o 0 Figure 5. Calibration Curve for the 0.218 in. Diameter Orifice

FLow Rate. W (Ib/hr.) 0 w O o - 0 0 i..- 0 a,~~~~~~~~~~s o~~~~~~~~~~~~ Figure 6. Calibration Curve for the 0.312 in Diameter Orifice.

3.50 3.00 a.50 I /0" 1.00 - 0 40 80 120 160 200 240 280- 320 360 400 FrzquarLcy c ps) Figure 7. Calibration Curve for the Turbine Type Flowmeter.

280 d 40 200 160 0 40 0 0.4 0.8 I. I. 2. 2.4 Flow RaLt. W( SPm) Figure 8. Flowmeter Output Voltage (Peak-to-Peak) versus Flow rate. *" / ~~~~~~~~~~~ y 310 ---------------- -- -- ------------- I / Figure 8. Flowmeter Outp~ut Vloltage (Peak-to-Peak) versus Flow rate. 2.8 3.2

OSCILLOSCOPE ILO.. tai AMPLIFIER Flow Rate by Means of the Flowmeter.

vvvv vvvv o 0\ TO POTENTIOMETER Figure 10. Voltage-divider Network for the Test Section Voltage Drop Measurement.

/ TEST SECTION I I Figure 11. The Pressure Tap and Manometer Connections.

0.02 0.008 — 20.006 SFmooih tube.r data 0.004 0.002 0.001 - -,, - 10s 2 4 6 8 10o 4 6 8 10s Ne Figure 12. Friction Factor versus Reynolds Number for Adiabatic Runs.

200 IP4 0 (ii Fe4 PJ LO U) IA V3 to W %D:a I~ 0.80 0.72 0.64 056 0.48 8 0.40 > 3 0.32 0.24 0.16 0.08 0.0 5 6 7 8 10O PRESSURE TAPS (5 INCHES APART) Figure 13 Pressure Profiles and Steam Quality Curves for a Series of Non-Adiabatic Runs.

4000 2000 800 600 400,00 G 1.38 O-b/h.f,o 80 A -.zSx~o X B %/T S~h s6 0 Z 61I0s 0 1,65 x I0, ~ 1.50ox 10, * iSO' \\ 10 0.01 0.02 0.04 Q06 0.08 O1 0.2 0.4 0.6 0.8 1.0 2. 4 6 8 10 o 579 0143 0 jI 0.01~~~~~ ~~~~ ~~ 0.02 0.0S) Q0X.801 OZ 0+ 0....4 6 8 Figure 14. Plot of R versus X for G = 1.38 x 105 lb/hr ft2

1000 800 600 400 200,.. a. 100 I0 0; 80 60 II 40 20 10 - 0.01 I.1 0.2 0A4 0.6 0.8 0573 0.13 -x ^ \^) rs" n Figure 15. Plot of R versus X for G = 2.76 x 105 lb/hr ft2

1000 800 600 400 200 I I I I I I - I I I I I o 0. pc N 0 s 100 80 & - 4.14 O^ (NR =3. 10)s a 2.5 x 10 BTUo/hft. oa 2.0 x O ___ __ ___ o 1.75 x 105 \ + I.ZO x O \ I I l 60 40 20 tO 0.01 o.02 0.04 0.06 0.08 0.1 0.2 0.4 / 0.571 0.6 0.8 1.0 (r' I-X 4 6 8 10 Figure 16. Plot of R versus X for G = 4.14 x 105 lb/hr ft2.

-43 r0 hi bi tL 0 C: 44 v~ 106 4.A4 2.76 I 0 00 -1I I 4+-_+ — 4.0 0 4 i 6 0% I I - Bubble or froth Dispersed or fog 1I 10i I I I I - I I I I _ I I I II I N Annular U Plug - slug I 104 I I I I 0 6 10 20 40 60 80 100 5tzam Qualty (x weigth prcent Figure 17. Comparison of the Experimental Results with the Steam-Water System Flow Pattern Chart for 14.7 psia (chart taken from reference 16).

-44 4000 2000 1000 800 600 r o N 400 200 100 80 60 40 ZO 10 0.01 0.02 0.04 0.06 0.08 0.1 0.4 0.6 0.8 1.0 ~= - (u)sl0571 ( s0143 (IX's' X Figure 18. Comparison of the R-X curves in the Liquid-Dispersed Region.

-45 4000 aoo0 1000 800 600 400 In cu d C3 I Im zoo 100 80 60 40 20 - 0.01 0.02 0.04 0.06 0.08 0.1 0.Z 0.4 0.6 0.8 1.0 VL s ( H 0 143 ('-X Vs( )'' (/ \T I Figure 19. Plot of R[10-5G]O25 Region versus X in the Liquid-Dispersed

2000 1000 840 / 600 --- 1.31I. 08.01.2.4.6.8 020R. /. / 600 / t L i - e/g/o. 2 / I00 0 40 0.01 O.O 0.04 0.06 0.08 0.2 0.4 0. 0.8 1.0 40 0 G m4.14,5O5b/hr.fti 20 0.01 O.Oa 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 X Figure 20. Plot of R[10- G]-0'1 versus X in the Liquid-Dispersed Region.

-47 0( & o so d I5 w i ~s C M a a: on( vor V) ~0 40 60 80 100 MEASURED PRESSURE DROP (inches of water) Figure 21. Comparison of the Measured Pressure Drop with the Predictions of the Martinelli-Nelson Correlation.

0 L4 tB a -. > 012 I I 10 20 30 40 HEATED LENGTH ( Inchs) Figure 22. Comparison of the Measured and Predicted Pressure Drops along the Test Section.

0.8 0.6 0' A \00 I 0.4 A 0.2 0 0.05 0.10 0. 15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 QUALITY. D Figure 23. Coefficient m versus steam quality.

1.0 1.0 ~~~0.8 _ —- - - ^ _ —----------------- 7 —------— o. _8 l0~ ~~ |^ O Ao G=1.38x105Ib/ hr.R 0 G-2.76 x O lb/hr.ff! 0.6 ____________, / / o G= 4.14 x IOs Ib0hr. ft.. 6 0.4 0.4 0 _ ___ ____ ____ ____ ____ ____ ____ _____ 10 -4 X el C ( (tS/hr..7 Figure 24. Coefficients m and n versus 10. X 7. G

-51 270 260 250 240 Z30 270 260 250 240 230 260 250 240 r-4 230 V 220 H 250 X 240 2a10 I 220 240 220 210 230 220 210 200 220 210 10 15 20 25 30 35 40 DISTANCE FROM TEST SECTION INLET (INCHES) G. 1.38s 105b./hr.t ti- =205~F Figure 25. Inner Wall Temperatures for G = 1.38 x 105 lb/hr ft2, tin = 205, q/A = 0 - 2 x 105 BTU/hr ft2 45 50

-52 INNER WALL TE1PERATURE A OUPPER _ LOVER 2 Xe - 22.9 %?80 2 80 _ _ _ _ _ _ __- _ _ __ —---- _ _ _ _ __ —------- -_ _270 250 ____ —_...........~...... 260 280 28 r 1VA I.5 x 10BTU/hr.l t 270 X — _____5 —- -- ------ IT - __* --- - 0 -- 250 240 230 260 - zA~~~~~~o~~~ ~~~~VA-.105 BTU/hr-.t X~- 11.2/ 250 _ —_240 230 220 2.30 220 240 CL/ - 1I/A. - 2.5 104' "TU/'. 2303.~= 2.5 % z3o 210 - 230 A = -BTU/hr.f 210 _^_______ ________ ________ J __________'______________ — X4 —.2 *A_____ 220:1210 I I L 1 I 1 1 LL I 200 I 0 5 10 15 20 25 30 35 40 DISTANCE FROM TEST SECTION INLET (INCHES) 45 50 IG-2.7T6o0 1b./hKrft2 tin= 205F Figure 26. Inner Wall Temperatures for G = 2.76 x 105 lb/hr ft2, tin = 2050P, q/A = 10 - 2 x 105 BTU/hr ft2

-53 290 280 270 260 250 240 280 270 260 250 240 Z230 O 260 250 < 240 P4; 230 1, 220 250 240 230 220 240 230 220 21Q 230 220 210 200 INNER WALL TEMPERATURE { LOWERA A /A 2 x 10s BTU/hr. tt x, =1 1.6 A 0 I..~~~~~~ E I E S l l LSa~~~~~~~~~~~~~~~~~/A. 5x I04 BTU/hr.f 0 0A _ _ _ _._ h.~~~~~~ <19~~~~~~~/A = 105 BTU/hr. it.? OX: 57.1.0 % V/Al 5 x 10 BTU/hr. it! XZ a 3.3 % I/A -2. 5 I~o BTU/hrft IX, 1.4 % V/A. 104BTU/hr.t'. _______ _______ ______ _______ ______ _______ _ ____O__ _ C. 0.0% 0 5 10 15 20 25 30 35 DISTANCE FROM TEST SECTION INLET (INCHES) G = 4.14x 105 SI hr.it f'= 205 F | 40 45 50 Figure 27. Inner Wall Temperatures for G = 4.14 x 105 lb/hr ft2, tin = 205~P, q/A = 10 - 2 x 105 BTU/hr ft2

-54 Figure 28, Figure 30. Figure 29. Figure 31. Figures 28 - 32. Photographs of Unsteady Stratified Slug Flow Patterns at the Test Section Outlet. G = 1.38 x 105 lb/hr ft2, Xe = 5 5%, q/A = 25,000 Btu/hr ft2

-55 Figure 33. Figures 33 - 34 Photographs of Unsteady Stratified Slug Flow Patterns at the Test Section Outlet G = 2.76 x 105 lb/hr ft2, Xe = 2.5%, q/A = 25,000 Btu/hr ft2

Figure 35. G = 1.38 x 105 lb/hr ft2, Xe = 14%, q/A = 61,000 Btu/hr ft, W = 290 lb/hr Figure 36. G = 2.76 x 105 lb/hr ft2, Xe = 5.3, q/A = 50,000 Btu/hr ft2, W = 580 lb/hr J1 0\ I Figure 37. G 4.14 x 105 lb/hr ft2, Xe = 4%, q/A = 61,000 Btu/hr ft, W = 870 lb/hr Figures 35 - 37 Photographs of Annular Flow Patterns at the Test Section Outlet.

-57 Figure 38. G = 1.38 x 105 lb/hr ft2 Xe = 29%, q/A = 125,000 Btu/hr ft W = 290 lb/h Figure 39. G = 1.38 x 105 lb/hr ft2 X = 47%, q/A = 200,000 Btu/hr ft2, W = 290 lb/hr Figures 38 - 39. Photographs of Fog (or Liquid-dispersed) Flow Patterns at the Test Section Outlet

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-5914. Lockhart, R. W. and Martinelli, R, C. "Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes." Chemical Engineering Progress, 45, 39, (1949). 15. Martinelli, R. C. and Nelson, D. B. "Prediction of Pressure Drop During Forced-Circulation Boiling of Water." Trans. ASME, 70 695, (1948). 16. Goldmann, K., Firstenberg, H., and Lombardi, C. Burnout in Turbulent Flow - A Droplet Diffusion Model. Presented at the ASME-AIChE Heat Transfer Conference, Buffalo, New York, Paper No. 60-HT-34, August 15-17, 1960. 17. Dickinson, N. L. and Welch, C. P. "Heat Transfer to Supercritical Water." Trans. ASME, 80, 746, (1958).