FLOW REGIME MAPPING, VOIDQUALITY RELATIONS AND PRESSURE DROP IN TWO PHASE FLOW


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1 FLOW REGIME MAPPING, VOIDQUALITY RELATIONS AND PRESSURE DROP IN TWO PHASE FLOW Dr. J. Michael Doster Nuclear Enineerin Department North Carolina State University
2 INTRODUCTION Twophase lows (e.. steam and water) occur in many nuclear reactor components. For eample, the steam enerators and pressurizer in Pressurized Water Reactors and the reactor core reion o Boilin Water Reactors are classic eamples o where steam and water low toether as a twophase luid. The compleity o the processes associated with twophase low has required that analyst combine some orm o phenomenoloical modelin with empirical correlations. As it is virtually impossible to ind one epression that is valid over the entire rane o twophase conditions, correlations are usually developed that apply to speciic "low reimes" or low patterns. This requires that we be able to identiy these low reimes and the transition rom one low reime or heat transer reime to another. A number o low reimes have been ound to eist eperimentally by visually observin low patterns associated with the low o liquidvapor mitures throuh transparent tubes. While the number and characteristics o speciic low reimes are somewhat subjective, our principal low reimes are almost universally accepted. These include Bubbly Flow (a &b), Slu Flow (c), Churn or ChurnTurbulent (d), and Annular (e). These patterns are illustrated in Fiure 1. (a) (b) (c) (d) (e) Fiure 1: Typical Flow Reimes (From Thermohydraulics o TwoPhase Systems or Industrial Desin and Nuclear Enineerin, by J. M. Delhaye, M. Giot and M. L. Riethmuller Measurements on airwater systems can oten provide insiht into the behavior o more eneral twophase low systems. This typically requires that the airwater system have provisions or visualization o the low pattern, direct measurement o the air and liquid low rates, pressure drop and measurement o the vapor and liquid volume ractions. Visualization o the low patterns requires that at least some portion o the test section be transparent. While a number o techniques are available or measurin volume raction, one o the most direct is to measure the attenuation o a collimated beam o amma rays. A twophase/airwater acility has been constructed in the R3 Bay in the Nuclear Enineerin Department. Instrumentation or pressure drop and low rate provide an analo sinal which can be interaced to the computerized data acquisition system on the SPWRF. This acility can be used to enerate low reime "maps" which are used to predict low patterns based on system parameters such as liquid and vapor velocities, volume ractions, etc., to validate voidquality models such as the ZuberFindlay Model discussed in class, and to investiate the pressure loss in a twophase system. Flow Reime Maps Flow reime maps are a means o predictin low reimes based on local system variables. While no universally accepted map has been developed, typically the low patterns are identiied on the basis o liquid and vapor
3 velocities, volume ractions and densities. A number o low reime maps are available in the literature. An eample o one such map or vertical uplow o air and water is iven in Fiure. The coordinates are liquid and vapor lu (j and j respectively) where the liquid lu is deined as j v and similarly or the vapor lu j v. Fiure : Flow pattern boundaries or vertical uplow o air and water at 15 psia (From Govier and Aziz) VoidQuality Relations It can be shown, that void and quality can be related to the Drit Velocity by 1 1 V 1 G j where V j is a correlated parameter, and enerally a unction o low reime. Given void raction, quality and mass lu, the Drit Velocity is iven by Frictional Pressure Drop V j G
4 In sinlephase low, rictional losses are correlated in the orm P L D v L G D c c where is the sinlephase riction actor. It has been observed eperimentally, that in lowin twophase systems, the pressure drop can be much reater than that in a sinlephase system with the same mass lu. The classical approach in correlatin twophase rictional losses is to multiply the equivalent sinlephase loss by an empirical twophase multiplier o, P ( ) L D G The simplest model or the twophase multiplier is the homoeneous model which ives o c 1. o. TWOPHASE AIR WATER SYSTEM (TEQUILA) The twophase air water system TEQUILA provides the capability or low reime visualization alon with simultaneous measurements o void raction, liquid velocity, vapor velocity, vapor temperature and pressure drop. From these measurements, the low quality and the total system mass lu can be determined. Flow Reime Visualization: The viewin reion o TEQUILA is a one inch diameter clear pipe. Flow patterns rom bubbly to annular are clearly visible. At hih liquid and vapor velocities, visualization can be enhanced throuh the use o a stroboscope which acts to "reeze" the vapor phase. Liquid Velocity: Liquid velocity is measured directly with a paddlewheel type low meter placed in the low line prior to the liquid enterin the viewin section. The low meter produces a 40 milliamp sinal which can be read directly by the LABTECH Notebook data acquisition hardware and sotware on the SPWRF. Vapor Velocity: Vapor velocity is measured directly by a hot wire anemometer placed in the air line prior to enterin the viewin section. Like the liquid low meter, the anemometer produces a 40 milliamp sinal which is read by the SPWRF data acquisition system. Vapor Volume Fraction: Vapor volume raction is measured by use o a amma densitometer. The densitometer relates the vapor volume raction to the attenuation o a collimated photon beam as it passes throuh the viewin section. As air and water have very dierent mass attenuation coeicients, the count rate is a stron unction o the amount o vapor present in the pipe. The void raction can be shown to be related to the count rate, subject to certain assumptions, by ln( C / C ) ln( C / C ) where: C = Count rate or an arbitrary volume raction C = Count rate or all liquid in the pipe ( = 0) C = Count rate or all air in the pipe ( = 1). In a lowin two phase system, the count rate and the void raction at any location are a unction o time and the low reime. In low reimes where the liquid and vapor are uniormly dispersed alon the channel (e.. bubbly and annular) the void raction will be relatively constant with time. In slu low, the void raction in the viewin 4
5 window o the densitometer will chane siniicantly as the vapor slus pass into view. The averae void raction can be determined by t 1 ( t) dt t0 where the time dependent void raction is obtained rom the time dependent count rate usin the equation above. The time dependent count rate can be obtained directly rom the countin system. Flow Quality: The low quality is deined to be the low raction o vapor in a two phase system, i.e. m m m At steady state, the liquid and vapor low rates in the viewin section are the same as the liquid and vapor low rates measured in the individual low lines. As the cross sectional area o the three low paths are the same, this implies low quality is iven by v v v where the liquid and vapor properties are those measured in their respective low lines. It should be noted, that in an airwater system, the vapor density is much lower than that in a steamwater system, and as a result care must be taken in the selection o liquid and vapor velocities in order to achieve reasonable values o quality. This is illustrated in Fiure 3 below or an air density o lbm/t 3. Total System Mass Flu: The mass lu in the viewin section is iven by G m m m v v A A as the cross sectional areas are equal. The liquid and vapor properties are aain measured in their respective low lines. 5
6 Quality v = 100 v = 80 v = 60 v = 40 v = v = v = Liquid Velocity (t/sec) Fiure 3: Quality Vs Water and Air Velocity EXPERIMENTAL PROCEDURE: FLOW REGIME MAPPING AND VOIDQUALITY RELATIONS The objective o this laboratory is to study the evolution o twophase low patterns and develop voidquality relationships or an airwater system. 1) Determine the count rate in the viewin section under zero low conditions or all air and all water in the pipe. ) For constant values o mass lu, measure void raction, liquid velocity and vapor velocity over the ull rane o low conditions. Note the low reime or each measurement (you may wish to record the low patterns photoraphically). Low liquid velocities can be obtained simply by natural circulation. Caution should be taken at hih liquid and vapor lows as vibrations in the pipin system can alter the sourcedetector eometry or the amma densitometer. 3) Plot low reime versus liquid and vapor lu on the Govier and Aziz map. Compare your results to this map and the Hewitt and Roberts map iven in the reerences (Todreas and Kazimi). Note, at steady state, the liquid mass low rate in the liquid line and the viewin section are equal. The same holds true or the vapor mass low rate. This implies v A v A k k line k k k viewin section where k, indicates the appropriate phase. Since the cross sectional areas are equal, and i we assume the densities are constant, v v j. k line k k viewin section k viewin section 6
7 4) Plot void raction as a unction o quality and mass lu. You should indicate dierent low reimes with dierent symbols. This will indicate i there is a low reime dependence. Compute the Drit Velocity as a unction o low reime and compare your results to those in the literature. EXPERIMENTAL PROCEDURE: TWOPHASE PRESSURE FRICTIONAL LOSSES 1) Measure the pressure drop under sinlephase liquid and sinle phase vapor conditions rom zero velocity to ull low in the horizontal pipin section. ) Measure liquid velocity, vapor velocity and pressure drop over the ull rane o low conditions. Note the low reime or each measurement (you may wish to record the low patterns photoraphically). Low liquid velocities can be obtained simply by natural circulation. Caution should be taken at hih liquid and vapor lows. Note: The pipe diameter in the horizontal section is smaller than that where the liquid and vapor velocities are measure and the proper corrections should be made. 3) Compute and plot the rictional pressure drop as a unction o mass lu or both sinlephase and twophase conditions. 4) Compute and plot the twophase riction multiplier as a unction o quality and mass lu. Note: Compare to the homoeneous multiplier. o P P 1 G 5) Correlate the two phase multiplier in terms o the Martinelli Parameter
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