Experimental Investigation of an Application of Two-Phase ...

EXPERIMENTAL INVESTIGATION OF AN APPLICATION OF TWO-PHASE FLOWDIFFERENTIAL PRESSURE MEASUREMENT IN VERTICAL SQUARE CHANNEL

Ondrej BurianDepartment of Energy EngineeringFaculty of Mechanical Engineering

Czech Technical University in PragueTechnicka 4, 166 07 Praha 6, Czech Republic

Email: [email protected]

Vaclav DostalDepartment of Energy EngineeringFaculty of Mechanical Engineering

Czech Technical University in PragueTechnicka 4, 166 07 Praha 6, Czech Republic

Email: [email protected]

ABSTRACT

The experimental work described in this paper deals withan experimental research of two-phase flow focused on thestudy of thermal hydraulics of steam generating facilities forNPPs, like BWR reactors and steam generators. The resultsof this research can be used for development of new methodsfor the control and measurement of the operating parameters ofthese facilities at normal and abnormal operational conditions.Moreover the results are also applicable for a development ofa method for a determination of two-phase flow regimes bypressure fluctuation analysis. The main idea of those methods isbased on the measurement of pressure and pressure difference insteam-water mixture and their further analysis by mathematicalmethods of signal processing. Based on the results of theseanalysis, represented by statistical and frequency parametersof pressure signal, it is possible to determine other parametersof two-phase flow such as void fraction, slip ratio and flowregime of two-phase flow. This method may be applied to thesteam generator, where it can be used for a measurement of agenerated steam flow rate by the measurement of a differentialpressure between two points located at the outer shell of thesteam generator at steam-water mixture level. This method hasseveral advantages, over other methods and might improve thetotal efficiency of the power plant. In this paper the validationmethod at low pressure is presented. For this experimental workan experimental facility was made consisting of 1.5 m tall squarechannel with the dimensions of 200 x 200 mm. This channelwas equipped with electrical heaters with power of 9 kW in

the bottom part and they serve for production of steam-watermixture. This facility was used for a measurement of an absolutepressure and a pressure difference of two-phase flow for variousconditions - power and geometries of grid elements. A set ofpressure data for every measurement was analyzed by basicstatistical methods and results of those analyzes for variousconditions were compared. This comparison was focused on thedetermination of dependencies among a parameters of analyzedpressure signal from a heater power and geometry of a gridwhich have significant influence on void fraction. The resultsof this comparison are presented and discussed in this paperas well as the method used for the statistical analysis. Furtherpossibilities and limitation of this method are described, mainlythe performance of the measurement instrumentation that has asignificant influence on the final result. In the conclusion theapplicability of this method for real power facilities and nextdirection of this research are discussed.

KEYWORDS: Two-phase flow, boiling, void fraction, pressurefluctuation measurement

NOMENCLATUREA Flow area of experimental section [m2]Ah Area of holes in internals [m2]Ag Area of steam fraction in cross section [m2]Bo Bond number [-]L Characteristic number - size of bubbles [m]

Proceedings of the 2016 24th International Conference on Nuclear Engineering ICONE24

June 26-30, 2016, Charlotte, North Carolina

ICONE24-60684

1 Copyright © 2016 by ASME

Pcs Wetted perimeter [m]Rcs Relative cross section [-]Sr Slip ratio [-]dh Hydraulic diameter [m]g Gravitational constant 9.807 m/s2

〈x〉 Steam quality [-]〈α〉 Void fraction [-]ρg Density of steam fraction [kg/m3]ρm Density two-phase muxture [kg/m3]ρl Density of liquid fraction [kg/m3]σ Surface tension [N/m]; standard derivation [-]µ mean of data set [-]

INTRODUCTIONIn this work a series of experiments focused on determina-

tion of significant parameters of two-phase flow by the differen-tial pressure analysis was carried out. Significant two-phase flowparameters are mean a void fraction, steam quality, slip ratio andmass flux. This work is based on assumptions that the differen-tial pressure measured in two-phase volume between two pointslocated above each other decreases with increasing void fraction.The aim of this work is to find dependencies between differentialpressure and two-phase parameters and discussion about possi-ble method for its analysis.

Void fraction, two-phase flow regiment and Bond dimen-sionless number are parameters that are observed in this work.The key parameter that has significant influence on measured dif-ferential pressure is the void fraction, see Eqn. (1). Void fractioncan be defined as the fraction of the cross-sectional area that isoccupied by the gas phase.

〈α〉=Ag

A(1)

With knowledge of this parameter we can determinate otheroverall and particular parameters of two-phase flow. These pa-rameters include mixture density Eqn. (2), quality1 Eqn. (3) andetc.

ρm = ρl(1−〈α〉)+ρg〈α〉 (2)

〈x〉1−〈x〉

=ρg

ρlSr〈α〉

1−〈α〉(3)

Bond number2, see Eqn. (4), can be defined as the ratio ofbody force to surface tension force. It characterizes steam shocks

1With knowledge of slip ratio.2Bond number may be also known as Eotvos number

due to energy relief from hot and cold liquid mixing.

Bo =(ρl−ρg)gL2

σ(4)

Including another measured parameter, a size of bubbles, itis possible to summarize a regiment of two-phase flow to Bondnumber. When mixture mass flux and one fraction velocity areknown we can define the other fraction velocity and slip ratio.The dependency between Bond number and differential pressurein two-phase mixture is described in this work. Dependencies ofother mentioned parameters are the aim of future experimentalwork.

Due to the character of boiling and two-phase flow whichare quasi-stationary processes [5] statistical and frequency anal-yses are also important. Based on these analyses it is possible tofind other dependencies between statistical parameters of mea-sured pressure difference and parameters of two-phase flow. Itis also possible to find some dependencies between shape fre-quency spectra chart and parameters of two-phase flow [1]. Theresults of just the statistical analysis of pressure fluctuation arementioned in this work. The possibilities of frequency analysisare briefly mentioned as well.

EXPERIMENTAL SETUP APPROACHFor the purpose of this experimental work, a special experi-

mental setup was designed and manufactured. The main part ofthis setup is a 1,5 m tall square channel experimental section ofabout 200 x 200 mm cross-section size. This section is used tosimulate two-phase volume by a set of electrical heaters locatedin the bottom part of the section. The total power of all heaters is9 kW. The power is adjustable by 1 kW. A volumetric heat rate ofset of heaters is designed in the same way as in steam generatortype VVER 1000.

In the upper part of the section three positions of variableinternals are located. These internals are used to increase hy-draulics resistance of two-phase flow and as dummies of steamgenerator internals. Distances of positions of the internals fromthe bottom are given in Tab.1

On the outer shell two couples of polycarbonate windowsthat are used for observing two-phase flow regiments inside thesection are located. On the outer shell seven measurement pointsare located. These points are used for measuring local pres-sure and temperature in two-phase volume. Measuring differ-ential pressure between two points is also possible. The sketchof experimental section with internals and instrumentation is dis-played in Fig. 2.

For pressure measurement a transmitters with accuracyabout 0,1 % FSO and response time 5 ms are used. For differ-ential pressure a transmitters with accuracy about 0,065 % FSOand response time 270 ms are used.


FIGURE 1. EXPERIMENTAL SETUP

TABLE 1. THE TABLE OF ELEVATION OF MEASURED POINTSAND INTERNAL POSITIONS

Position Elevation [mm]

m1, m2 285

m3, m4 500

m5 650

m6 800

m7 1330

i1 575

i2 1130

i3 1280

EXPERIMENTSFor study of dependencies of differential pressure and two-

phase flow parameters a set of several experiments have beencarried out until now [4]. These experiments were focused onmeasurement pressure, differential pressure and their fluctuation

FIGURE 2. SKETCH EXPERIMENTAL SECTION

in various conditions that included various powers of heaters andvarious hydraulic resistance. The various hydraulics resistanceswere set by various configurations of channel internals. The per-forated stainless steel plate with about 5 mm holes was used asinternals. In one case an orifice with 30 mm diameter was usedfor simulation of higher hydraulic resistance. The measured con-figurations are described in Tab. 2. Three configurations of in-ternals were measured. In all cases internals from simple per-forated plate with 5 mm holes were installed in two upper posi-tions. They were used to increase the hydraulic resistance andvoid fraction in steam-water volume. The internal in the bottomposition i1 that was located between differential pressure mea-surement points was changed during every experiment. Duringall experiments water level was controlled at 1300 mm level soconditions of pool boiling were simulated.

Two differential pressures were measured, one being locatedbetween points m1 and m6 and the other one between points m3


and m5. Between both couples of measured points the first posi-tion for internal is located. The distance between the first coupleof measured points is 800 mm and is marked dp1. The distancebetween the second couple of measured points is 150 mm and ismarked dp2.

The differential pressure transmitters that were used wereconnected to the measured points by impulse lines. The mea-sured pressure difference increased with higher void fraction.This paradox [4] can be explained as a result of connection ofpressure transducers to experimental section. Differential pres-sure between two measured points can be expressed by Eqn. 5,where indexes U and B signifies connection of pressure trans-mitter - upper and bottom, h signifies vertical distance betweenmeasured point and level of mixture and ∆h signifies vertical dis-tance between couple of measured points.

∆p = pB− pU = hBρmg−hU ρmg = ∆hρmg (5)

With respect on decrease a two-phase mixture density withincrease a void fraction, is obvious that this differential pressureshould decrease with increasing void fraction. This value ofdifferential pressure we get as a difference of value measured bysimple pressure transmitter connected straight.

In case of differential pressure transmitter, which must beconnected by impulse lines, is situation quite different. Dueto connection of pressure transmitter we have to calculate withlocation of instrument toward a measured points. Meassuredpressure, which is connected by impulse line, is a sum of twoparts: hydrostatic pressure from two-phase mixture and hydro-static pressure from water in vertical part of impulse line. In ourcase were located a differential pressure transmitters at the levelof bottom measured points. So measured pressure at bottompoints was consists of only part from hydrostatic pressure fromtwo-phase mixture. Meassured differential pressure for thisconfiguration we can expressed by Eqn. 6 or in simplified formby Eqn. 7.

∆p = pU − pB = [(hB−hU )ρl +hU ρm]g−hBρmg (6)

∆p = ∆h(ρl−ρm)g (7)

For check of differential pressure and for comparison ofother type of measurement configuration absolute pressures atmeasurement points m1 and m6 were also measured by absolutepressure transmitter. The main results of these experiments aresummarized in Fig. 3-5. In these figures dependencies betweenpower of heaters, which has straight relationship to void fraction,

TABLE 2. THE TABLE OF MASURED CONFIGURATION

Configuration Power [kW] Perforatedplate�� 5 mm

Orifice�� 30 mm

1 3,6,7,8,9 2 (i2, i3) 0

2 3,6,7,8,9 3 (i1, i2, i3) 0

3 3,4,5,6,7,8,9 2 (i2, i3) 1 (i1)

and measured differential pressure are shown. Fig. 3 shows dif-ferential pressure dependency on distance 800 mm computed asthe difference of absolute pressure measured by pressure trans-mitters. Fig. 4 shows differential pressure dependency measuredon distance 800 mm by differential transmitter and Fig. 5 showsdifferential pressure dependency measured on distance 150 mmby differential pressure transmitter.

Other parameters of the two-phase flow are summarized in

FIGURE 3. DIFFERENCE OF PRESSURE MEASURED BE-TWEEN POINTS m1 AND m6 (MEASURED BY COUPLE OF PRES-SURE TRANSMITTERS)

Tab. 3. Besides measured differential pressure, void fraction,Bond number and the type of flow regime are presented. Theseparameters were determined based on numerical image process-ing of images of two-phase flow acquired through upper poly-carbonate windows. The void fraction was determined based onthe division of detected area of bubbles by total area of acquiredimage of two-phase flow. The size of bubbles used for determi-nation of Bond number was determined based on comparison the


FIGURE 4. DIFFERENTIAL PRESSURE MEASURED BE-TWEEN POINTS m1 AND m6

FIGURE 5. DIFFERENTIAL PRESSURE MEASURED BE-TWEEN POINTS m3 AND m5

bubbles dimension with reference dimension in the image corner.From these figures we can see that all dependencies are not

linear. The significant point is when the power of heaters is set to6 kW. Up to this power the differential pressure rapidly increases/ decreases3 with more power in all cases. This dependency canbe explained by the fact that up to this power the value of gen-erated steam is so high that it flows through the internal with-out increasing the pressure under the internal and deceleration

3In case Fig. 3

FIGURE 6. DEPENDENCY OF DIFFERENTIAL PRESSUREMEASURED BETWEEN POINTS m1 AND m6 ON BOND NUM-BER

of incoming bubbles. The result of this process is rapid increaseof void fraction in observed space between measurement points.This increase of void fraction can be measured as increase / de-crease of differential pressure.

For generalization of power of heaters corresponding to thisspecific case Bond number was computed from observed size ofbubbles. The generalized results are summarized in Tab. 3 andFig. 6.

It is also possible to describe the three measured configura-tions. These can be described by relative cross section(8) andhydraulic diameter(9) of the internal in position i1. These pa-rameters are summarized in Tab. 4.

Rcs =Ah

A(8)

dh =4APcs

(9)

PRESSURE FLUCTUATION ANALYSISAnother significant way to characterize parameters of

two-phase flow is statistical analysis of pressure fluctuationduring two-phase flow. Due to the character of boiling andtwo-phase flow phenomena which is a quasi-stationary processit does not yield stable state of measured differential pressure.


TABLE 3. THE TABLE OF SUMMARISED RESULTS OF EX-PERIMETS

Config.No.

P[kW]

∆p1[kPa]

α [-] Bo[-] regiment

1

3 0.291 0.121 0.400 bubbly

6 0.349 0.191 0.640 bubbly

7 0.469 0.210 4.330 bubbly

8 0.436 0.202 4.844 bubbly

9 0.591 0.249 5.386 bubbly

2

3 0.329 0.189 0.400 bubbly

6 0.369 0.248 1.441 bubbly

7 0.715 0.272 5.021 bubbly

8 0.795 0.287 5.386 bubbly

9 0.918 0.299 5.764 bubbly dispersed

3

3 0.476 0.308 0.400 bubbly



8 1.176 0.493 11.568 slug

9 1.311 0.523 12.969 slug

TABLE 4. THE TABLE OF HYDRAULIC PARAMETERS OF IN-TERNALS AT POSITION i1

internal / configuration Rcs [-] dh [m]

empty space / 1 1 0.2

perforated plate / 2 0.354 0.005

oriffice / 3 0.018 0.03

Its value is dynamically changing over time as a result of bubblenucleation and ebullition on heater surface and bubble flowalong the height of channel.

The main assumption for the next analysis deals with amodel of statistical distribution of differential pressure fluc-tuation around middle value. The assumption of Gaussian4

distribution was confirmed by the analysis of differential pres-sure at all measured configurations. Fig. 7 shows an example

4Also called Normal distribution.

FIGURE 7. EXAMPLE OF DIFFERENTIAL PRESSURE DISTRI-BUTION FOR PO 9 kW AT CONFIGURATION 2

of this analysis when the power of heaters is set to 9 kW atconfiguration No.1, the fitting of histogram of measured differ-ential pressure by the curve of Gaussian distribution confirmsassumption of Gaussian distribution.

The parameters that can characterise Gaussian distribution(10) are mean of distribution (µ), which characterise middleposition of distribution, and standard derivation (11), whichcharacterise width of distribution.

f (x|µ,σ) =1

σ√

2πe−

(x−µ)2

2σ2 (10)

σ =

√N

∑i=1

pi(xi−µ)2 (11)

These parameters are represented in case of distribution dif-ferential pressure by mean of and standard deviation of set ofvalues of measured differential pressure. At this experimentalwork were obtained sets of experimental data for each configu-ration in time 10 minutes with sampling period 0.5 seconds. It isset of 1200 values for ach measurement.

Fig. 8 shows distributions of differential pressure fluctu-ation for measured configuration No.2. From this pictures it isobvious that the width of distribution is dependent on the powerof heaters5. With higher power the area of differential pressure

5That sets void fraction in this case. Can also be generalized by Bond number


FIGURE 8. DIFFERENTIAL PRESSURE DISTRIBUTION ATCONFIGURATION 2

distribution becomes wider and flatter. This fact is significantfrom two points of view.

At power level of up to 6 kw the differential pressure distri-butions are so wide and flat. This fact makes straight determina-tion of void fraction based on simple measurement of differentialpressure at real-time application impossible. At higher void frac-tion the determination of the mean value of the measured differ-ential pressures is needed.

This dependency can be also used to determinate parametersof two-phase flow but it was impossible with the current exper-imental apparatus to make any general conclusions. For betterunderstanding of dependencies between parameters of two-phaseflow and the width of differential pressure distribution more mea-surements at high values of void fraction are needed. Such futurework could provide information about the shape of differentialpressure distribution at higher void fraction and attempt to applythe theory of Gaussian distribution model.

Yet another way to characterize two-phase flow fluctuationcan be based on frequency analysis of differential pressure fluc-tuation. This theory deals with assumption that the differentialpressure in stable state is a periodic signal that is composed frominfinite6 series of sine and cosine signals. Based on this assump-tion it is possible to analyze the signal with methods from thefield of signal processing such as Discrete Fourier Transform(DFT), Discrete Wavelet Transform (DWT) and mainly DiscreteHilber Transform (DHT). Based on these methods it is possibleto transform pressure fluctuation from time domain to frequencydomain and open a new point of view on this phenomena.

The main problem of this way is the need for a set of dif-

6In ideal interpolation.

ferential pressure data acquired with very short sampling time7.Very short sampling time is necessary to find high fraction offrequencies which can give image of signal in frequency domaincontaining differences dependent on parameters of two-phaseflow.

This method has not been applied on data measured duringthis experimental work. The reason is that used instrumentationis not able to acquire data faster than 1 kHz. The minimum sam-pling time of data acquisition unit is 1 ms, the minimum samplingtime of pressure transmitters is 5 ms and the minimum samplingtime of differential pressure transmitters 270 ms. The verifica-tion of this method will thus be done as future work with fasterinstrumentation.

CONCLUSIONBased on the obtained data the following conclusions can

be drawn for three methods of differential pressure analysis.These conclusions are not universal, but they can be appliedwithin a short range of operating conditions corresponding tothe experimental conditions, i.e. atmospheric pressure and voidfraction up to 0.3. The hydraulic resistance of internals also hasa significant influence on the results. In the further experimentalwork the range of conditions will be extended to the area ofhigher void fraction.

Differential pressure analysisThe interdependence of differential pressure and void frac-

tion or Bond number in two-phase volume It was confirmed. Thisdependency is nonlinear. In this experimental work the changein behavior was observed at power of about 6 kW. Above thispower void fraction and Bond number increase faster. The slopeof this increase becomes higher with higher hydraulic resistanceof internals or at the outlet from the experimental facility.

At all configuration of instrumentation the measured valueof differential pressure was very low. It depended on the dis-tance between the measurement points. Maximum pressure isgiven by pressure of water column between these two points. Incase of differential pressure transmitter this limit pressure couldoccur in case of void fraction 1, when experimental section isfilled only by steam. This situation is impossible at used experi-mental setup.

In case of two single pressure transmitter this limit pressureoccur in case of void fraction 0, when experimental section isfilled only by water.

The measured differential pressure was much smaller. It wasunder 1 kPa in case of 800 mm between the points and under 0.2kPa in case of 150 mm between the points. The low measureddifferential pressure required a high accuracy of instrumentation.

7Les then 0.1 msec. It’s 10 kHz


From this point of view it is better to use differential pressuretransmitters. These instruments require complicated connectionand it is necessary to correct for position of instrument againstthe measurement points.

Application of couple of simple pressure transmitter is notso accurate, but on the other hand required more simple connec-tion without compensation for positon of the instruments. In thisexperimental work both ways of differential pressure measure-ment were tested. Both method were confirmed to be applicable.From practical scope of view it is important that differential pres-sure transmitters, used in industrial applications, are applicablefor this method of identification of parameters of two-phase flow.

The main problem for industrial application of this method isthe fact, that due to pressure fluctuation it is impossible to use di-rectly measured values, but is necessary to compute mean valuefrom the set of data. This fact makes it impossible to use thismethod for a real-time application.

Differential pressure fluctuation statistical analysisThe method of statistical analysis of differential pressure

fluctuation distributions can be good tool to analyze two-phaseflow parameters and boiling conditions based on the study ofwidth and shape of the particular distribution. So far we did notobtain enough results to make final conclusion.

However, at all measurements in this work it was confirmedthat the width of Gaussian distribution increases with higher voidfraction. For better description of this method more experimentsat higher void fraction will be done in the future, to confirm thisbehavior of Gaussian distribution. We also intend to confirm thisbehavior at higher pressure.

Differential pressure fluctuation frequency analysisThis method could not be performed on the existing data set

due to high sampling time of 500ms, which was used because ofthe available instrumentation.

For application of this method faster instrumentation is nec-essary. That includes pressure transmitters with short responsetime and acquisition unit with short sampling time.This fact and the need of data post-processing limits the indus-trial application this method.

REFERENCES[1] Hao Ding, Zhiyao Huang: Hilbert-Huang transform

based signal analysis fro the characterisation of gas-liquidtwo-phase flow. Flow Measurement and Instrumentation12(2007) 37-46, 2006.

[2] Shaban H., Tavoularis S: Identification of flow regimein vertical upward air-water pipe flow using differentialpressure signal and elastic maps. International Journal of

Multiphase Flow 61(2014) 62-72, 2014.

[3] Vial C., Poncin S. at al.: A simple method for regimeidentification and flow characterisation in bubble columnsand airlift reactors. Nancy: Laboratoire des Sciences duGene Chimique, 2001.

[4] Burian O., Dostal V.: Measurement and analysis of lowpressure drop in two-phase flow. LemTech, 2014.

[5] Ruspini L., Marcel Ch., Clausse A.: Two-phase flow insta-bilities: A review. International Journal of Heat and Masstransfer 71(2014) 521-548.


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