Droplet size determination in evaporator tubes

Droplet size determination in evaporator tubes

Citation for published version (APA):

Geld, van der, C. W. M. (1986). Droplet size determination in evaporator tubes. (Report WOP-WET; Vol. 86.004). Technische Universiteit Eindhoven.

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DROPLET SIZE DETERMINATION IN EVAPORATOR TUBES

C.W.M. van der Geld

...

--

...

'--8!8LtOTHEEK

1---... ----____

-J

8606191 .

-"---1

T,H.E!!\·JOHOVEN

Report WOP-WET 86.004

Eindhoven University of Technology May 1986

TABLE OF CONTENTS ABSTRACT NOMENCLATURE List of symbols Acronyms Subscripts LIST OF FIGURES

1 Introduction and scope

1 .1 Some history of dry-out investigations at EUT

1 .2 Some history of droplet size detection 1.3 On droplet impingement studies

2 Thermo void probe measuring strategy 2.1 Determination of droplet size

2.1.1 First estimates of droplet size 2.1.1.1 First estimates; r

th,1 2.1.1.2 Correction parameters; r

th,2

2.1.2 Theoretical analysis of heat transfer during evaporation 2.1.2.1 Newton's cooling of a cylinder; 1 D case

2.1.2.2 Instantaneous spot cooling of a cylinder; rotatoric symmetry

2.1.2.3 Uniform cooling; radial temperature drop 2.1.2.4 Non-uniform, bounded heat flows

2.1.2.5 Non-uniform, non-local cooling and reheating 2.1.2.6 Some typical evaporation curves

2.1.3 Measuring stategy and computation method 2.1.4 Experimental verifications

2.1.4.1 Thermo void probe measuring device 2.1.4.2 Experimental set ups

2.1.4.3 Large diameter thermocouple measurements 2.1.4.4 TVP verification measurements

2.1.4.5 On void fraction estimation 2.1.4.6 Varying measurement conditions 2.2 On droplet velocity measurements

3 A computation model for estimation of droplet size at dry-out 3.1 Modeling assumptions and semiempirical equations 3.2 Additional governing equations

3.3 Solution procedure with measured wall temperatures 3.4 Discussion of results 4 On droplet impingement 4.1 Experimental results 4.2 Governing equations 4.3 Solution procedure 4.3.1 Collocation method

4.3.2 Dynamic contact angle algorithm 4.4 On the results

5 Suggestions for further work

5.1 Some design and conditioning improvements 5.2 Droplet velocity measurements

5.3 Other applications

5.4 Theoretical droplet impingement studies 6 Conclusions

REFERENCES

ACKNOWLEDGEMENTS

ABSTRACT

DROPLET SIZE DETERMINATION IN EVAPORATOR TUBES

Two ways of measuring droplet size are presented :

- a detection device, the "thermo void probe", to measure the amount of

cooling caused by evaporation of a droplet on a thermocouple at several

moments of time in order to allow for comparison with theoretically calculated values;

- a rather indirect, computational method that requires the measurement of system parameters and wall temperature after dry out has occurred in a vertical test section.

Results are compared with those obtained with conventional methods.

Droplet velocities were measured with a thermo void probe with time-of-flight method.

The dynamic spreading of a droplet on a surface was numerically studied with a collocation method.

NOMENCLATURE List of symbols Roman letters a B c thermal diffusivity

(m

2

_/s)

2aa(1 + I( d_k/2) )

I

dkA

temperature drop at 0,4 t (see figure 12) x

temperature drop at 0,3 t (see figure 12) x

temperature drop at 1,25 t (see figure 12) x

constant proportional to the augmentation rate of a heat current (equation 2.26)

Cd friction coefficient of droplets (equation 3.5)

C

k thermocouple constant defined by equation 2.3.b

C heat capacity (J!kg.K)

p

C _pv heat capacity of vapour (J!kg.K)

d droplet diameter (m)

d_k = 2R

ko Effective diameter of rod representing a thermocouple (m)

d upper bound of droplet diameter according to computations

max

(section 3.3)

dv droplet velocity in axial direction relative to vapour phase

(m/s)

d diameter of thermocouple wire (m)

o

tube diameter (m)

D

f = 2Rfo ~iameter of evaporating liquid film

E magnitude of electric potential (V)

G total mass flux (kg/m2_s)

G_d parameter that accounts for temperature dependance of (H P ) G_m parameter that accounts for temperature dependance of ( A PCp) G_k parameter that accounts for temperature dependance of (R

k)

G mass flux of vapour (kg/m2_s)

v

H specific heat of evaporation (J!kg)

I R

~2~2

I

~ ~.

Relative importance of second to first derivative of temperature (-)

I(d

k!2) approximately equals 1

1 mean radius of thermocouple welding

b f (m-3)

n num er 0 droplets per unit of volume

v

p pressure (Pa)

r r_th,1 r_{th ,2} r w R_f Rk Sea) t t x T a T avg k T 'inlet T o Tsat T 'tc T v T tLJ

heat flux towards hot junction of a thermocouple (W/m2) radiative heat flux between droplets and tube wall (W/mZ) total heat flux to droplets (W/m2

)

convective heat flux between vapour and droplets (W/m2) heat flux between tube wall and impinging droplets (W/m2) amount of heat (J)

=

r_th,1 • First estimate of droplet radius (m) (Figure 14) radial coordinate (m)

first estimate of droplet radius {m} (section 2.1.1.1) second estimate of droplet radius (m) (section 2.1.1.2)

=

r th ,2 = r / 4> w ( m )

=

D_f

/2.

Radius of evaporating liquid film (m)

=

d

k/2. Effective radius of rod representing a thermocouple measurement error of quantity a

time (s)

time measured between droplet impingement and maximum temperature drop (s) (see figure 12)

ambient or environmental temperature

(oc)

measured mean temperature level

(oe)

temperature at the inlet of a test section

(oe)

initial temperature of thermocouple

(oe)

saturation temperature

(oc)

temperature of thermocouple

(oc)

vapour temperature (oC)

inner wall temperature of a tube (oC)

mean vapour velocity (m/s) (section 2.1.3) droplet velocity (m/s)

liquid velocity (m/s)

x

=

x • Distance of centre of evaporating liquid film to thermocou-o

pIe welding

x _a = G / G. Actual steam quality (-) _v

x equilibrium steam quality (-) (equation 3.11)

e

x = x. Distance of centre of evaporating liquid film to thermouple o

welding (m)

Greek letters

a convective heat transfer coefficient (W/m2K)

a

wv convective heat transfer coefficient between wall and vapour

B 6 £ 1 £ v

e

e

tx JJ v P d P 1 p v 0" T (W/m2K) (equation 3.1)

=

Of / r _w

=

2R_f / r _w

(-)

Dirac's delta function

void fraction (-)

absorption coefficient of liquid (equation 3.3.b) absorption coefficient of vapour (equation 3.3.c) T - T • Temperature relative to environment (ae)

a

maximum temperature drop measured during evaporation of a droplet on a thermocouple

heat conductivity (W/mK)

dynamic viscosity of vapour (kg/m.s)

mass density of droplet (kg/m3

)

mass density of liquid (kg/m3

)

mass density of vapour (kg/m3₎

surface tension (N/m) (section 1.3) time of evaporation of a droplet

normalized temperature (equation 2.23)

normalized temperature for non-local heat extraction (section 2.1.2.5)

~ " normalized temperature for non-uniform heat currents

(section 2.1.2.4)

~ "' normalized temperature for non-uniform, non-local heat extraction

(section 2.1.2.5)

~ 00 correction parameter for subcooling and superheating (section 2.1.1.2)

~ 01 correction parameter for spheroidal effect (section 2.1.1.2)

~ 10 correction parameter (sections 2.1.1.2 and 2.1.2)

w

=

x /

I

4a t

x

Acronyms

Bi Biot number (equation 2.7.a)

D1F measure of differences between vapour temperature gradients (eq. 3.19)

EUT Eindhoven University of Technology

Fo Fourier number (equation 2.7.b)

LH5 left hand side

MK5 international system of standard units

Nu Nusselt number (section 2.1.2.6)

O(a) Pr Pr v Re Red Re v RH5 order of magnitude of a

Prandtl number (section 2.1.2.6)

- U

c

I

A • Vapor Prandtl number

- v pv v

Reynolds number (section 2.1.2.6)

= p d (v - v

l )

I

u • Droplet Reynolds number

v v v

= G x

Diu •

Vapor Reynolds number

a v

right hand side

51 international system of standard units

TC thermocouple

TVP thermo void probe

Subscripts

S,r = r . Partial derivative of s.

This notation is only used if total as well as partial derivatives are used in a chapter.

Other subscripts : see list of symbols.

LIST OF FIGURES

1 3-D Heat transfer topography

2 Burn out fluxes at natural circulation (1966) 3 Burn out heat flux versus inlet subcooling (1970)

Influence of pressure and surface roughness

4 Burn out flux and pressure drop versus subcooling (1970) 5 Burn out quality versus mass flux (1976)

6 Dry-out wal temperatures versus steam quality in the presence of a cooling spot (1977)

7 Droplet impingement and evaporation history on a capillary tube 8 Spreading factor versus impact energy

Influence of static contact angle

9 Normalized temperature curves; influence of B 10 Normalized temperature curves; influence of c

11 Normalized temperature curves; influence of Xo and Of 12 Cooling curve schematics and measuring parameters

13 Estimation of evaporation location from measured parameters 14 Flow chart for the calculation of droplet size

15 Thermo void probe measuring device (collage) 16 Thermo void probe electric conditioner

17 Specimen of temperature history; 10 mm thermocouple

18 Specimen of temperature history; 0,1 mm thermocouple

19 Specimen of temperature history; plateau reheating

20 Droplet velocity measurement with time-of-flight method

21 Droplet hitting a thermocouple in downflow

22 Flow chart of calculation procedure of mean droplet diameter at dry-out

23 Computational results at point of dry-out for various start conditions

24 Computational results; steam temperature and quality 25 Computational results; heat fluxes at dry-out

26 Adiabatic droplet impingements on a stainless steel bar

27 Droplet impingement and evaporation history on a thermocouple

28 Coordinate system, collocation angles (N=9) and dynamic contact angle

29 Dynamic contact angle versus interfacial velocity parameter

30 Schematics of signal conditioning with a compensation 31 Schematic of a solid fuel combustion chamber

1 INTRODUCTION AND SCOPE

It is common experience, that accurate measurements of droplet sizes and velocities in superheated steam are difficult to achieve (see, for example, Nijhawan et al., 1980, Azzopardi, 1979 and Oelhaye and Cognet, 1984). Optical methods, favorable since they do not affect the flowfield of study (see Hirleman, 1983, Drallmeier and Peters, 1986, Jones, 1977 and McGreath and Beer, 1976) are often difficult to apply at elevated pressures (see Van der Geld, 1985). Two measuring strategies for the determination of droplet sizes in superheated steam were developed and studied. nne method is

t

X ::J r l

<0-...,

ro OJ :t:

oNB departure from nucleate boiling

I

,

I

,

,

I I , I I I I , 1 , , 1

critical heat flux

I~

,,",$o,

/

... , ',::" I I

,

/ - 0 ° ,

,

\ , I , ~ I ~ I ,

~

/ \~~~

\

/;..",

"

O),l

/~~~

\

~!oo.

...

:~/

'~\';:[:': ~Qj

, /

/

~ljl

\

~

\

, ' .

"~::

6' I I lo~ \ '" \ I .::? 0 I l;-I /I~\~ \ , ::.;. O)Qj ,/~ I / ' \ \ / . (1;<" l , f I I \ I .4< I ,.;. I \ I 0'" I...., " \ , I 'h~ ~ \ I 1 ~ I ;~, \ I <' I I \

'_.v

"

,f I I \ \ ,,(Ji I I \ \ I '" I I \ \ I I I \ \ I , I \ \ ' I I 0.\ I I \'\ \ , , I ~ \ , ,

,

~

\ \

"

I ('I' \ \ , , \ 1 I St \ \ I &~ \ \ I 9v<l.l' ,I " J.ty ,\ I

"'"

"

1

Heat transfer topography

(after a drawing by G.L. Shires)

3-D Heat transfer topography 17

electro-mechanical and intrusive, and the other method is based on a semi-empirical physical model.

1.1 Some history of critical heat flux investigations at EUT

At the European Two Phase Flow Group Meeting 1981 in Eindhoven, G.l. Shires

presented heat transfer topography in a three dimensional schematical drawing. Figure 1 is based on his drawing.

It clearly shows that critical heat flux may occur at low steam qualities, when it is called departure from nucleate boiling (DN8), but equally well at high steam qualities, when it is usually called dry out.

The research presented in this paper finds application in experimental and theoretical studies of dry out and the transition from annular flow to dispersed droplet flow, called point of dry out.

Natural circulation

t

T = 200 DC sat ... 160 ft E u "- Burn out ~ x ::l .--! 140

_'"

<0-...,

_...

"

('()

...

,

,

!Il

...

" ,

:r

...

" 120

1r...

---

-,'

Instability threshold 100

o

10 20

Inlet subcooling (OC) ~

Figure 2

Burn out fluxes at natural circulation (1966)

During the last two decades, critical heat flux research at the Eindhoven University of Technology (EUT) gradually shifted from the low quality region in the sixties to the moderately high quality region in the seventies and

and the very high quality region in the early eighties.

In 1963 the influence of tube geometry and unequal heating on burn out was investigated by Bowring and Spigt in a 7-rod bundle (see Spigt, 1963). One of the findings was, that burn out heat flux seemed to decrease with increasing test section length. Until ca. 1967 much research was performed on a contract basis, e.g. in collaboration with Euratom (ISPRA). At that time Germans, Frenchmen and Italians joined the research team in Eindhoven

(*).

Early measurements are reported by Anonymous (1966) and Spigt (1966). They deal with natural circulation at several pressure levels in a closed loop with a vertical test tube heated by electrical current.

A typical result is shown in figure 2. The occurrence of an instability threshold led to careful analyses of causes and effects of instabilities

(Spigt. 1966). Some notes on the possible occurrence of two different

mechanisms of heat transport, already clear from figure 1, will be given later.

In collaboration with Westinghouse Electric Corporation (Atomic power divisions), in Eindhoven the effects were studied of flow agitation and special pipe configurations on critical heat flux (Tong et al., 1966). The following conclusions were stated :

- The decrease of critical heat flux due to the proximity of unheated walls at a constant local quality can be minimized by an additional mixing effect generated by the roughness of the unheated wall. This benefit of roughness is more significant at higher flow rates.

- The amount of reduction of the critical heat flux due to the line contact with an unheated wall at a constant local quality is smaller at higher water mass velocity.

In 1966 Spigt and Boot report some new progress made with burn out research with a 7-rod cluster fuel element.

In 1970 a research program was started in collaboration with Interatom, Gesellschaft fur Kernenergieverwertung in Schiffbau und Schiffart (GKSS), Reactor Centre Netherlands (RCN). Stability characteristics and interchannel mixing of "Otto Hahn" reactor cooling system were investigated (see Anonymous, 1971).

(*)

P.G.M.T. Boot, private communications 19

The effects of an additional unheated wall, agitation were further studied by Vinke during his The inlet velocity was carefully kept constant,

wall roughness and flow Msc thesis work (1970). among other things by throttaling and smoothening the flow inlet, and measurements of temperature, velocity and mixing rate were performed locally in a rectangular duct with two transparent walls.

t

----~ E ₂₇₅ u

"

~

----~ ~ 2~ 0 c ~ ~ n ~ ₂₂₅ m x ~ ~ ~ ~ 200 ro ru z 175 Figure 3

Additional rough plate P 4 bar

P 4 bar

30 40

Rectangular test section

2200 x 30 x 10 mm Heated surface 200 x 20 mm Inlet velocity 1 m/s 50 60 T - T (OC) sat inlet

Burn out heat flux versus inlet subcooling (1970) Influence of pressure and surface roughness

Some typical and interesting results are shown in figure 3. It clearly shows that heat transfer is improved if hydrodynamical mixing in the duct is intensified or if system pressure is increased.

Figure 3 also exhibits the fact that two different mechanisms of heat

transfer may occur

differences between at bulk each and system pressure. At near wall temperatures

large subcoolings, are large. Strong oscillations in temperature, heat flux and pressure are observed. Bubbles originating from the wall presumably enter into the fast core flow stochastically, but more easily than at relatively low subcoolings, when hardly any oscillations are found. In both regions of subcooling, heat

transfer is improved if subcooling is increased, since the latter effectuates a better mixing rate and better supply of fresh water to the wall.

t

t~

2 ~ '--'

----

275 N c

0

0 ~

"

~ ~ _1,62 u

....

w 250 m ~ ~ ~ 0 m _w c ~ ~ ~ ~ ~ ₂₂₅ w > ~ 1,47 0 m ~ x 0 ~ ~ ~ 200 P 2,1 bar ~ ~ w ~ _{Inlet velocity} = 1 m/s ~ m ~ W m I 1,32 m w 175 ~ ~ 30 40 50 60 70 T - T (DC) sat inlet ~ Figure 4

Burn out flux and pressure drop versus subcooling (1970)

From these considerations, radial void distributions can be suggested as a means to indicate the subcooling region present.

Figure 4 demonstrates how transition from one subcooling region into the other is associated with a minimum pressure drop over the test section.

Critical heat fluxes at low steam qualities were found to depend on surface roughness, surface contaminations, aging of test materials and other parameters of the actual test configuration. Burn out at high steam qualities, on the contrary, was found to depend mainly on flow parameters such as averaged void fraction, steam velocity, etc ••

An example of this is given by figure 5, in which some results of Boat et ale (1976) are shown.

As a follow up of an exercise of the European Two Phase Flaw Group (Rome, 1973), also the influence of a local heat flux disturbance was studied in

Eindhoven (Boot et al., 1977). Some typical results are shown in figure 6.

If the heat flux is decreased at some point were dry-out is already present, alternate condensation and superheating induce a propagating perturbation of flow and wall temperatures.

0,8

t

>-~ ... ~ ~ 0,7 ~ :J o C H t5 0,6 0,5 ~ __ - 40 W/cm' 50 W/cm' ---~ Nimonic 75 tube diameter 10/12 mm heated length 4,1 m 1000 Figure 5 1500 Mass flux (kg/m's)~

Burn out quality versus mass flux (1976) 2000

In 1982, Van der Geld et al. presented a simple method for calculating

post-dryout wall temperatures. Temperature values calculated with this model were found to be very dependant on the droplet size at the point of dry-out. This droplet radius was estimated from a maximum Weber number.

In subsequent years, the modeling equations were therefore order to be able to predict droplet parameters at point of measured values of the wall temperature. A computer program Clevers, 19B4) to perform the computations.

in dry-out from was written (R.

In this paper the calculation model and computer program are presented. To be able to verify computational results it was found most desirable to halle some direct means of measuring droplet size. To this end, the thermo

void probe was developed. The next section and chapter 2 are devoted to this droplet detection method.

t

u o 450 400 350 300 60 W/cm' 50 W/cm' 0,5 0,6 0,7 Figure 6 Inlet quality 0,5 ~ass flux 1500 kg/m's Tube diameter 10/12 mm Arrows indicate locations of heat flux disturbance (length 100 mm)

0,8 0,9

Steam quality ~

Dry-out wall temperatures versus steam quality in the presence of a cooling spot (1977)

In 1984 it was attempted to combine these two experimental methods of droplet parameter determination in a 39 mm diameter tube in the large test facility described by Van der Geld (1985). Unfortunately the power supply was insufficient to create dry-out situations in the 8,23 m long test section.

Further experiments, with smaller bore tubes, are planned.

1.2 Some history of droplet size detection

In 1974, C.A.A. van Paassen in Delft published his investigations of atomization and evaporation processes using droplet detection thermocouples. The detection method was based on the fast temperature fall if a droplet evaporates on the hot junction of a thermocouple. The detection technique was analyzed and applied to a wide range of test conditions, but especially to spray coolers in attemperators at elevated pressures; droplet velocities ranged up to 40

mls

both in air and superheated steam. His results were very satisfactory.

L.O.C. Heusdens, a MSc. student of Van Paassen, in 1976 made a numerical

study of heat flow and temperatures in a detection thermocouple,

disentangled the influences of some aspects of the cooling process, and

extended in this way the range of applicability of droplet detection

thermocouples.

In later years, experiments have succesfully been carried out at pressures up to 100 bar (Van Lier and Van Paassen, 1980). A report is in preparation and more experiments are contemplated

(*).

The Delft investigations yielded starting points for the Eindhoven research described in chapter 2 of this paper. This chapter describes, inter alia: - a theoretical approach to the cooling process of a detection

thermocou-ple on which a drothermocou-plet evaporates;

- a study of the interconnections and relative importance of correc-tion parameters;

- a measuring strategy to facilitate droplet size calculations;

The theoretical results made it possible to give a practical form to the measurement analysis;

- an introduction to droplet velocity measurements by means of time of flight method.

Calculations were verified by measurements performed by van der Looy (1983), Boonekamp (19B4), Boot, and Van Bommel (1986).

1.3 On droplet impingement studies

It is clear, that a better knowledge of droplet behaviour on thermocouples of various sizes would lead to improved prediction methods and hence would contribute to a more accurate way of measuring droplet size and velocity by thermocouple detection methods. In the course of the work on the thermo void probe (see chapter 2), it was therefore decided to look into droplet behaviour on surfaces in both experimental and theoretical manner.

If a droplet hits a surface that has a much higher temperature than the droplet, an insulating vapour film is formed inbetween the surface and the droplet. This Leidenfrost phenomenon (Leidenfrost, 1756) or spheroidal effect (8outigny, 1850) was first mentioned by Boerhaave (1732).

In 1965, L.H.J. Wachters reported experimental impingement studies with highly superheated surfaces. He found a breakup of droplets if the Weber number

We = 2 P d v ~ r / 0

exceeded a value of ca. 80. In his thesis, Wachters shows and examines high speed cinefilm recordings.

Recent studies of liquid drop behaviour on very hot surfaces are reported by Adams and Clare (1983), Makino and Michiyoshi (1984), Mizomoto et al. (1986), Zhang and Yang (1983).

Much less appears to have been published about the impact and spreading of droplets on surfaces that are only slightly higher in temperature than impinging droplets. In this case the Leidenfrost

important. Experimental investigations were reported

(1967), while Hoffman (1975) reported interesting

general nature.

phenomenon is not

by Ford and Furmidge measurements of a more

In chapter four, some new measurements of isothermal droplet impingement on curved surfaces are reported. Also, a numerical model for the calculation of droplet spreading on flat surfaces is presented. Use was made of a collocation method.

A collocation method has succesfully been applied to bubble growth by Zijl (1977), and to bubble implosion by Sluyter and Van Stralen (1982). The

collocation method presented in chapter four for droplets (a kind of "inversed bubble" case) was developed in collaboration with Mr. W. Sluyter of the department of Physics (EUT).

In addition an algorithme was developed to account for the dynamic contact angle where the liquid-vapour boundary touches the surface.

Although work is still in progress, this can be considered as a first step towards improved prediction methods for the spreading of droplets on slightly superheated, curved surfaces (see, for example, figure 7).

Figure 7 (overleaf)

t o 33,67 0,37 34,78 0,74 35,52 1,11 36,26 1,48 37,0 ms

2 THERMO VOID PROBE MEASURING STRATEGY

An intrusive detection device, the "thermo void probe", is based on two thermocouples (diameters are, for example, 0,026 and 0,10 mm) that penetrate

a dispersed

~oplet

flow. The couples are heated by the superheated steam

and are cooled down slightly each time a droplet evaporates on it. Resulting cooling and reheating curves are analyzed to infer droplet size and, if possible, droplet velocity.

2.1 DETERMINATION OF DROPLET SIZE

A thermocouple, heated by superheated registers

fall if a droplet hits the hot junction and evaporates

a fast temperature there (see also

section

1.2).

Resulting cooling and reheating temperature curves are

analyzed in this section.

2.1.1 First estimates of droplet size

2.1.1.1 First estimate; r_th,1 If a droplet at saturation temperature, Tsat'

evaporates completely on a thermocouple that has temperature T

tc higher than

T a total heat

'sat' (2.1)

is extracted from the environment of the droplet. Here H denotes the specific heat of evaporation, and r the mean droplet radius. This radius

will be estimated from the time required for ,evaporation, T, and the

maximum temperature drop of the thermocouple junction during evaporation,

denoted with

e

tx. It is assumed that

- evaporation heat is only extracted from the thermocouple;

- vapour is not superheated by heat from the thermocouple;

- temperature drops in radial direction are neglected;

the heat flux towards the hot junction,

q,

is constant in time;

- the droplet impinges on the thermocouple welding, and flattens to a circular liquid film with radius R

f•

during time of a circular cylinder with radius Rk

=

0,5 d k

Here the material constant

I (

A pC) is obtained by averaging over the

p

corresponding values for chrome 1 and alumel.

Elimination of Q

v from (2.1) and (2.2) yields

Let t denote the time required to reach maximum temperature drop after

x

droplet impingement. If T is estimated by t , equation

(2.3)

yields a first

x

estimate of the actual droplet radius.

Equation

(2.3)

has been derived, in slightly different way, by Van Paassen

(1974).

2.1.1.2 Correction parameters; r_th,2 To improve the accuracy of the above

droplet radius estimation, the correction parameters <I> 00' <I> 01' <I> 10' are

introduced in the following way

(2.4)

The parameter <I> compensates for subcooling of the liquid and superheating

00

of the vapour produced

(2.5)

where T b is the liquid temperature at the moment the droplet collides with su

the hot junction, and p _{vap p,vap sup} C (T - Tsat) represents the vapour enthalpy

yielded by the thermocouple.

This subcooling or superheating enhances the

measured, whence,j, ~ 1.

'I' 00

temperature difference

If heat is also extracted from the surrounding vapour at temperature T ,

vall this can be accounted for by the time averaged value of lhe parameter

(2.6)

Here Tvap denotes the vapour temperature, Tfilm droplet after spreading on the hot junction,

temperature of the

the thermocouple

temperature, and (l and (l tc corresponding heat transfer coefficients.

vap

Usually the (l / (l t ratio is much less than 1, and the value of <Il 01 is

vap c

close to 1. Only if a vapour film occurs between the liquid film and the

thermocouple, (l tc is reduced and <Il 01 may be different from 1. This

phenomenon is called the spheroidal effect, see section 1.3.

Quantification of this effect is often cumbersome, but experiments (see

section 2.1.4) showed that it may be neglected if (T

tc- Tsat) is in the

order of 30 K or less.

Expressions (2.5) and (2.6) have been derived before by Van Paassen (1974).

A droplet may evaporate partially if its speed at collision is high, or if

its diameter is large compared to the thermocouple size. Experiments showed

that good results can be obtained if R

tc is about 8 times as large as r.

Section 2.1.4 will deal with thermocouple measurements, while more details

on droplet collision phenomena are given in chapter 4.

The parameter <Il

10 accounts for :

- heat exchange between thermocouple and surrounding vapour;

heat fluxes in the thermocouple wires that are not constant in time; If the droplet temperature is lower than T t' initial heat fluxes

sa are highest;

- droplet impingement at some distance from the hot junction;

If a droplet impinges at a greater distance from the thermocouple

junction, time of evaporation is larger and

e

tx is smaller.

- the fact that in the evaporation process the liquid film has a finite extent.

In section 2.1.3 a measuring strategy and a computation method for <Il

10 will

2.1.2 Theoretical analysis of heat transfer during evaporation

In this section the evaporation of a droplet on a thermocouple is considered in more detail than in section 2.1.1. The interconnections and relative importance is evaluated of the various effects that should be accounted for by the correction parameter ~10 that was introduced in section 2.1.1.

The analysis starts with a simplified cooling problem, from which some interesting conclusions can be drawn. This case is also of practical importance, as will be demonstrated in section 2.1.4.7.

More complicated cooling situations are subsequently studied with the aid of some assumptions that are based on the conclusions of the simplified cooling problem.

Typical theoretical cooling curves are calculated and compared with the aid of a computer. Main features and dependencies of the correction parameter

~ 10 are deduced in this way.

=2~.~1~.=2~.~1~N~e~w~t~0~n~'~s~~c~0~0~l~i~n~g __ =0~f __ a=-~c~y~l~i~n~d~e~r~;~~1~D~~c=a=s=e~. Let a thermocouple be

represented by an infinitely long cylinder with radius R

=

D/2. The

consequences of this simplification will be accounted for in the measuring strategy of section 2.1.3 and in chapter 5, where thermo void probe design adaptations are discussed.

At initial moment t = 0 the cylinder has a uniform temperature T and is o

placed in a medium with temperature T , that is constant a

than T. The radial temperature profile in the cylinder o

Newton's cooling from the outside, and is determined by dimensionless parameters

(2.7.a) Bi = R a / A (Siot number)

(2.7.b) Fo

=

a t / R2 (Fourier number)

in which a denotes the thermal diffusivity A / pC.

P

in time and less is affected by the following two

The ranges of SI values that are typical for Thermo Void Probe (TVP) application are listed below :

(2.8.a)

(2.8.b)

(2.8.c)

(2.8.d)

o

E (26.10- 6 , 5.10-4) m a

~

5,35.10-6 m2/s A ~ 26 W/mK a E (100, 104 ) W/m2_K

These values will be further discussed in section 2.1.2.6.

Let

e

~ T - T • The governing heat equation in cilindrical coordinates is: a

(2.9)

The last term on the RHS of equation (2.9) can be neglected in the present case.

It is noted that there was no need to introduce a partial derivative notation like

a e

or

or

e

,r

in this chapter since no total derivates are involved.

The following boundary condition is obtained from Fourier's conduction law and Newton's law at the surface:

(2.10)

_{- cr:r}

d T (R,t) + JL

_A

(T - T(R,t) _a 0

( ) ( -4 -2) .

From 2.B Biot numbers are calculated in the range 10 ,10 ,whlle Fo

approximately equals BOOO t. For these small Biot numbers the exact series solution of the present cooling problem, which can be found in Carslaw and Jaeger (1959) for example, can be truncated to yield

(2.11) (T(r,t) - T ) _o

I

(T - T ) _{a a} ~ 1 - J (-Rr

12

Bi) exp(-2 Bi Fa)

0

Let T _surf T(R,t) and let

B 2 Bi F 0 / t ::;: 2 a a

I

(A. R)

cylinder is small as compared to (T - T f). The cooling process depends

a sur

merely on heat transfer between the surrounding medium and the surface of the cylinder. From (2.11) a relaxation time equal to 1/8 is deduced.

Let I denote the relative importance of the first term on the RHS of (2.9) with respect to the second term on the RHS of that equation, i.e.

At the surface, I(R) = 1, as can easily be demonstrated with the aid of the following equations:

L

J

= -

J

d Z 0 1

2.1.2.2 Instantaneous spot cooling of a cylinder; rotatoric symmetry. If a spherical droplet impinges on a thermocouple that has a diameter, 0, larger than the droplet diameter, it will spread out quickly (see chapter 4). Since cooling mainly uniform and external, and since relevant 8iot numbers are very small, it is now worthwhile to look into some elementary cases in which rotatoric symmetry is assumed. Finite droplet size will be accounted for in section 2.1.2.5.

Consider again a cylinder at an initially uniform temperature T • Striving _a towards solutions of more general problems, a cooling explosion at time t

=

o

and axial location x = 0 is now studied.

Again the governing heat equation is given by (2.9), in which the last term on the RHS is now important during the entire cooling process. As soon as axial temperature gradients become small, the cooling problem for each cross section has some bearings to the one discussed in the previous section (2.1.2.1). It is therefore expected, that the first term on the RHS of (2.9) contributes to wall cooling curves characteristics in about the same way as in the uniform cooling case of section 2.1.2.1. This assumption can be formally phrased as follows.

In a region close to the wall, where

e

(r) ~ O. a local heat transfer

coefficient a (r) can be defined by

(2.12) a(r) q(r) /

e

(r) _ A d

e / e

(r)

d r

Differentiation of this defining equation yields

Note that a (R) can be replaced by a • From this relation and the defining equation of I (see section 2.1.2.1), one easily establishes

I(R) Bi + a R) / (~)

r R

In the case of uniform cooling I(R) equals 1, as was seen in section 2.1.2.1. For TVP applications, the Biot number has values in the range

(10-

4

, 10-2), and I(R) can therefore be approximated as follows;

(2.13)

In analogy with the case of uniform cooling it is now postulated that

(2.14) ~ (R) «

1

d x

e

e

x (R) and ~ d t e d (R) «

1

d

e

t (R)

The consistancy of this approach can of course be checked by putting a solution into equation (2.13) to evaluate the terms in (2.14).

With the definition

(2.15) B (1 + I(R) )

the following equation is now derived from equations

(2.9)

and

(2.10).

It describes the temperature profile along the surface:

(2.16) d 8 (R)

d t (R)

Let 6(x) be Dirac's delta-function and Q be the total heat extracted from the thermocouple during the cooling process. Let ~ be equal to

Since Q = _{1T P Cp}

It

_oo/''dx (Tsurf(t=O) - To)' the axial surface temperature profile imposed by an explosive spot cooling at t=o can be written as

Equation (2.16) with boundary condition (2.17) can be solved in the usual way, by splitting of variables and by a Fourier transformation, to yield: (2.18) 8 _sur f(x,t) = (0/ (2pC _p 1TR~/1Ta _~ t» exp( - - - - B _{4a t} x2 t)

2.1.2.3 Uniform cooling; radial temperature drop. Now suppose that heat q is extracted uniformly during the time T • If t < T then :

(2.19)

_a

_{surf(x,t) = 0}

_f

t _{dt' q exp(-}

4~t'

2

Using an adapted Laplace transformation the integral in

primitivated to obtain:

(2.19) was

(2.20)

e

f(x,t) ={q / 4pC T 1(a8)} .{exp(/(Bx2/a».(-1 + erf(

sur p

+

l(x

2/4a t) ) ) + exp(- I(Bx2_{/a».(1 + erf(1'I31t -}

_l(x

2_{/4a t) ) ) }}

Ifx=O:

(2.21 )

a

f(Ott) = q erf( 1l3f) / (2p C T 1T R~

sur p ~ )

If B

=

0, t

=

T and x = 0 equation (2.19) yields

(2.22) 8 surfeD, T) = q / ('IT

It

I(

1T A p C_p T) )

The suffix "surf" will now be dropped. Strictly speaking only surface temperatures will be calculated in the following. but in view of the results of section 2.1.2.1 and because of the fact, that Biot numbers are less than 0,01 , temperature drops inside the cylinder are small as compared to the

temperature difference T - T •

a surf

With this prerequisite the weighted thermocouple radius,

Bk,

can be

substituted by R

k• Equation (2.22) with this substitution was already employed in section 2.1.1.

2.1.2.4 Non-uniform, bounded heat fluxes. Define, for t ~ T:

(2.23) ~ (x,t, T) =

e

(x,t) /

e

(0, T)

where

e

(x, t) and

e

(0, follow from equations (2.20) and (2.21 )

respectively. Let an amount of heat, q, be extracted by a heat current that is uniformly rising in the time interval

(0,

1):

(2.24) q(t)

=

2q t / 12

Note that q

=

IT

dt q(t) and that Q(t)

=

(2/ T )

o

t

f

dt' q / 1 , if t ::ii 1 •

o

The latter integral implies that during each time interval dt' a spot heat sink of strength q/1 has become active. The heat current

q

is therefore a superposition of heat currents of the type discussed in section 2.1.2.3.

For the heat current defined by equation (2.24) the following normalized temperature profile holds:

(2.25)

t

~1!(x,t,1,2) = (2/1)

J

dt'f.(x,t-t',1) o

The index 2 will soon become clear.

A more general heat current is defined by

(2.26) q(t) = c q t / 12 + d q / 1

with d

=

1 - c/2. The second term on the RHS of equation (2.26) was already treated in section 2.1.2.3, while the first term on the RHS of (2.26) contains the parameter c that was equal to 2 in equation (2.25). If t::iii 1 :

(2.27) t; "(x,t, T ,c) = (c/2) ~ II(X,t, T ,2) + (1 - c/2) f. (x,t, 1 )

I f t> T then

(2.28) ~ "(x,t, 1 ,2)

=

(2/ T ) tdt't;(x,t-t',1) o

wi th for t > T :

(2.29) ~ (x.t, T) =

(e

(x,t) -

e

(x,t-T) ) /

e

(0, T)

in which two continual, uniform heat currents with equal strength but different starting point were combined.

2.1.2.5 Non-uniform, non-local cooling and reheating. If a droplet impinges on a surface it will spread out to form a thin circular liquid film with approximately constant radius R

f (see section 1.3 and its references). Let its centre be at distance x from the thermocouple welding, and let y measure the

a

axial distance from its centre. It is now assumed that heat extracted in the volume between y and y + dy is proportional to the area covered by the film, which equals 2R_fdY

1(1 -

(Y/R

f

)2).

If Q denotes the instantaneous heat release caused by the liquid film, then

yields the following expressions for the normalized temperature distributions due to a circular liquid film with radius R

f :

(2.31 )

(2.32)

Of course, if t exceeds T , then ~" , ( t)

Since ~ =

e

(x, t) / 8 (0, T), the correction parameter 4>10 (see section 2.1.1.2) is given by

(2.33) 4>~O= E;,~x • I(t

x

I

T)

where ~ '" denotes the maximum value of the normalized temperature curve max

that is represented by

E;,"'.

2.1.2.6 Some typical evaporation curves. The notation for c, d, T and x

o' Rf is adopted from the previous sections 2.1.2.

Equations (2.8) and (2.15) show that typical B values lie in the range 0 -300, if I(R) ~ 1. Values of the product

B.T

are therefore less than about 20.

t

8 en ~ 0

...,

u ro

....

en 4 c -rl TI ro OJ H D. U1 0 glass

~

beeswax cellulose acetate o 2 4 6 -6 Impact energy (10 Nm) - - - - t ...

After Ford and Furmidge (1967) data for water on various substances

Figure 8

Spreading factor versus impact energy Influence of static contact angle

It is noted that for chromel-alumel, values of the thermal diffusivity, a, may vary from 5,3.10-6 m2_{/s at 380 K up to 6,3.10-}6 _m2_{/s at 800 K.}

The convective heat transfer coefficient, ~ , depends on thermocouple geometry and flow parameters, but can be derived from values of :

Nu

=

~ 0 / A-Pr

=

p C / A p Re

=

V 0 / v (Nusselt number) (Prandtl number) (Reynolds number)

Nu

=

a + b (T tc

I

Values of the correlation parameters a, b, c, d and e are given by Grober et ale (1961), and depend on thermocouple geometry and Re. Typical values for a cylindrical geometry are a=O; b=0,8; c=0,25; d=O,39; e=0,31.

Typical values of a for TVP application range from 100 up to 104 W/m2_{K, as} already noted in expression (2.8).

The spreading of a droplet is measured by the radius of the droplet film after collision, R_f, or by the ratio

8

= 2Rf/r. Spreading phenomena are considered in more detail in chapter 4. If the impact energy, the sum of kinetic and

f ° -6 Q ° 4 d

sur ace energles of a droplet, less than 6.10 Nm, ~ varles between an 8 (see figure 8, adapted from Ford and Furmidge, 1967). For impact energies

-9

less than 10 Nm the spreading is determined by the static contact ,¢

(270 _{for water on nickel) in the following way}

(2.34)

s

3 = 32 sin3

¢I

{1 - COS¢)2 (2 + cos¢)

yielding a value of 4,4 for the water-nickel combination.

A nominal value of 8 for TVP application is 6. A typical droplet diameter is

-5 -5

5.10 m, and a typical value of R

f is therefore 8.10 m. o ... <D ... <D c. a

'"'

"0 Q) k ::J

...,

'"

k Q) g. Q)

...,

-0 Q) N 0r1 ...; ro

~ ~

o~----~~

____

~~~

________________ - ,

0,2 0,4 0,6 0,8

--

-x :: 0 o

o '"

0 f B :: 0

1,oJ---~---~----~----_T---r_----~---0,05 0,10 0,15 0,20 0,25 0,30 Time (5) __ Figure 9

Normalized temperature curves; influence of B

It will be demonstrated in section 2.1.4.5 that an uncertainty in the value of

of about 70

%

is still acceptable for droplet size estimation.

~ r> 0 <D "-([)

..

a. 0 1-1 -0 III 1-1 ::J

...,

co 1-1 III a. E III ..., -0 III N .,..; .-! co E

t

1-1 0 Z 0 __ ---, 0,4 0,8 1,2 0,05 0,10 0,15 0,20 Figure 10 x ,. 0 o

o ,.

0 f C ,. 0 0,25 0,30 Time (s) _

Normalized temperature curves; influence of c

Typical cooling curves were calculated from equations (2.31) and (2.32). It

turned out that if x ~ , cooling curves with distinct features were

o

obtained that could be analyzed in a relatively easy way.

~

a

r> 0 ([) "-([) 0,2 a. 0 0,4 1-1 -0 III 1-1 ::J

...,

ro _0,6 H III a. E III

...,

-0 0,8 Q) N .,..; ,....; co E

t

1,0 H 0 Z _0,05 0,10 Figure 11

o ,.

10-4 C

=

2/3 B,. 25 f -4 Xo ,. 3.10 Of = 0 C,. 2/3 B,. 0 0,15 0,20 0,25 0,30 Time ( 5 ) _

The following conclusions concerning cooling curve characteristics were drawn:

the product B T generally has great influence (see figure g);

if a heat flux is not constant in time, results are notably affected only if Icl > 2/3 (see figure 10);

the spreading of a droplet has hardly any influence (see, e.g., figure

11) ;

if a droplet impinges besides the thermocouple junction, i.e. if IXol >

0, cooling curves are strongly altered, although the possible

influence of c is strongly reduced (see, for example, figure 11).

2.1.3 Measuring strategy and computation method

In view of the conclusions reached in section 2.1.2.6, the accuracy of the correction parameter ¢10' and hence of the droplet size determination, is

mainly dependent on the knowledge of the evaporation time, T, and the

evaporation location, x • An estimate of T is offered by t (see section

o x

2.1.1), but there is no way of estimating x directly. Since calculations

o

showed (see also section 2.1.2.6) that the initial slope of a cooling curve is strongly influenced by variations in x

o' this slope was quantified by the

temperature ratio 81/82 (see figure 12) and used for estimating x •

o

t

1.2St_x 0.4 tx "--~-+c 0.3 tX--l* ... Figure 12 T Time_ Tavg k

Cooling curve schematics and measuring parameters

For given values of the parameter c and the droplet film width Of

=

2R

f,

equations (2.31) and (2.32) allow for the computation of T and 81/82 for

each set of given values of x and t • This was done by solving the equation

o x

by varying T while keeping other parameters constant. The results for c = 0

and Of = 0 were used to construct figure 13 that yields first estimates x

if not only tx but also B1/B2 is measured from a cooling curve.

Since figure 13 contains many such curves, each corresponding to some value of B, it was named "calibration field", rather than "estimation curve", in the corresponding box of figure 14.

Ul5 1,8 1,75 1,15

t

1.65 N 1,6 CD ... 1.55 CD 1,5 US t.4 1.35 1.3 1.25 1.2 1.15 1.1 UlS

[E

D,=O .04 .08 .12 .18 ,20 .24 ,28 ,32 .36.4 ,44 .46 ,52 .56 .6 Figure 13 W=X/~­_x

Estimation of evaporization location from measurement parameters

This figure 14 summarizes the whole computation method of droplet size, and will now be further discussed.

Apart from parameters defined in figure 12 or listed in the nomeclature, in figure 14 the following notations are used:

a thermal diffusivity (m2_/s)

B 2an (1 + I(d_k/2) ) / d_k A d

k ::;;: 2Rk• Effective diameter of the rod that repre-sents a thermocouple (m)

d <p diameter of thermocouple wire (m) G

d parameter that accounts for temperature dependance

of (H P )

G parameter that accounts for temperature dependance

m

of (A p

e )

p

G_k parameter that accounts for temperature dependance

1 r I' W T _avg k T sat v vapor of (R k)

radius of thermocouple welding

::;;: r_th,1 ' the first estimate of droplet radius (m) ::;;: I' th, 2 ::;;: I' / ¢ w (m)

measured mean temperature level (ae)

saturation temperature (ae)

mean vapor velocity as estimated from mesured superficial velocities (m/s)

vd droplet velocity, either measured directly (section 2.2)

or estimated from v , I' and correlations (m/s) vapor

x ::;;: x_o' the location of evaporation as measured from the thermocouple welding (m)

S

::;;:

_{Of / rw ::;;: 2Rf / rw (-)}

w ::;;: x / 14a t

x It is noted that I(d

k/2) approximately equals 1.

In calculation block 1, a value for r r_th,1 is determined from equation (2.3) with the aid of the parameter

e

_k that depends on G

d, Gm and Gk• In calculation block 2, ¢10 is iteratively determined by minimizing

(2.35) II (8./8. 1 - 8. /8. 1 ) 2

i=1,2,3 1 1+ calculated 1 1+ measured

where 8

4 81 (cyclic permutation). Each individual quadratic term W9S given a lower bound to minimize these three factors together.

The three input parameters 8₁/8₂, 8

BEGIN CALCULATION BLOCK 2 v vapor

...

B

...

tx

...

~/B2 W tx INPUT a

...

CAUBRATION Tav9k CURVE B,/B2 } B,/B3 B2 /B3 Of t. Ot _x Gk dk _CALIBRATION CURVE Gm

...

CALIBRATION

Tavgk CURVE YES

Gd CALIBRATION

Tsal CURVE

NO

Figure 14

Flow chart for the calculation of droplet size

of the three unknowns x, 1 , and c (see also equation (2.32)). The value of

B was set equal to 4a il

I (

A d

k) •

Since the droplet film diameter, Of' was found to have only a minor effect on the calculated results (see also section 2.1.2.6) and since only rough

estimates for

S

can be given, this spreading factor

S

was kept constant

each iteration of block 2. The value of 8 can be adjusted once

(see figure 14).

The varying of Of by ± 70

%

resulted in a spread of ± 10

%

in the calculated

values of ¢ 10'

Only if distinct, ' , thermocouple readings are being analyzed, i.e.

only if x :;:; 14a or w ;;; 0,62, and if the drople is found to evaporate on

the thermocouple welding, i.e. if x < 0,95 1 , the effective diameter, d_k,

is adapted to some value larger than d¢ and close to 2· 1, and calculation block 2 is entered again (see figure 14).

If the thermocouple junction has about the same diameter as the thermocouple wires, this procedure is unnecessary since d

k is equal to d¢ at every

location. The manufacturing of small cylindrical thermocouples is possible (see chapter 5).

2.1.4 Experimental verifications

2.1.4.1 Thermo void probe measuring device. The intrusive measuring device

primarily consists of two thermocouples inserted in a tube of highly

degassed ceramic that is reinforced by a stainless steel capillary tube (see figure 15).

The outer diameter of the ceramic tube is 1,2 mm, while wire diameters used are in the range 0,026 - 0,1 mm. Although thermocouple junctions shown in

figure 15 are large as compared to the wire diameter, it is possible to

manufacture thermocouples in almost a cylindrical shape (see chapter 5). Teflon shieldings and a lava sealant in a special mounting unit (see figure 15) electrically insulate the thermocouples from the stainless steel tube wall that can be heated with Joule's heat, and allow for a pressure drop of more than 200 bar in the device.

The mounting unit is readily installed in a tube (see figure 15) with use of O-rings. Therefore rapid replacement and easy repair are possible. An electric connector at the end of the unit also facilitates quick replacement

(see figure 15).

Figure 15 (overleaf)

Thermo void probe measuring device

THERMAL VOID PROBE

thermocouples in a ceramic tube

mounting unit

unit mounted in a test tube

A TVP unit encompasses two thermocouples. Each thermocouple is

electronically conditioned in the way depicted in figure 16. The optional

thermocouple (T/C

2) is at constant temperature level close to the mean

temperature of a TVP thermocouple, and is used to increase the sensitivity

of the conditioning and hence the measurements accuracy if the TVP is

operated at high system pressures.

I sntht'll!'1d1 plafle Offset

ric

C===

Htdlt-in

Figure 16

Thermo void probe electric conditioner

The conditioner has an automatic ice point compensator.

Cer,>:';,al power suer>,,·

..

:-.. ~ tch

.. 1:>-' ~r '

A TVP unit can be mounted on locations wher.e the electric potential is

different from the earth (common) ground potential. The signals are

registred and monitored in the way described by Van der Geld (1985).

2.1.4.2 Experimental set ups. Measurements were performed in two

experimental set ups:

Type I (Enlarged TVP simulation set up)

Droplets were produced with the aid of adapted capillary tubes; superheated steam heated up a chromel-alumel thermocouple made of bars with a diameter of 10 mm. The system pressure at measurement

Type

location was about 1 bar.

Inlet temperature of droplets was measured with another thermocouple just before they were released from a capillary tube.

Droplet sizes and velocities were measured with high speed

fotography, and weight of droplets was measured with the aid of a precision balance after gathering a number of droplets on ice so as to prevent evaporation.

:IT (actual TVP set up)

Droplet detection thermocouples of a thermo void probe (see section

2.1.4.1) catched droplets produced by liquid atomizers in

superheated steam. System pressures up to 10 bar.

Droplet sizes and velocities were measured with high speed

cinematography (frame speed 4000 pictures per second) and with a

laser doppler velocitometer.

Thermocouple readings were analyzed with the aid of a Hewlett Packard frequency analyzer (HP 5420A).

2.1.4.3 Large diameter thermocouple measurements. A typical temperature

measured with the 10 mm diameter thermocouple bar (type I

measurement. see section 2.1.4.2) is shown in figure 17.

I measurements allowed for repetition of droplet impingement and

keeping constant of droplet size, and hence for reduction of the error in the mean value of the calculated droplet radius. Relative reading errors for input parameters amounted to

3 % for S(B. / S.) / (B. / B.) 1 J 1 J 4 % for S(

e

t ) /

_e

_tx 1 % for Set ) / t _{x x} % for S(T_avg ) / T , k avgk

Typical relative errors for calculated parameters amounted to

7 % for S( Cl ) / Cl

2

%

for droplet size determination by measuring weight loss

The result for a typical test, after averaging over a number of droplets was

r_th,2 = 1,45 ± 0,03 mm

while weight loss measurement yielded

rweight

=

1,46 ± 0,02 mm

t

u o 154 20 Figure 17 60 100 140 Time (5) _

Specimen of temperature history; 10 mm thermocouple

In general the agreement between values of r_th,2 and rweight was very good.

2.1.4.4 TVP verification measurements. A typical temperature history

~~~~--~--~~~~~~--~~~~~~~

measured with a TVP is shown in figure 18; the diameter of the thermocouple amounted to 0,10 mm.

The best results were obtained with droplets with diameters in the range 0,04 - 0,07 mm and with thermocouple diameters of 0,0265 mm and 0,1 mm. From 18 droplet size measurements during a single test run a mean droplet

radius of 0,04 ± 0,003 mm was calculated. For error estimates see section

2.1.4.3. The temperature drop

e

tx varied between 20 K and 71 K for the

9nal1er couple, and between 3 K and 9 K for the larger couple. 20 to 40

%

of

the total evaporation took place at the smaller thermocouple.

t

120 u 0 QJ '-' :J -'-' ro '-' (l) I I 117 E ill t-114

f'~

/ I 1 \

I

I

I

_, 0,5 Figure 18 , I

I

j J I 1,5 2 Time (5) ..

Specimen of temperature history; 0,1 mm thermocouple

This experiment was repeated without the smallest, leading thermocouple. The mean droplet radius was determined under the same conditions with the

aid of only the 0,1 mm thermocouple. The result was 0,036 ± 0,004 mm, which

is in good agreement with the former result.

No other means of comparison was available, since high speed cine recordings for these specific experiments were found to be systematically unsuccesful.

2.1.4.5 On void fraction estimation. Figure 18 clearly shows how the vapor void fraction, £ , can be estimated from

(2.36) 1 - £ = (1/A ).

N~

T) _1 4 1T r3 / 3

t . vd avg

with At = effective scattering cross sectional area (1T d2 /4);

N(T) / T = number of hits per second, which can be determined directly from a thermocouple reading (see figure 18; vd

=

mean droplet velocity;

r = mean droplet radius. avg

At high steam qualities, the droplet velocity can be estimated from the superficial steam velocity and some correlation for the relative droplet velocity as a function of the droplet size (see chapter 3). Another way is to measure droplet velocities directly, and will be discussed in section 2.2.

No accurate comparison data were available for the calculated values of the vapor void fraction.

2.1.4.6 Varying measurement conditions. In annular-mist flow a water film is flowing adjacent to the tube wall. If such a water film can reach the top of a superheated thermo void probe, the reheating of thermocouples after evaporation of the initial cooling water may appear to happen non-uniformly. Special precautions have to be taken to prevent this from happening.

Figure 19 clearly shows that "isothermal plateaus" occur during the heating up of a thermocouple. High speed fotography showed that in downflow these

plateau's were caused by some water, that was gathered underneath the

capillary tube of a TVP, moving towards the thermocouple and evaporating there. Not until all this water was evaporated the isothermal plateaus had disappeared.

It is noted that temperature rises inbetween the isothermal plateaus are described by equation (2.11) of section 2.1.2.1.

An effective way to avoid plateau-heating at annular-mist flow is the

mounting of some water barrier near the end of the capillary tube of a TVP unit. A small piece of stainless steel that surrounds the capillary tube proved to be efficient.

The following practical recommendations are added to the measuring strategy