Critical heat flux prediction in rod bundles under upward low mass flux densities

Nuclear Engineering and Design 183 (1998) 249 – 259

Critical heat flux prediction in rod bundles under upward low mass flux densities V.B. Khabensky a, S.D. Malkin a, V.V. Shalia a, B.I. Nigmatulin b,* b

a Russian Research Center ‘Kurchato6 Institute’, 1 Kurchato6 Sq., Moscow 123182, Russian Federation Research and Engineering Center of Nuclear Plants Safety, Bezymyannaya 6, Electrogorsk, Moscow 142530, Russian Federation

Received 21 March 1996; received in revised form 30 December 1997; accepted 30 December 1997

Abstract The analysis of experimental data and results of calculations for heat transfer crisis in heated channels under low upward coolant mass flux densities is presented. This analysis allows the determination of the basic features of the boiling crisis phenomenon. It is shown that the methods currently used for critical heat flux (CHF) prediction have insufficient accuracy in the given range of parameters. A new relationship for the CHF calculation is presented. It should be used for the water–water energy reactor (WWER) and uran – graphite channel reactor — Chernobyl-type (RBMK) rod bundles, and is verified by the test data. The comparison of results obtained by a new CHF correlation and the relationship used in RELAP5/MOD3.1 Code is presented. It is shown that the latter overpredicts the CHF values at atmospheric pressure and for xcr \0.4 and does not provide conservative estimations for the RBMK fuel bundles. © 1998 Elsevier Science S.A. All rights reserved.

1. Introduction A review of the literature shows that a limited amount of theoretical and test data on heat transfer crisis at low velocities and pressures have been published (McAdams et al., 1949; Averin and Krujilin, 1959; Mirshak et al., 1959; Labuntsov, 1961; Macbeth, 1964; Bergles et al., 1967; Gaspary et al., 1973; Knobel et al., 1973; Lucchini and Marinelli, 1974; Katto, 1979, 1981; Mishima Abbre6iations: CHF, critical heat flux; RBMK, uran – graphite channel reactor (Chernobyl-type); WWER, water – water energy reactor (PWR-type). * Corresponding author. Fax: +7 09643 30515; e-mail: [email protected]

and Ishii, 1982; Rogers et al., 1982; Mishima and Nishihara, 1985a,b; Mishima et al., 1987; El-Genk et al., 1988; El-Genk and Rao, 1991; Domashev, 1994; Kim et al., 1995; Sergeev et al., 1995; Umekawa et al., 1995). These data show certain difficulties of crisis phenomena investigation. They are: superposition of various mechanisms of crisis appearance; the problem of localization of the crisis point and estimation of parameters at that moment; strong influence of the external circulation loop, strong influence of structure peculiarities of the test facility and channel geometry on the crisis phenomena; necessity of accounting for hydrodynamic interaction of parallel channels in multichannel systems such as reactor cores.

0029-5493/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0029-5493(98)00156-3

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Published experimental and theoretical results on heat transfer crisis for given conditions do not clarify the influence of different design and regime parameters on critical heat flux (CHF) value and are often contradictory. The correlations for CHF suggested are not versatile and usually describe experimental data on a particular test facility within a narrow range of parameters. Analysis of the test data allows some relationships to be obtained for the improvement of the CHF correlations for the low upward coolant velocities (rw B300 kg (m2 · s) − 1). These experimental data are considered below.

2. Analysis of experimental data

2.1. Stable coolant flowrate The most complete experimental investigations on heat transfer crisis in tubes, annular and slot channels under upward flow conditions are presented in Mishima and Ishii (1982), Rogers et al. (1982), Mishima and Nishihara (1985a,b), Mishima et al. (1987), El-Genk et al. (1988), El-Genk and Rao (1991), Kim et al. (1995), Umekawa et al. (1995) and Sudo et al. (1995). The same data on rod assemblies are presented in Smolin and Polyakov (1967), Gaspary et al. (1973), Lucchini and Marinelli (1974), El-Genk and Rao (1991) and Sergeev et al. (1995). The main results obtained in these works are discussed below. In Mishima and Nishihara (1985a), coolant stable delivery in the circulation loop is provided by strong throttling at the channel inlet. Some results of these tests are shown in Fig. 1. The main tendencies shown in this figure are in accordance with the data of other authors (Lucchini and Marinelli, 1974; Mishima and Ishii, 1982; Rogers et al., 1982; El-Genk and Rao, 1991; Mishima and Nishihara, 1985a,b; Mishima et al., 1987; Kim et al., 1995) for tubes, annular and slot channels and rod bundles. For low mass flux densities (rw B 180–250 kg (m2 · s) − 1), the critical heat flux depends practically in linear way on the mass velocity and

reaches its minimal value at rw = 0, which corresponds to the critical channel power with no coolant delivery (q Tcr = N Tcr/H). The critical power N Tcr is defined by known relationships presented, for example, in Balunov et al. (1987) or Spart et al. (1987). It is shown in Fig. 1 that at some boundary mass flux density (rw)b, the gradient of qcr from rw decreases significantly. For rw\(rw)b, one can use the relationships for qcr derived for heated channels and rod bundles on the basis of experimental and calculational investigations for middle and high mass flux densities. Thus, (rw)b presents the lower limit of calculational relationship applicability for high mass flux density. Transition between these two regions (small and large derivatives (qcr/(xcr ) in experimental investigations (Mishima and Ishii, 1982; Rogers et al., 1982) takes place under mass flux densities in the range rw = (160–300) kg (m2 · s) − 1. The mass flux density value corresponding to the point of sharp change of (qcr/(xcr may be found according to Mishima and Nishihara (1985a,b) from the condition of the approximate equality between velocities of the two-phase flow and the phase driftage.

Fig. 1. Critical heat flux in slot channel vs. mass flow rate under upward coolant flowing by Mishima and Nishihara (1985b). (1) Dtin :15°C; (2) Dtin :40°C; (3) Dtin :70°C.

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In fact, for certain parameter ranges, especially under small heat flux values, the heat transfer crisis arising is governed by a liquid film break on the heated surface by steam flow having a critical velocity. The steam velocity is defined as follows: wv =C0 j+Vnj

(1)

where j is a mixture velocity, C0 =1.2, and Vnj is a phase drift velocity obtained from Khabensky et al. (1994). Eq. (1) shows that with C0 jB Vnj, steam velocity and hence critical steam velocity strongly depend on phase drift velocity. The actual velocity increases, therefore, in comparison with the balance one and provides stronger growth of the critical heat flux. If C0 j\ Vnj, drift velocity influence on critical steam velocity is diminished and the gradient of the critical heat flux from mass flux density decreases. Therefore (qcr/(xcr decreases also. The boundary mass flux density corresponding to gradient (qcr/(xcr change may be estimated from the condition: C0 j=kVnj

(2)

Taking into account that rlVnj rvVnj at k=3, we can get according to Mishima and Nishihara (1985a): (rw)b =

rlVnj C0

(3)

The values of (rw)b obtained by Eq. (3) for experiments (Rogers et al., 1982; Mishima and Nishihara, 1985a,b) are: (rw)b :200 kg (m2 · s) − 1, which correspond to experimental data. The values of (rw)b obtained by Eq. (3) for RBMK and WWER rod bundles conditions are in the range 270 – 320 kg (m2 · s) − 1, depending on circulation loop pressure. Hence, for RBMK working channels and WWER rod bundles, we assume (rw)b =300 kg (m2 · s) − 1.

2.2. The thermohydraulic instability influence on heat transfer crisis Experimental investigations (Mishima and Nishihara, 1985a,b; Mishima et al., 1987; Khabensky and Gerliga, 1995; Kim et al., 1995;

Fig. 2. Influence of inlet throttling on heat transfer crisis in tube under upward coolant flowing by Mishima and Nishihara (1985b). Dtin =40°C.

Umekawa et al., 1995) show that when there is a weak inlet coolant throttling in heated channels at low mass flux densities and pressures, thermohydraulic instability often takes place. Fig. 2 presents test data (Mishima and Nishihara, 1985b) for the same experimental channel under two different conditions. In the first case, the stable inlet delivery takes place, while the in the second one there is slight inlet throttling. In the latter case, flow thermohydraulic instability like density waves was observed. It can be seen in Fig. 2 that thermohydraulic instability decreases the critical heat flux more than 2-fold. Similar results have been obtained recently (Kim et al., 1995) for identical channels in a loop with forced convection (stable coolant flowrate) and in a loop with natural convection (experimentally observed flow thermohydraulic instability). It is shown in Umekawa et al. (1995) that thermohydraulic instability impacts indirectly on heat transfer crisis through coolant delivery and mass steam quality decrease during the oscillation cycle of the flow parameters. This influence depends on flowrate oscillation amplitude and frequency as well as on transient heat conductivity in the fuel rod, and on transient heat transfer from the rod

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surface into the coolant. Attempts to obtain the correction coefficients, taking into account twophase flow thermohydraulic instability for critical heat flux values obtained by steady-state relationships, were unsuccessful. In order to do this, the user needs not only to find the stability boundary but also the oscillation parameters for the instability region. They can be derived only by means of numerical solution of transient conservation equations both for the test channel and for the whole circulation loop. The possibility of using the transient thermohydraulic mathematical model of a steam-generating channel with steady-state closure relationships for the critical heat flux for heat transfer crisis prediction is shown in Umekawa et al. (1995). This paper presents results of experimental investigations of the heat transfer crisis in tubes under inlet harmonic oscillations delivery with various amplitude and frequency values. The results of numerical solution of the transient thermohydraulic model of a channel with corresponding boundary and initial conditions are also presented. The comparison of experimental data and results of calculation from Umekawa et al. (1995) is presented in Fig. 3; their coincidence is usually good.

Fig. 3. Comparison of results of calculation and test data on delivery oscillation amplitude and frequency influence on qcr by Umekawa et al. (1995). G0 = 400 kg (m2 · s) − 1, P=0.4 MPa, Tin =80°C. (1–3) Experiment; (4–6) calculation (Umekawa et al., 1995); (7–9) Eq. (4). (1, 4, 7) t =2 s; (2, 5, 8) t= 2 s; (3, 6, 9) t= 6 s.

The critical heat flux decreases with increasing relative oscillation amplitude, DG/G0. With increasing oscillation period, t, the critical heat flux decreases and stabilizes at a certain level, according to Ozawa and Umekawa (1994):





qcr = a(Tw − Tl) 1− exp − 0.5 where tT =



rwCpw r 2out − r 2in a 2rin



n

t tT

−1

(4)

(5)

Here, rin, rout are the tube internal and external radii, and a is the heat transfer coefficient given by the steady-state relationship. Thus, the numerical calculation based on the transient thermohydraulic model with a steadystate closure relationship for critical heat flux can be used for prediction of the heat transfer crisis under flow oscillations. Since the coolant delivery oscillation parameters in the channel may also depend on the external circulation loop, the complete mathematical thermohydraulic model, including both heated channel and loop, is to be solved.

3. Analysis of relationships for CHF calculation Experimental data on heat transfer crisis under low velocities are scarce, especially for rod bundles, and as a result, uncertainty in the understanding of the crisis mechanism causes a low accuracy of calculational relationships for the CHF. A typical comparison between experimental data (Mishima and Nishihara, 1985a; Mishima et al., 1987) and well known calculational relationships is given in Figs. 4 and 5. The low accuracy of these relationships, even for such simple geometry as tubes and slot channels, is evident. CHF values obtained experimentally are significantly lower than those calculated. That is why these relationships cannot be used for reactor safety analysis. Recently, there have been published relationships for CHF prediction which generalize experimental data for low coolant velocities and

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Fig. 4. Comparison of experimental data on crisis in slot channel with calculational relationships under upward coolant flow by Mishima and Nishihara (1985a). Relationship 1 (Katto, 1981); relationship 2 (Mirshak et al., 1959); relationship 3 (Labuntsov, 1961); relationship 4 (Macbeth, 1964); relationship 5 (Kirillov et al., 1984).

pressures at the stable coolant flowrate (Mishima and Ishii, 1982; Mishima and Nishihara, 1985a,b, 1987; Mishima et al., 1987; Mishima and Nishihara, 1987). They are as follows: (a) For low mass flux densities: q*cr = q*cr T + q*cr =

Fcs Diin (rw)* Hh



Fcs Di (rw)* 1 + in H h

(6a)



(6b)

q*cr = q*cr T +A(rw)*

(6c)

where q*cr =

qcr h[lrvg Dr]0.5

(rw)* =

rw [lrvg Dr]0.5

Also, q*cr T = N Tcr/H is the critical heat flux at (rw)in =0; l= [s/(g Dr)]0.5 is Laplace’s constant; A is an empirical constant; and Fcs and H are the cross-section area and the channel heat transfer surface, respectively. (b) For moderate and high mass flux densities:



 n

q*cr = q*cr,0 1 + 12

Diin h

2

(7a)

q*cr =

Fcs Diin (rw)* H h

(7b)

where q *cr,0 = 0.155 is the relationship for the heat transfer crisis in a pool of saturated liquid. Eq. (7a) is recommended for the stable channel mass flowrate. With ‘soft’ circulation, loop q *cr,0 in Eq. (7a) falls to q *cr,0 = 0.046. Even qualitative analysis of Eqs. (6) and (7) shows that they are not universal and generalize only experimental data obtained on particular test facilities for a restricted parameter range. For example, Eq. (6a), derived from Kim et al. (1995), and Eq. (6b), derived from Mishima and Ishii (1982), generalize test results at x *cr,out = 0 and x *cr,out : 1, respectively. The authors do not explain under which conditions this range is realized and do not recommend the relationship for 0B x *cr,out B 1. Eq. (6c), derived from Mishima and Nishihara (1985a), is an approximation of experimental data and should not be used for the geometry of other channels or for other regime parameters. Similar remarks should be made for the relationships Eqs. (7a) and (7b) for middle and high

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Fig. 5. Comparison of experimental data on crisis in tubes with calculational relationships under upward coolant flow by Mishima et al. (1987). Dtin = 70°C. Relationship 1 (Katto, 1981); relationship 2 (Kirillov et al., 1984); relationship 3 (Macbeth, 1964).

mass densities. Eq. (7a), derived from Mishima et al. (1987), is in fact a relationship for the boiling crisis in the pool; it is helpful only for channels with a small value of L/deq and is useless for RBMK and WWER rod bundles. Eq. (7b) determines the critical heat flux only for x *cr,out = 0, which is outside of RBMK and WWER regime parameters. At present, Groeneveld’s interpolation technique is most commonly used for low mass flux densities and pressures, and is incorporated in the RELAP5/MOD3.1 code (Carlson et al., 1990). However, because of the scarcity of experimental data used for its development, it has a low accuracy.

We shall try to obtain a new, more accurate correlation for CHF prediction at low upward coolant mass flux densities for RBMK and WWER rod bundles.

4. A new correlation for CHF prediction in RBMK and WWER rod bundles at rwB 300 kg (m2 · s) − 1 To obtain a new relationship for CHF in RBMK and WWER rod bundles at low mass flux densities, we shall use previously mentioned general physical tendencies: 1. Minimal critical heat flux at (rw)in = 0 can be determined by known relationships for rod

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bundles with no inlet delivery (see, for example, Balunov et al., 1987; Spart et al., 1987). 2. For rw =0 – 300 kg (m2 · s) − 1, CHF changes linearly. 3. CHF at rw =300 kg (m2 · s) − 1 is defined by the relationship for rod bundles used under middle and high mass flux densities. In this case, rw = 300 – 400 kg (m2 · s) − 1 is the application lower boundary. Different mechanisms of boiling crisis are possible at middle and high mass flux densities in rod bundles. For example, Fig. 6 summarizes experimental data (Jukov, 1994) for qcr(xcr) with different mass flux densities for WWER-440 rod bundles. For high mass flux densities, the relationship qcr =f(xcr) has three regions of alternative qcr change. In the first region (small xcr), with xcr increase, CHF decreases monotonously and practically linearly. Sometimes this region is called the ‘departure of nucleate boiling’ (crisis of the first kind). In the second, CHF behavior is characterized by high values of derivative (qcr/(xcr . Sometimes, this region is called ‘the dryout crisis’ (crisis of the second kind). The third region corresponds to monotonous CHF change with quality and is called ‘the wetting crisis’. With mass flux densities decrease (Fig. 6), the first kind of crisis region grows, and the gradient of CHF by quality decreases. At rw 0500 kg (m2 · s) − 1, the first kind of crisis region extends along the whole xcr range.

255

Therefore, when determining qcr at rw = 300 kg (m2 · s) − 1 in the whole range of xcr, one may use the first kind of crisis relationship, which is recommended for rod bundles with a lower application limit of rw= 300–400 kg (m2 · s) − 1. For this purpose, the correlation presented in Smolin and Polyakov (1967) which is verified by test data for RBMK and WWER rod bundles, may be used: qcr = 0.65A(p)(rw)0.2(1−x)1.2

(MW m − 2)

(8)

where

Á1.3–4.36 · 10 − 2p; pE 3 MPa A(p)= Í1.16; 1.00pB 3 MPa Ä1.16p 0.15; pB 1.0 MPa

(9)

Eq. (8) is obtained by CHF test data processing for RBMK and WWER rod bundles at 0 B x *cr,out B 1 and has high accuracy at rw= 0–300 kg (m2 · s) − 1. Taking into account all the facts mentioned above, we assume that the improved CHF correlation for RBMK and WWER rod bundles at rw = 0–300 kg (m2 · s) − 1 may be expressed in the following form:



qcr = 1−



rw T rw q cr + q 300 300 cr rw = 300

(10)

where q Tcr = N Tcr/H is the average critical heat flux at rwin = 0; N Tcr is the critical power of the rod bundle at rwin = 0 determined by Balunov et al. (1987) or Spart et al. (1987); H is the rod bundle heat transfer surface; qcr rw = 300 is the critical heat flux at rw = 300 kg (m2 · s) − 1. At rw =300 kg (m2 · s) − 1, Eq. (8) is as follows: qcr = 2A(p)(1−x)1.2

(11)

Using Eq. (11), Eq. (10) is:



qcr = 1− Fig. 6. Experimental relationship between critical heat flux and local quality for WWER-440 rod bundle, P =7.4 MPa by Jukov (1994). (1) rw= 600 kg (m2 · s) − 1; (2) rw= 1500 kg (m2 · s) − 1; (3) rw= 2500 kg (m2 · s) − 1.



rw T rw q cr + A(p)(1− x)1.2 300 150

(MW m − 2)

(12)

where A(p) is defined by Eq. (9), and q Tcr is calculated by the following relationship:

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Fig. 7. Comparison of Eq. (12) with experimental data in rod bundle (Lucchini and Marinelli, 1974); P =7.0 MPa, Dtsub = 10 – 80°C. (1 – 3) Experimental data in 16-rod bundle (Lucchini and Marinelli, 1974); (4–6) Eq. (12); (1, 4) rw=115 kg (m2 · s) − 1; (2, 5) rw= 250 kg (m2 · s) − 1; (3, 6) rw= 500 kg (m2 · s) − 1. T cr

q = 6.75 · 10

−9

hr 0.5 v [sg(rl −rv)]0.25 H

  n

× 1+

rv rl

0.25

−2

(MW m − 2)

(13)

Eq. (12) allows CHF to be calculated for RBMK and WWER rod bundles for rw = 0 –300 kg (m2 · s) − 1.

Fig. 8. Comparison of Eq. (12) critical heat flux and experimental data in rod bundle (Smolin and Polyakov, 1967); P= 3.0 MPa. (1, 2) Experimental data in three-rod bundle (Smolin and Polyakov, 1967); (3, 4) Eq. (12); (1, 3) rw=150 kg (m2 · s) − 1; (2, 4) rw= 250 kg (m2 · s) − 1.

this range of parameters. The subcooling influence is indirect and is depicted in Fig. 11. In reality, according to Eq. (12), for given pressure and mass flux densities, CHF depends on critical quality qcr = f(xcr). If xcr decreases, qcr increases. With the inlet subcooling increase, for the maintenance of a given xcr it is necessary to increase the heat flux. However, Fig. 11 demonstrates that the critical heat flux increase is not so

5. Validation of the correlation Eq. (12) is verified by available experimental data on the heat transfer crisis in rod bundles under low mass flux densities. Comparison of the results of calculations by Eq. (12) and test data (Smolin and Polyakov, 1967; Lucchini and Marinelli, 1974; El-Genk and Rao, 1991; Sergeev et al., 1995) is given in Figs. 7 – (10). Despite the fact that the experimental data have been obtained in different ranges of parameters: pressure, quality (xcr) and coolant inlet subcooling (Dtin), Figs. 7–10 show that the agreement is rather good. It should be mentioned that Eq. (12) provides good agreement with the test data with different subcooling, although the latter is not included in Eq. (12) explicitly. This fact allows the conclusion that the boiling crisis has a ‘local character’ for

Fig. 9. Comparison of Eq. (12) with Becker’s experimental data for rod bundle from El-Genk and Rao (1991). P= 0.3– 0.64 MPa, Dtsub =35 – 110°C. (1 – 3) Becker’s experimental data for rod bundle from El-Genk and Rao (1991); (4 – 6) Eq. (12); (1, 4) rw= 65 kg (m2s) − 1; (2, 5) rw =155 kg (m2 · s) − 1; (3, 6) rw=245 kg (m2 · s) − 1.

V.B. Khabensky et al. / Nuclear Engineering and Design 183 (1998) 249–259

Fig. 10. Comparison of Eq. (12) critical heat flux with experimental data for 19-rod bundle by Sergeev et al. (1995). (1 – 3) Experimental data at Tin = 60°C: (1) P= 2 bar; (2) P=4 bar; (3) P= 6 bar; (4) Eq. (12).

257

Fig. 11. Influence of coolant inlet subcooling on critical heat flux under channel uniform heating. Dtin2 \Dtin1. (1) Relationship qcr =f(x); (2) relationship of heat flux in channel from outlet steam quality.

strong as the heat flux increase caused by the inlet subcooling increase (Dqcr BDq). CHF values given by Eq. (12) are compared with those obtained by the RELAP5/MOD3.1 code. The results for the RBMK rod bundle are presented in Table 1. At P\ 0.1 MPa and xcr \0.4, the RELAP5/ MOD3.1 CHF correlation significantly overestimates the critical heat flux and does not provide conservative estimations for the RBMK rod bundles.

6. Conclusions The analysis of test data for the heat transfer crisis and relationships for CHF prediction in rod bundles for upward coolant flow at rw B 300 kg (m2 · s) − 1 is fulfilled. It is shown that the accuracy of known CHF correlations for rod bundles and more simple channels in a given range of mass flux densities and low pressures is not sufficient.

Table 1 Comparison of qcr (MW m−2) in RBMK-1000 working channel by Eq. (12) (numerator) and RELAP5/MOD3.1 (denominator) xcr

p (MPa)

rw1 (kg (m2 · s)−1) 0

25

50

100

150

200

250

300

0.1

0.1 3 7

0.01/0.10 0.01/0.35 0.01/0.45

0.09/0.18 0.13/0.76 0.11/0.75

0.16/0.32 0.24/1.42 0.21/1.20

0.30/0.66 0.47/2.80 0.40/2.15

0.55/0.74 0.79/3.15 0.67/2.38

0.80/0.81 1.10/3.50 0.94/2.60

1.05/1.12 1.48/3.80 1.25/2.61

1.30/1.43 1.85/4.1 1.55/2.62

0.4

0.1 3 7

B0.01/0.08 B0.01/0.25 B0.01/0.30

0.05/0.15 0.07/0.55 0.06/0.40

0.12/0.26 0.16/1.06 0.14/0.60

0.26/0.50 0.34/2.10 0.30/0.95

0.41/0.58 0.57/2.35 0.48/1.28

0.55/0.65 0.80/2.60 0.65/1.60

0.73/0.91 1.04/2.78 0.88/1.74

0.90/1.17 1.27/2.95 1.10/1.88

0.6

0.1 3 7

0.01/0.05 0.01/0.16 0.01/0.20

0.05/0.12 0.07/0.38 0.06/0.25

0.08/0.24 0.12/0.77 0.11/0.35

0.15/0.45 0.22/1.55 0.20/0.55

0.25/0.51 0.35/1.63 0.30/0.70

0.34/0.56 0.48/1.70 0.40/0.85

0.45/0.66 0.63/2.03 0.53/1.00

0.55/0.75 0.78/2.35 0.65/1.15

0.8

0.1 3 7

B0.01/0.03 0.01/0.08 0.01/0.09

0.02/0.06 0.04/0.14 0.03/0.15

0.04/0.11 0.06/0.27 0.05/0.26

0.07/0.21 0.10/0.52 0.08/0.48

0.11/0.23 0.16/0.59 0.14/0.56

0.15/0.24 0.21/0.66 0.19/0.63

0.20/0.27 0.27/0.74 0.25/0.69

0.25/0.30 0.33/0.82 0.30/0.75

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A new correlation for CHF prediction in rod bundles is suggested. This correlation has an ‘interpolational’ character and gives its boundary values: for the ‘blind’ channel (at rw “ 0) and for the case with high mass flux densities (rw “ 300 kg (m2 · s) − 1). The relationship suggested in this paper is verified by available experimental data for CHF in rod bundles. It is shown that its accuracy is rather high. The relationship suggested is compared with the CHF calculational algorithm used in RELAP5/ MOD3.1 code for the RBMK core channel within a wide range of parameters. It is shown that the CHF relationship used in RELAP5/MOD3.1 significantly overestimates CHF test data and values given by Eq. (12) and therefore does not provide conservative estimations for the RBMK rod bundles.

7. Nomenclature Cp F g h H i j N P q r T Vnj w x

specific heat cross-section area acceleration due to gravity evaporation heat heat transfer surface enthalpy mixture velocity power pressure heat flux density tube radius temperature phase drift velocity velocity equilibrium quality

Greek symbols a heat transfer coefficient r density s surface tension t oscillation period Subscripts b, lim boundary parameter cr critical

ex in l out T v w

external parameters at inlet; internal liquid parameters at outlet ‘blind’ vapor wall

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