Rod bundle

For annuli only, appheation of a factor of O.lOiDo/Dif is recommended for Eqs. (5-81) and (5-82). For more accurate semiempirical relationships for tubes, annuh, and rod bundles, refer to Dwyer [Am. Inst. Chem. Eng. J., 9, 261 (1963)]. 

Further information on liquid-metal heat transfer in tube banks is given by Hsu for spheres and elliptical rod bundles [Int. J. Heat Mass Transfer, 8, 303 (1965)] and by Kahsh and Dwyer for oblique flow across tube banks [Int. ]. Heat Ma.ss Transfer, 10, 1533 (1967)]. For additional details of heat transfer with liqmd metals for various systems see Dwyer (1968 ed., Na and Nak supplement to Liquid Metals Handbook) and Stein ( Liquid Metal Heat Transfer, in Advances in Heat Transfer, vol. 3, Academic, New York, 1966). 

The above conclusion must certainly be taken with a measure of reserve as regards the mass velocity, for at very low velocities it appears reasonable to expect that the relative motion between vapor and liquid in a boiling channel will be affected sufficiently to influence the burn-out flux. Barnett s conclusion also applies to simple channels, whereas Fig. 35 discussed in Section VIII,C shows that a rod-bundle system placed in a horizontal position is likely to incur a reduction in the burn-out flux at mass velocities less than 0.5 x 106 lb/hr-ft2, presumably on account of flow stratification. Furthermore, gravitational effects induced in a boiling channel by such means as swirlers placed inside a round tube can certainly increase the burn-out flux as shown by Bundy et al. (B23), Howard (H10), and Moeck et al. (Ml5). 

Effectively what Barnett (B3) did was to confirm the validity of Eq. (18) using burn-out data for water in round tubes. Subsequently, Eq. (18) was applied to more extensive round-tube data (M3, Tl), to annuli (B6), rectangular channels (M3), and rod-bundle arrangements (M4), using simple mathematical expressions for A and C, and a consistently high accuracy was achieved. Details of the respective correlations obtained are given in Section VIII. 

Burn-out data and descriptive details of 24 different rod-bundle geometries, representing all known published work up to 1965, have been compiled and analyzed by Macbeth (M4). Data that have subsequently appeared are given by Matzner (M10), Janssen (J2), Edwards and Obertelli (El), Becker et al. (B11), Moeck (M14), and Hesson (H3). All these data refer to water, and in most of the bundles the direction of water flow is vertically upwards, parallel to the heated rods however, a few tests have also been made with the bundles horizontal, also using parallel flow. Nearly all the experiments have been performed at around 1000 psia, so that the correlation of rod-bundle data must be restricted to this pressure alone. 

Fig. 32. Example of the linear effect of inlet subcooling on burn-out in a rod bundle using water at 1015 psia [from Matzner (M9)].

Fig. 34. A simple geometry relationship with the basic burn-out flux for rod bundles. (j)o x 10" 6 = Ki G x 10 6)1/2. Details of the rod bundles are given in Table V.

TABLE V. Geometry parameters and K, and K2 Values for 1000 psia (Nominal) Rod-Bundle Data ... 

Fio. 35. Effect on burn-out of rod-bundle orientation. Bundle geometry as described for bundle No. 4, Table V. Test pressure 1215 psia. 

There are several possible explanations of the apparent conflict between Figs. 34 and 35. One possible explanation, for example, would be that the vertical upflow curve drawn in Fig. 34 may not be a straight line, but should perhaps curve upwards (the data itself shows some signs of this) toward the uppermost point of the horizontal flow line, which corresponds to the rod bundle in question. It will be seen later, however, that this would not appear to be the explanation. In addition, there is the fact that all the horizontal flow data in Fig. 34, as well as the new data in Fig. 35, are for a test pressure of 1215 psia, whereas the vertical upflow data in Fig. 34 refer to 1000 psia. Although there is no evidence to indicate the effect of pressure in the case of rod-bundle systems with round tubes, it is found that increasing pressure from... 

The analysis given in Macbeth (M4) continues by assuming that the term dh effectively represents the cross-sectional geometry of the normal rod-bundle data. If this assumption is correct, then the general correlation [Eq. (18)], may be applied by representing A and C as functions of G and dh for a given pressure. It was found that simple power functions were adequate, and a correlation was obtained by computer optimization which predicted 97% of the vertical-upflow normal data (Nos. 6-15 inclusive in Table V) to within 12%. 

Among the additional data examined, the only non-normal characteristics found were for some of the results in (M10), which again, as in the earlier investigation (M4), apply to 19-rod bundles with wire-wrap supports. The consistent pattern that now seems to be emerging is that it is only the use of wires wrapped around the rods that causes nonnormal characteristics. It seems that the addition of a wrap around the complete bundle, as was the case for test sections No. 10 and 11 in Table V, prevents the nonnormal characteristics from appearing. 

An annular test section consisting of a heated rod inside an unheated shroud tube is of particular interest, since it raises the question of whether or not, from the point of view of burn-out behavior, it belongs to the family of rod bundles. Barnett (B6) has examined the question and has found clear evidence in support of the idea. 

The first step was to correlate the annulus data, which, fortunately, are mostly for a pressure of 1000 psia, the same as is the case for rod bundles. A compilation of the 1000 psia data is included in Barnett s report (B6), most of the experimental work being due to Janssen and Kervinen (J3), a summary of the range of system parameters involved in the total of 744 experimental results listed is given below (in all cases, the central rod is uniformly heated, and there is liquid water inlet with vertical upflow) ... 

Having obtained an accurate correlation for the annulus data at 1000 psia, Barnett applied it, for the same pressure, to the rod-bundle data, and Figs. 36 and 37 are two very convincing demonstrations of the connection that clearly exists between an annulus and a rod bundle. The method used in applying the annulus correlation was to assume a dt value equal to the diameter of the rods in the bundle considered, and a d0 value such that both annulus and bundle had the same heated equivalent diameter dh. All the normal rod-bundle data with vertical upflow were found to be well represented by the annulus correlation, but the nonnormal data showed the same disparity that was found in the rod-bundle analysis. Thus, we have a further indication that the non-normal rod bundles are showing markedly different burn-out behavior. 

Fig. 36. Comparison of burn-out data for a 4-rod bundle (No. 9, Table V) with Barnett s annulus correlation [from Barnett (B6)].

The above result for the 9-in. wrap is interesting, since the drop in burnout flux it causes is similar to the effect of using 9-in. wraps in rod bundles. In the previous section, these bundles were identified as having nonnormal characteristics. 

The connection that has been shown in Section VIII to exist between burn-out in a rod bundle and in an annulus leads to the question of whether or not a link may also exist between, for example, a round tube and an annulus. Now, a round tube has its cross section defined uniquely by one dimension—its diameter therefore if a link exists between a round tube and an annulus section, it must be by way of some suitably defined equivalent diameter. Two possibilities that immediately appear are the hydraulic diameter, dw = d0 — dt, and the heated equivalent diameter, dh = (da2 — rf,2)/ however, there are other possible definitions. To resolve the issue, Barnett (B4) devised a simple test, which is illustrated by Figs. 38 and 39. These show a plot of reliable burn-out data for annulus test sections using water at 1000 psia. Superimposed are the corresponding burn-out lines for round tubes of different diameters based on the correlation given in Section VIII. It is clearly evident that the hydraulic and the heated equivalent diameters are unsuitable, as the discrepancies are far larger than can be explained by any inaccuracies in the data or in the correlation used. 

All the references to burn-out have thus far been concerned with uniformly heated channels, apart from some of the rod bundles where the heat flux varies from one rod to another, but which respond to analysis in terms of the average heat flux. In a nuclear-reactor situation, however, the heat flux varies along the length of a channel, and to find what effect this may have, some burn-out experiments on round tubes and annuli have been done using, for example, symmetrical or skewed-cosine axial heat-flux profiles. Tests with axial non-uniform heating in a rod bundle have not yet been reported. 

B6. Barnett, P. G., A correlation of burn-out data for uniformly heated annuli and its use for predicting burn-out in uniformly heated rod bundles, AEEW-R.463 (1966). 

B8. Batch, J. M., and Hesson, G. M., Comparison of boiling burn-out data for 19-rod bundle fuel elements with wires and warts, HW 80391, G. E. Hanford Lab., Richland. Washington (1964). 

BIO. Becker, K. M., A correlation for burn-out predictions in vertical rod bundles, paper presented at Symp. Boiling and Two-Phase Flow, EURATOM, ISPRA, June 1966. 

H3. Hesson, G. M., Fitzsimmons, D. E., and Batch, J. M., Experimental boiling burnout heat fluxes with an electrically heated 19-rod bundle test section, BNWL-206 (1965). 

M4. Macbeth, R. V., Burn-out analysis. 5. Examination of published world data for rod bundles, AEEW-R.358 (1964). 

M14. Moeck, E. O., Dryout in a 19-rod bundle cooled by steam/water fog at 515 psia, ASME Paper 65-HT-50 (1965). 

Transient Two-Phase Flow in Rod Bundles Pressure Drop in Two-Phase Flow... 

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