A criterion based on independent parameters for distinguishing departure from nucleate boiling and dryout in water cooled systems

Abstract

The critical heat flux is an important parameter for the design of steam generators in conventional steam boilers and in water cooled nuclear reactors; and reliable predictive correlations or models are required for calculation and design purposes. Notwithstanding the large number of studies which have been carried out in the past, at the authors' knowledge no criterion has been developed to forecast the occurrence of a departure from nucleate boiling (DNB) or dryout type thermal crisis on the basis of the fluid inlet parameters and the channel geometry. Therefore thermal-hydraulic designers have to rely on their judgement or on the knowledge of the nominal conditions of the system. The main aim of this work is to demonstrate that there exists the possibility of discriminating between DNB and dryout on the basis of independent parameters. As a first-level approach, two CHF characters were defined, corresponding to the critical thermodynamic quality achieved at the thermal crisis x cr : at quality lower than zero the crisis was assumed to be of DNB type, while at quality higher than zero the crisis was assumed to be of dryout type. According to the wide experimental evidence, the transition from DNB to dryout is a continuous one and depends on several parameters. In practical terms, the thermal crisis may be of DNB type even with critical quality slightly higher than zero. Therefore, a second approach was adopted which is based on the physically well justified assumption that when the critical thermodynamic quality is lower than zero the thermal crisis is (almost certainly) of DNB type, while when the critical thermodynamic volumetric quality x vol, cr is higher than 50 % (i.e. the vapour phase is predominant over the liquid phase) it seems reasonable to assume that the thermal crisis is of dryout type. This latter approach implies that a certain number of data cannot be classified, i.e. those data having x cr > 0 and x vol, cr < 50 %. In this study, a comprehensive data base of 16 844 data points was analysed with a synergetic approach based on a neural network methodology coupled with a physical thermal- hydraulic one. First a network was trained based on all the available information, i.e. the fluid inlet conditions and the geometric and physical parameters (a total of 11 input variables). Then the network structure was modified by reducing or grouping the input parameters based on the thermal-hydraulic expertise and a new network was trained. The iteration of this process led to the identification of three parameters which seem to drive the physical phenomenon, i.e. the mass flux G, the inlet quality x in , and the ratio between the duct length and diameter L D . The product Gx in was considered as representative of the ‘specific degree of subcooling’ introduced in the duct. Starting from this consideration, an analytical criterion was found which is based only on two parameters and is able to classify the data points on the basis of the ratio −Gx in G 0 )/( L D ) , where is G 0 a constant having the dimensions of a mass flux. In the case of the first approach, this simple criterion allowed us to correctly classify 97.1 % of data for the overall database (DB-1), and 99.3 % of data when a sub-group of consistent and accurately verified data was considered (DB-2). In the case of the second approach, the percentage of correct classifications was 98.4 and 99.1 % for DB-1 and DB-2 data, respectively. These results therefore seem to demonstrate the possibility of distinguishing DNB from dryout on the basis of inlet parameters. The proposed criterion can be modified on the basis of a more detailed knowledge of the thermal crisis mechanism, but nevertheless the procedure adopted here can be entirely applied.