Systematic and exact scaling analysis of the single-phase natural circulation flow: The hydraulic similarity

• A unique hydraulic time scale along with a set of system-level and local dimensionless hydraulic numbers were derived.
• The tube or pipe diameter scaling ratio should be related to the length scaling ratio.
• Three sets of scaling criteria for a full-pressure reduced-size model have been proposed.
• Means for the evaluation of the scaling distortion have also been suggested.

For the study of the hydraulic similarity in a single-phase natural circulation loop, the integral momentum equation is non-dimensionalized with respect to the initial flow kinematic energy of reference section, without intuitively specifying any reference parameters. By this mean, a unique hydraulic time scale, characterizing the system hydraulic response, is identified along with two dimensionless physical numbers: the dimensionless flow resistance number and the dimensionless gravitational force number. From the integral momentum equation, the mass flow rate at steady state is also obtained. The identified dimensionless parameters are then applied to derive a set of scaling criteria for the design of a full-pressure reduced-size similar model for a PWR (Pressurized Water Reactor). For exact hydraulic similarity, it was found for the first time that the cross sectional area scaling ratio should be related to the axial length scaling ratio. In addition, it is also found out that the relative cross-sectional area ratio should be preserved in order to preserve the flow resistances. Moreover, the scaling ratio for the number of the U-tubes was found to be unity if exact hydraulic similarity is pursued for the whole system. Three sets of scaling criteria for the design of a full-pressure model for a PWR are summarized in a table for different application. The accuracy and applicability of this proposed scaling method is demonstrated by proposing a simple loop and a PWR-like system, by scaling down the systems to get two corresponding models with this proposed scaling methodology, and by comparing the model results with their corresponding prototype results. Furthermore, the method for the evaluation of both system-level and local hydraulic scaling distortions are addressed.