Interrogating common clarification models for unit operation systems with dynamic similitude

Surface overflow rate (SOR), plug flow reactor (PFR) and continuously stirred tank reactor (CSTR) are common models for clarification unit operations (UO). With wide deployment in engineering practice and regulation, through tools from spreadsheets to complex numerical codes, these models are formulated based upon conceptualized system geometry (e.g., rectangular channel) and idealized hydrodynamics (plug flow or well-mixed conditions). Yet the hydrodynamics and geometry of actual UO systems can be complex and substantially different from these assumptions. As a result, the applicability and generalizability of these models require critical and systematic interrogation. This study examines the predictive capability and generalizability of these common models for a hydrodynamic separator (HS), tanks, rectangular clarifiers and an urban drainage basin based on physical model data and high-fidelity large-eddy simulation (LES). Moreover, this study presents a novel application of dynamic similitude to developing a more generalized and physically interpretable model based on the hypothesis that PM and PM-partitioned constituent separation in a UO can be approximated solely through the dimensionless settling velocity W (Hazen number). Based on this hypothesis and dynamic similitude, a similarity modified gamma model (SMG) is proposed and tested. With dynamic similitude and W, results show common models are not robust and generalizable for predicting PM separation with error ranging from 30 to 50% and can significantly oversize a clarifier up to 904%. The non-linear characteristics of PM separation are shown to have a critical role in clarifications system design scalability and economics. In contrast, the SMG model is robust and generalizes the PM separation for geometrically similar systems, irrespective of particle density, particle size distribution (PSD), and loading conditions. The developed theory and proposed SMG model also can simplify and reduce the effort as well as expense of physical model testing while serving as an adjuvant for numerical simulations of clarification systems. Results also reveal commercial HS systems do not outperform simple plain tank geometries. The complex turbulence vortical structures pose significant challenges for UO system analysis and design.