Contents lists available at ScienceDirect Journal of Water Process Engineering journal homepage: www.elsevier.com/locate/jwpe Global velocity gradient evaluation: An innovative approach using CFD modeling applied to water and wastewater treatment plants Danieli Soares de Oliveira a, ⁎ , Clainer Bravin Donadel b a Department of Production Engineering, Federal Institute of Espírito Santo – campus Cariacica, Rodovia G. José Sette, 184, Itacibá, Cariacica-ES, 29150-410, Brazil b Department of Electrical Engineering, Federal Institute of Espírito Santo – campus Vitória, Av. Vitória, 1729, Jucutuquara, Vitória-ES, 29078-040, Brazil ARTICLEINFO Keywords: CFD modeling Global velocity gradient Helically coiled tube flocculators Hydrodynamics Water and wastewater treatment ABSTRACT ThispaperproposesanalternativeapproachforestimatingtheGlobalVelocityGradientparameter( G)through hydrodynamic characteristics using Computational Fluid Dynamics Modeling (CFD). In the design of water and wastewatertreatmentplants,severalhydraulicandgeometricparametersareneededtoguaranteetheefficiency ofthetreatmentprocesses.Amongtheseparameters, G isestimatedusingempiricalequationsorprototypes.The use of empirical equations is a simple and fast way to estimate G but they are often incompatible with the geometryoftheunit,leadingtoahighnumberoferrors.Ontheotherhand,theuseofprototypesleadstohigher accuracy,buttheirconstructionistimeconsumingandcanbeverycostly.Thus,anin-depthanalysisofthebasic equations for obtaining G and of CFD modeling aspects can assist in obtaining this parameter without using empirical equations or prototypes. The proposed approach was tested in six flocculation units based on helical geometry (called Helically Coiled Tube Flocculators -HCTFs). As a result, a high correlation between G ob- tained from prototypes (used as reference) and G obtained from the corresponding CFD modeling results was verified(withadeterminationcoefficienthigherthan0.9995),indicatingthatthisapproachcanbeapromising tool for designing new water and wastewater treatment units and the improvement of existing ones. 1. Introduction The Global Velocity Gradient ( G),definedinCampandStein[1]as ametricoftheagitationdegreeoftheliquidmassinsideareactor,isan important design parameter in water and wastewater treatment units (especiallyinflocculators).Inthesecases,theagitationmustbeenough topromoteaninteractionbetweenvariousparticlestoformlargerflocs for later removal by sedimentation/flotation; and the agitation cannot promotethedisintegrationoftheflocspreviouslyformed,whichwould undermine the efficiency of the process. Two different methodologies were used to evaluate G: empirical equations and prototyping. Empirical equations are developed for standardized configurations such as straight tubes and helically coiled tubes.Asanexample,VigneswaranandSetiadi[2]andAl-Hashimiand Ashjyan [3] present G prediction models based on experimental results intheirstudies.Theuseofempiricalequationsisastraightforwardand fast way to estimate G, but they are frequently incompatible with the unit geometry, leading to a high number of errors. The use of prototypes to evaluate G is widespread due to its high accuracy. However, their construction requires a considerable amount of time and can be very costly, especially when units with several geometrical characteristics are built. As an example, Oliveira and Teixeira[4]built30differenthelicalflocculationunitstoobtain G with distinct reactor lengths, winding diameter and tube diameter. In the literature, Computational Fluid Dynamics (CFD) modeling has been applied to improve the water and wastewater treatment pro- cess [5–7]. In this way, the use of CFD modeling to evaluate G is a promising tool for the design and improvement of new and existing units since it is unnecessary to build prototypes and several different configurationscanbetestedwithminimaleffort.Thispaperproposesa novel approach for estimating G through hydrodynamic characteristics using CFD. The remainder of this paper is organized as follows: Section 2 pre- sentsaliteraturereviewconcerningthemainaspectsof G evaluation;in Section 3, the proposed methodology is presented; in Section 4, nu- merical results are presented and the results obtained through the ap- plication of the proposed methodology are discussed in detail. The conclusions to this are presented in Section 5. 2. Literature review Thepioneeringworkinthestudyof G wascarriedoutbyCampand https://doi.org/10.1016/j.jwpe.2018.12.009 Received 2 July 2018; Received in revised form 2 December 2018; Accepted 27 December 2018 ⁎ Corresponding author. E-mail addresses: danieli@ifes.edu.br (D.S.d. Oliveira), cdonadel@ifes.edu.br (C.B. Donadel). Journal of Water Process Engineering 28 (2019) 21–27 2214-7144/ © 2019 Elsevier Ltd. All rights reserved. T