Influence of flow regime and thermal power on residence time distribution in tubular Joule Effect Heaters

Abstract

To improve treatment homogeneity in tubular Joule Effect Heater (JEH), geometric modifications could be used even in laminar regime inducing flow perturbation and mixing.As a response variable, residence time distribution (RTD) is an important parameter and it has been commonly used in determining the performances of industrial heat exchangers.In present work, our objectives were (i) to investigate the impact of processing conditions (flow regime, heat flux) on RTD in an industrial JEH equipped with smooth and modified tubes, (ii) to contribute to the estimation of treatment homogeneity versus global energetic performances of heat exchanger and (iii) to validate a general reactor model.Analytical solution and systemic analysis of RTD signals were reported.The evolutions of mean reduced variance, β 2 against efficiency number, Eff for smooth ( β 2 = 0.00129 · Eff − 0.0300, R 2 = 0.992) and modified ( β 2 = 0.000547 · Eff − 0.0169, R 2 = 0.979) tubes exhibited a similar and linear relationship.Under the conditions investigated (38 < Re < 10,000, 4 < Pr < 950 with Newtonian fluids), treatment homogeneity was significantly improved by modified geometry and strong interactions between heat transfer and hydrodynamics.A significant decrease in reduced variance under both laminar ( β ST 2 = 0.1054 · Exp - 0.00518 · P / ( ρ · Q ) , β MT 2 = 0.0661 · Exp - 0.00342 · P / ( ρ · Q ) ) and turbulent ( β ST 2 = 0.00624 · Exp - 0.00447 · P / ( ρ · Q ) , β MT 2 = 0.00108 · Exp - 0.00195 · P / ( ρ · Q ) ) regimes was observed versus heat energy.However geometric modification and heat treatment affected the residence time distribution and specifically reduced variance, β 2 within same order of magnitude.Systemic analysis of experimental data enabled to evaluate two reactor models:Dispersed Plug Flow (DPF) and Plug Flow (PF) + 2 Continuous Stirred Tank Reactor (CSTR) with and without convolution and with 1 or 2 degrees of freedom.Second model could be considered as the most accurate model to predict RTD in JEH with an accurate degree of confidence for residence time and reduced variance estimation ( τ = 0.995 · t s R 2 = 0.64, error < 3% and β 2 = 0.3119 · β exp 2 0.73 R 2 = 0.98 ) and a simplified model with only 1 degree of freedom can be used.