2084
Operating Hydrocyclone Air-Core Analysis Using a Sparsity‑Based
Electrical Resistance Tomography (ERT) Algorithm
Suharika Diddi, Narasimha Mangadoddy, Phanindra Jampana
Department of Chemical Engineering, IIT Hyderabad, Kandi (V), Telangana, India
ABSTRACT: This paper discusses air-core identification in experimental work and the utilization of Electrical
Resistance Tomography (ERT) to provide insights into air-core dynamics and visualization. The importance
of ERT image reconstruction algorithms in accurately reconstructing the air core is emphasized. The study
employs a relaxation of polynomial optimization (RBO) to enhance ERT analysis, which reformulates the binary
optimization for computational efficiency. The experimental data of two-phase and three-phase flows has been
studied using the RBO algorithm. Notably, the RBO algorithm effectively aligns with the theoretical trend of
air-core size concerning feed pressure in two-phase operations. A quantitative assessment of the RBO algorithm
is conducted using the threshold technique, with comparative analysis involving the Gauss-Newton (GN) one-
step algorithm. The study delves into the performance evaluation of the RBO method across various spigot
variations, pressure fluctuations, and scenarios involving 20 wt% solids. Phase diagrams are shown for two-
phase and three-phase flow conditions of laboratory hydrocyclone operated with water and slurry for different
spigots, solids content, and feed pressures utilizing the improved ERT algorithm developed in this study.
INTRODUCTION
Hydrocyclone is an essential separation device used in min-
eral processing industries, particularly in comminution,
separation, and product handling for extracting valuable
materials from ore (Radman 2014). They separate over-
sized particles in grinding circuits in the comminution
stage and efficiently separate clean coal, iron, diamonds,
etc. In refineries, they are used for the separation of oil from
water (Bradley 1965). The widespread use of hydrocyclones
across industries is attributed to their structural simplic-
ity, high throughput, compact size, and cost-effective, low
maintenance (Cui et al., 2014). The traditional design of
an industrial hydrocyclone, depicted in Figure 1, typically
comprises a cylindrical section followed by a conical sec-
tion with a specific cone angle responsible for inducing flow
reversal.
Hydrocyclone design contains a single feed inlet and
two product outlets: the vortex finder and spigot (Vakamalla
and Mangadoddy 2017). The separation process utilizes
fluid pressure to initiate rotational motion, facilitating
relative movement among suspended particles in the fluid.
The tangential inlet of the fluid initiates outer rotational
motion, termed the free vortex. Simultaneously, the coni-
cal geometry of the hydrocyclone produces an inward rota-
tional motion known as the forced vortex. Each particle
within the hydrocyclone experiences two primary opposing
forces: one directed outward, induced by centrifugal force,
and the other-directed inward radially, caused by the fluid’s
drag force (Rakesh, Kumar Reddy, and Narasimha 2014).
Due to the high centrifugal forces at play, larger par-
ticles are propelled toward the wall and conveyed to the
underflow discharge at the spigot. Simultaneously, smaller
particles remain in the liquid near the centre, initiating a
Operating Hydrocyclone Air-Core Analysis Using a Sparsity‑Based
Electrical Resistance Tomography (ERT) Algorithm
Suharika Diddi, Narasimha Mangadoddy, Phanindra Jampana
Department of Chemical Engineering, IIT Hyderabad, Kandi (V), Telangana, India
ABSTRACT: This paper discusses air-core identification in experimental work and the utilization of Electrical
Resistance Tomography (ERT) to provide insights into air-core dynamics and visualization. The importance
of ERT image reconstruction algorithms in accurately reconstructing the air core is emphasized. The study
employs a relaxation of polynomial optimization (RBO) to enhance ERT analysis, which reformulates the binary
optimization for computational efficiency. The experimental data of two-phase and three-phase flows has been
studied using the RBO algorithm. Notably, the RBO algorithm effectively aligns with the theoretical trend of
air-core size concerning feed pressure in two-phase operations. A quantitative assessment of the RBO algorithm
is conducted using the threshold technique, with comparative analysis involving the Gauss-Newton (GN) one-
step algorithm. The study delves into the performance evaluation of the RBO method across various spigot
variations, pressure fluctuations, and scenarios involving 20 wt% solids. Phase diagrams are shown for two-
phase and three-phase flow conditions of laboratory hydrocyclone operated with water and slurry for different
spigots, solids content, and feed pressures utilizing the improved ERT algorithm developed in this study.
INTRODUCTION
Hydrocyclone is an essential separation device used in min-
eral processing industries, particularly in comminution,
separation, and product handling for extracting valuable
materials from ore (Radman 2014). They separate over-
sized particles in grinding circuits in the comminution
stage and efficiently separate clean coal, iron, diamonds,
etc. In refineries, they are used for the separation of oil from
water (Bradley 1965). The widespread use of hydrocyclones
across industries is attributed to their structural simplic-
ity, high throughput, compact size, and cost-effective, low
maintenance (Cui et al., 2014). The traditional design of
an industrial hydrocyclone, depicted in Figure 1, typically
comprises a cylindrical section followed by a conical sec-
tion with a specific cone angle responsible for inducing flow
reversal.
Hydrocyclone design contains a single feed inlet and
two product outlets: the vortex finder and spigot (Vakamalla
and Mangadoddy 2017). The separation process utilizes
fluid pressure to initiate rotational motion, facilitating
relative movement among suspended particles in the fluid.
The tangential inlet of the fluid initiates outer rotational
motion, termed the free vortex. Simultaneously, the coni-
cal geometry of the hydrocyclone produces an inward rota-
tional motion known as the forced vortex. Each particle
within the hydrocyclone experiences two primary opposing
forces: one directed outward, induced by centrifugal force,
and the other-directed inward radially, caused by the fluid’s
drag force (Rakesh, Kumar Reddy, and Narasimha 2014).
Due to the high centrifugal forces at play, larger par-
ticles are propelled toward the wall and conveyed to the
underflow discharge at the spigot. Simultaneously, smaller
particles remain in the liquid near the centre, initiating a