Particle volume flow rate measurement by combination of dual electrical capacitance tomography sensor and plug flow shape model

Highlights

• Particle volume flow rate measurement by dual ECT combined plug flow shape model.

• Particle plug flow is divided into three regions: Tip, Filling and Tail regions.

• Measurement of velocity and volume flow rate of plug flow using permittivity signal.

• Volume flow rate shows good agreement with high speed camera's result.

• Absolute error of our method is less than conventional Cross-correlation method.

Abstract

Particle volume flow rate Q_PLUG^· in plug flow through a cross section of horizontal pipe has been accurately measured by a combination of dual electrical capacitance tomography sensor and plug flow shape model (dECT-PFSM). The plug flow shape model divides the trapezoidal shape of the plug flow into three flow regions which are Tip, Filling, and Tail regions. The plug flow volume V_PLUG is estimated by velocity and length which are measured in each region by the normalized permittivity signal changes obtained from the dECT images under the plug flow in the trapezoidal shape. The path time difference of the plug flow Δt_PLUG is also measured. The total volume flow rate of the plug flow is subsequently obtained from the sum of the plug flow volume of the three regions divided by Δt_PLUG. Consequently, the volume flow rate of the plug flow obtained by dECT-PFSM Q_{ECT, PFSM}^· is compared with that of high-speed camera (HSC) as reference and conventional cross-correlation (CC) method. The absolute error E_abs of the proposed method is less than that of the CC method. The dECT-PFSM method is, therefore an affordable noninvasive technique for accurate determination of the volume flow rate of the plug flow.

Introduction

The particle volume flow rate in the steel making industries is one of the key parameters in particles-gas two-phase flow in order to characterize the particle-gas two-phase flow [1]. An accurate, reliable, on-line and non-invasive measurement method of particle volume flow rate is necessary to achieve the efficient utilization of energy and raw materials [2].

The particle-gas two-phase flow is investigated for dense phase flow because dense phase flow is commonly used in steel industry [3]. A flow in the dense phase where the particles travel in plugs that occupy the entire pipe cross-section is called a plug flow. In horizontal pipe the plug flow is determined as a stationary particle group and a flowing particle group. The stationary particle group usually occurs in the last part of the plug flow [4]. Conventionally, the volume flow rate of the particles in the particle-gas two-phase flow was measured using digital imaging [5] and a radiometric sensor [6,12]. These methods are invasive, unsuitable for low-velocity measurements and ineffective for use with large pipes.

As a non-invasive visualization method, Electrical Capacitance Tomography (ECT) method is useful for the particle plug flow measurement [[7], [8], [9], [10], [11]]. In order to measure the volume flow rate of the particle plug flow, the velocity and the cross-sectional area of the particle plug flow are needed. To measure the velocity of the particle plug flow, a dual ECT (dECT) sensor is used. The velocity is calculated by the path time of two signals detected by the dECT sensor and the distance between two sensors' center position. Some researchers used dECT sensor combining cross-correlation (CC) method which was used for velocity estimation in order to obtain the particle volume flow rate of plug flow [13]. However, the difficulty of CC method in velocity estimation is to decide the precise signal peaks detected by the dECT sensor in order to estimate time delay. Thus, the accuracy of CC method also depends on the stability of the flow shape [14]. Moreover, the CC method is measured the mean velocity and the time average volume flow rate of the particle group. To overcome the limitation of time delay estimation, V. Mosorov currently proposed a new cumulative-signals-based method to determine the time delay of noised signals [15]. Although this method is more accurate than the CC method for estimating time delay while using highly noised signals, this method did not emphasize one plug flow condition because the velocity is suddenly changed in dECT sensor under the plug flow condition. Therefore, the authors consider the velocity variation during the plug flow passing through dECT sensor based on the signal obtained by dECT sensor combined with a plug flow shape model which estimates the velocities in several regions of the plug flow in order to measure the particle volume flow rate for single plug flow in the particle-gas flow.

This paper proposes a novel measurement method of the particle volume flow rate for the particle plug flow in a pipe. A plug flow shape model combined with dECT sensor is established to measure the particle volume flow rate. The plug flow shape model divides a plug flow into three regions: Tip, Filling, and Tail regions. The signal path time difference, velocity, length and volume of plug flow are determined at each region based on the normalized permittivity signal obtained by dECT sensor. Thereafter, the volume flow rate is obtained from the sum of the volumes at the three regions and the signal path time difference. In experiment, the experimental results obtained by the proposed method is validated with the high-speed camera (HSC) and CC methods in terms of the velocity, length, and volume flow rate for seven experiments.