Particle residence time distributions in a vortex-based solar particle receiver-reactor: An experimental, numerical and theoretical study

Highlights

• Particle residence time distributions measured in a novel solar particle receiver.

• Systematic variation of particle size, gas volumetric flow rate and inlet velocity.

• Two regimes of particle behaviour, characterised by the Stokes and Froude numbers.

• Compartment model of plug flow reactor followed by two interconnected CSTRs.

Abstract

We report a joint experimental, numerical and theoretical study of particle residence times in a novel vortex-based vessel for thermal processing of suspended particles. The tracer pulse-response method, in which the particle phase itself is employed as the tracer, is used to measure the particle residence time distribution (RTD) within a laboratory-scale model of a class of Solar Expanding Vortex Receiver-Reactor (SEVR). The operating parameters of particle size, gas volumetric flow rate and inlet velocity were systematically varied to assess their influence on the particle RTD and to determine the mechanisms controlling the behaviour of the two-phase flow in the SEVR. The particle RTD behaviour is also described by a compartment model consisting of a small plug flow reactor followed by a series of two interconnected continuously-stirred tank reactors (CSTRs).

Introduction

The residence time distribution (RTD) of particles is widely used to characterise the performance of thermo-chemical particle reactors. The RTD of particles describes the probability distribution of the residence times of particles within a vessel for a given set of operational conditions, which is difficult to predict a priori without experimental data due to the complexity of two-phase gas-particle flows. This is particularly the case in strongly recirculating flows such as those in swirling turbulent systems, owing to their non-linear behaviour (Allal et al., 1998, Lede et al., 1987, Li et al., 2008). One such type of swirling particulate device is the vortex-based class of solar particle receiver-reactors, in which particles are conveyed by a vortex flow of gas through the irradiation zone from a solar concentrator. This two-phase gas-particle flow is confined within a cylindrical cavity in devices that have been demonstrated with several solar thermochemical applications at laboratory-scale (Davis et al., 2017, Steinfeld et al., 1992, Z'Graggen et al., 2006). Knowledge of the particle RTD within a vessel is needed because most particulate vessels do not conform well to the classical idealisation of either a well-stirred reactor, with uniform properties through the vessel, or a plug-flow reactor, in which all fluid and particles have the same residence time (Danckwerts, 1953, Nauman, 2008). Furthermore, the behaviour of particles is likely to be different from that of the transporting gas (Lede et al., 1987), particularly for cases where the Stokes number of the gas-particle flow is greater than unity (Chinnici et al., 2015). The overall objective of the present paper is, therefore, to support the development of vortex-based solar particle receiver-reactors and similar vortex-based particle devices by providing both new experimental data and understanding of the particle RTD within them.

Vortex-based solar particle receiver-reactors, typically referred to as Solar Vortex Receivers (SVRs), have been demonstrated experimentally at laboratory-scale for the thermal decomposition of natural gas (Hirsch and Steinfeld, 2004), the steam-gasification of carbonaceous feedstocks (Z'Graggen et al., 2006) and the calcination of alumina (Davis et al., 2017). Each of these investigations was conducted with a configuration in which the concentrated solar radiation is introduced into a cylindrical cavity through an aperture sealed by a transparent quartz window to directly irradiate a suspension of reacting particles in a vortex flow of gas. The vortex gas-particle flow proceeds through the cavity and exits with elevated temperature reported of order 1000°C. This class of solar particle receiver-reactor has the advantage of highly efficient heat transfer to the particle phase due to both direct irradiation by concentrated solar radiation and indirect irradiation due to the cavity effect, as demonstrated by the high values of chemical conversion reported for residence times on the order of seconds. Additionally, SVRs also have the potential to operate without a window, so that the cavity is open to the atmosphere (Chinnici et al., 2015, Moumin et al., 2019, Steinfeld et al., 1992). Whether the SVR operates atmospherically-open or as a closed system with a window, detailed RTD data for both cases is required. However, no previous direct measurements of particle residence time have been reported for such an entrained flow solar particle receiver-reactor, which differs significantly from alternative solar particle receivers, such as falling curtain and centrifugal type receivers that do not have a gaseous flow. The particle trajectories within an entrained flow device are highly dependent on the gaseous flow field. In the absence of measured data, previous assessments have relied on the nominal particle residence time, based on the ratio of receiver internal volume to gas volumetric flow rate (τ_nom = V_r/V̇_gas). However, both the gas and particle phase residence times in a vortex flow configuration can differ significantly from this nominal residence time and will likely exhibit a wide distribution of residence times (Shilapuram et al., 2011). Therefore, it is desirable to characterise not only the mean residence time, τ̅_p, but also the full function of the RTD, including its normalised variance, σ_p² = σ_p,t²/τ̅_p² (Buffham and Mason, 1993, Gao et al., 2011) and the time required for a given fraction of particles (e.g. 90% of the inlet stream) to exit the vessel. For this reason, we aim to characterise the full function of the distribution of particle residence times in a SVR for a series of operating conditions.

An alternative class of SVR technologies has recently been developed, with a view to capitalising on the high energy conversion efficiency of the original device developed by Z'Graggen et al. (2006), while also mitigating some of its limitations. The new class of vortex-based device reduces the transport of particles through the aperture (Chinnici et al., 2015, Chinnici et al., 2016) and also generates a RTD that increases with the particle size for particles larger than a critical value characterised by the Stokes number (Chinnici et al., 2015). This is desirable because large particles require longer residence time for heating and reaction than small ones. The new configuration, termed the Solar Expanding-Vortex Particle Receiver-Reactor (SEVR), has a conical inlet section at the opposite end of the cylindrical cavity to the aperture and a radial outlet at the aperture end of the cavity (Chinnici et al., 2015). The different orientation of the outlet (radial) to that of the flow (tangential) is important to inhibit the exit of larger particles from the chamber due to their greater inertia. These proposed mechanisms have been partially validated by an experimental investigation into the flow field (Chinnici et al., 2016), but no direct assessments of particle RTD are available for either the SVR or the SEVR devices. The radially-oriented outlet of the SEVR, together with the conical expansion represents a significant departure of the device from earlier SVR configurations which could be idealised as a cyclone within a cylindrical tube; a configuration that has been extensively researched previously (Cortés and Gil, 2007). While there is a limited amount of work on single-phase flows in similar devices to SEVRs used in combustion applications (Syred, 2006, Valera-Medina et al., 2009), there is still a need to understand two-phase flow in cylinders with conical expansions and a radially-oriented outlet. Hence, a further aim of the present investigation is to provide new understanding of the influence on the particle RTD of the key controlling parameters of particle size, gas flow rate and inlet velocity, spanning the range of configurations that can be classified as a SEVR.

The influence of receiver orientation on the performance of SVRs is also of interest because the alignment of gravity relative to the axis of the SVR will influence both its optical and thermal performance. For example, Chinnici et al. (2015) proposed that a vertical orientation helps to recirculate particles to the base of the conical section where velocity is greatest to facilitate their recirculation. While the significance of the orientation on the optical performance of the solar concentrator is beyond the scope of the present assessment, it should be noted that together with central tower systems (Ho and Iverson, 2014), there is significant growth in the development of beam-down solar concentrating systems (Bellan et al., 2019, Chirone et al., 2013, Kodama et al., 2014, Tregambi et al., 2016, Yogev et al., 1998), together with many variations between these two extremes. In addition, no experimental measurements are available of the influence of receiver orientation on the particle residence time within any configuration of SVR. Hence, there is a need to assess the role of alignment relative to gravity of the SEVR on the particle RTD.

Experimental methods with which to measure particle residence time within particle processing vessels have advanced from those measuring only a mean value (Lede et al., 1987, Li et al., 2008, Szekely and Carr, 1966) to those measuring the full distribution of residence times in micro-detail. Particle RTDs are typically measured with the well-established stimulus response method of detecting the concentration with time of tracer particles using techniques such as phosphorescence (Harris et al., 2002), colour (Kieviet and Kerkhof, 1995), ferromagnetism (Guío-Pérez et al., 2013), chemically-doping (Kang et al., 1989), difference in electrical permittivity (Cai et al., 2014) and size (Mitsutani et al., 2005). However, methods requiring the off-line detection of the tracer (Kang et al., 1989, Kehlenbeck et al., 2002, Kieviet and Kerkhof, 1995, Mitsutani et al., 2005) have temporal resolution on the order of 10⁻²–10⁰ Hz, which is insufficient for a vortex-based particulate vessel at laboratory-scale, whose residence time is on the order of seconds. Optical measurement of particles offer a fast response, inline and non-intrusive method of tracer detection that can be based on light emission, scattering or extinction (Amaral et al., 2015). Such tracer particle detection methods have been used to measure particle RTDs in similar devices to SVRs (Lede et al. (1987) Allal et al. (1998) and are suitable for operation in dilute particle volume fraction regimes so that the injection of particles has negligible impact on the steady-state gas flow (Elghobashi, 1994). However, previous assessments of particle RTD in similar particle devices with optical techniques have not measured the particle RTD as a function of Stokes number (or particle size), so that it is impossible to distinguish the effect of particle diameter from that of turbulence on the particle RTD. In recent work, monodisperse particles have been used to isolate the influence of Stokes number in jet flows (Lau and Nathan, 2016), and in the present case, offer the possibility of using the light extinction method to isolate the influence of Stokes number (and particle size) on the RTD within a vortex-based particulate vessel. Therefore, a further aim of the paper is to isolate the influence of Stokes number on the particle RTD through evolution of previous methods, notably through the use of inlet and outlet optical extinction measurements of a pulse of monodisperse particles introduced to the inlet of a particulate device.

Simple flow models of reactors typically assume either a uniform residence time in a plug flow reactor, PFR, or perfect mixing of the flow in a continuously-stirred tank reactor, CSTR, (Danckwerts, 1953, Nauman, 2008), although real receiver-reactors deviate from these ideal flows. Hence it has become common to use the compartment modelling approach to model a real device as the sum of ideal flow reactors (PFRs and CSTRs) by comparison with measured RTDs. This analytical approach advances understanding of the device and provides a useful design tool (Gao et al., 2012), having been applied to circulating fluidised beds (Guío-Pérez et al., 2013, Kehlenbeck et al., 2002) and a liquid-solid classifier (Mitsutani et al., 2005). A further aim of the present investigation is, therefore, to seek to decompose the measured particle RTDs of the SEVR into a combination of ideal reactors.

In summary, the aim of the present investigation is to determine the influence of key controlling dimensionless parameters on the particle RTD within vortex-based particulate vessels employing a conical expansion and radially oriented outlets classed as Solar Expanding Vortex Receivers. This is to be done by systematic and independent variation of particle size, inlet velocity and gas volumetric flow rate during steady-state operation. To enable this, we aim to use the well-established pulse response method of particle RTD measurement and inlet/outlet optical extinction measurements of monodisperse particles, so that the influence of particle size may be isolated. The present investigation is undertaken in a beam-down orientation with gravity aligned in the same direction as the central axis of the device as the simplest configuration, while alternative orientations of gravity at various angles to the axis are reported separately (Davis et al., 2019). Additionally, this paper aims to assess the similarities of vortex-based solar particle receivers to the operation of common ideal reactors with a view to relating this to the large-scale dynamics of the device. The measurements presented here are for the device operating with isothermal room temperature conditions because of the need to understand the isothermal particle residence time behaviour before assessing the effects of temperature and buoyancy.