Numerical simulation of particulate flow in interconnected porous media for central particle-heating receiver applications
Graphical abstract
Calculated volume fraction distributions of white sand and proppant particles with a single 2.7 cm thick porous block on top of bottom slit.
Introduction
Concerns regarding climate change due to high levels of CO2 emissions, coupled with the rise in fossil fuel costs and heightened concerns regarding the safety of nuclear power, have motivated increased research and development efforts on renewable energy sources in many countries around the world. As a part of these efforts, a 300 kWth concentrated solar power (CSP) test facility is being constructed at the Riyadh Techno Valley development on the campus of King Saud University (KSU) in Riyadh, Saudi Arabia (Golob et al., 2014). The system uses a central receiver power tower as the energy collection subsystem and a gas turbine as the power conversion subsystem.
Among the unique features of this facility is that the energy collection and storage medium will be solid particles (for example sand or other granular material). Solar radiation incident on a heliostat field is concentrated on a receiver through which the sand flows by gravity and is heated to as high as 1000 °C. In addition to serving as the heat collection medium, the sand also serves as the thermal energy storage medium by directing the solar-heated sand exiting the receiver to an insulated storage bin. The sand leaving the bottom of the hot storage bin flows over a heat exchanger where heat is transferred from the sand to the gas turbine cycle working fluid (air). A multi-pass, finned-tube, cross flow heat exchanger will be used for initial testing of the KSU CSP test facility. Other heat exchanger designs, including a direct-contact heat exchanger and a fluidized bed heat exchanger will be evaluated. The KSU system design avoids the temperature limitations and high costs of conventional heat transfer fluids and storage media. It also does not require water cooling; hence, it alleviates many of the obstacles and objections to increased use of CSP in desert environments.
Work on the KSU CSP test facility builds on earlier research on solar particle heating receiver (SPR) concepts, particularly the work of Sandia National Laboratory (Martin and Vitko, 1982, Chen et al., 2006, Ho et al., 2009, Siegel et al., 2010, Ho and Iverson, 2014). Several other direct (Wu et al., 2014) and indirect receiver (Diver, 1987, Glatzmaier, 2011) concepts have also been reported in the literature. The KSU system design overcomes the shortcomings identified by Sandia regarding SPR technology. Specifically, the SPR in the KSU system allows the particulates to flow through a porous structure or a series of chevron mesh screens (instead of a free-falling curtain), thereby significantly increasing the particles’ residence time within the receiver (Al-Ansary et al., 2013). This, in turn, allows the desired temperature rise of the particle stream (e.g. increase from ∼600 °C at the inlet to 1000 °C at the exit) to be readily achieved without the need to recirculate the particles through the receiver cavity prior to transferring them to the hot storage bin. Additionally, the KSU SPR design significantly decreases convective heat losses (because of the reduction in heat transfer area), as well as material (i.e. particulate) loss from the receiver, thereby increasing the receiver efficiency (Golob et al., 2014).
The sand exiting the heat exchanger accumulates in a “cold” (i.e. ∼600 °C) storage bin from which it is returned to the top of the receiver via a variable-speed particle lift. While the operational control strategy for the KSU facility has not been fully developed, it is expected that, for part-load operation, the lift speed (i.e. the particles flow rate) will be controlled to maintain the desired receiver outlet temperature.
Several studies have been made to investigate the behavior of falling particles within solid particle heating receivers. Chen et al. (2006) used computational fluid dynamics (CFD) to determine the velocity and temperature distribution within a free-falling particle receiver. Their analysis is limited to cases where the solid particle volume fraction inside the solar absorber is very low. In a follow-up study, Siegel et al. (2010) tracked the particle motion and the gas flow within a free-falling solid particle receiver. They compared their simulation results against experimentally-measured velocity and temperature distributions and showed good agreement. The particle volume fractions in their simulation are still relatively low (<10%). Grena (2009) treated the stream of solid particles as a single-phase fluid within the solar absorber and determined the resulting velocity and temperature distributions for different particle sizes and radiation exposure times.
None of the models reported in the literature to date addresses the unique aspects of the KSU SPR design, namely, the interactions between the particles and the stationary porous structure (or sequence of mesh screens) through which they flow. Most prior models assume a relatively low particle volume fraction, and therefore, cannot be expected to accurately model the particle/particle and particle/structure interactions within the KSU SPR design. Slowing down of the particles as they flow through the porous structure leads to significantly higher particle volume fractions (within the interstitial regions of the porous structure). Additionally, while a portion of the concentrated solar power incident on the receiver is directly absorbed by the particles, the majority of it is first absorbed by the porous structure and is later conducted across the interconnected ligaments of the structure and “convected” to the particle stream flowing through it. This will lead to higher porous structure temperatures (vis-à-vis the local particle temperatures). While convection losses from the receiver are expected to be lower than those for a free-falling curtain because of the reduction in convective heat transfer area (Golob et al., 2014), the extent and effect of the elevated porous structure temperature on radiation heat losses and, hence, the overall efficiency of the receiver, are yet to be quantified. The temperature difference between the porous structure and the particles flowing through it will depend on the thermal resistance between the structure and the particles. Future experiments using the Georgia Tech Solar Simulator Test Facility will be used to quantify this effect.
In order to optimize the design and operational parameters of a SPR with an interconnected porous structure (or discrete sequence of mesh screens), an extensive modeling effort funded in part by the SunShot program of the US Department of Energy has been undertaken. Our initial effort was focused on quantifying the most important attribute of the KSU SPR concept, namely, its ability to increase the particles’ residence time within the receiver. The goal is to develop an experimentally-validated numerical model to quantify the effects of various porous receiver and particles’ characteristics on the mass flux within the receiver. The model can be used by the SPR designer to identify the characteristics of the porous medium and solid particles necessary to obtain the desired mass flux (i.e. residence time). The initial effort described in this paper has focused on modeling of particle flow in an un-heated (i.e. isothermal) system and the associated validation experiments. Comparison between the test data and model predictions are presented. Future models will include solar heating and heat transfer effects; validation experiments associated with these models will be conducted at the Georgia Tech Solar Simulator Test Facility.
Section snippets
Numerical modeling approach
In general, there are two different modeling approaches for the simulation of gas–solid two phase flow. One is the discrete element method (DEM) which tracks individual particle motion separately, while gas motion is accounted for by solving the averaged Navier–Stokes equation (Kloss et al., 2009). The other modeling approach is based on a two-fluid formulation which treats each phase as an interpenetrating medium by solving a similar set of conservation equations (Du et al., 2006a, Du et al.,
Experimental setup
As noted earlier, two types of experiments have been performed to validate the numerical model. The purpose of the first experiment is to check the validity of the granular two-fluid modeling approach for solid particulate-gas flow, while the second experiment is aimed at checking the validity of the packed bed model for simulating the stationary porous medium. A schematic diagram of the experimental apparatus used in both experiments is shown in Fig. 1. The apparatus is essentially a flow loop
Model setup
Fig. 4 is a schematic representation of the simulation geometry for the benchmarking experiments (see Section 3 above). Here, a two-dimensional simulation geometry has been used since the test section has a longer depth (distance in the direction perpendicular to the cross section shown in Fig. 4, namely 15 cm) compared to the slit width (maximum of 2 cm). The geometry shown in Fig. 4 corresponds to the second type of experiments; it depicts the stationary cylindrical rod lattice used to simulate
Benchmarking test of granular two-fluid model
The first experiment has been conducted using fracking sand with four different slit widths of 3.5, 5.4, 7.8, and 9.8 mm at the bottom of the test section. Fig. 6 shows the calculated steady state particle volume fraction distributions within the computational domain for the four slit width values. In all cases, the particle bed within the test section plenum is closely packed with a nearly uniform volume fraction of ∼60%. As the slit width increases, the particle volume fraction in the ambient
Concluding remarks
In this investigation, a numerical model for particulate flow within a stationary porous structure has been developed. The application of interest is solar particle-heating receivers in concentrated solar power systems based on an innovative receiver concept developed by researchers at King Saud University and Georgia Institute of Technology. The model utilizes the Eulerian–Eulerian two-fluid formulation for solid–gas flow, coupled with a packed bed representation of the stationary porous
Acknowledgements
Financial support for Dennis L. Sadowski, S.I. Abdel-Khalik, Sheldon M. Jeter and Hany Al-Ansary was provided in part by the US Department of Energy through subcontracts to SunShot Award number DE-EE0000595-1559 to Sandia National Laboratories. Computational resources and financial support for Taegyu Lee, Sehwa Lim, and Seungwon Shin were provided in part by Hongik University, Seoul, South Korea. Additional computational resources and financial support for Seungwon Shin were provided by Georgia
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