Elsevier

Powder Technology

Volume 342, 15 January 2019, Pages 99-107
Powder Technology

Prediction on drag force and heat transfer of spheroids in supercritical water: A PR-DNS study

https://doi.org/10.1016/j.powtec.2018.09.051Get rights and content

Highlights

  • Momentum and heat transfer of spheroids in SCW are studied.

  • Effects of SCW properties, particle shape and Reynolds number are discussed.

  • Correlations for Cd and Nu of spheroids in SCW are established.

Abstract

To carry out numerical simulations on the particle-laden supercritical water (SCW), one needs to know drag coefficient (Cd) and average Nusselt number (Nu) of the solid particles in SCW according to the high temperature and pressure conditions. This study conducts particle-resolved direct numerical simulations (PR-DNS) to obtain Cd and Nu of spheroids in SCW whose physical properties significantly change with temperature and pressure. A series of case studies are designed to match different working conditions. Effects of variable physical property parameters of SCW on Cd and Nu of spheroids are discussed. Numerical results show that the variable viscosity of SCW plays a more important role in influencing on Cd of spheroids in SCW rather than density, thermal conductivity or specific heat capacity. All these four parameters could affect Nu and the largest effect comes from the specific heat capacity. New correlations of Cd and Nu for spheroids in SCW are proposed according to the numerical results which can facilitate the phase coupling in multi-phase flow modellings of SCW.

Introduction

Using supercritical water (SCW) as the working fluid to achieve the fluidization of coal or biomass for producing high-quality fuels is more and more popular because SCW has many advantages such as high reaction efficiency and H2 selectivity while the whole gasification process is clean for the environment [[1], [2], [3], [4]]. To understand the complex behavior in these SCW reactors from macro scale, one needs to work out what is happening from particle scale or mesoscale related to effective fluid-particle momentum and heat transfer processes [5,6]. However, due to the required high pressure and temperature with complex multi-phase interactions, only limited knowledge of these fundamentals of SCW has been known so far. Forming a reliably scientific guide for controlling, designing and scaling up of the current industrial devices of SCW is still in its infancy.

Computer simulations are useful tools to help accelerate this investigation. One of the most frequently used techniques now is the coupling of computational fluid dynamics and discrete element method (CFD-DEM) [7] which can provide new insights into the multiphase flow and present the complicated phenomenon which is difficult to observe via experimental tools [8]. It is known that the governing equations for CFD-DEM contain unclosed terms (the source terms) which need to be modeled through average treatments [9]. This is because the size of CFD meshes has to be larger than one single particle in CFD-DEM which ignores the detailed resolution of the fluid field around each particle [10]. The main responsibility of these average models is to evaluate drag coefficient (Cd) and average Nusselt number (Nu) by means of correlations which should be known prior to the CFD-DEM run [9]. Establishment of these correlations can be achieved by either experiment or numerical simulation [11].

Recently, using the so-calledparticle-resolved direct numerical simulation (PR-DNS) to understand the fluid-solid interaction (FSI) mechanism and establish the quantitative connection between micro- and macro-scale (from microscale realization to averaged descriptions) information is not uncommon at all [6,11,12]. The rapid development of computer hardware and acceleration algorithm makes PR-DNS a powerful tool for model development and validation at a wide parameter range. In PR-DNS, CFD meshes are generated at a level much smaller than the characteristic size of each solid particle and particle-occupied domains are treated as stationary or moving solid boundaries to the CFD solver. By doing so, both momentum and heat transfer between solid and fluid phases can be quantitatively evaluated. ‘PR-DNS’ is thus named by this unique feature to explicitly obtain interphase force and heat flux rather than to use those average models. Due to the fact that almost all the fluid dynamics and FSI details are available in PR-DNS for further statistics, Tenneti and Subramaniam claimed PR-DNS as the first-principle approach for developing accurate models for interphase momentum, energy and heat transfer in fluid-solid flows [12]. More impressively, according to the numerical simulation results of Bokkers et al. on fluidized beds, it is reported that Cd proposed based on PR-DNS has even better performance than those based on experimental data in predicting the bubble formation in the reactor [13].

In this paper, we use PR-DNS to evaluate Cd and Nu of spheroids in SCW. As just aforementioned, these two dimensional parameters are pivotal to enclose the governing equations in CFD-DEM [9]. Otherwise, inaccurate drag force and heat transfer could affect the movement and energy exchange of each individual particle and even cause un-physical particle and temperature distributions. This is particularly true for a SCW reactor containing particles with irregular shapes (especially biomass materials). Spheroids are always regarded as perfect approximations for non-spherical particles and thus adopted in this study.

In fact, various PR-DNS have been presented in recent years to evaluate Cd and Nu for spheres and spheroids in conventional flows. The relevant work for spheres has been well documented in our previous study [14]. Therefore, we only highlight those simulation researches on spheroids here. For example, Hölzer and Sommerfeld studied the drag, lift and moment coefficients of a single spheroid and other particle shapes with the consideration of particle rotations using LBM simulations [15]. Rong et al. proposed a correction of the voidage on the drag force model based on LBM simulations of a flow through packed beds of uniform spheroids [16]. Ouchene et al. carried out full body-fittedDNS for three different spheroids from low to moderate Reynolds numbers. They made a full discussion on the discrepancy between their numerical results and existing correlations. It's pointed out by Ouchene et al. that the accuracy of several correlations is obviously under the acceptable level and further work is highly needed to construct new ones for spheroids outside the Stokes regime [17]. Zastawny et al. established new correlations of the drag, lift and torque coefficients for spheroids and other three non-spherical particles. They also considered the influence of the incident angle in their correlations [18]. However, heat transfer between the solid-fluid phases was entirely ignored in all the aforementioned work.

Richter and Nikrityuk used the ANSYS FLUENT software to investigate Cd and Nu for spheroids [19] by considering the effect of the attacking angle [20]. They found that both particle shape and its orientation play a key role in influencing Cd and Nu. Ke et al. conducted LBM simulations to study Cd and Nu of spheroids [14] and scalene prolate ellipsoids [21] with different aspect ratios and more accurate correlations were established based on the numerical results. He et al. used their in-house code to conduct PR-DNS to study momentum transfer [22] and heat transfer with a constant-heat flux boundary condition [23] for an assembly of spheroids, respectively. The performance of existing correlations was evaluated according to their numerical results with suggestions given on how to use them. In addition to the 3D numerical simulations, 2D ones were also carried out as a cheaper approach to obtain the general trend. Examples are the new correlations of Cd and Nu for spheroids in Newtonian [24] and power-law [25] fluids based on 2D PR-DNS.

All the aforementioned work assumed that the working fluid is conventional with constant physical properties. As for Cd and Nu of solid particles in SCW, much less studies have been reported. Wei et al. conducted PR-DNS to study the flow separation from a spherical particle [26] and heat transfer [27,28] in SCW, respectively. However, in-depth discussion is needed because the simulation of Wei et al. is in 2D and only ideal spheres are considered. 2D investigations have natural difficulties on non-spherical particles due to the simplification on dimensions. Wu et al. carried out 3D PR-DNS to study Cd of a spherical particle [29] and a cylindrical particle [30], respectively. However, relevant Nu was not reported because heat transfer was ignored during the calculation. It is worthwhile mentioning that Wu et al. picked several temperature points with corresponding physical properties and discussed Cd at each temperature, respectively. Therefore, no much discrepancy was found between SCW and the conventional fluid at different Re.

Compared with PR-DNS on the conventional fluid, the key point for SCW that must be considered is the variation of physical parameters with temperature and pressure [31,32]. The present study aims to help fill this knowledge gap and the obtained results could serve for those CFD-DEM simulations of SCW containing non-spherical particles and heat transfer. However, it needs to point out that the effect of the incident angle is not considered in this study.

The remainder of the paper is organized as follows. Section2 briefly presents governing equations and computational issues. Section3 provides verification cases of the current model. Section4 discusses case studies and presents new correlations of Cd and Nu for spheroids in SCW based on the numerical results. Effects of each varying physical parameter on Cd and Nu are also discussed. Finally, main findings are summarized in Section5.

Section snippets

Governingequationsandcomputationalissues

Since considered Re is not high in this study (Re ≤ 200), the governing equations for steady state flows are adopted as shown below:ρu=0uρu=p+μuuρh=kTwhere: ρ fluid density, u velocity vector, p pressure, μ dynamic viscosity, h enthalpy, k thermal conductivity, T temperature. We use a commercial package (ANSYS FLUENT15.0) to solve Eq.1. Unlike those conventional calculations based on constant thermos-physical fluid properties, ρ, k, μ and the specific heat capacity Cp for

Verification cases

In order to ensure the accuracy of the current modelling, we conduct a series of simulations on the conventional fluid with constant physical properties prior to the main discussions on SCW. This verification procedure is necessary since it is extremely difficult, if not impossible, to validate the obtained numerical results of SCW directly against the experimental data at the current stage of measurement techniques. We conduct two levels of verifications based on the data reported in previous

Resultsanddiscussion

Unlike the conventional fluid, the physical properties of SCW would significantly change with temperature and pressure as shown in Fig. 5. In this study, the temperature ranging from 647 K to 657 K is considered at P = 23 MPa because the pseudo-critical temperature point of SCW is around 650 K under this pressure. Other parameters for calculations are TL = 647 K, TH = 657 K and the fluid is SCW as shown in Fig. 5. Note that Re and Pr = 3.07 in the SCW calculations are calculated based on the

Concludingremarks

In this study, PR-DNS are conducted on cold SCW passing over hot spheroids. Cd and Nu at different working conditions are obtained. Key influence of SCW properties on the two important parameters is discussed and the main discrepancy between the behavior of the conventional fluid and SCW is highlighted. According to the numerical results, new correlations are established. Main findings are summarized as follows:

  • 1.

    The changing trends of Cd and Nu of SCW with Ar and Re are similar with the

Nomenclature

    a, b, c

    Principal semi-axes

    Ar

    Aspect ratio

    Cd

    Total drag coefficient

    Cdf

    Frictional component of the total drag coefficient

    Cdp

    Pressure component of the total drag coefficient

    Cp

    Specific heat capacity

    dp

    Volume-equivalent sphere diameter, m

    h

    Enthalpy, J/kg

    Nu

    Average Nusselt number

    Pr

    Prandtl number

    Re

    Reynolds number

    T

    Temperature, K

    TL

    Low temperature in the system, inlet and initial temperature of the fluid, K

    TH

    High temperature in the system, constant temperature of the particle, K

    u

    Fluid velocity vector, m/s

    uc

Greek letters

    κ

    Thermal conductivity, W/(mK)

    μ

    Dynamic viscosity, Pa·s

    μc

    Dynamic viscosity at the inlet boundary, Pa·s

    ρ

    Fluid density, kg/m3

    Φ

    Crosswise sphericity

Acknowledgements

The authors sincerely acknowledge the financial supports from the National Key R&D Program of China(2016YFB0600101-4), the NSFC project(51606040) and the Natural Science Foundation of Jiangsu Province(BK20160677) on this research.

Special thank goes to Prof. Hui Jin from the State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, for helpful discussions on SCW.

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