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Applied Energy

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Charge and discharge behavior of elemental sulfur in isochoric hightemperature thermal energy storage systems

K. Nithyanandama,⁎, A. Bardea, R. Baghaei Lakehb, R.E. Wirza

a Energy Innovation Laboratory, Department of Mechanical and Aerospace Engineering, University of California Los Angeles (UCLA), Los Angeles, CA 90095, United StatesbMechanical Engineering Department, California State Polytechnic University, Pomona, CA 91768, United States

H I G H L I G H T S

• Elemental sulfur is a low-cost and stable candidate for high temperature TES.

• Experimentally validated CFD model elucidates heat transfer performance of sulfur.

• Sulfur shows high charge/discharge performance for high temperature applications.

• Thermal discharge rate is higher than competing PCM based technologies.

• Functional correlation between Nusselt and Rayleigh numbers is developed.

A R T I C L E I N F O

Keywords:SulfurThermal energy storage (TES)Thermal charge and discharge rateNatural convectionNusselt and Rayleigh numberConcentrating solar power (CSP)

A B S T R A C T

Thermal energy storage with elemental sulfur is a low-cost alternative to molten salts for many medium to high-temperature energy applications (200–600 °C). In this effort, by examining elemental sulfur stored isochoricallyinside isolated pipes, we find that sulfur provides attractive charge/discharge performance since it operates inthe liquid-vapor regime at the temperatures relevant to many important applications, such as combined heat andpower (CHP) plants and concentrating solar power (CSP) plants with advanced power cycle systems. The isolatedpipe configuration is relevant to shell-and-tube thermal battery applications where the heat transfer fluid flowsover the storage pipes through the shell. We analyze the transient charge and discharge behavior of sulfur insidethe pipes using detailed computational modeling of the complex conjugate heat transfer and fluid flow phe-nomena. The computational model is validated against experiments of a single tube with well-defined tem-perature boundary conditions and internal temperature measurements. The model results evaluate the influenceof pipe diameter on charge and discharge times, heat transfer rate, and Nusselt number due to buoyancy drivenconvection currents. Depending on the Rayleigh number (pipe diameter), the average Nusselt number obtainedfor discharge is 3–14 times higher than proposed solid-liquid phase change technologies based on molten salt,which are limited in their performance due to conduction based solidification and low thermal conductivity. Theresults show competing trade-offs between increase in heat transfer coefficient, thermal energy stored in sulfur,and increase in charge and discharge time with increase in pipe diameter. A preferred pipe diameter can bedetermined for target applications based on their requirements and these competing trade-offs. A validatedfundamental correlation for Nusselt number as a function of Rayleigh number for charge and discharge is de-veloped that can be used to design the sulfur-based thermal storage system for transient operation.

1. Introduction

Thermal energy storage (TES) is a vital part of the energy storageportfolio with wide application space. Notable among them are energystorage needs to help relieve the strain on the power grid coping withincreased penetration of intermittent renewables, such as solar energy,and increasing the flexibility and efficiency of combined heat and

power (CHP) facilities. For instance, in utility-scale concentrating solarpower (CSP) plants, TES enables it to operate at 60–75% capacitycompared to only about 25% of their actual capacity when not usingTES. TES stores additional harvested solar energy during off-peak hoursand provides the energy required for power generation during peakdemand or non-solar hours [1]. TES is also an essential and importantpart of CHP for increased flexibility and load shifting. Industrial plants

https://doi.org/10.1016/j.apenergy.2017.12.121Received 4 April 2017; Received in revised form 6 December 2017; Accepted 30 December 2017

⁎ Corresponding author.E-mail address: kartn87@ucla.edu (K. Nithyanandam).

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T

that require high temperature heat for their manufacturing processemploy CHP plants that are sized based on the heat requirements andnot optimized for the value of electricity generated. Integrating a TEShelps decouple the usage of heat from the generation of electricity, thusallowing the electricity to be generated when it is most valuable for theuser facility while constantly supplying high temperature heat for un-interrupted plant operation. Overall, TES in CHP plants improve systemeconomics by increasing efficiency and reducing the payback period[2].

The state-of-the-art thermal energy storage systems utilize moltensalt mixtures as the storage medium due to their low vapor pressure,high specific heat and chemical stability [3,4], and several CSP plantshave adopted this technology [5,6]. The total cost of any TES system isdominated by the costs of the storage fluid and storage tank [7,8]. Thecosts for these molten salt TES systems are well in excess of the US DOETES target of $15/kWht (∼$35/kWht–$78/kWht) due to the high costassociated with storage fluid [3,4]. In addition, they cannot operate athigh temperatures (> 565 °C) for high efficiency power generationapplications, which is not attractive from a long-term investmentstandpoint. Therefore, state-of-the-art two-tank molten salt TES is costprohibitive and technological advancements that reduce the cost of TESare necessary for wide scale adoption of renewables such as utility-scaleCSP, and profitable growth of industrial CHP.

Previous efforts investigated storing thermal energy in a phasechange material that involves phase transition between solid and liquidstate [9,10] or high energy density supercritical fluids [11–13]. How-ever, the requirement of additional enhancement features such as heatpipes, metal foams, etc. to augment the heat transfer performance of thelow thermally conductive phase change material [9,14], and the re-quirement of thick walls to withstand high pressures in supercriticalfluids incurs additional costs to the TES systems [8,11]. A compre-hensive review of the various high temperature thermal energy storagetechnologies can be found in the literature [3,15,16].

Researchers at University of California, Los Angeles (UCLA) havediscovered a new approach that involves storing thermal energy inelemental fluids, based on materials such as highly abundant and in-expensive sulfur [17]. Sulfur is the 13th most abundant element onearth and 23% of global sulfur supply is produced in the United Statesand Canada [18]. The typical price of sulfur is around 0.06–0.08 $/kg[18,19], which is about one order of magnitude lower than the cost ofnitrate salt mixtures used in the state-of-the-art two-tank molten saltTES system. As a basic element, sulfur exhibits negligible thermal de-gradation and high energy storage capacity stemming in part from thebond energies associated with various allotropic transformations[20,21], which makes it an ideal candidate for high-temperature TESsystems. Accordingly, elemental sulfur based TES offers both low cost,which is well below US Department of Energy cost objective of 15 $/kWht [4], and high temperature stability to above 1000 °C [21], thusaddressing the two main challenges associated with state-of-the-arttwo-tank molten salt systems.

Previous studies have proposed the use of elemental sulfur andsulfur based compounds in an isobaric configuration [21,22] and de-monstrated sulfur based cycles for thermochemical energy storage [23].However, Wirz et al. [17] was the first to propose elemental sulfur in anisochoric configuration, which is considered in this study. A shell andtube TES concept [8,24] comprising of elemental sulfur encapsulatedinside sealed pipes and heat transfer fluid (HTF) flowing in the shell isenvisioned. Charging process involves circulating hot HTF—from solarfield in the case of CSP or waste heat from gas turbines in the case ofCHP—in the outer shell and transferring energy to sulfur that is storedin the form of excursion in internal energy. Cold HTF is circulatedduring discharging process—at night times in the case of CSP or timesat which the electricity selling price is low for turbine operation in thecase of CHP [2]—to extract thermal energy from the hot molten sulfur.The heated HTF may then be used to do work in a CSP power block togenerate electricity, or meet industrial heating needs. The heat transfer

Nomenclature

c specific heat [J/kg K]cs,avg=1165.4 temperature-averaged specific heat of sulfur [J/

kg K]D nominal pipe size [in.]Di pipe inner diameter [m]Do pipe outer diameter [m]Fo Fourier numberg= 9.81 gravitational acceleration [m/s2]h heat transfer coefficient [W/m2 K]h’ thermal convective conductance per unit pipe length [W/

mK]i internal energy [J/kg]k thermal conductivity [W/mK]ks,avg=0.19 temperature-averaged thermal conductivity of sulfur

[W/mK]Nu Nusselt numberp pressure [Pa]P specific thermal charge/discharge rate [kW/kg]Q specific thermal energy stored/discharged [kWh/kg]Q ̇ surface heat flux [W/m2]Ra Rayleigh numbert time [s]T temperature [°C]V velocity [m/s]

Subscripts and superscripts

avg average

C chargeD dischargei inner/initialo outers sulfurw wall

Greek symbols

β thermal expansion coefficient [1/K]θ non-dimensional temperatureμ viscosity [Pa s]μs,avg=0.06 (0.65) temperature averaged viscosity of doped (pure)

sulfur [Pa s]ρ density [kg/m3]ρs,avg= 1634.3 temperature averaged density of sulfur [kg/m3]τ strain tensor

Acronyms

CHP combined heat and powerCSP concentrating solar powerHTF heat transfer fluidNPS nominal pipe sizeTES thermal energy storage

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interactions between HTF and elemental sulfur during charge and dis-charge will induce free convection currents within molten sulfur. Thenatural convection currents result from the buoyancy forces within thestorage fluid in the combined presence of density gradient due totemperature gradient, and gravitational field [25]. In a previous studyinvolving supercritical fluids [12,13], it was shown that the nature ofbuoyancy driven convection currents plays an instrumental role in theperformance of TES systems. In addition, Nithyanandam et al. [26]presented preliminary results of the heat transfer behavior of sulfur fora narrow temperature range of 400–600 °C.

The objective of the present study is to investigate the heat transfermechanism inside the storage pipes of the sulfur based TES system fortemperature ranges between 200 °C and 600 °C, which is of interest tomany important applications such as high temperature CSP, and in-dustrial CHP. A computational model is developed and compared withexperimental results of a single tube with well-defined temperatureboundary conditions and internal temperature measurements. Withinthe temperature range of interest, a key characteristic exhibited bysulfur is the change in viscosity due to polymerization in liquid phase[27]. Nevertheless, trace amounts of organic substances, hydrogensulfide or polysulfanes, which are present in all commercial sulfursamples [28] reacts with sulfur to lower the viscosity by curtailing thechain-length of the polymeric sulfur [29–31]. Based on complementaryexperimental [26,32–34], and numerical investigation, we show thatthe thermal characteristics of low-viscous doped-sulfur (with traceamounts of H2S, etc.) concur with the experimental results. The flowstructures of buoyancy-driven convection currents within the moltensulfur stored isochorically inside the storage pipes was investigatedusing the validated computational model. The results evaluate the in-fluence of pipe diameter on the charge and discharge performance ofthe system, and information on the resulting heat transfer coefficient ispresented. A fundamental correlation between Nusselt number andRayleigh number for charge and discharge is obtained, which is ofprime interest for system level design and analysis of the low cost, highperformance sulfur based TES. The utility of the heat transfer correla-tion derived in this study for system level analysis of sulfur TES systemwas recently demonstrated by Shinn et al. [34].

2. Numerical model

The two-dimensional computation domain considered in this studyis shown in Fig. 1. Sulfur is stored inside the circular SS 316 pipes ofschedule 10 thickness. The choice of SS 316 as the candidate material

was based on careful consideration of strength and corrosion resistanceat high temperatures (200–600 °C). Sulfur has a modest vapor pressure[35] and experimental investigation of the pressure-temperature char-acteristics of sulfur enclosed in a pipe yielded a maximum pressure ofapproximately 180 psig at 600 °C. Subsequent calculations based onYoung-Laplace equation for hoop stress and assuming a design safetyfactor of 4.0 indicated that schedule 10 pipe wall thickness can beutilized for storing sulfur safely up to 600 °C.

Sulfur melts at 118.8 °C [36] and exists in liquid phase for thetemperature range of 200–600 °C considered in this study. Although theboiling point of sulfur at 1 atm is 444.6 °C [36], in an isochoric system,the rise in internal pressure during temperature excursion delaysboiling of sulfur. For instance, experiments conducted in our laboratoryshowed that the pressure inside the pipes was 180 psig at 600 °C, atwhich the boiling point of sulfur is slightly above 650 °C [36]. Hence,the assumption of single-phase, incompressible, molten sulfur is ap-plicable for the temperature range considered in this study, which isalso confirmed from the excellent agreement between the computa-tional and experimental results reported in Section 3. The temperaturedifference between the outer pipe wall and sulfur inside the pipe(Fig. 1) induces time-dependent buoyancy force within the fluid. Theformation of buoyancy driven convection currents within the moltensulfur impact the charge and discharge behavior, which is characterizedby the Rayleigh number (Eq. (1)):

=−

RagβD T T ρ c

μk( )i s w

3 2

(1)

where→= −g 9.81 m s 2 is the acceleration due to gravity, β is the thermal

expansion coefficient, ρ is the density, k is the thermal conductivity, μis the dynamic viscosity, Ts is the mean temperature of sulfur within thepipe, and Tw is the wall temperature. Experimental and numericalanalysis in the literature show that a fully turbulent natural convectionflow is established beyond a Rayleigh number of 109 for gases that havelow Prandtl number typically ranging between 0.1 and 1.0 [37,38],and> 1011 for liquids such as water with comparatively higher Prandtlnumber [38]. Based on the thermophysical properties of sulfur obtainedfrom literature (Fig. 2), the Prandtl number of sulfur for the tempera-ture range of 200–600 °C is greater than 40. The Rayleigh number forthe various pipe diameters considered in this study ranges from 106 toslightly above 109 (Table 1) and subsequently, the computations areperformed with laminar formulation similar to Ref. [12], which usedturbulent formulation only for Rayleigh number greater than 1012.

The coupled system of continuity, momentum and energy equations

Fig. 1. Schematic of the computational domainwith adopted mesh configuration, temperatureboundary, and initial conditions.

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governing the physical phenomena during thermal energy storage andretrieval in sulfur are:

∇→

=ρV·( ) 0 (2)

→

= −∇ + ∇ +D ρV

Dtp S

( )·τ g (3)

= −∇ ∇D ρi

Dtk T

( )·( ) (4)

where p is the pressure, t denotes time,→V denotes the velocity vector, τ

is the stress tensor, i is the internal energy expressed as =i cT , c is thespecific heat, T is the temperature, and D

Dtis the total derivative.

Temperature-dependent values for thermal conductivity, specific heatand viscosity of sulfur are used in the numerical simulations. Fig. 2depicts the properties obtained from the literature for density, specificheat, and thermal conductivity [36,39] as solid lines. The extrapolatedvalues in the temperature range for which the thermo-physical prop-erties are not available in the literature are shown as dashed lines inFig. 2. The density of sulfur is assumed constant at the temperature-averaged value of ρs avg, =1634.3 kg/m3. The momentum equation in-corporates a source term for the buoyancy force due to gravity based onBoussinesq approximation, =

→−S ρ g β T T( )g s avg ref, where the reference

temperature (Tref ) is taken to be the lower temperature (200 °C)

considered in this study and the thermal expansion coefficient is cal-culated to be × −3.62 10 4 K−1 (Fig. 2a). It is to be noted that

− = ≪β T T( ) 0.14 1C D ; thus, substantiating the validity of the Boussinesqapproximation for this study. For the wall of the SS 316 pipe only theconduction equation given by = −∇ ∇

∂

∂ρ c k T· ( )w w

Tt w is solved. The

density, specific heat and thermal conductivity of SS 316 pipe are7900 kg/m3, 559.9 J/kg K and 20.1W/mK, respectively.

The variations in the viscosity of the molten sulfur as a function oftemperature is shown in Fig. 2 for two purity grades of sulfur. Red linedenotes the viscosity variation of pure sulfur as reported by Bacon andFanelli [27] while the green line denotes the viscosity variation ofsulfur with trace amount of dopant (H2S, etc.), which results in a sig-nificant decrease (order of ∼103) in the viscosity spike as reported byFanelli [29], Rubero [30], and Timrot et al. [31]. The generation oftrace amount of H2S was qualitatively observed from gas chromato-graphy analysis in thermal cycling experiments of sulfur conducted inour laboratory. The two viscosities are selected to understand the sen-sitivity of viscosity parameter on the prediction capability and accuracyof numerical model to experimental results.

The computational domain was initially set at a constant tempera-ture of = °T 200 Ci for charge simulations and = °T 600 Ci for dischargesimulations. A constant wall temperature, Tw of 600 °C and 200 °C isimposed on the outer wall of the pipe for charge and discharge simu-lations, respectively. A no-slip boundary condition is imposed at theinterface between sulfur stored inside the tube and inner tube wall forthe momentum equation. The computations were continued until thedimensionless mean temperature of sulfur defined as: =

−

−θs

T TT T( )( )

s DC D

,reached 0.95 and 0.05 for charge and discharge, respectively. Thecorresponding time taken is defined as the charge (tC) and discharge(tD) time in this current study.

The numerical model was solved in ANSYS Fluent 14.0 [40]. Thecomputational grid was built of quadrilateral cells in the wall, and fluid(sulfur) region (Fig. 1), with mesh density greater than 700 cells/cm2

(typically cell elements in the order of 4000–250,000 for the pipe sizesconsidered in this study) determined based on a systematic grid re-finement process (Section 3). The SIMPLE algorithm was used for thepressure-velocity coupling and the time step in the calculation was set

Fig. 2. Thermo-physical properties of sulfur: (a) Density [36], (b) specific heat [36], (c) viscosity [27,29–31], (d) thermal conductivity [36,39] for the temperature range of 200–600 °C.The solid lines represent property values obtained from literature and the dotted lines represent the extrapolated values.

Table 1Dimensions of the pipe and the characteristic average Rayleigh number.

Nominal pipesize, D[inches]

Innerdiameter, Di

[cm]

Outerdiameter, Do

[cm]

Average Rayleigh number, Raavg

Doped sulfur(low-viscosity)

Pure sulfur(high-viscosity)

1 2.8 3.3 ×8.338 106 ×7.710 105

2 5.5 6.0 ×6.250 107 ×5.780 106

4 10.8 11.4 ×4.811 108 ×4. .449 107

6 16.2 16.8 ×1.600 109 ×1.480 108

8 21.2 21.9 ×3.598 109 ×3.328 108

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at 0.1 s since further decrease did not show any noticeable changes inthe transient results for the temperature and velocity. The convective-diffusive terms in the momentum and energy equations was solvedusing the second-order upwind scheme. At each time step during thesimulation, residual convergence values of 10−6 and 10−4 was imposedfor the momentum and continuity equations respectively, and a value of10−8 was used for the energy equation.

The present study involves the study of the influence of the pipedimensions on the charge and discharge performance of sulfur. Pipedimensions of 1″ NPS, 2″ NPS, 4″ NPS, 6″ NPS, and 8″ NPS—NPS standsfor Nominal Pipe Size—with wall thickness corresponding to schedule10 are considered in this study. Table 1 presents the inner (Di) and outerdiameter (Do) for these different pipe specifications [41] and the cor-responding average Rayleigh number (Raavg). The average Rayleighnumber is computed based on temperature averaged thermo-physicalproperties. The temperature averaged properties are obtained by nu-merical integration of the property curves shown in Fig. 2 representedby f T( ) over the interval 200–600 °C: ∫ f T dt( )· /400200

600 . The tempera-ture-averaged density (ρs avg, ), specific heat (cs avg, ), and thermal con-ductivity (ks avg, ) between 200 °C and 600 °C are calculated to be1634.3 kg/m3, 1165.4 J/kg K, and 0.19W/mK, respectively, which arealso used later in the post-processing of results in Section 3. The tem-perature averaged values for low- and high- viscosity (μavg) are calcu-lated to be 0.06, and 0.65 Pa-s, respectively. The numerical modelcomputes the transient and spatial temperature profiles in the compu-tational domain, which allows for calculation of the volumetric averagetemperature of enclosed sulfur (TS), and wall (Tw). In addition, thenumerical model outputs the transient variations in wall surface heatflux (Q ̇w) from which the overall heat transfer coefficient (h) andNusselt number (Nu) are computed as follows:

=−

h t Q tT T t

( )̇ ( )

(t) ( )w

w s (5a)

=Nu t h t Dk t

( ) ( )( )

i

(5b)

3. Results and discussion

The adopted computational model was first verified by grid re-finement study. A systematic mesh refinement study was performed toobtain the best mesh density (number of cell elements per unit cross-sectional area of the pipe) for the computations. Fig. 3 shows the timehistory of mean sulfur temperature obtained for pipe of diameter 4″NPS (Table 1) with progressively increasing mesh densities from 110cells/cm2 to 1090 cells/cm2. The equivalent number of cell elements forthe 4″ NPS pipe range from 10,000 to 100,000 as noted within par-entheses. As mesh density gets finer, the solution approximately reachesa limiting case. The difference in solution predicted by the mesh den-sities of 720 cells/cm2 and 1090 cells/cm2 is negligible while thecomputational cost increases prohibitively. Hence, the final computa-tions were performed using the mesh density of 720 cells/cm2.

The computational model was then validated by comparing the si-mulated results obtained for thermal charging of sulfur stored insidestainless steel pipe. The details of single element experimental test fa-cility with resistive heating fabricated for validation of the computa-tional model are reported in Refs. [26,32–34] and is summarized herein a concise manner. Sulfur was contained in a stainless steel (grade316) pipe measuring 2″ NPS (Sch. 40) in diameter and 41″ in length.The pipe was wrapped with heater tape and insulated with flexibleceramic insulation. Thermocouples were installed on the pipe surfaceand inside sulfur to record the radial and axial temperatures. The lo-cation of the thermocouples inside sulfur is shown in the inset of Fig. 4.The entire setup was heated first until all the thermocouples recordedan initial temperature of 200 °C. The experiment was then conducted bysetting the temperature set point across all the eight heaters to be

600 °C. The recorded surface temperatures formed the boundary con-dition for the numerical model validation, and the numerical predic-tions of the temperature profile inside sulfur are compared with theinternal thermocouples (TS1-3) to determine the validity of the model.

Since the experiment involved a constant set-point temperature of600 °C and the internal thermocouples (TS1-3 in Fig. 4) were well insidethe tubes to be influenced by end effects, a two-dimensional model asdescribed in Section 2 is relevant. The transient wall temperatureprofile measured using the surface thermocouples in the experiments isimposed as a boundary condition for the numerical model. Fig. 4compares the results obtained from the computational model for thetemporal variation in temperature at the location of the internal ther-mocouples TS1, TS2, and TS3 with the experimental results. Thecomputational result obtained using the high viscosity variations forpure sulfur reported by Bacon and Fanelli [27] is depicted as chain-dashed line while the numerical result obtained using the low-viscosityvariations for sulfur with trace amounts of dopant such as H2S [30,31]is shown as the solid line, and the experimental results are denoted bymarkers. The predictions of the trends in temporal variation of sulfurtemperatures concurs well with experimental results.

Fig. 4d–f depict the viscosity, velocity, and temperature contours attime instant of 8min for low-viscosity sulfur while the contours illu-strated in Fig. 4g–i correspond to high-viscosity sulfur. The location ofthe thermocouples TS1-3 are shown by the red filled circles in thetemperature contours. The low viscosity of sulfur with dopants (Fig. 4d)relative to that of pure sulfur (Fig. 4g) contributes to stronger convec-tion currents as observed by the difference in magnitude of velocity(Fig. 4e and h). This culminates in a slower evolution of temperaturefield in high viscosity sulfur (Fig. 4i) compared to low-viscosity sulfur(Fig. 4f). Hence, the predicted temperatures at the thermocouple loca-tions are lower for high-viscosity sulfur (Fig. 4a–c) compared to ex-perimental results, especially at temperatures between 200 and 400 °C.At later time instants, the temperature predictions from both high-(pure sulfur) and low- (doped sulfur) viscosity models converge becauseof relatively smaller difference in viscosity values at high temperatures(Fig. 2c). The average errors (standard deviation) between the lowviscosity model predictions and the experimental data measured byTS1, TS2, and TS3 are 1.1% (0.8), 0.8% (0.5), and 3.6% (2.0), re-spectively, compared to 2.1% (3.3), 3.8% (4.2), and 8.5% (7.4), re-spectively obtained for high viscosity model predictions. Overall, thesulfur viscosity with trace amounts of dopants agrees very closely withthe experimental result for the full temperature range of 200–600 °C,and is used for the remainder of the study. Additional validation resultsfor different sets of experiments are reported in Refs. [26,32–34], whichprovide further confidence in the validity of the model.

Following model validation, the computational model is utilized tounderstand the thermal charge and discharge dynamics of sulfur. Fig. 5

Fig. 3. Transient variation of mean sulfur temperature for various mesh densities.

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elucidates the temperature, velocity and viscosity contours inside sulfurduring charging at various time instants for a pipe inner diameter of10.8 cm, corresponding to 4″ NPS, Schedule 10. The streamlines in-dicate the buoyancy driven convection currents and the density ofstreamlines represent the intensity of the currents. As a result of thenatural convection currents, heated sulfur becomes less dense and flowsup along the hot wall (Fig. 5a–c) and descends along the interior of thepipe, thus efficiently transferring thermal energy to the inner coldsulfur. The natural convection current pattern follows the velocityprofile shown in Fig. 5d–f. Stronger convection currents are observedcloser to the region near the hot wall as delineated by the denserstreamlines (Fig. 5a–c) and high velocity magnitude (Fig. 5d–f) near thewall. As seen from Fig. 5d–f, the velocity and intensity of naturalconvection currents decrease considerably due to decrease in tem-perature difference between the wall and sulfur. With progression oftime, thermal stratification is observed, and only localized recirculationcells near the bottom of the pipe persist because the downward grav-itational force dominate the upward buoyancy force.

Fig. 6 illustrates the temperature, velocity and viscosity contoursinside sulfur during discharging at various time instants for a pipe innerdiameter of 10.8 cm, corresponding to 4″ NPS, Schedule 10. Thestreamlines pattern are characterized by two counter-rotating naturalconvection cells on either half of the vertical diametral axis. The naturalconvection currents originate from the top as cold, denser sulfur movesdown along the center of the pipe (convection cells in the middle) and

the cold wall (convection cells near the wall) due to gravitational forcewhile hot, lighter sulfur moves to the top due to buoyancy force. Astime progresses, the central convection cells are localized to the topportion of the pipe while the buoyancy driven convection cells ad-joining the colder wall plays the dominant role (Fig. 6b and c). Acomparison of the velocity profiles of discharge in Fig. 6d–f with that ofcharge in Fig. 5d–f reveal that the intensity of natural convection cur-rents is slightly lesser during discharge process. As discharge proceedsfrom = °T 600 Ci to = °T 200 CD the viscosity increases with decreasingtemperature (Fig. 2c) and vice versa for charging. This leads to theformation of relatively high viscous regime close to the cold wall duringdischarge (Fig. 6g–i), which combined with decreasing temperaturedifference between the wall and sulfur restricts the intensity of con-vection currents (Fig. 6d–f). On the contrary, during charge, the de-crease in viscosity with increasing temperature (Fig. 5g–i) assists inmaintaining relatively strong convection current throughout the pro-cess.

A parametric study of the effects of pipe diameter on the charge anddischarge performance of the storage system was conducted. As notedearlier, for the case of charging, the initial and the outer wall boundarytemperatures are 200 °C and 600 °C, respectively and vice versa fordischarging. The contour plots in Fig. 7 show the temperature profileand the streamlines of the buoyancy-driven flow field for various pipediameters during charge (Fig. 7a–d) and discharge (Fig. 7e–h) at timeinstants corresponding to when the mean temperature of sulfur is

Fig. 4. Comparison of numerical results obtained for transient variation in sulfur temperature at the location of (a) top (TS1), (b) middle (TS2), and (c) bottom (TS3) thermocouples withexperimental data. Contours of (d, g) viscosity, (e, h) velocity, and (f, i) temperature obtained for low-viscosity and high-viscosity sulfur at time instant of t=8min.

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400 °C. The buoyancy-driven flow field during charge is characterizedby a pair of counter-rotating vortices with rising flow along the hot pipewall for small pipe diameters (Fig. 7a–c) and an additional pair ofsecondary vortices are formed near the bottom of the pipe for largerpipe diameters (Fig. 7d). Counter-rotating vortices are also formedduring discharge (Fig. 7e–h) with the flow descending along the coldpipe wall. In contrast to charge, the secondary vortices at larger pipediameter are established near the top of the pipe (Fig. 7g and h) becauseof the reversal in rotation direction of the recirculation cells. Thecooling of sulfur from high temperature (600 °C) and low viscous state(Fig. 2c) during discharge is accompanied by higher activity of thenatural convection currents initially that leads to the onset of secondaryvortices at comparatively smaller pipe diameters (Fig. 7e–h) thanduring thermal charge process (Fig. 7a–d). The secondary convectioncells are most likely induced by curvature-driven centrifugal instabilitythat takes the form of counter-rotating Taylor-Görtler vortices [42] andare observed for larger pipe diameters (larger Rayleigh number). Weobserved a loss in symmetry of the buoyancy convection currents for 8″NPS pipe diameter (higher Rayleigh number) that is readily apparentduring discharge (Fig. 7h). This is possibly due to non-oberbeck-bous-sinesq (NOB) convection effects arising from the influence of non-lineartemperature dependent sulfur viscosity on the formation of viscous andthermal boundary layers near the pipe wall, which has also been

observed for other fluids in the literature [43,44]. Detailed character-ization of this behavior will be investigated in a future study.

Fig. 8a and c present the temporal evolution of volume-averagedtemperature of sulfur during charging and discharging, respectively forvarious pipe dimensions (Table 1). As mentioned in Section 2, thetemporal variations are illustrated until the dimensionless mean tem-perature of sulfur defined as: =

−

−θs

T TT T( )( )

s DC D

, reached 0.95 and 0.05 forcharge and discharge, respectively. Additionally, the predictions of thenumerical model for pipe diameter of Di=10.8 cm corresponding to 4″NPS schedule 10, without accounting for the buoyancy driven con-vection currents (g=0m s−2) is also plotted to emphasize the role ofbuoyancy driven convection currents in augmenting the charge anddischarge performance. In general, with increase in pipe diameter ittakes longer time to charge and discharge, primarily due to the increasein energy content within the pipe. As explained earlier, the buoyancydriven convection currents assist in improving the charge and dischargeperformance as seen by the longer charge and discharge times observedfor conduction dominated case in Fig. 8a and c. Completion of dis-charge process takes longer than charge as observed from comparingFig. 8a and c. The temperature difference between the wall and sulfur( −T Tw s) is the driving force for charge and discharge process, whichdecreases with time. In contrast to charge, the increase in viscosity withdecreasing sulfur temperature near pipe wall combined with decreasing

Fig. 5. Contours of (a–c) temperature, (d–f) velocity, and (g–i) viscosity evolution within sulfur for different time instants during thermal charge process.

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Fig. 6. Contours of (a–c) temperature, (d–f) velocity, and (g–i) viscosity evolution within sulfur for different time instants during thermal discharge process.

Fig. 7. Streamlines of the buoyancy-driven flow and the temperature contours for different pipe diameters at time instants corresponding to mean sulfur temperature of 400 °C.

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driving force during discharge moderates the intensity of convectioncurrents (Fig. 6), resulting in longer discharge time compared to charge.

Fig. 8b and d depict the instantaneous specific thermal charge anddischarge rate of sulfur, respectively, which follow the slopes of tran-sient evolution of temperature curves (Fig. 8a and c). The rates ofthermal charge and discharge are initially higher due to the strong ef-fects of buoyancy driven convection currents (Fig. 8b and d). Withprogression of time, the slope reduces due to slow down of the activity

of natural convection currents with concomitant decrease in the tem-perature difference between the wall and temporally varying sulfur(Fig. 8a and c). For a given pipe diameter, thermal charge rate isslightly higher than discharge rate due to reasons mentioned earlier forthe relatively longer completion of discharge compared to charge. Thespecific rates of thermal charge and discharge are higher for smallerpipe diameters due to larger surface area per unit volume of pipe. In aTES system involving heat exchange between HTF and storage media,

Fig. 8. Transient evolution of (a) sulfur temperature, (b) charge rate during thermal charge process, and (c) sulfur temperature, (d) discharge rate during thermal discharge process forvarious pipe diameters.

Fig. 9. Effect of pipe diameter and transient temperature evolution on (a, c) convective conductance, and (b, d) Rayleigh number during thermal charge and discharge process.

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the temperature difference between the HTF and storage media de-creases from inlet to the outlet [45], and faster thermal charge/dis-charge rates are essential especially near the outlet. Since smaller dia-meter pipes provide higher thermal charge and discharge rates(Fig. 8b and d), while larger diameter pipes can store higher energy perunit length with reasonable charge/discharge rates (Fig. 8b and d), afrustum shaped sulfur pipe with decreasing diameter from the HTF inletto outlet can provide combined benefits.

Fig. 9a and c illustrate the thermal convective conductance per unitlength of the pipe, which is the product of heat transfer coefficient (Eq.(5a)) and surface area of pipe: ′ = ×h h πD( )i , for various cases, which isa more generalized way of quantifying the performance of various de-signs [46]. Fig. 9b and d show the temporal variation of the Rayleighnumber based on the mean wall and sulfur temperatures, calculatedfrom Eq. (1) to aid in the discussion of trends observed for thermalconvective conductance. Initially, high thermal convective conductanceare observed in the vicinity of 200 °C (Fig. 9a) and 600 °C (Fig. 9c),during thermal charge and discharge, respectively. This is attributed tothe transient thermal response of the storage medium to step change insurface temperature that confines the temperature variations to thinboundary layer near the wall at early stages leading to high heat flux.The trends of the thermal convective conductance following the initialtransients can be explained with reference to the Rayleigh numberevolution with time illustrated in Fig. 9b and d. For instance, in Fig. 9a,for a given pipe diameter, the thermal convective conductance fol-lowing the initial transients, increases with increase in sulfur tem-perature due to the corresponding increase in Rayleigh number inFig. 9b—due to decrease in sulfur viscosity as depicted in Fig. 2c—upuntil ∼540 °C. Subsequently, the decrease in temperature differencebetween wall and sulfur leads to drastic drop in Rayleigh number andthermal convective conductance. Similarly during discharge, followingthe initial transients near 600 °C, the reduction in thermal convectiveconductance with decreasing sulfur temperature follows two regimes:(1) gradual decrease as Rayleigh number decreases with increasingviscosity from 600 °C to 200 °C, (2) drastic drop near 200 °C due toacute decrease in Rayleigh number with decreasing temperature dif-ference ( −T Tw s). Fig. 9a and c show that for a given pipe diameter thethermal convective conductance of charging is higher than that ofdischarging because of higher Rayleigh number (Fig. 9b and d).

The performance of the system for various pipe diameters wasquantified in terms of charge and discharge time, charge and dischargeaverage thermal convective conductance and Nusselt number in Fig. 10.The charge and discharge time increases with increase in pipe diameteras illustrated in Fig. 10a because of higher energy content. The thermalconvective conductance is higher for larger pipe diameters compared tosmaller pipe diameters due to the higher surface area available for heattransfer interaction between the wall and sulfur, and stronger convec-tion currents due to larger Rayleigh number (Fig. 10b). The Nusseltnumber in Fig. 10c increases with increase in pipe diameter or Rayleighnumber. The Nusselt number for discharge is lower than charge forreasons mentioned earlier. Nevertheless, depending on the Rayleighnumber, the average Nusselt number obtained for discharge is 3–14times higher than competing molten salt PCM based technologies(Nuavg∼ 8) that are glacially slow in their discharge performance dueto conduction based solidification, and low thermal conductivity [9].Based on the trends observed for variation of average Nusselt numberwith average Rayleigh number (Fig. 10c), we obtained the followingcorrelation:

= × −Nu a Ra aavg avga

1 32 (6)

Where a1 = 0.909; a2 = 0.242; a3 = 1.612 for charge and a1 = 0.545;a2 = 0.238; a3 = 0.790 for discharge. The non-dimensional heattransfer correlation developed in this study has generalized applic-ability. Since Rayleigh number is a function of both pipe diameter andtemperature difference between wall and sulfur (Eq.(1)), the correlation

provided in Eq. (6) can be used to predict the heat transfer coefficient ofsulfur stored inside pipes (Fig. 1) for various pipe diameters and ex-ternal wall temperature conditions during thermal charge and dis-charge. Recently, Shinn et al. [34] demonstrated the utility of the de-veloped generalized heat transfer correlation of sulfur (Eq. (6)) forcharacterizing the performance of shell and tube based sulfur TESsystem.

The validity of the above expression is checked by utilizing it in ananalytical expression derived for the transient response of sulfur duringthe charge and discharge process. An overall energy balance for thevolumetric average sulfur temperature based on lumped approximationcan be expressed as:

=−dT

dth πD T T

ρ c πD( )( )

( /4)s avg i s w

s s i2 (7)

Since the conduction resistance of the pipe wall is significantlysmaller—at least two orders of magnitude—than the convectivethermal resistance within sulfur—owing to the small wall thickness ofschedule 10 pipes and high thermal conductivity of stainless steel—thewall temperature can be safely assumed to be the outer surfaceboundary temperature, namely TC during charge and TD during dis-charge. Based on the aforementioned assumption, the analytical

Fig. 10. Influence of pipe diameter on (a) charge and discharge time, (b) average thermalconvective conductance; and (c) variation of average Nusselt number with averageRayleigh number.

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solution for charge (Eq. (8a)) and discharge (Eq. (8b)) can be expressedin the non-dimensional form as:

= − − × ×θ Nu FoCharge: 1 exp( 4 )s avg (8a)

= − × ×θ Nu FoDischarge: exp( 4 )s avg (8b)

where = − −θ T T T T( )/( )s s D C D , and Fourier number, Fo is defined as=Fo α t D/s avg i,

2. The thermal diffusivity, αs avg, in the Fourier number isbased on the temperature-averaged sulfur properties as discussed inSection 2. The transient dimensionless sulfur temperature computedfrom Eq. (8) is compared with the results from CFD simulation inFig. 11. As observed from Fig. 11, the analytical results based on thedeveloped correlation for Nusselt number (Eqs. (6)–(8)) predicts theCFD results with a high degree of accuracy with a root mean squarederror in the range of 0.003–0.009. The expression presented for Nusseltnumber in Eq. (6) can be directly used for system level design andanalysis of thermal energy storage with sulfur as the storage materialfor the range of Rayleigh number considered in this study.

Table 2 summarizes the key results obtained from the present study

for a single pipe encapsulating sulfur. There is a trade-off between in-crease in charge and discharge time with increase in pipe diameter, andthe increase in thermal convective conductance and thermal energystored in sulfur per unit length of pipe with increase in pipe diameter.Table 2 also shows the breakdown of energy stored in the wall andsulfur for different pipe diameters. It is readily observed that the per-centage of energy stored in sulfur increases with increase in pipe dia-meter due to the increase in sulfur to wall weight ratio (Table 2) andstarts plateauing beyond pipe diameter of 4″ NPS. Although, a rigorouscost analysis is not reported in the present study, comparing the specificcost of stainless steel SS 316 (∼3 $/kg) with that of sulfur (∼0.06 $/kg), it is noted that larger pipe diameters will yield low-cost TESsystem. Nevertheless, based on the application needs, a smaller pipediameter is most suitable for applications requiring ultra-fast charge/discharge performance and a larger pipe diameter is most suitable forcost-effective large-scale energy storage solutions. Since the percentageof energy stored in sulfur increases sparingly with increase in pipediameter beyond 6″ NPS, it can be reasoned that the preferred storagepipe diameter that meets the competing requirements of both low-costand fast charge/discharge lies in the vicinity of 4″ NPS to 6″ NPS. Shinnet al. [34] deduced similar conclusions using a detailed system and costmodel of the sulfur TES system using the heat transfer correlation de-rived in this study. As noted earlier, a frustum shaped sulfur containerwith larger diameter near the HTF inlet—where the temperature dif-ference between HTF and sulfur is high—and smaller pipe diameternear the HTF outlet—where the temperature difference between HTFand sulfur is relatively low—will provide the combined benefits of fastcharge/discharge, high thermal convective conductance, and lessnumber of pipes requirement (low-cost). System-level studies [45] withsulfur TES integrated to different applications such as CSP, CHP plants,etc. will be undertaken in the future to determine the optimum designbased on the application needs.

4. Conclusions

The study investigates the heat transfer mechanisms and charge/discharge performance for isochorically-contained sulfur over a tem-perature range of 200–600 °C, as directly applicable for thermal energystorage systems in high temperature CSP and CHP plants. Strong un-derstanding of the heat transfer behavior of sulfur is developed anddemonstrated via excellent correlation between computational andexperimental efforts. Investigations of the influence of pipe diameter onthe charge and discharge performance show that the Nusselt numberincreases with pipe diameter due to the corresponding increase inRayleigh number. Discharge time is slightly longer than charge due tothe formation of relatively high viscous regime close to the cold wall atlower temperatures, which moderately limits the activity of naturalconvection currents. Depending on the Rayleigh number (pipe dia-meter), the average Nusselt number obtained for discharge is 3–14

Fig. 11. Comparison of dimensionless sulfur temperature obtained from analytical solu-tion based on the developed correlation (Eqs. (6) and (8)) with results obtained from CFDmodel.

Table 2Key performance metrics obtained for various pipe diameters.

Nominal pipe diameter, D[inches]

Charge (discharge) time, tC(D)[min]

Sulfur (wall) weight,WS(W) [kg/m]

Energy stored in sulfur (wall),QS(W) [kWht/m]

Charge (discharge) avg. thermal convectiveconductance, h′avg [W/mK]

1 3.01 1.01 [0.48*] 0.14 [51.2%**] 25.17(6.16) (2.09) (0.13) (14.40)

2 7.07 3.88 [0.99*] 0.53 [68.3%**] 41.89(14.84) (3.93) (0.25) (22.93)

4 15.88 14.97 [1.79*] 2.07 [79.8%**] 71.70(34.98) (8.36) (0.52) (38.04)

6 27.55 33.69 [2.43*] 4.61 [84.2%**] 92.58(57.97) (13.84) (0.87) (50.05)

8 32.28 57.69 [2.89*] 7.91 [86.4%**] 114.54(80.63) (19.96) (1.25) (61.76)

* W W/S w.** × +Q Q Q100/( )S S W .

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times higher than competing solid-liquid phase change technologiesbased on molten salt, which are limited in their performance due toconduction based solidification and low thermal conductivity.

The results summarized in Table 2 show a trade-off between theincrease in charge/discharge time, increase in charge/discharge con-vective conductance, and increase in thermal energy stored in sulfur perunit length of pipe with increase in pipe diameter, which warrantssystem level investigation based on cost, heat transfer rate, entropygeneration minimization, exergetic efficiency, etc. to obtain the op-timum pipe diameter. The results clearly show that a smaller pipediameter is preferred for applications requiring ultra-fast charge/dis-charge performance, while a larger pipe diameter is most suitable forcost-effective large scale energy storage solutions. The validated fun-damental correlation obtained for Nusselt number as a function ofRayleigh number for charge and discharge provided in the study can beused for system level design and analysis of sulfur based thermal energystorage system for a wide range of applications, including high tem-perature CHP and CSP. Overall, the study provides important insightinto the high-temperature heat transfer behavior of sulfur and showsthe utility of the model in better understanding the sulfur heat transferphysics for making informed engineering choices.

Acknowledgment

This work was supported by the ARPA-E Award DE-AR0000140,Southern California Gas Company Grant Nos. 5660042510,5660042538, and California Energy Commission Contract No. EPC-14-003. Their support is greatly appreciated.

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