Conjugated heat and mass transfer during flow melting of a phase change material slurry in pipes

Energy 99 (2016) 58e68

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Conjugated heat and mass transfer during flow melting of a phase change material slurry in pipes X.J. Shi, P. Zhang* Institute of Refrigeration and Cryogenics, MOE Key Laboratory for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 19 March 2015 Received in revised form 31 August 2015 Accepted 14 January 2016 Available online xxx

PCS (phase change materials slurries) are very useful for thermal energy storage. TBAB (tetra-n-butyl ammonium bromide) CHS (clathrate hydrate slurry) is a promising PCS, which is composed of TBAB hydrate crystal and TBAB aqueous solution. In the present study, the flow melting characteristics of TBAB CHS through pipes were numerically investigated. The solideliquid two-phase nature of TBAB CHS was numerically investigated using the EulerianeEulerian multiphase model. And the interphase heat and mass exchange between TBAB hydrate crystals and TBAB aqueous solution was numerically modeled by considering the phase change phenomenon. Moreover, the diffusion of TBAB salt (solute) in TBAB aqueous solution was also numerically investigated. The numerical results showed that the liquid temperature increased more quickly than the solid temperature because of the latent heat involved. Moreover, the local heat transfer coefficient decreased in the thermally fully-developed region because of the increasing temperature difference between the wall and fluid. When the solid particles were almost fully melted, the fluid temperature increased more quickly than the wall temperature due to the absence of phase change, resulting in the increase of the local heat transfer coefficient. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Phase change material slurry Solid-liquid two-phase flow Conjugated heat and mass transfer Flow melting

1. Introduction In recent years, the energy and environment issues attract intensive attention. In total energy consumption, the electricity consumed by the refrigeration and air-conditioning system accounts for a large proportion, in particular during summer time. Meanwhile, the emission of the conventional refrigerants like CFCs and HCFCs induces many environment issues, such as ozone layer depletion. In order to alleviate the aforementioned issues, the secondary-loop refrigeration and air-conditioning system incorporated with cold storage is considered as a promising solution [1]. In the secondary-loop refrigeration and air-conditioning system, the charging amount of environmentally harmful refrigerant can be reduced significantly because the cold energy can be carried by the secondary refrigerant. In addition, in order to adjust the timediscrepancy between the power supply and demand, the cold storage technology can shift the peak electricity load to off-peak time, resulting in more effective energy utilization [2].

* Corresponding author. Tel.: þ86 21 34205505; fax: þ86 21 34206814. E-mail address: [email protected] (P. Zhang). http://dx.doi.org/10.1016/j.energy.2016.01.033 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

The cold storage in a secondary-loop air-conditioning system is commonly implemented through sensible heat storage and latent heat storage. In the first method, water is commonly used as the cold storage medium due to its easy implementation and low cost. In the second method, the cold storage is commonly implemented by using the PCS (phase change materials slurries), whose cold storage capacity is much larger than that of the water due to the phase change involved. The most commonly used PCS is ice slurry, which is composed of ice particles and water. However, the generation of ice slurry requires subzero temperature due to the existence of supercooling phenomenon. Therefore, the cold charging process of cold storage air-conditioning system using ice slurry is energy-intensive because of the subzero freezing temperature, which limits its practical application [3]. In recent years, a promising PCS, TBAB (tetra-n-butyl ammonium bromide) CHS (clathrate hydrate slurry), has been subjected to intensive investigation. Oyama et al. [4] investigated the fundamental thermo-physical properties of TBAB CHS and they found that the phase-change temperature of TBAB hydrate crystal was in the range of 0e12
C, which was more suitable for the cold storage air-conditioning system than that of ice slurry. And the cold storage capacity of TBAB CHS was about 2e4 times of that of chilled

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

Nomenclature A B cp C CD CL CTD ds Dpipe ess esw F g g0 h H DH I kqs K L m_ M n P Pr q_

thermal conductivity ratio of liquid phase to solid phase modified volume fraction ratio of solid phase to liquid phase specific heat, J kg1 K1 mass concentration of TBAB aqueous solution, wt% drag force coefficient lift force coefficient turbulent dispersion force coefficient solid particle diameter, m pipe diameter, m particleeparticle restitution coefficient particle-wall restitution coefficient force, N gravity acceleration, m s2 radial distribution function heat transfer coefficient, W m2 K1 enthalpy, J kg1 latent heat, J kg1 unit vector diffusion coefficient auxiliary parameter distance from the pipe wall, m mass transfer rate, kg m3 s1 molar mass, g mol1 hydration number pressure, Pa Prandtl number heat flux, W m2

water due to large latent heat of TBAB hydrate crystal. Moreover, TBAB CHS had good fluidity because the diameter of TBAB hydrate crystals was only about 0.2e0.5 mm, which was beneficial for the pumping of TBAB CHS as secondary refrigerant. During the cold release process, TBAB CHS is pumped from the storage tank to the user side and is melted to release cold energy on the user side. Therefore, the pressure drop and flow pattern of PCS are key factors for the application of the secondary refrigerant because the pressure drop determines the pumping power consumption and the flow pattern is closely relevant to the cold release as well as pressure drop. Moreover, the heat transfer coefficient of PCS during the cold release process dominates the performance of the secondary-loop air-conditioning system used in the buildings. Therefore, the knowledge of the flow and heat transfer characteristics of TBAB CHS during the flow melting process is essential for its application in the secondary-loop air-conditioning systems. So far, many investigations have been carried out to understand the flow and heat transfer characteristics of TBAB CHS. Darbouret et al. [5] measured the pressure drops of TBAB CHS and they concluded that TBAB CHS exhibited Bingham fluid behavior in laminar flow region. Kumano et al. [6] reported the flow and heat transfer characteristics of TBAB CHS in horizontal circular pipes under a constant wall heat flux of 5000 W m2, and the heat transfer coefficient was obtained by measuring the wall temperature and fluid temperature. However, the heat flux was so small that few solid particles were postulated to be melted along the flow direction. Ma et al. [7] investigated the flow and heat transfer characteristics of TBAB CHS in circular tubes with the diameters of 6.0 mm and 14.0 mm under constant heat flux within 29,190e58,500 W m2.

Re s U v T Z

59

Reynolds number ratio of distance to radius mean velocity, m s1 velocity, m s1 temperature, K auxiliary parameter

Greek letters gsl momentum exchange coefficient dsl energy exchange coefficient z bulk viscosity, mPas Qs granular temperature, K l thermal conductivity, W m1 K1 m viscosity, mPas r density, kg m3 ssl dispersion Prandtl number G diffusion coefficient, m2 s1 t shear stress, Pa f volume fraction, vol% w specularity coefficient jqs collisional dissipation of energy, kg m1 s3 u mass concentration, wt% Subscripts f fluid in inlet l liquid loc local m mean s solid w wall

They reported the local heat transfer coefficient along the flow direction by measuring the wall temperature and estimating the fluid temperature numerically. Zhang and Ye [8] also carried out investigation on the forced flow and heat transfer characteristics of TBAB CHS in mini-tubes with the diameters of 2.0 mm and 4.5 mm under constant wall heat flux within 22,121e34,607 W m2. They reported the local heat transfer coefficient along the flow direction using the energy balance approach, and it was reported that type B TBAB CHS was more beneficial to be used as the cold storage and transport medium because of smaller pressure drop and larger heat transfer coefficient. Due to the two-phase nature of TBAB CHS, the phase distribution and temperature distribution are important to obtain comprehensive knowledge on the interphase heat and mass transfer mechanism. However, to the best knowledge of the authors, the local solid fraction distribution and the local temperature distributions of solid and liquid phases during the flow melting process have not been reported because of the experimental difficulty. Hence, more efforts are need to be devoted to the investigation of the interphase heat and mass transfer mechanism of TBAB CHS. In view of the aforementioned technical difficulties in experimental investigation, CFD (computational fluid dynamics) is a promising way to obtain comprehensive knowledge on the flow and heat transfer characteristics of TBAB CHS. The solideliquid two-phase flow is mainly modeled by the Eulerian-Lagrangian and EulerianeEulerian approaches. The former approach assumes the liquid phase to be a continuum and track the solid particles through the flow field. However, such approach ignores the collision interaction among solid particles, which has massive influence on the

60

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

solid particle distribution, in particular at high solid volume fraction. In the EulerianeEulerian approach, the liquid and solid phases are both treated as interpenetrating continua. Although the EulerianeEulerian approach has not been adopted to study the flow of TBAB CHS, this approach has been successfully utilized in many kinds of solideliquid two-phase flows, such as sand-water [9] and ice slurry [10,11]. Niezgoda-Zelasko and Zalewski [10] has utilized the EulerianeEulerian approach to model isothermal ice slurry flow in horizontal circular pipes and the velocity distribution and solid volume fraction distribution were obtained. Wang et al. [11] also utilized EulerianeEulerian approach to study the ice slurry flow in straight pipes. However, the numerical modeling of heat transfer characteristics of solideliquid two-phase fluid was rarely reported. Hence, the EulerianeEulerian approach in consideration of the phase change of solid particles will be attempted to model the flow and heat transfer characteristics of TBAB CHS in the present study. In the present study, an EulerianeEulerian approach based on kinetic theory of granular flow in consideration of the interphase heat and mass exchange were utilized to model the flow melting of TBAB CHS in horizontal circular pipes under constant wall heat flux. The numerical results of the pressure drops and the variation of the wall temperatures were compared with the experimental data in order to validate the numerical models. The validated models were adopted to explore the flow melting process of TBAB CHS, in which the temperature distribution, solid volume fraction distributions and local heat transfer coefficient were obtained and analyzed for comprehensive knowledge on the flow and heat transfer characteristics of TBAB CHS. Moreover, TBAB salt in TBAB hydrate crystal would be melted and diffused into TBAB aqueous solution during melting process. Therefore, the diffusion of TBAB salt (solute) in TBAB aqueous solution was also numerically investigated in order to accurately describe such thermo-fluidic phenomena.

2. Mathematical modeling The CFD model employed in the present study utilizes kinetic theory of granular flow to describe the particleeparticle interactions. The solid particles are assumed to be spherical, inelastic and smooth. In the present study, the liquid and solid phases are both treated as interpenetrative continua and the governing equations of continuity, momentum and energy conservation are solved for each phase.

2.1. Continuity equations The continuity equations are specified for each phase, which are written as

v ðf r Þ þ V$ðfl rl ! v l Þ ¼ m_ sl vt l l

(1)

v ðf r Þ þ V$ðfs rs ! v s Þ ¼ m_ ls vt s s

(2)

with the constraint

fl þ fs ¼ 1

2.2. Momentum equations The momentum equations are written for each phase, in which the interphase momentum exchange is considered. Thus for the liquid phase, the momentum equation is expressed as

v ðf r ! v Þ þ V$ðfl rl ! v l! v l Þ ¼ V$tl þ fl rl g  fl VP þ ðm_ sl ! vs vt l l l !  m_ ls v l Þ þ M sl (4) where tl is the liquid phase stress, g is the gravitational acceleration, P is the pressure, ðm_ sl ! v s  m_ ls ! v l Þ represents the interphase momentum exchange caused by melting of TBAB hydrate crystals, M is the interphase momentum exchange composed of lift force FL, drag force FD and turbulent dispersion force FTD. For the solid phase, the momentum equation can be formulated as

v ðf r ! v s Þ þ V$ðfs rs ! v s! v s Þ ¼ V$ts þ fs rs g  fs VP  VPs vt s s þ ðm_ ls ! v l  m_ sl ! v s Þ þ M ls (5) where Ps is the solid pressure, which is defined as Eq. (6) according to the kinetic theory of granular flow.

Ps ¼ as rs Qs þ 2rs ð1 þ ess Þf2s g0 Qs

(6)

where ess is the restitution coefficient of particleeparticle collision, which will be determined by sensitivity analysis, g0 is the radial distribution function, Qs is the granular temperature. The radial distribution function, g0, is a correction factor that modifies the probability of collisions between solid particles when the solid phase becomes dense, and it can be formulated as [9]

2 g0 ¼ 41 

fs fs;max

!1=3 31 5

(7)

where fs,max is the maximum solid volume fraction depending on the solid particle shape and size distribution, and it is assigned to be 0.52 for the simple cubic packing of the monodispersed spherical particles. The granular temperature, Qs , accounts for the kinetic energy of random motion of solid particles [12], and it is estimated by solving the fluctuating energy balance equation, as shown in Eq. (8).

  3 v ðfs rs Qs Þ þ V$ðfs rs ! v s Qs Þ ¼ Ps V! v s I þ ts V! vs 2 vt þ V$ðkQs VQs Þ þ dsl  jQs (8) where kQs is the energy diffusion coefficient, dsl is the energy exchange between the liquid and solid phases, jqs is the collisional dissipation of energy. The detailed formulas for describing the above terms can be referred to the reference [13].

(3)

where the subscripts l, s denote the liquid phase and solid phase, respectively, r is the density, f is the volume fraction, ! v is the velocity vector, m_ is the mass transfer rate between solid and liquid phases induced by the melting of TBAB hydrate crystals.

2.3. Energy conservation In EulerianeEulerian multiphase model, separate enthalpy equations are adopted for each phase:

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

    v ðf r H Þ þ V$ðfi ri ! v i Hi Þ ¼ V$ le;i VTi þ ti $V! v i  hv Ti  Tj vt i i i   þ m_ ji Hj  m_ ij Hi (9) where the subscript, i, denotes solid or liquid phase when i ¼ s or l, the subscript, j, denotes the opposite phase, H is the enthalpy, T is the temperature, le,i is the effective thermal conductivity, hv is the volumetric interfacial heat transfer coefficient, ðm_ ji Hj  m_ ij Hi Þ is the energy exchange between two phases caused by the interphase mass transfer. In the near-wall region, the heat is transferred from the wall to the solid particles through point contact. Therefore, the thermal conductivity of solid particles near the pipe wall needs to be modified because the thermal conductivity of solid particles is measured through face contact. According to Legawiec and Ziolkowski [14], the effective thermal conductivity of solid particles near the wall can be expressed as

hv ¼

61

6fs hsl ds

(19)

where hv is the solideliquid heat transfer coefficient, which is given by Gunn's [16] correlation as

hsl ¼



 l1 h 1=3 1:33  2:4f1 1:2f21 Re0:7 þ 7 þ 10f1 þ 5f21 s Pr ds 

i 1=3  1 þ 0:7Re0:2 s Pr (20)

Therefore, the mass transfer rate from solid phase to liquid phase can be derived as

m_ sl ¼ hv ðT1  Ts Þ=DH

(21)

where DH represents the latent heat of TBAB hydrate crystal. 2.4. Diffusion of solute (TBAB salt) in the liquid phase

lw e;s ¼ 3ll fs sK

ðL=ds  0:5Þ

(10)

where

s ¼ 2L=ds  K¼

A A1

(11) 2    1s A1 lnðAÞ  s 1 A A

(12)

where L is the distance from the pipe wall, ds is the solid particle diameter, A is the ratio of liquid thermal conductivity to solid thermal conductivity: A ¼ ll/ls. For the liquid phase, the effective thermal conductivity near the pipe wall is formulated as [14]

lw e;l ¼ fl ll

ðL=ds  0:5Þ

(13)

In the main flow region, the effective thermal conductivities of liquid and solid phases are also affected by the solid volume fraction and they are estimated as [15]:

 pffiffiffiffiffi

lm fs ll e;l ¼ 1  lm e;s

pffiffiffiffiffi ¼ fs ðbA þ ð1  bÞZÞll

3

b ¼ 7:26  10

(22)

where C is the mass concentration of TBAB aqueous solution, G is the diffusion coefficient, which is 2  109 m2 s1 according to Flury and Gimmi [17], S is the source term caused by the melting of TBAB hydrate crystal, which is formulated as

S ¼ m_ sl  uH  m_ sl  ð1  uH Þ  (15)

(16)

where

 10=9 f B ¼ 1:25 s fl

vðrl fl CÞ þ V$ðrl ! v l fl CÞ  Dðrl Gfl CÞ ¼ S vt

(14)

where Z is formulated as

3 2 2 4 A1 B A B1 Z¼  0:5ðB þ 1Þ5 2 A ln B   B 1  AB 1  A 1  AB

When TBAB hydrate crystals are melted, TBAB salt (solute) and water molecules are dissociated and diffuse into TBAB aqueous solution, resulting in the change in mass concentration of TBAB aqueous solution. Moreover, TBAB salt will diffuse in TBAB aqueous solution due to the heterogeneity of mass concentration of TBAB aqueous solution. Therefore, the distribution of TBAB aqueous solution concentration needs to be investigated in order to accurately describe such thermo-fluidic phenomena. In addition, the mass concentration of TBAB aqueous solution significantly affects the thermo-physical properties of both TBAB aqueous solution and TBAB CHS as well as the phase-change temperature of TBAB hydrate crystal, as can be seen from the phase diagram of TBAB hydrate crystal discussed later. The diffusion equation is formulated as

(17)

(18)

In order to solve the energy conservation equations, the volumetric interfacial heat transfer coefficient, hv, is essential and it can be estimated by multiplying the solideliquid heat transfer coefficient with the specific interfacial area, which is described as

C 1C

(23)

where uH is the mass concentration of TBAB salt in the hydrate crystal, which is estimated as uH ¼ MTBAB =ðMTBAB þ n  MH2 O Þ, where M is the molar mass, n is the hydration number, which is 26.0 for type A hydrate crystal and 38.0 for type B hydrate crystal. The first term on the right side of Eq. (23) represents the mass transfer rate of TBAB salt from hydrate crystals and the second term accounts for the dilution of the mass concentration of aqueous solution caused by the water transferred from TBAB hydrate crystal to TBAB aqueous solution. 2.5. Interphase forces The interphase forces between the solid and liquid phases mainly include drag force, lift force and turbulent dispersion force. The drag force, which plays a key role in the solideliquid two-phase flow, can be formulated as

  F D;i ¼ gsl ! vi vj!

(24)

62

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

where gsl is the solideliquid momentum exchange coefficient and it is formulated as [13]

gsl ¼

3CD rl fs fl 4ds j! v sj vl!

(25)

4:8 0:63 þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Res =j! v sj vl!

!2 (26)

The lift force caused by the slip velocity is defined in the following equation [18]

  vj! v lÞ F L;i ¼ CL fs rl ! v i   ðV  !

(27)

where CL is the lift force coefficient, which is assigned to be 0.2. The turbulent dispersion force accounts for the interphase turbulent momentum transfer, resulting in more uniform distribution of solid volume fraction. The turbulent dispersion force can be described as [19]

F TD;i

mt;i ¼ CTD gsl ssl

(29)

Tpc; B ¼ 272:3 þ 100:56  C  306:14  C 2 þ 291:35  C 3 (30)

where CD is the drag force coefficient that is expressed as

CD ¼

Tpc; A ¼ 267:7 þ 96:046  C  128:4  C 2

Vfj Vfi  fj fi

! (28)

where CTD is the turbulent dispersion coefficient, and it is assigned to be 1; ssl is the dispersion Prandtl number, and it is 0.9.

In the numerical calculation, the mass transfer from the solid phase to liquid phase occurs only when the solid temperature is higher than the phase-change temperature corresponding to the local mass concentration of TBAB aqueous solution. Hence, the diffusion equation, Eq. (22), is utilized to capture the distribution of mass concentration of TBAB aqueous solution in the present study. 2.8. Boundary and initial conditions At the inlet, uniform volume fractions, velocities and temperatures of solid and liquid phases are specified. For the outlet, atmospheric pressure outlet boundary condition is adopted. At the pipe wall, no-slip wall condition is applied for the liquid phase and JohnsoneJackson partial-slip condition is adopted for the solid phase [22]. The slip characteristics between the solid particles and pipe wall are dominated by the particle-wall restitution coefficient esw, and the specularity coefficient w, which accounts for the parallel and tangential momentum losses of the solid particles caused by the collision, respectively. Moreover, a constant heat flux is applied at the pipe wall. In addition, the initial conditions of TBAB CHS in the entire flow field are assigned to be the same as those at the inlet. 3. Numerical procedures

2.6. Turbulence equations For the turbulent flow, the per-phase kε turbulence model is adopted for both the liquid and solid phases in order to capture the comprehensive features of TBAB CHS flow. The detailed k and ε equations describing the per-phase turbulence model are in standard form and they can be referred to the reference [20].

2.7. Thermo-physical properties of solid and liquid phases Shown in Table 1 is the thermo-physical properties of solid and liquid phases [7,21], which vary with the temperature and the mass concentration of TBAB aqueous solution. It was reported by Oyama et al. [4] that two types of TBAB hydrate crystals can be generated in TBAB aqueous solution, i.e., types A and B. The two types of TBAB hydrate crystals have different hydration numbers of 26 and 38, resulting in different transmittance, crystal morphology and equilibrium temperature. The thermo-physical properties of two types of TBAB hydrate crystals only vary slightly with the temperature; hence the constant values are utilized here. For TBAB aqueous solution, the density and thermal conductivity are from the literature [7]. The viscosity of TBAB aqueous solutions at mass concentration of 5.0 wt%, 20.0 wt% and 40.0 wt% are measured using BROOKFIELD RST-CC rheometer (uncertainty: 1% FS) and fitted as a exponential function of temperature, as shown in Table 1. The viscosity of TBAB aqueous solution at mass concentration in the range of 5.0e40.0 wt % was interpolated. In addition, the phase-change temperature of TBAB hydrate crystal is essential for the heat transfer characteristics of TBAB CHS. Shown in Fig. 1 is the phase diagram of TBAB hydrate crystal [21]. As can be seen, the phase change temperatures of two types of TBAB hydrate crystal are affected by the mass concentration of TBAB aqueous solution significantly, which can be fitted as

Three-dimensional models of the circular horizontal pipe are built for the investigation of the flow and heat transfer characteristics of TBAB CHS using the commercially available software ANSYS-FLUENT 14.5. The length and diameter of the circular pipes are the same as the experimental conditions reported in the literature. In the present study, structured hexahedron grid cells are adopted in the mesh generation and the grids near the wall are refined so as to comprehensively capture the complex flow and heat transfer characteristics. After grid-independence analysis, the grids for different pipes are determined. For example, 792,000 grid cells with 720 on the pipe cross-section and 1100 along the flow direction are adopted for a pipe with a diameter of 6.0 mm and length of 1.1 m. The finite volume integral approach is utilized to discretize the governing equation, where the second-order scheme is adopted. And the phase-couple SIMPLE algorithm is used to solve the discrete equations. During the iterative computation of the discrete equations, the numerical calculations are treated as convergent while all the residuals are lower than 1.0  104. Moreover, the time step is initially assigned to be 0.001s in order to promote the convergence. When the convergence rate is fast enough, the time step is increased to 0.005s in order to accelerate the computation. The numerical solution is considered to reach steady state when the mass-average temperature and solid volume fraction at the outlet do not change with the time. 4. Results and discussion 4.1. Pressure drop of TBAB CHS in circular pipes So far, there are few experimental data on the velocity and solid volume fraction distribution of TBAB CHS in circular pipes being reported, which are due to the technical difficulty of

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

63

Table 1 Thermo-physical properties of TBAB aqueous solutions and TBAB hydrate crystal [7,21].

TBAB aqueous solution

Property

Value

Density (kg m3) Viscosity (mPa s)

ml; c5 ¼ 0:6 þ 1:92  eðT273:15Þ=19:76 ðC ¼ 5 wt%Þ

rl ¼ 1003:706  0:3959T þ 102:883C ml; c20 ¼ 1:34 þ 4:07  eðT273:15Þ=14:74 ðC ¼ 20 wt%Þ

TBAB hydrate crystal (type A)

TBAB hydrate crystal (type B)

ml; c40 ¼ 2:23 þ 17:2  eðT273:15Þ=13:64 ðC ¼ 40 wt%Þ

Thermal conductivity (W m1 K1) Specific heat (kJ kg1 K1) Density (kg m3) Diameter (mm) Specific heat (kJ kg1 K1) Thermal conductivity (W m1 K1) Latent heat (kJ kg1) Density (kg m3) Diameter (mm) Specific heat (kJ kg1 K1) Thermal conductivity (W m1 K1) Latent heat (kJ kg1)

experimental measurement. Therefore, only the numerical pressure drops were compared with the experimental results to validate the numerical models. Fig. 2 shows the comparison between the numerical pressure drops and experimental data [7,8] at different velocities and solid volume fractions, where there is no heating on the pipe wall. And the particleeparticle restitution coefficient ess, particle-wall restitution coefficient esw and particlewall specularity coefficient w were 0.9, 0.95, 0.2, respectively, which were determined referring to the previous numerical investigation [23] and sensitivity analysis. As shown in Fig. 2(a), the pressure drop of type A TBAB CHS was higher than that of type B TBAB CHS at the same velocity and similar solid mass fraction. Such phenomenon was mainly caused by the difference of size and morphology between type A and type B TBAB hydrate crystals, as concluded by Zhang and Ye [8]. Hence, type B TBAB CHS was more beneficial for practical application because of the reduction of pumping power of TBAB CHS used as secondary refrigerant. Fig. 2(b) shows the comparison of pressure drop variation with solid volume fraction. It was noticed that the experimental pressure drop of TBAB CHS did not always increase as the increase in solid volume fraction, which was also reported by Kumano et al. [24]. Such phenomenon was explained by Ma et al. [7] and Kumano et al. [24] as “laminarizing effect”. Although the numerical pressure drop did not show such phenomenon, the numerical and experimental pressure drops were generally in good agreement within the deviation in a range of 15.0% to þ12.0%, which validated the numerical models.

ll ¼ 0.5810.564C 4.03 1080.0 0.5 2.22 0.42 193.2 1030.0 0.3 2.0 0.47 199.6

Ma et al. [7] also calculated the fluid temperature numerically using a simplified 1-D model, thus the local heat transfer coefficient were estimated according to the following formula:

hloc ¼

(31)

where q_ is the wall heat flux, Tw is the wall temperature, Tm,f is the mean fluid temperature on the cross-section of the pipe. Fig. 4 shows the comparison of the numerical local heat transfer coefficient obtained by Ma et al. [7] and the present study. In the investigation carried out by Ma et al. [7], the mean fluid temperature was estimated by the energy balance equation using a simplified 1-D numerical model, in which the flow behavior and the interphase heat and mass exchange were not considered. Hence, there was discrepancy between the results of the present study and Ma et al. [7]. However, the general variation tendencies of the heat transfer coefficient are similar. It was noticed that the local heat transfer coefficient at wall heating of 993 W decreased more quickly than that of 605 W because the wall temperature increased more quickly, as shown in Fig. 3. Moreover, the local heat transfer coefficient at wall heating of 993 W increased beyond 0.8 m from the inlet because the mean fluid temperature increased quickly, resulting from the low solid volume fraction near the outlet.

286

4.2. Wall temperature and heat transfer coefficient along the flow direction

284 282

T (K)

In order to validate the heat and mass transfer model of TBAB CHS, the numerical models were utilized to investigate the flow melting of type B TBAB CHS in a circular pipe with a diameter of 6.0 mm and length of 1.1 m, which was the same as the experimental condition of Ma et al. [7]. The numerical wall temperatures were compared with the experimental results, as shown in Fig. 3. As can be seen, the numerical wall temperature and the experimental results were in good agreement with the deviation in a range of 0.6 to 0.5
C. It was noticed that the wall temperature at a heating of 993 W increased more quickly than that of 605 W due to more energy supplied. Moreover, the wall temperature at a heating of 993 W almost kept constant near the outlet, because the solid particles near the outlet were almost melted at an intensive heating.

q_ Tw  Tm;f

280 278

Type A [21] Fitted curve of type A (Eq. 29) Type B [21] Fitted curve of type B (Eq. 30)

276 274 0

5 10 15 20 25 30 35 40 45 Mass concentration of TBAB aqueous solution, C (wt%) Fig. 1. Phase diagram of TBAB hydrate crystal [21].

64

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

300 298 296

6.0 mm, 993 W, 0.806 m/s, 17.7 vol%: Ma et al. [7] Present study

T (K)

294 292 290 288

6.0 mm, 605 W, 0.71 m/s, 18 vol%: Ma et al. [7] Present study

286 284 282 0.0

0.2

0.4

0.6

Axial distance (m)

0.8

1.0

Fig. 3. Comparison between the numerical wall temperatures and the experimental data [7].

4.3. Flow and heat transfer characteristics of TBAB CHS The comprehensive flow and heat transfer characteristics of type B TBAB CHS is investigated by taking the numerical results of type B TBAB CHS flow melting in 6.0 mm pipe under wall heating of 993 W as an example. Figs. 6e8 show the numerical results, which are obtained under the conditions of Tin ¼ 276.9 K, fin ¼ 17.7 vol%,

4000 3800

Dpipe=6.0 mm 605 W, 0.71 m/s, 18 vol% (Ma et al. [7]) 605 W, 0.71 m/s, 18 vol% (Present study) 993 W, 0.806 m/s, 17.7 vol% (Ma et al. [7]) 993 W, 0.806 m/s, 17.7 vol% (Present study)

3600 -2 -1

Zhang and Ye [8] investigated the heat transfer characteristics of TBAB CHS flowing through a 4.5 mm diameter mini-tube, and the wall temperature was measured. In order to estimate the local heat transfer coefficient, they also numerically calculated the fluid temperature using a one-dimensional model, in which the fluid temperature and solid volume fraction on the cross-section of the pipe was assumed uniform. The comparison of the wall temperature and local heat transfer coefficient from the literature and the present study are shown in Fig. 5(a) and (b). The predictions of the wall temperature were in good agreement with the measured results, as show in Fig. 5(a). However, similar to the cases in Fig. 4, there was discrepancy between the local heat transfer coefficients obtained in the present study and those from the literature, as shown in Fig. 5(b), resulting from the different numerical models used in the calculation.

hloc (W K m )

Fig. 2. Comparison between the numerical pressure drops and experimental data [7,8]: (a) Variation of pressure drop with velocity, (b) Variation of pressure drop with solid volume fraction.

U ¼ 0.806 m s1, q_ ¼ 47,915 W m2 (i.e., Q ¼ 993 W) and C0 ¼ 5.3 wt %. It should be claimed that the distributions of wall temperature and heat transfer coefficient are shown in Figs. 3 and 4. Fig. 6 shows the distribution of solid volume fraction of TBAB CHS. As seen in Fig. 6(a) and (b), the solid volume fraction distribution was almost symmetrical due to the small density difference between type B TBAB hydrate crystal and TBAB aqueous solution, which was within 3%, as shown in Table 1. According to the previous study [9,11], the solid volume fraction distribution was also affected by the mean flow rate and the mean solid volume fraction. Higher mean flow rate and solid volume fraction would lead to more homogeneous distribution of the solid volume fraction due to the more intensive particleeparticle collision. However, the nearly symmetrical distribution of TBAB CHS in the present study was mainly dominated by the small density difference between the solid and liquid phases according to the sensitivity analysis. In the near-wall region, some solid particles were repelled away from the pipe wall due to the particle-wall collision. Such phenomenon in the solideliquid two-phase flow was also observed in the previous experiments [25,26]. Kaushal and Tomita [25] have measured the solid volume fraction of glass-water slurry and they found that the glass particles were repelled away from the pipe wall in particular at small inlet flow rate and inlet solid volume fraction. Gillies and Shook [26] also reported that the solid volume fraction of sand

3400 3200 3000 2800 2600 2400 2200 0.0

0.2

0.4

0.6

Axial distance (m)

0.8

1.0

Fig. 4. Comparison of the numerical local heat transfer coefficients in the present study with those obtained by Ma et al. [7].

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

65

slurry near the wall was lower than that in the center region. Meanwhile, many solid particles were melted because of the heating loaded on the pipe wall. Hence, the solid volume fraction near the wall decreased quickly along the flow direction, as shown in Fig. 6(a) and (b). It can also be seen that the solid volume fraction distribution at 0.01 m showed different tendency with those at other locations. In the case of 0.01 m, the solid particles near the wall were repelled away from the pipe wall; however the solid particles in the center region were still not affected by the flow and heat transfer because of the inlet effect. Therefore, the solid particles that were repelled away from the wall agglomerated at about ±0.75R, resulting in a higher local solid volume fraction. Fig. 7 shows the temperature distribution of TBAB CHS. As shown in Fig. 7(a), the liquid temperature near the pipe wall increased more quickly than that at the pipe center region because the heat was transferred from the pipe wall. On the other hand, the solid temperature shown in Fig. 7(b) increased much more slowly than the liquid temperature, in particular in the center region. This was because that TBAB hydrate crystals were melted at temperature higher than the phase-change temperature, resulting in the release of latent heat. The temperature difference between the solid and liquid phases was also found in many other solideliquid twophase slurry flows, such as micro-nano-size PCS in microchannels

Fig. 6. Solid volume fraction distribution of TBAB CHS (Tin ¼ 276.9 K, uin ¼ 17.7 vol%, U ¼ 0.806 m s1 and q_ ¼ 47,915 W m2, C0 ¼ 5.3 wt%): (a) along the vertical symmetry axis of different pipe cross-sections, (b) on the central symmetrical plane of the pipe.

with constant wall heat flux or wall temperature [27] and slush nitrogen in horizontal pipes with constant heat flux [28]. As can also be seen in Fig. 7, the temperatures at the upside and downside were not completely symmetrical, which was due to the slight sedimentation of solid particles. Fig. 8 shows the distribution of the mass concentration of TBAB aqueous solution. As can be seen, the mass concentration of TBAB aqueous solution increased rapidly near the wall because a lot of TBAB salt in TBAB hydrate crystals was released due to the melting of TBAB hydrate crystal and diffused into TBAB aqueous solution. On the other hand, the mass concentration of TBAB aqueous solution in the center region increased gradually with the decrease in solid volume fraction, as shown in Fig. 6. It was apparent that such variation of the mass concentration of TBAB aqueous solution would result in significant change of the thermo-physical properties of both TBAB aqueous solution and TBAB CHS as well as the phase-change temperature of TBAB hydrate crystal. For example, the phase change temperature of type B TBAB hydrate crystal increased from 276.7 K to 282.8 K while the mass concentration of TBAB aqueous solution increased from 5.0 wt% to 30.0 wt%, as shown in Fig. 1. Therefore, the melting of TBAB hydrate crystals occurred at higher temperature near the wall than that at the pipe center region. In order to clarify the heat transfer characteristics between the pipe wall and the fluid, the heat flux transferred from the wall to the solid and liquid phases were estimated as

q_ i ¼ le;i

Fig. 5. Comparison of the wall temperatures and local heat transfer coefficients in the present study with those from the literature [8]: (a) wall temperature, (b) local heat transfer coefficient.

 vTi  vr wall

(32)

Shown in Fig. 9 is the heat flux transferred to the solid and liquid phases and the effective thermal conductivity of the solid phase at the pipe wall. As seen in Fig. 9, the effective thermal conductivity of solid phase at the wall decreased quickly along the flow direction and it was close to zero at the outlet, resulting from the rapid

66

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

Fig. 7. Temperature distribution on the central symmetrical plane of the pipe (Tin ¼ 276.9 K, uin ¼ 17.7 vol%, U ¼ 0.806 m s1 and q_ ¼ 47,915 W m2, C0 ¼ 5.3 wt%): (a) liquid temperature, (b) solid temperature.

decrease in solid volume fraction near the wall, as shown in Fig. 6. Therefore, the heat flux transferred from the wall to the solid phase was very small and the heat on the wall was mainly transferred to the liquid phase, as shown in Fig. 9. Consequently, the heat flux loaded at the pipe wall was mainly absorbed by the liquid phase, resulting in quick temperature increase of liquid phase, as shown in Fig. 7(a). And then the temperature difference between the solid particles and surrounding liquid led to the interphase heat transfer. Thus the solid particles would be melted when the solid temperature was higher than the phase-change temperature of TBAB hydrate crystal. Fig. 10 shows the mean temperature of TBAB CHS on the pipe cross-section along the flow direction. As can be seen, the mean liquid temperature increased more quickly than the mean solid temperature because the heat loaded on the wall was mainly absorbed by the liquid phase and the heat transferred from the liquid phase to solid phase mainly contributed to the latent heat released by TBAB hydrate crystals. Fig. 11 shows the mean mass transfer rate and mean solid volume fraction along the flow direction. As can be seen, the mean mass transfer rate increased rapidly in the entrance region and decreased in the fully-developed region. Meanwhile, the mean solid volume fraction decreased with the melting of TBAB hydrate crystals. It was noticed that the variation of mean fluid temperature, mass transfer rate and solid volume fraction experienced three stages, which can be interpreted as follows:

increased due to the increase in the mass concentration of TBAB aqueous solution, as shown in Fig. 8. (2) In Region II between about 0.1 and 0.8 m, a lot of solid particles near the wall were melted and the solid volume fraction near the wall decreased quickly from about 8.0 vol% to 0.5 vol%, as shown in Fig. 6. And TBAB hydrate crystals in the pipe center region were difficult to be melted. Therefore, the mean mass transfer rate from the solid phase to liquid phase decreased along the flow direction, as shown in Fig. 11. Consequently, the contribution of phase change of TBAB hydrate crystals to the heat exchange decreased along the flow direction, resulting in decreasing local heat transfer coefficient from 3320.0 W m2 K1 to 2300.0 W m2 K1, as shown in Fig. 4. Similar to Region I, the mean solid temperature also increased slowly corresponding to the increasing phase-change temperature in Region II. (3) In Region III beyond 0.8 m from the inlet, the mean solid volume fraction was close to zero, as shown in Fig. 11. Thus the heat transferred from the liquid phase to solid particles mainly contributed to the sensible heat, resulting in quicker increase in the mean temperatures of solid and liquid phases, as shown in Fig. 10. Thus, the temperature difference between the pipe wall and fluid decreased beyond 0.8 m from the inlet, resulting in increasing heat transfer coefficient from 2300.0 W m2 K1 to 2670.0 W m2 K1, as shown in Fig. 4.

(1) In Region I, about 0.1 m from the inlet, the mean fluid temperature increased from 276.9 K to about 279.0 K, as shown in Fig. 10. Meanwhile, the wall temperature increased rapidly from the initial value to about 293.0 K, as shown in Fig. 3, which was much quicker than that of the mean fluid temperature. Hence, the heat transfer coefficient decreased quickly to about 3120.0 W m2 K1 in Fig. 4 due to the rapid increase in temperature difference between the wall and fluid. Moreover, the mass transfer rate also increased rapidly from about 40.0 kg m3 s1 to 120.0 kg m3 s1, as shown in Fig. 11, resulting from the thermal developing of TBAB CHS in the entrance region of the pipe. It was also noticed in Fig. 10 that the mean solid temperature increased slowly along the flow direction, because the phase-change temperature

Fig. 12 shows the schematic illustration of the melting process of TBAB CHS in heated pipe. During the melting process of TBAB CHS, the solid particles were melted and the solid volume fraction decreased along the flow direction. After TBAB hydrate crystals were almost fully melted, TBAB CHS can be considered as single phase fluid. Meanwhile, the mass concentration of TBAB aqueous solution was changed due to the melting of TBAB hydrate crystal and diffusion of TBAB salt (solute) in TBAB aqueous solution. As can be seen in Fig. 12, the mass concentration of TBAB aqueous solution increased rapidly near the wall due to the intensive melting of TBAB hydrate crystals. Meanwhile, the mass concentration of TBAB aqueous solution increased gradually in the center region due to the melting of TBAB hydrate crystal and diffusion of TBAB salt from the near-wall region.

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

67

Fig. 10. Mean fluid temperature of TBAB CHS in the pipe cross-section along the flow direction.

(1) The numerical pressure drops and wall temperatures agreed well with the experimental data, indicating that the EulerianeEulerian multiphase approach coupled with heat and mass transfer model were appropriate for modeling the flow melting of TBAB CHS in horizontal circular pipes.

(2) When TBAB CHS flowed through horizontal pipes under constant wall heat flux, the heat was mainly absorbed by the liquid phase due to the point contact between the solid particles and pipe wall. The temperature difference between the liquid and solid phases induced the interfacial heat exchange, resulting in the melting of solid particles. (3) In the entrance region, the local heat transfer coefficient decreased rapidly due to the rapid increase in the wall temperature. In the thermally fully-developed region, mass transfer rate from the solid particles to liquid phase decreased because the rapid decrease of solid volume fraction near the wall impeded the phase change. Therefore, the local heat transfer coefficient decreased along the flow direction due to the decreasing contribution of phase change to the heat exchange. Moreover, the solid temperature increased slowly corresponding to the increasing phasechange temperature caused by the increase in mass concentration of TBAB aqueous solution. After the solid volume fraction was close to zero, the heat mainly contributed to the sensible heat, resulting in quicker increase in the fluid temperature. Hence, the temperature difference between the wall and fluid decreased along the flow direction, resulting in increase in the local heat transfer coefficient.

Fig. 9. Heat flux from the pipe wall to the solid and liquid phases and the effective thermal conductivity of solid phase at the pipe wall.

Fig. 11. Mean mass transfer rate and mean solid volume fraction along the flow direction.

Fig. 8. The distribution of mass concentration of TBAB aqueous solution (Tin ¼ 276.9 K, uin ¼ 17.7 vol%, U ¼ 0.806 m s1 and q_ ¼ 47,915 W m2, C0 ¼ 5.3 wt%): (a) along the vertical symmetry axis of different pipe cross-sections, (b) on the symmetrical plane of the pipe.

5. Conclusions In the present study, the flow and heat transfer characteristics of TBAB CHS through horizontal circular pipes were investigated numerically using EulerianeEulerian multiphase model based on kinetic theory of granular flow coupled with heat and mass transfer models. After validation of the numerical model, it was applied to interpret the flow and heat transfer characteristics of TBAB CHS. The conclusions were drawn as follows:

68

X.J. Shi, P. Zhang / Energy 99 (2016) 58e68

Fig. 12. Schematic illustration of the melting process of TBAB CHS in heated pipe.

Acknowledgment This research is jointly supported by the National Natural Science Foundation of China under the Contract No. 51176109 and NSFC-JSPS Cooperative Project under the contract No. 51311140169.

References [1] Mosaffa AH, Garousi FL, Infante Ferreira CA, Rosen MA. Advanced exergy analysis of an air conditioning system incorporating thermal energy storage. Energy 2014;77:945e52. [2] Sanaye S, Fardad A, Mostakhdemi M. Thermoeconomic optimization of an ice thermal storage system for gas turbine inlet cooling. Energy 2011;36: 1057e67. [3] Li G, Hwang Y, Radermacher R, Chun HH. Review of cold storage materials for subzero applications. Energy 2013;51:1e17. [4] Oyama H, Shimada W, Takao E, Kamata Y, Takeya S, Uchida T. Phase diagram, latent heat, and specific heat of TBAB semiclathrate hydrate crystals. Fluid Phase Equilibr 2005;234:131e5. [5] Darbouret M, Cournil M, Herri JM. Rheological study of TBAB hydrate slurries as secondary two-phase refrigerants. Int J Refrig 2005;28:663e71. [6] Kumano H, Hirata T, Tomoya K. Experimental study on the flow and heat transfer characteristics of a tetra-n-butyl ammonium bromide hydrate slurry (second report: heat transfer characteristics). Int J Refrig 2011;34:1963e71. [7] Ma ZW, Zhang P, Wang RZ, Furui S, Xi GN. Forced flow and convective melting heat transfer of clathrate hydrate slurry in tubes. Int J Heat Mass Transfer 2010;53:3745e57. [8] Zhang P, Ye J. Experimental investigation of forced flow and heat transfer characteristics of phase change material slurries in mini-tubes. Int J Heat Mass Transfer 2014;79:1002e13. [9] Ekambara K, Sanders RS, Nandakumar K, Masliyah JH. Hydrodynamic simulation of horizontal slurry pipeline flow using ANSYS-CFX. Ind Eng Chem Res 2009;48(17):8159e71. [10] Niezgoda-Zelasko B, Zalewski W. Momentum transfer of ice slurry flows in tubes, modeling. Int J Refrig 2006;29(3):429e36. [11] Wang JH, Wang SG, Zhang TF, Liang YT. Numerical investigation of ice slurry isothermal flow in various pipes. Int J Refrig 2013;36(1):70e80.

[12] Gidaspow D. Multiphase flow and fluidization: continuum and kinetic theory descriptions. 1st ed. New York: Academic Press; 1994. [13] Syamlal M, Brien TJO. Computer simulation of bubbles in a fluidized bed. AIChE Symp Ser 1989;85:22e31. [14] Legawiec B, Ziolkowski D. Structure, voidage, and effective thermal conductivity of solids within near-wall region of beds packed with spherical pellets in tubes. Chem Eng Sci 1984;49:2513e20. [15] Zehner P, Schluender EU. Warmeleitfaehig eit von schuettungen bei maessignen temperaturen. Chem Eng Technol 1970;42:933e41. [16] Gunn DJ. Transfer of heat or mass to particles in fixed and fluidised beds. Int J Heat Mass Transfer 1978;21:467e76. [17] Flury M, Gimmi T. Solute diffusion, in methods of soil analysis. Soil Sci Soc Am 2002:1323e51. [18] Drew DA, Lahey RT. Analytical modeling of multiphase. In: Particulate twophase flow. Boston: Butterworth-Heinemann; 1993. p. 509e66. [19] Burns ADB, Frank T, Hamill I, Shi JM. The favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. In: Fifth International Conference on Multiphase Flow, Yokohama, Japan; 2004. [20] Launder BE, Spalding DB. Lectures in mathematical models of turbulence. London, England: Academic Press; 1972. [21] Zhang P, Ma ZW, Shi XJ, Xiao X. Thermal conductivity measurements of a phase change material slurry under the influence of phase change. Int J Therm Sci 2014;78:56e64. [22] Johnson PC, Jackson R. Frictional-collisional constitutive relations for granular materials with application to plane shearing. J Fluid Mech 1987;176:67e93. [23] Kong L, Zhang C, Zhu J. Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds. Particuology 2014;13: 114e23. [24] Kumano H, Hirata T, Tomoya K. Experimental study on the flow and heat transfer characteristics of a tetra-n-butyl ammonium bromide hydrate slurry (first report: flow characteristics). Int J Refrig 2011;34:1953e62. [25] Kaushal DR, Harita T, Tomita Y. Experimental investigation for near-wall lift of coarser particles in slurry pipeline using g-ray densitometer. Powder Technol 2007;172:177e87. [26] Gillies RG, Shook CA. Concentration distributions of sand slurries in horizontal pipe flow. Part Sci Technol Int J 1994;12:45e69. [27] Hao YL, Tao YX. A numerical model for phase-change suspension flow in microchannels. Numer Heat Trans 2014;46:55e77. [28] Zhang P, Jiang YY. Forced convective heat transfer of slush nitrogen in a horizontal pipe. Int J Heat Mass Transfer 2014;71:158e71.