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Applied Thermal Engineering 64 (2014) 201e208

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Sliding flow method for exergetically efficient packed bed thermalstorage

Hitesh Bindra a,c,*, Pablo Bueno b, Jeffrey F. Morris c,d

aCUNY Energy Institute, City College of New York, NY 10031, USAb Southwest Research Institute, San Antonio, TX 78238, USAc Levich Institute, City College of New York, NY 10031, USAdDepartment of Chemical Engineering, City College of New York, NY 10031, USA

h i g h l i g h t s

� The effect of pressure drop on fractional exergy destruction in packed bed thermal storage is quantified, that is 2e6%.� Sliding flow method (SFM) decouples the thermal behavior and pressure drop effects in packed bed thermal storage.� The SFM significantly improves the exergy efficiency and also reduces the design constraints on thermal storage systems.

a r t i c l e i n f o

Article history:Received 18 July 2013Accepted 13 December 2013Available online 24 December 2013

Keywords:Packed bedThermal storageExergyPressure drop

* Corresponding author. CUNY Energy Institute, CiYork, NY 10031, USA.

E-mail addresses: hbindra@che.ccny.cuny.edu(H. Bindra).

1359-4311/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.12.02

a b s t r a c t

The feasibility of a thermal energy storage method is highly dependent on its exergetic efficiency. Thetwo major components which cause exergy destruction in packed bed thermal energy storagemethods are pressure drop and temperature dispersion. It is difficult to prevent exergy destructionwith existing packed bed type thermal storage systems because the effect of most physical parameterson the pressure drop is opposite to that on the mixing or axial dispersion. We propose a new slidingflow strategy in which fluid inlet and outlet ports change as the temperature front in the bed moves.In this design the typical distance between two simultaneously active inlet and outlet ports will beapproximately equal to twice the axial dispersion length. The computations presented in this papershow that the sliding flow method (SFM) is expected to perform significantly better than existingmethods and will result in substantial reduction in exergy destruction. The major advantage of theSFM is its ability to decouple thermal behavior and pressure drop effects, thus reducing the designconstraints.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Economical energy storage is currently in high demand formatching the grid demand curve and providing dispatchability tointermittent renewable energy sources. The existing electrical en-ergy storage, i.e. batteries, is not an economically viable option;therefore, other alternatives are being considered. There are manyon-going efforts to develop energy storage ideas e chemical, elec-trical, mechanical, and thermal methods. Thermal energy is the

ty College of New York, New

, nuchembins@gmail.com

All rights reserved.8

most common form used in power production so it makes sense tofind efficient ways to store it.

As thermal energy has limited capacity to do mechanical work,it is essential to know the amount of useful energy that can berecovered from its storage. The best possible parametric method toevaluate the performance of thermal energy storage is by calcu-lating the fractional exergy recovery or exergy efficiency. Therefore,to achieve higher exergetic performance, several high temperatureenergy storage ideas are being investigated and improved today.Most of these ideas can be broadly classified as phase change,reversible thermochemical, and sensible heat methods. Phasechange and reversible thermochemical methods operate favorablyonly over limited temperature ranges at which the phase changeand chemical reactions occur respectively. Among the sensible heatmethods, molten salt tank storage and packed bed solid storage are

Fig. 1. Comparison of Ergun equation and RUC model for range of particle sizes.Operating conditions and property values: rf ¼ 20 kg/m3, mf ¼ 3.6 � 10�5 Pa s, ε ¼ 0.35and v ¼ 0.3 m/s.

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208202

popular. However, molten salt methods have lower energy den-sities than packed bed methods because their operating tempera-ture range is narrow owing to upper (decomposition temperature)and lower (solidification temperature) limits on the material. Rockor packed beds for heat storage have been tested for many decadesbut major technological challenges remain, including difficulty inproducing sharp thermal gradients and the presence of high pres-sure drops. Both of these problems can lead to lower exergy re-covery which should be quantified to provide practical designguidelines.

Several researchers have developed methods to evaluate theexergy recovery of generic and mixed tank thermal storage sys-tems [1e3]. Recently, Bindra et al. [4] performed an exergy anal-ysis on packed bed thermal storage based on a multiphase thermalmodel. The model quantified the drop in exergy efficiency due toheat losses and axial dispersion. This work was validated againstexperimental data and showed that for large, practical scale sys-tems, heat losses, and therefore exergy destruction due to them,are minimal. Therefore, thermal exergy evaluation on the basis ofaxial dispersion analysis is sufficient but to compute overall exergyrecovered, work done against the pressure drop should also beincluded.

Here, we will integrate exergy losses due to pressure drop andaxial dispersion to evaluate overall exergy recovery. As shown inour previous work, and elsewhere [5], axial dispersion is a cu-mulative process and results in reduction in utilization fraction ofthe bed after each cycle if the bed is not filled completely.Therefore, one way to have a constant utilizable bed length is tofill the storage completely up to its steady state and recover theheat until the whole bed is at lowest temperature. Various modelsto quantify pressure drop inside packed beds have been developedand validated [6,7]. These models can be used to quantify workrequired to overcome the pressure drop and corresponding exergydestroyed. Now we will integrate both of these models (i.e. axialdispersion and pressure drop) to quantify the overall exergyefficiency.

As some of the important physical parameters haveopposing effects on axial dispersion and pressure drop, it isimportant to use this exergy evaluation method for optimalsystem design. Their opposing effects limit the number ofpossible designs which are exergetically feasible. As thermalstorage is considered as a new additional system for existingpower plants and proven thermal power plant designs, it re-duces the practical scope of integration with limited designsand operating range. In the sliding flow method, designed byBindra & Bueno [8], operation beyond this optimum regime isallowed and results in reduction of exergy loss. The physicalprinciples governing the sliding flow method remain the sameas in our previous work but inlet and outlet ports of the bedchange as the temperature front moves in the packed bed,effectively following the thermal front. The name sliding flow isused to emphasize that the flow path is also made to slidethrough the bed. A more detailed description of the method isprovided in later sections. This study will extend our previousmodel by integrating pressure drop into the exergy calculation,introduce the details of the sliding flow method and finallydiscuss the advantages of the new method based on overallexergy analysis.

2. Pressure drop model

The simplest and most commonly used model to predict pres-sure drop inside packed beds was developed by Ergun [6]. It hasbeen consistently used for wide range of applications for fixed andfluidized beds. The Ergun equation is as follows,

DPDx

¼ 150ε2

ð1� εÞ3mf v

d2pþ 1:75

ε

ð1� εÞ3rf v

2

dp(1)

where, DP is the pressure drop across packed bed, H is the length/height of the packed bed, ε is the porosity, mf is viscosity of fluid, rf isthe density of fluid, dp is the diameter of spherical particles, and v isthe fluid velocity. This equation provides satisfactory results forspherical particles, but due to its semi-empirical nature it is difficultto adapt it for other types of particles. The derivation of the Ergunmodel is based on the assumption of straight parallel channelswhich is very different from the reality of randomly packed beds.After the Ergun equation, various new models were devised to suitparticular applications of fixed or fluidized beds. Recently, a generalpurpose model was introduced by du Plessis and Woudberg [9].This model considers the flow in the porous regions more realis-tically by dividing the packed bed into 3-dimensional representa-tive unit cells, with each region having equivalent flow diameterbased on the porosity. Due to the division of geometry into repre-sentative unit cells, this model is called the RUC model. The accu-racy of this model was validated by Allen [10] for several massvelocities and particle sizes. Therefore we will use this model, inwhich the pressure drop per unit length is given by

DPDx

¼ mf v

d2p

264 25:4ð1� εÞ43�

1� ð1� εÞ13��

1� ð1� εÞ23�2 þ CdRep

2ε�1� ð1� εÞ23

�2375

(2)

where, Cd is drag coefficient and Rep is the Reynolds number basedon individual particle.

Fig. 1 compares the Ergun equation with the RUC model. Forlarger particle sizes both the models tend to converge but forsmaller particle sizes, the RUC model predicts higher pressure dropas compared to the Ergun equation. Hence, exergy estimates usingthe RUC model will give conservative values. Work done against

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208 203

this pressure drop (or to compensate for this pressure drop), can bedefined as

Wpd ¼Ztp

DP _mrf

dt (3)

where, Wpd is the work done, _m is the mass flow rate, and tp is thetime period for the storageerecovery cycle. This is the total workdone during the heat storage or recovery process. Density valuesused in Equation (3) are related to the spatio-temporal temperatureand pressure values of the fluid stream via the ideal gas law at aninlet pressure of 30 atm. During storage the bed temperature in-creases and during recovery it decreases. The effect of temperaturewill cause substantial change in the density of fluid streamwhich inturn has considerable impact on pressure drop and work donecalculations.

3. Exergy recovery evaluation

The inclusion of pressure drop into thermal models for evalu-ating exergy efficiency of regenerators [11] and solar air heaters[12] has been done previously. We will use the same approach forthis storage system. Before proceeding, we re-state that from ourprevious work [4] the exergy of the inlet gas/fluid storing the en-ergy in bed is given by

Xst ¼Ztp

�_mCpf ðTin � T0Þ � _mCpfT0 ln

�TinT0

��dt; (4)

where, Cpf is the specific heat of fluid and T is the temperature. Thesubscripts ‘in’ and ‘0’ represent ‘hot inlet’ and ‘reference’ conditionsrespectively. However, this hot gas/fluid is used to store this energyin packed bed for the cycle time period tp, and therefore duringrecovery cycle the exergy of outlet fluid (at temperature Tout) isequal to

Xrec ¼Ztp

�_mCpf ðTout � T0Þ � _mCpfT0 ln

�ToutT0

��dt: (5)

Fractional exergy recovery or thermal exergy efficiency of thestorage system is defined as

hth ¼ Xrec

Xst; (6)

ignoring the pressure drop effects. However, pressure drop effectsare generally significant for packed beds and should be consideredto evaluate the net exergy recovery. The net fractional exergy re-covery can thus be expressed as

hex ¼ Xrec � 2Wpd

Xst(7)

hex ¼ Xrec

Xst� 2Wpd

Xst(8)

hex ¼ hth � hpd (9)

where, hth is thermal exergy efficiency and hpd is fractional exergydestroyed due to pressure drop.

hex ¼

Ztp

qf þ1� hcarnothcarnot

ln qfhcarnot

1� hcarnot

� �þ 1

� �� �dt

Ztp

1þ 1� hcarnothcarnot

ln1

1� hcarnot

� �� �dt

�

Ztp

_mDPstrst

þ _mDPrecrrec

� �dt

_mCpf Tin � T0ð Þ

� 1Ztp

1þ 1� hcarnothcarnot

ln1

1� hcarnot

� �� �dt

(10)

where, hth is thermal exergy efficiency and hpd is fractional exergydestroyed due to pressure drop.

hex ¼

Ztp

qf þ1� hcarnothcarnot

ln qfhcarnot

1� hcarnot

� �þ 1

� �� �dt

Ztp

1þ 1� hcarnothcarnot

ln1

1� hcarnot

� �� �dt

�

Ztp

DPstrst

þ DPrecrrec

� �dt

Cpf Tin � T0ð Þ

� 1Ztp

1þ 1� hcarnothcarnot

ln1

1� hcarnot

� �� �dt

(11)

where, hcarnot is the Carnot efficiency based on reference temper-ature, T0 and hot inlet temperature, Tin. Therefore, the overallexergy efficiency includes the thermal exergy efficiency (first termof Equations (8)e(11)), which was evaluated in previous work [4],and the effect of pressure drop in exergy destruction (second termof Equations (8)e(11)). The second term has pressure drop in thenumerator which signifies higher fractional exergy loss with higherpressure drop. The denominator of the second term has Tin � T0which implies that higher inlet temperature for storage will lead tolower fractional exergetic loss with same amount of pressure dropthrough the storage bed. Therefore, it is desirable to operate thesystem at maximum possible temperature for better performanceof thermal storage. In this analysis the Carnot efficiency is assumedto be 72% based on an inlet temperature of 800 �C and ambienttemperature of 25 �C.

4. Description of sliding flow method

The conventional method of storing thermal energy in packedbeds has the flow entering from one end of the bed and leaving atthe other end. In order to avoid any confusion we will name thisconventional approach as ‘original method’. In the original method,the fractional length of dispersed front, i.e. ratio of dispersedtemperature front to the total length, determines the destroyedexergy from the bed. The longer the length of the bed, the smaller isthe fractional thermal exergy destruction, but a longer bed alsocauses higher pressure drop, which results in exergy destruction aswell. In addition, for most of the cases where it is intended torecover thermal energy from flue gas, the pressure drop is limitedby the existing set-up and design. For these reasons, it is required todesign systems which incur higher pressure drops but lower axialdispersion. One easy operational configuration which can fulfill

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208204

both these requirements is to reduce mass velocity, but theextended filling times will result in higher losses to ambience [4].And, the limitation the low flow rate places on recovery of storedheat may be operationally unacceptable. Due to these constraints, anovel design [8] termed the sliding flow method (SFM) has beendeveloped, which can reduce fractional axial dispersion and pres-sure drop simultaneously. This method is named ‘sliding flow’ asthe flow path, inlet and outlet ports to the storage vessel/system,change during the storage operation as the temperature frontmoves in the bed unlike the original storage method. In the SFM,instead of a bed with one inlet and outlet, the bed is divided intomany segments such that the length of each segment is roughlyequal to the length of the dispersed front. The arrangement is suchthat fluid inlet and outlet can be connected to any of these seg-ments. Illustration of this design is shown in Fig. 2, where a fulllength packed bed is divided into four segments.

During the storage portion of a cycle, hot fluid is introduced tothe first segment and after transferring its heat into the first twosegments, it exits through the second bed outlet. With thisarrangement, the pressure drop, across the portion of the packedbed in which the flow takes place, is only a fraction of the pressuredrop incurred in the original method. After the first segment is fullysaturated or the fluid exiting from it reaches its steady top tem-perature, there is no need to feed more hot fluid to the firstsegment. At that point a switch is made to introduce hot fluid at theentrance of the second segment and cold fluid exits from the end ofthe third segment. This changeover is done again after saturatingthe second segment. Then the fluid is fed into the third segmentand leaves out of fourth segment. Therefore with this method theinstantaneous flow path is always equal to the length of two seg-ments, or in other words, for this example, the pressure drop is

Fig. 2. Schematic of earlier packed bed thermal storage and sliding flow (new)method. a) Existing method with flow path; b) Showing division of storage bed intofour segments with flow entering first segment and leaving second; c) Flow enteringsecond segment and leaving third segment; d) Flow entering third segment andleaving fourth.

always half as compared to the pressure drop in original methodwith full packed bed always in-line. This method of separatingpressure drop effects from heat transfer effects ensures that axialdispersion remains the same.

In this simple illustration example, we divided our bed into foursegments but the number of segments and divisions can bemade aslarge as is necessary or convenient. If there were six segments withtwo carrying flow at any instant, the pressure drop will becomeone-third of the pressure drop inside the full packed bed and so on.However due to division into segments, the system requires addi-tional valves and piping which can lead to higher capital costs.Further optimization based on this increment in capital costs andreduction in operating costs is required to make final decisions, butthat is beyond the scope of this work. The assumptions of uniformflow distribution and negligible wall effects result in formulation ofa thermal convectionediffusion model in the axial direction. Thisthermal model, along with intraparticle diffusion effects, was pre-sented in previous work [4]. The intraparticle diffusion effects canbe ignored as the properties and operation of the system ensurethese effects are negligible. The more appropriate thermal modelshould include the effect of temperature on thermo-physicalproperties of the materials such as specific heat, density and ther-mal conductivity. This model can be written as

v

vt

�rf CpfTf

�þ v

v

vx

�rf CpfTf

�¼ v

vx

�kfvTfvx

�� hfs

�Tf � Ts

�

� bw

�Tf � T0

�;

(12)

v

vt

�rsCpsTs

¼ v

vx

�kfvTfvx

�þ hfs

�Tf � Ts

�: (13)

where, k is thermal conductivity, hfs is fluidesolid volumetric heattransfer coefficient and bw is the wall heat transfer coefficient. Thetemperature dependence of the properties is listed in Table 1[13,14].

Density, as shown in Table 1, is computed from ideal gas lawwhere M ¼ 29 and R are the molecular weight and universal gasconstant respectively. Ignoring the effect of temperature onthermo-physical properties, the model in non-dimensional formleads to following set of equations:

vqfvs

þ vqfvX

¼ 1Peaf

v2qfvX2 � Stfs

�qf � qs

�� Stw

�qf � q0

�; (14)

vqsvs

¼ 1Peas

v2qsvX2 þ kStfs

�qf � qs

�: (15)

where, q is dimensionless temperature, X is dimensionless length, sis dimensionless time, Pea is Axial Peclet number, St is Stantonnumber, and k is ratio of fluid to solid phase specific heat. Thesubscripts ‘f’, ‘s’ and ‘w’ stand for fluid, solid and wall respectively.Two significant non-dimensional parameters are introduced in thismodel, Stw ¼ bwH=ðrCpÞf v and Stfs ¼ 6haH=ðrCpÞf dpv, are used for

Table 1Dependence of thermo-physical properties on temperature.

rf (kg/m3) PM/RTCpf (J/kg/K) 9:584� 10�4T2

f � 4:314� 10�1Tf þ 1061kf (W/m) 9.789 � 10�5Tf þ 1 � 10�4

ks (W/m) �0.07Ts þ 39

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.35 0.4 0.45 0.5 0.550.75

0.8

0.85

0.9

0.95

1

θθ

Fig. 3. a) Comparison of dimensionless temperature results with two models. b)Zoom-in view shows higher axial dispersion for model with temperature dependentproperties.

Table 2Properties and conditions used in all numerical cases.

rf (kg/m3) 20Cpf (J/kg/C) 1000ks (W/m/C) 20ha (W/m2/C) 280ε 0.35v (m/s) 0.3mf (Pa s) 3.6 � 10�5

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208 205

quantitative analysis. Initial and boundary conditions of the bed forcomputing the storage process are

qf ;sðX; s < 0Þ ¼ 0; (16)

qf ðX ¼ Xen; s � 0Þ ¼ 1: (17)

More details about the hot fluid entrance boundary conditionfor each segment will be discussed in the next section. Similarly forthe recovery process, after the storage time sst, the initial andboundary conditions can be mathematically stated as

qf ðX; s < 0Þ ¼ qf ðX; sstÞ; (18)

qsðX; s < 0Þ ¼ qsðX; sstÞ; (19)

qf ðX ¼ Xen; s � 0Þ ¼ 0: (20)

For all computations, a zero axial gradient boundary condition isassumed at the exit. The comparison of results from models withtemperature dependent properties and constant properties speci-fied at average temperature (Table 2) are plotted in Fig. 3. Resultsshow slight increase in the axial dispersion length with the use oftemperature dependent properties. However, as this work is onlyintended to use the thermal and pressure drop models for pre-senting a novel design methodology i.e. SFM, to keep the exergycalculations simple we will use constant properties at averagetemperature values. In future work, more accurate models will beused to compare against experimental data.

5. Results and discussion

The contributions of the two components (thermal andpressure-drop) on the fractional exergy recovery or exergy effi-ciency are determined by two methods. The thermal component,hth, is computed using the solution of themodel, as described in ourprevious work [4]. Analysis conducted in that work included theeffect of wall heat losses, axial dispersion and intra-particle diffu-sion modeled with the non-dimensional parameters: wall Stantonnumber Stw, fluidesolid Stanton number Stfs and Peclet number ofeach particle Pefp ¼ d2pv=4aH respectively. But as stated earlier,here, only the effect of axial dispersion will be considered as wallheat losses are small for large vessel cross-section and intra-particle diffusion is small for particles in the bed with the numer-ical assumption that Pefp < 300.

The fluidesolid Stanton number was varied to compute itsimpact on thermal component of fractional exergy recovery; Stfs isdirectly related to height or length of the bed, H, and inverselyrelated to particle diameter, dp. Temperature value at each discretelocation is used to estimate corresponding density and resultantpressure drop between two consecutive discrete locations. Thus,total pressure drop at any instant is computed as the sum of thepressure drop between two consecutive discrete locations. Thepressure drop component, hpd, as described in Equation (11), iscomputed for the original method for a range of physical parame-ters and results are shown in Figs. 4 and 5.The overall exergy effi-ciency as a function of particle size and length is also shown. Somephysical factors of interest such as packing particle size and bedlength have direct impact on pressure drop through the bed.Smaller particle size results in higher pressure drops. But smallerparticle size results in lower axial dispersion and thus results inhigher thermal exergy recovery. Therefore, the reduction in particlesize introduces competing effects. The plot of overall exergy effi-ciency (Fig. 4) as a function of particle size shows that at first exergyefficiency increases sharply with increasing particle size as

pressure drop decreases. The peak exergy efficiency as predicted bythe model is 84% which is appreciably lower than exergy efficiencypredicted in our previous work, i.e. 89%, which was computedwithout including pressure drop effects. Then after reaching a peakvalue, exergy efficiency starts gradually down as the reduction inthermal exergy efficiency dominates. Similarly, increasing packedbed length causes a reduction in fractional axial dispersion butincreased pressure drop through the bed. For this reason increasingthe bed length first leads to improvement in the exergy efficiencybut then leads to a decrease when pressure drop effects startdominating (Fig. 5). Exergy destruction due to pressure drop cannot

Fig. 4. Exergy efficiency evaluation using original method for wide range of particlesizes for a fixed bed length of 15 m.

Fig. 6. Progress of temperature front in sliding flow method. Each curve indicates thecompletion of storage in that segment for the corresponding feed-in strategy. Forexample, 1st segment curve means feed inlet was in the first segment and that firstsegment is completely filled to top temperature.

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208206

be neglected and amounts to 2e10% depending upon the length ofthe bed and size of particles used in the bed (Fig. 4).

The analysis of the SFM is done with the same thermal andpressure dropmodel as described in the last two sections. In case ofthermal modeling, the generic boundary conditions and initialconditions mentioned in the last section are changed with eachchange in feed inlet and exit points. Parameters for the thermalmodel remain the same as the temperature front inside thesegmented bed behaves in the same way if the bed was an integralunit. The change of feed entrance and exit is done when thesegment which is being fed has fluid leaving as at inlet tempera-ture, i.e. when

qf ðX ¼ 0:25;0:5;0:75Þ ¼ 1; (21)

for a four segment system with feed entrance at X ¼ 0, 0.25, 0.5,respectively. Results obtained from the thermal model for the SFMas shown in Fig. 5 are equivalent to the original method.

The pressure drop incurred in the bed is directly dependentupon length of the bed, through which the flow must be driven. Asdescribed before, in case of the SFM only two segments of the bedare in the flow path at any instant. If the bed is divided into four

Fig. 5. Exergy efficiency evaluation using original method for wide range of bedlengths for a fixed particle diameter 3 mm.

segments, the pressure drop through the packed bed in the SFM ishalved as compared to the pressure drop value of original method.Similarly, in order to improve thermal component of exergy effi-ciency, axial dispersion can be improved by increasing the bedlength or reducing the particle size. The use of SFM ensures thatsuch a change will not impact the pressure drop since the numberof segments can be increased to keep the pressure drop componentof exergy destruction lower. In order to make a comparison be-tween original method and the SFM (with four segments) quanti-tatively, we choose an example system for which total bed length orvolume is the same for both cases. Then we vary the particlediameter for both the systems and see its effect on exergy. Theeffect of particle size on the exergy for the original method wasalready shown in Fig. 4 with its two components plotted individ-ually. Now the same calculation is performed for the SFM which isexpected to perform in a similar manner thermally but will incurmuch lower pressure drop. Results showing the comparison be-tween the two methods are plotted in Fig. 7. As smaller size par-ticles in the bed produce more pressure drop, the effect of slidingflow method is more pronounced for smaller particle sizes.

The basic design philosophy for a packed bed thermal storagecan considerably benefit from this method. In this approach,depending upon the fraction of dispersion length such as 25%, 17%,12.5%, or 10%, the packed bed can be divided into 4, 6, 8, 10 seg-ments respectively with two segments always in the flow path. Theidea can be extended to arbitrary fractional dispersion length andcan be optimized based on practical needs.

6. Practical implications

We address here issues related to implementation of the slidingflow method. The first point to consider in the application of theSFM is that it involves a decoupling of the pressure-drop imposedconstraints from the thermal dispersion and loss issues associatedwith packed bed thermal storage. To achieve this decoupling comeswith a cost in terms of extra equipment, but the method allowssubstantially greater flexibility in the design of a packed bed stor-age system. The ideal situation of being able to state the economicbenefit for particular applications is rendered difficult, in large partbecause direct economical impact of such a method involves the

Fig. 7. Improvement in overall exergy of the system using sliding flow method forwide range of particle sizes for a fixed bed height of 15 m.

H. Bindra et al. / Applied Thermal Engineering 64 (2014) 201e208 207

fixed costs of piping and specialized equipments (e.g., high tem-perature dampers or valves) whose price can vary across the globalmarket. However, significant direct implications of this method canbe assessed qualitatively and this is our purpose in this briefdiscussion.

The operating costs of a storage system can be reduced signifi-cantly due to decrease in pressure drop and maintaining higherefficiency (Fig. 6). The major technological challenge of usingpacked bed thermal storage is the indirect impact the storage canhave on design of the solar receiver field in the target application ofCSP (Concentrating Solar Power) plants. In particular, compensa-tion for higher pressure drop through the storagemodules forces anupstream solar receiver to withstand higher pressure, and this cancause design complications. The pressure drop reduction with theuse of sliding flowmethod can be seen to remove such a constraint.Similarly, most gas turbines exhaust flue gases at high temperature,but to capture this high energy through packed bed storagemethods result in excessive back pressure at the turbine exhaust,with substantial reduction of turbine efficiency. The loss of effi-ciency can be avoided if the SFM is used in a thermal storage unitdownstream of a gas turbine, with potentially significantimprovement in the overall system efficiency in conversion of fuelto work. As a final example of the implications in practice, weshowed in our previous work [4] that lower intra-particle diffusion(i.e. non-negligible thermal resistance within the storage medium)leads to poor energy recovery: a consequence is that efficient use ofmaterials such as concrete, which have low thermal diffusivity, ispossible only if the particle size is much smaller as compared to thealumina particles used in the earlier work [4]. Smaller particle sizeleads to higher pressure drops with original method but with theSFM this effect can be avoided. Hence, the SFM provides potentialfor expanding both the process applications (e.g., to lower pressuresystems, as in the gas turbine example) or to a broader class ofstorage materials.

7. Conclusions

Pressure drop in packed bed thermal storage system causes asubstantial destruction of exergy which is compensated by addi-tional work done by fluid machinery. This additional work plays acritical role in determining the performance of storage and shouldalways be included in the performance modeling. The fractional

exergy destruction due to pressure drop is around 2e10% for anypractically feasible packed bed thermal storage system.

Higher pressure drop not only causes exergy destruction butalso makes the storage design difficult by adding back pressure onother integrated equipment or systems. In order to solve thesechallenges a new method, named here as ‘sliding flow method’ [8]is introduced. This method can reduce the pressure drop of thesystem and reduces exergy destruction. The thermal performanceof the SFM is same as of the original method, as thermal frontprogresses in similar manner. The SFM decouples the thermal ef-fects from pressure drop effects and reduces the number of con-straints for the design selection. The numerical example used in thepaper for the SFM with four segments shows the considerableimprovement in the overall exergy of the system by reducing thepressure drop. If pressure drop can be reduced in these processsystems it can reduce the operating costs.

In case of solar energy systems or grid thermal storage systemswhere there is no additional cost of fuel, operating costs are theonly major costs outside the capital expenditure and need to beincurred all throughout the life-cycle of the system. Therefore,minimization of operating costs can significantly impact thefeasibility of the solar energy. The sliding flowmethod has potentialapplications for any heat and mass transfer operation which in-volves packed beds such as adsorption or gas purification. Largescale demonstration for this method can be a useful contribution.

Nomenclaturerf density (kg/m3)Cpf specific heat (J/kg/C)ðrCpÞf ¼ εrf Cpf volumetric specific heat of fluid (J/m3/C)k ¼ ðrCpÞf =ðrCpÞs ratio of thermal capacity fluid to solidPeaf ;s ¼ ðrCpÞf ;sHv=kf ;s Peclet number based on thermal diffusion

in solids/fluidsks thermal conductivity of solid particles (W/m/C)ha surface heat transfer coefficient (W/m2/C)ε porosityv velocity of fluid (m/s)mf viscosity (Pa s)H length of the bed (m)dp particle diameter (m)q dimensionless temperatureX ¼ x/H dimensionless spatial dimensions ¼ tv/H dimensionless timetp time period for storage and recovery (s)h fractional exergy or exergy efficiency (0e1)

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