Design and Evaluation of Pebble Bed Regenerator with Small Particles

Available online at www.sciencedirect.com

ScienceDirect Materials Today: Proceedings 3 (2016) 3784–3791

www.materialstoday.com/proceedings

ICMRA 2016

Design and Evaluation of Pebble Bed Regenerator with Small Particles Kuldeep Panwara*, D.S. Murthya a

G. B. Pant University of Agriculture &Technology, Pantnagar, U. S. Nagar- 264531, India

Abstract The paper aims to study the design and thermal characteristics of pebble bed thermal regenerators with small particles. With the help of mathematical modeling of regenerator, codes are written in MATLAB software to evaluate various parameters of design of the pebble bed regenerator. Regenerator length, switching time, thermal mean residence time and various other design parameters for maximum single-pass efficiency, maximum heat storage factor and maximum thermal efficiency are calculated. A comparison between the co-current and counter current flow within the regenerators is done in the paper.

© 2016 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of International conference on materials research and applications-2016. Keywords:Pebble-bed; regenerator; porous; heat storage factor; switching time

1. Introduction Heat Exchangers are used to transfer heat from one fluid to other. On the basis of how the heat is transferred between the fluids the heat exchangers are classified as direct contact heat exchangers and indirect contact heat exchangers or transmural heat exchangers. Indirect contact heat exchangers are further classified as Recuperators, storage type exchangers and fluidized bed heat exchangers [1]. In recuperators, two fluids are separated by a wall through which heat is transferred. There is no mixing of fluids since the fluids are separated by thin wall. In contrast, in storage type heat exchanger the fluid is made to pass through a pebble bed (matrix) which in turn absorbs and delivers the heat stored from one fluid to another.

* KuldeepPanwar. Tel.: +91-976-030-5410; fax: +91-594-423-3338. E-mail address: [email protected] 2214-7853 © 2016 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of International conference on materials research and applications-2016.

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

3785

This process is completed in storage type exchangers in two cycles i.e., heating cycle and cooling cycle. In heating cycle hot gas flow through the exchanger and the heat is stored in the pebble bed, In cooling cycle the cold gas is made to flow through the same passage and pebble bed delivers the heat to cold fluid. Thus the heat in storage type heat exchanger is not transferred through the wall as in recuperators but it is stored and rejected by pebble bed. This type if storage heat exchangers are called regenerators [2]. Regenerators have very large area of applications such as in metallurgical industries, glass manufacturing, air separation plants, storage of solar energy, incineration of VOC’s and many more. In order to have continuous operation, two or more parallel fixed bed regenerators are used in such a way that one fixed bed has hot gas passing, simultaneously in other bed the cold gas is made to pass [3]. This arrangement of two parallel fixed bed regenerators is shown in Fig.1. In Fig.1.green and red colour represents cooling and heating cycles respectively. For optimal continuous working of regenerator it is very important to operate the opening and closing of valve at appropriate time intervals.

Fig.1. Continuous working parallel fixed bed regenerator

2. Mathematical Modeling Regenerators are of two types – packed bed regenerators or pebble bed regenerators and plate regenerators. Pebble bed regenerator can have large and small particles. This paper aims to design and evaluate pebble bed regenerator with small particles. Mathematical modelling of pebble bed with small particles has following assumptions:  Heat loss from walls and ends is neglected.  Conduction in solid particles is neglected.  Eddy transport in gas is neglected.  Conduction in gas is neglected. The mathematical model for pebble bed regenerator with small particles is given by [4].The method is based on representing the unit thermal response of regenerator by gamma function of the system variance.

3786

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

2.1 Dimensionless variance of the impulse response

 D2 

2 Pe h,eff





  1  Pe 1  e h ,eff  1    Pe h,eff 

k g ,eff

k so,eff

Effective axial transport coefficien t

(1)

G g2 C 2 pg d p



Effective conductivity of thebed with no gas flow

6h p 1   R 

(2)

Contribution to effective axial conduction by gas particle heat trans fer

k so,eff can be estimated from [4] : k  s  kg 

k so,eff kg

RJh 

 k  0.280.757log R  0.057log s  kg 

    

   

(3)

2.876 0.3023  Re p Re0p.35

  g C pg  Jh  C pg G g  k g hp

   

2

3

(4)

Pe gh  Pe gm and

Pe gm  Bo

L dp

(5)

1 0. 3 0.5   Bo Sc Re p 1  3.8 Re p Sc

(6)

where, Peh,effis gas Peclet number, Gg is superficial mass velocity (kg/m2s), Cpg is mean specific heat for gas (kJ/kg 0 C), dpis particle diameter (m), hpis gas-particle heat transfer coefficient (W/m20C), εR is porosity, ks is solid conductivity (W/m 0C), kg is gas conductivity (W/m 0C), Jhis heat transfer factor, Rep is particle Reynolds number, Pegmis Peclet number for mass transfer, Bo Bodenstein number for mass transfer, L is regenerator length (m), Sc is Schmidt number. 2.2 Single Pass Efficiency Single-pass efficiency is the fraction of heat recovered from the hot-gas stream.The regenerator breakthrough curve can be represented with good accuracy by a gamma distribution function of the system variance as follows: 

t hesp  u   

1  1  2 D

   

 D2



 1   1  D2   x  x e dx

(7)

0

With M=1/ σD2, τs=θ/μ single pass efficiency can be represented by Eq. (8)

 1 Esp    1  1   s

 M s M 1 e  M s  * t he  sp  M  

(8)

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

3787

The formula for thermal efficiency for co-current, periodic, symmetric operation [5] is given by Eq. (9).

E  s  

E sp  s  

 2n  1E N

sp (( 2n  1) s )  4nE sp

2n s   2n  1E sp 2n  1

(9)

n 1

Once Espis known, Heat storage factor can be calculated by Eq. (10)

q  Esp * s

(10)

For optimum performance of regenerator heat transported by bulk flow of gas should be at a finite rate, while all other heat-transfer resistances perpendicular to flow direction is zero [6].For optimal regenerator the thermal mean residence time equals the switch off time, θs = μsand hence τs = 1.The optimal regenerator expression for single-pass efficiency at (τs = 1) will be given by Eq. (11).

Esp 1  1 

1

2M The expression for efficiency at (τs = 1) will be given by Eq. (12). E 1  2Esp 1  1

(11)

(12)

3. MATLAB Algorithm Mathematical modelling of pebble bed regenerator with small particles helps to formulate a complete MATLAB algorithm for optimum design of regenerator as shown in Fig. 2.

Fig. 2. MATLAB Algorithm for Pebble bed regenerator with small particles

3788

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

4. Results and Discussions On the basis of mathematical modelling of pebble bed regenerator we can approach the two basic problems i.e., at given flue/hot gas rate and properties and inlet hot and cold gas temperature we can design the pebble bed regenerator for desired efficiency and with known efficiency of existing pebble bed regenerator we can calculate optimal switching time for improving the current efficiency. In the current paper two parallel pebble bed regenerators with periodic, concurrent swing operation and small particle diameter of 0.06 m are modelled to get data related to the thermal characteristics of the regenerator. Hot flue gas at 8000C enters in one of the parallel regenerators and cold gas at 100 0C enters other regenerator. The diameter of the regenerator is 4 m with porosity varying from 0.2 to 0.8 at an interval of 0.2. Mass flow rate of gas is 72,000 kg/h with viscosity 3e-5 kg/m-s. The thermal conductivity of particles is 0.5 W/m 0C and the switching time of hot and cold gas is 7.2 h. With the help of mathematical modelling codes are written in MATLAB software whose algorithm is shown in Fig. 2. It can be seen from Fig. 3, that the efficiency of regenerator is dependent of its length and one has to find an optimal length for maximum efficiency. In the present case the efficiency is maximum at regenerator length of 18 m. This variation in the efficiency with length of regenerator can be understand by the fact thatin regenerator with greater length the hot fluid residence time is higher which means more heat is transferred to the bed which in turn increases the thermal efficiency, but it has to be carefully seen that if we go on increasing the length of regenerator it will further decreases the efficiency because with increase in length the thermal resistance offered by the solids also increases, which in turn decreases the efficiency of regenerator.

Fig. 3. Variation of Efficiency with the length of regenerator

Fig. 4. Variation of Efficiency of regenerator with dimensionless switching time

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

3789

Switch time of regenerator means the time period at which the flows of hot and cold gases will be switched in the parallel regenerators. While designing the regenerator it is very important to have best switching time because is it higher or lower than the optimum switching time the efficiency of the regenerator is adversely effected as shown in Fig. 4. Further the porosity of the regenerator bed is also a very important factor to enhance the efficiency of the regenerator as shown in Fig. 5. the porosity is varied from 0.2 to 0.8 and the maximum efficiency is at 0.64. Single-pass efficiency of regenerator is defined as the fraction of heat recovered from the hot-gas stream. Fig. 6, Fig. 7(a), Fig. 7(b) shows the variation of single-pass efficiency with thermal mean residence time, switching time and regenerator length. It is very much evident from Fig. 6 that higher is the thermal mean residence time i.e. for longer time the hot gas is in the regenerator higher will be the efficiency i.e. hot gas will transfer more heat to the regenerator bed. Similarly single-pass efficiency of the regenerator will be highest at largest bed length for the same reason as shown in Fig. 7(b).

Fig. 5. Variation of Efficiency of regenerator with porosity

Fig. 6. Variation of Single-pass Efficiency of regenerator with thermal mean residence time

3790

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

Dimensionless switching time (τs) is defined as the ratio of switching time (θs) to thermal mean residence time (µs). It means higher the value of τs lower will be µs because both are inversely proportional that is why at higher value of dimensionless switching time the single-pass efficiency is lower because the thermal mean residence time is lower in Fig. 7(a) which means hot gas is for smaller period of time in the regenerator. Figure 8 shows the variation of heat storage factor with regenerator length. Heat storage factor is defined as the ratio of thermal energy actually stored to maximum thermal energy storage in solids. Since the thermal mean residence time is inversely proportional to the heat storage factor, at higher length of regenerator bed the thermal mean residence time is higher in turn decreases the heat storage factor as shown in Fig. 8.

(a)

(b)

Fig. 7. Variation of Single-pass Efficiency of regenerator with switching time & length

Fig. 8. Variation of Heat storage factor of regenerator with regenerator length

At last in Fig.9 comparison between co-current and counter flow is made with the regenerator bed length. It is seen from the comparison in Fig. 9 that during co-current gas flow the efficiency of regenerator is initially increasing but later it decreases with increases in length because with increase in length the thermal resistance offered by the solids also increases, which in turn decreases the efficiency of regenerator.

Kuldeep Panwar/ Materials Today: Proceedings 3 (2016) 3784–3791

3791

In contrast during counter flow the efficiency goes on increasing with the length because due to counter flow the cold gas enters the regenerator from outlet of hot gas due to which maximum heat is absorbed by the cold gas in each cycle, hence the efficiency is observed increasing.

Fig. 9. Variation of efficiency of co-current and counter current with regenerator length

5. Conclusions The single pass efficiency ( i.e., the fraction of heat recovered from the hot-gas stream ) of pebble bed regenerator can be improved by increasing length (capital cost) at the expanse of a reduced heat-storage factor. Regenerators which are working on symmetric co-current operation their optimal efficiency is obtained at τs = 1.Without any redesign, just by changing the switching time to optimal value, we can improve efficiency of regenerator drastically.The comparison between concurrent and counter current shows that in co-current operation, bigger does not necessarily mean better, We double the efficiency by reducing the regenerator length from 30 m to 18 m.Without any redesign, just by changing the flow direction, efficiency increases from 0.4 to 0.9 (for L=30m). References [1] F.W. Schmidtand A.J.Willmott, Thermal energy storage and regeneration, McGraw-Hill, New York, 1981. [2] P. Pinel, C.A. Cruickshank, I.B. Morrison, A. Wills, A review of available methods for seasonal storage of solar thermal energy in residential applications. Renewable and Sustainable Energy Reviews. 15 (2011) 3341–3359. [3] R.K.Shah and A.L. London, laminar flow forced convection in ducts, Academic press, New York, 1978 . [4] V. Hlavacek and J.Votrubra, Steady state operation of Fixed bed reactors and Monolithic structures. ChemicalReactor Theory- A Review, Prentice-Hall, Englewood Cliffs, New Jersey, 1977. [5] M.P. Dudikovicand P.A.Ramachandran Chem., Eng., Sci. 40 (1985) 1629. [6] P.M. Park, H.C. Cho, H.D. Shin Unsteady thermal flow analysis in a heat regenerator with spherical particles.International Journal of Energy Resources. 27:2 (2003) 161-172.