Ejector design and performance evaluation for recirculation of anode gas in a micro combined heat and power systems based on solid oxide fuel cell

Applied Thermal Engineering 54 (2013) 26e34

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Ejector design and performance evaluation for recirculation of anode gas in a micro combined heat and power systems based on solid oxide fuel cell Liso Vincenzo*, Nielsen Mads Pagh, Kær Søren Knudsen Aalborg University, Pontoppidanstræde 101, 9220 Aalborg, Denmark

h i g h l i g h t s < An ejector model for SOFC-based mCHP system is presented. < A novel ejector designing procedure is provided. < A validation method for ejector designing is proposed. < Ejector and mCHP system performances are discussed.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 May 2012 Accepted 19 January 2013 Available online 29 January 2013

In this paper, a theoretical analysis of an ejector for micro combined heat and power systems based on Solid Oxide Fuel Cell (SOFC) for small-scale residential applications is presented. A novel detailed procedure for the ejector designing is provided and its effectiveness is validated through a comparison with testing results. The ejector geometry is analysed in terms of component efficiency. The SOFC system performance with regard the recirculation of anode gas is finally discussed. Results show that fuel inlet temperature and the diameter of the ejector mixing chamber of the ejector largely affect the ejector performance. A large mixing chamber diameter allows a high entrainment ratio but causes a worse ejector efficiency suggesting a highest efficiency still ensuring the required entrainment ratio. At system level, it is shown that the degree of fuel pre-reforming affects the recirculation ratio. Besides, if anode gas recirculation is implemented the system capital cost decreases due to reduction in size of ancillary components. The high electrical efficiency achieved by the system reduces the heat output and makes it more attractive when less heat is demanded. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: micro-CHP SOFC Anode gas recycle Ejector Energy System Simulation

1. Introduction Ejectors are able to transfer momentum and energy from a high energy primary fluid to a low energy secondary fluid through the work provided by turbulent mixing and entrainment. Ejectors were first applied in steam-driven locomotive, later they have been used in vapour compressor refrigeration and heat pump industry [1]. Nowadays ejectors are applied in the food, chemical and oil industries [2]. Recirculate part of the exhaust anode gases in SOFCbased mCHP systems by means of ejector is also a viable option. In this case, instead of generating steam for the reforming reaction

* Corresponding author. Tel.: þ45 21370207. E-mail address: [email protected] (L. Vincenzo). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.01.021

externally, the steam produced in the electrochemical reactions at the anode can be used in the pre-reformer process. By re-using part of the heat, the recirculation of anode gases lowers the mCHP heat output of the system. This can make SOFCbased systems a competitive technology in hot countries where little heat is needed during the winter, or in cases where the mCHP is added to a pre-existing natural gas boiler. Riensche et al. [3] reported that the main advantages of anode gas recirculation are no external steam production, a reduced number of cells in stack due to lower in-cell fuel utilization, and a lower steam concentration in the exhaust gas improving the overall system efficiency. An additional advantage is that the demineralized and deionized water used to produce steam can be re-used instead of being added by an external operator. The disadvantage is that higher compression energy for the fuel ejector is

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

Nomenclature A AGR Cpd Cpm LHV Ma mCHP kP P r,R SOFC STCR S/C Rg Ru V V_ Wcomp

area (m2) anode gas recycle ratio pressure recuperation coefficient diffuser (e) pressure recuperation coefficient mixing (e) lower heating value Mach number micro combined heat and power system specific heat gas ratio pressure (bar) radius (m) solid oxide fuel cell steam to carbon ratio (e) steam to carbon ratio (e) gas constant (J kmol1 K1) universal gas constant 8314 (J kmol1 K1) velocity (ms1) volume flow rate (m3 s1) compressor work (N m2)

necessary to achieve the recycle. This is common in case the system is used for residential applications as the natural gas is distributed at relatively low pressure compared to the industrial gas distribution grid. In this specific application ejectors require features such as high recirculation ratio, low pressure increment and high temperature of operation. The primary fluid is methane preheated to 400e500  C, while the secondary one is the cell exhaust anodic flow, mainly composed of carbon dioxide and steam at a temperature around 900  C. Ejector design can be performed using different levels of detail. This ranges from conservation equations applied to a control volume consisting of the ejector to CFD analysis of a given geometry and operating conditions. The majority solves the one dimensional mass, momentum and energy conservation equations applied to the ejector control volume with the assumption that the flow is incompressible, inviscid and adiabatic [4,5]. This approach was later further developed by applying one dimensional CFD in Ref. [6]. As discussed by Zhu et al. [7], the secondary flow area in SOFC anode gas ejector applications is larger than in previous applications and a one dimensional approach therefore leads to larger errors in performance simulations. Zhu et al. [7] presents an ejector design and simulation method applying a two dimensional velocity model for the secondary flow to account for the increased importance of two dimensional due to a larger secondary flow area. The model is applied to a pressurized SOFC system with an electrical output of 240 kW. In the present work a mass, momentum and energy balance is added to model the mixing chamber and the diffuser. This modification gives a better indication of the ejector outlet gas characteristics (P, V, T) which is important when a system analysis is carried on. In fact, previous models such as the one by Zhu et al. [7,8] or Marsano et al. [2] do not consider the gas properties at the diffuser outlet. Next a system analysis is conducted in order to estimate the benefit in terms of efficiency gain of the recirculation. The ejector performance can be defined into three modes of operation, i.e., back flow, subcritical and critical modes depending by operating conditions [9]. In the subcritical mode and back flow mode, the flow is characterized by unexpected fluctuations and a decrease in the required STCR for reforming process and fuel cell.

27

Greek symbols r density (kg m3) hel electrical efficiency (e) g heat capacity ratio (e) Jp Isentropic coefficient of primary flow (e) xexp friction loss coefficient in mixing process (e) u recirculation Ratio (e) Subscript D dp M P t S 0 1 2 3 4 5

diffuser designing point mixed primary throat secondary ejector inlet primary flow at nozzle throat nozzle exit mixing chamber inlet mixing chamber outlet ejector exit

For this reason the ejector model described in this work is assumed operating in critical mode. In this condition the pressure of the actuating fluid is equal or higher than the pressure of the induced fluid in the mixing section entry and the secondary flow is accelerated by the primary flow and always shocks at the mixing chamber inlet. 2. Aim and methodology The aim of this work is to study the recirculation of anode gas in a SOFC-based mCHP system for single family application with an electric output of 1 kW. Ejector models have previously been developed for bigger plant scale. In fact, in Refs. [2,10] models for a SOFC-based mCHP with an electric output of 250 kW are presented. Comparing to the model in Ref. [7], in the present model mass, momentum and energy balance are added in the mixing chamber and diffuser in order to calculate the gas properties at the diffuser outlet. Based on the this model, a novel designing procedure for the ejector is defined; next the design data obtained in the present work are compared with those obtained by Marsano et al. [2] assuming that the ejector operates on the three dimensional operating surface showed by Ref. [11]. The designing parameter (i.e. throat diameter, mixing chamber diameter.) is evaluated in a parametric study also in terms of ejector efficiency. Finally a system analysis in conducted on a small scale SOFC-based mCHP plant. 3. Ejector performance parameters In this study the following indicators are considered in order to evaluate the ejector performance. The entrainment ratio represents the proportion of entrained flow compared to the primary flow and it is defined as:

u¼

_S m _P m

(1)

_ S, m _ P are the mass flow rates of the primary flow and the where m secondary flow. As the secondary flow molar composition is not fixed, also the entrainment ratio changes during the operation.

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L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

Ejector efficiency for compressible flow is expressed on energy basis using the following Eq. (12) [12]: PM;5 TP;0 PS;0

hejector ¼ u$

TS;0

ðgS 1Þ gS

$

1

PM;5 PP;0

1

(2)

ðgP 1Þ gP

The subscripts P, S, and M refer respectively to the primary driving flow (fresh fuel), the secondary flow (anode depleted gas), and the mixed flow at the ejector outlet, respectively at Section 0 and 5 of the ejector r as shown in Fig. 1. Eq. (2) shows that efficiency increase substantially when the volumetric flow rate difference between the motive and propelled streams decrease. The STCR of the mixed primary and recycled flow, calculated as:

STCR ¼

n_ H2 O n_ CO;Recycle þ n_ CH4 ;Fuel þ n_ CH4 ;Recycle

(3)

is an important parameter to evaluate the carbon formation in the reforming process and fuel cell and therefore constraints the operation of the ejector. As shown in (3), CH4 is present in the anode outlet, however n_ CH4 ;Recycle can be neglected, because of its very low molar fraction. 4. Ejector model An ejector is a pump like device in which a primary motive fluid entrains and drives a secondary fluid. The primary fluid is accelerated from a high pressure to a large velocity to create a low pressure region in the ejector. The low pressure created accelerates the secondary fluid due to the resulting negative pressure gradient in the direction of flow of the primary and secondary fluid flows. This acceleration occurs in the suction chamber section of the ejector. The primary and secondary fluid enter the mixing chamber where the primary and secondary flows mix. The flow is then decelerated in a diffuser to obtain a high pressure. Ejectors can operate with a subsonic or supersonic primary fluid. The following assumptions are made in the derivation of the design method [7]:

P m

D

T

D

4.1. Section 0e1: nozzle In order to accelerate the primary flow to supersonic Mach number a convergentedivergent nozzle is used. In the convergent section the primary flow is assumed to be compressed isentropically. To account for non-ideal process, the effects of frictional and mixing losses are taken into account by using some coefficients introduced in the isentropic relations. The parameters are obtained experimentally and differ widely differed within the range of 0.8e1.0, depending on ejector geometries and operating conditions [13]. Assuming that at the nozzle throat primary flow is reached sonic condition i.e. Ma ¼ 1 and considering negligible the velocity at Section 0 when compared with the velocity at Section 1, we can define the formula for the primary mass flow rate as follows [7]:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  JP kP;0 Rg;P;0 TP;0 $

2 kP;0 þ 1



kP;0 þ1

ð

Þ

2$ kP;0 1

(4)

In the previous equation an isentropic coefficient, JP ¼ 0.98, is used to account the flow friction loss in the nozzle. The average gas constant, Rg,P, and density of the fuel, rp,0, are defined as:

P

P

The third assumption causes energy to be generated in the ejector model albeit in small amounts in comparison to the energy magnitude of the secondary flow. This generation of energy in the model is accounted in a constant parameter [7]. Losses due to viscous effects are also accounted for using empirical constants. The ejector diagram is represented in Fig. 1. The section numbers used throughout this paper are specified in the diagram.

_ P;1 ¼ rP;0 $At m

Θ

T

T

 The ejector is assumed operating in critical mode.  The primary flow is uniformly radially distributed.  A velocity boundary layer at the nozzle outlet between primary and secondary flow exists.  The primary flow is fully heated to the temperature of the secondary flow. The heat energy transferred from the secondary flow to the primary flow is assumed to be negligible. Therefore TS,0 ¼ TS,3 ¼ TP,3. The secondary mass flow rate is generally five times that of the primary flow and has a much higher temperature.  Temperature and pressure of both flows are uniformly radially distributed.  Both the flows can behave as ideal gases inside the ejector. At the temperatures encountered in the ejector water vapour also behaves as an ideal gas.  Fiction losses coefficients are included in the isentropic relationship.

 P RU $ nP;0;j ; j ¼ 1; M  Rg;P ¼ P nP;0;j $M0;j ; j ¼ 1; M

m

m

D

(5)

and

rp;0 0

1 2 3

P: Primary flow S: Secondary Flow M: Flow in mixing chamber Fig. 1. Schematic diagram of an ejector.

4

5

P i n Mi PP;0 PP;0 i P;0 0 ¼ ¼ P Rg;P;0 $TP;0 TP;0 Ru niP;0

(6)

i

The specific heat gas ratio kP,0 is calculating using the fundamental equation for ideal gas:

cp ¼

kRg k1

(7)

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

29

4.2. Section 2e3: suction chamber

4.3. Section 3e4: mixing chamber

The primary flow expands fully in the suction chamber the primary flow fans out without mixing with the entrained flow until at cross section 2 (hypothetical throat). Zhu et al. [7] assumes that the primary flow expands fully to the ambient pressure of the secondary flow when the primary flow reaches section 3 so that PP,3 ¼ PS,3. The secondary flow is assumed to have the same pressure at section 3 as at section 0 and therefore PS,3 ¼ PS,0, implying a small acceleration of the secondary flow between section 0 and 3 causing a negligible pressure drop. This leads to the assumption PP,3 ¼ PS,0. It is important to note therefore that if the secondary flow is accelerated greatly from inlet conditions then the pressure drop form section 0 to 3 will no longer be negligible and PS,3 < PS,0. In section 3 it is assumed that ambient pressure and temperature of the expansion flow can be represented by those of surrounding secondary flow. Using the isentropic flow and energy balance laws for the primary flow from Section 1 to Section 3 the relationships among the Mach number, velocity, flow diameter of the primary flow at Section 3 can be written as [7]:

In the mixing section primary and secondary flow are fully mixed. In the mixing process mass, energy and momentum conservation are applied. Considering constant section over the mixing chamber A3 ¼ A4, the mass balance among section 3 and 4 can be written as:

MaP;3

VP;3

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  kP;3 1 u t2$ PP;0 =PS;0 kP;3  2 ¼ kP;3  1

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ MaP;3 $ kP;3 $Rg;P;3 $TP;3

(8)

 nv þ1 nv R23 RP;3 nv 1 nv þ 1 R3  2nv þ1 ! nv R23 RP;3 nv 1  2nv þ 1 R3

Q th;34 ¼ Ekin;34

(15)

with

  _M Q th;34 ¼ hM;4  hM;3 $m

(16)

and

(17)

The momentum balance is:

(18) The loss of total pressure in the mixing chamber is calculated using the Bernoulli equation including a pressure recuperation coefficient of the mixing chamber cpm ¼ 0.8 [10]:

1 1 2 2 PM;4 þ $rM;4 $VM;4 ¼ PM;3 þ $cpm $rM;3 $VM;3 2 2

(19)

4.4. Section 4e5: diffuser

(10)

A conical diffuser with an angle of 10 and a length 8 times the mixing chamber diameter is considered according to recommendations in Ref. [7]. The loss of total pressure in the diffuser is calculated via the Bernoulli equation as shown in the previous section including instead a pressure recuperation coefficient of the diffuser cpd ¼ 0.75.

1 2 PM;5 ¼ PM;4 þ $hpd cpd rM;4 VM;4 2

(11)

(12)

This term accounts the nonlinear velocity distribution of the flow in the mixing chamber.

(20)

where hpd is the efficiency of total pressure conservation in an ideal diffuser:

hpd ¼ 1  ðA4 =A5 Þ2

where rS,0 is calculated as in Eq. (6), R3 represents the radius of the mixing chamber and the exponent nv can be expressed by:

  ln 1  RP;3 =R3   nv ¼ ln MaP;3

(14)

The energy conservation equation can be written as:

(9)

where xexp is a coefficient accounting for the frictional loss due to the mixing of two flows. In this study, it is assumed xexp ¼ 0.98. In section 3, primary and secondary flow are separated by a mixing layer. The secondary flow is outside and is assumed to have a nonlinear velocity distribution [7]. At critical mode, the layer between the primary flow and secondary flow is considering in the choking condition (M ¼ 1). The mass flow rate of the secondary flow is obtained based on the exponential function as:

_ S;3 ¼ 2pVP;3 rS;0 m

_ M;j ¼ rM;j $Aj $VM;j ; j ¼ 3; 4 m

_ P;3 VP;3 þ AS;3 PS;3 þ m _ S;3 VS;3 ¼ AM;4 PM;4 þ m _ M;4 VM;4 AP;3 PP;3 þ m



DP;3

(13)

with:

  2 2 _ M;3 $ VM;3 Ekin;34 ¼ 1=2$m  VM;4

To determine the cross sectional area of the primary flow at section 3, mass conservation is applied between section 1 and 3 for the primary flow. In this approach the velocity of the primary flow at section 3 is required. The velocity at section 3 can be determined from the Mach number for the primary flow at section 3, MP,3. MP,3 is determined by applying conservation of energy for the primary flow between section 0 and section 3 yielding Eq. (10):

! kP;3 þ1  2 þ kP;3  1 $Ma2P;3 4$ðkP;3 1Þ Dt pffiffiffiffiffiffiffiffiffiffiffiffiffi$ ¼ kP;3 þ 1 xexp MaP;3

_ M;3 ¼ m _ M;4 m

(21)

The outlet temperature TM,5 is determined by the isentropic expansion relationship:

 kp;5 1 TM;5 ¼ TM;4 $ PM;5 =PM;4 kp;5

(22)

Finally mass and energy conservation is applied as described in the previous section in Eq. (13) and Eq. (15). 4.5. Designing of recirculation ejector Jet ejectors are designed to perform at a particular optimum point. Deviation from this optimum point can dramatically reduce

30

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

ejector efficiency [12]. The method used for determining the ejector geometry for given mass flow rate of primary and secondary flow has to provide maximum energy of the mixture at the outlet. The primary concept to improve jet ejector performance is to minimize momentum differences between the motive and propelled streams [14]. In order to accomplish this task, two main ejector parameters are to be designed, namely the throat diameter, Dt, and the mixing chamber diameter, Dm. These dimensions also reflect the mixed pressure, temperature and STCR. Other designing dimensions such as the length of the suction chamber, mixing chamber and diffuser are not critical [8]. In order to determine the primary and secondary mass flow rate, a mass balance of the anode gas recirculation loop is defined as depicted in Fig. 2. A steam methane pre-reforming process is considered downstream the anode ejector. The molar Input/Output of the anode recirculation loop control volume is:

n_ in;CH4 þ n_ in;O2 ¼ ð1  AGRÞn_ Anode;out

(23)

Table 1 Nominal condition of operation of a SOFC based micro-CHP system. Key parameters

Value

Pressure loss in the recycle loop Outlet ejector pressure Inlet temperature of primary flow Inlet temperature of secondary flow STCR at ejector outlet Isentropic coefficient of primary flow Jp Friction loss during the mixing process xexp micro-CHP electric efficiency hel Fuel inlet mass flow [g/s] System electric output

0.080 bar 1.13 bar 620 K 1180 K 2.3 0.98 0.98 0.48 0.044 1 kW

Nominal operational SOFC parameters Fuel cell average temperature Fuel utilization Anode exhaust gas composition [Molar %] CO CO2 H2 H2O

1073 K 0.8 [] 3.785 29.58 4.895 61.74

where the Anode Gas Recycle Ratio, AGR, is defined as:

n_ Anode;rec AGR ¼ n_ Anode;out

(24)

n_ in;CH4 is the fuel input mass flow rate, n_ in;O2 is mass flow rate of the oxygen ions produced via the fuel cell electrochemical reaction and n_ Anode;rec represents the anode exhaust gas recirculated. In Table 1 the input parameters used in the simulation are provided. Assuming an electrical efficiency based on lower heating value of 48% [4,3] and methane LHV ¼ 802,340 [J/mol], it is possible to calculate the required fuel input for a certain electric power according to the relationship:

n_ CH4 ¼ Pel =hel

(25)

Mass flow rate of secondary flow is determined from the mass balance in Eq. (23) assuming an anode exhaust gas composition as in Table 1 [2] with a fuel utilization factor, Uf of 0.85. It is worth mentioning that the cell outlet gas composition is sensitive to Uf. In particular decreasing Uf, less steam is produced by the electrochemical reaction, hence also the outlet cell steam content decreases. As a STCR at the ejector Outlet greater than 2 is required at the Pre-reformer, the recirculation ratio and entrainment ratio can be easily calculated from Eqs. (1) and (24). To achieve an STCR of 2.3 at the pre-reformer inlet, 62% of the anode outlet gas (on a molar basis) must be recirculated and the ejector entrainment ratio at nominal condition is around five. In Fig. 3 the effect of amount of anode gas recycled on the STCR of the mixed flow is shown. Anode ejector requires an Entrainment Ratio of between 5 and 7 at nominal condition considering anode outlet composition of 60% water.

4.5.1. Ejector dimensioning algorithm Given the equations in Sections 4.1e4.4 the throat diameter Dt and mixing chamber diameter D3 can be determined according to the following algorithm.  Once assumed the Pel and hel calculate the mp with Eq. (25) _ P , STCR and secondary flow compositions _ S from m  Calculate m with Eq. (3)  Calculate the entrainment ratio designing point, udp with Eq. (1)  Calculate the throat diameter Dt and area At imposing PP,0, TP,0 _ P with Eq. (4) and m  Calculate MaP,3 from PS,0 with Eq. (8); PS,0 is equal to the pressure loss in the recirculation loop  Calculate VP,3 considering TP,0 ¼ TS,0 _ S with Eq. (11)  Calculate m  Pressure and Temperature of the ejector outlet gas are determined with the mass, energy and momentum balance described in Sections 4.3 and 4.4. _ S obtained  Calculate the entrainment ratio this time using the m with Eq. (11)  Determine the difference between the required entrainment ratio, udp, and the effective entrainment ratio calculated with the previous equation. If the difference is greater or smaller than the allowable maximum difference predefined, the diameter DM is modified accordingly and the process is iterated  In case required entrainment ratio is not achieved another option is to change the primary flow inlet temperature TP,0 and reiterate the calculation. The governing equations are non-linear and closely coupled, therefore the problem is solved iteratively as depicted in the flowchart in Fig. 4. Anode recirculation SOFC

CH

Anode Steam reformer

D D

S/C

Electrolyte

S/C T

AGR

Cathode

Fig. 2. Schematic diagram of the recirculation loop.

X

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

2.5

31

calculation result. In fact, keeping all other parameters constant, when DM is increased, more secondary flow is entrained whereas increasing TP,0, the primary mass flow rate decreases. The effect of mixing chamber diameter and primary flow temperature is shown in Figs. 5 and 6.

carbon formation

STCR [-]

2

1.5

1

0.5 0.3

0.35

0.4

0.45

0.5

AGR [-]

0.55

0.6

0.65

Fig. 3. STCR for different anode gas recirculation ratio.

The outlet static pressure, PM,5, is evaluated for a defined geometry and compared with the required value. The difference between these two values is used to adjust primary flow pressure and ejector geometry until convergence is reached. The back pressure is the same of the downstream component (e.g. Reformer). As seen in the two calculation loops, Mixing Chamber Diameter, DM, and the inlet fuel temperature TP,0 are chosen as designing parameters in the calculation loops to achieve the required entrainment ratio, udp. These two parameters highly affect the

Pel STCR

Equation 4

ms mP

Initial value TP,0

Equation 4

PP,0 mp,0

5. System performance analysis on the anode side

At

PS,0

Equation 8

TS,0

Equation 9 10

4.5.2. Designing results validation When operating in supersonic regime, the primary flow expands at supersonic speed entraining the secondary stream. The secondary mass flow rate becomes independent of the back flow. In this case the ejector operation is considered in critical mode [15]. In Fig. 7 the operation of the ejector in critical mode is shown. The fuel inlet (primary flow) temperature and anodic exhaust conditions are kept constant. When the primary flow pressure increases, the mass flow also increases. At the same time the secondary mass flow rate decreases due to a larger area occupied by the primary flow in the mixing chamber. Carrol and Dutton [11] showed that a constant area ejector in critical mode is constrained to operate somewhere on a three dimensional surfaces. When the primary to secondary stagnation pressure ratio PP,0/PS,0 and the mixed stream static to secondary stagnation pressure ratio PM,5/PS,0are known, the mass flow ratio u can be found. This surface is considered for a fixed At/AM and TS,0/ TP,0. Starting with this consideration, the designing data obtained in the present work are compared with those obtained by Marsano et al. [2]. The main results obtained for the ejector on-design operation conditions are listed in Table 2. Additionally, ejector outlet gas characteristics (P, T) provided by this model are shown. In order to evaluate the ejector efficiency defined in Eq. (2), a parametric analysis is conducted varying critical designing values. High primary flow inlet temperature and STCR increases ejector efficiency (Figs. 8 and 9). Increasing the mixing chamber diameter the efficiency decreases (Fig. 10). From equation Eq. (4) it appears _ P;1 is directly proportional to the that the inlet mass flow rate, m nozzle throat area, At, and inlet pressure, PP,0. As the inlet pressure is proportional to the compressor work, which determines the system parasitic load, a large At is desirable. However, large At will affect the entrainment ratio.

A system level analysis is conducted on the anode gas recycle loop as depicted in Fig. 2. The simulation is run in EES, a general

MP,3

Initial Value D3

9 i P,0

T

VP,3 DP,3

i+1 P,0

=T

±

8.5

Equation 11

8

Equation 13 to 22

7.5 i+1 DiP,3 = DP,3 +

7

VM,5 PM,5 TM,5 mM,5 6.5

? 6

PM,5 End Fig. 4. Calculation flowchart for ejector designing.

5.5 0.003

0.0032

0.0034

0.0036

0.0038

DM [m]

0.004

0.0042

Fig. 5. Entrainment ratio for different mixing chamber diameters.

0.0044

32

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34 Table 2 Ejector simulation results compared with experimental results.

8

7.5

7

6.5

6

Parameter

Reference

Present model

D [%]

PP,0/PS;0 PP,0 [Bar] PS,0[Bar] AM/At At [mm2] AM [mm2] Dt [mm] DM [mm] TS,0/TP,0 TP,0 [K] TS,0 [K] STCR

2.64 10.06 3.8 41.25 9.13 376.5 3.41 21.9 1.9 673 1280 2.4 7.2

2.68 2.8 1.04 41.0 0.14 5.72 0.42 2.7 1.9 620 1180 2.4 7.8 1055 1.05

1.5

u 5.5 300

350

400

450

500

Tp,0 [K]

550

600

650

700

Fig. 6. Entrainment ratio for different fuel inlet temperature.

equation-solving program that can numerically solve a system of non-linear algebraic equations [16]. Performance parameters are chosen and compared for both configurations as shown in Table 3. A steam reformer is used to partially convert methane into hydrogen for the SOFC. The model considers only the steam methane reforming reaction:

CH4 þ H2 O#CO þ 3H2

h

DH  þ 206 kJ mol1

i

(26)

CO þ H2 O#CO2 þ H2

h i DH  41 kJ mol1

(27)

By keeping the STCR above the limit for carbon deposition, carbon formation reactions can be neglected. This is a greatly simplified reaction scheme because the cracking process is usually highly complex and will often result in many types of products. The model assumes ideal gas behaviour. The chemical equilibrium constant is based on the change in Gibbs free energy. Enthalpies of reaction are calculated on a chemical equilibrium based on the law of mass action. The simultaneous chemical equilibrium composition of both reactions (26) and (27), is calculated by the following equations system:

ni;e ¼ ni;0 þ

X

ni;j xj



(28)

1.5

0.8 0.8

where ni,e is the equilibrium moles of species i, ni,0 is the initial mole number of species i, ni,j is the stoichiometric coefficient of species i in reaction j, and xj is the extent of reaction j [17]. For steam reforming in smaller scale, a heat exchanger design can be used where the steam is heated to 450e650  C. The fuel and steam exchange heat with the SOFC outlet gas which are previously burned. The products of the steam reformer consist of mainly CO and H2 This is fed in the anode side of the SOFC. The heat exchanged between the heating fluid and reaction channel is therefore modelled by assuming that the heat required for the reforming process is:

  _ f $ hf ;in  hf ;out Q Heat Exchanged ¼ m

followed by the water gas shift reaction: 

Temperature at ejector outlet T5 [K] Pressure at ejector outlet P5 [bar]

0.6

(29)

_ f is mass flow [kg s1] and h is enthalpy [J kg1]. where m The solid oxide fuel cell typically operates at temperatures near 800  C or higher. At these high temperatures, fast electrochemical reaction kinetics is achieved. As the fuel cell stack is supplied with only partially reformed natural gas, some of the reforming will take place inside the SOFC stack. This affects the operation of the stack, since the concentration of hydrogen at the inlet is proportional to the degree of pre-reforming. The assumptions relating to the internal reforming are as follows:  The composition at the SOFC stack inlet is the same as at the pre-reformer outlet;  Only H2 is consumed by the anode reaction. CH4 and CO are converted via fast steam reforming and equilibrium of water gas shifting; 1

ejector

[-]

0.8

0.6

0.4

0.2

0 500 Fig. 7. Mass flow rate, entrainment ratio and STCR at different fuel inlet pressures at critical mode.

550

Tp,0 [K]

600

Fig. 8. Ejector efficiency for different fuel temperature.

650

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

33

Table 3 Performance comparison between a base mCHP system without anode recirculation and a configuration which include anode recirculation.

1

Fuel compressor work [W] Reforming process heat duty [W] Boiler duty [W] Air blower and water pump consumption [W] Recovered heat [W] Electrical efficiency

0.6

ejector

0.4

0.2

0 1

1.2

1.4

1.6

1.8

2

STCR

2.2

2.4

2.6

Fig. 9. Ejector efficiency for different STCR.

The fuel cell model employed in this simulation is described in detail. In particular the, the reactions considered at the cathode side are the internal reforming processes are steam methane reforming and water gas shift (Eqs. (26) and (27)). It is assumed a complete conversion of the steam reforming reaction, therefore CH4 will not be present in the fuel cell outlet. The water gas shift reaction is considered reaching chemical equilibrium. The anode depleted gas, which is not recirculated, is fed into a burner to generate heat. It is assumed that all the fuel is completely oxidized to Carbon dioxide and steam. In order to produce to required fuel flow a centrifugal compressor is considered. The work to achieve a politropic compression can be calculated as follows [18]:

Wcomp ¼

 n1

 n  p V_ Pout n in in 1 hp n1 Pin

(30)

where hp is the polytropic efficiency, i.e. ratio between polytropic power and actual power, n is the polytropic coefficient, V_ in is the volumetric flow rate, Pin and Pout are the inlet and outlet pressures of the compressor, respectively. An estimate of the polytropic efficiency as a function of volumetric flow rate were used based on [18]:

hP ¼ 0:017ln V_ in þ 0:7

(31)

Base configuration

AGR configuration

5

14.5

497

418

290 20

0 0

452 40%

420 48%

0.55

2.8

Degre of Pre-reforming [-]

[-]

0.8

0.5 0.45 0.4 0.35 0.3 0.25 0.608

0.61

0.612

0.614

0.616

0.618

0.62

0.622

AGR [-] Fig. 11. Anode recirculation ratio at different degree of pre-reforming.

Finally the polytropic coefficient, n, can be estimated from the heat capacity ratio, g ¼ cp/cv, as follow:

n ¼

ghP ghP  g þ 1

(32)

Table 3 presents a performance comparison between a base mCHP system without anode recirculation and one including anode recirculation. As shown in the table the fuel compressor work increases when applying recirculation. When including the recirculation of the anode gases, the anode exhaust gases are mixed with fresh fuel. Less heat is exchanged in

0.9

-14.4

0.85

0.8

Wcomp [W]

ejector

[-]

-14.3

0.75

-14.2

0.7 -14.1

0.65 0.0045

0.0047

0.0049

0.0051

DM [m]

0.0053

Fig. 10. Ejector efficiency for different mixing chamber diameter.

0.0055

0.6

0.604

0.608

0.612

AGR [-]

0.616

Fig. 12. Power consumption for different anode recirculation ratio.

0.62

34

L. Vincenzo et al. / Applied Thermal Engineering 54 (2013) 26e34

the endothermic reforming process because of the high temperature and already reformed exhausted gases, as shown in Table 3. The AGR configuration is not provided with an external boiler and water pump, this gives an extra-gain to the system in terms of parasitic power loss to the AGR configuration. The recovered heat decreases in the AGR configuration as more heat is recirculated lowering also the mCHP heat-to-power output ratio of the mCHP system. Increasing the recirculation ratio, and therefore the STCR, the sensible heat available in exhaust gas for recovery is reduced. Overall this leads to a higher electrical efficiency as shown in Table 3. Fig. 11 shows that, increasing the degree of pre-reforming, more exhaust gases are recirculated in order to maintain the appropriate STCR. Besides, as show in Fig. 12 the compressor work increases when more anode exhaust gas is recirculated. This is the main drawback of the anode gas recirculation, however the power consumption is still low compared to the mCHP system power output. 6. Conclusions In this paper a model of a fuel ejector for recirculation of anodic gas in a small scale mCHP plant based on SOFC is presented and validated. By re-using the steam rich anode exhaust gas, the recirculation of anode gas has the advantage to avoid the production of steam for the reforming process in an external boiler. The ejector geometry is evaluated using the component efficiency. Furthermore, the performances of an anode gas recirculation SOFC system integrated with a fuel ejector are investigated. The simulation results reveal that the inlet primary flow temperature largely affects the ejector entrainment ratio and the component efficiency. High temperatures favour both entrainment and efficiency (Figs. 6 and 8). This is an important parameter to be controlled both when designing and controlling the ejector operation. When the secondary mass flow increases also the STCR the mixed flow increases in favour of a better efficiency (Fig. 9). A large mixing chamber diameter allows a high entrainment ratio but causes a worse ejector efficiency (Figs. 5 and 10). For this reason a trade-off has to be reached during the component design in order to obtain the highest efficiency still ensuring the required entrainment ratio. The system analysis shows that when operating the reforming process with different degree of pre-reforming also the AGR will change. In particular, for a low degree of Pre-reforming less steam is required and therefore less exhaust gas needs to be recirculated (Fig. 11). Compressor work increases when employing the anode gas recirculation, however the system electrical efficiency is still higher than in the base configuration. This is due a better heat management and reduction of power usage of ancillary components (i.e. Air blower and Water pump) (Table 3).

More heat is internally recovered in the AGR case. This lowers the mCHP heat output making the system more attractive in hot regions where little heat is needed during the winter, or in cases where the mCHP is added to a pre-existing natural gas boiler (Table 3). If anode gas recirculation is implemented, the system capital cost decreases due to reduction in size of ancillary components (i.e. fuel preheater/pre-reformer, steam generator and water pump) (Table 3). References [1] Y. Zhu, W. Cai, C. Wen, Y. Li, Numerical investigation of geometry parameters for design of high performance ejectors, Applied Thermal Engineering 29 (56) (2009) 898e905. [2] F. Marsano, L. Magistri, A.F. Massardo, Ejector performance influence on a solid oxide fuel cell anodic recirculation system, Journal of Power Sources 129 (2) (2004) 216e228. [3] E. Riensche, J. Meusinger, U. Stimming, G. Unverzagt, Optimization of a 200 kw SOFC cogeneration power plant. part ii: variation of the flowsheet, Journal of Power Sources 71 (1e2) (1998) 306e314. [4] R.J. Braun, Optimal Design and Operation of Solid Oxide Fuel Cell Systems for Small-scale Stationary Applications, PhD thesis, University of WisconsinMadison USA, 2002. [5] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., Wiley, 2002. [6] M.L. Ferrari, A. Traverso, L. Magistri, A.F. Massardo, Influence of the anodic recirculation transient behaviour on the SOFC hybrid system performance, Journal of Power Sources 149 (2005) 22e32. [7] Y. Zhu, W. Cai, C. Wen, Y. Li, Fuel ejector design and simulation model for anodic recirculation SOFC system, Journal of Power Sources 173 (2007) 437e449. [8] Y. Zhu, W. Cai, Y. Li, C. Wen, Anode gas recirculation behavior of a fuel ejector in hybrid solid oxide fuel cell systems: performance evaluation in three operational modes, Journal of Power Sources 185 (2) (2008) 1122e1130. [9] B.J. Huang, J.M. Chang, C.P. Wang, V.A. Petrenko, A 1-d analysis of ejector performance analyse unidimensionnelle de la performance d’un jecteur, International Journal of Refrigeration 22 (5) (1999) 354e364. [10] C. Stiller, Design, Operation and Control Modelling of SOFC/GT Hybrid Systems, PhD thesis, Norwegian University of Science and Technology, Norway, 2006. [11] B.F. Carrol, J.C. Dutton. Caeopt2: A Computer Program for Supersonic Ejector Optimisation Report No. Uilu-eng-85-4006, Technical report, Department of Mech and Ind Eng, University of Illinois, Urbana-Champaign, Urbana, USA, 1985. [12] V. Dvorak, Shape Optimization and Computational Analysis of Axisymmetric Ejector e Paper Ref: Isaif8e0040, in: Proceedings of the 8th International Symposium on Experimental and Computational Aerothermodynamics of Internal Flows, Lyon - France (2007). [13] B.J. Huang, C.B. Jiang, F.L. Fu, Ejector performance characteristics and design analysis of jet refrigeration system, ASME Journal of Engineering for Gas Turbines and Power 107 (1985) 792802. [14] S. Watanawanavet, Optimization of a High-efficiency Jet Ejector by Computational Fluid Dynamic Software. Master’s thesis, Texas A&M University, USA, 2006. [15] R. Yapici, H.K. Ersoy, Performance characteristics of the ejector refrigeration system based on the constant area ejector flow model, Energy Conversion and Management 46 (18e19) (2005) 3117e3135. [16] F-Chart, Ees e Engineering Equation Solver (2012). [17] A. Ovenston, J.R. Walls, Chemical thermodynamic study of the conversion of fossil fuels to prime chemical feedstocks with steam, Chemical Engineering Science 35 (3) (1980) 627e633. [18] R. Smith, Chemical Process Design and Integration, Wiley, 2008, ISBN 978-0471-48681-7.