Abstract Introduction

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2018-01-1369

Published 03 Apr 2018

Design and Optimization of Exhaust Gas Heat Recovery System Based on Rankine Cycle and Organic Cycles Saisri Aditya Kanchibhotla and Shreyas Joshi University of North Carolina Charlotte Saiful Bari University of South Australia Citation: Kanchibhotla, S.A., Joshi, S., and Bari, S., “Design and Optimization of Exhaust Gas Heat Recovery System Based on Rankine Cycle and Organic Cycles,” SAE Technical Paper 2018-01-1369, 2018, doi:10.4271/2018-01-1369.

Abstract

I

n this paper, a waste heat recovery (WHR) system is designed to recover heat from the exhaust of a diesel-genset having an engine of 26.57 kW. The Rankine Cycle (RC) and the Organic Rankine Cycle (ORC) are used to produce additional power using water, R113, R124 and R245fa as the working fluids. Water as the working fluid gives the best improvement of 13.8% power improvement with 12.2% bsfc reduction, but fails to produce any power at the lowest operating power of 5.8 kW due to lower exhaust temperature and higher boiling point of water. This is when the WHR system is designed at the rated power of 26.57 kW. Designing at lower power of 20.0 kW improves the enhancements at this and

Introduction

I

nternal combustion (IC) engines have been the primary source for transportation and power generation even after a century of its invention [1, 2, 3]. Efforts to replace it with various alternatives are going on which still seems to be farfetched. In comparison to their early versions, modern engines are extremely efficient and clean [4, 5, 6, 7, 8]. A modern diesel engine is able to achieve brake thermal efficiency of 42% at its optimum operating point [9]. It is indicated by Caton that approximately 40% of the combustion energy is lost by the engine in the form of exhaust heat, and additional 30% is lost as heat to the coolant [9, 10]. The world fuel crises that took place in 1970's led to concerted efforts for the improvement in the efficiency of engines and replacement of fossil fuels [11]. The subsequent drop in fuel costs following these fuel crises reduced the urgency of increased demand for fuel conservation, but recent concerns with petroleum usage and its climate impacts resulted in a resurgence for the need to develop fuel efficient engines [9] and alternative fuels [7, 11]. This situation implores engine manufacturers and researchers to opt for different technologies to increase the efficiency of IC engines [12, 13, 14, 15, 16] and find alternative fuels. Diesel engines are used for a wide range of applications © 2018 SAE International. All Rights Reserved.

lower powers but reduces the improvement at the rated power of 26.57 kW. This design again fails to produce any power at the lowest power. On the other hand, R113, R124 and R245fa which have much lower boiling points manage to produce additional power at the lowest power, but the improvements at other powers are lower than those produced by water as the working fluid. At the rated power of 26.57 kW, the power improvements are 7.1%, 4.6% and 10.6% with corresponding bsfc reductions of 6.6%, 4.6% and 9.6% with R113, R124 and R245fa, respectively. These lower improvements are due to lower pressure ratios at the expander which are 76, 6, 4 and 9 for water, R113 R124, and R245fa, respectively at the rated power.

as its thermal efficiency is relatively higher when compared to that of other IC engines [15, 17, 18]. Diesel engine is the most common source of power in remote locations including agricultural applications [15]. About 10-15% of the world power production is dependent on diesel engine power plants [1]. The improvement in the efficiency of these engines can contribute to the major part of fuel conservation worldwide. Technologies such as high injection pressure, Direct Injection, Homogeneous charge compression Ignition [19, 20] and the combination of high-boost-pressure and advanced timing of injection [21, 22, 23, 24] have been developed to increase the thermal efficiency of diesel engines. As mentioned earlier, the engine loses around 40% of its combustion energy through the exhaust gas. Hence, recovering energy from the exhaust gas is the best way to improve the overall thermal efficiency of the engines. In 1976, Mack Trucks engineers Patel and Doyle designed, built and tested a bottoming RC system to recover heat from the exhaust of an engine [15, 25]. But this system was feasible for large heavy duty trucks whose exhaust gas temperature varied in-between 500 and 700°C [15]. There are many ways to recover heat from the exhaust flow such as RC, ORC and Turbo Charger (TC). Steam Rankine Cycle (SRC) is commonly used to recover waste heat in industrial

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DESIGN AND OPTIMIZATION OF EXHAUST GAS HEAT RECOVERY SYSTEM BASED ON RANKINE CYCLE

applications where the exhaust temperatures from the engines range from 500 to 800°C [26, 27]. In SRC, water is used as the working fluid. Water is compressed using a pump and then it is boiled and superheated using the exhaust heat from the engine. This superheated vapor is used to run a turbine/ expander and then, the steam is condensed in a condenser and supplied to the pump to repeat the whole process again [28] as shown in Figure 1. ORC is a modified form of SRC where the working fluid is replaced with organic fluids and refrigerants. ORC is mainly used in applications where the exhaust temperatures range from 150 to 400°C [29, 30]. ORCs can be classified based on the shape of the saturated vapor line in the temperature versus entropy diagram. Figure 2 shows the overhanging curve while Figure 3 shows the bell-shaped coexistence curve. ORC is also classified based on the working pressure of the fluid. A transition of liquid-vapor phase can be observed in the fluid in subcritical pressures whereas this transition is absent in fluids that work under super critical pressures [29]. Sprouse and Depcik concluded that R113 gives the highest efficiency for ORC than any other organic fluids [31]. Refrigerants can also be used as the working fluid to run ORC. To extract heat from the exhaust flows whose temperatures are below 350°C, fluids with lower boiling points are preferred [31]. R124 is a nonpoisonous refrigerant whose boiling point is -12.2°C and the boiling point of R113 and R245fa are 47.5°C and 15.3°C, respectively compared to water whose boiling point is 100°C, all at atmospheric pressure. Hence, R113, R124 and R245fa would be suitable for low temperature applications. Wang et al [32] conducted research on WHR system using R11, R141b, R113, R123, R245fa and R245ca and found that R11, R141b, R113 and R123 showed better efficiency than the others. On the other hand, R245fa is the most environmental-friendly

FIGURE 3 T-s diagram of R-124

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FIGURE 1 T-s diagram of water

FIGURE 2 T-s diagram of R113


working fluids. Therefore, in this research R113, R124 and R245fa organic fluids are chosen to evaluate their performance due to their relative merits in terms of toxicity, efficiency and environmental-friendliness. Of course, water is also chosen as the working f luid which is cheap, non-toxic and environmental-friendly. In this paper, a diesel engine which is used to run a 26 kW generator is considered, and a heat recovery system is designed to improve its overall efficiency by producing additional power. The test results of the simulations that are carried on the WHR system using different fluids at different load operations of the engine are presented. First, the recovery system is designed at the rated power operation with water as the working fluid. Then, this WHR system is run at other powers by varying the inlet pressure and mass flow rate of the working fluid to the expander, keeping the dimensions of the heat exchangers constant. Thereafter, the design is optimized for a power lower than rated power using water as the working fluid. This optimized design is run for other powers and the © 2018 SAE International. All Rights Reserved.


3


results are compared with the simulations performed with WHR designed at the rated power. Later, the WHR system is designed to run at the rated power using organic fluids R113, R124 and R245fa. The results of these simulations are compared to determine which fluid is more suitable for the usual operating range of the gen-set.

The WHR system is designed for a diesel-gen-set. The engine is a 4-stroke, 4-cylinders, direct-injection, water-cooled Toyota 13B diesel engine which is connected to a 50 kVA generator. The rated capacity of the engine is 26.57 kW at 1500 rpm. The generator is connected to a load cell to consume the load of the generator. Airflow rate is measured with the help of an inclined manometer with an accuracy of ±0.01 kPa. Fuel flowrate is measured with a digital weighing scale and a stop watch. The weighing scale has an accuracy of ±1 g. Temperatures at different points are measured with K-type thermocouples and a digital gauge with an accuracy of ±1°C. Burdon tube pressure gages are used to measure the pressures at different points with an accuracy of ±2%. The experimental set-up is shown in Figure 4 with an expected WHR system. The expander is also connected to a generator to produce additional electrical power. The actual test data of the gen-set used to design the WHR system is shown in Table 1.

Modelling of the Rankine cycle Shell and tube type heat exchangers with staggered configuration is selected to design the WHR system as shown in


Experimental Setup

TABLE 1 Operating characteristics of the engine

Speed (rpm)

Actual Power (kW)

Exhaust gas Temperature (°C)

Exhaust mass flowrate (kg/hr)

1500

5.28

185

180.04

1500

10.61

238

180.05

1500

16.08

309

180.07

1500

21.48

389

180.84

1500

26.57

479

180.91

1500

31.58

587

188.42

Figure 5. For better performance, relative transverse pitch (S T/D) is varied in-between 1.25 and 2.5. Stainless steel is selected as the tube material with thermal conductivity k = 30 W/m-K. Fouling factors are assumed for the exhaust gas to be 0.001761 m2-K/W, steam = 0.000088 m2-K/W and water = 0.000175 m2-K/W [34, 35]. For super-heater, boiler and economizer exhaust gases flows through tube side of the heat exchangers and the working fluid flows through the shell side. For convenience to be used in equations, exhaust gas is subscripted as ‘ex’ and working fluid as ‘fl’. Also, subscript ‘out’ represents outlet and ‘in’ represents inlet. The actual exhaust temperature and exhaust mass flow rates of the engine are given as the inlet conditions to the super-heater heat exchanger, and the temperatures of the fluid are calculated using the following equations,

exC p,ex (Tex ,in - Tex ,out ) (1) qhot = m

fl C p, fl (Tfl ,out - Tfl ,in ) (2) qcold = m

q he = U o AF DTlm (3)

DTlm =

FIGURE 4 Experimental setup

(Tex ,out - Tfl ,in ) - (Tex ,in - Tfl ,out ) é (Tex ,out - Tfl ,in ) ù ln ê ú êë (Tex ,in - Tfl ,out ) úû

(4)

Where, qhe is the heat transfer rate between exhaust gas ex is and working fluid through the wall of heat exchanger, m the mass flow rate of the exhaust gas, Cp, ex is the specific heat of the exhaust gas, Tex, in and Tex, out stand for the inlet and outlet temperatures of the exhaust flow. ∆Tlmis the log mean fl , Tfl, in and Tfl, out stand for mass flow temperature difference, m rate, inlet temperature and outlet temperature of the working fluid. The overall heat transfer coefficient is computed using the following equation,


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Uo =

1 éD ù ln ê o ú D D ë Di û + 1 + F Fi + o + o o Dihi k ho 2

(5)

Where, Fi is the inner fouling resistance of the tube, Do is the outer diameter of the tube, Di is the inner diameter of the tube, hi is the convective heat transfer coefficient for tube


4


FIGURE 5 Tube and shell heat exchanger with staggered configuration [33]

In boiler, the heat required to change the phase of the working fluid from liquid to vapor state is given by,

qex = Wex (Tex ,in - Tex ,out ) (13)

fl h fg (14) q fl = m


The outlet temperature of the working fluid remains same as the inlet.

side flow, k is the thermal conductivity of the tube material, ho is the convective heat transfer coefficient for the shell side flow, and Fo is the outer fouling resistance of the tube.

Condenser In condenser, the working fluid flows through the tube side and the condensing fluid (another stream of water) through the shell side. The phase change occurs in the working fluid and quality of the working fluid changes from 1 to 0 while maintaining outlet temperature same as the inlet. Here, the condensing f luid is represented using the subscript 'cf'. Outlet temperature of the condensing fluid is calculated using the following equation: U A æ - o ö W Tcf ,out = Tcf ,in + (Tfl ,in - Tcf ,in ) ç 1 - e cf ÷ (15) ç ÷ è ø

Outlet Temperatures

Super-heater and Economizer The exhaust outlet temperatures from the super heater and economizer are calculated using the following equation:

The heat transfer rate required for the phase change is given by,

é ù é 1 1 ù ê ú Uo A ê ú ê 1 - e êë Wex W fl úû ú Tex ,out = Tex ,in - ( Tex ,in - Tfl ,in ) ê ú (6) é 1 1 ù Uo A ê ú ú ê Wex êë Wex W fl úû -e ê ú êë W fl úû Where, A is the outer surface area of the tubes inside super heater/economizer. Capacity rates for the exhaust and working fluids are given by:

ex C p,ex (7) Wex = m

fl C p, fl (8) W fl = m

Where, Cp, ex is the specific heat capacity for the exhaust gas, Cp, fl is the specific heat capacity of the working fluid. Working fluid outlet temperature is computed using the following equation:

Tfl ,out = Tfl ,in +

Wex (Tex ,in - Tex ,out ) (9) W fl

The heat transfer rates for tube and shell are given by:

qex = Wex (Tex ,in - Tex ,out ) (10)

q fl = W fl (Tfl ,out - Tfl ,in ) (11)

Boiler The temperature of the exhaust gas coming out through the boiler is given by following equation: U A æ - o ö Tex ,out = Tex ,in - (Tex ,in - Tep ) ç 1 - e Wex ÷ (12) ç ÷ è ø Where, Tep stands for evaporation temperature of the working fluid.

cf h fg (16) q fl = m

qcf = Wcf (Tcf ,out - Tcf ,in ) (17)

cf is the mass flow rate of the condensing fluid Where, m hfg is the enthalpy of vaporization of the working fluid.

Convective Heat Transfer Coefficient Internal Flow Th roug h Tu bes (E xcept Condenser) Bulk temperature of the fluid flowing through the tube of each heat exchanger is the average of the inlet and outlet exhaust gas temperatures of the respective heat exchanger. Mean velocity of the flow is obtained as velocity varies over the length of the heat exchanger. The Reynolds number for the flow through the heat exchanger at this mean velocity is calculated using following equation:

Re Dh =

r um D h (18) m

Where, ρ is the density of the fluid, um is the mean velocity of the flow, Dh is the hydraulic diameter of the tube and μ is the dynamic viscosity of the fluid. Reynolds numbers are used to compute friction factor using the following formula: For Turbulent Flow,

æ 2e 1 9.35 = 3.48 - 1.7373 ln ç + ç ff è Dh Re Dh f f

ö ÷ (19) ÷ ø

For Laminar Flow,

ff =

64 (20) Re Dh © 2018 SAE International. All Rights Reserved.


The effect of developing region on the apparent friction factor can be approximately accounted for using the equation: æ æ D ö0.7 ö f » f f ç 1 + ç h ÷ ÷ (21) ç è L ø ÷ è ø Where, f is the apparent friction factor, f f is the friction factor, L is the total length of the pipe. The Gnielinski [36] relation of Nusselt number for the flow inside the tube is as follows: æ ff ö ç ÷ ( Re Dh - 1000 ) Pr è8ø Nu = Dh (22) 2 ff 1 + 12.7 Pr 3 - 1 8

(

5


)

where , C = 1.0 and m = 0.7 Heat transfer coefficient for the pipe wall is assumed to be at constant heat flux. It is computed as: hi =

Nu Dh k (24) Di

Where, hi is the heat transfer coefficient for fluid flowing through the tube, and k is the thermal conductivity External Flow Shell Side (Except Boiler) Average surface temperature is computed at the inlet and outlet of the shell side of each heat exchanger. Reynolds number for the shell side flow is calculated using free stream velocity of the fluid based on properties evaluated at the film temperature, which is the average of the free stream and the surface temperature. This Reynolds number is calculated using following equation: r Vmax Do Re D = (25) m Where, ρ is the density of the working fluid, Vmax is the maximum velocity of the working fluid, μ is the viscosity of the working fluid. The average Nusselt number for the flow inside the tubes is calculated using Churchill and Bernstein [37] correlation. Žukauskas [38] provides correlation and correction factors for values of Reynolds numbers 30 < Re < 107 and Prandtl numbers 0.7 < Pr < 500. The equation to compute the average Nusselt number is mentioned below: 1

0.5 3 Nu D = 0.3 + 0.62 Re D Pr0.25 2 é 0.4 ö 3 ù ê1 + æç ÷ ú êë è Pr ø úû

ho =

é æ Re D ö0.625 ù ê1 + ç ú 5 ÷ êë è 2.82 ´ 10 ø úû

for 1´ 102 < Re D < 1´ 107

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0.80

and Re D Pr > 0.2

(26)

Nu D k (27) Do

Where, Nu D is the average Nusselt number.

Heat Transfer Coefficient Boiler The heat transfer coefficient inside the boiler is calculated as follows:

for 0.5 < Pr < 2000 and 2300 < Re Dh < 5 ´ 106

Where, Pr stands for the Prandtl number. The approximate average Nusselt number is given by, -m é æ x ö ù NuDh » NuDh ê1 + C ç (23) ú ÷ è Dh ø úû êë

The average heat transfer coefficient for the external flow at the shell side is obtained using the average Nusselt number as follows:

h

4

3

= hconv

4

3

+ hrad h

1

3

(28) 1

hconv

é kv 3 rv ( rl - rv ) g ( h fg + 0.8 c p,v (Ts - Tsat ) ) ù 4 =C ê ú (29) mv Dt (Ts - Tsat ) êë úû hrad =

(

e s Ts 4 - Tsat 4

(Ts - Tsat )

) (30)

q¢s = h DTlm (31)

Where, C = 0.729 for tube, hconv is the convective heat transfer coefficient. kv is vapor thermal conductivity of the liquid, ρl and ρv are the liquid and vapor densities of the fluid. hfg is the enthalpy of vaporization of the fluid, μv is the dynamic viscosity of the vapor. hrad is the heat transfer coefficient of radiation, ε is the surface emissivity, σ is the StefanBoltzmann constant, Ts is the temperature of the surface and Tsat is the saturation temperature of the fluid, q s¢ is heat flux of the surface. Condenser The Nusselt number for the flow inside the condenser is calculated using following equation: 1

é rl g ( rl - rv ) h¢ fg D 3 ù 4 (32) h D Nu D = D = C ê ú kl êë ml kl (Tsat - Ts ) úû

The latent heat is modified based on the correction term. This correction term accounts for the nonlinearity of the temperature profile due to convection effects. For this reason, instead of hfg, Dobson and Chato [39] recommended using a modified latent heat. This modified latent heat (h¢ fg ) is given by:

h¢ fg = h fg + 0.375 c p,l (Tsat - Ts ) (33)

Where kl stands for liquid thermal conductivity of the fluid, hD is the convective heat transfer coefficient,´ C is the correlation constant for horizontal tube (0.555), h fg is the modified latent heat.

Pressure and Heat losses Both pressure and heat losses are considered during calculations to reflect the actual scenario. Internal flow pressure

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losses in the tubes are evaluated using the relation given by [34]. In equation form: Dp =

f L r um 2 (34) 2 Di

Where, f is the apparent friction factor, um is the mean velocity, L is tube length. External flow pressure losses are evaluated using the relation given by: Dp =

N X r Vmax 2 f (35) 2

Where, N is the number of rows, X is the correction factor, f is friction factor. To account for heat losses from the shell to the atmosphere the following equation is used: q = UADTlm (36)

The overall heat transfer coefficient (Uo) is calculated using the method described earlier. In previous study, there was airflow in the lab due to the radiator fan and also, due to fan cooling the engine room. The actual velocity was measured and used to calculate the convective heat transfer coefficient (h o) [40] using the following equation as suggested by Whitaker [41]: Num =

æm ö hm D = 0.4 Re 0.5 + 0.06 Re 2/3 Pr 0.4 ç ¥ ÷ k è mw ø

(

)

0.25

(37)

Where: 40 < Re < 105 0.67 < Pr < 300

0.25