- Email: [email protected]
Analysis of the liquefaction process of exhaust gases from an underwater engine
PERGAMON
Applied Thermal Engineering 18 (1998) 1243±1262
Analysis of the liquefaction process of exhaust gases from an underwater engine G.S. Lee a, S.T. Ro b,* a
b
Department of Mechanical Engineering, University of Ulsan, Ulsan 680-749, Korea Department of Mechanical Engineering, Seoul National University, Seoul 151-742, Korea Received 30 October 1997
Abstract In operating underwater engines, such as in exploring submarines, the dumping of the exhaust gas out of the engine requires a large portion of the total power, frequently amounting to 25±30% of the power generated. This can be solved by liquefying the exhaust gas and storing it. In the present study, two liquefaction systems are simulated to enhance the overall eciency; one is a closed cycle diesel cycle and the other is a closed cycle lique®ed natural gas (LNG) engine. LNG was chosen as a fuel not only because it is economical but also because its cold energy can be utilized within the liquefaction system. Since a mixture of oxygen and carbon dioxide is used as an oxidizer, liquefying carbon dioxide is the major concern in this study. To further improve this system, the intercooling of the compressor is devised. The power consumed for the liquefaction system is examined in terms of the related properties, including pressure and temperature of the carbon dioxide vessel as a function of the mass fraction of the exhaust gas that enters the compressor. The present study shows that much gain in the power and reduction of the vessel pressure could be achieved in the case of the closed cycle LNG engine. The compression power was remarkably low, typically only 6.3% for the closed cycle diesel engine and 3.4% for the closed cycle LNG engine, respectively, of net engine power. For practically, a design±purpose map of the operating parameters of the liquefaction systems is also presented. # 1998 Elsevier Science Ltd. All rights reserved.
Nomenclature a b Bc
recirculated mole of carbon dioxide in the engine recirculated mole of oxygen in the engine theoretical quantity of carbon dioxide produced per oxygen burnt (supplied oxygen) (kg/kg (O2))
* Author to whom all correspondence should be addressed. 1359-4311/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 9 8 ) 0 0 0 0 9 - X
1244 Bf fc fL h Lcd Lox Mi m5 m9 PCV Pcvcd Qcon Qcv Qintc Qloss QLNG QPHX TCV Te u ucvf x7 x9 Xi
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262 fuel consumption per oxygen burnt (supplied oxygen) (kg/kg (O2)) incoming fraction of exhaust gas to the compressor liquefaction fraction of carbon dioxide from the compressed exhaust gas enthalpy (kJ/kg) heat loss coecient of carbon dioxide vessel (kJ/kg (O2)8C) heat loss coecient of oxygen vessel (kJ/kg (O2)8C) molecular weight of i-component (kg/kmol) incoming mass of exhaust gas to the compressor per oxygen burnt (=m7) discharging mass of exhaust gas from the Co2 vessel per oxygen burnt pressure in the carbon dioxide vessel carbon dioxide partial pressure in the carbon dioxide vessel supplied or consumed cold energy in the precooler and the carbon dioxide vessel (kJ/kg (O2)) supplied or consumed cold energy in the carbon dioxide vessel (kJ/kg (O2)) supplied or consumed cold energy in the intercooler (kJ/kg (O2)) absorbed heat by the temperature dierence between the oxygen or carbon dioxide vessel and surroundings (kJ/kg (O2)) supplied cold energy by LNG (kJ/kg (O2)) supplied or consumed cold energy in the precooler (kJ/kg (O2)) temperature in the carbon dioxide vessel surrounding water temperature internal energy (kJ/kg) internal energy of saturated liquid carbon dioxide in the carbon dioxide vessel (kJ/kg) mass fraction of oxygen in the incoming exhaust gas to the precooler inlet mass fraction of oxygen in the discharging exhaust gas from the carbon dioxide vessel mole fraction of i-state
1. Introduction Much research and development of engines for underwater vehicles has been done due to the high level of interest in underwater development. An underwater engine, especially in exploring submarines, should have good operating characteristics in deep sea (3000±6000 m). The power sources operating underwater engines can be battery, radioisotope Rankine cycle, thermoelectric generator, or nuclear power. However, the most promising source is either a fuel cell or a closed cycle heat engine (CCHE). CCHE in an underwater engine usually adopts the Stirling engine or the closed cycle diesel engine (CCDE) [1±3]. In the power generation process of CCHE, the exhaust gas containing water vapour, soot, oxygen and carbon dioxide is emitted from the combustion process. The moisture in the gas can be easily eliminated by liquefaction, and the soot can be reduced by increasing oxygen concentration. To get rid of the carbon dioxide in the gas, absorbing systems using absorbents and a liquefaction system have typically been adopted. This absorbing system, however, has disadvantages, such as additional loading of absorbents and additional power necessary for incoming seawater as an absorbent. Therefore, the object of this work is to reduce the power consumption by adopting a liquefaction system of carbon dioxide. When CCDE is used for power generation, oxygen (as an oxidizer) should be supplied in a gas state vaporized from the liquid oxygen vessel. In recent research, a system where carbon dioxide from the exhaust gas is lique®ed and stored in a vessel was proposed, using the heat of
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1245
vaporization of oxygen [4]. Part of the dehydrated exhaust gas is supplied to the liquefaction system and the remaining part is recirculated to the engine for adjusting combustion temperature. The exhaust gas entering the liquefaction system is compressed and then cools down in the precooler. The theoretical quantity of carbon dioxide in the exhaust gas (produced by the stoichiometric quantity of oxygen during the combustion process) is lique®ed in a carbon dioxide vessel by the cold energy of liquid oxygen, and the others are supplied to the diesel engine as an intake after being mixed with oxygen. If a closed cycle gas engine is used for a power generating apparatus and lique®ed natural gas (LNG) [5] is used as its fuel, a more eective liquefaction system could be designed with the simultaneous use of the cold energies of LNG and liquid oxygen. It will be called the closed cycle LNG engine (CCLE) henceforth. The characteristics of the exhaust gas of CCHE for an underwater engine are dierent from those of the exhaust gas of a non-underwater engine, because CCHE keeps higher concentrations of carbon dioxide amounting to more than 70% in the dehydrated exhaust gas for adjusting the temperature of the combustion gas. Therefore, the liquefaction of exhaust gas can be considered as the liquefaction of carbon dioxide from the mixed gas of carbon dioxide and oxygen. Consequently, the design of the underwater engine using a closed cycle heat engine will be focused on the treatment of the exhaust gas. The important point of present study will concentrate on the design of the liquefaction system of the gas. In this study, two types of exhaust gas liquefaction system in the underwater engine, CCDE and CCLE, are designed, and design or operation data are determined by simulation.
Fig. 1. Schematic diagram for the liquefaction system of exhaust gas from a closed cycle diesel engine.
1246
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
2. Exhaust gas liquefaction system for a closed cycle diesel engine The liquefaction system of the exhaust gas in a CCDE is displayed schematically in Fig. 1. The relevant combustion equation in the diesel engine (assuming its fuel as cetane (C16H34)) is C16 H34 24:5 bO2 aCO2 416CO2 17H2 O aCO2 bO2 :
1
In the above combustion process, the exhaust gas here is not discharged to the environment as it is, but is recirculated in a closed cycle. The schematic of the mass ¯ow is drawn in Fig. 2(a) in connection with the above combustion equation. As is clearly shown in Fig. 2(a), the moisture (amounting to 17H2O) is ®rst withdrawn from the process by dehydrating. Then a fraction of 1 ÿ fC enters directly into the mixer, while the rest of the exhaust gas (fraction of
Fig. 2. Mass ¯ow chart for the two closed cycle engines. (a) Closed cycle diesel engine, (b) closed cycle LNG engine.
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1247
fC) is pressurized in the liquefaction system. Similarly, a fraction of fL (in terms of the CO2 mass, fLfC (16 + a) CO2) is lique®ed and drained from the system. To make the process a steady-state closed cycle, the liquefaction of CO2 should be controlled in such a way that the lique®ed mass of CO2 is exactly equal to 16CO2. Fig. 2(a) also shows that a total of (1 ÿ fL)fC(16 + a)CO2+fCbO2 enters into the mixer after the liquefaction process. Finally, in the combustor, diesel fuel is burned in the mixed gas from the mixer composed of both the oxygen, amounting to 24.5 O2, and the recirculated exhaust gas (see Fig. 2(a)). Overall, the coecient 24.5 represents the stoichiometry of the oxygen, and the coecients a and b stand for the excess CO2 and O2 recirculating in the system. The values of a and b are important since they aect the state of the exhaust gas, and in turn alter the combustion temperature. In this study, these values are monitored to keep the combustion temperature at 2000 K. The liquefaction temperature dierence between oxygen and carbon dioxide is so great that oxygen can be considered noncondensable gas and only carbon dioxide is assumed to be lique®able. For example, at 0.8 MPa, the liquefaction temperature of carbon dioxide is ÿ468C and that of oxygen is ÿ1578C. For the sake of simplicity in calculation, the degree of dissociation of carbon dioxide at this temperature was neglected because the relatively low degree of the dissociation has little eect on the energy equation of the above combustion equation. Referring to Fig. 2(a) and applying the mass conservation equation to the entire system, we can obtain the following equation: MC16 H34 24:5MO2 17MH2 O 16 afC fL MCO2 :
2
Here, fC is de®ned as the incoming mass fraction to the compressor among the dehydrated exhaust gas and fL is de®ned as the liquefaction fraction of carbon dioxide from the compressed exhaust gas. From the comparison between Eq. (1) and Eq. (2), the relationship between fC and fL becomes fC fL
16 : 16 a
3
A close examination of Fig. 2(a) indicates that the condition of fC(16 + a)CO2 is equal to (i.e. fL=1) or greater than 16 CO2 to operate in a steady state; therefore, there exists a minimum fC (equivalent to fL=1 in Eq. (3)). Since the noncondensable oxygen recirculates intact in the liquefaction system, the mass conservation equation for oxygen is m9 x9 m7 x7 :
4
The mass conservation equation for carbon dioxide is m7 ÿ m9 BC ;
5
where BC (=0.8982) is the theoretical quantity of carbon dioxide produced by the oxygen burnt. From Eqs. (1), (4) and (5), we can obtain the following relations for m7 and m9. In addition, the inlet and exit oxygen concentrations of the liquefaction system are also found.
1248
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
16 aMCO2 bMO2 BC fC 24:5MO2 1 ÿ x7 =x9 16 a 1 ÿ fL MCO2 bMO2 m9 fC m7 ÿ BC 24:5MO2
m7
m7;O2 bMO2 m7 16 aMCO2 bMO2 m9;O2 bMO2 x9 : m9 16 a 1 ÿ fL MCO2 bMO2 x7
6a 6b
7a 7b
Here, the oxygen concentrations are represented as the functions of a, b and fL. The energy equation of the system including the carbon dioxide vessel and the precooler is represented as Eq. (8a) with the following assumptions. The carbon dioxide vessel is large enough to maintain steady state during the liquefaction process so that the charging process of the liquid carbon dioxide has little eect on the behavior of temperature and pressure in the vessel. Also we assumed that the mass fraction of the vapour in the vessel and its rate of the change are very small except the initial period of liquefying process. Therefore, dmcv/ dt = dmcvf/dt and the rate of change in internal energy in the vessel becomes dUcv/ dt = ucvfdmcvf/dt. With the above assumptions, the energy equation for the subsystem combined with precooler and the vessel can be expressed as follows. m7 ÿ m9 ucvf ÿQcon m7 h7 ÿ m9 h9 Qloss
8a
Qloss mox Lcd Te ÿ TCV
8b
Qcon QPHX QCV :
8c
Qcon is supplied by the cold energy of oxygen and is consisted of two parts. As shown in Fig. 1, one part of the cold energy is the latent heat supplied by the saturated liquid oxygen through the vaporizing process in the carbon dioxide vessel, and the other part is the sensible heat supplied by the saturated vapour oxygen through the superheating process in the precooler. The cold energy values are 197.9 kJ/kg and 162.5 kJ/kg, respectively. The heat losses in the carbon dioxide and the oxygen vessel are considered and Lcd represents the heat loss coecient of the carbon dioxide vessel. The analysis and calculation procedure is as follows. From a given a, b and fC, we can ®nd the mass ¯ow rate and the mole fractions of inlet and outlet in the liquefaction system of exhaust gas. We also assumed that the state of the vent of the vessel is equivalent to the vapour state of the carbon dioxide vessel. Assuming the temperature in the vessel, we can ®nd the vessel pressure from the composition, and then the thermodynamic properties at the inlet and outlet of the system can be calculated. The step is repeated until the assumed temperature in the vessel satis®es the energy Eq. (8). The ®nal temperature and pressure make it possible to ®nd the power consumption to pressurize the exhaust gas from the inlet pressure of the compressor to the vessel pressure. The compressor was assumed to be three-stage, each stage with equivalent pressure ratio and isentropic compression. Inserting the intercooler between each stage, the inlet gas temperatures
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1249
Table 1 Simulation conditions of liquefaction system for closed cycle diesel engine Variables
Values
Combustion gas temperature External water temperature, Te Inlet temperature of dehydrated exhaust gas, T5a Inlet pressure of dehydrated exhaust gas, P5a
2000 K 108C 208C 1.013 bar
CO2 mole fraction of dehydrated exhaust gas, X5,CO2
97%, 72%
Oxygen delivery temperature, T4 Liquid oxygen temperature, T1 O2 vessel unit heat loss coecient, Lox CO2 vessel unit heat loss coecient, Lcd The mass of CO2 produced per unit mass of O2 burnt, BC Fuel consumption per unit mass of O2 burnt, Bf Cold energy of O2
08C 08C 0.02 kJ/kg (O2)8C 0.02 kJ/kg (O2)8C 0.8982 kJ/kg (O2) 0.2888 kJ/kg (O2) 360.4 kJ/kg (O2)
of each stage were assumed to maintain a constant 208C. The pressure losses in the system were neglected and heat losses except at the oxygen and carbon dioxide vessels were also neglected. Simulation was performed with the use of the above equations along with the input variables from Table 1. The properties of oxygen and carbon dioxide were calculated by the PROPATH V8.1 [6] and exhaust gas was assumed to be a mixture of ideal gases.
3. Exhaust gas liquefaction system for closed cycle LNG engine An exhaust gas liquefaction system in CCLE as a power-generating unit is shown schematically in Fig. 3. The liquefaction system consists of several parts: a compressor for pressurizing the exhaust gas to the vessel pressure, a precooler for lowering the exhaust gas temperature by use of the cold energies of both LNG and liquid oxygen, a carbon dioxide vessel for liquefying and restoring carbon dioxide, and an intercooler for precooling exhaust gas in each inlet of compressor stages. Although the liquefaction system of CCLE is similar to that of CCDE, it is dierent from that of CCDE in that the cold energy of LNG s added as a new cold energy source and the surplus cold energy makes it possible to cool down the inlet gas of each compressor stage. Assuming that LNG is a mixture of methane and ethane by mole fraction of 90 to 10, we can obtain the combustion equation in the gas engine as follows: 0:9CH4 0:1C2 H6 2:15 bO2 aCO2 41:1CO2 2:1H2 O aCO2 bO2 :
9
Here, excess carbon dioxide a and excess oxygen b represent the quantities of the recirculated oxygen and carbon dioxide per one mole of LNG. For the CCLE, a mass ¯ow chart similar to Fig. 2(a) is shown in Fig. 2(b). As clearly shown in Fig. 2(b), to make the entire system within
1250
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 3. Schematic diagram of the liquefaction system of exhaust gas from a closed cycle LNG engine.
the dashed line a steady state, 2.1H2O as well as 1.1CO2 should be withdrawn and the fuel (0.9CH4+0.1C2H6) as well as the newly supplied oxygen (2.15O2) should be provided. The deriving procedure of mass conservation for the CCLE is almost the same as in the CCDE shown in Fig. 2(a) and thus was replaced by Fig. 2(b). As in Eq. (1), a and b were selected to keep the combustion gas temperature 2000 K. Similar to the CCDE, mass conservation equation for the entire system and related equation are given by the following: 0:9MCH4 0:1MC2 H6 2:15MO2 2:1MH2 O 1:1 afc fL MCO2 fC fL
1:1 : 1:1 a
10 11
Fig. 2(b) also indicates that the condition of fC (1.1 + a) CO2 is equal to (i.e. fL=1) or greater than 1.1 CO2 to operate in a steady state; therefore, there exists minimum fC (equivalent to fL=1 in Eq. (11)). Mass conservation equations between states 7 and 9 in Fig. 3 are the same as Eqs. (4) and (5) except the values of the participating parameters. From Eq. (9), oxygen mass and concentration at states 7 and 9 are given below: 1:1 aMCO2 bMO2 BC fC 2:15MO2 1 ÿ x7 =x9 1:1 a 1 ÿ fL MCO2 bMO2 m9 fC m7 ÿ BC 2:15MO2
m7
12a 12b
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
m7;O2 bMO2 m7 1:1 aMCO2 bMO2 m9;O2 bMO2 x9 ; m9 1:1 a 1 ÿ fL MCO2 bMO2
x7
1251
13a 13b
where BC (=0.7035) is the carbon dioxide generated by the supplied oxygen. The energy equation for the combined system of the carbon dioxide vessel and the precooler is represented as follows: m7 ÿ m9 ucvf ÿ Qcon m7 h7 ÿ m9 h9 Qloss
14a
Qloss mox Lcd Te ÿ Tcv
14b
Qcon QPHX QCV QPHX;O2 QLNG
14c
where Qcon is composed of the cold energies of LNG and oxygen. Although the method of analysis for CCLE is similar to that of CCDE, the minimum temperature in the vessel and the inlet temperature in each stage of the compressor are con®ned to ÿ538C in order to prevent the solidi®cation of carbon dioxide. In the case of the LNG engine, the supplied cold energy can be greater than the demanded cold energy. That case is dierent from that of CCDE and the possible surplus cold energy is dissipated into seawater. Maximum supplied cold energy to the subsystem containing the precooler and the carbon dioxide vessel is 364.4 kJ/kg (O2), which is the sum of sensible heat of oxygen 162.5 kJ/kg (O2) and of LNG cold energy 201.9 kJ/kg (O2). The LNG cold energy 201.9 kJ/kg (O2) was calculated from the resultant value (LNG cold energy per unit LNG from the isobaric extraction process suggested by Lee et al. [7]) (LNG consumption per unit supplied oxygen in this system) = 798.5 0.2529. Equal pressure ratio and isentropic compression are assumed with each stage of the threestage compressor. In front of each stage, there are intercoolers using the cold energy of liquid oxygen, and the maximum supplied cold energy is 197.9 kJ/kg (O2). Similar to the case of the carbon dioxide vessel, the minimum temperature of the exhaust gas in each intercooler is limited to ÿ538C and the surplus cold energy is dissipated to seawater. The other assumptions for analysis are the same as those of the case of CCDE and some input parameters are shown in Table 2.
4. Result and discussions Every calculation was carried out in terms of unit supplied oxygen (1 kg/s). The combustion temperature is assumed as 2000 K. In order to maintain the combustion temperature 2000 K, the theoretical quantity of carbon dioxide should be removed, as was discussed earlier. Therefore, discussion will be focused on compression power, consumed cold energy, carbon dioxide vessel pressure and temperature, and inlet temperature of compressor. Among the various values of compressor inlet carbon dioxide concentration, the two cases, X5,CO2=97% and 72% are chosen for both CCDE and CCLE. The supplied cold energy for CCDE is the
1252
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262 Table 2 Simulation conditions of liquefaction system for closed cycle LNG engine Variables
Values
Combustion gas temperature External water temperature, Te Inlet temperature of dehydrated exhaust gas, T5a Inlet pressure of dehydrated exhaust gas, P5a
2000 K 108C 208C 1.013 bar
CO2 mole fraction of dehydrated exhaust gas, X5,CO2
97%, 72%
Inlet temperature of compressor Temperature in the CO2 vessel Oxygen delivery temperature, T4 Liquid oxygen temperature, T1 O2 vessel unit heat loss coecient, Lox CO2 vessel unit heat loss coecient, Lcd The mass of CO2 produced per unit mass of O2 burnt, BC Fuel consumption per unit mass of O2 burnt, Bf Maximum cold energy supplied to precooler and CO2 vessel Maximum cold energy supplied to compressor intercooler
> ÿ 538C > ÿ 538C <08C 08C 0.02 kJ/kg (O2)8C 0.02 kJ/kg (O2)8C 0.7035 kJ/kg (O2) 0.2529 kJ/kg (O2) 364.4 kJ/kg (O2) 197.9 kJ/kg (O2)
constant value of 360.4 kJ/kg (O2), while the maximum supplied cold energy for CCLE is 562.3 kJ/kg (O2), which is the sum of 197.9 kJ/kg (O2) in the intercooler of the compressor and 364.4 kJ/kg (O2) in the precooler and the carbon dioxide vessel. 4.1. Liquefaction system for CCDE Fig. 4 shows compression power, carbon dioxide vessel pressure and temperature, and liquid fraction in the carbon dioxide vessel as a function of fC in the case of the inlet carbon dioxide concentration X5,CO2=97%. Here, the minimum value of the compression power is 130 kJ/kg (O2) near fC=0.175. The compression power can be expressed as a product of mass ¯ow rate and enthalpy dierence. Enthalpies are functions of temperature, pressure, and inlet or exit carbon dioxide concentration. Inlet mass ¯ow rate m5 is an increasing function of fC. Since theoretical quantity of carbon dioxide (16CO2) should be lique®ed to maintain the constant combustion temperature, the liquefying fraction fL decreases and the outlet oxygen concentration x9 also reduces. The carbon dioxide vessel pressure is determined by the enthalpies of states 7 and 9 as well as the supplied cold energy to both the precooler and the carbon dioxide vessel. The temperature in the carbon dioxide vessel rises if the required cold energy is greater than the supplied cold energy of oxygen 360 kJ/kg (O2). The partial pressure of carbon dioxide increases monotonically because the partial pressure is a monotonic increasing function of temperature. On the other hand, the vessel pressure is a function of carbon dioxide partial pressure and mole fraction, i.e. PCV=Pcvcd/(1 ÿ X9). In Fig. 4, below optimum fC (corresponding to minimum compression power), since the decrease in oxygen mole fraction is signi®cantly greater than the increase in carbon dioxide partial pressure, the carbon dioxide vessel pressure
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1253
Fig. 4. Isentropic compressor work, pressure, temperature, outlet O2 mass fraction and liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle diesel engine (X5,CO2=97%).
tends to decrease with increasing fC. Above optimum fC, since the decrease in oxygen concentration in the outlet of the carbon dioxide vessel is very small, the vessel pressure mainly depends on the increase in the carbon dioxide partial pressure. Therefore, the minimum of compression power results from the existence of the minimum vessel pressure. For the case of X5,CO2=72%, compression power and related variables are shown in Fig. 5. Compression power has a minimum value of 320 kJ/kg (O2) near fC=0.225. The temperature and pressure in the carbon dioxide vessel and the carbon dioxide concentration in the outlet of the vessel show similar trends to those shown in Fig. 4, but the vessel pressure is shifted to the
1254
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
higher level and the change rates of all the related variables are more gradual than those shown in Fig. 4. 4.2. Liquefaction system for CCLE When CCLE is used, compression power, demanded cold energy, pressure and temperature in the carbon dioxide vessel, liquefaction fraction and outlet oxygen concentration in the exhaust gas liquefaction system are shown as a function of fC for the case of X5,CO2=97% and 72% in Fig. 6 and 7, respectively. First, we will concentrate on the case of X5,CO2=97%.
Fig. 5. Isentropic compressor work, pressure, temperature, outlet O2 mass fraction and liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle diesel engine (X5,CO2=72%).
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1255
Fig. 6. Isentropic compressor work, consumed cold energy, pressure, temperature, outlet O2 mass fraction and the liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle LNG engine (X5,CO2=97%).
1256
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 7. Isentropic compressor work, consumed cold energy, pressure, temperature, outlet O2 mass fraction and the liquefaction fraction of Co2 in the CO2 vessel as a function of fC for the liquefaction system of the closed ctycle LNG engine (X5,CO2=72%).
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1257
Compression power has minimum value of 75.7 kJ/kg (O2) near fC=0.15 and its slope at the right of fC=0.37 is steeper than that at the left. Inspection of the trend of temperature in the carbon dioxide vessel shows that for the constant temperature region, the supplied cold energy is greater than the demanded cold energy to the precooler and carbon dioxide vessel. It also shows that for the region of increasing temperature, the temperature in the carbon dioxide vessel should be increased to match the demanded cold energy with the maximum supplied cold energy. The changing point corresponds to fC=0.37. The vessel pressure decreases drastically at ®rst and then maintains nearly constant value, and ®nally increases in a trend of temperature variation. The ®rst emergence of drastically decreasing region mainly results from the drastic decrease in the outlet oxygen concentration of the carbon dioxide vessel. The next one can be explained by the fact that the outlet oxygen concentration is nearly constant and the carbon dioxide partial pressure is constant due to the constant temperature in the vessel. The ®nal one results from the fact that the carbon dioxide partial pressure increases due to increasing temperature in the vessel and the outlet oxygen concentration remains nearly constant. The compressor inlet temperature associated with compression power is shown in Fig. 8. Until fC=0.33 is reached from the minimum fC, the demanded cold energy to the intercooler is smaller than the supplied cold energy so that the inlet temperature of compressor is constant. Beyond fC=0.33, the inlet temperature of compressor should be increased to match the demanded cold energy with the maximum supplied cold energy. Therefore, we can ®nd that lower compressor power results from the lower pressure ratio due to low temperature in the carbon dioxide vessel and the low compressor inlet temperature due to the intercooling eect. In Fig. 7, for the case of X5,CO2=72%, the minimum compression power 159 kJ/kg (O2) occurs near fC=0.22. The trends of compressor power are divided into three regions. The ®rst region is up to fC=0.25, where the supplied cold energy for intercooling is enough to cool the exhaust gas so that the compressor inlet temperature is the constant value of ÿ538C as shown
Fig. 8. Compressor inlet temperature for the LNG engine as a function of fC.
1258
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
in Fig. 8. In this region, the compression power has nearly constant value of 159 kJ/kg (O2). The second region is from fC=0.25 to fC=0.37. In this region the supplied cold energy for intercooling is smaller than the demanded cold energy so that compressor inlet temperature increases, but the vessel pressure decreases so that compression power increases slightly. The third region starts from fC=0.37, where compression power increases more steeply due to the increase in temperature and pressure in the carbon dioxide vessel (resulting from the shortage of the cold energy for liquefaction of exhaust gas) and due to the increase in compressor inlet temperature (resulting from the shortage of the cold energy for intercooling). As for vessel pressure, the region where the vessel pressure decreases results from both the constant value of carbon dioxide partial pressure (corresponding to constant temperature in the vessel) and the decrease in the outlet oxygen concentration from the carbon dioxide vessel. Over fC=0.37, the pressure increases due to the increase of the temperature in the vessel. The compressor inlet temperature is shown in Fig. 8. In case of X5,CO2=97%, enough cold energy for intercooling is provided up top the higher fC than in case of X5,CO2=72%. Due to lower carbon dioxide vessel pressure in case of X5,CO2=97%, the outlet pressure of each stage is lower so that the cold energy for intercooling is lower than that of X5,CO2=72%. 4.3. Comparison between CCDE and CCLE Compression power with respect to fC for CCDE and CCLE are shown in Fig. 9. Assuming that the two engines have the same thermal eciency and power, we will compare compression power consumption between the two. Taking the heating value of LNG as 50,000 kJ/kg (LNG) [8] and that of diesel (cetane) as 44,000 kJ/kg (C16H34) [9], the ratio of the diesel fuel mass ¯ow rate to the LNG fuel mass ¯ow rate is 1.136. However, since the fuel consumption per unit supplied oxygen is Bf=0.2888 kg (C16H34)/kg (O2) for CCDE and Bf=0.2529 kg (LNG)/kg (O2) for CCLE, respectively, the ratio of oxygen consumption of CCDE to that of CCLE is 1.136 0.2529/0.288831. Hence, we can compare the compression power consumption of the two without further compensation.
Fig. 9. Compressor work as a function of fC.
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1259
Fig. 10. Mass ¯ow rate into the compressor as a function of fC.
From Fig. 9, it is observed that the compression power of CCLE (which uses the cold energy of oxygen to cool each stage of compressor to ÿ538C) amounts to 50% of compression power of CCDE (which uses seawater at 108C to cool each stage). Fig. 10 exhibits the mass ¯ow rate of the exhaust gas into the compressor per unit supplied oxygen. In order to liquefy the theoretical carbon dioxide for the same value of fC, higher mass ¯ow rate is needed for CCDE than for CCLE, and such is the case for X5,CO2=72% than for X5,CO2=97%. The vessel pressure with respect to fC is suggested in Fig. 11. It is observed that the carbon dioxide vessel pressure associated with the diesel engine is nearly twice the carbon dioxide vessel pressure associated with the LNG engine. The reason is that utilizing both the oxygen cold energy and the LNG cold energy simultaneously can reduce the carbon dioxide vessel pressure associated with the LNG engine.
Fig. 11. CO2 vessel pressure as a function of fC.
1260
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 12. CO2 temperature in the CO2 vessel as a function of fC.
The temperature trends in the carbon dioxide vessel are show in Fig. 12. CCLE maintains lower temperature in the vessel with the supply of enough cold energy, so the temperature variation in the vessel is smaller than that for the case of CCDE. The portion of the exhaust gas compression power out of net engine power can be calculated according to the following steps. The eciency of the two engines is assumed as 25%. For the case of diesel engine, the lower heating value of the fuel is 44,000 kJ/kg (C16H34) so that the output per unit fuel is 11,000 kJ/kg (C16H34). Since the fuel consumption per unit supplied oxygen in CCDE is Bf=0.2888 kg (C16H34)/kg (O2), the output per unit supplied oxygen is 11,000 0.2888 = 3176.8 kJ/kg (O2). The compression power in Fig. 3 will be 150 kJ/kg (O2) when we choose a design point to be fC=0.2 in Fig. 3 (with consideration of the vessel pressure, its trends, and the minimum compression power). With the assumption of the isentropic compression eciency of 75%, actual compression power is 200 kJ/kg (O2). Therefore, the ratio for the actual compression power to the output is 200/3176.8 = 6.3%. For the case of CCLE, since the lower heating value of fuel is 50,000 kJ/kg (LNG), the output per unit LNG is 12500 kJ/kg (LNG). Since the fuel consumption per unit supplied oxygen in CCLE is Bf=0.2529 kg (LNG)/kg (O2), the output per unit supplied oxygen is 12,500 0.2529 = 3161 kJ/kg (O2). The compression power in Fig. 6 is about 80 kJ/kg (O2) when we choose a design point to be fC=0.2 in Fig. 6 (with consideration of the vessel pressure, its trends and the minimum compression power associated with constant temperature of the compressor inlet). With the assumption of isentropic compression eciency of 75%, actual compression power is 106.7 kJ/kg (O2). Therefore, the ratio of the actual compression power to the output of CCLE is 106.7/3161 = 3.4%. 5. Conclusions In order to treat the exhaust gas from underwater engines eectively, the liquefaction systems of exhaust gas for both CCDE and CCLE were designed and analyzed. Several
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1261
remarks were drawn as follows. The ratio for compression power to the net engine power is 6.3% for CCDE and 3.4% for CCLE, which is much lower than that of the carbon dioxide absorbing system (with the exhaust gas dealing power consumption of 15%). In particular, CCLE has more advantages in reducing compression power and the carbon dioxide vessel pressure. In the case of CCDE, the carbon dioxide vessel pressure should be raised to liquefy the theoretical quantity of carbon dioxide due to the de®ciency of the cold energy supplied. This requires increasing compression power. More compression power is needed to lower carbon dioxide concentration of exhaust gas, because higher pressure is needed to liquefy the theoretical quantity of carbon dioxide. We can select a design point corresponding to the lower vessel pressure, its gradual change with respect to incoming fraction of the exhaust gas to the compressor (fC), and the lower compression power. The design point can be selected as fC=0.19 for the case of carbon dioxide mole fractions of 97% entering into the compressor, and fC=0.26 for 72%. In the case of CCLE, since the carbon dioxide vessel pressure maintains low values over a wide range of fC and each stage of the compressor also keeps lower temperatures such as ÿ538C with the help of sucient supplied cold energy, the compression power is only 50% that of diesel engines. The design point can be determined in such a way that a proper value of fC is chosen to satisfy lower vessel pressure with its smaller variation, lower temperature in compressor inlet, and lower compression power. The design point can be selected as 0.2 and 0.24 of fC for the case of the carbon dioxide mole fraction of 97% and 72% entering into the compressor, respectively In considering lower consumption power and lower vessel pressure, CCLE rather than CCDE has advantages, and so does the higher carbon dioxide concentration rather than the lower one in the system. Therefore, it is desirable to use CCLE and to maintain lower oxygen concentration in exhaust gas for reducing compression power and for lowering vessel pressure, but the actual engine should be designed by considering various factors, including overall eciency and power, availability and safety of fuel, design purpose and possibility of manufacturing, and economics etc. Acknowledgements The authors are very grateful to the ®nancial support provided by the Turbo and Power Machinery Research Center (TPMRC) at Seoul National University References [1] G. Sattler, Air-independent propulsion: the current state of art, Defence Systems International 94/95 (1994) 127±131. [2] R. Brenner, A closed cycle diesel system for submarines, Marine Defence June (1993) 162±164. [3] J.G. Hawley, Underwater vehicle power system technology, Marine Defence December (1993) 302±307. [4] A. Brighenti, G. Minelli, A.D. Rosa, The cryo-thermal engine underwater power system: performance, dynamics and control. in: Oceans '89 Marine Technology Society. Seattle. 1989, pp. 832±842.
1262
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
[5] G. Acker Jr., C.E. Brett, S. Bell, K.C. Midki, Y.K. Song, Experience using LNG as a marine engine fuel, Marine Technology Society Journal 23 (1989) 33±39. [6] PROPATH Group, PROPATH: a program package for thermophysical properties. Version 8.1, 1993. [7] G.S. Lee, Y.S. Chang, M.S. Kim, S.T. Ro, Thermodynamic analysis of extraction processes for the utilization of LNG cold energy, Cryogenics 36 (1) (1996) 35±40. [8] H.J. Song, A study on power generation technology utilizing LNG cold energy. Korea Electric Power Research Institute, 1985. [9] J.B. Heywood, Internal Combustion Engine Fundamentals. McGraw-Hill, New York, 1989, p. 915.
Applied Thermal Engineering 18 (1998) 1243±1262
Analysis of the liquefaction process of exhaust gases from an underwater engine G.S. Lee a, S.T. Ro b,* a
b
Department of Mechanical Engineering, University of Ulsan, Ulsan 680-749, Korea Department of Mechanical Engineering, Seoul National University, Seoul 151-742, Korea Received 30 October 1997
Abstract In operating underwater engines, such as in exploring submarines, the dumping of the exhaust gas out of the engine requires a large portion of the total power, frequently amounting to 25±30% of the power generated. This can be solved by liquefying the exhaust gas and storing it. In the present study, two liquefaction systems are simulated to enhance the overall eciency; one is a closed cycle diesel cycle and the other is a closed cycle lique®ed natural gas (LNG) engine. LNG was chosen as a fuel not only because it is economical but also because its cold energy can be utilized within the liquefaction system. Since a mixture of oxygen and carbon dioxide is used as an oxidizer, liquefying carbon dioxide is the major concern in this study. To further improve this system, the intercooling of the compressor is devised. The power consumed for the liquefaction system is examined in terms of the related properties, including pressure and temperature of the carbon dioxide vessel as a function of the mass fraction of the exhaust gas that enters the compressor. The present study shows that much gain in the power and reduction of the vessel pressure could be achieved in the case of the closed cycle LNG engine. The compression power was remarkably low, typically only 6.3% for the closed cycle diesel engine and 3.4% for the closed cycle LNG engine, respectively, of net engine power. For practically, a design±purpose map of the operating parameters of the liquefaction systems is also presented. # 1998 Elsevier Science Ltd. All rights reserved.
Nomenclature a b Bc
recirculated mole of carbon dioxide in the engine recirculated mole of oxygen in the engine theoretical quantity of carbon dioxide produced per oxygen burnt (supplied oxygen) (kg/kg (O2))
* Author to whom all correspondence should be addressed. 1359-4311/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 9 8 ) 0 0 0 0 9 - X
1244 Bf fc fL h Lcd Lox Mi m5 m9 PCV Pcvcd Qcon Qcv Qintc Qloss QLNG QPHX TCV Te u ucvf x7 x9 Xi
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262 fuel consumption per oxygen burnt (supplied oxygen) (kg/kg (O2)) incoming fraction of exhaust gas to the compressor liquefaction fraction of carbon dioxide from the compressed exhaust gas enthalpy (kJ/kg) heat loss coecient of carbon dioxide vessel (kJ/kg (O2)8C) heat loss coecient of oxygen vessel (kJ/kg (O2)8C) molecular weight of i-component (kg/kmol) incoming mass of exhaust gas to the compressor per oxygen burnt (=m7) discharging mass of exhaust gas from the Co2 vessel per oxygen burnt pressure in the carbon dioxide vessel carbon dioxide partial pressure in the carbon dioxide vessel supplied or consumed cold energy in the precooler and the carbon dioxide vessel (kJ/kg (O2)) supplied or consumed cold energy in the carbon dioxide vessel (kJ/kg (O2)) supplied or consumed cold energy in the intercooler (kJ/kg (O2)) absorbed heat by the temperature dierence between the oxygen or carbon dioxide vessel and surroundings (kJ/kg (O2)) supplied cold energy by LNG (kJ/kg (O2)) supplied or consumed cold energy in the precooler (kJ/kg (O2)) temperature in the carbon dioxide vessel surrounding water temperature internal energy (kJ/kg) internal energy of saturated liquid carbon dioxide in the carbon dioxide vessel (kJ/kg) mass fraction of oxygen in the incoming exhaust gas to the precooler inlet mass fraction of oxygen in the discharging exhaust gas from the carbon dioxide vessel mole fraction of i-state
1. Introduction Much research and development of engines for underwater vehicles has been done due to the high level of interest in underwater development. An underwater engine, especially in exploring submarines, should have good operating characteristics in deep sea (3000±6000 m). The power sources operating underwater engines can be battery, radioisotope Rankine cycle, thermoelectric generator, or nuclear power. However, the most promising source is either a fuel cell or a closed cycle heat engine (CCHE). CCHE in an underwater engine usually adopts the Stirling engine or the closed cycle diesel engine (CCDE) [1±3]. In the power generation process of CCHE, the exhaust gas containing water vapour, soot, oxygen and carbon dioxide is emitted from the combustion process. The moisture in the gas can be easily eliminated by liquefaction, and the soot can be reduced by increasing oxygen concentration. To get rid of the carbon dioxide in the gas, absorbing systems using absorbents and a liquefaction system have typically been adopted. This absorbing system, however, has disadvantages, such as additional loading of absorbents and additional power necessary for incoming seawater as an absorbent. Therefore, the object of this work is to reduce the power consumption by adopting a liquefaction system of carbon dioxide. When CCDE is used for power generation, oxygen (as an oxidizer) should be supplied in a gas state vaporized from the liquid oxygen vessel. In recent research, a system where carbon dioxide from the exhaust gas is lique®ed and stored in a vessel was proposed, using the heat of
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1245
vaporization of oxygen [4]. Part of the dehydrated exhaust gas is supplied to the liquefaction system and the remaining part is recirculated to the engine for adjusting combustion temperature. The exhaust gas entering the liquefaction system is compressed and then cools down in the precooler. The theoretical quantity of carbon dioxide in the exhaust gas (produced by the stoichiometric quantity of oxygen during the combustion process) is lique®ed in a carbon dioxide vessel by the cold energy of liquid oxygen, and the others are supplied to the diesel engine as an intake after being mixed with oxygen. If a closed cycle gas engine is used for a power generating apparatus and lique®ed natural gas (LNG) [5] is used as its fuel, a more eective liquefaction system could be designed with the simultaneous use of the cold energies of LNG and liquid oxygen. It will be called the closed cycle LNG engine (CCLE) henceforth. The characteristics of the exhaust gas of CCHE for an underwater engine are dierent from those of the exhaust gas of a non-underwater engine, because CCHE keeps higher concentrations of carbon dioxide amounting to more than 70% in the dehydrated exhaust gas for adjusting the temperature of the combustion gas. Therefore, the liquefaction of exhaust gas can be considered as the liquefaction of carbon dioxide from the mixed gas of carbon dioxide and oxygen. Consequently, the design of the underwater engine using a closed cycle heat engine will be focused on the treatment of the exhaust gas. The important point of present study will concentrate on the design of the liquefaction system of the gas. In this study, two types of exhaust gas liquefaction system in the underwater engine, CCDE and CCLE, are designed, and design or operation data are determined by simulation.
Fig. 1. Schematic diagram for the liquefaction system of exhaust gas from a closed cycle diesel engine.
1246
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
2. Exhaust gas liquefaction system for a closed cycle diesel engine The liquefaction system of the exhaust gas in a CCDE is displayed schematically in Fig. 1. The relevant combustion equation in the diesel engine (assuming its fuel as cetane (C16H34)) is C16 H34 24:5 bO2 aCO2 416CO2 17H2 O aCO2 bO2 :
1
In the above combustion process, the exhaust gas here is not discharged to the environment as it is, but is recirculated in a closed cycle. The schematic of the mass ¯ow is drawn in Fig. 2(a) in connection with the above combustion equation. As is clearly shown in Fig. 2(a), the moisture (amounting to 17H2O) is ®rst withdrawn from the process by dehydrating. Then a fraction of 1 ÿ fC enters directly into the mixer, while the rest of the exhaust gas (fraction of
Fig. 2. Mass ¯ow chart for the two closed cycle engines. (a) Closed cycle diesel engine, (b) closed cycle LNG engine.
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1247
fC) is pressurized in the liquefaction system. Similarly, a fraction of fL (in terms of the CO2 mass, fLfC (16 + a) CO2) is lique®ed and drained from the system. To make the process a steady-state closed cycle, the liquefaction of CO2 should be controlled in such a way that the lique®ed mass of CO2 is exactly equal to 16CO2. Fig. 2(a) also shows that a total of (1 ÿ fL)fC(16 + a)CO2+fCbO2 enters into the mixer after the liquefaction process. Finally, in the combustor, diesel fuel is burned in the mixed gas from the mixer composed of both the oxygen, amounting to 24.5 O2, and the recirculated exhaust gas (see Fig. 2(a)). Overall, the coecient 24.5 represents the stoichiometry of the oxygen, and the coecients a and b stand for the excess CO2 and O2 recirculating in the system. The values of a and b are important since they aect the state of the exhaust gas, and in turn alter the combustion temperature. In this study, these values are monitored to keep the combustion temperature at 2000 K. The liquefaction temperature dierence between oxygen and carbon dioxide is so great that oxygen can be considered noncondensable gas and only carbon dioxide is assumed to be lique®able. For example, at 0.8 MPa, the liquefaction temperature of carbon dioxide is ÿ468C and that of oxygen is ÿ1578C. For the sake of simplicity in calculation, the degree of dissociation of carbon dioxide at this temperature was neglected because the relatively low degree of the dissociation has little eect on the energy equation of the above combustion equation. Referring to Fig. 2(a) and applying the mass conservation equation to the entire system, we can obtain the following equation: MC16 H34 24:5MO2 17MH2 O 16 afC fL MCO2 :
2
Here, fC is de®ned as the incoming mass fraction to the compressor among the dehydrated exhaust gas and fL is de®ned as the liquefaction fraction of carbon dioxide from the compressed exhaust gas. From the comparison between Eq. (1) and Eq. (2), the relationship between fC and fL becomes fC fL
16 : 16 a
3
A close examination of Fig. 2(a) indicates that the condition of fC(16 + a)CO2 is equal to (i.e. fL=1) or greater than 16 CO2 to operate in a steady state; therefore, there exists a minimum fC (equivalent to fL=1 in Eq. (3)). Since the noncondensable oxygen recirculates intact in the liquefaction system, the mass conservation equation for oxygen is m9 x9 m7 x7 :
4
The mass conservation equation for carbon dioxide is m7 ÿ m9 BC ;
5
where BC (=0.8982) is the theoretical quantity of carbon dioxide produced by the oxygen burnt. From Eqs. (1), (4) and (5), we can obtain the following relations for m7 and m9. In addition, the inlet and exit oxygen concentrations of the liquefaction system are also found.
1248
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
16 aMCO2 bMO2 BC fC 24:5MO2 1 ÿ x7 =x9 16 a 1 ÿ fL MCO2 bMO2 m9 fC m7 ÿ BC 24:5MO2
m7
m7;O2 bMO2 m7 16 aMCO2 bMO2 m9;O2 bMO2 x9 : m9 16 a 1 ÿ fL MCO2 bMO2 x7
6a 6b
7a 7b
Here, the oxygen concentrations are represented as the functions of a, b and fL. The energy equation of the system including the carbon dioxide vessel and the precooler is represented as Eq. (8a) with the following assumptions. The carbon dioxide vessel is large enough to maintain steady state during the liquefaction process so that the charging process of the liquid carbon dioxide has little eect on the behavior of temperature and pressure in the vessel. Also we assumed that the mass fraction of the vapour in the vessel and its rate of the change are very small except the initial period of liquefying process. Therefore, dmcv/ dt = dmcvf/dt and the rate of change in internal energy in the vessel becomes dUcv/ dt = ucvfdmcvf/dt. With the above assumptions, the energy equation for the subsystem combined with precooler and the vessel can be expressed as follows. m7 ÿ m9 ucvf ÿQcon m7 h7 ÿ m9 h9 Qloss
8a
Qloss mox Lcd Te ÿ TCV
8b
Qcon QPHX QCV :
8c
Qcon is supplied by the cold energy of oxygen and is consisted of two parts. As shown in Fig. 1, one part of the cold energy is the latent heat supplied by the saturated liquid oxygen through the vaporizing process in the carbon dioxide vessel, and the other part is the sensible heat supplied by the saturated vapour oxygen through the superheating process in the precooler. The cold energy values are 197.9 kJ/kg and 162.5 kJ/kg, respectively. The heat losses in the carbon dioxide and the oxygen vessel are considered and Lcd represents the heat loss coecient of the carbon dioxide vessel. The analysis and calculation procedure is as follows. From a given a, b and fC, we can ®nd the mass ¯ow rate and the mole fractions of inlet and outlet in the liquefaction system of exhaust gas. We also assumed that the state of the vent of the vessel is equivalent to the vapour state of the carbon dioxide vessel. Assuming the temperature in the vessel, we can ®nd the vessel pressure from the composition, and then the thermodynamic properties at the inlet and outlet of the system can be calculated. The step is repeated until the assumed temperature in the vessel satis®es the energy Eq. (8). The ®nal temperature and pressure make it possible to ®nd the power consumption to pressurize the exhaust gas from the inlet pressure of the compressor to the vessel pressure. The compressor was assumed to be three-stage, each stage with equivalent pressure ratio and isentropic compression. Inserting the intercooler between each stage, the inlet gas temperatures
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1249
Table 1 Simulation conditions of liquefaction system for closed cycle diesel engine Variables
Values
Combustion gas temperature External water temperature, Te Inlet temperature of dehydrated exhaust gas, T5a Inlet pressure of dehydrated exhaust gas, P5a
2000 K 108C 208C 1.013 bar
CO2 mole fraction of dehydrated exhaust gas, X5,CO2
97%, 72%
Oxygen delivery temperature, T4 Liquid oxygen temperature, T1 O2 vessel unit heat loss coecient, Lox CO2 vessel unit heat loss coecient, Lcd The mass of CO2 produced per unit mass of O2 burnt, BC Fuel consumption per unit mass of O2 burnt, Bf Cold energy of O2
08C 08C 0.02 kJ/kg (O2)8C 0.02 kJ/kg (O2)8C 0.8982 kJ/kg (O2) 0.2888 kJ/kg (O2) 360.4 kJ/kg (O2)
of each stage were assumed to maintain a constant 208C. The pressure losses in the system were neglected and heat losses except at the oxygen and carbon dioxide vessels were also neglected. Simulation was performed with the use of the above equations along with the input variables from Table 1. The properties of oxygen and carbon dioxide were calculated by the PROPATH V8.1 [6] and exhaust gas was assumed to be a mixture of ideal gases.
3. Exhaust gas liquefaction system for closed cycle LNG engine An exhaust gas liquefaction system in CCLE as a power-generating unit is shown schematically in Fig. 3. The liquefaction system consists of several parts: a compressor for pressurizing the exhaust gas to the vessel pressure, a precooler for lowering the exhaust gas temperature by use of the cold energies of both LNG and liquid oxygen, a carbon dioxide vessel for liquefying and restoring carbon dioxide, and an intercooler for precooling exhaust gas in each inlet of compressor stages. Although the liquefaction system of CCLE is similar to that of CCDE, it is dierent from that of CCDE in that the cold energy of LNG s added as a new cold energy source and the surplus cold energy makes it possible to cool down the inlet gas of each compressor stage. Assuming that LNG is a mixture of methane and ethane by mole fraction of 90 to 10, we can obtain the combustion equation in the gas engine as follows: 0:9CH4 0:1C2 H6 2:15 bO2 aCO2 41:1CO2 2:1H2 O aCO2 bO2 :
9
Here, excess carbon dioxide a and excess oxygen b represent the quantities of the recirculated oxygen and carbon dioxide per one mole of LNG. For the CCLE, a mass ¯ow chart similar to Fig. 2(a) is shown in Fig. 2(b). As clearly shown in Fig. 2(b), to make the entire system within
1250
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 3. Schematic diagram of the liquefaction system of exhaust gas from a closed cycle LNG engine.
the dashed line a steady state, 2.1H2O as well as 1.1CO2 should be withdrawn and the fuel (0.9CH4+0.1C2H6) as well as the newly supplied oxygen (2.15O2) should be provided. The deriving procedure of mass conservation for the CCLE is almost the same as in the CCDE shown in Fig. 2(a) and thus was replaced by Fig. 2(b). As in Eq. (1), a and b were selected to keep the combustion gas temperature 2000 K. Similar to the CCDE, mass conservation equation for the entire system and related equation are given by the following: 0:9MCH4 0:1MC2 H6 2:15MO2 2:1MH2 O 1:1 afc fL MCO2 fC fL
1:1 : 1:1 a
10 11
Fig. 2(b) also indicates that the condition of fC (1.1 + a) CO2 is equal to (i.e. fL=1) or greater than 1.1 CO2 to operate in a steady state; therefore, there exists minimum fC (equivalent to fL=1 in Eq. (11)). Mass conservation equations between states 7 and 9 in Fig. 3 are the same as Eqs. (4) and (5) except the values of the participating parameters. From Eq. (9), oxygen mass and concentration at states 7 and 9 are given below: 1:1 aMCO2 bMO2 BC fC 2:15MO2 1 ÿ x7 =x9 1:1 a 1 ÿ fL MCO2 bMO2 m9 fC m7 ÿ BC 2:15MO2
m7
12a 12b
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
m7;O2 bMO2 m7 1:1 aMCO2 bMO2 m9;O2 bMO2 x9 ; m9 1:1 a 1 ÿ fL MCO2 bMO2
x7
1251
13a 13b
where BC (=0.7035) is the carbon dioxide generated by the supplied oxygen. The energy equation for the combined system of the carbon dioxide vessel and the precooler is represented as follows: m7 ÿ m9 ucvf ÿ Qcon m7 h7 ÿ m9 h9 Qloss
14a
Qloss mox Lcd Te ÿ Tcv
14b
Qcon QPHX QCV QPHX;O2 QLNG
14c
where Qcon is composed of the cold energies of LNG and oxygen. Although the method of analysis for CCLE is similar to that of CCDE, the minimum temperature in the vessel and the inlet temperature in each stage of the compressor are con®ned to ÿ538C in order to prevent the solidi®cation of carbon dioxide. In the case of the LNG engine, the supplied cold energy can be greater than the demanded cold energy. That case is dierent from that of CCDE and the possible surplus cold energy is dissipated into seawater. Maximum supplied cold energy to the subsystem containing the precooler and the carbon dioxide vessel is 364.4 kJ/kg (O2), which is the sum of sensible heat of oxygen 162.5 kJ/kg (O2) and of LNG cold energy 201.9 kJ/kg (O2). The LNG cold energy 201.9 kJ/kg (O2) was calculated from the resultant value (LNG cold energy per unit LNG from the isobaric extraction process suggested by Lee et al. [7]) (LNG consumption per unit supplied oxygen in this system) = 798.5 0.2529. Equal pressure ratio and isentropic compression are assumed with each stage of the threestage compressor. In front of each stage, there are intercoolers using the cold energy of liquid oxygen, and the maximum supplied cold energy is 197.9 kJ/kg (O2). Similar to the case of the carbon dioxide vessel, the minimum temperature of the exhaust gas in each intercooler is limited to ÿ538C and the surplus cold energy is dissipated to seawater. The other assumptions for analysis are the same as those of the case of CCDE and some input parameters are shown in Table 2.
4. Result and discussions Every calculation was carried out in terms of unit supplied oxygen (1 kg/s). The combustion temperature is assumed as 2000 K. In order to maintain the combustion temperature 2000 K, the theoretical quantity of carbon dioxide should be removed, as was discussed earlier. Therefore, discussion will be focused on compression power, consumed cold energy, carbon dioxide vessel pressure and temperature, and inlet temperature of compressor. Among the various values of compressor inlet carbon dioxide concentration, the two cases, X5,CO2=97% and 72% are chosen for both CCDE and CCLE. The supplied cold energy for CCDE is the
1252
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262 Table 2 Simulation conditions of liquefaction system for closed cycle LNG engine Variables
Values
Combustion gas temperature External water temperature, Te Inlet temperature of dehydrated exhaust gas, T5a Inlet pressure of dehydrated exhaust gas, P5a
2000 K 108C 208C 1.013 bar
CO2 mole fraction of dehydrated exhaust gas, X5,CO2
97%, 72%
Inlet temperature of compressor Temperature in the CO2 vessel Oxygen delivery temperature, T4 Liquid oxygen temperature, T1 O2 vessel unit heat loss coecient, Lox CO2 vessel unit heat loss coecient, Lcd The mass of CO2 produced per unit mass of O2 burnt, BC Fuel consumption per unit mass of O2 burnt, Bf Maximum cold energy supplied to precooler and CO2 vessel Maximum cold energy supplied to compressor intercooler
> ÿ 538C > ÿ 538C <08C 08C 0.02 kJ/kg (O2)8C 0.02 kJ/kg (O2)8C 0.7035 kJ/kg (O2) 0.2529 kJ/kg (O2) 364.4 kJ/kg (O2) 197.9 kJ/kg (O2)
constant value of 360.4 kJ/kg (O2), while the maximum supplied cold energy for CCLE is 562.3 kJ/kg (O2), which is the sum of 197.9 kJ/kg (O2) in the intercooler of the compressor and 364.4 kJ/kg (O2) in the precooler and the carbon dioxide vessel. 4.1. Liquefaction system for CCDE Fig. 4 shows compression power, carbon dioxide vessel pressure and temperature, and liquid fraction in the carbon dioxide vessel as a function of fC in the case of the inlet carbon dioxide concentration X5,CO2=97%. Here, the minimum value of the compression power is 130 kJ/kg (O2) near fC=0.175. The compression power can be expressed as a product of mass ¯ow rate and enthalpy dierence. Enthalpies are functions of temperature, pressure, and inlet or exit carbon dioxide concentration. Inlet mass ¯ow rate m5 is an increasing function of fC. Since theoretical quantity of carbon dioxide (16CO2) should be lique®ed to maintain the constant combustion temperature, the liquefying fraction fL decreases and the outlet oxygen concentration x9 also reduces. The carbon dioxide vessel pressure is determined by the enthalpies of states 7 and 9 as well as the supplied cold energy to both the precooler and the carbon dioxide vessel. The temperature in the carbon dioxide vessel rises if the required cold energy is greater than the supplied cold energy of oxygen 360 kJ/kg (O2). The partial pressure of carbon dioxide increases monotonically because the partial pressure is a monotonic increasing function of temperature. On the other hand, the vessel pressure is a function of carbon dioxide partial pressure and mole fraction, i.e. PCV=Pcvcd/(1 ÿ X9). In Fig. 4, below optimum fC (corresponding to minimum compression power), since the decrease in oxygen mole fraction is signi®cantly greater than the increase in carbon dioxide partial pressure, the carbon dioxide vessel pressure
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1253
Fig. 4. Isentropic compressor work, pressure, temperature, outlet O2 mass fraction and liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle diesel engine (X5,CO2=97%).
tends to decrease with increasing fC. Above optimum fC, since the decrease in oxygen concentration in the outlet of the carbon dioxide vessel is very small, the vessel pressure mainly depends on the increase in the carbon dioxide partial pressure. Therefore, the minimum of compression power results from the existence of the minimum vessel pressure. For the case of X5,CO2=72%, compression power and related variables are shown in Fig. 5. Compression power has a minimum value of 320 kJ/kg (O2) near fC=0.225. The temperature and pressure in the carbon dioxide vessel and the carbon dioxide concentration in the outlet of the vessel show similar trends to those shown in Fig. 4, but the vessel pressure is shifted to the
1254
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
higher level and the change rates of all the related variables are more gradual than those shown in Fig. 4. 4.2. Liquefaction system for CCLE When CCLE is used, compression power, demanded cold energy, pressure and temperature in the carbon dioxide vessel, liquefaction fraction and outlet oxygen concentration in the exhaust gas liquefaction system are shown as a function of fC for the case of X5,CO2=97% and 72% in Fig. 6 and 7, respectively. First, we will concentrate on the case of X5,CO2=97%.
Fig. 5. Isentropic compressor work, pressure, temperature, outlet O2 mass fraction and liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle diesel engine (X5,CO2=72%).
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1255
Fig. 6. Isentropic compressor work, consumed cold energy, pressure, temperature, outlet O2 mass fraction and the liquefaction fraction of CO2 in the CO2 vessel as a function of fC for the liquefaction system of the closed cycle LNG engine (X5,CO2=97%).
1256
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 7. Isentropic compressor work, consumed cold energy, pressure, temperature, outlet O2 mass fraction and the liquefaction fraction of Co2 in the CO2 vessel as a function of fC for the liquefaction system of the closed ctycle LNG engine (X5,CO2=72%).
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1257
Compression power has minimum value of 75.7 kJ/kg (O2) near fC=0.15 and its slope at the right of fC=0.37 is steeper than that at the left. Inspection of the trend of temperature in the carbon dioxide vessel shows that for the constant temperature region, the supplied cold energy is greater than the demanded cold energy to the precooler and carbon dioxide vessel. It also shows that for the region of increasing temperature, the temperature in the carbon dioxide vessel should be increased to match the demanded cold energy with the maximum supplied cold energy. The changing point corresponds to fC=0.37. The vessel pressure decreases drastically at ®rst and then maintains nearly constant value, and ®nally increases in a trend of temperature variation. The ®rst emergence of drastically decreasing region mainly results from the drastic decrease in the outlet oxygen concentration of the carbon dioxide vessel. The next one can be explained by the fact that the outlet oxygen concentration is nearly constant and the carbon dioxide partial pressure is constant due to the constant temperature in the vessel. The ®nal one results from the fact that the carbon dioxide partial pressure increases due to increasing temperature in the vessel and the outlet oxygen concentration remains nearly constant. The compressor inlet temperature associated with compression power is shown in Fig. 8. Until fC=0.33 is reached from the minimum fC, the demanded cold energy to the intercooler is smaller than the supplied cold energy so that the inlet temperature of compressor is constant. Beyond fC=0.33, the inlet temperature of compressor should be increased to match the demanded cold energy with the maximum supplied cold energy. Therefore, we can ®nd that lower compressor power results from the lower pressure ratio due to low temperature in the carbon dioxide vessel and the low compressor inlet temperature due to the intercooling eect. In Fig. 7, for the case of X5,CO2=72%, the minimum compression power 159 kJ/kg (O2) occurs near fC=0.22. The trends of compressor power are divided into three regions. The ®rst region is up to fC=0.25, where the supplied cold energy for intercooling is enough to cool the exhaust gas so that the compressor inlet temperature is the constant value of ÿ538C as shown
Fig. 8. Compressor inlet temperature for the LNG engine as a function of fC.
1258
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
in Fig. 8. In this region, the compression power has nearly constant value of 159 kJ/kg (O2). The second region is from fC=0.25 to fC=0.37. In this region the supplied cold energy for intercooling is smaller than the demanded cold energy so that compressor inlet temperature increases, but the vessel pressure decreases so that compression power increases slightly. The third region starts from fC=0.37, where compression power increases more steeply due to the increase in temperature and pressure in the carbon dioxide vessel (resulting from the shortage of the cold energy for liquefaction of exhaust gas) and due to the increase in compressor inlet temperature (resulting from the shortage of the cold energy for intercooling). As for vessel pressure, the region where the vessel pressure decreases results from both the constant value of carbon dioxide partial pressure (corresponding to constant temperature in the vessel) and the decrease in the outlet oxygen concentration from the carbon dioxide vessel. Over fC=0.37, the pressure increases due to the increase of the temperature in the vessel. The compressor inlet temperature is shown in Fig. 8. In case of X5,CO2=97%, enough cold energy for intercooling is provided up top the higher fC than in case of X5,CO2=72%. Due to lower carbon dioxide vessel pressure in case of X5,CO2=97%, the outlet pressure of each stage is lower so that the cold energy for intercooling is lower than that of X5,CO2=72%. 4.3. Comparison between CCDE and CCLE Compression power with respect to fC for CCDE and CCLE are shown in Fig. 9. Assuming that the two engines have the same thermal eciency and power, we will compare compression power consumption between the two. Taking the heating value of LNG as 50,000 kJ/kg (LNG) [8] and that of diesel (cetane) as 44,000 kJ/kg (C16H34) [9], the ratio of the diesel fuel mass ¯ow rate to the LNG fuel mass ¯ow rate is 1.136. However, since the fuel consumption per unit supplied oxygen is Bf=0.2888 kg (C16H34)/kg (O2) for CCDE and Bf=0.2529 kg (LNG)/kg (O2) for CCLE, respectively, the ratio of oxygen consumption of CCDE to that of CCLE is 1.136 0.2529/0.288831. Hence, we can compare the compression power consumption of the two without further compensation.
Fig. 9. Compressor work as a function of fC.
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1259
Fig. 10. Mass ¯ow rate into the compressor as a function of fC.
From Fig. 9, it is observed that the compression power of CCLE (which uses the cold energy of oxygen to cool each stage of compressor to ÿ538C) amounts to 50% of compression power of CCDE (which uses seawater at 108C to cool each stage). Fig. 10 exhibits the mass ¯ow rate of the exhaust gas into the compressor per unit supplied oxygen. In order to liquefy the theoretical carbon dioxide for the same value of fC, higher mass ¯ow rate is needed for CCDE than for CCLE, and such is the case for X5,CO2=72% than for X5,CO2=97%. The vessel pressure with respect to fC is suggested in Fig. 11. It is observed that the carbon dioxide vessel pressure associated with the diesel engine is nearly twice the carbon dioxide vessel pressure associated with the LNG engine. The reason is that utilizing both the oxygen cold energy and the LNG cold energy simultaneously can reduce the carbon dioxide vessel pressure associated with the LNG engine.
Fig. 11. CO2 vessel pressure as a function of fC.
1260
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
Fig. 12. CO2 temperature in the CO2 vessel as a function of fC.
The temperature trends in the carbon dioxide vessel are show in Fig. 12. CCLE maintains lower temperature in the vessel with the supply of enough cold energy, so the temperature variation in the vessel is smaller than that for the case of CCDE. The portion of the exhaust gas compression power out of net engine power can be calculated according to the following steps. The eciency of the two engines is assumed as 25%. For the case of diesel engine, the lower heating value of the fuel is 44,000 kJ/kg (C16H34) so that the output per unit fuel is 11,000 kJ/kg (C16H34). Since the fuel consumption per unit supplied oxygen in CCDE is Bf=0.2888 kg (C16H34)/kg (O2), the output per unit supplied oxygen is 11,000 0.2888 = 3176.8 kJ/kg (O2). The compression power in Fig. 3 will be 150 kJ/kg (O2) when we choose a design point to be fC=0.2 in Fig. 3 (with consideration of the vessel pressure, its trends, and the minimum compression power). With the assumption of the isentropic compression eciency of 75%, actual compression power is 200 kJ/kg (O2). Therefore, the ratio for the actual compression power to the output is 200/3176.8 = 6.3%. For the case of CCLE, since the lower heating value of fuel is 50,000 kJ/kg (LNG), the output per unit LNG is 12500 kJ/kg (LNG). Since the fuel consumption per unit supplied oxygen in CCLE is Bf=0.2529 kg (LNG)/kg (O2), the output per unit supplied oxygen is 12,500 0.2529 = 3161 kJ/kg (O2). The compression power in Fig. 6 is about 80 kJ/kg (O2) when we choose a design point to be fC=0.2 in Fig. 6 (with consideration of the vessel pressure, its trends and the minimum compression power associated with constant temperature of the compressor inlet). With the assumption of isentropic compression eciency of 75%, actual compression power is 106.7 kJ/kg (O2). Therefore, the ratio of the actual compression power to the output of CCLE is 106.7/3161 = 3.4%. 5. Conclusions In order to treat the exhaust gas from underwater engines eectively, the liquefaction systems of exhaust gas for both CCDE and CCLE were designed and analyzed. Several
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
1261
remarks were drawn as follows. The ratio for compression power to the net engine power is 6.3% for CCDE and 3.4% for CCLE, which is much lower than that of the carbon dioxide absorbing system (with the exhaust gas dealing power consumption of 15%). In particular, CCLE has more advantages in reducing compression power and the carbon dioxide vessel pressure. In the case of CCDE, the carbon dioxide vessel pressure should be raised to liquefy the theoretical quantity of carbon dioxide due to the de®ciency of the cold energy supplied. This requires increasing compression power. More compression power is needed to lower carbon dioxide concentration of exhaust gas, because higher pressure is needed to liquefy the theoretical quantity of carbon dioxide. We can select a design point corresponding to the lower vessel pressure, its gradual change with respect to incoming fraction of the exhaust gas to the compressor (fC), and the lower compression power. The design point can be selected as fC=0.19 for the case of carbon dioxide mole fractions of 97% entering into the compressor, and fC=0.26 for 72%. In the case of CCLE, since the carbon dioxide vessel pressure maintains low values over a wide range of fC and each stage of the compressor also keeps lower temperatures such as ÿ538C with the help of sucient supplied cold energy, the compression power is only 50% that of diesel engines. The design point can be determined in such a way that a proper value of fC is chosen to satisfy lower vessel pressure with its smaller variation, lower temperature in compressor inlet, and lower compression power. The design point can be selected as 0.2 and 0.24 of fC for the case of the carbon dioxide mole fraction of 97% and 72% entering into the compressor, respectively In considering lower consumption power and lower vessel pressure, CCLE rather than CCDE has advantages, and so does the higher carbon dioxide concentration rather than the lower one in the system. Therefore, it is desirable to use CCLE and to maintain lower oxygen concentration in exhaust gas for reducing compression power and for lowering vessel pressure, but the actual engine should be designed by considering various factors, including overall eciency and power, availability and safety of fuel, design purpose and possibility of manufacturing, and economics etc. Acknowledgements The authors are very grateful to the ®nancial support provided by the Turbo and Power Machinery Research Center (TPMRC) at Seoul National University References [1] G. Sattler, Air-independent propulsion: the current state of art, Defence Systems International 94/95 (1994) 127±131. [2] R. Brenner, A closed cycle diesel system for submarines, Marine Defence June (1993) 162±164. [3] J.G. Hawley, Underwater vehicle power system technology, Marine Defence December (1993) 302±307. [4] A. Brighenti, G. Minelli, A.D. Rosa, The cryo-thermal engine underwater power system: performance, dynamics and control. in: Oceans '89 Marine Technology Society. Seattle. 1989, pp. 832±842.
1262
G.S. Lee, S.T. Ro / Applied Thermal Engineering 18 (1998) 1243±1262
[5] G. Acker Jr., C.E. Brett, S. Bell, K.C. Midki, Y.K. Song, Experience using LNG as a marine engine fuel, Marine Technology Society Journal 23 (1989) 33±39. [6] PROPATH Group, PROPATH: a program package for thermophysical properties. Version 8.1, 1993. [7] G.S. Lee, Y.S. Chang, M.S. Kim, S.T. Ro, Thermodynamic analysis of extraction processes for the utilization of LNG cold energy, Cryogenics 36 (1) (1996) 35±40. [8] H.J. Song, A study on power generation technology utilizing LNG cold energy. Korea Electric Power Research Institute, 1985. [9] J.B. Heywood, Internal Combustion Engine Fundamentals. McGraw-Hill, New York, 1989, p. 915.