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Performance evaluation of power generation system with fuel vapor turbine onboard hydrocarbon fueled scramjets
Energy 77 (2014) 732e741
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Performance evaluation of power generation system with fuel vapor turbine onboard hydrocarbon fueled scramjets Duo Zhang, Jiang Qin, Yu Feng, Fengzhi Ren, Wen Bao* School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2014 Received in revised form 15 September 2014 Accepted 18 September 2014 Available online 18 October 2014
In order to evaluate the performance of a new power generation system in which the generator is driven by the fuel vapor turbine, the pyrolysis characteristics and the compositions of pyrolyzed fuel mixture are experimentally studied. An algorithm is developed for the calculation of isentropic enthalpy drop of fuel vapor using a real gas model based on the SRK (SoaveeRedlicheKwong) equation of state. Fuel vapor is a variable mixture of fuel and its cracking products at different temperatures and pressures, making its physical properties variable. The working capacity of fuel vapor is dramatically enhanced in the pyrolysis reaction process. Benefiting from the high enough working capacity, the fuel vapor turbine still has enough power to drive a generator in addition to a fuel pump. The low-grade heat energy absorbed by fuel is transformed into high-grade mechanical/electrical energy by this system to achieve better energy utilization. Evaluation results indicate that this thermodynamic power generation system can be operated in a wide range of temperature to support the off-design operation of a scramjet. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Energy recovery Fuel turbine Power generation Isentropic enthalpy drop Scramjet
1. Introduction Energy recovery has been a hot issue in all kinds of engines in recent years. One primary approach is to establish a bottoming Rankine cycle for the recovery of waste heat of engine at low/medium temperatures. Yu et al. [1] indicated an improvement of 6.1% in thermal efficiency of a diesel by ORC (organic Rankine cycle). Gao et al. [2] developed a Rankine cycle with a reciprocating piston expander to increase the engine power by 12% on a turbocharged 80 kW/2590 r/min diesel engine. Boretti [3] considered applying the Rankine cycle on a hybrid car powered by gasoline engine and predicted a total increase of 8.2% in fuel conversion efficiency with the ORC system fitted on both the exhaust and the coolant. Carcasci et al. [4] proposed an ORC for waste heat recovery from gas turbines and pointed out that different working fluid should be used for different source temperature. Overall, there are plenty of studies on energy recovery from different engines at ground and they indicate encouraging prospect in energy conservation. For flight vehicles especially hypersonic aircrafts and missiles powered by scramjet, an extremely high temperature is encountered in the combustor [5], making energy recovery more necessary
* Corresponding author. No.92, West Da-Zhi Street, Harbin, Heilongjiang 150001, PR China. E-mail address: [email protected] (W. Bao). http://dx.doi.org/10.1016/j.energy.2014.09.046 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
to keep high efficiency of the engine. Meanwhile, a practical problem is that a large amount of power is desperately needed by the auxiliary systems for fuel feeding, environment control and radar. The flight ranges will be greatly limited by the capacity of onboard battery if there is no other onboard power generation system. It is therefore of great significance to build an energy recovery system with power generation for practical operation on hypersonic vehicles. Scramjets are usually regeneratively cooled by fuel for safe sustained-operation [6]. Energy recovery is achieved in the shape of heat recovery by fuel injection after cooling the engine. However, the heat recovered by fuel is not transformed into mechanical/ electrical energy. Based on regenerative cooling, Sforza [7] considered a semi-closed Rankine cycle for power generation using fuel as the working fluid. A dedicated turbine is used to extract power from the fluid to drive a generator. Although the generating capacity is huge, the mass penalty introduced by the semi-closed cycle is obvious and it is of little realistic meaning. Qin et al. [8] developed an open cooling cycle, which contained a turbine in the flowpath to transfer enthalpy from fuel to mechanical work. Bao et al. [9] extended the open cooling cycle to hydrocarbon fueled scramjet and pointed out that both increased heat sink and power output by the turbine are obtained by this recooling cycle. Although the recooling cycle is capable of power output, it is not designed and optimized for the purpose of power generation and it is still difficult for a short term application. Some attention has been paid
D. Zhang et al. / Energy 77 (2014) 732e741
Nomenclature a, b, a Cp Cv Cp,0 Cv,0 dh dp f k k0dec M Mw m mg ml p pc Ru S T Tc Tr
parameters in the SRK equation of state constant pressure specific heat capacity, J kg1 K1 constant volume specific heat capacity, J kg1 K1 constant pressure specific heat capacity for ideal gas, J kg1 K1 constant volume specific heat capacity for ideal gas, J kg1 K1 enthalpy drop of a discrete process, J kg1 pressure drop of a discrete process, Pa mole fraction of gas product mole fraction of liquid product mass fraction of n-decane in liquid product molecular weight, kg mol1 molecular weight of fluid mixture, kg mol1 total mass flow rate, kg s1 mass flow rate of gas product, kg s1 mass flow rate of liquid product, kg s1 pressure, Pa critical pressure, Pa universal gas constant, J mol1 K1 parameter function temperature, K critical temperature, K reduced temperature
to MHD (magneto hydrodynamics) power generation for scramjets [10]. However, its potential application is hypersonic flight with a Mach number higher than 10, where hydrogen will be utilized as the propellant to provide enough cooling for effective operation of the superconducting magnets. Another relevant topic is fuel feeding on scramjets. The fuel powered turbopump commonly used in a rocket engine has been considered for fuel feeding on a hydrogen fueled scramjet [11]. The concepts of fuel feeding cycles in liquid rocket, such as expander cycle, gas generator cycle, staged combustion cycle and coolant bleed cycle, have been developed to regeneratively cooled scramjet. Among these cycles, the expander cycle containing a fuel powered turbopump is relatively simple in structure, and it has the best performance in terms of specific impulse, and is called topping cycle in liquid rocket. A similar fuel feeding cycle in hydrocarbon fueled scramjet is also proposed in the SFSFC (Storable Fuel Scramjet Flowpath Concepts) Program, and it utilizes a hydrocarbon fuel powered turbopump for fuel feeding [12]. However, no more technical details are published further. The key point of turbopump feeding systems is energy conversion from the heated propellant to mechanical power by the turbine. Therefore, if a fuel powered turbopump is connected with a generator, it has the potential to be a simple and efficient onboard power generation system capable of fuel feeding on scramjet as shown in Fig. 1. Fuel is pumped into the cooling jacket of a scramjet to cool the engine walls. The fuel pressure in the cooling jacket is usually higher than its critical pressure to avoid film boiling, which causes the deterioration of heat transfer [13]. After absorbing the heat transferred from the combustor, the fuel temperature rises rapidly in the cooling jacket. When it is higher than its critical temperature, the fuel becomes supercritical. At the outlet of the cooling passage, the turbine is driven by supercritical fuel and the shaft power of the turbine is delivered to the pump and the generator. Fuel is then injected into the combustor after it powers the turbine. In view of energy recovery, the low-grade heat energy
V v vc w x z
g Dh Dp ε
h k r
733
volume flow rate of gas components, L s1 specific volume, m3 kg1 critical volume, cm3 mol1 specific power, J kg1 mole fraction of species fuel conversion rate specific heat ratio enthalpy drop, J kg1 pressure head of pump, Pa binary interaction coefficient work efficiency effective exponent for isentropic process density, kg m3
Subscripts dec n-decane f fluid final the final state gen generator i,j specific product number initial the initial state pump pump s isentropic process T isothermal process turb turbine
dissipated from the combustor is absorbed by the coolant and then transformed into high-grade mechanic/electric energy by this system. Both energy recovery and power generation are achieved by this system onboard scramjets. However, the regenerative cooling process of hydrocarbon fuels is much complex than that of hydrogen, which remains a pure substance in the whole cooling process. At a relatively high temperature, endothermic reactions take place and hydrocarbon fuels crack into small hydrocarbons (CH4, C2H4, C2H6, etc.) to offer extra chemical heat sink, which is urgently needed for scramjets [14]. The fuel temperature and pressure in the cooling passages will change during the acceleration or off-design operation of scramjets, and their variations have great influence on the chemical reactions in the cooling passages and the compositions of final products in the turbines [15]. Therefore, the working fluid powering the turbine is fuel vapor, a variable mixture of hydrocarbon fuel and its cracking products.
Fig. 1. Schematic diagram of onboard power generation with fuel vapor turbine.
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In this article, experimental determination of fuel vapor composition is carried out under different operating conditions. Then, the thermal properties of fuel vapor are calculated using the SRK (SoaveeRedlicheKwong) equation of state as a real gas. A general numerical method is used to calculate the isentropic enthalpy drop of the real gas to determine the working capacity of fuel vapor. Finally, the performance of the generating system is evaluated. 2. Experimental determination of fuel vapor composition The compositions of fuel vapor mixtures vary with both temperature and pressure [16]. The composition of fuel vapor at different temperatures and pressures is necessary to predict the working capacity of a turbine. Although the composition of practical hydrocarbon fuel is complex, its major components are straight chain alkanes, branched chain alkanes, cycloalkanes and aromatics. n-Decane is employed in this paper as the surrogate fuel. As shown in Fig. 2, a one-stage fuel heating and cracking system is developed to run the experiments. It consists of a fuel box, a reciprocating plunger pulsation-free pump, a flow meter, a flow tube reactor, a pressure regulator, a DC (direct current) heating power, a condenser and a sample system. The maximum operating pressure is 8 MPa, and the fuel can be heated up to 1000 K at the exit of the tube reactor, which is a thin-wall circular (3 mm o.d. 1 mm i.d. 1000 mm in length) high-temperature alloy tube. The tube is placed horizontally and heated by direct current from the DC power, which can provide a heating capability of more than 1 MW m2. A K-type shielded thermocouple is placed directly at the exit of the tube reactor to measure the final fuel temperature with an uncertainty of ±2 K. The test is started by purging the reactor tube with nitrogen to remove oxygen. The fuel pressure inside the tube reactor is regulated by the back pressure regulator to achieve the preset value. The pressure is measured by Rosemount 3051 transducer (uncertainty: ±0.075%). The mass flow rate of n-decane in the reactor is controlled using the reciprocating plunger pulsation-free pump and measured by a Micro Motion Elite CMF010 mass flow meter (uncertainty: ±0.1%), and the mass flow rate is kept constant at 1 g s1. A bypass duct is mounted at the exit of tube reactor to sample the cracked fuel. The bypass valve is manually opened when the fuel temperature and pressure are stable under the desired condition. And after being cooled down to room temperature, the cracked fuel flows into a liquid/gas separator. More detailed information about the experiment can be found in Ref. [17]. After flowing through the liquid/gas separator, the volume flow rate of gas product is measured using a gas rotameter, and then analyzed using a GC (gas chromatograph). The liquid products are
Fig. 2. Schematic diagram of one-stage fuel heating and cracking system.
collected for 60 s, weighted, and analyzed using a GCeMS (gas chromatographemass spectrometer). Fuel conversion rate can be given as shown below.
z ¼ 1 ml $k0dec m $100%
(1)
m ¼ mg þ ml
(2)
mg ¼ ðSMi fi Þ$V=22:4
(3)
k0dec ¼ Mdec $kdec
. X Mdec $kdec þ Mj $kj
(4)
The pyrolysis of n-decane is studied through experiments under three different supercritical pressures (3 MPa, 4 MPa and 5 MPa). The fuel conversion rates at different temperatures and pressures are shown in Fig. 3 and the marks on the lines represent the experimental results. The initial pyrolysis of fuel may take place in the liquid state. However, the process is slow. The main pyrolysis process begins at supercritical state with a temperature of approximately 770 K and the conversion rate of n-decane increases as the temperature rises. When the final fuel temperature reaches 940 K, the conversion rates of fuel are much higher than 50%, which means the fuel vapor is mainly composed of the cracked product species. The pyrolysis process is also influenced by the operating pressure in the tube reactor. When the flow rate remains constant, a higher pressure makes a greater density of the fluid and a slower fluid velocity extending the residence time. A longer residence time can raise the conversion rate of n-decane. The distribution of product species of n-decane at 5 MPa is shown in Fig. 4 and the values in the figure represent the mole fractions of the species in fuel vapor. Generally, the mole fractions of the products change greatly with temperature, and there is no regular pattern for all the product species. The pressure also has an effect on the distribution of product species of n-decane. However, its effect on the relative scale of the product mole fractions is not obvious. Thus the histograms of the experiment results at 3 MPa and 4 MPa are not shown here and the detailed information can be found in Ref. [17]. 3. Thermophysical properties of fuel vapor With the composition of fuel vapor obtained by experiment, the thermophysical properties can be calculated based on equation of state. Because of the existence of un-cracked n-decane and
Fig. 3. Conversion of n-decane vs. temperature and pressure.
D. Zhang et al. / Energy 77 (2014) 732e741
735
Fig. 4. Distribution of product species of n-decane at 5 MPa.
products with large molecular weights in fuel vapor, the compressibility factor can decrease down to 0.1 and cause one order of magnitude of error if using ideal gas law [18]. Thus, the SRK equation of state is used to describe the peVeT behavior of fuel vapor more realistically than equation of state of ideal gas over a broad range of thermophysical states. The SRK equation of state for a multi-component mixture can be given by
p¼
rRu T aa r2 ðMw brÞ Mw ðMw þ brÞ
(5)
For a mixture with determined composition at known temperature and pressure, its density can be derived using Eq. (5). In the parameters calculation of Mw, a, a and b, some basic properties of the relevant components are needed and they can be found in Ref. [19]. The detailed calculation process is shown in Appendix A [20]. The specific heat capacity and the specific heat ratio for a multi-component mixture can also be calculated based on the SRK equation of state with the basic thermodynamic relations as shown in Appendix B [20]. In order to evaluate the accuracy and applicability of the SRK equation of state, the thermodynamic properties such as density, constant-pressure specific heat and specific heat ratio have been calculated for n-decane and its main pyrolysis product separately over a range of operating pressures and temperatures relevant to fuel vapor turbine. For validation of the pure fluid, the reference data is taken from NIST (National Institute of Standards and Technology) REFPROP (Reference Fluid Thermodynamic and Transport Properties) [21]. In terms of the density profiles vs. temperature for different
component, Fig. 5 presents a comparison between the NIST data and the results obtained by the SRK equation of state at different pressures. In comparison with the NIST data, the SRK equation of state has generally good predicting accuracy for n-decane and other small hydrocarbons. The maximum predicting error for n-decane is 10% at the pressure of 5 MPa and the temperature of 750 K. Figs. 6 and 7 present comparisons of constant-pressure specific heat and specific heat ratio separately between the NIST data and the results obtained by the SRK equation of state. Similarly, good agreements are obtained for n-decane and small hydrocarbons during the presented temperature and pressure range. Therefore, the SRK equation of state is applicable for predicting the thermodynamic properties of ndecane and its pyrolysis product within the focused parameter space. The following is to predict the thermodynamic properties of pyrolyzed fuel vapor using the SRK equation of state. The fuel vapor is assumed as a multi-component mixture whose composition is determined by the experiment above. As shown in Fig. 8, the density of fuel vapor decreases rapidly as the temperature rises mainly because of the pyrolysis process which produces hydrocarbons with small molecular weights. The density is also increased obviously by a higher pressure of fuel vapor according to the equation of state. However, in the temperature range of rapid pyrolysis (860 Ke900 K), a higher pressure produces more hydrocarbons with small molecular weight to neutralize the increase in density caused by a higher pressure. Thus the density of fuel vapor varies greatly with the temperature and the pressure, and this will further influence other properties of fuel vapor. The variation of specific heat ratio of fuel vapor is shown in Fig. 9 and non-monotonic variations with temperature are observed. In the temperature range of mild pyrolysis (lower than 860 K), the main composition of the mixture is n-decane and its specific heat
Fig. 5. Validation of density for pure fluid calculated by the SRK equation of state.
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Fig. 6. Validation of constant-pressure specific heat for pure fluid calculated by the SRK equation of state.
Fig. 7. Validation of specific heat ratio for pure fluid calculated by the SRK equation of state.
ratio decreases when the temperature rises in this temperature range which is just over the critical temperature of n-decane. On the contrary, the main composition of the mixture is the cracking products with small molecular weight in the temperature range of rapid pyrolysis and the specific heat ratio of the mixture increases as the temperature rises. In addition, it is found that a higher pressure makes a higher value of specific heat ratio of fuel vapor. Generally, the occurrence of pyrolysis in hydrocarbon fuels makes the fuel vapor a more complex working fluid. The composition of fuel vapor changes from pure n-decane to a mixture of small hydrocarbons (CH4, C2H4, C2H6, etc.) when the temperature rises. So the thermophysical properties change greatly in different
states, and this will have an effect on the characteristics of isentropic enthalpy drop.
Fig. 8. Density of fuel vapor vs. temperature and pressure.
Fig. 9. Specific heat ratio of fuel vapor vs. temperature and pressure.
4. Calculation of isentropic enthalpy drop In the analysis of gas turbine, the working fluid is generally treated as ideal gas and the isentropic enthalpy drop can be easily calculated using thermodynamic relations. In a steam turbine, the isentropic enthalpy drop can be calculated using steam tables. However, in the case of fuel vapor turbine with a variable mixture of cracked hydrocarbons, a generalized method is needed to take the effect of real gas into account. To simplify the analysis the chemical
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reaction in the turbine is ignored because the residence time in the turbine is much shorter than that in the heating tube. Therefore, the composition of fuel vapor in the turbine is supposed to be the same as that at the exit of the heating tube. For an isentropic expansion, the effective exponent k can be expressed as
v vp k¼ p vv s
(6)
The thermodynamic equation denotes the relationship
g
vp vv
¼ T
vp vv s
(7)
So the effective exponent can be presented in the following form
gv vp k¼ p vv T
(8) Fig. 10. Tep chart for a discrete isentropic expansion process.
where ðvp=vvÞT can be calculated using the SRK equation of state through partial differentiation
vp Ru T aað2v þ bÞ ¼ þ 2 2 vv T ðv bÞ v2 þ bv
(9)
For a specific isentropic expansion, the following equation holds.
Z
dp dv þk ¼0 p v s
(10)
The isentropic enthalpy drop of an expansion process from the initial state to the final state can be expressed as Tfinal Z
Dhs ¼
Cp T; p dT þ
pfinal " Z pinitial
Tinitial
vv vT vT
# dp
vv vT
vp vp ¼ vT v vv T
(12)
In our work, it is assumed that the initial temperature Tin and pressure pin and the final pressure pout of an isentropic expansion are available. However, the final temperature can't be directly derived because of the variation of the effective exponent and the specific heat capacity with the temperature and the pressure of a mixture. A numerical method is used to accurately calculate the isentropic enthalpy drop for an expansion process. The basic thought is to divide the entire isentropic expansion process into several discrete processes. In each of them, the temperature and the pressure have little change so that the thermophysical properties and the effective exponents can be approximately treated as constants. The entire isentropic enthalpy drop is the numerical integration of all the discrete processes. For each discrete isentropic expansion process as shown in Fig. 10, the key is to calculate the final temperature T2 from the known values of initial temperature T1 and initial pressure p1 derived from the previous step of calculation and the step length of pressure dp. A numerical approximation method is used to calculate the final temperature T2. First, there must be a value of DT large enough to make the final temperature T2 between T1 and T1 DT although T2 is not known at this moment. Beginning with T1 and T1 DT as the initial values, a suitable numerical algorithm, such as
(13)
where p2 is equal to p1 dp and v2 can be calculated by the SRK equation of state in Eq. (5) at the state of (T2,p2). k is the average value of the effective exponent throughout the discrete process and it can be calculated as the arithmetic mean of k1 and k2. The isentropic enthalpy drop of the discrete process dhs can be derived using the following equation
dhs ¼ Cp ðT1 T2 Þ þ
p
p1 vk1 ¼ p2 vk2
(11)
p
where Dhs is the isentropic enthalpy drop and ðvv=vTÞp can be calculated by the cycle relationship
dichotomy, can be used to solve final temperature T2 at a high precision. Because of the tiny change of state in the discrete process, the effective exponent k and the specific heat capacity Cp could be treated as constants. And Eq. (10) can be written in the following form
vv vT vT
! dp
(14)
p
where Cp is the average value of the specific heat capacity, v is the average value of the specific volume and T is the average value of the temperature. They can be calculated as the arithmetic mean of values at the initial state (T1,P1) and the final state (T2,P2) of the discrete process. ðvv=vTÞp can be calculated at the average state ðT; PÞ of the discrete process. The enthalpy drop of the entire isentropic expansion can be derived using the following equation
Dhs ¼
X
dhs
(15)
The program block diagram for the calculation of Dhs is shown in Fig. 11. The effective exponents at the initial state of isentropic expansion for fuel vapor are calculated by Eq. (8) and shown in Fig. 12. The effective exponents of isentropic expansion of fuel vapor increase as the temperature and pressure rise. Obvious differences can be seen between the effective exponents of isentropic expansion shown in Fig. 12 and the specific heat ratios shown in Fig. 9. If fuel vapor is assumed to be ideal gas, the effective exponent becomes equal to the specific heat ratio according to Eq. (8) because ðvp=vvÞT equals to p/v for ideal gas. Then obvious errors may occur in the calculation of the final state of isentropic expansion and the isentropic enthalpy drop. The isentropic enthalpy drops of fuel vapor and n-decane at expansion ratio of 2 from different initial states are shown in Fig. 13. The curves of fuel vapor have two sections in general. In the temperature range of un-cracking (below 800 K), the isentropic
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D. Zhang et al. / Energy 77 (2014) 732e741
Fig. 11. Program block diagram of the calculation procedures of Dhs.
enthalpy drops are below 30 kJ kg1 from different initial temperature and pressure of the expansion. These values increase slightly as the temperature rises. In the temperature range of pyrolysis, the isentropic enthalpy drops increase rapidly as the temperature rises and reach the value of 100 kJ kg1 at 940 K. The change trend of the isentropic enthalpy drops of fuel vapor is obviously different from those of other ordinary working fluids. The
rapid increase is mainly caused by the cracking reactions, which produce more and more hydrocarbon gases with relatively smaller molecular weights. Compared with n-decane, these light hydrocarbon gases (CH4, C2H4, C2H6, etc.) have relatively higher effective exponents, which cause greater isentropic enthalpy drop. Compared with fuel vapor, the isentropic enthalpy drop of pure ndecane, which is assumed not to have any crack reaction, shows
Fig. 12. Effective exponents of fuel vapor vs. temperature and pressure.
Fig. 13. Isentropic enthalpy drop of fuel vapor and n-decane vs. initial temperature and pressure at expansion ratio of 2.
D. Zhang et al. / Energy 77 (2014) 732e741
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only slight increase during the whole temperature range as presented in line without marks. This indicates the significant effect of pyrolysis on the increase in the isentropic enthalpy drop of fuel vapor. It is worth noting that the initial pressure also has an important effect on the isentropic enthalpy drop through its influence on the thermophysical properties and the products of cracking reaction. As shown in Fig. 13, a higher initial pressure usually causes a higher isentropic enthalpy drop for a specific expansion ratio in the temperature range of pyrolysis. 5. Performance evaluation of power generation system with fuel vapor turbine In order to evaluate the performance of the power generation system as shown in Fig. 1, the work efficiencies of turbine, pump and generator are assumed and the specific power of them can be expressed as
wturb ¼ hturb $hs
(16)
Dp hpump $r
(17)
wgen ¼ hgen $ wturb þ wpump
(18)
wpump ¼
where the negative sign in Eq. (17) indicates that the pump is a power consumer while the turbine and the generator are power producers. hturb, hpump and hgen are assumed to be 0.6, 0.6 and 0.8 in the following calculations according to engineering experience [11]. Such assumptions of work efficiencies are commonly used in work related to cycle performance evaluation [9]. Compared with the high pressure in the cooling channels, the loss of pressure in a well-designed regenerative cooling channel is much smaller. Besides, the fuel box is usually pre-pressurized against cavitation in the pump. Thus, the value of the pressure at the inlet of the turbine can be assumed to be the pressure increase Dp by the pump in Eq. (17) approximately in cycle analysis. The temperature at the inlet of the pump is assumed to be 300 K and the density r is 730 kg m3. Pressure has little effect on the density of n-decane at this temperature because it is liquid. The power balance characteristics of the generation system at expansion ratio of 2 are illustrated by Fig. 14. It gives the specific work of the turbine, the pump and the generator at different temperature and pressure at the inlet of the turbine. The temperatures and pressures shown in this figure can be achieved at different flying conditions including freestream Mach number and fuel air ratio. Normally, a higher freestream Mach number brings more energy into the engine and makes the temperature of the coolant higher. Excluding the specific power consumed by the pump for fuel pressurization, the fuel vapor turbine still has adequately enough power to drive the generator for onboard power generation. The specific power generation capacity is less than 10 kJ kg1 in the temperature range of mild pyrolysis (below 850 K), and it increases to about 40 kJ kg1 when the pyrolysis is nearly finished. It is also noticed that this onboard power generation system with fuel vapor turbine has the potential to operate in a wide range of temperature from un-cracking region to complete pyrolysis region to support the off-design operation of the engine. If the cooling system of the engine is allowed to operate at a higher pressure, the fuel vapor turbine can be operated at a larger expansion ratio to produce a greater power generation capacity. The specific power generation capacity at an operating pressure of
Fig. 14. Specific power of fuel vapor turbine, pump and generator vs. inlet temperature and pressure of turbine at expansion ratio of 2.
5 MPa is illustrated by Fig. 15 for different expansion ratios of the turbine. When the expansion ratio increases from 2 to 5, the maximum specific power generation capacity increases from 40 kJ kg1 to 108 kJ kg1. Therefore, increasing the expansion ratio of the turbine is an effective way to improve the performance of the power generation system. However, the growth rate of the specific power generation capacity decreases as the expansion ratio increases. The expansion ratio needs to be balanced with the operating pressure and other problems for practical applications. Assuming that the heating value and the total heat sink of endothermic hydrocarbon fuel are about 44 MJ kg1 and 4 MJ kg1 accordingly and the combustion efficiency is about 90%, the regeneratively cooled engines can recover about 10% of the heat released by fuel compared with engines without regenerative cooling. When the fuel vapor turbine generating system is in application, a small part (about 3% when the expansion ratio of turbine is 5) of the recovered low-grade heat is transformed into high-grade electrical energy further. Although the energy extraction from cooling fuel has an adverse effect on the engine's thrust in view of energy conservation, the total effect is less than one percent of the heating value of fuel. Overall, it is beneficial to trade off such little engine thrust for onboard power generation as well as fuel feeding to achieve more reasonable energy utilization and better overall performance of the hypersonic vehicle.
Fig. 15. Specific generating power at 5 MPa vs. inlet temperature and expansion ratio of turbine.
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D. Zhang et al. / Energy 77 (2014) 732e741
h pffiffiffiffiffiffii2 ai ¼ 1 þ Si 1 Tri
6. Conclusions (1) Fuel vapor is a variable mixture of fuel molecules and their cracking products which are mainly gaseous hydrocarbons under different thermal conditions. The composition of fuel vapor varies greatly before and after the pyrolysis process. (2) Because of the complexity and variability of fuel vapor, it is necessary to treat it as a real gas for thermophysical property estimation. The SRK equation of state is applicable for the calculation of fuel vapor at high temperatures (above 750 K) and moderate pressures (below 5 MPa). (3) The working capacity of fuel vapor is different from other ordinary working fluids. The cracking reaction has a remarkable effect on the increase in the isentropic enthalpy drop of fuel vapor. (4) The fuel vapor turbine has adequately enough power to drive the generator for power generation in addition to fuel supply when the expansion ratio of turbine is 2. A power generation capacity with a magnitude of 100 kJ kg1 onboard a scramjet is available when the expansion ratio of turbine is 5 at an inlet temperature of 940 K. (5) This onboard power generation system can be operated in a wide range of fuel temperature from un-crack region to pyrolysis region to support the off-design operation of the engine. Based on heat recovery by regenerative cooling, this generating/feeding system transforms recovered low-grade heat into high-grade electrical/mechanical energy further to achieve more reasonable energy utilization and better overall performance of the hypersonic vehicle with negligible performance loss of the engine.
Tri ¼
T Tci
(A.7)
(A.8)
Si ¼ 0:48508 þ 1:5517ui 0:15613u2i
(A.9)
For hydrogen [18], Eq. (A.7) is modified as Eq. (A.10)
aH2 ¼ 1:202 expð0:30228Tr Þ
(A.10)
The basic property parameters including Tci, pci, ui, Mi for species i can be found in Ref. [19]. Appendix B
Cv ¼ Cv;0 þ
T v2 br ðaaÞln 1 þ bMw vT 2 Mw
(B.1)
, T vp 2 vp Cp ¼ Cv þ 2 vr T r vT r
(B.2)
g ¼ Cp Cv
(B.3)
where
Cv;0 ¼
N X
! xi Cv;0;i Mw
(B.4)
i¼1
Acknowledgments
Cv;0;i ¼ Cp;0;i Ru
This work was supported by National Natural Science Foundation of China (Program for Youth, No. 51106037), General Program (No. 51276047) and for Innovative Research Groups (No. 51121004).
N X
xi Mi
(A.1)
rRu 1 v r2 ðaaÞ ðMw brÞ Mw vT r ðMw þ brÞ
(B.6)
(B.7)
x i bi
(A.3)
pffiffiffiffiffiffiffiffiffi N X N X pffiffiffiffiffiffiffiffi v ai aj v ðaaÞ ¼ xi xj ai aj vT vT i¼1 j¼1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ai aj ai aj 1 εij
(A.4)
xi xj aij aij
i¼1 i¼1
b¼
r
¼
(A.2)
N X N X
N X
where Cv,0,i and Cp,0,i are the constant volume and constant pressure heat capacities of ideal gas for species i in J mol1 K1 and they can also be found in Ref. [19]. The derivatives v=vTðaaÞ and v2 =vT 2 ðaaÞ can be expressed below:
i¼1
aa ¼
vp vT
vp Mw Ru T aa rð2Mw þ brÞ ¼ vr T ðMw brÞ2 Mw ðMw þ brÞ2
Appendix A
Mw ¼
(B.5)
(B.8)
i¼1
aij aij ¼
where
The interaction parameters εij are determined experimentally and are known for very limited combinations of binary mixture. In situations involving mixtures of n-alkanes and n-alkenes, εij is usually close to zero. In the present study, therefore, all the values of them are assumed to be zero for simplification [20].
ai ¼ 0:42747
bi ¼ 0:08664
2 R2u Tci pci
(A.5)
Ru Tci pci
(A.6)
!1=2 !1=2 pffiffiffiffiffiffiffiffiffi v ai aj 1 ai vaj 1 aj vai þ ¼ 2 aj vT 2 ai vT vT
(B.9)
sffiffiffiffiffiffiffi!# " vai Si T ¼ pffiffiffiffiffiffiffiffiffi 1 þ Si 1 Tc;i vT TTc;i
(B.10)
pffiffiffiffiffiffiffiffiffi N X N X pffiffiffiffiffiffiffiffi v2 ai aj v2 ðaaÞ ¼ xi xj ai aj 2 vT vT 2 i¼1 j¼1
(B.11)
where
D. Zhang et al. / Energy 77 (2014) 732e741
pffiffiffiffiffiffiffiffiffi v2 ai aj vT 2
1 1 ¼ 2 ai aj
!1=2
vai vaj 1 ai vT vT 4 a3j
!1=2
vaj vT
2
!1=2 !1=2 v2 aj 1 aj vai 2 1 ai þ 4 a3i 2 aj vT vT 2 1=2 2 1 aj v ai þ 2 ai vT 2 sffiffiffiffiffiffiffi!# " v2 ai 1 S2i 1 Si T q ffiffiffiffiffiffiffiffiffiffiffiffi ¼ þ 1 1 þ S i 2 TTc;i 2 T 3 T Tc;i vT 2 c;i
(B.12)
(B.13)
For hydrogen, the derivatives are expressed as
vaH2 1 ¼ aH2 0:30228 Tc;i vT v2 aH2 1 ¼ aH2 0:30228 Tc;i vT
! (B.14)
!2 (B.15)
References [1] Yu G, Shu G, Tian H, Wei H, Liu L. Simulation and thermodynamic analysis of a bottoming organic Rankine cycle (ORC) of diesel engine (DE). Energy 2013;51: 281e90. [2] Gao W, Zhai J, Li G, Bian Q, Feng L. Performance evaluation and experiment system for waste heat recovery of diesel engine. Energy 2013;55:226e35. [3] Boretti A. Recovery of exhaust and coolant heat with R245fa organic Rankine cycles in a hybrid passenger car with a naturally aspirated gasoline engine. Appl Therm Eng 2012;36:73e7.
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[4] Carcasci C, Ferraro R, Miliotti E. Thermodynamic analysis of an organic Rankine cycle for waste heat recovery from gas turbines. Energy 2014;65: 91e100. [5] Yang Q, Chang J, Bao W. Thermodynamic analysis on specific thrust of the hydrocarbon fueled scramjet. Energy 2014;76:552e8. http://dx.doi.org/10. 1016/j.energy.2014.08.052. [6] Huang H, Spadaccini L, Sobel D. Fuel-cooled thermal management for advanced aeroengines. J Eng Gas Turb Power Trans ASME 2004;126:284e93. [7] Sforza P. Electric power generation onboard hypersonic aircraft. 2009. AIAA 2009-5119. [8] Qin J, Bao W, Zhou W, Yu D. Performance cycle analysis of an open cooling cycle for a scramjet. J Aerosp Eng 2009;223:599e607. [9] Bao W, Qin J, Zhou W, Zhang D, Yu D. Power generation and heat sink improvement characteristics of recooling cycle for thermal cracked hydrocarbon fueled scramjet. Sci China Technol Sci 2011;54:955e63. [10] Riggins D. Analysis of the magnetohydrodynamic energy bypass engine for high-speed airbreathing propulsion. J Propul Power 2004;20:779e92. [11] Kanda T, Masuya G, Wakamatsu Y. Propellant feed system of a regeneratively cooled scramjet. J Propul Power 1991;7:299e301. [12] Chen F, Tam W, Shimp N, Norris R. An innovative thermal management system for a Mach 4 to Mach 8 hypersonic scramjet engine. 1998. AIAA 19983734. [13] Qin J, Bao W, Zhou W, Yu D. Flow and heat transfer characteristics in fuel cooling channels of a recooling cycle. Int J Hydrogen Energy 2010;35: 10589e98. [14] Bao W, Zhang S, Qin J, Zhou W, Xie K. Numerical analysis of flowing cracked hydrocarbon fuel inside cooling channels in view of thermal management. Energy 2014;67:149e61. [15] Qin J, Zhang S, Bao W, Zhou W, Yu D. Thermal management method of fuel in advanced aeroengines. Energy 2012;49:459e68. [16] Ward T, Ervin J, Zabarnick S, Shafer L. Pressure effects on flowing mildlycracked n-decane. J Propul Power 2005;21:344e55. [17] Zhou W, Jia Z, Qin J, Bao W, Yu D. Experimental study on effect of pressure on heat sink of n-decane. Chem Eng J 2014;243:127e36. [18] Gascoin N, Gillard P. Dynamic study of coupled heavy hydrocarbon pyrolysis and combustion. Combust Sci Technol 2012;184:2136e53. [19] Poling B, Prausnitz J, O'Connell J. The properties of gases and liquids. 5th ed. New York, USA: McGraw-Hill; 2004. [20] Meng H, Yang V. A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme. J Comput Phys 2003;189:277e304. [21] REFPROP version 9.0, NIST standard reference database 23. America: The U.S. Secretary of Commerce; 2010.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Performance evaluation of power generation system with fuel vapor turbine onboard hydrocarbon fueled scramjets Duo Zhang, Jiang Qin, Yu Feng, Fengzhi Ren, Wen Bao* School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 February 2014 Received in revised form 15 September 2014 Accepted 18 September 2014 Available online 18 October 2014
In order to evaluate the performance of a new power generation system in which the generator is driven by the fuel vapor turbine, the pyrolysis characteristics and the compositions of pyrolyzed fuel mixture are experimentally studied. An algorithm is developed for the calculation of isentropic enthalpy drop of fuel vapor using a real gas model based on the SRK (SoaveeRedlicheKwong) equation of state. Fuel vapor is a variable mixture of fuel and its cracking products at different temperatures and pressures, making its physical properties variable. The working capacity of fuel vapor is dramatically enhanced in the pyrolysis reaction process. Benefiting from the high enough working capacity, the fuel vapor turbine still has enough power to drive a generator in addition to a fuel pump. The low-grade heat energy absorbed by fuel is transformed into high-grade mechanical/electrical energy by this system to achieve better energy utilization. Evaluation results indicate that this thermodynamic power generation system can be operated in a wide range of temperature to support the off-design operation of a scramjet. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Energy recovery Fuel turbine Power generation Isentropic enthalpy drop Scramjet
1. Introduction Energy recovery has been a hot issue in all kinds of engines in recent years. One primary approach is to establish a bottoming Rankine cycle for the recovery of waste heat of engine at low/medium temperatures. Yu et al. [1] indicated an improvement of 6.1% in thermal efficiency of a diesel by ORC (organic Rankine cycle). Gao et al. [2] developed a Rankine cycle with a reciprocating piston expander to increase the engine power by 12% on a turbocharged 80 kW/2590 r/min diesel engine. Boretti [3] considered applying the Rankine cycle on a hybrid car powered by gasoline engine and predicted a total increase of 8.2% in fuel conversion efficiency with the ORC system fitted on both the exhaust and the coolant. Carcasci et al. [4] proposed an ORC for waste heat recovery from gas turbines and pointed out that different working fluid should be used for different source temperature. Overall, there are plenty of studies on energy recovery from different engines at ground and they indicate encouraging prospect in energy conservation. For flight vehicles especially hypersonic aircrafts and missiles powered by scramjet, an extremely high temperature is encountered in the combustor [5], making energy recovery more necessary
* Corresponding author. No.92, West Da-Zhi Street, Harbin, Heilongjiang 150001, PR China. E-mail address: [email protected] (W. Bao). http://dx.doi.org/10.1016/j.energy.2014.09.046 0360-5442/© 2014 Elsevier Ltd. All rights reserved.
to keep high efficiency of the engine. Meanwhile, a practical problem is that a large amount of power is desperately needed by the auxiliary systems for fuel feeding, environment control and radar. The flight ranges will be greatly limited by the capacity of onboard battery if there is no other onboard power generation system. It is therefore of great significance to build an energy recovery system with power generation for practical operation on hypersonic vehicles. Scramjets are usually regeneratively cooled by fuel for safe sustained-operation [6]. Energy recovery is achieved in the shape of heat recovery by fuel injection after cooling the engine. However, the heat recovered by fuel is not transformed into mechanical/ electrical energy. Based on regenerative cooling, Sforza [7] considered a semi-closed Rankine cycle for power generation using fuel as the working fluid. A dedicated turbine is used to extract power from the fluid to drive a generator. Although the generating capacity is huge, the mass penalty introduced by the semi-closed cycle is obvious and it is of little realistic meaning. Qin et al. [8] developed an open cooling cycle, which contained a turbine in the flowpath to transfer enthalpy from fuel to mechanical work. Bao et al. [9] extended the open cooling cycle to hydrocarbon fueled scramjet and pointed out that both increased heat sink and power output by the turbine are obtained by this recooling cycle. Although the recooling cycle is capable of power output, it is not designed and optimized for the purpose of power generation and it is still difficult for a short term application. Some attention has been paid
D. Zhang et al. / Energy 77 (2014) 732e741
Nomenclature a, b, a Cp Cv Cp,0 Cv,0 dh dp f k k0dec M Mw m mg ml p pc Ru S T Tc Tr
parameters in the SRK equation of state constant pressure specific heat capacity, J kg1 K1 constant volume specific heat capacity, J kg1 K1 constant pressure specific heat capacity for ideal gas, J kg1 K1 constant volume specific heat capacity for ideal gas, J kg1 K1 enthalpy drop of a discrete process, J kg1 pressure drop of a discrete process, Pa mole fraction of gas product mole fraction of liquid product mass fraction of n-decane in liquid product molecular weight, kg mol1 molecular weight of fluid mixture, kg mol1 total mass flow rate, kg s1 mass flow rate of gas product, kg s1 mass flow rate of liquid product, kg s1 pressure, Pa critical pressure, Pa universal gas constant, J mol1 K1 parameter function temperature, K critical temperature, K reduced temperature
to MHD (magneto hydrodynamics) power generation for scramjets [10]. However, its potential application is hypersonic flight with a Mach number higher than 10, where hydrogen will be utilized as the propellant to provide enough cooling for effective operation of the superconducting magnets. Another relevant topic is fuel feeding on scramjets. The fuel powered turbopump commonly used in a rocket engine has been considered for fuel feeding on a hydrogen fueled scramjet [11]. The concepts of fuel feeding cycles in liquid rocket, such as expander cycle, gas generator cycle, staged combustion cycle and coolant bleed cycle, have been developed to regeneratively cooled scramjet. Among these cycles, the expander cycle containing a fuel powered turbopump is relatively simple in structure, and it has the best performance in terms of specific impulse, and is called topping cycle in liquid rocket. A similar fuel feeding cycle in hydrocarbon fueled scramjet is also proposed in the SFSFC (Storable Fuel Scramjet Flowpath Concepts) Program, and it utilizes a hydrocarbon fuel powered turbopump for fuel feeding [12]. However, no more technical details are published further. The key point of turbopump feeding systems is energy conversion from the heated propellant to mechanical power by the turbine. Therefore, if a fuel powered turbopump is connected with a generator, it has the potential to be a simple and efficient onboard power generation system capable of fuel feeding on scramjet as shown in Fig. 1. Fuel is pumped into the cooling jacket of a scramjet to cool the engine walls. The fuel pressure in the cooling jacket is usually higher than its critical pressure to avoid film boiling, which causes the deterioration of heat transfer [13]. After absorbing the heat transferred from the combustor, the fuel temperature rises rapidly in the cooling jacket. When it is higher than its critical temperature, the fuel becomes supercritical. At the outlet of the cooling passage, the turbine is driven by supercritical fuel and the shaft power of the turbine is delivered to the pump and the generator. Fuel is then injected into the combustor after it powers the turbine. In view of energy recovery, the low-grade heat energy
V v vc w x z
g Dh Dp ε
h k r
733
volume flow rate of gas components, L s1 specific volume, m3 kg1 critical volume, cm3 mol1 specific power, J kg1 mole fraction of species fuel conversion rate specific heat ratio enthalpy drop, J kg1 pressure head of pump, Pa binary interaction coefficient work efficiency effective exponent for isentropic process density, kg m3
Subscripts dec n-decane f fluid final the final state gen generator i,j specific product number initial the initial state pump pump s isentropic process T isothermal process turb turbine
dissipated from the combustor is absorbed by the coolant and then transformed into high-grade mechanic/electric energy by this system. Both energy recovery and power generation are achieved by this system onboard scramjets. However, the regenerative cooling process of hydrocarbon fuels is much complex than that of hydrogen, which remains a pure substance in the whole cooling process. At a relatively high temperature, endothermic reactions take place and hydrocarbon fuels crack into small hydrocarbons (CH4, C2H4, C2H6, etc.) to offer extra chemical heat sink, which is urgently needed for scramjets [14]. The fuel temperature and pressure in the cooling passages will change during the acceleration or off-design operation of scramjets, and their variations have great influence on the chemical reactions in the cooling passages and the compositions of final products in the turbines [15]. Therefore, the working fluid powering the turbine is fuel vapor, a variable mixture of hydrocarbon fuel and its cracking products.
Fig. 1. Schematic diagram of onboard power generation with fuel vapor turbine.
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In this article, experimental determination of fuel vapor composition is carried out under different operating conditions. Then, the thermal properties of fuel vapor are calculated using the SRK (SoaveeRedlicheKwong) equation of state as a real gas. A general numerical method is used to calculate the isentropic enthalpy drop of the real gas to determine the working capacity of fuel vapor. Finally, the performance of the generating system is evaluated. 2. Experimental determination of fuel vapor composition The compositions of fuel vapor mixtures vary with both temperature and pressure [16]. The composition of fuel vapor at different temperatures and pressures is necessary to predict the working capacity of a turbine. Although the composition of practical hydrocarbon fuel is complex, its major components are straight chain alkanes, branched chain alkanes, cycloalkanes and aromatics. n-Decane is employed in this paper as the surrogate fuel. As shown in Fig. 2, a one-stage fuel heating and cracking system is developed to run the experiments. It consists of a fuel box, a reciprocating plunger pulsation-free pump, a flow meter, a flow tube reactor, a pressure regulator, a DC (direct current) heating power, a condenser and a sample system. The maximum operating pressure is 8 MPa, and the fuel can be heated up to 1000 K at the exit of the tube reactor, which is a thin-wall circular (3 mm o.d. 1 mm i.d. 1000 mm in length) high-temperature alloy tube. The tube is placed horizontally and heated by direct current from the DC power, which can provide a heating capability of more than 1 MW m2. A K-type shielded thermocouple is placed directly at the exit of the tube reactor to measure the final fuel temperature with an uncertainty of ±2 K. The test is started by purging the reactor tube with nitrogen to remove oxygen. The fuel pressure inside the tube reactor is regulated by the back pressure regulator to achieve the preset value. The pressure is measured by Rosemount 3051 transducer (uncertainty: ±0.075%). The mass flow rate of n-decane in the reactor is controlled using the reciprocating plunger pulsation-free pump and measured by a Micro Motion Elite CMF010 mass flow meter (uncertainty: ±0.1%), and the mass flow rate is kept constant at 1 g s1. A bypass duct is mounted at the exit of tube reactor to sample the cracked fuel. The bypass valve is manually opened when the fuel temperature and pressure are stable under the desired condition. And after being cooled down to room temperature, the cracked fuel flows into a liquid/gas separator. More detailed information about the experiment can be found in Ref. [17]. After flowing through the liquid/gas separator, the volume flow rate of gas product is measured using a gas rotameter, and then analyzed using a GC (gas chromatograph). The liquid products are
Fig. 2. Schematic diagram of one-stage fuel heating and cracking system.
collected for 60 s, weighted, and analyzed using a GCeMS (gas chromatographemass spectrometer). Fuel conversion rate can be given as shown below.
z ¼ 1 ml $k0dec m $100%
(1)
m ¼ mg þ ml
(2)
mg ¼ ðSMi fi Þ$V=22:4
(3)
k0dec ¼ Mdec $kdec
. X Mdec $kdec þ Mj $kj
(4)
The pyrolysis of n-decane is studied through experiments under three different supercritical pressures (3 MPa, 4 MPa and 5 MPa). The fuel conversion rates at different temperatures and pressures are shown in Fig. 3 and the marks on the lines represent the experimental results. The initial pyrolysis of fuel may take place in the liquid state. However, the process is slow. The main pyrolysis process begins at supercritical state with a temperature of approximately 770 K and the conversion rate of n-decane increases as the temperature rises. When the final fuel temperature reaches 940 K, the conversion rates of fuel are much higher than 50%, which means the fuel vapor is mainly composed of the cracked product species. The pyrolysis process is also influenced by the operating pressure in the tube reactor. When the flow rate remains constant, a higher pressure makes a greater density of the fluid and a slower fluid velocity extending the residence time. A longer residence time can raise the conversion rate of n-decane. The distribution of product species of n-decane at 5 MPa is shown in Fig. 4 and the values in the figure represent the mole fractions of the species in fuel vapor. Generally, the mole fractions of the products change greatly with temperature, and there is no regular pattern for all the product species. The pressure also has an effect on the distribution of product species of n-decane. However, its effect on the relative scale of the product mole fractions is not obvious. Thus the histograms of the experiment results at 3 MPa and 4 MPa are not shown here and the detailed information can be found in Ref. [17]. 3. Thermophysical properties of fuel vapor With the composition of fuel vapor obtained by experiment, the thermophysical properties can be calculated based on equation of state. Because of the existence of un-cracked n-decane and
Fig. 3. Conversion of n-decane vs. temperature and pressure.
D. Zhang et al. / Energy 77 (2014) 732e741
735
Fig. 4. Distribution of product species of n-decane at 5 MPa.
products with large molecular weights in fuel vapor, the compressibility factor can decrease down to 0.1 and cause one order of magnitude of error if using ideal gas law [18]. Thus, the SRK equation of state is used to describe the peVeT behavior of fuel vapor more realistically than equation of state of ideal gas over a broad range of thermophysical states. The SRK equation of state for a multi-component mixture can be given by
p¼
rRu T aa r2 ðMw brÞ Mw ðMw þ brÞ
(5)
For a mixture with determined composition at known temperature and pressure, its density can be derived using Eq. (5). In the parameters calculation of Mw, a, a and b, some basic properties of the relevant components are needed and they can be found in Ref. [19]. The detailed calculation process is shown in Appendix A [20]. The specific heat capacity and the specific heat ratio for a multi-component mixture can also be calculated based on the SRK equation of state with the basic thermodynamic relations as shown in Appendix B [20]. In order to evaluate the accuracy and applicability of the SRK equation of state, the thermodynamic properties such as density, constant-pressure specific heat and specific heat ratio have been calculated for n-decane and its main pyrolysis product separately over a range of operating pressures and temperatures relevant to fuel vapor turbine. For validation of the pure fluid, the reference data is taken from NIST (National Institute of Standards and Technology) REFPROP (Reference Fluid Thermodynamic and Transport Properties) [21]. In terms of the density profiles vs. temperature for different
component, Fig. 5 presents a comparison between the NIST data and the results obtained by the SRK equation of state at different pressures. In comparison with the NIST data, the SRK equation of state has generally good predicting accuracy for n-decane and other small hydrocarbons. The maximum predicting error for n-decane is 10% at the pressure of 5 MPa and the temperature of 750 K. Figs. 6 and 7 present comparisons of constant-pressure specific heat and specific heat ratio separately between the NIST data and the results obtained by the SRK equation of state. Similarly, good agreements are obtained for n-decane and small hydrocarbons during the presented temperature and pressure range. Therefore, the SRK equation of state is applicable for predicting the thermodynamic properties of ndecane and its pyrolysis product within the focused parameter space. The following is to predict the thermodynamic properties of pyrolyzed fuel vapor using the SRK equation of state. The fuel vapor is assumed as a multi-component mixture whose composition is determined by the experiment above. As shown in Fig. 8, the density of fuel vapor decreases rapidly as the temperature rises mainly because of the pyrolysis process which produces hydrocarbons with small molecular weights. The density is also increased obviously by a higher pressure of fuel vapor according to the equation of state. However, in the temperature range of rapid pyrolysis (860 Ke900 K), a higher pressure produces more hydrocarbons with small molecular weight to neutralize the increase in density caused by a higher pressure. Thus the density of fuel vapor varies greatly with the temperature and the pressure, and this will further influence other properties of fuel vapor. The variation of specific heat ratio of fuel vapor is shown in Fig. 9 and non-monotonic variations with temperature are observed. In the temperature range of mild pyrolysis (lower than 860 K), the main composition of the mixture is n-decane and its specific heat
Fig. 5. Validation of density for pure fluid calculated by the SRK equation of state.
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D. Zhang et al. / Energy 77 (2014) 732e741
Fig. 6. Validation of constant-pressure specific heat for pure fluid calculated by the SRK equation of state.
Fig. 7. Validation of specific heat ratio for pure fluid calculated by the SRK equation of state.
ratio decreases when the temperature rises in this temperature range which is just over the critical temperature of n-decane. On the contrary, the main composition of the mixture is the cracking products with small molecular weight in the temperature range of rapid pyrolysis and the specific heat ratio of the mixture increases as the temperature rises. In addition, it is found that a higher pressure makes a higher value of specific heat ratio of fuel vapor. Generally, the occurrence of pyrolysis in hydrocarbon fuels makes the fuel vapor a more complex working fluid. The composition of fuel vapor changes from pure n-decane to a mixture of small hydrocarbons (CH4, C2H4, C2H6, etc.) when the temperature rises. So the thermophysical properties change greatly in different
states, and this will have an effect on the characteristics of isentropic enthalpy drop.
Fig. 8. Density of fuel vapor vs. temperature and pressure.
Fig. 9. Specific heat ratio of fuel vapor vs. temperature and pressure.
4. Calculation of isentropic enthalpy drop In the analysis of gas turbine, the working fluid is generally treated as ideal gas and the isentropic enthalpy drop can be easily calculated using thermodynamic relations. In a steam turbine, the isentropic enthalpy drop can be calculated using steam tables. However, in the case of fuel vapor turbine with a variable mixture of cracked hydrocarbons, a generalized method is needed to take the effect of real gas into account. To simplify the analysis the chemical
D. Zhang et al. / Energy 77 (2014) 732e741
737
reaction in the turbine is ignored because the residence time in the turbine is much shorter than that in the heating tube. Therefore, the composition of fuel vapor in the turbine is supposed to be the same as that at the exit of the heating tube. For an isentropic expansion, the effective exponent k can be expressed as
v vp k¼ p vv s
(6)
The thermodynamic equation denotes the relationship
g
vp vv
¼ T
vp vv s
(7)
So the effective exponent can be presented in the following form
gv vp k¼ p vv T
(8) Fig. 10. Tep chart for a discrete isentropic expansion process.
where ðvp=vvÞT can be calculated using the SRK equation of state through partial differentiation
vp Ru T aað2v þ bÞ ¼ þ 2 2 vv T ðv bÞ v2 þ bv
(9)
For a specific isentropic expansion, the following equation holds.
Z
dp dv þk ¼0 p v s
(10)
The isentropic enthalpy drop of an expansion process from the initial state to the final state can be expressed as Tfinal Z
Dhs ¼
Cp T; p dT þ
pfinal " Z pinitial
Tinitial
vv vT vT
# dp
vv vT
vp vp ¼ vT v vv T
(12)
In our work, it is assumed that the initial temperature Tin and pressure pin and the final pressure pout of an isentropic expansion are available. However, the final temperature can't be directly derived because of the variation of the effective exponent and the specific heat capacity with the temperature and the pressure of a mixture. A numerical method is used to accurately calculate the isentropic enthalpy drop for an expansion process. The basic thought is to divide the entire isentropic expansion process into several discrete processes. In each of them, the temperature and the pressure have little change so that the thermophysical properties and the effective exponents can be approximately treated as constants. The entire isentropic enthalpy drop is the numerical integration of all the discrete processes. For each discrete isentropic expansion process as shown in Fig. 10, the key is to calculate the final temperature T2 from the known values of initial temperature T1 and initial pressure p1 derived from the previous step of calculation and the step length of pressure dp. A numerical approximation method is used to calculate the final temperature T2. First, there must be a value of DT large enough to make the final temperature T2 between T1 and T1 DT although T2 is not known at this moment. Beginning with T1 and T1 DT as the initial values, a suitable numerical algorithm, such as
(13)
where p2 is equal to p1 dp and v2 can be calculated by the SRK equation of state in Eq. (5) at the state of (T2,p2). k is the average value of the effective exponent throughout the discrete process and it can be calculated as the arithmetic mean of k1 and k2. The isentropic enthalpy drop of the discrete process dhs can be derived using the following equation
dhs ¼ Cp ðT1 T2 Þ þ
p
p1 vk1 ¼ p2 vk2
(11)
p
where Dhs is the isentropic enthalpy drop and ðvv=vTÞp can be calculated by the cycle relationship
dichotomy, can be used to solve final temperature T2 at a high precision. Because of the tiny change of state in the discrete process, the effective exponent k and the specific heat capacity Cp could be treated as constants. And Eq. (10) can be written in the following form
vv vT vT
! dp
(14)
p
where Cp is the average value of the specific heat capacity, v is the average value of the specific volume and T is the average value of the temperature. They can be calculated as the arithmetic mean of values at the initial state (T1,P1) and the final state (T2,P2) of the discrete process. ðvv=vTÞp can be calculated at the average state ðT; PÞ of the discrete process. The enthalpy drop of the entire isentropic expansion can be derived using the following equation
Dhs ¼
X
dhs
(15)
The program block diagram for the calculation of Dhs is shown in Fig. 11. The effective exponents at the initial state of isentropic expansion for fuel vapor are calculated by Eq. (8) and shown in Fig. 12. The effective exponents of isentropic expansion of fuel vapor increase as the temperature and pressure rise. Obvious differences can be seen between the effective exponents of isentropic expansion shown in Fig. 12 and the specific heat ratios shown in Fig. 9. If fuel vapor is assumed to be ideal gas, the effective exponent becomes equal to the specific heat ratio according to Eq. (8) because ðvp=vvÞT equals to p/v for ideal gas. Then obvious errors may occur in the calculation of the final state of isentropic expansion and the isentropic enthalpy drop. The isentropic enthalpy drops of fuel vapor and n-decane at expansion ratio of 2 from different initial states are shown in Fig. 13. The curves of fuel vapor have two sections in general. In the temperature range of un-cracking (below 800 K), the isentropic
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D. Zhang et al. / Energy 77 (2014) 732e741
Fig. 11. Program block diagram of the calculation procedures of Dhs.
enthalpy drops are below 30 kJ kg1 from different initial temperature and pressure of the expansion. These values increase slightly as the temperature rises. In the temperature range of pyrolysis, the isentropic enthalpy drops increase rapidly as the temperature rises and reach the value of 100 kJ kg1 at 940 K. The change trend of the isentropic enthalpy drops of fuel vapor is obviously different from those of other ordinary working fluids. The
rapid increase is mainly caused by the cracking reactions, which produce more and more hydrocarbon gases with relatively smaller molecular weights. Compared with n-decane, these light hydrocarbon gases (CH4, C2H4, C2H6, etc.) have relatively higher effective exponents, which cause greater isentropic enthalpy drop. Compared with fuel vapor, the isentropic enthalpy drop of pure ndecane, which is assumed not to have any crack reaction, shows
Fig. 12. Effective exponents of fuel vapor vs. temperature and pressure.
Fig. 13. Isentropic enthalpy drop of fuel vapor and n-decane vs. initial temperature and pressure at expansion ratio of 2.
D. Zhang et al. / Energy 77 (2014) 732e741
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only slight increase during the whole temperature range as presented in line without marks. This indicates the significant effect of pyrolysis on the increase in the isentropic enthalpy drop of fuel vapor. It is worth noting that the initial pressure also has an important effect on the isentropic enthalpy drop through its influence on the thermophysical properties and the products of cracking reaction. As shown in Fig. 13, a higher initial pressure usually causes a higher isentropic enthalpy drop for a specific expansion ratio in the temperature range of pyrolysis. 5. Performance evaluation of power generation system with fuel vapor turbine In order to evaluate the performance of the power generation system as shown in Fig. 1, the work efficiencies of turbine, pump and generator are assumed and the specific power of them can be expressed as
wturb ¼ hturb $hs
(16)
Dp hpump $r
(17)
wgen ¼ hgen $ wturb þ wpump
(18)
wpump ¼
where the negative sign in Eq. (17) indicates that the pump is a power consumer while the turbine and the generator are power producers. hturb, hpump and hgen are assumed to be 0.6, 0.6 and 0.8 in the following calculations according to engineering experience [11]. Such assumptions of work efficiencies are commonly used in work related to cycle performance evaluation [9]. Compared with the high pressure in the cooling channels, the loss of pressure in a well-designed regenerative cooling channel is much smaller. Besides, the fuel box is usually pre-pressurized against cavitation in the pump. Thus, the value of the pressure at the inlet of the turbine can be assumed to be the pressure increase Dp by the pump in Eq. (17) approximately in cycle analysis. The temperature at the inlet of the pump is assumed to be 300 K and the density r is 730 kg m3. Pressure has little effect on the density of n-decane at this temperature because it is liquid. The power balance characteristics of the generation system at expansion ratio of 2 are illustrated by Fig. 14. It gives the specific work of the turbine, the pump and the generator at different temperature and pressure at the inlet of the turbine. The temperatures and pressures shown in this figure can be achieved at different flying conditions including freestream Mach number and fuel air ratio. Normally, a higher freestream Mach number brings more energy into the engine and makes the temperature of the coolant higher. Excluding the specific power consumed by the pump for fuel pressurization, the fuel vapor turbine still has adequately enough power to drive the generator for onboard power generation. The specific power generation capacity is less than 10 kJ kg1 in the temperature range of mild pyrolysis (below 850 K), and it increases to about 40 kJ kg1 when the pyrolysis is nearly finished. It is also noticed that this onboard power generation system with fuel vapor turbine has the potential to operate in a wide range of temperature from un-cracking region to complete pyrolysis region to support the off-design operation of the engine. If the cooling system of the engine is allowed to operate at a higher pressure, the fuel vapor turbine can be operated at a larger expansion ratio to produce a greater power generation capacity. The specific power generation capacity at an operating pressure of
Fig. 14. Specific power of fuel vapor turbine, pump and generator vs. inlet temperature and pressure of turbine at expansion ratio of 2.
5 MPa is illustrated by Fig. 15 for different expansion ratios of the turbine. When the expansion ratio increases from 2 to 5, the maximum specific power generation capacity increases from 40 kJ kg1 to 108 kJ kg1. Therefore, increasing the expansion ratio of the turbine is an effective way to improve the performance of the power generation system. However, the growth rate of the specific power generation capacity decreases as the expansion ratio increases. The expansion ratio needs to be balanced with the operating pressure and other problems for practical applications. Assuming that the heating value and the total heat sink of endothermic hydrocarbon fuel are about 44 MJ kg1 and 4 MJ kg1 accordingly and the combustion efficiency is about 90%, the regeneratively cooled engines can recover about 10% of the heat released by fuel compared with engines without regenerative cooling. When the fuel vapor turbine generating system is in application, a small part (about 3% when the expansion ratio of turbine is 5) of the recovered low-grade heat is transformed into high-grade electrical energy further. Although the energy extraction from cooling fuel has an adverse effect on the engine's thrust in view of energy conservation, the total effect is less than one percent of the heating value of fuel. Overall, it is beneficial to trade off such little engine thrust for onboard power generation as well as fuel feeding to achieve more reasonable energy utilization and better overall performance of the hypersonic vehicle.
Fig. 15. Specific generating power at 5 MPa vs. inlet temperature and expansion ratio of turbine.
740
D. Zhang et al. / Energy 77 (2014) 732e741
h pffiffiffiffiffiffii2 ai ¼ 1 þ Si 1 Tri
6. Conclusions (1) Fuel vapor is a variable mixture of fuel molecules and their cracking products which are mainly gaseous hydrocarbons under different thermal conditions. The composition of fuel vapor varies greatly before and after the pyrolysis process. (2) Because of the complexity and variability of fuel vapor, it is necessary to treat it as a real gas for thermophysical property estimation. The SRK equation of state is applicable for the calculation of fuel vapor at high temperatures (above 750 K) and moderate pressures (below 5 MPa). (3) The working capacity of fuel vapor is different from other ordinary working fluids. The cracking reaction has a remarkable effect on the increase in the isentropic enthalpy drop of fuel vapor. (4) The fuel vapor turbine has adequately enough power to drive the generator for power generation in addition to fuel supply when the expansion ratio of turbine is 2. A power generation capacity with a magnitude of 100 kJ kg1 onboard a scramjet is available when the expansion ratio of turbine is 5 at an inlet temperature of 940 K. (5) This onboard power generation system can be operated in a wide range of fuel temperature from un-crack region to pyrolysis region to support the off-design operation of the engine. Based on heat recovery by regenerative cooling, this generating/feeding system transforms recovered low-grade heat into high-grade electrical/mechanical energy further to achieve more reasonable energy utilization and better overall performance of the hypersonic vehicle with negligible performance loss of the engine.
Tri ¼
T Tci
(A.7)
(A.8)
Si ¼ 0:48508 þ 1:5517ui 0:15613u2i
(A.9)
For hydrogen [18], Eq. (A.7) is modified as Eq. (A.10)
aH2 ¼ 1:202 expð0:30228Tr Þ
(A.10)
The basic property parameters including Tci, pci, ui, Mi for species i can be found in Ref. [19]. Appendix B
Cv ¼ Cv;0 þ
T v2 br ðaaÞln 1 þ bMw vT 2 Mw
(B.1)
, T vp 2 vp Cp ¼ Cv þ 2 vr T r vT r
(B.2)
g ¼ Cp Cv
(B.3)
where
Cv;0 ¼
N X
! xi Cv;0;i Mw
(B.4)
i¼1
Acknowledgments
Cv;0;i ¼ Cp;0;i Ru
This work was supported by National Natural Science Foundation of China (Program for Youth, No. 51106037), General Program (No. 51276047) and for Innovative Research Groups (No. 51121004).
N X
xi Mi
(A.1)
rRu 1 v r2 ðaaÞ ðMw brÞ Mw vT r ðMw þ brÞ
(B.6)
(B.7)
x i bi
(A.3)
pffiffiffiffiffiffiffiffiffi N X N X pffiffiffiffiffiffiffiffi v ai aj v ðaaÞ ¼ xi xj ai aj vT vT i¼1 j¼1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ai aj ai aj 1 εij
(A.4)
xi xj aij aij
i¼1 i¼1
b¼
r
¼
(A.2)
N X N X
N X
where Cv,0,i and Cp,0,i are the constant volume and constant pressure heat capacities of ideal gas for species i in J mol1 K1 and they can also be found in Ref. [19]. The derivatives v=vTðaaÞ and v2 =vT 2 ðaaÞ can be expressed below:
i¼1
aa ¼
vp vT
vp Mw Ru T aa rð2Mw þ brÞ ¼ vr T ðMw brÞ2 Mw ðMw þ brÞ2
Appendix A
Mw ¼
(B.5)
(B.8)
i¼1
aij aij ¼
where
The interaction parameters εij are determined experimentally and are known for very limited combinations of binary mixture. In situations involving mixtures of n-alkanes and n-alkenes, εij is usually close to zero. In the present study, therefore, all the values of them are assumed to be zero for simplification [20].
ai ¼ 0:42747
bi ¼ 0:08664
2 R2u Tci pci
(A.5)
Ru Tci pci
(A.6)
!1=2 !1=2 pffiffiffiffiffiffiffiffiffi v ai aj 1 ai vaj 1 aj vai þ ¼ 2 aj vT 2 ai vT vT
(B.9)
sffiffiffiffiffiffiffi!# " vai Si T ¼ pffiffiffiffiffiffiffiffiffi 1 þ Si 1 Tc;i vT TTc;i
(B.10)
pffiffiffiffiffiffiffiffiffi N X N X pffiffiffiffiffiffiffiffi v2 ai aj v2 ðaaÞ ¼ xi xj ai aj 2 vT vT 2 i¼1 j¼1
(B.11)
where
D. Zhang et al. / Energy 77 (2014) 732e741
pffiffiffiffiffiffiffiffiffi v2 ai aj vT 2
1 1 ¼ 2 ai aj
!1=2
vai vaj 1 ai vT vT 4 a3j
!1=2
vaj vT
2
!1=2 !1=2 v2 aj 1 aj vai 2 1 ai þ 4 a3i 2 aj vT vT 2 1=2 2 1 aj v ai þ 2 ai vT 2 sffiffiffiffiffiffiffi!# " v2 ai 1 S2i 1 Si T q ffiffiffiffiffiffiffiffiffiffiffiffi ¼ þ 1 1 þ S i 2 TTc;i 2 T 3 T Tc;i vT 2 c;i
(B.12)
(B.13)
For hydrogen, the derivatives are expressed as
vaH2 1 ¼ aH2 0:30228 Tc;i vT v2 aH2 1 ¼ aH2 0:30228 Tc;i vT
! (B.14)
!2 (B.15)
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