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Thermal management method of fuel in advanced aeroengines
Energy 49 (2013) 459e468
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Thermal management method of fuel in advanced aeroengines Jiang Qin, Silong Zhang, Wen Bao*, Weixing Zhou, Daren Yu School of Energy Science and Engineering, Harbin Institute of Technology, No. 92, West Da-Zhi Street, Harbin, Heilongjiang 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 12 June 2012 Received in revised form 25 October 2012 Accepted 26 October 2012 Available online 27 November 2012
The method to improve the heat sink utilization of fuel is the primary issue for thermal management of advanced aeroengines. In order to study the methods to control the fuel heat sink utilization, a one dimensional model of flow and heat transfer process in a single cooling channel of endothermic hydrocarbon fuel cooled scramjet in terms of endothermic reaction is developed, which is validated by corresponding experimental data. Different methods are put forwarded to control the utilization level of fuel heat sink and effective residence time of fuel during fuel cooling process is defined to distinguish global method and local method. The control of fuel mass flow rate or the height of cooling channel can be regarded as a global method, while the control of operating pressure in the cooling process can be considered as a local method. Analytical results indicate that the control methods can effectively improve the fuel heat sink utilization. However, the efficiency of the global method is limited by the allowable wall temperature. In contrast, the local method can be used not only to control the utilization of fuel heat sink, but also to improve the heat transfer and pressure drop performance of fuel. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermal management Fuel heat sink Control method Effective residence time
1. Introduction Thermal management of fuel in advanced aeroengines is always a significant challenge especially for advanced aeroengines used to power aircraft, rockets, and missiles. As flight speed increases to a supersonic or hypersonic regime, the temperature of ram air taken on board a vehicle becomes so high that the fuel has to be used as the primary coolant to cool the structure of vehicle [1]. The engines for future aircraft are projected to operate at high pressures and fuel/air ratios, which exacerbate their thermal management task. Thermal management has become one of the key concerns, and scramjet is the one with the largest heat load of all the advanced aeroengines. In order to meet the thermal management requirement for an aeroengine with high flight Mach number, endothermic hydrocarbon fuels has to be used to replace the conventional hydrocarbon fuel and to provide extra heat sink for cooling through endothermic thermal cracking [2]. It is a very efficient method to increase the fuel heat sink by developing an endothermic hydrocarbon fuel [3]. However, the utilization of fuel heat sink has the following limitations as detailed below. 1. The highest heating temperature of fuel is limited by the allowable wall temperature of thermal structure, which reduces the
* Corresponding author. E-mail address: [email protected] (W. Bao). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.050
practical utilization of fuel heat sink because the total amount of fuel heat sink is mainly determined by the temperature of fuel [4]. 2. The temperature of fuel must be kept safely below the coking temperature and the upper limit Mach number of a hydrocarbon fueled airbreathing hypersonic aeroengine is restricted to Ma8 because coking must be avoided within the cooling channel at all cost [5]. 3. The heating of Airframe (external surface) at a high Mach number will cause a significant heating of fuel tank which decreases the heat sink capacity of fuel (coolant) [6]. 4. The lack of heat sink confines a hypersonic vehicle to a relatively low flight speed. Because more fuel than required has to be carried for the mission when fuel heat sink is insufficient and the excess fuel has to be abandoned [7]. Therefore, it is very important to make full use of heat sink of fuel under limitations in addition to the development of fuel with high heat sink. Some researchers have further pointed out recently that fuel heat sink is affected not only by temperature, but also by velocity and pressure [8]. However, the previous studies are carried out theoretically. The fuel heat sink in a real engine is confined by the structure of engine and the size of its cooling passage, and the engine can work in a wide range of conditions with different Mach numbers and fuel/air ratios, and its heat load and cooling requirement may also vary greatly. All of these will further increase the difficulty in making full use of heat sink. So, with a scramjet used as the object of study and endothermic hydrocarbon fuel used for cooling of the scramjet, different schemes are worked out in accordance with the design and operating characteristics of a fuel
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Nomenclature A Cp D Ea ff h I k L Lp mf Nu P Pr qw Q R Re s
pre-exponential factor, s1 constant-pressure specific heat of hydrocarbon fuel, J/ (kg K) hydraulic diameter of cooling channel, m activation energy, J/mol friction factor heat sink, J/kg electric current, A reaction rate, s1 length of cooling channel segment, m length of pipe, m mass flow rate, kg/s Nusselt number pressure, Pa Prandtl number heat flux, W/m2 heat absorption, W/m universal constant, J/(mol K) Reynolds number thickness of wall, m
cooling system so that the fuel heat sink available can be fully utilized. 2. Description of scramjet and cooling-channel As shown in Fig. 1, the scramjet is located on the lower surface of a hypersonic vehicle and consists of a series of ramps that merge with the lower surface of the vehicle, and a cowl which helps capture the air compressed by the vehicle fuselage and the engine ramps. The major components of the engine are inlet, isolator, combustor, and nozzle. The combustor section experiences the highest heat flux. The nozzle, isolator and inlet experience lower heat fluxes, and among them, the inlet experiences the lowest heat fluxes. The typical ramp heat fluxes of a scramjet vary from 2 to 20 MW/m2. As shown in the upper portion of Fig. 1 [9], the cooling channels are the rectangular ducts encircling the thermal structure of engine and they can be described using channel width (W), channel height (H), fin thickness (t), and heated wall thickness (s).
t T U u W x Z
l m r
time, s temperature, K voltage, V velocity, m/s width of the cooling channel, m axial coordinate, m conversion of fuel thermal conductivity of metal wall material, W/(m.K) dynamic viscosity, Pa s fuel density, kg/m3
Subscripts c coolant ci coolant inlet co coolant outlet crack cracking reaction f fuel g gas j segment number w wall wc coolant side wall wg gas side wall
As shown in Fig. 1, the working process of the cooling system can be described as follows: the fuel of the engine is firstly pumped into the cooling channels to fully cool the thermal structure of the engine, and then the heated fuel is injected into the combustor as propellant to generate the thrust. In order to avoid the deterioration of heat transfer caused by boiling phenomenon, the pressure in the cooling channels is kept above the critical pressure of the fuel. 3. Computational model A one-dimensional model is usually used to study the flow and heat transfer characteristics of a reactive flow and to design the structure of a cooling channel [10]. A one-dimensional flow and heat transfer model with the cracking reaction taken into consideration is used in this article to study ways and means to control the utilization of fuel heat sink. During either the calculations or the experiments reported in this paper, the coolant is working under supercritical condition to avoid the deterioration of heat transfer. Under the supercritical pressure, the phase of fuel changes continually without boiling. Ward et al. built a numerical model to simulate the flow and heat transfer characteristics of aviation fuel under supercritical conditions, and boiling phenomenon is not considered to exist under such conditions [11]. In addition, the thermodynamic properties of fuel change greatly along with the increase in temperature, especially when the temperature is near the critical point. So the real thermodynamic properties of fuel must be considered. The properties of fuel and its cracked products are obtained from National Institute of Standards and Technology (NIST) Thermodynamic and Transport Properties of Pure Fluids database and NIST Chemistry Web Book [12]. 3.1. Geometry model and basic assumptions
Fig. 1. Schematic of scramjet engine with typical heat fluxes.
As shown in the upper portion of Fig. 1, the cooling jacket of a scramjet is composed of many single rectangular cooling channels. With a usual and reasonable assumption, coolant flow and heat flux are assumed to be uniform across the cross section of a scramjet [13]. Under such an assumption, the fuel mass flow rate and heat flux of each single channel are the same, and so, a single
J. Qin et al. / Energy 49 (2013) 459e468
cooling channel with constant area and rectangular duct geometry is used as the study object and shown in Fig. 2. The basic analysis method employed here is assumed to be a steady state quasi one-dimensional energy balance across the regenerative cooling jacket. To further simplify the analysis, an analytical model is developed under the following assumptions: 1) All the energy transferred across the coolant wall is absorbed by the coolant; 2) The wall-conduction in the axial direction is negligible; 3) The flow is fully developed; 4) All the thermophysic properties are regarded as different under different pressures and temperatures, and they are got using interpolation method from NIST database. The flow conditions of coolant are evaluated at the exit of each segment. 3.2. Energy balance in cooling channel For per unit mass endothermic hydrocarbon fuel, the heat transfer loss between fuel and engine wall in the cooling passage is ignored. The endothermic hydrocarbon fuel completes the cooling through both physical and chemical heat absorptions. There is
Q ¼ Qphy þ Qchem
(1)
where Qphy is the physical heat absorption and Qchem is the chemical heat absorption. As the pyrolysis reaction proceeds, the amount of smaller carbon molecules gas gradually increases, and the composition of cracked mixture changes simultaneously. Once a pyrolysis reaction takes place, the fuel becomes more degraded, with olefins initially appearing and the fuel in the cooling passage becomes a mixture of pyrolysis products and uncracked fuel. The percentage of each component in the cracked fuel mixture varies with conversion Z. Upon completion of a pyrolysis reaction, there is physical heat P absorption ( CpDT) which consists of the heat absorption of unreacted fuel and the heat absorption of pyrolysis products. The chemical heat absorption can be given by
Qchem ¼ Z$Hchem
(2)
where Hchem is the endothermic reaction heat, i.e. the heat absorbed by per unit mass fuel when it is fully cracked. As shown in the lower portion of Fig. 2, a typical segment with inlet temperature Tj and pressure Pj is subjected to heat flux qw. The following energy balance equation can be used together with the surface heat flux equation to calculate the outlet temperature of segment j with width W.
Qj ¼ qw ðxÞj WL
(3)
The outlet temperature of the segment is co-decided by physical heat absorption and chemical heat absorption. A reasonable fuel
461
temperature makes Eq. (1) tenable, and so, the level of physical and chemical heat absorptions and their proportion to the total heat absorption can be determined. 3.3. Convective heat transfer and flow model Once the coolant temperature is determined, the temperature distribution throughout the cooling channel can be evaluated. And Newton’s Law of cooling can be used to find the surface temperature,
Qj ¼ hj Tj;wc Tj;a AC
(4)
where AC ¼ WL is the non-finned convecting surface area shown in Fig. 2. And the properties of coolant can be evaluated at average temperature (Tj,a) throughout the segment. The next step is to calculate the film coefficient for convective heat transfer using the published correlations. The effects of boiling phenomenon on the heat transfer are neglected because the fuel works under supercritical condition. It is pointed out in Ref. [14] that classical heat transfer correlation can be applied to fuels JP-7, JP-8, JP-8þ100, JP-10 and RP-1 before the cracking reaction occurs. It is found by researchers in MIT that the heat transfer coefficient after cracking reaction is bigger than that before cracking reaction [15]. What is more, when a classical heat transfer correlation is adopted in the cracking zone of an endothermic hydrocarbon fuel, the relative error between experimental and calculated results is too large (nearly 50%) to be accepted [16]. Considering the complexity of heat transfer characteristics of fuel in cooling channel when cracking reaction occurs, before cracking reaction occurs, a heat transfer correlation without considering chemical reaction is taken from Ref. [17] and shown below.
0:333 Nu ¼ 0:027Re0:8 c Prc
mf mw
0:14 Tf < Tcrack
(5)
The heat transfer correlation of hydrocarbon fuel under the operating condition with a chemical reaction is modified using the experimental data as reported in Ref. [4]. The difference between gas side wall temperature Twg and coolant side wall temperature Twc can be given by
Qj ¼
l s
Twg Twc
(6)
where l is the thermal conductivity of wall material (superalloy). It is considered to vary with temperature and its value is given using an interpolation method according to Table 2. The coolant pressure drop can be estimated using DarcyWeisbach equation [18] and the equation does not take the effect of boiling on pressure drop into consideration because the fuel works under a supercritical condition.
DP ¼ ff
rLu2 2D
(7)
3.4. Properties of fuel
Fig. 2. Schematic of single cooling channel.
3.4.1. Description of fuel n-Decane is chosen as a fuel compound for the present study because it is a typical pure liquid hydrocarbon fuel with 10 carbon atoms in its molecule. It is the main component of hydrocarbon fuel and has carbon number and properties similar to those of liquid hydrocarbon material commonly used in aerospace applications. What is more, Ward et al. used n-Decane as the object for study because it has critical pressure, temperature and product distribution
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Table 1 Distribution of pyrolysis products of n-Decane. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Name
Formula
Hydrogen Methane Ethane Ethylene Propane Propylene n-butane Butane 1-pentene n-pentane 1-hexene n-hexane 1-heptene n-heptane 1-octene n-octane 1-nonene n-nonene
H2 CH4 C2H6 C2H4 C3H8 C3H6 C4H10 C4H8 C5H10 C5H12 C6H12 C6H14 C7H14 C7H16 C8H16 C8H18 C9H18 C9H20
Ea RT
k ¼ A$e
Mass fraction 80 ml/min, 3 MPa
Mass fraction 80 ml/min, 5 MPa
e 0.0301 0.1241 0.1773 0.1042 0.2532 0.0468 0.1662 0.0296
e 0.0295 0.1370 0.1634 0.1333 0.2361 0.0764 0.1678 0.0171
0.0236
0.0137
0.0204
0.0118
0.0157
0.0090
0.0088
0.0050
Nout ¼ Nin ekt
(8)
where vg and vres are the stoichiometric coefficients. The cracking rate constant is generally a function of fuel temperature. In addition, according to Arrhenius expression, reaction rate k can be expressed as
100
200
300
400
500
600
700
800
900
l/W m2 K1 11.3 12.56 14.24 15.49 16.75 18.42 19.68 21.35 23.02
(11)
where, Nin is total mole number of unreacted n-Decane at the inlet of each calculation segment, t is the time when fuel flows over the unit length. So it can be concluded that the thermal cracking rate is influenced by the flowing characteristic time. It can be seen through the further investigation of Eq. (11) that only the time that the fuel flows from the position the fuel starts to crack to the cooling channel exit has effect on the cracking reaction, so that time is defined as effective residence time and can be given by
ZXout
seffect ¼
1 dx u
(12)
Xcrack
where seffect is the effective residence time. 4. Validation of model For the flow and heat transfer procedure of hydrocarbon fuel with cracking reaction under supercritical condition, the reaction rate and the products of reaction have their significant effect on the flow and heat transfer characteristics. In this paper, the cracking process is approximated as an overall reaction process and the percentage of cracked products does not vary with temperature and pressure. However, in a real system, the reaction varies with temperature and pressure. So it is necessary to verify
Table 3 Reaction rate constants. Parent fuel Ward et al. P ¼ 3.45 MPa and T ¼ 500e600 C Ward et al. P ¼ 3.45e11.38 MPa and T ¼ 550e600 C Stewart et al. P ¼ 2.96 MPa and T ¼ 440e535 C Jiang QIN et al. P ¼ 3 MPa and T ¼ 300e650 C
Table 2 Variation of thermal conductivity of GH3128 along with temperature. T/ C
(10)
where N is the mole number of unreacted n-Decane. From Eq. (10), the total mole number of unreacted n-Decane at the outlet of each calculation segment can be given by
3.4.2. Composition of cracked products An endothermic reaction known as thermal cracking occurs when n-Decane is heated to a temperature above 773 K. The details of product distribution got from our measurements on the experimental table are shown in Table 1 and the values in the table are average over many experiments. The PPD (proportional product distribution) model built by Ward et al. [11] is adopted in this paper. The products and their distribution in a general PPD model are kept unchanged while the pressure and the temperature change at a conversion below 35%, and the relative error can be lower than 3%. In this paper, the PPD model is used at a conversion above 35%, the relative error is higher than that of Ward because of the effect of a secondary reaction which occurs under a higher conversion. However, on the basis of Ward’s work, the PPD model is validated using our own experimental data. The relative error is within 15% even if the conversion is as high as 70% and it is still acceptable in this paper because this paper focus on the utilization of fuel heat sink, not the chemical kinetic model. According to the general PPD model based on experimental data used in this paper, the percentage of cracked products does not vary with temperature and pressure. The cracking process can be approximated as an overall reaction which can be expressed as
where A and Ea are given in Table 3. The values of A and Ea in Table 3 are got from the previous study and our own experiments. Using the value derived from our experiments, the results of the model are in good agreements with the experimental data. The validation was carried out and shown in the following part. The reaction rate of Eq. (8) is assumed to be of the first order. The variation of Arrhenius form, the unreacted n-Decane with a total mole number can be given by
dN ¼ kN dt
similar to those of a real jet fuel [11]. Therefore, the results obtained with n-Decane might be extended to other hydrocarbon fuel with just minor modifications. What is more, the present study focuses on the fundamental aspects of heat sink utilization, so it is proper to use nDecane as project for the study. The chemical formula of n-Decane is C10H22 and the critical temperature and critical pressure of n-Decane are 617.7 K and 2.11 MPa respectively.
n Decane/vg gases þ vres residual
(9)
f
Jiang QIN et al. P ¼ 5 MPa and T ¼ 300e650 C
neDecane Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1
Ea,
63
Ea,
2.1 1015 63
Ea,
1.6 1015 64 2.4
Ea,
1.10 1015.91.5 60.2
Ea,
1.6 1015 58.8 1.7 1015
J. Qin et al. / Energy 49 (2013) 459e468
the computational model to see if it can be used to get the convincing results. 4.1. Experimental apparatus As shown in Fig. 3, an experimental set-up is built and used to investigate the flow characteristic, heat transfer and cracking characteristics of hydrocarbon fuel under supercritical conditions. A system with electric heating is used for the present study because the system can be used to simulate the real heating procedure in the engine. The heat flux and characteristic size of the cooling passage are in good agreement with those of a real engine. The system can be used for the study of pyrolysis reaction regimes over a long period. The facilities consist primarily of a fuel reservoir, a fuel pump, a fuel reactor (tube), an electric heating power and a fuel cooler. The test section is a GH3128 superalloy pipe and it can be easily used to heat fuel to 1000 K. The pump is a constant-flux pump which can be used to provide a constant and continuous flow flux. The flow rate is not affected by the load pressure, and it has a safety pressure as high as 40 MPa. The range of flow is from 0 to 80 ml/min. The test section is a 1 m long pipe with an inner diameter of 1 mm and an outer diameter of 3 mm, and it is horizontally placed on an experimental table. The two ends of the pipe are wrapped with two copper electrodes. The pipe is heated using a direct current supply, and it has the power of 3 kW. The power used to heat the pipe can be adjusted by changing the voltage and electric current. There is no insulation around the pipe to avoid thermal loss. Heat leakage is calibrated by heating the pipe without fuel flowing through. Fuel is nitrogen-purged to remove the dissolved oxygen to improve the thermal stability of fuel. The entire system is purged with nitrogen prior to the introduction of fuel. Downstream the reactor, the products are quenched in a waterfed heat exchanger to room temperature and filtered before passing through a needle valve (back pressure valve) to regulate the system pressure. The needle valve can be used to ensure that the back pressure of the system can be kept constant during the experiment. The pipe wall temperature distribution is measured using Ktype thermocouples spot-welded to the outside surface of the pipe. The fuel temperatures at the inlet and outlet of the pipe are measured using a thermocouple inserted into the flow of fuel. Fuel
463
pressure is measured with the pressure gauges installed at the outlet of the pump and the upstream back pressure valve. The uncertainty associated with the measurement of wall temperature and the temperature of fuel is estimated to be less than 3 K, whereas that of pressure measurement is less than 1%. All the experimental data are recorded via a data acquisition system for analysis. The liquid and gaseous components of fuel are separately metered and analyzed. The gas products are analyzed using a gas chromatograph/mass spectrometry (GC7900/MS), which consists of flame ionization and thermal conductivity detectors, and the liquid portion of the stressed fuel is analyzed by liquid chromatography (LC). 4.2. Experimental procedure With a test section installed and tested for leak, tests were conducted by first purging the reactor pipe with nitrogen to remove any oxygen. The flow rate used in the experiments is 80 ml/min. Constant outlet pressures of 3 MPa, 4 MPa and 5 MPa were maintained throughout the experiment using a back pressure valve. The flow was pumped into (1 mm i.d.) GH3128 superalloy pipe. With fuel flow established, data logging was initiated and electrical power was supplied to the test section, and voltage was adjusted to obtain the desired exit fuel temperature. Once the outlet temperature of fuel reached its target value, the test was ran for a desired period of time or until the pipe was plugged with coke. Minor adjustments were made in the back pressure valve during the run to maintain a relatively constant pressure throughout the test. While there is no coking, the highest temperature of the fuel is 923 K throughout the experiment. 4.3. Experimental analysis procedure 4.3.1. Analysis of cracking products composition and conversion Cracked fuel comes out from the pipe and enters into the cooler, and gas and liquid components are separated one from another when cracked fuel flows out from the cooler. The volume flow of gas component is measured with a gas rotameter, and components of cracked products are online analyzed by gas chromatography. The liquid products are collected into a liquid collector and then analyzed by GCeMS. These analyses above include the volumetric
Fig. 3. Single tube test apparatus schematic.
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J. Qin et al. / Energy 49 (2013) 459e468
flow rate of gas component V, specific composition of gas products (CH4, C2H4 and C2H6 et al.) and the corresponding mole fractions (va, vb, vc et al.); the mass flow rate of liquid component ml, including the specific composition of liquid cracking products (C4þ and C5þ et al.) and the corresponding mole fractions (v1, v2, v3 et al.), and the mass flow rate of remaining non-cracking fuel and corresponding mole fraction vres. The expression of fuel conversion can be given as shown below
Z ¼
1
ml vres mg þ ml
100%
(13)
4.3.2.2. Calculation of physical and chemical heat absorption. The unit mass total heat absorption of fuel is equal to the difference between the heating power and the heat loss, and it can then be used to divide the mass flow rate of fuel:
hf ¼
UI Qs mf
The total heat absorption of fuel is composed of physical and chemical heat absorption which is expressed by Eq. (1). Once a cracking reaction takes place, physical heat absorption is composed of the heat absorption of unreacted fuel and the heat absorption of cracking products as shown below.
where, the quantity of gas components can be given by
mg ¼ ðMa va þ Mb vb þ Mc vc þ :::Þ$V=22:4
(14)
where, mg e quantity of gas components; ml e quantity of liquid components; Ma, Mb and Mc e molar mass of gas components. 4.3.2. Analysis of fuel heat sink Before the cracking of hydrocarbon fuel, the fuel has only the capacity of physical heat absorption. Once cracking reaction occurs, the heat absorption capacity of endothermic hydrocarbon fuel includes physical and chemical heat absorption. In order to distinguish physical heat absorption from chemical heat absorption of hydrocarbon fuel, the following methods can be used to obtain the physical and chemical heat absorption. 4.3.2.1. Calculation of dissipated heat. Most of the heating power is absorbed by fuel, and little of the heating power dissipates to air through the heated tube wall. In order to obtain the quantity of heat absorbed by fuel, the heat loss of heated tube should be firstly obtained. The relationship between heat loss of heated tube and wall temperature can be analyzed as shown below. The tube is firstly heated without fuel to obtain the heat loss of heated tube. The heat absorbed by the heated tube is considered to be all dissipated to air when the heat balance is reached, because there is no fuel flowing through the tube. The relationship between the heat loss and the tube wall temperature can be obtained using the wall temperature and the heating power. Therefore, heat loss of tube Qs will be obtained at the same heated wall temperature in the actual heating process.
(15)
Qphy ¼
N X
"
j¼1
# vs Cps þ Z vc Cpc DT ð1 ZÞ s¼1 c¼1 C X
S X
Tj
Here the typical heat absorption temperature region is divided into calculation cells and the temperature increment of each cell is DT, N is the total number of calculated cells. And the average specific heat at a constant pressure of each component and the conversion is obtained from the outlet temperature of each cell. The chemical heat absorption of fuel is equal to the difference between the total fuel heat absorption obtained using Eq. (1) and the physical heat absorption obtained using Eq. (16). What is more, when the chemical heat absorption and the conversion of fuel Z is got from the experimental data, Hchem we defined in Section 3.2 can be calculated using Eq. (2) and the comparison between the Hchem calculated using the experimental data and the Hchem calculated by the composition measurements is carried out. 4.4. Results of validation Validation is conducted with a mass flow rate of 1 g/s, pressures of 3 MPa, 4 MPa, 5 MPa and a length of 1 m. The inner and outer diameters of the pipe are 1 mm and 3 mm. The operating condition and characteristic size of the pipe are in good agreement with those of the cooling passage in a real engine. The conversion and total heat sink of fuel at the exit are shown in Figs. 4 and 5. It can be seen from Fig. 4 that n-Decane starts to
b
a
experimental data calculation results
70
calculation results experimental data
50
Z(conversion, %)
Z(conversion, %)
60
40
30
50 40 30
20 20
10
10 0
0 773
823
873
923
Tout(fuel exit temperature, K)
3MPa
973
(16)
750
800
850
900
Tout(fuel exit temperature, K)
5MPa
Fig. 4. Conversion comparison of experimental data with calculated result.
950
J. Qin et al. / Energy 49 (2013) 459e468
x 106
3
3.5 experimental data calculation results
hf(fuel heat sink, J/kg)
hf(fuel heat sink, J/kg)
2 1.5 1 0.5 0
0
x 106 experimental data calculation results
3
2.5
465
2.5 2 1.5 1 0.5
373
473 573 673 773 873 Tout(fuel exit temperature, K)
973
a 3MPa
0 300
400
500
600
700
800
900
1000
Tout(fuel exit temperature, K)
b 5MPa
Fig. 5. Heat sink comparison of experimental data with calculated result.
crack when the temperature is higher than 773 K and the conversion increases along with the temperature at the pipe exit. As shown in Fig. 4, the results of the computational model is rather accurate and the relative error is within 15% under the experimental pressures. It can also be seen from Fig. 5 that the total heat sink increases approximately linearly along with the pipe exit temperature when the pipe outlet temperature is lower than 773 K, and the slope of the curve at each point is determined by the specific heat which varies with temperature and pressure. When the pipe outlet temperature is higher than 773 K, cracking reaction occurs, and the increasing rate of the total heat sink is greatly improved because the total heat sink consists of physical heat sink and chemical heat sink at this time. As shown in the figures, before cracking reaction occurs, the result obtained with the computational model matches well with the experimental result, with a relative error within 2%. While the relative error becomes larger when cracking occurs because PPD (proportional product distribution) mechanism is adopted in the computational model. In a PPD mechanism, the distribution of reaction products is assumed to be the same at different temperatures and pressures, which is not the situation in a real cracking reaction. However, the relative error is within 15%, which is acceptable for this study. It should be pointed out in particular that, before cracking reaction occurs, the heat transfer coefficient got from the computational model matches well with the experimental result, with a relative error within 15%. After cracking reaction occurs, the relative error becomes unacceptable. This is in line with what is reported in Ref. [14] and Ref. [16]. The researchers pointed out that classical heat transfer correlation can be used before cracking reaction occurs while the relative error between experimental result and calculated result is too large (nearly 50%) to be accepted when a classical heat transfer correlation is adopted in the cracking zone of endothermic hydrocarbon fuel. The heat transfer correlation is thus modified to get a more acceptable heat transfer coefficient based on experimental and theoretical similarity. However, because of the complexity of heat transfer characteristics the cracking reaction brings, it is hard to get a widely accepted heat transfer correlation up to now. In this paper, the precision of heat transfer correlation is not a key factor, so the heat transfer coefficient obtained using the computational model is considered acceptable.
5. Results and discussion 5.1. Selectivity of control methods It can be seen from Eqs. (9) and (11) that main factors having their effect on the heat absorption capacity of fuel by influencing the conversion of pyrolysis reaction are the temperature and flow velocity of fuel. According to the previous study, the residence time of fuel is the primary factor that determines the fuel heat sink [4]. So, in order to control the endothermic reaction process, the possible control parameters must be capable of having effect on the residence time of fuel. It can be seen through the careful observation of the working characteristics of fuel cooling process that either the design or the operation parameters of a cooling system can be used to control the utilization of fuel heat sink on the following two aspects: 1) The operation parameters of a cooling system, which mean the mass flow rate and the operating pressure of fuel in a cooling channel; 2) The design parameters of a cooling system, which mean the width and height of a cooling channel. 5.2. Design parameters of a cooling system The variation of channel in size has its effect on the velocity of fuel along the channel, and then on the residence time throughout the channel, which leads to the change in the utilization of fuel heat sink. In this paper, the height of channel is chosen as a major design parameter for the study on the effect of channel size on the utilization of fuel heat sink. The width of channel is not chosen as a major design parameter because the specific structure of an engine and the total number of channels should also be considered if the width of a channel is chosen. The change in channel width will indirectly change the total number of cooling channels across the section, thus the mass flow rate of fuel will be redistributed in each cooling channel. As shown in Fig. 6, the conversion of fuel increases with the increase of channel height (the highest conversion calculated here is as high as 80%, higher than the validated data which is confined by the experimental conditions, so the relative error here is larger),
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0.9
0.8 H=1mm H=1.5mm H=2.5mm
m=0.55g/s m=0.5g/s m=0.6g/s
0.8 0.7
0.6 Z(conversion, %)
Z(conversion,%)
0.7
0.5 0.4 0.3
0.6 0.5 0.4 0.3 0.2
0.2
0.1
0.1 0
0
0
10
20
30
40
50 60 x(cm)
70
80
0
10
20
30
90 100
40 50 60 x(cm)
70
80
90 100
Fig. 8. Conversion along the flow direction at different fuel mass flow rates.
Fig. 6. Conversion along the flow direction at different channel heights.
because the decrease of fuel velocity caused by the increase of channel height will increase the entire residence time of fuel in the cooling channel. However, it can be seen from Fig. 7 that the gasside wall temperature increases as the channel height increases, because the heat transfer coefficient decreases with the increase of channel height. Especially, the over-temperature of wall will occur when the channel height is large enough. So, although it is an effective way to control the heat sink utilization of fuel by reasonably designing the channel in size, the limitation of allowable wall temperature must be considered. In addition, it can be seen from Fig. 7 that the rate of increase of the gas-side wall temperature slows down after the fuel flows through some distance along the cooling channel (the same situation as what is shown in Fig. 9). It is because the temperature of fuel increases along with the distance of the cooling channel and when the fuel temperature is sufficient high, the fuel starts to crack, leading to an increase of the fuel’s heat absorption capacity per unit increase in temperature. The increased heat absorption capacity makes the rate of the increase of the fuel temperature slow down and the difference between the fuel temperature and the gas-side wall temperature is not affected at the same time, so the gas-side wall temperature also has a lower rate of increase when fuel starts to crack. 5.3. Operation parameters of cooling system In this paper, according to the characteristics of the experimental apparatus and the real scramjet working conditions, the back
pressure is kept constant when the fuel mass flow rate changes and so is the same condition when the back pressure changes. 5.3.1. Fuel mass flow rate As shown in Fig. 8, the conversion increases with the decrease of fuel mass flow rate in that the variation of the fuel mass flow rate has its effect on the temperature and velocity of fuel. The fuel mass flow rate decreases as the flow velocity decreases, and both the residence time of fuel in the cooling channel and the increase in fuel temperature. The effect of fuel mass flow rate on the fuel temperature and velocity increases the conversion of the fuel. However, it can be seen from Fig. 9 that the gas-side wall temperature is very close to the allowable temperature of the wall material when the fuel mass flow rate is 0.5 g/s, because the low velocity of fuel caused by the low fuel mass flow rate can cause a decrease in the heat transfer coefficient and there is an increase in the gas-side wall temperature. So, limited by the allowable temperature of wall material, the fuel mass flow rate cannot be too low, which make the heat sink unable to be fully released, and impose a limit on the ultimate heat sink of fuel. It can be seen from the analysis above that fuel mass rate is one of the ways to control the heat sink utilization of fuel, but it has its effect on the heat transfer characteristics, and it is then limited by the allowable temperature of wall material. What is more, the fuel mass flow rate is also limited by the fuel mass flow rate no matter fuel is used either as coolant or propellant. So, in short, there are many constraints for the use of fuel mass flow rate to control the heat sink utilization of fuel.
1000 H=1mm H=1.5mm H=2.5mm
1050 m=0.6g/s m=0.55g/s m=0.5g/s
1000
900
Twg(gas side wall temperature, K)
Twg(gas side wall temperature, K)
950
850 800 750 700
950 900 850 800 750 700 650
650 600
600
0
20
40
60
80
100
x(cm) Fig. 7. Gas-side wall temperature along the flow direction at different channel heights.
550
0
20
40
60
80
100
x(cm)
Fig. 9. Gas-size wall temperature along the distance at different fuel mass flow rates.
J. Qin et al. / Energy 49 (2013) 459e468 0.8 P=3MPa P=5MPa P=7MPa
0.7
Z(conversion, %)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
20
40
60
80
100
x(cm)
Fig. 10. Conversion of the fuel along the direction at different operation pressures.
467
helpful to lower the gas-side wall temperature, because the increase in operation pressure can affect the properties of fuel such as Cp, indirectly affecting the heat transfer coefficient of fuel. Compared to changing the velocity of fuel by changing the mass flow rate of fuel or the height of channel, only the velocity of fuel in the gas zone is changed when the operation pressure is changed. On one hand, the effect of control method on the heat sink release becomes more obvious, on the other hand, this control method can improve the heat transfer. So, in short, both the performance of heat transfer and the heat sink utilization of fuel benefit from the increase in operation pressure. When fuel is used as coolant at a high pressure, it functions to inhibit the boiling phenomenon and to improve the heat sink utilization of fuel, i.e. avoid the boiling phenomenon in the liquid zone and enhance the heat absorption capacity in the cracking zone. 6. Conclusion
It should also be pointed out in particular that the control of fuel mass flow rate is still a very important way to protect the engine from being burnout while fuel is used as coolant. During a practical operation of a scramjet, the engine can be prevented from being overheated by adjusting the fuel mass flow rate in accordance with the heat load and wall temperature. 5.3.2. Operating pressure in cooling channel It can be seen through further analysis that by controlling both the mass flow rate of fuel and the height of channel, the global velocity of fuel can be controlled, i.e. the time for the fuel to flow through the entire cooling channel, including both noncracking zone and cracking zones. However, only the time when the fuel temperature is higher than the start temperature of pyrolysis reaction has its effect on the heat sink utilization of fuel. Besides, the decrease of the velocity of fuel in the noncracking zone results in the deterioration of heat transfer, and overtemperature is then easy to occur and the heat sink utilization of fuel is limited. So, a control method which has its effect on the velocity of the fuel in the gas zone only should be found. Due to the fact that the density of fuel is proportional to the pressure of fuel in the gas zone under ideal condition at a constant temperature and it is barely affected by the variation of pressure while fuel is in the liquid zone, a control method is introduced to control the heat sink utilization of fuel by changing the operating pressure of fuel. As shown in Fig. 10, the conversion of fuel increases with the increase of operation pressure, because the velocity of fuel in the gas zone decreases with the increase in pressure and the variation of operation pressure only affect the velocity of fuel in the gas zone (Fig. 11). Meanwhile, the increase in operation pressure is very
In order to study the methods to control the heat sink utilization of hydrocarbon fuel and their actual control effects, scramjet is chosen as the object of study and a one dimensional model of the flow and heat transfer process in a single cooling channel in terms of cracking reaction is constructed and validated through experiments. Different schemes are worked out to control the heat sink utilization of fuel by changing the mass flow rate of fuel, the operating pressure of fuel, and the size of cooling channel. Effective residence time, which is the dominant part of the whole residence time in deciding the level of heat sink utilization, is defined to distinguish global method and local method. The heat sink control methods are classified into global and local methods in terms of their effect on effective residence time, in which a local method can only influence the effective residence time. Controlling the fuel mass flow rate and the channel size are regarded as global methods and controlling the operating pressure of fuel is classified as a local method. Local methods cannot only control the heat sink utilization, but also improve the heat transfer and pressure drop performance of fuel. The study results have shown that the control methods can effectively improve the level of fuel heat sink utilization. The conclusion of the control methods of heat sink utilization has guidance on the design of cooling channel and the operation of a cooling system. Acknowledgment This work was supported by National Natural Science Foundation of China (General Program, No. 51106037), for Distinguished Young Scholars (No. 50925625) and for Innovative Research Groups (No. 51121004), and the authors thank the reviewers for their valuable advice on this paper.
20
References
P=3MPa P=5MPa P=7MPa
18 16 u(fuel velocity,m/s)
14 12 10 8 6 4 2 0
0
20
40
60
80
100
x(cm)
Fig. 11. Fuel velocity along the direction at different operation pressures.
[1] Huang H, Spadaccini LJ, Sobel DR. Fuel-cooled thermal management for advanced aeroengines. J Eng Gas Turbines Power-Trans ASME 2004;126(2): 284e93. [2] Huang H, Sobel DR, Spadaccini LJ. Endothermic heat-sink of hydrocarbon fuels for scramjet cooling; 2002. AIAA-2002-3871. [3] Sobel DR, Spadaccini LJ. Hydrocarbon fuel cooling technologies for advanced propulsion. J Eng Gas Turbines Power-Trans ASME 1997;119(2):344e51. [4] Bao W, Li XL, Qin J, Zhou WX, Yu DR. Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooled scramjet. Appl Therm Eng. http:// dx.doi.org/10.1016/j.applthermaleng. 2011.09.036, IF¼1.823. [5] Albert HB. Hypersonic air-breathing propulsion efforts in the air force research laboratory; 2005. AIAA 2005e3255. [6] Edward T. Liquid fuels and propellants for aerospace propulsion: 1903e2003. J Propul Power 2003;19(6):1089e107. [7] Kanda T, Masuya G, Wakamatsu Y, Chinzei N, Kanmuri A. Parametric study of airframe-integrated scramjet cooling requirement. J Propul Power 1991; 17(3):431e6.
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[8] Daniau E, Bouchez M, Marie P, Gascoin N, Gillard P. Fuel reforming for scramjet thermal management and combustion optimization; 2005. AIAA 2005e3403. [9] Youn B, Millst AF. Cooling panel optimization for the active cooling system of a hypersonic aircraft. J Thermophys Heat Transf 1995;9(1):136e43. [10] Daniau E, Sicard M. Experimental and numerical investigations of an endothermic fuel cooling capacity for scramjet application; 2005. AIAA 2005e3404. [11] Ward TA, Ervin JS, Striebich RC, Zabarnick S. Simulations of flowing mildlycracked normal alkanes incorporating proportional product distributions. J Propul Power 2004;20(3):394e402. [12] Lemmon EW, Peskin AP, Friend DG. NIST 12: thermodynamic and transport properties of pure fluids. NIST Standard Reference Database Number 12, Version 5.0. NIST; 2000.
[13] Scotti SJ, Martin CJ, Lucas SH. Active cooling design for scramjet engines using optimization methods; 1988. NASA TM-100581. [14] Stiegemeier Benjamin, Lawrence, Michael Meyer, Cleveland, Taghavi Ray. A thermal stability and heat transfer investigation of five hydrocarbon fuels; 2002. AIAA-2002-3873. [15] Chen AY, Dang L. Characterization of supercritical JP-7’s heat transfer and coking properties; 2002. AIAA-2002-57. [16] Linne Diane L, Meyer Michael L, Edwards Tim, David A. Evaluation of heat transfer and thermal stability of supercritical JP-7 fuel; 1997. AIAA-1997-3041. [17] Zhong FQ, Fan XJ, Yu G, Li JG, Lu XN. Heat transfer of aviation kerosene at supercritical conditions; 2008. AIAA-2008-4615-242. [18] Parris DK, Landrum DB. Effect of tube geometry on regenerative cooling performance; 2005. AIAA 2005e4301.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Thermal management method of fuel in advanced aeroengines Jiang Qin, Silong Zhang, Wen Bao*, Weixing Zhou, Daren Yu School of Energy Science and Engineering, Harbin Institute of Technology, No. 92, West Da-Zhi Street, Harbin, Heilongjiang 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 12 June 2012 Received in revised form 25 October 2012 Accepted 26 October 2012 Available online 27 November 2012
The method to improve the heat sink utilization of fuel is the primary issue for thermal management of advanced aeroengines. In order to study the methods to control the fuel heat sink utilization, a one dimensional model of flow and heat transfer process in a single cooling channel of endothermic hydrocarbon fuel cooled scramjet in terms of endothermic reaction is developed, which is validated by corresponding experimental data. Different methods are put forwarded to control the utilization level of fuel heat sink and effective residence time of fuel during fuel cooling process is defined to distinguish global method and local method. The control of fuel mass flow rate or the height of cooling channel can be regarded as a global method, while the control of operating pressure in the cooling process can be considered as a local method. Analytical results indicate that the control methods can effectively improve the fuel heat sink utilization. However, the efficiency of the global method is limited by the allowable wall temperature. In contrast, the local method can be used not only to control the utilization of fuel heat sink, but also to improve the heat transfer and pressure drop performance of fuel. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermal management Fuel heat sink Control method Effective residence time
1. Introduction Thermal management of fuel in advanced aeroengines is always a significant challenge especially for advanced aeroengines used to power aircraft, rockets, and missiles. As flight speed increases to a supersonic or hypersonic regime, the temperature of ram air taken on board a vehicle becomes so high that the fuel has to be used as the primary coolant to cool the structure of vehicle [1]. The engines for future aircraft are projected to operate at high pressures and fuel/air ratios, which exacerbate their thermal management task. Thermal management has become one of the key concerns, and scramjet is the one with the largest heat load of all the advanced aeroengines. In order to meet the thermal management requirement for an aeroengine with high flight Mach number, endothermic hydrocarbon fuels has to be used to replace the conventional hydrocarbon fuel and to provide extra heat sink for cooling through endothermic thermal cracking [2]. It is a very efficient method to increase the fuel heat sink by developing an endothermic hydrocarbon fuel [3]. However, the utilization of fuel heat sink has the following limitations as detailed below. 1. The highest heating temperature of fuel is limited by the allowable wall temperature of thermal structure, which reduces the
* Corresponding author. E-mail address: [email protected] (W. Bao). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.10.050
practical utilization of fuel heat sink because the total amount of fuel heat sink is mainly determined by the temperature of fuel [4]. 2. The temperature of fuel must be kept safely below the coking temperature and the upper limit Mach number of a hydrocarbon fueled airbreathing hypersonic aeroengine is restricted to Ma8 because coking must be avoided within the cooling channel at all cost [5]. 3. The heating of Airframe (external surface) at a high Mach number will cause a significant heating of fuel tank which decreases the heat sink capacity of fuel (coolant) [6]. 4. The lack of heat sink confines a hypersonic vehicle to a relatively low flight speed. Because more fuel than required has to be carried for the mission when fuel heat sink is insufficient and the excess fuel has to be abandoned [7]. Therefore, it is very important to make full use of heat sink of fuel under limitations in addition to the development of fuel with high heat sink. Some researchers have further pointed out recently that fuel heat sink is affected not only by temperature, but also by velocity and pressure [8]. However, the previous studies are carried out theoretically. The fuel heat sink in a real engine is confined by the structure of engine and the size of its cooling passage, and the engine can work in a wide range of conditions with different Mach numbers and fuel/air ratios, and its heat load and cooling requirement may also vary greatly. All of these will further increase the difficulty in making full use of heat sink. So, with a scramjet used as the object of study and endothermic hydrocarbon fuel used for cooling of the scramjet, different schemes are worked out in accordance with the design and operating characteristics of a fuel
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J. Qin et al. / Energy 49 (2013) 459e468
Nomenclature A Cp D Ea ff h I k L Lp mf Nu P Pr qw Q R Re s
pre-exponential factor, s1 constant-pressure specific heat of hydrocarbon fuel, J/ (kg K) hydraulic diameter of cooling channel, m activation energy, J/mol friction factor heat sink, J/kg electric current, A reaction rate, s1 length of cooling channel segment, m length of pipe, m mass flow rate, kg/s Nusselt number pressure, Pa Prandtl number heat flux, W/m2 heat absorption, W/m universal constant, J/(mol K) Reynolds number thickness of wall, m
cooling system so that the fuel heat sink available can be fully utilized. 2. Description of scramjet and cooling-channel As shown in Fig. 1, the scramjet is located on the lower surface of a hypersonic vehicle and consists of a series of ramps that merge with the lower surface of the vehicle, and a cowl which helps capture the air compressed by the vehicle fuselage and the engine ramps. The major components of the engine are inlet, isolator, combustor, and nozzle. The combustor section experiences the highest heat flux. The nozzle, isolator and inlet experience lower heat fluxes, and among them, the inlet experiences the lowest heat fluxes. The typical ramp heat fluxes of a scramjet vary from 2 to 20 MW/m2. As shown in the upper portion of Fig. 1 [9], the cooling channels are the rectangular ducts encircling the thermal structure of engine and they can be described using channel width (W), channel height (H), fin thickness (t), and heated wall thickness (s).
t T U u W x Z
l m r
time, s temperature, K voltage, V velocity, m/s width of the cooling channel, m axial coordinate, m conversion of fuel thermal conductivity of metal wall material, W/(m.K) dynamic viscosity, Pa s fuel density, kg/m3
Subscripts c coolant ci coolant inlet co coolant outlet crack cracking reaction f fuel g gas j segment number w wall wc coolant side wall wg gas side wall
As shown in Fig. 1, the working process of the cooling system can be described as follows: the fuel of the engine is firstly pumped into the cooling channels to fully cool the thermal structure of the engine, and then the heated fuel is injected into the combustor as propellant to generate the thrust. In order to avoid the deterioration of heat transfer caused by boiling phenomenon, the pressure in the cooling channels is kept above the critical pressure of the fuel. 3. Computational model A one-dimensional model is usually used to study the flow and heat transfer characteristics of a reactive flow and to design the structure of a cooling channel [10]. A one-dimensional flow and heat transfer model with the cracking reaction taken into consideration is used in this article to study ways and means to control the utilization of fuel heat sink. During either the calculations or the experiments reported in this paper, the coolant is working under supercritical condition to avoid the deterioration of heat transfer. Under the supercritical pressure, the phase of fuel changes continually without boiling. Ward et al. built a numerical model to simulate the flow and heat transfer characteristics of aviation fuel under supercritical conditions, and boiling phenomenon is not considered to exist under such conditions [11]. In addition, the thermodynamic properties of fuel change greatly along with the increase in temperature, especially when the temperature is near the critical point. So the real thermodynamic properties of fuel must be considered. The properties of fuel and its cracked products are obtained from National Institute of Standards and Technology (NIST) Thermodynamic and Transport Properties of Pure Fluids database and NIST Chemistry Web Book [12]. 3.1. Geometry model and basic assumptions
Fig. 1. Schematic of scramjet engine with typical heat fluxes.
As shown in the upper portion of Fig. 1, the cooling jacket of a scramjet is composed of many single rectangular cooling channels. With a usual and reasonable assumption, coolant flow and heat flux are assumed to be uniform across the cross section of a scramjet [13]. Under such an assumption, the fuel mass flow rate and heat flux of each single channel are the same, and so, a single
J. Qin et al. / Energy 49 (2013) 459e468
cooling channel with constant area and rectangular duct geometry is used as the study object and shown in Fig. 2. The basic analysis method employed here is assumed to be a steady state quasi one-dimensional energy balance across the regenerative cooling jacket. To further simplify the analysis, an analytical model is developed under the following assumptions: 1) All the energy transferred across the coolant wall is absorbed by the coolant; 2) The wall-conduction in the axial direction is negligible; 3) The flow is fully developed; 4) All the thermophysic properties are regarded as different under different pressures and temperatures, and they are got using interpolation method from NIST database. The flow conditions of coolant are evaluated at the exit of each segment. 3.2. Energy balance in cooling channel For per unit mass endothermic hydrocarbon fuel, the heat transfer loss between fuel and engine wall in the cooling passage is ignored. The endothermic hydrocarbon fuel completes the cooling through both physical and chemical heat absorptions. There is
Q ¼ Qphy þ Qchem
(1)
where Qphy is the physical heat absorption and Qchem is the chemical heat absorption. As the pyrolysis reaction proceeds, the amount of smaller carbon molecules gas gradually increases, and the composition of cracked mixture changes simultaneously. Once a pyrolysis reaction takes place, the fuel becomes more degraded, with olefins initially appearing and the fuel in the cooling passage becomes a mixture of pyrolysis products and uncracked fuel. The percentage of each component in the cracked fuel mixture varies with conversion Z. Upon completion of a pyrolysis reaction, there is physical heat P absorption ( CpDT) which consists of the heat absorption of unreacted fuel and the heat absorption of pyrolysis products. The chemical heat absorption can be given by
Qchem ¼ Z$Hchem
(2)
where Hchem is the endothermic reaction heat, i.e. the heat absorbed by per unit mass fuel when it is fully cracked. As shown in the lower portion of Fig. 2, a typical segment with inlet temperature Tj and pressure Pj is subjected to heat flux qw. The following energy balance equation can be used together with the surface heat flux equation to calculate the outlet temperature of segment j with width W.
Qj ¼ qw ðxÞj WL
(3)
The outlet temperature of the segment is co-decided by physical heat absorption and chemical heat absorption. A reasonable fuel
461
temperature makes Eq. (1) tenable, and so, the level of physical and chemical heat absorptions and their proportion to the total heat absorption can be determined. 3.3. Convective heat transfer and flow model Once the coolant temperature is determined, the temperature distribution throughout the cooling channel can be evaluated. And Newton’s Law of cooling can be used to find the surface temperature,
Qj ¼ hj Tj;wc Tj;a AC
(4)
where AC ¼ WL is the non-finned convecting surface area shown in Fig. 2. And the properties of coolant can be evaluated at average temperature (Tj,a) throughout the segment. The next step is to calculate the film coefficient for convective heat transfer using the published correlations. The effects of boiling phenomenon on the heat transfer are neglected because the fuel works under supercritical condition. It is pointed out in Ref. [14] that classical heat transfer correlation can be applied to fuels JP-7, JP-8, JP-8þ100, JP-10 and RP-1 before the cracking reaction occurs. It is found by researchers in MIT that the heat transfer coefficient after cracking reaction is bigger than that before cracking reaction [15]. What is more, when a classical heat transfer correlation is adopted in the cracking zone of an endothermic hydrocarbon fuel, the relative error between experimental and calculated results is too large (nearly 50%) to be accepted [16]. Considering the complexity of heat transfer characteristics of fuel in cooling channel when cracking reaction occurs, before cracking reaction occurs, a heat transfer correlation without considering chemical reaction is taken from Ref. [17] and shown below.
0:333 Nu ¼ 0:027Re0:8 c Prc
mf mw
0:14 Tf < Tcrack
(5)
The heat transfer correlation of hydrocarbon fuel under the operating condition with a chemical reaction is modified using the experimental data as reported in Ref. [4]. The difference between gas side wall temperature Twg and coolant side wall temperature Twc can be given by
Qj ¼
l s
Twg Twc
(6)
where l is the thermal conductivity of wall material (superalloy). It is considered to vary with temperature and its value is given using an interpolation method according to Table 2. The coolant pressure drop can be estimated using DarcyWeisbach equation [18] and the equation does not take the effect of boiling on pressure drop into consideration because the fuel works under a supercritical condition.
DP ¼ ff
rLu2 2D
(7)
3.4. Properties of fuel
Fig. 2. Schematic of single cooling channel.
3.4.1. Description of fuel n-Decane is chosen as a fuel compound for the present study because it is a typical pure liquid hydrocarbon fuel with 10 carbon atoms in its molecule. It is the main component of hydrocarbon fuel and has carbon number and properties similar to those of liquid hydrocarbon material commonly used in aerospace applications. What is more, Ward et al. used n-Decane as the object for study because it has critical pressure, temperature and product distribution
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J. Qin et al. / Energy 49 (2013) 459e468
Table 1 Distribution of pyrolysis products of n-Decane. No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Name
Formula
Hydrogen Methane Ethane Ethylene Propane Propylene n-butane Butane 1-pentene n-pentane 1-hexene n-hexane 1-heptene n-heptane 1-octene n-octane 1-nonene n-nonene
H2 CH4 C2H6 C2H4 C3H8 C3H6 C4H10 C4H8 C5H10 C5H12 C6H12 C6H14 C7H14 C7H16 C8H16 C8H18 C9H18 C9H20
Ea RT
k ¼ A$e
Mass fraction 80 ml/min, 3 MPa
Mass fraction 80 ml/min, 5 MPa
e 0.0301 0.1241 0.1773 0.1042 0.2532 0.0468 0.1662 0.0296
e 0.0295 0.1370 0.1634 0.1333 0.2361 0.0764 0.1678 0.0171
0.0236
0.0137
0.0204
0.0118
0.0157
0.0090
0.0088
0.0050
Nout ¼ Nin ekt
(8)
where vg and vres are the stoichiometric coefficients. The cracking rate constant is generally a function of fuel temperature. In addition, according to Arrhenius expression, reaction rate k can be expressed as
100
200
300
400
500
600
700
800
900
l/W m2 K1 11.3 12.56 14.24 15.49 16.75 18.42 19.68 21.35 23.02
(11)
where, Nin is total mole number of unreacted n-Decane at the inlet of each calculation segment, t is the time when fuel flows over the unit length. So it can be concluded that the thermal cracking rate is influenced by the flowing characteristic time. It can be seen through the further investigation of Eq. (11) that only the time that the fuel flows from the position the fuel starts to crack to the cooling channel exit has effect on the cracking reaction, so that time is defined as effective residence time and can be given by
ZXout
seffect ¼
1 dx u
(12)
Xcrack
where seffect is the effective residence time. 4. Validation of model For the flow and heat transfer procedure of hydrocarbon fuel with cracking reaction under supercritical condition, the reaction rate and the products of reaction have their significant effect on the flow and heat transfer characteristics. In this paper, the cracking process is approximated as an overall reaction process and the percentage of cracked products does not vary with temperature and pressure. However, in a real system, the reaction varies with temperature and pressure. So it is necessary to verify
Table 3 Reaction rate constants. Parent fuel Ward et al. P ¼ 3.45 MPa and T ¼ 500e600 C Ward et al. P ¼ 3.45e11.38 MPa and T ¼ 550e600 C Stewart et al. P ¼ 2.96 MPa and T ¼ 440e535 C Jiang QIN et al. P ¼ 3 MPa and T ¼ 300e650 C
Table 2 Variation of thermal conductivity of GH3128 along with temperature. T/ C
(10)
where N is the mole number of unreacted n-Decane. From Eq. (10), the total mole number of unreacted n-Decane at the outlet of each calculation segment can be given by
3.4.2. Composition of cracked products An endothermic reaction known as thermal cracking occurs when n-Decane is heated to a temperature above 773 K. The details of product distribution got from our measurements on the experimental table are shown in Table 1 and the values in the table are average over many experiments. The PPD (proportional product distribution) model built by Ward et al. [11] is adopted in this paper. The products and their distribution in a general PPD model are kept unchanged while the pressure and the temperature change at a conversion below 35%, and the relative error can be lower than 3%. In this paper, the PPD model is used at a conversion above 35%, the relative error is higher than that of Ward because of the effect of a secondary reaction which occurs under a higher conversion. However, on the basis of Ward’s work, the PPD model is validated using our own experimental data. The relative error is within 15% even if the conversion is as high as 70% and it is still acceptable in this paper because this paper focus on the utilization of fuel heat sink, not the chemical kinetic model. According to the general PPD model based on experimental data used in this paper, the percentage of cracked products does not vary with temperature and pressure. The cracking process can be approximated as an overall reaction which can be expressed as
where A and Ea are given in Table 3. The values of A and Ea in Table 3 are got from the previous study and our own experiments. Using the value derived from our experiments, the results of the model are in good agreements with the experimental data. The validation was carried out and shown in the following part. The reaction rate of Eq. (8) is assumed to be of the first order. The variation of Arrhenius form, the unreacted n-Decane with a total mole number can be given by
dN ¼ kN dt
similar to those of a real jet fuel [11]. Therefore, the results obtained with n-Decane might be extended to other hydrocarbon fuel with just minor modifications. What is more, the present study focuses on the fundamental aspects of heat sink utilization, so it is proper to use nDecane as project for the study. The chemical formula of n-Decane is C10H22 and the critical temperature and critical pressure of n-Decane are 617.7 K and 2.11 MPa respectively.
n Decane/vg gases þ vres residual
(9)
f
Jiang QIN et al. P ¼ 5 MPa and T ¼ 300e650 C
neDecane Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1 Activation energy kcal/mol A factor A, s1
Ea,
63
Ea,
2.1 1015 63
Ea,
1.6 1015 64 2.4
Ea,
1.10 1015.91.5 60.2
Ea,
1.6 1015 58.8 1.7 1015
J. Qin et al. / Energy 49 (2013) 459e468
the computational model to see if it can be used to get the convincing results. 4.1. Experimental apparatus As shown in Fig. 3, an experimental set-up is built and used to investigate the flow characteristic, heat transfer and cracking characteristics of hydrocarbon fuel under supercritical conditions. A system with electric heating is used for the present study because the system can be used to simulate the real heating procedure in the engine. The heat flux and characteristic size of the cooling passage are in good agreement with those of a real engine. The system can be used for the study of pyrolysis reaction regimes over a long period. The facilities consist primarily of a fuel reservoir, a fuel pump, a fuel reactor (tube), an electric heating power and a fuel cooler. The test section is a GH3128 superalloy pipe and it can be easily used to heat fuel to 1000 K. The pump is a constant-flux pump which can be used to provide a constant and continuous flow flux. The flow rate is not affected by the load pressure, and it has a safety pressure as high as 40 MPa. The range of flow is from 0 to 80 ml/min. The test section is a 1 m long pipe with an inner diameter of 1 mm and an outer diameter of 3 mm, and it is horizontally placed on an experimental table. The two ends of the pipe are wrapped with two copper electrodes. The pipe is heated using a direct current supply, and it has the power of 3 kW. The power used to heat the pipe can be adjusted by changing the voltage and electric current. There is no insulation around the pipe to avoid thermal loss. Heat leakage is calibrated by heating the pipe without fuel flowing through. Fuel is nitrogen-purged to remove the dissolved oxygen to improve the thermal stability of fuel. The entire system is purged with nitrogen prior to the introduction of fuel. Downstream the reactor, the products are quenched in a waterfed heat exchanger to room temperature and filtered before passing through a needle valve (back pressure valve) to regulate the system pressure. The needle valve can be used to ensure that the back pressure of the system can be kept constant during the experiment. The pipe wall temperature distribution is measured using Ktype thermocouples spot-welded to the outside surface of the pipe. The fuel temperatures at the inlet and outlet of the pipe are measured using a thermocouple inserted into the flow of fuel. Fuel
463
pressure is measured with the pressure gauges installed at the outlet of the pump and the upstream back pressure valve. The uncertainty associated with the measurement of wall temperature and the temperature of fuel is estimated to be less than 3 K, whereas that of pressure measurement is less than 1%. All the experimental data are recorded via a data acquisition system for analysis. The liquid and gaseous components of fuel are separately metered and analyzed. The gas products are analyzed using a gas chromatograph/mass spectrometry (GC7900/MS), which consists of flame ionization and thermal conductivity detectors, and the liquid portion of the stressed fuel is analyzed by liquid chromatography (LC). 4.2. Experimental procedure With a test section installed and tested for leak, tests were conducted by first purging the reactor pipe with nitrogen to remove any oxygen. The flow rate used in the experiments is 80 ml/min. Constant outlet pressures of 3 MPa, 4 MPa and 5 MPa were maintained throughout the experiment using a back pressure valve. The flow was pumped into (1 mm i.d.) GH3128 superalloy pipe. With fuel flow established, data logging was initiated and electrical power was supplied to the test section, and voltage was adjusted to obtain the desired exit fuel temperature. Once the outlet temperature of fuel reached its target value, the test was ran for a desired period of time or until the pipe was plugged with coke. Minor adjustments were made in the back pressure valve during the run to maintain a relatively constant pressure throughout the test. While there is no coking, the highest temperature of the fuel is 923 K throughout the experiment. 4.3. Experimental analysis procedure 4.3.1. Analysis of cracking products composition and conversion Cracked fuel comes out from the pipe and enters into the cooler, and gas and liquid components are separated one from another when cracked fuel flows out from the cooler. The volume flow of gas component is measured with a gas rotameter, and components of cracked products are online analyzed by gas chromatography. The liquid products are collected into a liquid collector and then analyzed by GCeMS. These analyses above include the volumetric
Fig. 3. Single tube test apparatus schematic.
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flow rate of gas component V, specific composition of gas products (CH4, C2H4 and C2H6 et al.) and the corresponding mole fractions (va, vb, vc et al.); the mass flow rate of liquid component ml, including the specific composition of liquid cracking products (C4þ and C5þ et al.) and the corresponding mole fractions (v1, v2, v3 et al.), and the mass flow rate of remaining non-cracking fuel and corresponding mole fraction vres. The expression of fuel conversion can be given as shown below
Z ¼
1
ml vres mg þ ml
100%
(13)
4.3.2.2. Calculation of physical and chemical heat absorption. The unit mass total heat absorption of fuel is equal to the difference between the heating power and the heat loss, and it can then be used to divide the mass flow rate of fuel:
hf ¼
UI Qs mf
The total heat absorption of fuel is composed of physical and chemical heat absorption which is expressed by Eq. (1). Once a cracking reaction takes place, physical heat absorption is composed of the heat absorption of unreacted fuel and the heat absorption of cracking products as shown below.
where, the quantity of gas components can be given by
mg ¼ ðMa va þ Mb vb þ Mc vc þ :::Þ$V=22:4
(14)
where, mg e quantity of gas components; ml e quantity of liquid components; Ma, Mb and Mc e molar mass of gas components. 4.3.2. Analysis of fuel heat sink Before the cracking of hydrocarbon fuel, the fuel has only the capacity of physical heat absorption. Once cracking reaction occurs, the heat absorption capacity of endothermic hydrocarbon fuel includes physical and chemical heat absorption. In order to distinguish physical heat absorption from chemical heat absorption of hydrocarbon fuel, the following methods can be used to obtain the physical and chemical heat absorption. 4.3.2.1. Calculation of dissipated heat. Most of the heating power is absorbed by fuel, and little of the heating power dissipates to air through the heated tube wall. In order to obtain the quantity of heat absorbed by fuel, the heat loss of heated tube should be firstly obtained. The relationship between heat loss of heated tube and wall temperature can be analyzed as shown below. The tube is firstly heated without fuel to obtain the heat loss of heated tube. The heat absorbed by the heated tube is considered to be all dissipated to air when the heat balance is reached, because there is no fuel flowing through the tube. The relationship between the heat loss and the tube wall temperature can be obtained using the wall temperature and the heating power. Therefore, heat loss of tube Qs will be obtained at the same heated wall temperature in the actual heating process.
(15)
Qphy ¼
N X
"
j¼1
# vs Cps þ Z vc Cpc DT ð1 ZÞ s¼1 c¼1 C X
S X
Tj
Here the typical heat absorption temperature region is divided into calculation cells and the temperature increment of each cell is DT, N is the total number of calculated cells. And the average specific heat at a constant pressure of each component and the conversion is obtained from the outlet temperature of each cell. The chemical heat absorption of fuel is equal to the difference between the total fuel heat absorption obtained using Eq. (1) and the physical heat absorption obtained using Eq. (16). What is more, when the chemical heat absorption and the conversion of fuel Z is got from the experimental data, Hchem we defined in Section 3.2 can be calculated using Eq. (2) and the comparison between the Hchem calculated using the experimental data and the Hchem calculated by the composition measurements is carried out. 4.4. Results of validation Validation is conducted with a mass flow rate of 1 g/s, pressures of 3 MPa, 4 MPa, 5 MPa and a length of 1 m. The inner and outer diameters of the pipe are 1 mm and 3 mm. The operating condition and characteristic size of the pipe are in good agreement with those of the cooling passage in a real engine. The conversion and total heat sink of fuel at the exit are shown in Figs. 4 and 5. It can be seen from Fig. 4 that n-Decane starts to
b
a
experimental data calculation results
70
calculation results experimental data
50
Z(conversion, %)
Z(conversion, %)
60
40
30
50 40 30
20 20
10
10 0
0 773
823
873
923
Tout(fuel exit temperature, K)
3MPa
973
(16)
750
800
850
900
Tout(fuel exit temperature, K)
5MPa
Fig. 4. Conversion comparison of experimental data with calculated result.
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J. Qin et al. / Energy 49 (2013) 459e468
x 106
3
3.5 experimental data calculation results
hf(fuel heat sink, J/kg)
hf(fuel heat sink, J/kg)
2 1.5 1 0.5 0
0
x 106 experimental data calculation results
3
2.5
465
2.5 2 1.5 1 0.5
373
473 573 673 773 873 Tout(fuel exit temperature, K)
973
a 3MPa
0 300
400
500
600
700
800
900
1000
Tout(fuel exit temperature, K)
b 5MPa
Fig. 5. Heat sink comparison of experimental data with calculated result.
crack when the temperature is higher than 773 K and the conversion increases along with the temperature at the pipe exit. As shown in Fig. 4, the results of the computational model is rather accurate and the relative error is within 15% under the experimental pressures. It can also be seen from Fig. 5 that the total heat sink increases approximately linearly along with the pipe exit temperature when the pipe outlet temperature is lower than 773 K, and the slope of the curve at each point is determined by the specific heat which varies with temperature and pressure. When the pipe outlet temperature is higher than 773 K, cracking reaction occurs, and the increasing rate of the total heat sink is greatly improved because the total heat sink consists of physical heat sink and chemical heat sink at this time. As shown in the figures, before cracking reaction occurs, the result obtained with the computational model matches well with the experimental result, with a relative error within 2%. While the relative error becomes larger when cracking occurs because PPD (proportional product distribution) mechanism is adopted in the computational model. In a PPD mechanism, the distribution of reaction products is assumed to be the same at different temperatures and pressures, which is not the situation in a real cracking reaction. However, the relative error is within 15%, which is acceptable for this study. It should be pointed out in particular that, before cracking reaction occurs, the heat transfer coefficient got from the computational model matches well with the experimental result, with a relative error within 15%. After cracking reaction occurs, the relative error becomes unacceptable. This is in line with what is reported in Ref. [14] and Ref. [16]. The researchers pointed out that classical heat transfer correlation can be used before cracking reaction occurs while the relative error between experimental result and calculated result is too large (nearly 50%) to be accepted when a classical heat transfer correlation is adopted in the cracking zone of endothermic hydrocarbon fuel. The heat transfer correlation is thus modified to get a more acceptable heat transfer coefficient based on experimental and theoretical similarity. However, because of the complexity of heat transfer characteristics the cracking reaction brings, it is hard to get a widely accepted heat transfer correlation up to now. In this paper, the precision of heat transfer correlation is not a key factor, so the heat transfer coefficient obtained using the computational model is considered acceptable.
5. Results and discussion 5.1. Selectivity of control methods It can be seen from Eqs. (9) and (11) that main factors having their effect on the heat absorption capacity of fuel by influencing the conversion of pyrolysis reaction are the temperature and flow velocity of fuel. According to the previous study, the residence time of fuel is the primary factor that determines the fuel heat sink [4]. So, in order to control the endothermic reaction process, the possible control parameters must be capable of having effect on the residence time of fuel. It can be seen through the careful observation of the working characteristics of fuel cooling process that either the design or the operation parameters of a cooling system can be used to control the utilization of fuel heat sink on the following two aspects: 1) The operation parameters of a cooling system, which mean the mass flow rate and the operating pressure of fuel in a cooling channel; 2) The design parameters of a cooling system, which mean the width and height of a cooling channel. 5.2. Design parameters of a cooling system The variation of channel in size has its effect on the velocity of fuel along the channel, and then on the residence time throughout the channel, which leads to the change in the utilization of fuel heat sink. In this paper, the height of channel is chosen as a major design parameter for the study on the effect of channel size on the utilization of fuel heat sink. The width of channel is not chosen as a major design parameter because the specific structure of an engine and the total number of channels should also be considered if the width of a channel is chosen. The change in channel width will indirectly change the total number of cooling channels across the section, thus the mass flow rate of fuel will be redistributed in each cooling channel. As shown in Fig. 6, the conversion of fuel increases with the increase of channel height (the highest conversion calculated here is as high as 80%, higher than the validated data which is confined by the experimental conditions, so the relative error here is larger),
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J. Qin et al. / Energy 49 (2013) 459e468
0.9
0.8 H=1mm H=1.5mm H=2.5mm
m=0.55g/s m=0.5g/s m=0.6g/s
0.8 0.7
0.6 Z(conversion, %)
Z(conversion,%)
0.7
0.5 0.4 0.3
0.6 0.5 0.4 0.3 0.2
0.2
0.1
0.1 0
0
0
10
20
30
40
50 60 x(cm)
70
80
0
10
20
30
90 100
40 50 60 x(cm)
70
80
90 100
Fig. 8. Conversion along the flow direction at different fuel mass flow rates.
Fig. 6. Conversion along the flow direction at different channel heights.
because the decrease of fuel velocity caused by the increase of channel height will increase the entire residence time of fuel in the cooling channel. However, it can be seen from Fig. 7 that the gasside wall temperature increases as the channel height increases, because the heat transfer coefficient decreases with the increase of channel height. Especially, the over-temperature of wall will occur when the channel height is large enough. So, although it is an effective way to control the heat sink utilization of fuel by reasonably designing the channel in size, the limitation of allowable wall temperature must be considered. In addition, it can be seen from Fig. 7 that the rate of increase of the gas-side wall temperature slows down after the fuel flows through some distance along the cooling channel (the same situation as what is shown in Fig. 9). It is because the temperature of fuel increases along with the distance of the cooling channel and when the fuel temperature is sufficient high, the fuel starts to crack, leading to an increase of the fuel’s heat absorption capacity per unit increase in temperature. The increased heat absorption capacity makes the rate of the increase of the fuel temperature slow down and the difference between the fuel temperature and the gas-side wall temperature is not affected at the same time, so the gas-side wall temperature also has a lower rate of increase when fuel starts to crack. 5.3. Operation parameters of cooling system In this paper, according to the characteristics of the experimental apparatus and the real scramjet working conditions, the back
pressure is kept constant when the fuel mass flow rate changes and so is the same condition when the back pressure changes. 5.3.1. Fuel mass flow rate As shown in Fig. 8, the conversion increases with the decrease of fuel mass flow rate in that the variation of the fuel mass flow rate has its effect on the temperature and velocity of fuel. The fuel mass flow rate decreases as the flow velocity decreases, and both the residence time of fuel in the cooling channel and the increase in fuel temperature. The effect of fuel mass flow rate on the fuel temperature and velocity increases the conversion of the fuel. However, it can be seen from Fig. 9 that the gas-side wall temperature is very close to the allowable temperature of the wall material when the fuel mass flow rate is 0.5 g/s, because the low velocity of fuel caused by the low fuel mass flow rate can cause a decrease in the heat transfer coefficient and there is an increase in the gas-side wall temperature. So, limited by the allowable temperature of wall material, the fuel mass flow rate cannot be too low, which make the heat sink unable to be fully released, and impose a limit on the ultimate heat sink of fuel. It can be seen from the analysis above that fuel mass rate is one of the ways to control the heat sink utilization of fuel, but it has its effect on the heat transfer characteristics, and it is then limited by the allowable temperature of wall material. What is more, the fuel mass flow rate is also limited by the fuel mass flow rate no matter fuel is used either as coolant or propellant. So, in short, there are many constraints for the use of fuel mass flow rate to control the heat sink utilization of fuel.
1000 H=1mm H=1.5mm H=2.5mm
1050 m=0.6g/s m=0.55g/s m=0.5g/s
1000
900
Twg(gas side wall temperature, K)
Twg(gas side wall temperature, K)
950
850 800 750 700
950 900 850 800 750 700 650
650 600
600
0
20
40
60
80
100
x(cm) Fig. 7. Gas-side wall temperature along the flow direction at different channel heights.
550
0
20
40
60
80
100
x(cm)
Fig. 9. Gas-size wall temperature along the distance at different fuel mass flow rates.
J. Qin et al. / Energy 49 (2013) 459e468 0.8 P=3MPa P=5MPa P=7MPa
0.7
Z(conversion, %)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
20
40
60
80
100
x(cm)
Fig. 10. Conversion of the fuel along the direction at different operation pressures.
467
helpful to lower the gas-side wall temperature, because the increase in operation pressure can affect the properties of fuel such as Cp, indirectly affecting the heat transfer coefficient of fuel. Compared to changing the velocity of fuel by changing the mass flow rate of fuel or the height of channel, only the velocity of fuel in the gas zone is changed when the operation pressure is changed. On one hand, the effect of control method on the heat sink release becomes more obvious, on the other hand, this control method can improve the heat transfer. So, in short, both the performance of heat transfer and the heat sink utilization of fuel benefit from the increase in operation pressure. When fuel is used as coolant at a high pressure, it functions to inhibit the boiling phenomenon and to improve the heat sink utilization of fuel, i.e. avoid the boiling phenomenon in the liquid zone and enhance the heat absorption capacity in the cracking zone. 6. Conclusion
It should also be pointed out in particular that the control of fuel mass flow rate is still a very important way to protect the engine from being burnout while fuel is used as coolant. During a practical operation of a scramjet, the engine can be prevented from being overheated by adjusting the fuel mass flow rate in accordance with the heat load and wall temperature. 5.3.2. Operating pressure in cooling channel It can be seen through further analysis that by controlling both the mass flow rate of fuel and the height of channel, the global velocity of fuel can be controlled, i.e. the time for the fuel to flow through the entire cooling channel, including both noncracking zone and cracking zones. However, only the time when the fuel temperature is higher than the start temperature of pyrolysis reaction has its effect on the heat sink utilization of fuel. Besides, the decrease of the velocity of fuel in the noncracking zone results in the deterioration of heat transfer, and overtemperature is then easy to occur and the heat sink utilization of fuel is limited. So, a control method which has its effect on the velocity of the fuel in the gas zone only should be found. Due to the fact that the density of fuel is proportional to the pressure of fuel in the gas zone under ideal condition at a constant temperature and it is barely affected by the variation of pressure while fuel is in the liquid zone, a control method is introduced to control the heat sink utilization of fuel by changing the operating pressure of fuel. As shown in Fig. 10, the conversion of fuel increases with the increase of operation pressure, because the velocity of fuel in the gas zone decreases with the increase in pressure and the variation of operation pressure only affect the velocity of fuel in the gas zone (Fig. 11). Meanwhile, the increase in operation pressure is very
In order to study the methods to control the heat sink utilization of hydrocarbon fuel and their actual control effects, scramjet is chosen as the object of study and a one dimensional model of the flow and heat transfer process in a single cooling channel in terms of cracking reaction is constructed and validated through experiments. Different schemes are worked out to control the heat sink utilization of fuel by changing the mass flow rate of fuel, the operating pressure of fuel, and the size of cooling channel. Effective residence time, which is the dominant part of the whole residence time in deciding the level of heat sink utilization, is defined to distinguish global method and local method. The heat sink control methods are classified into global and local methods in terms of their effect on effective residence time, in which a local method can only influence the effective residence time. Controlling the fuel mass flow rate and the channel size are regarded as global methods and controlling the operating pressure of fuel is classified as a local method. Local methods cannot only control the heat sink utilization, but also improve the heat transfer and pressure drop performance of fuel. The study results have shown that the control methods can effectively improve the level of fuel heat sink utilization. The conclusion of the control methods of heat sink utilization has guidance on the design of cooling channel and the operation of a cooling system. Acknowledgment This work was supported by National Natural Science Foundation of China (General Program, No. 51106037), for Distinguished Young Scholars (No. 50925625) and for Innovative Research Groups (No. 51121004), and the authors thank the reviewers for their valuable advice on this paper.
20
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P=3MPa P=5MPa P=7MPa
18 16 u(fuel velocity,m/s)
14 12 10 8 6 4 2 0
0
20
40
60
80
100
x(cm)
Fig. 11. Fuel velocity along the direction at different operation pressures.
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