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Flow rate distribution of cracked hydrocarbon fuel in parallel pipes
Fuel 161 (2015) 105–112
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Flow rate distribution of cracked hydrocarbon fuel in parallel pipes Jiang Qin a, Yuguang Jiang a, Yu Feng a, Xiaojie Li a, Haowei Li a, Yaxing Xu a, Wen Bao a,⇑, Silong Zhang a, Jiecai Han b a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China
h i g h l i g h t s Mal-distribution of coolant causes a waste of heat sink and even over-temperature. Distribution of cracked hydrocarbon fuel in parallel pipes are studied. Two flow rate deviation amplification mechanisms are found. The mal-distribution mode varies with thermal deviation. Higher pressure suppresses the mal-distribution.
a r t i c l e
i n f o
Article history: Received 8 April 2015 Received in revised form 2 August 2015 Accepted 10 August 2015 Available online 17 August 2015 Keywords: Flow distribution Parallel pipes Hydrocarbon fuel Supercritical pressure
a b s t r a c t A model consisting of two parallel pipes with common inlet and outlet manifolds was established and used to run simulation and experimental study on the flow rate distribution of cracked hydrocarbon fuel in parallel pipes under supercritical pressure. Both simulation and experimental results indicated that mass flow rate and fuel temperature distribution of cracked hydrocarbon fuel in parallel pipes was closely related to the difference in fuel density in pipes. Two deviation amplification mechanisms were found. In addition, the mode of mal-distribution varies with thermal deviation and the distribution was effectively improved by the increase of pressure. And the total mass flow rate could hardly have any effects on the flow rate distribution. All these results could be used to help the full utilization of fuel heat sink and avoid over-temperature. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Scramjet is a promising propulsion system for hypersonic missile and reusable air-space integrated fight vehicle [1,2]. Due to high flight Mach number, the combustion temperature and heat transfer rate of a scramjet are very high. Thus, cooling becomes a major concern. Regenerative cooling is generally accepted as the most promising method [3]. Considering limited quantity of fuel on board, endothermic hydrocarbon fuel with extra chemical heat sink is used to further increase the cooling capacity [4–6]. Fuel flows through the parallel cooling channels as coolant to cool the wall before it’s injected into the combustor [7,8] while a supercritical pressure is kept in the channels to avoid boiling crisis. However, heat flux is not uniform or constant in the wall of a scramjet, which may lead to the mal-distribution of mass flow rate ⇑ Corresponding author at: 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.fuel.2015.08.015 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.
and fuel temperature in different channels. As a result, fuel heat sink is not fully utilized in the low temperature channels. Overtemperature may occur in the high temperature channels to cause thermal protection failure and damage to engine structure. Therefore, it’s of great significance to study the flow rate distribution of cracked hydrocarbon fuel in parallel channels under supercritical pressure so that the fuel heat sink could be fully utilized to avoid over-temperature. Much work has been done in recent years on boiler, solar power generator [9,10] and fuel cell [11,12] continuously, since the distribution characteristics are important to the safety and efficiency of above mentioned applications. Structure of inlet and outlet manifold has been another focus for the study on the flow rate distribution characteristics [13,14] of fluids including water, carbon dioxide and other refrigerants. Due to pyrolysis, the flow and heat transfer of hydrocarbon fuel is quite different from other fluids [15,16]. A lot of work has been done on the pyrolysis of hydrocarbon fuel through single heated channel experiments [17–20] to improve its chemical heat sink [21,22] and to avoid thermal oxidation coking [23,24].
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Nomenclature mt mA mB
q u h CP
l f qf DP Re d Hc k A Ea Ac
Ah Ainner Kc Kh DQ Dm DT f Dq Y R
total mass flow rate (kg/s) mass flow rate of pipe A (kg/s) mass flow rate of pipe B (kg/s) density of fuel (kg/m3) velocity of fuel (m/s) enthalpy (J/kg) constant-pressure specific heat (J/(kg K)) dynamic viscosity (Pa s) friction coefficient heat flux (W/m2) pressure drop (Pa) Reynolds number surface roughness chemical heat sink (J/kg) chemical reaction rate constant (s1) pre-exponential constant (s1) activation energy (J/mol) flow area of throttle in cold end (m2)
flow area of throttle in hot end (m2) flow area of pipe (m2) throttle coefficient for cold end throttle coefficient for hot end thermal deviation deviation in mass flow rate deviation in fuel temperature deviation in density mass conversion of reactant universal gas constant (J/(mol K))
Subscripts lc local resistance at cold end lh local resistance at hot end f frictional resistance 1 heating power Q 1 2 heating power Q 2
So far, the research on flow rate distribution of cracked hydrocarbon fuel in parallel channels is hardly found. Only Ran et al. (2012) studied the flow distribution of kerosene in parallel pipes before pyrolysis occurs [25]. A model consisting of two parallel pipes was established and used to run simulation and experimental study on the flow rate distribution of cracked hydrocarbon fuel in parallel pipes under supercritical pressure and the influences of thermal mal-distribution, pressure and total mass flow rate as well. 2. Modeling with parallel pipes 2.1. Geometry model and hypotheses In the scramjet, there’re usually hundreds of parallel cooling channels through which fuel flows to cool the thermal structure at a temperature of 300–1000 K. Two parallel pipes are used in the model as simplified cooling channels of scramjet, since the close-coupled characteristics of mass flow rate and fuel temperature is clearly presented in this configuration. Similar simplifications are common in studies about parallel systems [9,10]. The following are the hypotheses used by the modeling: (1) The radial difference in all parameters is ignored. (2) The kinetic energy and heat generated by the viscous effect of hydrocarbon fuel is ignored. (3) Channels are horizontal and gravitational potential energy of hydrocarbon fuel is constant. (4) Axial heat conduction of hydrocarbon fuel is ignored. (5) The effect of coke is ignored since the high flow velocity set in this work. 2.2. Mathematical model
Momentum conservation equation can be written as:
@ qu2 1 f 2 @P ¼ qu @x 2d @x
ð2Þ
where d is the equivalent diameter of a pipe and f is the friction coefficient.
@ ðquhÞ 4 ¼ qf q ð1 Y Þ k Hc @x d
ð3Þ
where Y is the mass conversion of reactant. Hc is the chemical heat sink of fuel. Hydrocarbon fuel is a complex mixture with most of its components following the complicated mechanism of pyrolysis including hundreds of species and reactions with possible interactions. In order to highlight the characteristics of mass flow rate distribution instead of the detailed chemical kinetic processes, the model is simplified using n-dodecane, one of the main components of hydrocarbon fuel and used in many related researches [26–28]. In addition, pyrolysis is considered as the first order reaction and global chemical mechanism is adopted. PPD assumption is used to describe the products of pyrolysis [29]. So the conservation equation of cracking products for ndodecane can be expressed as:
@ ðquY Þ ¼ q ð1 Y Þ k @x
ð4Þ
where k is the chemical reaction rate. Additional equations of physical properties based on NIST database are required to form a complete system. The density and constant-pressure specific heat of the mixture can be calculated from the mole percentage.
P xi q i P C p ¼ xi C p i
q¼
ð5Þ
A homogeneous one dimensional model was developed to demonstrate the steady state solution of mass flow rate and temperature distribution. The common inlet and outlet ensures the two parallel pipes an equal pressure drop and the total mass flow rate is set to be constant. Mass conservation equation can be expressed as:
This model is mainly used to qualitatively analyze the characteristics of the mass flow rate distribution of hydrocarbon fuel by using n-dodecane.
@ ðquÞ ¼0 @x
As shown in Fig. 1, two high temperature alloy pipes with an inner diameter of 2 mm were used to simulate the parallel cooling channels. China No. 3 kerosene (RP-3) was used as the fuel and
ð1Þ
3. Experimental set-up
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J. Qin et al. / Fuel 161 (2015) 105–112
Fig. 1. Schematic diagram of the experimental set-up.
900 800 700 600 500 400
200
10
15
20
25
Fig. 2. Comparison of outlet fuel temperature from model and experiment with thermal deviation 1.1.
13 12 11 10 9
ð7Þ
T fB T fA T fA
ð8Þ
7
The deviation in density is expressed as follows because of its significant effect on the flow rate distribution. qA and qB is respectively the fuel density at the outlet of pipes A and B.
6
qA qB qA
5
Total Heating Power (kW)
mA mB mB
DT f ¼
0
ð6Þ
where Q A and Q B are the heating power of pipes A and B respectively. Pipe B is considered as the deviation pipe for a larger heating power, while pipe A the standard pipe. The deviations caused by thermal non-uniformity are expressed as shown below. T fA and T fB is respectively the fuel temperature at the outlet of pipes A and B.
Dm ¼
Model solution of deviation pipe Model solution of standard pipe Experiment results of deviation pipe Experiment results of standard pipe
300
Mass Flow Rate (g/s)
QB QA QA
DQ ¼
1000
Fuel Temperature (K)
supplied through a ram pump and adjusted through a proportional valve. The heating power was regulated through a power control system to a specified proportion to simulate an uneven thermal load. Finally, the heated fuel was cooled through the water cooler and collected in the back pressure tank with nitrogen filled in advance to maintain a specified back pressure for the system. The total mass flow rate and back pressure of the system were kept constant during an experiment. Pressure sensors (Measuring range: 5 MPa. Accuracy: 0.5%FS) were installed in the inlet/outlet manifold and the back pressure tank. Thermocouples (Type K) were installed at outlet of each pipe to measure the temperature of heated fuel. The accuracy of thermocouples is 0.75% T, where T is the target temperature. Turbine flow meter was installed at the inlet of each pipe to measure the mass flow rate. Under steady-state condition, mass flow rate is equal in the whole pipe. The flow meter at the inlet also indicated the mass flow rate of heated fuel where thermocouple was fixed. The accuracy of the flow meter was 0.5% of the full scale (32.5 g/ s). Besides, the accuracy of power source current and voltage measurement is 0.5%FS (630 A, 44 V). During the experiment, the thermal deviation is achieved by a zigzag form electrode (showed in Fig. 1) as a boundary condition, which can be defined as:
8 Model solution of deviation pipe Model solution of standard pipe Experiment results of deviation pipe Experiment results of standard pipe
0
5
10
15
20
25
Total Heating Power (kW)
ð9Þ
Fig. 3. Comparison of mass flow rate from model and experiment with thermal deviation 1.1.
Figs. 2 and 3 show the comparison of model solution and experimental results with thermal deviation 1.1. Mal-distribution of
mass flow rate and fuel temperature happens when total heating power reaches 10 kW and fuel reaches the pseudo-critical point of kerosene (about 645 K) in pipe B. Then fuel in pipe A approaches pseudo-critical point with total heating power 15 kW, the deviations start to decrease. All deviations increase again with heating power 20 kW, when violent pyrolysis occurs [30] in pipe B. It
Dq ¼
4. Results and discussion 4.1. Model validation
J. Qin et al. / Fuel 161 (2015) 105–112
4.2. Distribution of mass flow rate and changes in fuel temperature in different temperature zones The distribution of mass flow rate is determined by the flow resistance in each pipe, which changes greatly with fuel property. For a certain pressure and geometry, fuel property is mainly determined by fuel temperature. So the whole temperature range should be classified in accordance with fuel property. The critical point of RP-3 is 645.04 K (Pc ¼ 2:33 MPa) [15]. RP-3 begins to crack at about 850 K [31,32]. These two representative points are chosen for classification of temperature zones. In addition, the states of hydrocarbon fuel are further classified into liquid state (<600 K), pseudo-critical state (600–700 K), supercritical state (700–850 K) and pyrolysis state (>850 K). As shown in Fig. 4 and Table 1, the whole range of fuel temperature curves of two heated pipes with thermal deviation 1.1 is classified into 5 zones. 4.2.1. Zone 1: both pipes in liquid state In Zone 1, mass flow rates of two pipes are almost even and fuel temperature in parallel pipes is slightly different due to the thermal deviation.
Table 1 Classification of fuel temperature zones. Zones
Standard pipe
Deviation pipe
Heating power range (kW)
1 2 3 4 5
Liquid state Liquid state Pseudo-critical state Supercritical state Pyrolysis state
Liquid state Pseudo-critical state Supercritical state Pyrolysis state Nearly complete pyrolysis
0–8.5 8.5–13.5 13.5–18.3 18.3–40.0 40.0–
20 18 16 14 12
1100
80
Fuel Temperature (K)
900
Zone5
800
60
Zone4
700 600
Standard Pipe Deviation Pipe 40 Fuel Temperature Deviation Experiment results of standard pipe Experiment results of deviation pipe Experiment results of Fuel Temperature Deviation 20
Zone3
500
Zone2
400 300 Zone1
200
Fuel Temperature Deviation (%)
1000
100 0
0 0
10
20
30
40
50
Total Heating Power (kW) Fig. 4. Outlet fuel temperature of simulation and experiment with thermal deviation 1.1.
80
60
10 8 Zone1
Zone2
40 Zone5
Zone4
Zone3
6 4
20
2 0
4.2.2. Zone 2: with deviation pipe in pseudo-critical state In Zone 2, an obvious deviation occurs in mass flow rate together with fuel temperature (as shown in Fig. 5). At this time, the fuel in the deviation pipe reaches its pseudo-critical point while the density falls rapidly. The velocity and flow resistance increase accordingly. Meanwhile, the fuel in the standard pipe remains in liquid state. The general effect is mass flow rate in the deviation pipe decreases while that in standard pipe increases, which in turn widens the deviation in fuel temperature. A circle of positive feedback arises: the deviation in fuel temperature increases with the increasing deviation in density, which leads to an increase in flow resistance deviation and finally causes larger deviation in mass flow rate. This is the first deviation amplification mechanism which occurs because of the physical changes at pseudo-critical state and follows a positive feedback mechanism. And mal-distribution causes the waste of fuel heat sink.
100 Standard Pipe Deviation Pipe Mass Flow Rate Deviation Experiment results of standard pipe Experiment results of deviation pipe Experiment results of Mass Flow Rate Deviation
Mass Flow Rate Deviation (%)
proves the model can be used to predict the trend of fuel temperature and mass flow rate.
Mass Flow Rate (g/s)
108
0
10
20
30
40
50
0
Total Heating Power (kW) Fig. 5. Mass flow rate of simulation and experiment with thermal deviation 1.1.
4.2.3. Zone 3: with standard pipe in pseudo-critical state In this zone, the fuel in standard pipe goes into the pseudocritical state while the fuel in deviation pipe just goes out. In contrast with Zone 2, the distributions of mass flow rate and fuel temperature become more even, which cause a peak of deviation between Zones 2 and 3. But the deviations don’t drop to zero and so the waste of heat sink continues. 4.2.4. Zone 4: with deviation pipe in pyrolysis state Both deviations begin to increase once again in Zone 4. The temperature of heated fuel in deviation pipe reaches 950 K, at which RP-3 cracks and the density falls rapidly once again. Similar to Zone 2, the positive feedback leads to an enormous increase in deviations in mass flow rate and fuel temperature. The deviation amplification mechanism of Zone 4 is due to the chemical reactions in the pyrolysis state and it follows a more complex positive feedback mechanism that affected by pyrolysis. Since pyrolysis can provides extra heat sink, the waste of heat sink in standard pipe becomes even larger. And the risk of overtemperature in channel wall increases as the temperature deviation broadens. 4.2.5. Zone 5: the state of nearly complete pyrolysis in deviation pipe Considering the possible over-temperature, simulation was used to do the research in higher temperature zone. The thermal deviation was 1.1 and total mass flow rate was 20 g/s. The maximum fuel temperature in the theoretical results is about 1100 K, at which chemical heat sink is almost fully utilized and high temperature alloy almost reaches its limit. As shown in Figs. 4–6, when most of the fuel in deviation pipe cracks, a decrease in deviations of both mass flow rate and density is observed, which causes the second peak of deviations in mass flow rate and density.
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J. Qin et al. / Fuel 161 (2015) 105–112
However, deviation in fuel temperature keeps increasing. That is because the specific heat of fuel decreases sharply with the end of pyrolysis and the enthalpy rise leads to a temperature rise larger enough to neutralize the increase of mass flow rate. It’s extremely dangerous that over-temperature will occur with the increasing deviation in fuel temperature. 4.2.6. Overall analysis It can be seen from the experiment above that: (1) the trend of deviations of mass flow rate and density are similar; and (2) they are both nonlinear and with two peaks. Theoretical analysis is carried out to explain such phenomenon. The flow resistance of each pipe is calculated using Eq. (10).
1
DP ¼
þ
A2inner
2 2dAinner
1
þ ¼x
Lf
2 2 in K c Ac
2q 2
m
q
þ
!
1 2K 2h A2h !
1 A2inner
qin
m2
Dm ¼
mA mB ¼ mA
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB xqB þ yqA qB pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB
xðqA qB Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB xqA þ yqA qB þ xqB þ yqA qB ¼ X Dq
ð13Þ
where X is positive and Dq is the deviation in density. The deviations in mass flow rate and density must have the same trend. Here the first law is explained. As for the 2nd law, when total heating power changes from Q 1 to Q 2 , the mass flow relative deviation can be expressed as shown below:
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq1B þyq1A q1B < Dm1 ¼ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi xq1A þyq1A q1B pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x q þy q q 2B 2A 2B : Dm2 ¼ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq þyq q
qout
m2
þ ym2
Considering the identical geometry of two pipes and the relatively small local flow resistance is in the no-throttle flow configuration, we assume that xA xB ¼ x; yA yB ¼ y. From Eq. (7),
2A
ð10Þ
Subscripts 1 and 2 represent total heating power Q 1 and Q 2 respectively. Fuel density in pipe A changes from q1A to q2A .
Considering the conservation of mass flow rate and pressure drop,
ð14Þ
2A 2B
q2A ¼ q1A þ DqA q2B ¼ q1B þ DqB
ð15Þ
Then
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq1B þ yq1A q1B xq2B þ yq2A q2B @ ðDmÞ Dm2 Dm1 1 ¼ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi @Q Q2 Q1 Q2 Q1 xq1A þ yq1A q1B xq2A þ yq2A q2B 2 x q1B þ xyq21B DqA x2 q1A þ xyq21A DqB þ xyðq1B q1A ÞDqA DqB 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ Q2 Q1 ðxq2A þ yq2A q2B Þðxq1A þ yq1A q1B Þ ðxq2A þ yq2A q2B Þðxq1B þ yq1A q1B Þ þ ðxq2B þ yq2A q2B Þðxq1A þ yq1A q1B Þ
(
m2
m2
A
B
xA q A þ yA m2A ¼ xB q B þ yB m2B mA þ mB ¼ mt
ð11Þ
ð16Þ
The second order infinitesimals are ignored and since the flow resistance effected by heating is dominating in this configuration, there’re x yq1A and x yq1B . Then we obtain that:
Then, the relationship between mass flow rate of each pipe and
DqA DqB @ ðDmÞ q1A q1B ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ @Q ðQ 2 Q 1 Þ q1Ax2q1B ðxq2A þ yq2A q2B Þðxq1A þ yq1A q1B Þ ðxq2A þ yq2A q2B Þðxq1B þ yq1A q1B Þ þ ðxq2B þ yq2A q2B Þðxq1A þ yq1A q1B Þ DqA DqB ¼ Yc
q1A
q1B
ð17Þ
the total mass flow rate can be given by:
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xB qA þyB qA qB < mA ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mt xB qA þyB qA qB þ xA qB þyA qA qB pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xA qB þyA qA qB : mB ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mt xB q þyB q q þ xA q þyA q q A
A B
B
A B
By means of the small deviation linearization, we obtain that
ð12Þ
8 @q > > < DqA ¼ @T f T ¼T f 1A þT f 2A T f 2A T f 1A f 2 @q > > : DqB ¼ @T f T f 1B þT f 2B T f 2B T f 1B Tf ¼
2
ð18Þ
110
J. Qin et al. / Fuel 161 (2015) 105–112
800
70
600
60
500
50 400
Zone5
40
300
30
200
20
100
10
Fuel Temperature (K)
80
Outlet Fuel Density Deviation (%)
700
Outlet Fuel Density (kg/m3)
1000
90 Standard Pipe Deviation Pipe Outlet Fuel Density Deviation
800
600
400 Standard Pipe with Thermal Deviation 1.2 Deviation Pipe with Thermal Deviation 1.2 Standard Pipe with Thermal Deviation 1.4 Deviation Pipe with Thermal Deviation 1.4
0
0 0
10
20
30
40
50
Total Heating Power (kW)
200 0
5
Fig. 6. Outlet fuel density of simulation with thermal deviation 1.1.
f
2
Since @ q=@T f < 0, the absolute value is used for convenience. Q 2 is assumed to be slightly larger than Q 1 , there’s T f 2B T f 1B T f 2A T f 1A . Besides, due to the thermal deviation, when heating power Q 1 , there’s T f 2B > T f 1A ! q1B < q1A . @ q=@T f of hydrocarbon fuel increases rapidly in pseudo-critical area and pyrolysis area. When fuel in deviation pipe and standard pipe crosses pseudo-critical area or pyrolysis area successively, @ðDmÞ=@Q changes from positive to negative, which leads to two peaks of the deviation curves considering Y c > 0.
15
20
25
Fig. 7. Outlet fuel temperature with thermal deviations 1.2 and 1.4.
16 Standard Pipe with Thermal Deviation 1.2 Deviation Pipe with Thermal Deviation 1.2 Standard Pipe with Thermal Deviation 1.4 Deviation Pipe with Thermal Deviation 1.4
14
Mass Flow Rate (g/s)
" @ ðDmÞ DqA DqB 1 @ q ¼ Yc ¼ Yc T T f 1A @Q q1A q1B q1A @T f T f ¼Tf 1A þT2 f 2A f 2A # 1 @ q T T f 1B q1B @T f T f ¼Tf 1B þT2 f 2B f 2B " 1 @ q ¼ Yc T þT T f 2B T f 1B q1B @T f T f ¼ f 1B 2 f 2B # 1 @ q T ð19Þ T f 1A q1A @T f T ¼T f 1A þT f 2A f 2A
10
Total Heating Power (kW)
12
10
8
6
4
0
5
10
15
20
25
Total Heating Power (kW) Fig. 8. Mass flow rate with thermal deviations 1.2 and 1.4.
4.3. Influence of thermal deviation Thermal deviation is very common in parallel cooling channels of scramjet, this paper carried out experiments of thermal deviation 1.1 (analyzed above), 1.2, 1.4 with back pressure kept at 2.5 MPa as shown in Figs. 7 and 8. With thermal deviation 1.2, fuel temperature of deviation pipe reaches 933.9 K. The deviations in mass flow rate and fuel temperature only emerge a single peak affected both transcritical effect and pyrolysis in deviation pipe (positive deviation factors). Increasing of the thermal deviation leads positive mal-distribution factors to gather together and larger deviation occurs (deviation of mass flow rate and fuel temperature respectively 39.1% and 36.36%). When the thermal deviation increases to 1.4, the deviations in mass flow rate and fuel temperature keep increasing through the whole experiment until the fuel temperature of deviation pipe reaches 943.18 K. It can be seen that as the thermal deviation increasing, the maldistribution mode varies. Positive deviation factors emerge together to make the distribution of mass flow rate and fuel temperature more uneven. 4.4. Influence of system pressure As shown in Figs. 9 and 10, when the pressure varies from 2.5 MPa to 3.5 MPa (all pressures are supercritical) with the same
thermal deviation of 1.2, deviations in mass flow rate and fuel temperature decreases, especially in the peak of deviations in pseudocritical area. According to the properties provided by NIST, rapid decrease of density of hydrocarbon fuel in pseudo-critical area disappears when pressure is high enough. So deviation in fuel temperature causes less deviation in density and flow resistance to make the mass flow rate distribution more uniform. The results indicate that the increase of pressure makes distributions of mass flow rate and fuel temperature are more even. 4.5. Influence of total mass flow rate Redistribution of mass flow rate is directly caused by flow resistance that vary with fuel temperature (i.e. hot resistance) is the main reason for mass flow rate mal-distribution. From this perspective, we can analyze the influence of total mass flow rate with ratio of the hot resistance as standard.
2
2
1 1 KmAin þ 12 qin þqoutL 2 f m2in þ Amin q1 q q 2 inner h h out out in DPhot ð 2 ÞAinner d ¼
2
2
2 DP t min min 1 1 1 1 L 1 2 þ f m þ KmAin þ q q þ in K c Ac Ainner qout qin 2qin 2 ð in out ÞA2 2qout h h d inner 2
2
2
1 1 1 L 1 1 þ f þ q1 2qout K h Ah 2 ðqin þqout ÞA2 A q inner out in d inner 2 ¼
2
2
2 1 1 1 1 1 1 L þ f þ 2q1 K 1A þ qout qin 2qin K c Ac Ainner 2 ðqin þqout ÞA2 h h out d inner 2 ð20Þ
J. Qin et al. / Fuel 161 (2015) 105–112
40
Fuel Temperature Deviation (%)
35 30 25 20 15 10 5
Back Pressure 2.5 MPa Back Pressure 3.0 MPa Back Pressure 3.5 MPa
0 -5 0
5
10
15
20
25
Total Heating Power (kW) Fig. 9. Deviation in outlet fuel temperature at the outlet under different supercritical pressure.
111
parallel pipes is developed and experiments in the same configuration with the model are carried out under supercritical pressure. Experimental and simulation results indicate that thermal deviation causes the mal-distribution of mass flow rate and fuel temperature through changes in density, which follows a positive feedback mechanism. And deviation in density is the key reason of mass flow rate mal-distribution. Other than a single deviation amplification mechanism of the common fluids, two deviation amplification mechanisms are found at pseudo-critical state and pyrolysis state of hydrocarbon fuel respectively, which is influenced both by physical and chemical effect. Furthermore, (1) The increase of thermal deviation causes positive deviation factors to gather together and more severe mal-distribution. (2) The increase of pressure makes the distribution of mass flow rate more uniform. (3) The variation of total mass flow rate has little effect on the distribution of mass flow rate. The results of this paper can be used to optimize the utilization of heat sink of fuel and avoid over-temperature in scramjet and other applications. Acknowledgements
30
This work was supported by General Program (No. 51476044), General Program (No. 51276047) and Innovative Research Groups (No. 51421063) of National Natural Science Foundation of China, and the authors thank the reviewers for their valuable advice on this paper.
25
References
20
[1] Curran ET. Scramjet engines: the first forty years. J Propulsion Power 2001;17 (6):1138–48. [2] Sreekanth S, Reddy NM. Study of transpiration cooling over a flat-plate at hypersonic mach numbers. J Thermophys Heat Transfer 1995;9(3):552–5. http://dx.doi.org/10.2514/3.701. [3] Huang H, Sobel DR, et al. Endothermic heat-sink of hydrocarbon fuels for scramjet cooling. AIAA-2002-3871; 2002. [4] Yue L, Lu X, Chi H, et al. Heat-sink enhancement of decalin and aviation kerosene prepared as nanofluids with palladium nanoparticles. Fuel 2014;121:149–56. [5] Gascoin N, Gillard P, Bernard S, et al. Pyrolysis of supercritical endothermic fuel: evaluation for active cooling instrumentation. Int J Chem Reactor Eng 2008;6:A5. [6] Gascoin N, Abraham G, Gillard P. Synthetic and jet fuels pyrolysis for cooling and combustion applications. J Anal Appl Pyrolysis 2010;89(2):294–306. [7] Gascoin N, Gillard P, Dufour E, Touré Y. Validation of transient cooling modeling for hypersonic application. J Thermophys Heat Transfer 2007;21 (1):86–94. [8] Gascoin N, Gillard P. Dynamic study of coupled heavy hydrocarbon pyrolysis and combustion. Combust Sci Technol 2012;184(12):2136–53. [9] Minzer U, Barnea D, Taitel Y. Flow rate distribution in evaporating parallel pipes—modeling and experimental. Chem Eng Sci 2006;61(22):7249–59. [10] Baikin M, Taitel Y, Barnea D. Flow rate distribution in parallel heated pipes. Int J Heat Mass Transfer 2011;54(19):4448–57. [11] Maharudrayya S, Jayanti S, Deshpande AP. Flow distribution and pressure drop in parallel-channel configurations of planar fuel cells. J Power Sources 2005;144(1):94–106. [12] Wang JY. Pressure drop and flow distribution in parallel-channel configurations of fuel cells: U-type arrangement. Int J Hydrogen Energy 2008;33(21):6339–50. [13] Wang CC, Yang KS, Tsai JS, et al. Characteristics of flow distribution in compact parallel flow heat exchangers, part II: modified inlet header. Appl Therm Eng 2011;31(16):3235–42. [14] Yue J, Boichot R, Luo L, et al. Flow distribution and mass transfer in a parallel microchannel contactor integrated with constructal distributors. AIChE J 2010;56(2):298–317. [15] Zhang CB, Xu GQ, Gao L, et al. Experimental investigation on heat transfer of a specific fuel (RP-3) flows through downward tubes at supercritical pressure. J Supercrit Fluids 2012:90–9. [16] Gascoin N, Gillard P, Abraham G, et al. Test bench dimensioned by specific numerical tool. Comput Aided Chem Eng 2008;25:835–40. [17] Hou L, Dong N, Sun D. Heat transfer and thermal cracking behavior of hydrocarbon fuel. Fuel 2013;103:1132–7. [18] Yu J, Eser S. Supercritical-phase thermal decomposition of binary mixtures of jet fuel model compounds. Fuel 2000;79(7):759–68. [19] Sun W, Liu G, Wang L, et al. Quasi-homogeneous catalytic cracking of JP-10 over high hydrocarbon dispersible nanozeolites. Fuel 2015;144:96–102.
40
Mass Flow Rate Deviation (%)
35
15 10 Back Pressure 2.5 MPa Back Pressure 3.0 MPa Back Pressure 3.5 MPa
5 0 0
5
10
15
20
25
Total Heating Power (kW) Fig. 10. Deviation in mass flow rate under different supercritical pressure.
According to Eq. (20), we obtain that proportion of hot resistance DP hot =DP total is not a function of mass flow rate. Theoretically the change of mass flow rate doesn’t affect the distribution of mass flow rate.In addition, from experiments with total mass flow rate 14 g/s, 20 g/s and 26 g/s (with thermal deviation 1.15 and back pressure 2.5 MPa), the peak value of deviation in mass flow rate varies from 31.87% to 34.15% and 33.42%. Meanwhile, the peak value of deviation in fuel temperature varies from 30.06% to 29.59% and 30.81%. It’s concluded that the peak value of deviation are nearly the same and the change of total mass flow rate has nearly no effect on the distribution of mass flow rate and fuel temperature of parallel pipes. According to the results, the slight change of scramjet fuel mass flow rate during a flight won’t affect the distribution of fuel mass flow rate in parallel cooling channels. Similarly, the slight drop of mass flow rate during the experiments affects little either.
5. Conclusions In order to study the characteristics of mass flow rate distribution of cracked hydrocarbon fuel in parallel pipes, a model of two
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[20] Liu Z, Bi Q, Feng J. Evaluation of heat sink capability and deposition propensity of supercritical endothermic fuels in a minichannel. Fuel 2015. [21] Ward Thomas A, Ervin Jamie S, Zabarnick Steven. Pressure effects on flowing mildly-cracked n-decane. J Propulsion Power 2005;21(2). [22] Wang QD, Hua XX, Cheng XM, et al. Effects of fuel additives on the thermal cracking of n-decane from reactive molecular dynamics. J Phys Chem A 2012;116:3794–801. [23] Tao Zhi, Fu Yanchen, Xu Guoqiang, et al. Experimental study on influences of physical factors to supercritical RP-3 surface and liquid-space thermal oxidation coking. Energy Fuels 2014;28:6098–106. [24] Gascoin N, Abraham G, Gillard P. Thermal and hydraulic effects of coke deposit in hydrocarbon pyrolysis process. J Thermophys Heat Transfer 2012;26 (1):57–65. [25] Hua ZH, Xu GQ, Wu HW, et al. Characteristics of flow distribution of aviation kerosene in parallel pipes under supercritical pressure. J Aerospace Power 2012. [26] Wang H, Ra Y, Jia M, et al. Development of a reduced n-dodecane-PAH mechanism and its application for n-dodecane soot predictions. Fuel 2014;136:25–36.
[27] Hao Jiangge, Wang Ying, Liu Guozhu, et al. Synthesis of ITQ-2 zeolites and catalytic performance in n-dodecane cracking. Chin J Chem Eng 2014;22:869–74. [28] Tolmachoff Erik D, Allmon William, et al. Analysis of a high throughput ndodecane fueled heterogeneous/homogeneous parallel plate microreactor for portable power conversion. Appl Energy 2014;128:111–8. [29] Jiang RP, Liu GZ, Zhang XW. Thermal cracking of hydrocarbon aviation fuels in regenerative cooling microchannels. Energy Fuels 2013;5:2563–77. [30] Sheu Jyh-Cherng, Zhou Ning, Krishenan Anantha. Thermal cracking of Norpar13 under near-critical and supercritical conditions. In: 34th AIAA/ASME/SAE/ ASEE joint propulsion conference and exhibit; 1998, doi: http://dx.doi.org/10. 2514/6.1998-3758. [31] Li XF, Hua XL, Cai J, et al. Convective heat transfer characteristics of China RP-3 aviation kerosene at supercritical pressure. Appl Therm Eng 2011. [32] Fan X, Yu G, Li J, et al. Effects of entry conditions on cracked kerosene-fueled supersonic combustor performance. Combust Sci Technol 2007;179 (10):2199–217.
Contents lists available at ScienceDirect
Fuel journal homepage: www.elsevier.com/locate/fuel
Flow rate distribution of cracked hydrocarbon fuel in parallel pipes Jiang Qin a, Yuguang Jiang a, Yu Feng a, Xiaojie Li a, Haowei Li a, Yaxing Xu a, Wen Bao a,⇑, Silong Zhang a, Jiecai Han b a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China School of Astronautics, Harbin Institute of Technology, Harbin 150001, PR China
h i g h l i g h t s Mal-distribution of coolant causes a waste of heat sink and even over-temperature. Distribution of cracked hydrocarbon fuel in parallel pipes are studied. Two flow rate deviation amplification mechanisms are found. The mal-distribution mode varies with thermal deviation. Higher pressure suppresses the mal-distribution.
a r t i c l e
i n f o
Article history: Received 8 April 2015 Received in revised form 2 August 2015 Accepted 10 August 2015 Available online 17 August 2015 Keywords: Flow distribution Parallel pipes Hydrocarbon fuel Supercritical pressure
a b s t r a c t A model consisting of two parallel pipes with common inlet and outlet manifolds was established and used to run simulation and experimental study on the flow rate distribution of cracked hydrocarbon fuel in parallel pipes under supercritical pressure. Both simulation and experimental results indicated that mass flow rate and fuel temperature distribution of cracked hydrocarbon fuel in parallel pipes was closely related to the difference in fuel density in pipes. Two deviation amplification mechanisms were found. In addition, the mode of mal-distribution varies with thermal deviation and the distribution was effectively improved by the increase of pressure. And the total mass flow rate could hardly have any effects on the flow rate distribution. All these results could be used to help the full utilization of fuel heat sink and avoid over-temperature. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Scramjet is a promising propulsion system for hypersonic missile and reusable air-space integrated fight vehicle [1,2]. Due to high flight Mach number, the combustion temperature and heat transfer rate of a scramjet are very high. Thus, cooling becomes a major concern. Regenerative cooling is generally accepted as the most promising method [3]. Considering limited quantity of fuel on board, endothermic hydrocarbon fuel with extra chemical heat sink is used to further increase the cooling capacity [4–6]. Fuel flows through the parallel cooling channels as coolant to cool the wall before it’s injected into the combustor [7,8] while a supercritical pressure is kept in the channels to avoid boiling crisis. However, heat flux is not uniform or constant in the wall of a scramjet, which may lead to the mal-distribution of mass flow rate ⇑ Corresponding author at: 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.fuel.2015.08.015 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.
and fuel temperature in different channels. As a result, fuel heat sink is not fully utilized in the low temperature channels. Overtemperature may occur in the high temperature channels to cause thermal protection failure and damage to engine structure. Therefore, it’s of great significance to study the flow rate distribution of cracked hydrocarbon fuel in parallel channels under supercritical pressure so that the fuel heat sink could be fully utilized to avoid over-temperature. Much work has been done in recent years on boiler, solar power generator [9,10] and fuel cell [11,12] continuously, since the distribution characteristics are important to the safety and efficiency of above mentioned applications. Structure of inlet and outlet manifold has been another focus for the study on the flow rate distribution characteristics [13,14] of fluids including water, carbon dioxide and other refrigerants. Due to pyrolysis, the flow and heat transfer of hydrocarbon fuel is quite different from other fluids [15,16]. A lot of work has been done on the pyrolysis of hydrocarbon fuel through single heated channel experiments [17–20] to improve its chemical heat sink [21,22] and to avoid thermal oxidation coking [23,24].
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Nomenclature mt mA mB
q u h CP
l f qf DP Re d Hc k A Ea Ac
Ah Ainner Kc Kh DQ Dm DT f Dq Y R
total mass flow rate (kg/s) mass flow rate of pipe A (kg/s) mass flow rate of pipe B (kg/s) density of fuel (kg/m3) velocity of fuel (m/s) enthalpy (J/kg) constant-pressure specific heat (J/(kg K)) dynamic viscosity (Pa s) friction coefficient heat flux (W/m2) pressure drop (Pa) Reynolds number surface roughness chemical heat sink (J/kg) chemical reaction rate constant (s1) pre-exponential constant (s1) activation energy (J/mol) flow area of throttle in cold end (m2)
flow area of throttle in hot end (m2) flow area of pipe (m2) throttle coefficient for cold end throttle coefficient for hot end thermal deviation deviation in mass flow rate deviation in fuel temperature deviation in density mass conversion of reactant universal gas constant (J/(mol K))
Subscripts lc local resistance at cold end lh local resistance at hot end f frictional resistance 1 heating power Q 1 2 heating power Q 2
So far, the research on flow rate distribution of cracked hydrocarbon fuel in parallel channels is hardly found. Only Ran et al. (2012) studied the flow distribution of kerosene in parallel pipes before pyrolysis occurs [25]. A model consisting of two parallel pipes was established and used to run simulation and experimental study on the flow rate distribution of cracked hydrocarbon fuel in parallel pipes under supercritical pressure and the influences of thermal mal-distribution, pressure and total mass flow rate as well. 2. Modeling with parallel pipes 2.1. Geometry model and hypotheses In the scramjet, there’re usually hundreds of parallel cooling channels through which fuel flows to cool the thermal structure at a temperature of 300–1000 K. Two parallel pipes are used in the model as simplified cooling channels of scramjet, since the close-coupled characteristics of mass flow rate and fuel temperature is clearly presented in this configuration. Similar simplifications are common in studies about parallel systems [9,10]. The following are the hypotheses used by the modeling: (1) The radial difference in all parameters is ignored. (2) The kinetic energy and heat generated by the viscous effect of hydrocarbon fuel is ignored. (3) Channels are horizontal and gravitational potential energy of hydrocarbon fuel is constant. (4) Axial heat conduction of hydrocarbon fuel is ignored. (5) The effect of coke is ignored since the high flow velocity set in this work. 2.2. Mathematical model
Momentum conservation equation can be written as:
@ qu2 1 f 2 @P ¼ qu @x 2d @x
ð2Þ
where d is the equivalent diameter of a pipe and f is the friction coefficient.
@ ðquhÞ 4 ¼ qf q ð1 Y Þ k Hc @x d
ð3Þ
where Y is the mass conversion of reactant. Hc is the chemical heat sink of fuel. Hydrocarbon fuel is a complex mixture with most of its components following the complicated mechanism of pyrolysis including hundreds of species and reactions with possible interactions. In order to highlight the characteristics of mass flow rate distribution instead of the detailed chemical kinetic processes, the model is simplified using n-dodecane, one of the main components of hydrocarbon fuel and used in many related researches [26–28]. In addition, pyrolysis is considered as the first order reaction and global chemical mechanism is adopted. PPD assumption is used to describe the products of pyrolysis [29]. So the conservation equation of cracking products for ndodecane can be expressed as:
@ ðquY Þ ¼ q ð1 Y Þ k @x
ð4Þ
where k is the chemical reaction rate. Additional equations of physical properties based on NIST database are required to form a complete system. The density and constant-pressure specific heat of the mixture can be calculated from the mole percentage.
P xi q i P C p ¼ xi C p i
q¼
ð5Þ
A homogeneous one dimensional model was developed to demonstrate the steady state solution of mass flow rate and temperature distribution. The common inlet and outlet ensures the two parallel pipes an equal pressure drop and the total mass flow rate is set to be constant. Mass conservation equation can be expressed as:
This model is mainly used to qualitatively analyze the characteristics of the mass flow rate distribution of hydrocarbon fuel by using n-dodecane.
@ ðquÞ ¼0 @x
As shown in Fig. 1, two high temperature alloy pipes with an inner diameter of 2 mm were used to simulate the parallel cooling channels. China No. 3 kerosene (RP-3) was used as the fuel and
ð1Þ
3. Experimental set-up
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J. Qin et al. / Fuel 161 (2015) 105–112
Fig. 1. Schematic diagram of the experimental set-up.
900 800 700 600 500 400
200
10
15
20
25
Fig. 2. Comparison of outlet fuel temperature from model and experiment with thermal deviation 1.1.
13 12 11 10 9
ð7Þ
T fB T fA T fA
ð8Þ
7
The deviation in density is expressed as follows because of its significant effect on the flow rate distribution. qA and qB is respectively the fuel density at the outlet of pipes A and B.
6
qA qB qA
5
Total Heating Power (kW)
mA mB mB
DT f ¼
0
ð6Þ
where Q A and Q B are the heating power of pipes A and B respectively. Pipe B is considered as the deviation pipe for a larger heating power, while pipe A the standard pipe. The deviations caused by thermal non-uniformity are expressed as shown below. T fA and T fB is respectively the fuel temperature at the outlet of pipes A and B.
Dm ¼
Model solution of deviation pipe Model solution of standard pipe Experiment results of deviation pipe Experiment results of standard pipe
300
Mass Flow Rate (g/s)
QB QA QA
DQ ¼
1000
Fuel Temperature (K)
supplied through a ram pump and adjusted through a proportional valve. The heating power was regulated through a power control system to a specified proportion to simulate an uneven thermal load. Finally, the heated fuel was cooled through the water cooler and collected in the back pressure tank with nitrogen filled in advance to maintain a specified back pressure for the system. The total mass flow rate and back pressure of the system were kept constant during an experiment. Pressure sensors (Measuring range: 5 MPa. Accuracy: 0.5%FS) were installed in the inlet/outlet manifold and the back pressure tank. Thermocouples (Type K) were installed at outlet of each pipe to measure the temperature of heated fuel. The accuracy of thermocouples is 0.75% T, where T is the target temperature. Turbine flow meter was installed at the inlet of each pipe to measure the mass flow rate. Under steady-state condition, mass flow rate is equal in the whole pipe. The flow meter at the inlet also indicated the mass flow rate of heated fuel where thermocouple was fixed. The accuracy of the flow meter was 0.5% of the full scale (32.5 g/ s). Besides, the accuracy of power source current and voltage measurement is 0.5%FS (630 A, 44 V). During the experiment, the thermal deviation is achieved by a zigzag form electrode (showed in Fig. 1) as a boundary condition, which can be defined as:
8 Model solution of deviation pipe Model solution of standard pipe Experiment results of deviation pipe Experiment results of standard pipe
0
5
10
15
20
25
Total Heating Power (kW)
ð9Þ
Fig. 3. Comparison of mass flow rate from model and experiment with thermal deviation 1.1.
Figs. 2 and 3 show the comparison of model solution and experimental results with thermal deviation 1.1. Mal-distribution of
mass flow rate and fuel temperature happens when total heating power reaches 10 kW and fuel reaches the pseudo-critical point of kerosene (about 645 K) in pipe B. Then fuel in pipe A approaches pseudo-critical point with total heating power 15 kW, the deviations start to decrease. All deviations increase again with heating power 20 kW, when violent pyrolysis occurs [30] in pipe B. It
Dq ¼
4. Results and discussion 4.1. Model validation
J. Qin et al. / Fuel 161 (2015) 105–112
4.2. Distribution of mass flow rate and changes in fuel temperature in different temperature zones The distribution of mass flow rate is determined by the flow resistance in each pipe, which changes greatly with fuel property. For a certain pressure and geometry, fuel property is mainly determined by fuel temperature. So the whole temperature range should be classified in accordance with fuel property. The critical point of RP-3 is 645.04 K (Pc ¼ 2:33 MPa) [15]. RP-3 begins to crack at about 850 K [31,32]. These two representative points are chosen for classification of temperature zones. In addition, the states of hydrocarbon fuel are further classified into liquid state (<600 K), pseudo-critical state (600–700 K), supercritical state (700–850 K) and pyrolysis state (>850 K). As shown in Fig. 4 and Table 1, the whole range of fuel temperature curves of two heated pipes with thermal deviation 1.1 is classified into 5 zones. 4.2.1. Zone 1: both pipes in liquid state In Zone 1, mass flow rates of two pipes are almost even and fuel temperature in parallel pipes is slightly different due to the thermal deviation.
Table 1 Classification of fuel temperature zones. Zones
Standard pipe
Deviation pipe
Heating power range (kW)
1 2 3 4 5
Liquid state Liquid state Pseudo-critical state Supercritical state Pyrolysis state
Liquid state Pseudo-critical state Supercritical state Pyrolysis state Nearly complete pyrolysis
0–8.5 8.5–13.5 13.5–18.3 18.3–40.0 40.0–
20 18 16 14 12
1100
80
Fuel Temperature (K)
900
Zone5
800
60
Zone4
700 600
Standard Pipe Deviation Pipe 40 Fuel Temperature Deviation Experiment results of standard pipe Experiment results of deviation pipe Experiment results of Fuel Temperature Deviation 20
Zone3
500
Zone2
400 300 Zone1
200
Fuel Temperature Deviation (%)
1000
100 0
0 0
10
20
30
40
50
Total Heating Power (kW) Fig. 4. Outlet fuel temperature of simulation and experiment with thermal deviation 1.1.
80
60
10 8 Zone1
Zone2
40 Zone5
Zone4
Zone3
6 4
20
2 0
4.2.2. Zone 2: with deviation pipe in pseudo-critical state In Zone 2, an obvious deviation occurs in mass flow rate together with fuel temperature (as shown in Fig. 5). At this time, the fuel in the deviation pipe reaches its pseudo-critical point while the density falls rapidly. The velocity and flow resistance increase accordingly. Meanwhile, the fuel in the standard pipe remains in liquid state. The general effect is mass flow rate in the deviation pipe decreases while that in standard pipe increases, which in turn widens the deviation in fuel temperature. A circle of positive feedback arises: the deviation in fuel temperature increases with the increasing deviation in density, which leads to an increase in flow resistance deviation and finally causes larger deviation in mass flow rate. This is the first deviation amplification mechanism which occurs because of the physical changes at pseudo-critical state and follows a positive feedback mechanism. And mal-distribution causes the waste of fuel heat sink.
100 Standard Pipe Deviation Pipe Mass Flow Rate Deviation Experiment results of standard pipe Experiment results of deviation pipe Experiment results of Mass Flow Rate Deviation
Mass Flow Rate Deviation (%)
proves the model can be used to predict the trend of fuel temperature and mass flow rate.
Mass Flow Rate (g/s)
108
0
10
20
30
40
50
0
Total Heating Power (kW) Fig. 5. Mass flow rate of simulation and experiment with thermal deviation 1.1.
4.2.3. Zone 3: with standard pipe in pseudo-critical state In this zone, the fuel in standard pipe goes into the pseudocritical state while the fuel in deviation pipe just goes out. In contrast with Zone 2, the distributions of mass flow rate and fuel temperature become more even, which cause a peak of deviation between Zones 2 and 3. But the deviations don’t drop to zero and so the waste of heat sink continues. 4.2.4. Zone 4: with deviation pipe in pyrolysis state Both deviations begin to increase once again in Zone 4. The temperature of heated fuel in deviation pipe reaches 950 K, at which RP-3 cracks and the density falls rapidly once again. Similar to Zone 2, the positive feedback leads to an enormous increase in deviations in mass flow rate and fuel temperature. The deviation amplification mechanism of Zone 4 is due to the chemical reactions in the pyrolysis state and it follows a more complex positive feedback mechanism that affected by pyrolysis. Since pyrolysis can provides extra heat sink, the waste of heat sink in standard pipe becomes even larger. And the risk of overtemperature in channel wall increases as the temperature deviation broadens. 4.2.5. Zone 5: the state of nearly complete pyrolysis in deviation pipe Considering the possible over-temperature, simulation was used to do the research in higher temperature zone. The thermal deviation was 1.1 and total mass flow rate was 20 g/s. The maximum fuel temperature in the theoretical results is about 1100 K, at which chemical heat sink is almost fully utilized and high temperature alloy almost reaches its limit. As shown in Figs. 4–6, when most of the fuel in deviation pipe cracks, a decrease in deviations of both mass flow rate and density is observed, which causes the second peak of deviations in mass flow rate and density.
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J. Qin et al. / Fuel 161 (2015) 105–112
However, deviation in fuel temperature keeps increasing. That is because the specific heat of fuel decreases sharply with the end of pyrolysis and the enthalpy rise leads to a temperature rise larger enough to neutralize the increase of mass flow rate. It’s extremely dangerous that over-temperature will occur with the increasing deviation in fuel temperature. 4.2.6. Overall analysis It can be seen from the experiment above that: (1) the trend of deviations of mass flow rate and density are similar; and (2) they are both nonlinear and with two peaks. Theoretical analysis is carried out to explain such phenomenon. The flow resistance of each pipe is calculated using Eq. (10).
1
DP ¼
þ
A2inner
2 2dAinner
1
þ ¼x
Lf
2 2 in K c Ac
2q 2
m
q
þ
!
1 2K 2h A2h !
1 A2inner
qin
m2
Dm ¼
mA mB ¼ mA
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB xqB þ yqA qB pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB
xðqA qB Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xqA þ yqA qB xqA þ yqA qB þ xqB þ yqA qB ¼ X Dq
ð13Þ
where X is positive and Dq is the deviation in density. The deviations in mass flow rate and density must have the same trend. Here the first law is explained. As for the 2nd law, when total heating power changes from Q 1 to Q 2 , the mass flow relative deviation can be expressed as shown below:
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq1B þyq1A q1B < Dm1 ¼ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi xq1A þyq1A q1B pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x q þy q q 2B 2A 2B : Dm2 ¼ 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq þyq q
qout
m2
þ ym2
Considering the identical geometry of two pipes and the relatively small local flow resistance is in the no-throttle flow configuration, we assume that xA xB ¼ x; yA yB ¼ y. From Eq. (7),
2A
ð10Þ
Subscripts 1 and 2 represent total heating power Q 1 and Q 2 respectively. Fuel density in pipe A changes from q1A to q2A .
Considering the conservation of mass flow rate and pressure drop,
ð14Þ
2A 2B
q2A ¼ q1A þ DqA q2B ¼ q1B þ DqB
ð15Þ
Then
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xq1B þ yq1A q1B xq2B þ yq2A q2B @ ðDmÞ Dm2 Dm1 1 ¼ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi @Q Q2 Q1 Q2 Q1 xq1A þ yq1A q1B xq2A þ yq2A q2B 2 x q1B þ xyq21B DqA x2 q1A þ xyq21A DqB þ xyðq1B q1A ÞDqA DqB 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ Q2 Q1 ðxq2A þ yq2A q2B Þðxq1A þ yq1A q1B Þ ðxq2A þ yq2A q2B Þðxq1B þ yq1A q1B Þ þ ðxq2B þ yq2A q2B Þðxq1A þ yq1A q1B Þ
(
m2
m2
A
B
xA q A þ yA m2A ¼ xB q B þ yB m2B mA þ mB ¼ mt
ð11Þ
ð16Þ
The second order infinitesimals are ignored and since the flow resistance effected by heating is dominating in this configuration, there’re x yq1A and x yq1B . Then we obtain that:
Then, the relationship between mass flow rate of each pipe and
DqA DqB @ ðDmÞ q1A q1B ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ @Q ðQ 2 Q 1 Þ q1Ax2q1B ðxq2A þ yq2A q2B Þðxq1A þ yq1A q1B Þ ðxq2A þ yq2A q2B Þðxq1B þ yq1A q1B Þ þ ðxq2B þ yq2A q2B Þðxq1A þ yq1A q1B Þ DqA DqB ¼ Yc
q1A
q1B
ð17Þ
the total mass flow rate can be given by:
8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xB qA þyB qA qB < mA ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mt xB qA þyB qA qB þ xA qB þyA qA qB pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xA qB þyA qA qB : mB ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mt xB q þyB q q þ xA q þyA q q A
A B
B
A B
By means of the small deviation linearization, we obtain that
ð12Þ
8 @q > > < DqA ¼ @T f T ¼T f 1A þT f 2A T f 2A T f 1A f 2 @q > > : DqB ¼ @T f T f 1B þT f 2B T f 2B T f 1B Tf ¼
2
ð18Þ
110
J. Qin et al. / Fuel 161 (2015) 105–112
800
70
600
60
500
50 400
Zone5
40
300
30
200
20
100
10
Fuel Temperature (K)
80
Outlet Fuel Density Deviation (%)
700
Outlet Fuel Density (kg/m3)
1000
90 Standard Pipe Deviation Pipe Outlet Fuel Density Deviation
800
600
400 Standard Pipe with Thermal Deviation 1.2 Deviation Pipe with Thermal Deviation 1.2 Standard Pipe with Thermal Deviation 1.4 Deviation Pipe with Thermal Deviation 1.4
0
0 0
10
20
30
40
50
Total Heating Power (kW)
200 0
5
Fig. 6. Outlet fuel density of simulation with thermal deviation 1.1.
f
2
Since @ q=@T f < 0, the absolute value is used for convenience. Q 2 is assumed to be slightly larger than Q 1 , there’s T f 2B T f 1B T f 2A T f 1A . Besides, due to the thermal deviation, when heating power Q 1 , there’s T f 2B > T f 1A ! q1B < q1A . @ q=@T f of hydrocarbon fuel increases rapidly in pseudo-critical area and pyrolysis area. When fuel in deviation pipe and standard pipe crosses pseudo-critical area or pyrolysis area successively, @ðDmÞ=@Q changes from positive to negative, which leads to two peaks of the deviation curves considering Y c > 0.
15
20
25
Fig. 7. Outlet fuel temperature with thermal deviations 1.2 and 1.4.
16 Standard Pipe with Thermal Deviation 1.2 Deviation Pipe with Thermal Deviation 1.2 Standard Pipe with Thermal Deviation 1.4 Deviation Pipe with Thermal Deviation 1.4
14
Mass Flow Rate (g/s)
" @ ðDmÞ DqA DqB 1 @ q ¼ Yc ¼ Yc T T f 1A @Q q1A q1B q1A @T f T f ¼Tf 1A þT2 f 2A f 2A # 1 @ q T T f 1B q1B @T f T f ¼Tf 1B þT2 f 2B f 2B " 1 @ q ¼ Yc T þT T f 2B T f 1B q1B @T f T f ¼ f 1B 2 f 2B # 1 @ q T ð19Þ T f 1A q1A @T f T ¼T f 1A þT f 2A f 2A
10
Total Heating Power (kW)
12
10
8
6
4
0
5
10
15
20
25
Total Heating Power (kW) Fig. 8. Mass flow rate with thermal deviations 1.2 and 1.4.
4.3. Influence of thermal deviation Thermal deviation is very common in parallel cooling channels of scramjet, this paper carried out experiments of thermal deviation 1.1 (analyzed above), 1.2, 1.4 with back pressure kept at 2.5 MPa as shown in Figs. 7 and 8. With thermal deviation 1.2, fuel temperature of deviation pipe reaches 933.9 K. The deviations in mass flow rate and fuel temperature only emerge a single peak affected both transcritical effect and pyrolysis in deviation pipe (positive deviation factors). Increasing of the thermal deviation leads positive mal-distribution factors to gather together and larger deviation occurs (deviation of mass flow rate and fuel temperature respectively 39.1% and 36.36%). When the thermal deviation increases to 1.4, the deviations in mass flow rate and fuel temperature keep increasing through the whole experiment until the fuel temperature of deviation pipe reaches 943.18 K. It can be seen that as the thermal deviation increasing, the maldistribution mode varies. Positive deviation factors emerge together to make the distribution of mass flow rate and fuel temperature more uneven. 4.4. Influence of system pressure As shown in Figs. 9 and 10, when the pressure varies from 2.5 MPa to 3.5 MPa (all pressures are supercritical) with the same
thermal deviation of 1.2, deviations in mass flow rate and fuel temperature decreases, especially in the peak of deviations in pseudocritical area. According to the properties provided by NIST, rapid decrease of density of hydrocarbon fuel in pseudo-critical area disappears when pressure is high enough. So deviation in fuel temperature causes less deviation in density and flow resistance to make the mass flow rate distribution more uniform. The results indicate that the increase of pressure makes distributions of mass flow rate and fuel temperature are more even. 4.5. Influence of total mass flow rate Redistribution of mass flow rate is directly caused by flow resistance that vary with fuel temperature (i.e. hot resistance) is the main reason for mass flow rate mal-distribution. From this perspective, we can analyze the influence of total mass flow rate with ratio of the hot resistance as standard.
2
2
1 1 KmAin þ 12 qin þqoutL 2 f m2in þ Amin q1 q q 2 inner h h out out in DPhot ð 2 ÞAinner d ¼
2
2
2 DP t min min 1 1 1 1 L 1 2 þ f m þ KmAin þ q q þ in K c Ac Ainner qout qin 2qin 2 ð in out ÞA2 2qout h h d inner 2
2
2
1 1 1 L 1 1 þ f þ q1 2qout K h Ah 2 ðqin þqout ÞA2 A q inner out in d inner 2 ¼
2
2
2 1 1 1 1 1 1 L þ f þ 2q1 K 1A þ qout qin 2qin K c Ac Ainner 2 ðqin þqout ÞA2 h h out d inner 2 ð20Þ
J. Qin et al. / Fuel 161 (2015) 105–112
40
Fuel Temperature Deviation (%)
35 30 25 20 15 10 5
Back Pressure 2.5 MPa Back Pressure 3.0 MPa Back Pressure 3.5 MPa
0 -5 0
5
10
15
20
25
Total Heating Power (kW) Fig. 9. Deviation in outlet fuel temperature at the outlet under different supercritical pressure.
111
parallel pipes is developed and experiments in the same configuration with the model are carried out under supercritical pressure. Experimental and simulation results indicate that thermal deviation causes the mal-distribution of mass flow rate and fuel temperature through changes in density, which follows a positive feedback mechanism. And deviation in density is the key reason of mass flow rate mal-distribution. Other than a single deviation amplification mechanism of the common fluids, two deviation amplification mechanisms are found at pseudo-critical state and pyrolysis state of hydrocarbon fuel respectively, which is influenced both by physical and chemical effect. Furthermore, (1) The increase of thermal deviation causes positive deviation factors to gather together and more severe mal-distribution. (2) The increase of pressure makes the distribution of mass flow rate more uniform. (3) The variation of total mass flow rate has little effect on the distribution of mass flow rate. The results of this paper can be used to optimize the utilization of heat sink of fuel and avoid over-temperature in scramjet and other applications. Acknowledgements
30
This work was supported by General Program (No. 51476044), General Program (No. 51276047) and Innovative Research Groups (No. 51421063) of National Natural Science Foundation of China, and the authors thank the reviewers for their valuable advice on this paper.
25
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Mass Flow Rate Deviation (%)
35
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25
Total Heating Power (kW) Fig. 10. Deviation in mass flow rate under different supercritical pressure.
According to Eq. (20), we obtain that proportion of hot resistance DP hot =DP total is not a function of mass flow rate. Theoretically the change of mass flow rate doesn’t affect the distribution of mass flow rate.In addition, from experiments with total mass flow rate 14 g/s, 20 g/s and 26 g/s (with thermal deviation 1.15 and back pressure 2.5 MPa), the peak value of deviation in mass flow rate varies from 31.87% to 34.15% and 33.42%. Meanwhile, the peak value of deviation in fuel temperature varies from 30.06% to 29.59% and 30.81%. It’s concluded that the peak value of deviation are nearly the same and the change of total mass flow rate has nearly no effect on the distribution of mass flow rate and fuel temperature of parallel pipes. According to the results, the slight change of scramjet fuel mass flow rate during a flight won’t affect the distribution of fuel mass flow rate in parallel cooling channels. Similarly, the slight drop of mass flow rate during the experiments affects little either.
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