Numerical analysis of flow and heat transfer characteristics of supercritical endothermic hydrocarbon fuel in taper tube

To enhance the cooling performance of the scramjet regenerative cooling system, a novel taper tube is proposed. Under supercritical pressure, the flow characteristics and heat transfer characteristics of endothermic hydrocarbon fuel (EHF) in taper tube, narrow cylindrical tube, and wide cylindrical tube are numerical investigated and compared. The results of the investigation of flow and heat transfer processes in the above three tubes indicate that the taper tube effectively facilitates the pyrolysis of n-decane and the n-decane conversion is increased by 3.94%, compared with narrow cylindrical tube. Compared with wide cylindrical tube, the taper tube enhances cooling effect and the wall temperature near the outlet is reduced by 50.16 K. The taper tube contributes to the cooling structure optimization and promotion of regenerative cooling system performance.


Introduction
Scramjet is a promising propulsion device for hypersonic vehicle, which becomes a research focus in the propulsion field.However, the combustion chamber of scramjet faces severe thermal environment, which brings great challenges to the existing thermal protection technology and materials.The regenerative cooling method, which uses endothermic hydrocarbon fuel as the cooling system coolant, an effective and realizable active thermal protection technology, is one of the most promising technologies [1,2].However, the regenerative cooling system application is restricted by a shortage of cooling capabilities.Hence, many optimized structures of cooling channel have been designed to enhance regenerative cooling performance, and the detailed endothermic hydrocarbon fuel flow characteristics and heat transfer characteristics in the optimized cooling tubes have been investigated via computational fluid dynamic (CFD) simulation [3,4].The cross-section optimization of regenerative cooling tubes, which significantly affects the cooling performance of regenerative cooling systems, has received extensive attention [5].Li et al. [6] researched the thermal cracking and carbon deposition phenomenon of EHF in the regenerative cooling tubes with different cross-section but same cross-sectional area, including rectangular, square, and circular cross-sections, based on electric heating experiment and CFD simulation.However, the optimization methods to improve pyrolysis and carbon deposition phenomenon were not proposed.

Geometry of cooling tubes and boundary conditions of model
In this study, three 2D numerical models which is shown in figure 1, are established to simulate the flow characteristic and heat transfer characteristic of EHF.According to the actual structure of the scramjet, the heating section length is set to be 1000 mm [9].Two adiabatic sections with the length of 100 mm are established to ensure the flow of fluid in the cooling tube model fully developed and strengthen stability of simulation, respectively.Each of tube is designed with a total radius of 1.5 mm, comprising the fluid model zone and the solid model zone.The inlet radius and outlet radius of taper tube (Tube-1) are 1 mm and 0.5 mm, respectively.For the adiabatic section, the fluid domain radius is constant.The fluid domain of taper tube shrinks smoothly along the direction of fluid flow in the heating section.The fluid domain radii of Tube-2 and Tube-3 are respectively 0.5 mm and 1 mm.The constant heat flux is defined on the heated surface.The mass flow tube inlet and pressure tube outlet are defined, and the tube inlet flow rate of mass in the three tubes is 3.0 g s -1 .The detailed values of boundary conditions are shown in table 1.

Governing equations and solution methods
The steady state flow and heat transfer characteristics of EHF are investigated with the commercial software ANSYS Fluent.The SIMPLEC algorithm is applied to resolve the coupling of pressure and velocity.The conservation equation of mass, conservation equation of momentum, conservation equation of energy, and conservation equation of species transport are listed as following: Conservation equation of mass: The conservation equation of species transport, which is used to describe the thermal cracking of EHF: ) where the mass source term Si in the conservation equation of species transport is expressed as: =     (5) The nickel-base superalloy (GH3128) is selected as wall metal material.In the solid domain, the conservation equation of energy is expressed as: ∇ • (∇) = 0 (6) The SST k-ω turbulence model is used to describe the fluid turbulent flow in three tubes, which is a low speed and incompressible flow constrained by walls.

Pyrolysis mechanism
The model fuel, n-decane, is chosen in this work, which has similar thermo-physical properties to aviation kerosene.The PPD model (proportional product distribution model of n-decane), which is a one-step surrogate thermal cracking reaction model, is selected to describe the pyrolysis in the regenerative cooling tube [10].
The thermal cracking reaction rate of n-decane is calculated by: =    −  () ⁄ (10) In the simulation model of regenerative tubes, the pre-exponential factor (Apy) detail value is set to 1.6×1015 s -1 and the activation energy (Ea) detail value is set to 2.63655×10 8 J kg -1 mol -1 .Due to the transcritical process and pyrolysis, the EHF thermos-physical properties in the regenerative cooling tubes change drastically.To descript the thermos-physical properties accurately, the SUPERTRAPP Software from NIST, which is widely applied in the former research, is used in this work.And both the n-decane thermo-physical properties and the thermo-physical properties of mixture of its pyrolytic products are calculated by SUPERTRAPP.

Validation of regenerative cooling tube model
To validate the reaction model, a 2D axisymmetric numerical model is established.The geometry of regenerative cooling tubes and boundary conditions of regenerative cooling tube model are consistent with those in the experiment research.A 2D structural mesh, generated by ANSYS ICEM, is used for the validation after the mesh independence test being made [26].The axial velocity of fluid in the tube and n-decane mass fraction are chosen for the comparison between numerical simulation and experiment.The maximum error is less than 10%.Three meshes of taper tube are established for mesh independence verification.The detailed information of three meshes is shown in table 2. The boundary conditions of regenerative cooling tube in this test are consistent with those shown in table 1.The axial heating wall temperature distributions of three meshes are compared.From figure 2, the maximum error of mesh independence verification is less than 10%.Hence, mesh-2 is chosen in this research.Moreover, the value of y+ is less than 1.0, which ensure the first layer of the mesh falls into the viscus sublayer.

Effect of taper tube on velocity characteristics
When the inlet flow rate of mass is constant, the fluid velocity is significantly influenced by tube cross-sectional area.The fluid velocity along the centerline of three tubes is illustrated in figure 3. Due to the smaller cross-sectional area, in main segment, fluid flows more quickly in tube-2 compared to that in tube-1, which is beneficial to heat fluid and enhance n-decane cracking reaction.In the initial segment, fluid velocity of tube-1 and tube-3 are nearly equivalent.As the cross section of tube-1 shrinks, fluid flows more rapidly than that in tube-3, which contribute to cooling the metal wall.In comparison to tube-3, tube-1's outlet velocity rises by 155.13%.In addition, fluid is significantly accelerated along flow direction, which is thermal acceleration phenomenon caused by heating and pyrolysis.And in the end segment, fluid flows more quickly in tube-1 than tube-2, due to more significant acceleration phenomenon carried by more dramatic pyrolysis.

Effect of taper tube on temperature characteristics
Figure 4 shows that, the wall temperature of tube-2, benefited by faster coolant flow rate, is lower than that of other tubes, especially in initial segment.Accompanied by the shrinkage of cross section, the wall temperature of tube-1 closes to that of tube-2 and it's a decrease of 50.16K compared to that of tube-3.There is a soaring temperature in the wall of tube-3, and this phenomenon is weakened in tube-1.

Figure 4.
Wall temperature profile of three tubes.Figure 5 shows that, the EHF close to the solid wall gets heated quickly in the tube-1 and tube-3, which contributes to the n-decane thermal cracking reaction.However, there is a concentration of high temperature fluid in tube-3, which may cause thermal damage to the wall metal material.In tube-1, this phenomenon is so weak that it can be ignored.There is significant thermal stratification in tube initial segment.The main fluid is not fully heated, which degrades cooling performance and weakens pyrolysis of n-decane.At the rear, the fluid is sufficiently heated, and this phenomenon is diminished.

Effect of taper tube on temperature characteristics
For the regenerative cooling system, the EHF should be as thoroughly cracked as possible to fully use the EHF chemical heat sink and enhance its combustion performance.From figure 6, the pyrolysis of n-decane is greatly enhanced by fairly high fluid temperature.Comparing between tube-1 and tube-2, the thermal cracking reaction conversion of n-decane inside tube-1 is increased, due to extended mainstream flow resident time accompanied by elevated fluid temperature.The total conversions in three tubes are shown in table 3.  3. Total conversion of n-decane in three tubes.

Tube number Total conversion of n-decane
Tube-1 60.47% Tube-2 56.53% Tube-3 98.88% Due to the promotion of pyrolysis reaction by higher temperature and longer residence time, as exhibited in figure 7, the n-decane in tube-1 begins to crack earlier than in tube-2.In addition, there is a concentration of reaction product near the wall, which hinders heat transfer between main fluid and metal wall carried by low thermal conductivity of reaction product.

Results and discussion
To improve the cooling capacity and heat transfer performance of active regenerative cooling system, a novel taper tube is proposed.The flow characteristic and heat transfer characteristic of n-decane in the taper tube are numerically researched and compared with two traditional straight cylindrical tubes.The results indicate that the taper tube effectively slows down the flow and raises the temperature of the fluid in initial segment, which facilitates the thermal cracking reaction of n-decane and contributes to the earlier onset of the cracking reaction.Compared with narrow cylindrical tube (Tube-2), the total conversion in taper tube is increased by 3.94%.As the cross section shrinks, the fluid flow is accelerated, resulting in lower wall temperature.Compared with wide cylindrical tube (Tube-3), the wall temperature of taper tube near the outlet is reduced by 50.16 K.This work may provide reference for structural design of regenerative cooling tube.

Figure 2 .
Figure 2. Heating wall temperature profile of three meshes.

Figure 3 .
Figure 3. Fluid velocity profile of centerline in three tubes.

Figure 5 .
Figure 5. Temperature contours of fluid in three tubes.

Figure 6 .
Figure 6.Conversion axial profile of n-decane in three tubes.

Figure 7 .
Figure 7. Conversion contours of n-decane in three tubes.

Table 1 .
Detailed values of boundary conditions

Table 2 .
Detailed mesh information of three taper tube meshes.