Study of the effect of rotating channel rib structure on fuel flow and heat transfer characteristics

Hypersonic vehicles can be affected by incoming hot air. In order to ensure that the power generation turbine blades can operate properly, the fuel in the engine is used to cool the turbine blades. In this paper, the heat transfer characteristics of fuel in smooth and 45° ribbed channels under rotating conditions are investigated. Their results show that, unlike the smooth channel, the heat transfer coefficient of the 45° ribbed channel decreases as Ro increases under the combined influence of the rib structure and the physical properties of the fuel. The rib structure disrupts the high-velocity fluid near the trailing surface of the centrifugal section, which promotes doping between the fuels and weakens the effect of the Coriolis force. The Nu increase in ribbed channels ranged from 11.4% to 55.1% compared to smooth channels.


Introduction
With the increase in auxiliary systems and the need to perform multiple missions, hypersonic vehicles are consuming more and more electricity [1].As the flight distance increases, it is not possible for batteries to provide power supply for a long period of time.Among them, the ram air turbine is more mature and can provide sufficient power for the vehicle [2-3].However, high incoming temperatures can burn the turbine blades, so coolant is needed to reduce the turbine temperature.At this point, only kerosene can be used as a coolant can reduce the blade temperature [4].
Air cooling solutions have been widely used [5].For enhancing heat transfer, most of the cooling channels have ribbed walls [6].When ribbed channels are used, the orientation and angle of inclination of the rib structure affects the separation and re-attachment of the air, which phenomenon affects the heat transfer [7].Wang et al [8] studied the cooling channel with wave rib structure.He found that rib height and rib angle were more associated with heat transfer.Larger wave rib heights enhance transfer of heat.Wang et al [9] studied the effect of interrupted rib structure on air heat transfer effectiveness.He found that the spacing and angle of inclination of the intersegmental ribs affected heat transfer.Suitable interrupted rib spacing and inclination angle can improve the heat transfer in the channel.
When kerosene is used for cooling, it is subjected to high temperatures coming from the turbine blades, so its physical properties change.Therefore the effect of physical properties needs to be emphasized when using kerosene to cool the turbine blades.For static ribbed straight passages, increasing the height of the rectangular ribs or appropriately decreasing the spacing of the rectangular ribs enhances the flow mixing of kerosene in the passages and thus enhances the heat transfer [10][11][12].Rough ribbed channels will improve the heat transfer of kerosene compared to smooth channels and there exists a rib height ratio for optimum heat transfer [13].Among them, literature [14] studied the effect of having different heights of truncated ribs on kerosene.Their numerical calculations show that there exists an optimum range of pitch ratios within which the channels have the strongest heat transfer performance.Literature [15] numerically studied the effect of bending ribs on kerosene in a stationary channel.Their numerical calculations revealed that the bending ribs disrupted the thermal boundary layer, resulting in a reduction of the thermal boundary layer thickness.From the above literature, it can be seen that the rib structure within the stationary channel creates a vortex, which promotes the mixing of kerosene and improves the heat transfer.The fluid medium studied in this paper is compressible.Since rotation causes the pressure of kerosene to rise, this results in the flow of kerosene appearing compressible.The compressibility of kerosene affects changes in physical properties and heat transfer.
Most of the research on kerosene at this stage focuses on the stationary channel.However there are few studies related to the cooling of kerosene in the channel during rotation.Especially, the phenomenon about the heat transfer of kerosene in the ribbed channel during rotation has not been investigated.Based on this, this paper delves into the differences and commonalities of kerosene heat transfer phenomena in smooth and ribbed channels during rotation.The heat transfer mechanism of kerosene in ribbed channels is obtained.

Calculation method
The classical channel [7] is used in this paper to study the effect of rib structure on kerosene.Where the inclination of the ribs is adopted at 45°.The hydraulic diameter of the channel is D and the length of the heating section is 12 D. The height and width of the ribs are the same with e=0.125 D and the rib spacing is 10 e.The computational model is shown in figure 1.
The Reynolds number of the channel inlet kerosene is set to 28000 and the inlet temperature is set to 630K.Where the number of rotations Ro of the cooling channels ranges from 0 to 3.2.The heating section is at a constant temperature.The SST turbulence model is used in this paper to calculate the effect of rib structure on kerosene heat transfer phenomena [10][11].Structural meshing of cooling channels by ICEM software.Its mesh with ribbed channels is shown in figure 2. The mesh validation is shown in figure 3. Therefore, in this paper, models with a number of grid nodes greater than 1 million are used for numerical calculations.

Ro= wD V in
(1) Where V in refers to the speed of importation.The formula for the convective heat transfer coefficient is shown in (2).

Nu= hD λ (3)
Where λ is the thermal conductivity of kerosene.As can be seen from figure 4 -figure 6, the pressure, density and thermal conductivity increase with increasing Ro.As a result of the rotational action, the pressure of the kerosene rises.The increase in pressure causes the density and thermal conductivity of kerosene to increase.The pressure, density and thermal conductivity stratification of the kerosene is evident during rotation.The stratification of the pressure during rotation is evident, thus leading to stratification of the physical property during rotation.As Ro increases, the increase in density of kerosene causes a decrease in velocity.Also, the increase in thermal conductivity decreases the channel Nusselt number as Ro increases.As can be seen in figure 7 -figure 9, the velocity of kerosene decreases significantly as Ro increases.Therefore, the effectiveness of heat transfer in ribbed channels decreases as Ro increases.As can be seen in figure 8 -figure 9, when rotating, the Coriolis force makes the kerosene in the centrifugal section move towards the trailing edge surface, resulting in an increase in kerosene velocity in the vicinity of this location.This results in an enhanced heat transfer coefficient at the trailing edge wall of the centrifugal section.However, a comparison of figure 8 -figure 9 shows that the rib structure destroys the high velocity region and weakens the Coriolis force.Therefore, for the ribbed channel, the rib structure and the variation of kerosene physical properties are the main factors affecting the heat transfer coefficient at this time.As seen in figure 10, at static, h is generally higher in the centrifugal and centripetal sections due to the rib structure.When rotating, the pressure of the kerosene increases, thus leading to an increase in density.An increase in density causes a decrease in velocity and therefore weakens the enhancement of the h.The h in the centripetal section decreases significantly due to the decrease in kerosene velocity during rotation.The Coriolis force leads to a slight increase in the h at the trailing edge of the centrifugal section.In this case, the effect of the decrease in the h in the centripetal section is greater than the effect of the slight increase in the h at the trailing edge of the centrifugal section.Therefore the h of the ribbed channel decreases when rotating.

Figure 11. Heat transfer coefficient distribution.
As seen in figure 11, for a smooth channel, its h grows first and then reduces.At low Ro, the Coriolis force will result in a rise in h in the smooth channel.The h decreases at high Ro because the velocity drop due to density increase at higher Ro is very significant.As seen in figure 11, the h of the ribbed channel decreases significantly as Ro increases.The decrease in its h is large.The explanation is that the ribbed structure disrupts the high velocity fluid in the centrifugal section and reduces the action of the Coriolis force.At this point, the effects caused by the Coriolis force are less than those caused by the ribs.Also, the density of kerosene increases as Ro increases, especially at high Ro the density increases dramatically.The higher density leads to a decrease in the velocity of the kerosene, which reduces the heat exchange between the kerosene and the wall, leading to a decrease in h.For ribbed channels, the effect of density and rib structure on heat transfer will be more pronounced.Thus for ribbed structures, the h gradually decreases.The increase in h for ribbed channels compared to smooth channels ranges from 11.2% to 54.6%.In summary, it can be seen that the ribbed structure weakens the action of the Coriolis force, which in turn accentuates more the effect of increased density.We can see from figure 12 that the rib structure has an evident impact on the Nu.Among them, the Nu of the ribbed channel is greater than the Nu of the smooth channel.For smooth channels, Nu grows and then declines as Ro increases.However, for ribbed channels, Nu decreases as Ro increases.For ribbed channels, the kerosene pressure rises as Ro increases.The increase in pressure leads to a significant increase in the thermal conductivity of kerosene.For ribbed channels, the h decreases slowly as Ro increases.Therefore, Nu with ribbed channels decreases dramatically under the influence of thermal conductivity.For smooth channels, the thermal conductivity of kerosene rises gradually as Ro increases.When at lower Ro, the heat transfer coefficient rises significantly as Ro increases.The

45° rib Smooth
increase in Nusselt number for ribbed channels compared to smooth channels ranged from 11.4% to 55.1%.

Conclusion
In this study, the special heat transfer phenomenon of kerosene in a rotating ribbed channel is investigated.The effect of rib structure and Ro on the heat transfer pattern of kerosene is analysed.Its conclusions are as follows: Unlike the smooth channel, the h of the ribbed channel decreases as Ro increases under the combined influence of the rib structure and the physical properties of the kerosene.The increase in heat transfer coefficient for ribbed channels compared to smooth channels ranges from 11.2% to 54.6%.The ribbed structure disrupts fluids with higher velocities in the centrifugal section and promotes blending between kerosene.When rotating, the rib structure weakens the Coriolis force, making the effect of kerosene density enhancement more prominent.The rib structure improves the Nu of the channel.The increase in Nu for ribbed channels compared to smooth channels ranged from 11.4% to 55.1%.

Figure 1 .
Figure 1.Schematic diagram of the model.

Figure 3 .
Figure 3. Grid sensitivity validation.The formula for Ro is shown in (1).

Figure 7 .
Kerosene velocity in ribbed channels at stationary.(a) Centrifugal section (b) Centripetal section Figure 8. Kerosene velocity in ribbed channel at Ro=2.9.(a) Centrifugal section (b) Centripetal section Figure 9. Velocity of kerosene in the smooth channel at Ro = 2.9.
(a) Smooth, Ro=0 (b) Rib, Ro=0 (c) Rib, Ro=2.9 Figure 10.Distribution of heat transfer coefficients on the trailing edge surface for ribbed channels at different Ro.

Figure 12 .
Figure 12.Nusselt number distribution.We can see from figure12that the rib structure has an evident impact on the Nu.Among them, the Nu of the ribbed channel is greater than the Nu of the smooth channel.For smooth channels, Nu grows and then declines as Ro increases.However, for ribbed channels, Nu decreases as Ro increases.For ribbed channels, the kerosene pressure rises as Ro increases.The increase in pressure leads to a significant increase in the thermal conductivity of kerosene.For ribbed channels, the h decreases slowly as Ro increases.Therefore, Nu with ribbed channels decreases dramatically under the influence of thermal conductivity.For smooth channels, the thermal conductivity of kerosene rises gradually as Ro increases.When at lower Ro, the heat transfer coefficient rises significantly as Ro increases.The [1] Zhang D, Qin J, Feng Y, Ren F and Bao W 2014 Performance evaluation of power generation system with fuel vapor turbine onboard hydrocarbon fueled scramjets Energy 77 732-41 [2] Li H, Qin J, Bao W and Huang H 2019 Performance improvement of gaseous hydrocarbon fuel driven thermal power generation systems for hypersonic vehicles Energy Conversion and Management 199 111949 [3] Li H, Qin J, Jiang Y, Zhang D, Cheng K, Bao W and Huang H 2018 Experimental and theoretical investigation of power generation scheme driven by thermal cracked gaseous hydrocarbon fuel for hypersonic vehicle Energy Conversion and Management 165 334-343 [4] Sun H, Qin J, Li H, Huang H and Yan P 2019 Research of a combined power and cooling system based on fuel rotating cooling air turbine and organic Rankine cycle on hypersonic aircraft Energy 189 116183 [5] Han J C and Zhang Y M 1992 High performance heat transfer ducts with parallel broken and vshaped broken ribs International Journal of Heat and Mass Transfer 35(2) 513-523 [6] Srinath, V., Ekkad, And, Je-Chin and Han 1997 Detailed heat transfer distributions in two-pass square channels with rib turbulators International Journal of Heat and Mass Transfer 40 (11) 2525-2537 [7] Al-Hadhrami L and Han J 2003 Effect of rotation on heat transfer in two-pass square channels with five different orientations of 45° angled rib turbulators International Journal of Heat and Mass Transfer 46(4) 653-669 [8] Wang L, Wang S, Wen F, Zhou X and Wang Z 2018 Effects of continuous wavy ribs on heat transfer and cooling air flow in a square single-pass channel of turbine blade International Journal of Heat and Mass Transfer 121 514-533 [9] Wang L, Wang S, Liu W, Wen F, Zhou X and Wang Z 2018 Numerical predictions on heat transfer and flow characteristics in a straight channel with different geometric parameters wavy ribs Applied Thermal Engineering 140 245-265 [10] Li X, Zhang S, Qin J and Bao W 2020 Parametric analysis on the thermal behavior of cracking hydrocarbon fuel flow inside asymmetry heated cooling channels with micro-ribs International Journal of Heat and Mass Transfer 160 120154 [11] Zhang J, Han H and Zhu Q 2020 Multi-objective optimization of the cooling performance of a mini-channel with boot-shaped ribs in transcritical regions using rsm and moga Numerical Heat Transfer.Part a, Applications 78(12) 737-755 [12] Li X, Zhang S, Ye M, Qin J, Bao W, Cui N, Liu X and Zhou C 2020 Effect of enhanced heat transfer structures on the chemical recuperation process of advanced aero-engine Energy 211 118580 [13] Wang H, Luo Y, Gu H, Li H, Chen T, Chen J and Wu H 2012 Experimental investigation on heat transfer and pressure drop of kerosene at supercritical pressure in square and circular tube with artificial roughness Experimental Thermal and Fluid Science 42 16-24