Thermal-hydraulic performance analysis of the supercritical fuel printed circuit heat exchanger with zigzag flow channels

Printed Circuit Heat Exchanger (PCHE), which uses the supercritical fuel RP-3 as the cold fluid and the air as the hot fluid, is considered a promising candidate for CCA (Cooled Cooling Air) system heat exchanger selection due to its high compactness and efficiency. In this paper, the numerical method of the supercritical fuel PCHE with Zigzag channels is established, and an experimental system is designed and built to verify the accuracy of the numerical method. The influence of inlet temperature, mass flow rate, and outlet pressure of the fuel on the thermal-hydraulic performance is numerically investigated. The inlet temperature of fuel is ranged from 100 to 500°C, the mass flow rate of fuel is from 6 to 10g/s, and the outlet pressure of fuel is ranged from 3 to 6MPa. The results demonstrate that the fuel exhibits higher heat transfer coefficients and pressure drop caused by higher mean turbulent kinetic energy as the increase of the inlet temperature and mass flow rate. The flow and heat transfer performance of the fuel does not change significantly with pressure change since its thermophysical properties decrease slightly with increased pressure. The flow and heat transfer correlations for the tested PCHE are proposed with the numerical results. The newly developed Fanning friction factor correlation predicts almost 100% of the numerical data within the ±5% error band, and the newly developed heat transfer correlation predicts 94.4% of the numerical data within the ±10% error band.


Introduction
With the cooling requirements of the hot parts of the aircraft gradually increasing, a technical means to improve the cooling quality of the cooling air called CCA (Cooled Cooling Air) technology [1] and the heat exchanger which is the core component of CCA are attracting more attention in the aircraft thermal management system.And through this heat exchanger, the supercritical fuel cools the cooling air before the air enters the cooling structure in the turbine blades.Since the Heatric company [2] successfully developed Printed Circuit Heat Exchanger (PCHE) in 1985, PCHE has been widely used in many occasions, such as high-temperature gas-cooled reactors (HTGRs), supercritical CO 2 Brayton cycle, and offshore LNG Floating Storage and Regasification Unit (FSUR) [3][4][5][6][7][8].Compared with traditional heat exchangers, PCHE has the characteristics of an extremely compact structure, high efficiency, hightemperature and high-pressure tolerance, etc. [9], so using PCHE in CCA system has potential technical advantages and great application prospects.The hydraulic diameters of the flow channels in the PCHE are usually within the range of 0.5-2mm [10], and the flow channel forms are various whose channel shape includes straight, Zigzag, fin, etc. [9,7,11], and cross-section shape includes semicircle, rectangle, triangle, etc. [11,12].The thermal-hydraulic performance of the PCHE has attracted much attention due to the complex flow and heat transfer characteristics caused by the complex structure.
The heat transfer and flow characteristics of supercritical CO 2 in the PCHEs have been studied in order to improve the performance of the PCHE in the supercritical CO2-based Breton cycle.Chu et al. [6] and Liu et al. [13] both studied the heat transfer between supercritical CO 2 and cooling water in PCHEs with straight channels by the experimental method.Zhang et al. [14] analyzed the detailed local buoyancy effect of supercritical CO 2 in a straight-type PCHE with semicircular channels by conducting CFD investigations on the coupled heat transfer.Meshram et al. [15] evaluated the performance of the straight and Zigzag channel PCHE for supercritical CO 2 cycle regenerators, and the results show that the Nusselt number increases linearly with the Reynolds number in both types of channel geometry.Nikitin et al. [16] investigated the heat transfer and flow characteristics of the Zigzag-channel PCHE with a supercritical CO 2 working fluid by both experimental and numerical method, and proposed the empirical correlations for the local heat transfer coefficient and Fanning factor.Sui et al. [17] proposed a generic 1D modeling methodology to study the performance of the supercritical CO 2 PCHEs with Zigzag-channel.Chu et al. [18] also developed the correlations for the Nusselt number and the Fanning friction factor for airfoil-fin PCHE, but the correlations could only be used in airfoil-fin PCHE with supercritical CO 2 as the working medium, and the maximum error was up to 5%.Wang et al. [11] calculated the heat transfer and flow characteristics of straight-type PCHEs with rectangular channels of different widths under different mass fluxes by numerical method.Jeon et al. [19] investigated the thermal performances of PCHEs with semicircular, triangular, rectangular, and elliptical cross-sectional shape channels respectively by numerical method, and it was found that the cross-sectional shapes of PCHE channels had no significant effect on the thermal performance when the hydraulic diameters of different channels are the same.Some flow and heat transfer correlations of the supercritical CO 2 in the Zigzag channels PCHE from references are given in table 1 [20][21][22][23].The PCHEs using helium as the working medium are usually used as the intermediate heat exchangers in HTGRs, and their thermal-hydraulic performances are extensively studied.Alon et al. [24] studied the thermal-hydraulic performance of the PCHE with a Zigzag flow pattern by experiments, fitted Nusselt models for the supercritical CO 2 and helium data, and the models matched the experimental data to within ±15%.Chen et al. [25] developed the correlations for the Fanning friction factor and Nusselt number for the Zigzag channel with 15° pitch angle, and compared them with the existing correlations for straight channel based on experimental data for PCHE with helium, and the results showed that Zigzag channel with small pitch angle almost had no advantage in laminar flow zone in terms of heat transfer performance, but obvious advantage in flow transition zone.Chen et al. [26] studied the influence of some structural parameters on the flow and heat transfer characters of the helium in the PCHE in a high-temperature helium test facility at The Ohio State University, developed new pressure drop and heat transfer correlations for the Zigzag channels with a roundness at each bend, and found that further increasing the Zigzag angle beyond 30° is not recommended for high-temperature helium-to-helium applications.Mylavarapu et al. [27] carried out thermal-hydraulic tests based on hightemperature helium testing equipment and compared the experimental data obtained with the correlations based on circular channels, and it is found that the Nusselt number was slightly larger than the corresponding circular tubes.
The flow and heat transfer characteristics of nitrogen, methane, and fresh fluids are investigated in order to investigate other fields of the PCHE application.Taking PCHE as a vaporizer for LNG, Zhao et al. [28] compared the thermal-hydraulic performance of airfoil fin PCHE with straight channel PCHE with the experiment of nitrogen in PCHE and found that the airfoil-fin PCHE had the better performance.Cai et al. [29] studied the effects of operating parameters on the thermal-hydraulic performances with supercritical methane and supercritical methane-ethane mixture as flow media in a Zigzag channel PCHE, which worked as a cooler between compressors in the liquefaction process of natural gas and developed new flow and heat transfer correlations based on the simulation results.Wang et al. [30] used PCHE as an intermediate heat exchanger in an accelerator-driven system, adopting helium as the cold fluid and lead-bismuth eutectic (LBE) as the hot fluid, and studied thy thermal-hydraulic performance of it by numerical method, and the results showed that LBE has a high heat transfer rate in the radial direction and a superior degree of field synergy, which ensures a strong heat transfer performance.
According to the above analysis, there are relatively few researches on the supercritical fuel PCHE for CCA system among many researches on PCHEs.The flow and heat transfer characteristics of supercritical fuel in the PCHE are not clear due to the lack of reliable experimental and numerical data.
In this study, a supercritical fuel PCHE with Zigzag channels is numerically investigated by using the actual working conditions in CCA system.The numerical simulation scheme of the supercritical fuel PCHE has been established, and its accuracy is verified against the experimental data in the built experimental system.The influence of the fuel inlet temperature, mass flow rate, and outlet pressure on the flow and heat transfer characteristics of the supercritical fuel PCHE is numerically investigated, and the correlations for the Nusselt number and Fanning friction factor are proposed, respectively.

Physical model and numerical method
The physical model studied in this paper is a supercritical fuel PCHE.The Fuel RP-3 under the supercritical pressure is used for the cold fluid, the air is used for the hot fluid, and 304 stainless steel is used for the solid section of the PCHE model.It is composed of two plates with cold side flow channels for fuel, two plates with hot side flow channels for air, and inlet and outlet flow channels as shown in figure 1.The detailed structures of the flow channel are shown in figure 2.   The commercial CFD software, ANSYS Fluent 2022, has been used.The SIMPLE algorithm is used to realize the pressure-velocity coupling and the governing equations are solved by the second-order upwind scheme for the steady-state simulations.The solution is thought to converge when the residuals reach 1.0×10 -6 .The boundary conditions of the mass flow inlet and pressure outlet are used for cold and hot fluids, respectively.The other detailed parameters are listed in table 3. The thermophysical properties of RP-3 are generally predicted by a surrogate model in the numerical process.Figure 5 shows the thermophysical properties of the surrogate model computed using an internal code varying with temperature under different pressures [31].And the thermophysical properties of the fuel are compiled in Fluent through User Defined Functions.The air density is calculated by the ideal gas model.The viscosity, specific heat capacity, and thermal conductivity are calculated by kinetic theory, and the molar mass of air is set at constant 28.96 g/mol.

Governing equations
In this paper, considering that the fuel RP-3 and air under the steady flow state, and the effect of gravity is small, the governing equations do not contain the unsteady terms and gravity terms.
The continuity equation: The momentum equation: where τ ij represents the shear stress tensor and it can be calculated by: Reynolds stress hypothesis equation: The energy conservation equation: Considering that the temperature and pressure conditions of RP-3 in this study did not meet the cracking conditions [32][33][34], chemical reactions were not considered in the whole flow process.
Therefore, the internal heat source generated by chemical reactions could be omitted from the energy conservation equation, and the simplified form of the energy conservation equation is expressed as follow: RNG k-ε turbulence model [32] is used to study the thermal-hydraulic performance of supercritical fuel in the PCHE.The constitutive equations and transport equations of this turbulence model are given below.
The constitutive equation: The turbulent kinetic energy equation: The equation of dissipation rate of turbulent kinetic energy: where C μ , C ε1 and C ε2 are constants; f μ , f 1 and f 2 are functions; S k represents the source terms of the turbulent kinetic energy equation and S ω represents the source terms of the equation of the dissipation rate of turbulent kinetic energy.
P k represents the turbulent kinetic energy generation term caused by shear forces, and it can be calculated by: Γ k and Γ ω represent the effective diffusion coefficients and they are given as follows: where σ k and σ ε represent Pr numbers of turbulent kinetic energy and dissipation rate of turbulent kinetic energy, respectively.

Parameter definitions
The convective heat transfer coefficient can be calculated by: ℎ =  �  −  � (13) where A is the area of heat transfer surfaces, and T w and T f are the average fluid temperature and the average wall temperature respectively.
And d h is the hydraulic diameter of the flow section, defined as: where A c is the cross-sectional area of a single channel and P c is the perimeter.The Reynolds number and Prandtl number can be expressed as follows: where u is the velocity of the fluid, , ,  and c p represent the density, dynamic viscosity, thermal conductivity, and specific heat at constant pressure of the fluid, respectively.The Fanning friction factor and Nusselt number can be defined as: where ∆p represents the pressure drop and L represents the length of the flow channel.Performance Evaluation Criteria (PEC) [35][36] is used to comprehensively measure the flow and heat transfer performance of the PCHE, and it can be calculated by:

Mesh independence verification
Four sets of grids with various numbers of grid-point are selected for mesh independence verification, which ranges from 5.5 million to 12.76 million.The pressure drop and temperature difference between the inlet and outlet are employed as the evaluation parameters.Finally, the mesh with 10.14 million grids is used as the independent solution because the monitoring point parameters for this mesh vary <1% from those of the finest mesh, as shown in figure 6.

Numerical method verification
In order to verify the accuracy of the numerical method, the supercritical flow and heat transfer experimental system has been designed and built, as shown in figure 7. The driving force of the air comes from the outdoor compressor, and the driving force of the fuel comes from the high-pressure cylinder in front of the tank.The electric heater is powered by 380V AC-regulated power, which can make the air temperature at the entrance of the experimental section reach 773K.The fuel heater is heated by two heating electrodes clamped on the heating tube, and it is supplied by two voltageregulating transformers.The fuel and air downstream of the experimental section are cooled by water coolers to the ambient temperature and then excluded from the experimental system.Thermocouples, as well as absolute and differential pressure gauges, are installed at all inlets and outlets.And the mass flow rates of working fluids are measured by the flowmeters at the inlet of the PCHE.The pressure parameters to be measured during the experiment include the absolute pressure of air and fuel at the inlet of the test section and the differential pressure between the inlet and outlet of the experimental model.In order to satisfy the demand for pressure measurement, a pressure extraction joint is designed and processed.The pressure-taking interface is set on the side of the steady flow section with a length, and the opening diameter is 0.8mm, which can reduce the impact on the mainstream and increase the accuracy of pressure and differential pressure measurement values.Thereafter, the data of flow rate, temperature, absolute pressure, and differential pressure are perceived by a data acquisition unit.When the experimental setup has reached a pre-designated steady-state operating condition, all the measurements are stored at 3s intervals.In order to verify the accuracy of the numerical method proposed in Section 2, the numerical results obtained by using three different models (RNG k-ε, Laminar, Transition SST) under typical working conditions are compared with the experimental results as shown in figure 8.The air inlet temperatures in cases A and B are set as 500℃, the air inlet mass flow rates are 6.4g/s, the air outlet pressures are 1MPa, the fuel inlet mass flow rates are 8g/s, the fuel outlet pressures are 3MPa, and the fuel inlet temperatures are set as 100℃ and 200℃, respectively.It can be obtained that the numerical results by RNG k-ε turbulence model are the closest to the experimental results, and the absolute relative deviations are less than 10%, which indicates that the numerical method has high practicability and accuracy in the prediction of flow and heat transfer characteristics of the supercritical fuel in the PCHE.

Analysis of flow and heat transfer characteristics
Figure 9a and 9b illustrates the temperature distributions of the fuel and air in the cross section.It can observe that the thermal boundary layer of the fuel is thicker than that of air.This is due to the higher thermal conductivity of fuel than the air, resulting in a larger heat transfer rate in the radial direction.Depending on the numerical results, the convective heat transfer coefficient of fuel is about 2.3 times of air because the mean specific heat of fuel is higher than that of air, which leads to its higher heat transfer capacity.In order to explain this conclusion more intuitively, the temperature gradients of the bulk fluids and the velocity vectors for both fluids are given in figure 9a and 9b separately, as well as the intersection angle between them.One can see that on the fuel side, the velocity vector and the temperature gradient vector are closer to parallel than the air.This phenomenon indicates that the fuel has a superior field synergy degree, which ensures its stronger heat transfer performance.And the result of pressure in figure 6 shows that the pressure drop of the air side is about 16 times larger than that of the fuel side, that is because of the larger wall shear force of the air side, which shows in figure 9c  The results of temperature distribution in figure 10a show that the temperature of the fuel in the middle channels is lower than that on both sides, because the velocity of the fuel is different through each channel at the plate entrance (figure 10a) and the lower flow rate in the middle channels leads to its poor heat transfer performance.It is observed from the pressure distribution as shown in figure 10b that the pressure of the fuel in the middle channel is slightly lower than that in other channels and there is large flow resistance in the shunt position because of the existence of a sharp point at the junction.It can also be seen that the fuel pressure at the outlet of separate flow channels is different, resulting in a large pressure drop when they are mixed together at the confluence.As the temperature of fuel increases along its flow direction, the density decreases, and the velocity increases, the heat transfer capacity and the flow resistance increase, so the process of temperature rise and pressure drop is faster along the flow direction.Figure 10b shows the velocity distribution of the fuel in the flow channels.It can be seen that the flow direction of the fuel encounters a forceful change at the bent portions in Zigzag channel, thus, the bulk flow gradually closes to the inner corner, and resumes normal in down flow region.In other words, the morphology of the boundary layer is concerned at the bent portion.Combined with the turbulent kinetic energy distribution shown in figure 10c, larger turbulent kinetic energy is observed in the down flow regions near the bent, it promotes the local turbulence and mixing effect.And it is the strong mixing effect that enhances the local heat transfer performance, but brings an extreme penalty of flow resistance as well.Part of large turbulent kinetic energy vanishes as the flow develops non-corners, therefore, the heat transfer enhancement is weakened, the flow resistance is reduced.

Effect of working conditions of fuel on thermal-hydraulic performance
When the influence of different inlet temperatures and mass flow rate of the fuel is studied, the inlet temperature ranges from 100℃ to 350℃, the inlet mass flow rate is set as 6g/s, 8g/s, and 10g/s, the outlet pressure is set as 3MPa, and those of the air are fixed at 500℃, 6.4g/s and 1MPa.
Figure 11 shows the variations of the pressure drop and heat transfer coefficient of the fuel in the PCHE under different inlet temperatures and mass flow rates of fuel.The pressure drop and heat transfer coefficient increase with the increasing inlet temperature.When the inlet temperature increases from 100℃ to 350℃, the heat transfer coefficient will decrease by 220% to 280%, and the pressure drop will increase by 40% to 50%.And the heat transfer coefficient will increase by 15% to 35%, and the pressure drop will increase by 150% to 160%, as the inlet mass flow rate increases from 6g/s to 10g/s.Combined with the thermophysical properties of the fuel shown in figure 5, the density of the fuel decreases with the increasing inlet temperature.The mean velocity of the fuel in the PCHE increases with the increase of inlet temperature and mass flow rate, resulting in the increase of pressure drop of the fuel as shown in figure 11a.The temperature difference between hot and cold fluids in the PCHE provides the driving force for heat transfer.Therefore, with the increase of the fuel inlet temperature, heat transfer coefficient of the fuel in the PCHE decreases as shown in figure 11b.
In order to show the turbulent intensity at different inlet mass flow rate, the cases with the inlet mass flow rate of 6g/s, 10g/s and inlet temperature of 100℃ are selected for analysis.To describe the turbulence intensity of supercritical fuel flow, the variation of turbulent kinetic energy (TKE) with the dimensionless length X+ is provided in figure 12.The dimensionless length of the channel can be calculated by:  + =   (22) where X is the traveled length of the fluid, and L is the length of the flow channel.The wave distribution of the turbulent kinetic energy shown in figure 12 is caused by the change of the fluid flow direction at the bend of Zigzag channel, which is consistent with the result shown in figure 10c.And it can be noted from figure 12 that the increase of the mean velocity caused by the increase of mass flow rate increases the turbulent kinetic energy of the fuel, which leads to the increase of heat transfer coefficient with the increase of mass flow rate.With the increase of inlet temperature, the temperature difference between cold fuel and hot air decreases, and the overall heat transfer performance of PCHE decreases.Therefore, the increase of heat transfer coefficient caused by increasing mass flow rate is small, that is, the difference of heat transfer coefficient is small at higher inlet temperature (especially 350℃) as shown in figure 11b.
As shown in figure 13, the overall performance evaluation of the PCHE decreases monotonously with the increase of the inlet temperature.This is explained by the fact that the heat transfer performance will decrease and the pressure drop will increase with the increase of the inlet temperature, and the two factors cause the decrease of the PEC together.The effect of mass flow rate change on the overall performance of PCHE is not monotonic, as shown in figure 13.The promoting effect of the mass flow rate increase on heat transfer is more important than that of flow resistance under the low mass flow rate, so the overall performance increases as the mass flow rate increases.When the mass flow rate increases to more than a certain critical value, the large mass flow rate has a significant effect on pressure drop, so the overall performance gradually decreases with the mass flow rate increases.The effect of outlet pressure of the fuel on the thermal-hydraulic performance is investigated that the inlet temperature of fuel is set as 350℃ and the fuel mass flow rate is kept constant at 8g/s.The variable tendencies of the pressure drop and the heat transfer coefficient with different outlet pressure are shown in figure 14.In the process of increasing the outlet pressure from 3MPa to 6MPa, the heat transfer coefficient will remain almost constant, and the pressure drop will decrease by 7-25%.The comparison between the numerical results shown in figures 11 and 14 demonstrates that the outlet pressure has less impact on the thermal-hydraulic performance (h, ∆p and PEC) of the PCHE than the inlet temperature and mass flow rate in the studied temperature and pressure range, because the pressure has little effect on the fuel thermophysical properties, especially at higher pressure in the range of working conditions studied.

Flow and heat transfer correlations development
The variation of the Fanning friction factor versus the mean Re for the tested PCHE is presented in figure 15.With the mean Re increases from 620 to 4000, the Fanning friction factor goes down monotonously from 0.059 to 0.045.The trend of the Fanning friction factor with the mean Re leads to a conclusion that there is no obvious transition from laminar flow to turbulent flow in the tested PCHE with Zigzag channels within the scope of the numerical conditions.By summarizing the numerical results, a new empirical correlation is proposed to predict the Fanning friction factor of the tested PCHE, as shown in equation (23).
= 0.101  −0.0859 (700 ≤   ≤ 5000) (23) where Re m represents the mean Reynolds number of the fuel.The manner in which the values of f predicted by equation ( 23) and other correlations [20,23] presented in table 1 which are established based on supercritical CO 2 for the PCHE with Zigzag channels varying from the numerical ones is shown in figure 16.Gnielinski [38] developed an empirical correlation formula with a wider application range for the flow resistance characteristics of single-phase fluid working medium in a single pipe, as shown in equation (24), and it is also compared in figure 16.
= [0.79ln()− 1.64] −2 (24) It can be seen from figure 16 that the new developed flow correlation predicts 92.5% of the data within the ±5% error band, and the prediction performance accuracy of the new correlation is much higher than that of other correlations.The calculated Fanning friction factors using new developed correlation are about 4.5% smaller than the experimental results obtained by the experimental system shown in Section 3.1.And the reasons for the difference are that the numerical simulation cannot perfectly simulate the manufacturing error of the tested PCHE and many conditions during the experiment including the location arrangement of the parameter measurement point.
The prediction values of the Fanning friction factor correlation established based on supercritical CO 2 for the PCHE with Zigzag channels are higher than the newly developed ones as shown in figure 16.The reason is that the velocity of supercritical CO 2 is higher than that of fuel under the same Re according to equation ( 15) due to the viscosity of fuel is much higher (about 10 times) than that of the supercritical CO 2 [37], and it will cause the pressure drop of supercritical CO 2 is higher at the same condition [20][23].The prediction values of the new correlation for f are closer to Gnielinski's correlation than others, and the predicted values by new correlation at high Re are higher than those predicted by Gnielinski's due to the influence of the flow channel bends and heat exchanger inlet/outlet heads on the flow.25) and other correlations listed in table 1 with the numerical result is conducted, as shown in figure 18.The new developed heat transfer correlation predicts 96.5% of the data within the ±10% error band, and the accuracy of its prediction for the tested PCHE is much higher than that of other correlations. = 0.00271  0.402   2.254 (700 ≤   ≤ 5000, 3.7 ≤   ≤ 7.7) where Pr m represents the mean Prandtl number of the fuel.It can be noted from figure 18 that all of the predicted Nu from the three heat transfer correlations which are proposed by supercritical CO 2 are about much higher than the numerical results.The specific heat [37] and velocity of the supercritical CO 2 are higher than those of the fuel under the same Re, so the overall heat transfer coefficient of the PCHE with supercritical CO 2 is higher [21] at the same condition, and that leads to the higher Nu predicted by the heat transfer correlations from Refs.[20] and [21].The thermoproperties of the fluid mainly affect the Pr value in the Nu correlation.Since the exponent of Pr in the new developed correlation is quite different from the existed correlation [20][21][22], the Nu of the fuel under the studied conditions in this paper predicted by the existed correlation shows the irregular distribution law as shown in figure 18.

Conclusions
This paper focuses on the supercritical fuel PCHE applied to the Cooled Cooling Air system in the aeroengine, a three-dimensional numerical approach for the PCHE with Zigzag channels adopting fuel RP-3 as the cold source and air as the hot source is established, and the accuracy of the numerical method is verified by the built experimental system.The influence of inlet temperature, mass flow rate and outlet pressure on the thermal and hydraulic performance of the tested PCHE is numerically investigated.Some main conclusions are shown as the following: The flow and heat transfer characteristics of the supercritical fuel PCHE is investigated.The fuel has a strong heat transfer performance than the air.The bent portions in Zigzag channel improve the heat transfer performance but bring great flow resistance as well by changing the bulk flow direction, and the heat transfer performance of the intermediate channels is lower because of the lower mass flow rate caused by the flow non-uniformity of the fluid at the inlet junction.And there is large flow resistance in the shunt and confluence position of the flow channels.
When the inlet temperature increases from 100℃ to 350℃, the heat transfer coefficient will decrease by 220% to 280%, and the pressure drop will increase by 40% to 50%, because of the weakening of the heat transfer driving force.And the heat transfer coefficient will increase by 15% to 35%, and the pressure drop will increase by 150% to 160%, as the inlet mass flow rate increases from 6g/s to 10g/s, due to the increasing mean turbulent kinetic energy of fuel in the PCHE caused by the increase of the inlet and mass flow rate.And the overall performance of the PCHE will be enhanced with the increase of inlet temperature, but it will be enhanced first and then reduced with the increase of the mass flow rate.The thermal-hydraulic performance of the PCHE changes little with the change of outlet pressure of the fuel.
Correlations for the Fanning friction factor and Nusselt number for the tested PCHE are proposed to predict the flow and heat transfer characteristics of the fuel.The newly developed Fanning friction factor correlation predicts 92.5% of the numerical data within the ±5% error band, and the newly developed heat transfer correlation predicts 96.5% of the numerical data within the ±10% error band.

Figure 1 .
Figure 1.Calculation model of the supercritical fuel PCHE.

Figure 5 .
Figure 5.The variation of thermophysical properties of RP-3.

Figure 7 .
Figure 7. Schematic diagram of the experimental system for supercritical fuel PCHE.The temperature difference of fuel in the test section can be expressed by: fuel in fuel out fuel t t ΔT , , − =

Figure 8 .
Figure 8.Comparison between experimental and numerical results under Cases A and B.

Figure 9 .
Figure 9. Wall shear stress and temperature distribution in cross section.

Figure 10 .
Figure 10.Velocity, pressure, and turbulent kinetic energy distribution of fuel side in cross section.

Figure 11 .
Figure 11.The flow and heat transfer characteristics under different inlet temperature and mass flow rate.

Figure 12 .
Figure 12.Local turbulent kinetic energy versus X + under different inlet mass flow rate.

Figure 13 .
Figure 13.The performance evaluation criteria under different inlet temperature and mass flow rate.

Figure 14 .
Figure 14.The flow and heat transfer characteristics under different outlet pressure.

Figure 15 .
Figure 15.The distribution of f along Re m .

Figure 16 .
Figure 16.The comparison of numerical f with the predicted ones.The variation of the Nu versus the mean Re and the mean Pr for the tested PCHE is presented in figure 17.The heat transfer correlation for the tested PCHE is developed as shown in equation (25), and the comparison of the Nusselt numbers predicted by equation (25) and other correlations listed in table1with the numerical result is conducted, as shown in figure18.The new developed heat transfer correlation predicts 96.5% of the data within the ±10% error band, and the accuracy of its prediction for the tested PCHE is much higher than that of other correlations.

Figure 17 .
Figure 17.The distribution of Nu along Re m and Pr m .

Figure 18 .
Figure 18.The comparison of numerical Nu with the predicted ones.

Table 1 .
Some correlations of supercritical CO2 for PCHEs with Zigzag channels.