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Numerical investigation of a compact tube heat exchanger for hypersonic pre-cooled aero-engine
Journal Pre-proofs Numerical investigation of a compact tube heat exchanger for hypersonic precooled aero-engine Wenhao Ding, Qitai Eri, Bo Kong, Zhen Zhang PII: DOI: Reference:
S1359-4311(19)34077-3 https://doi.org/10.1016/j.applthermaleng.2020.114977 ATE 114977
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
13 June 2019 13 January 2020 19 January 2020
Please cite this article as: W. Ding, Q. Eri, B. Kong, Z. Zhang, Numerical investigation of a compact tube heat exchanger for hypersonic pre-cooled aero-engine, Applied Thermal Engineering (2020), doi: https://doi.org/ 10.1016/j.applthermaleng.2020.114977
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Numerical investigation of a compact tube heat exchanger for hypersonic pre-cooled aero-engine Wenhao Dinga, Qitai Eria*, Bo Konga*, Zhen Zhangb a School of Energy and Power Engineering, Beihang University, Beijing, 100191,China b China Academy of Aerospace Aerodynamics, Beijing, 100074,China * To whom correspondence should be addressed: Qitai Eri, Bo Kong E-mail address of Qitai Eri: [email protected] E-mail address of Bo Kong: [email protected]
Abstract The compact tube heat exchanger is a key component of pre-cooled aero-engine. The pressure drop and flow distortion of the heat exchanger have a crucial effect on the performance characteristics of pre-cooled aero-engines including thrust and stability. However, it is difficult to simulate directly because of its extremely complex geometry. Therefore, a porous model and a dual cell heat exchanger model are utilized in this paper to simulate the pressure drop and heat transfer, respectively. The method is verified by comparing to previous experimental results. The simulation results are in good agreement with that of the experiment. The flow field characteristics of the heat exchanger and the effect of heat exchanger entrance conditions on the performance of the heat exchanger are studied in detail. It is found that uneven mass flux caused by the special geometry of the heat exchanger leads to non-uniform heat transfer and pressure drop along its axis. This subsequently results in flow distortion at the exit of the heat exchanger. Especially for the total temperature distortion, it will result in the reduction of stable work margin of the compressor. In addition, the changes of velocity, total temperature and total pressure affect the pressure drop and flow distortion. These effects are predominantly caused by changes in the flux distribution and velocity. Key words: Compact tube heat exchanger, Pre-cooled aero-engine, Flow
distortion, Porous model, Dual cell model
Nomenclature heat capacity, J/K C πΆπ Specific heat capacity, J/(kgΒ·K) Heat transfer coefficient, w/(m2Β·K) β Ratio of specified heats, π Mass flow rate, kg/s π Pressure, pascal π β Total pressure, pascal π Heat transfer rate, w π Temperature, K π
πβ π£ ΞΌ Ο ππ π π ππ’ ππ
Total temperature, K Velocity, m/s Viscosity, NΒ·s/ m2 Density, kg/m3 Mach number, Reynolds number, Nusselt number, Prandtl number, -
1. Introduction In the development of hypersonic propulsion systems, the pre-cooled aero-engine has become a major focus because of its applicability over wide range of flight conditions including reusable horizontal takeoff and landing [1,2,3]. Hydrogen powered pre-cooled aero-engine can reduce greenhouse gas emissions οΌ this more efficient engine is considered as a main direction of the potential cleaner aviation, which can weaken the effects of aviation on the global atmosphere [4,5,6]. The heatexchange-medium helium having good thermal conductivity is used to cool the hightemperature air flow, which provides high reliability and high compressor efficiency [7,8,9]. The compact tube heat exchanger is a key component of the pre-cooled aeroengine [10]. The performance of the heat exchanger has a major effect on the performance of the engine. The heat exchanger is located between the intake and the compressor. High-temperature air entering the aero-engine flows through the heat exchanger to be cooled under high-speed flight conditions. The air is cooled to a temperature where the compressor can operate normally [11]. The heat exchanger is
usually axisymmetric in order to match the geometry of the aero-engine. The inlet and outlet geometry and size of the heat exchanger are the same as the outlet of the intake and the inlet of the compressor, respectively. Furthermore, the heat exchanger tube bundles are small in diameter, numerous in numbers, and are densely packed to allow the high-temperature air entering the aero-engine to cool rapidly. Experimental studies of the pro-cooled heat exchanger with small bore tubes have been carried out, including studies of design, manufacture, and performance [12,13, 14,15]. Distortion of the air flow through the heat exchanger results in reduced stability of the compression components and decreases the thrust of the aero-engine. In addition, air flow through the heat exchanger may cause large total temperature distortion due to uneven heat transfer. Total temperature distortion has negative impacts on engine operation, resulting in the reduction of the stall margin, and the engine is more tending to surge [16,17]. Among them, the high pressure compressor is most sensitive to temperature distortion [18]. Thus, there is a need to study the flow characteristics and distortion of compact tube heat exchangers used for pre-cooled aero-engines. The simulation of the three-dimensional flow and heat transfer process in compact tube heat exchangers is very difficult due to the large number of tube bundles in the heat exchanger. Therefore, a simplified simulation approach for the flow and heat transfer of compact tube heat exchanger is necessary. Hammock [19] presented a crossflow, staggered-tube heat exchanger analysis for high enthalpy flow. Empirical correction characteristics were presented by comparing the empirical and experimental results. Kritikos et al. [20] investigated the thermal efficiency of a staggered elliptic-
tube heat exchanger for aero-engine applications with two different methods. Namely, the exact geometry cell and the porous medium approaches were used. It was shown that both approaches can be used for the detailed investigation of the thermal performance of the heat exchanger. An et al. [21] studied the thermal and hydraulic characteristics of a cross-flow finned tube heat exchanger using the porous medium model and found the simulation results agreed well with the experimental data. Zhang et al. [22] studied the heat transfer in the intermediate heat exchanger of a sodiumcooled fast reactor with the porous model and heat exchanger model. This approach was able to replicate the pressure drop and heat transfer characteristics of the detailed model. Missirlis et al. [23] studied an aero-engine heat exchanger using the porosity model, and found that this approach could effectively simulate the heat exchanger in the respects of heat transfer and pressure drop. The simplified simulation methods provide the means to numerically simulate the compact tube heat exchanger of a precooled aero-engine. In this paper, a numerical simulation method for axisymmetric compact tube heat exchanger is established. The simulation method is validated with experimental results. A porous model and dual cell model are used to simulate the pressure drop and heat transfer, respectively. The flow characteristics and heat transfer performance of the heat exchanger and the influence of entrance boundary conditions on the performance of the heat exchanger are studied. 2. The compact tube heat exchanger model A schematic of the intake and heat exchanger investigated in this study is shown in
Fig.1. Both the intake and the heat exchanger are axisymmetric. The axial length of the heat exchanger is 1000mm, the external diameter is 1000mm and the internal diameter is 700mm, as shown in Fig.2. The specified structure of heat exchanger tube is shown in Fig.3, and the detailed sizes of the heat exchanger tube bundle are marked. The flow of the shell-side is high-temperature air flow. The flow of the tube-side is lowtemperature supercritical helium.
Fig. 1. Schematic of the intake and heat exchanger
Fig. 2. Typical view of the heat exchanger
Fig. 3. Specified structure of the heat exchanger tube (mm)
As the heat exchanger is axisymmetric and efficient, the temperature variation in the heat exchanger is very large. A temperature difference of 900K is produced when the
air travels through the heat exchanger under high-speed flight conditions. Thus the properties of air vary greatly due to the temperature differences. In view of this situation, the heat transfer zone is divided into five zones in the radial direction and each zone has its own working parameters. The simulation model structure with its boundary conditions is shown in Fig. 4, and the domain was considered as axisymmetric for simulations.
Fig. 4. Simulation model structure of the heat exchanger with boundary conditions
The flow characteristics of the heat exchanger and the effect of entrance conditions on the heat exchanger are studied. The main parameters of interest are the total pressure recovery, total pressure distortion, and total temperature distortion. The equation of total pressure recovery is expressed by Eq. 1. The equation of steady distortion coefficient is expressed by Eq. 2. ο³i ο½ π·=
pi* pin*
πΌ β πππ₯ β πΌ β πππ πΌ β ππ£π
(1)
(2)
where Ξ± represents the respective total pressure and total temperature. 3. Simulation methods The numerical simulations were carried out using the commercial software ANSYS
Fluent 15.0. Porous model and dual cell model were used to simulate the pressure drop and heat transfer, respectively. 3.1 Porous model For the fluid flowing through the compact tube heat exchanger, the flow region is regarded as porous media to estimate the pressure drop. The government equations are presented below for mass, momentum and energy: ο² οΆο² ο« ο ο§( ο² v ) ο½ 0 οΆt
ο² ο²ο² ο΅ο² ο΅ο² οΆο² v ο« οο§( ο² vv) ο½ οοp ο« οο§(ο΄ ) ο« ο² g ο« S οΆt
(3)
(4)
where π is the superficial velocity in porous media, and π is the additional vector momentum source term of porous media. ο² ο² οΆ ( ο² E ) ο« οο§(v( ο² E ο« p )) ο½ οο§(keff οT ο« (ο΄ eff ο v)) ο« S h οΆt
(5)
The first two terms on the right-hand side of energy equation represent energy transfer due to conduction and viscous dissipation, respectively. And Sh represents the heat source term. Finite volume method is used for governing equations, and space discretization using second-order upwind. SIMPLE algorithm is employed to solve equations. The air flow in the simulation domain is considered as compressible flow, although the velocity of air is relatively low after the deceleration in the intake and the Mach number is no more than 0.3. For the porous model, the resistance is regarded as a pressure loss source term [24].Both viscous loss and inertial loss were considered. The viscous loss is the primary mechanism for pressure drop in low velocity magnitude, and the inertial loss is primary
in high velocity magnitude. For a simple porous media, the additional momentum source term is presented as: π
π π = β(πΌππ + 0.5ππ2|π£|ππ)
(6)
where πΌ is the permeability of porous media and c2 is the inertial loss coefficient. In this study, the viscous loss and inertial loss are considered simultaneously. In addition, because the flow is axisymmetric, the loss coefficient is considered in the axial and radial direction. In order to get the viscous and inertial loss coefficient, the empirical correction of Kays & London [25] is used. The specified formula is shown below: βp = πΊ2 β π β π΄π π’ππ,π/(2 β π β π΄πππ) π = 0.55π π β0.18
(7) (8)
where G is the maximum flux, π΄π π’ππ,π is the heat transfer area, π΄πππ is the minimum flow area, π is the friction factor. The relationship of pressure drop and free flow velocity can be obtained using the empirical correction, allowing the loss coefficient to be calculated. And the porosity defined as the ratio of the volume of air flowing through the heat exchanger to the overall volume of the heat exchanger is 0.7328 for this heat exchanger, calculated from the geometry of heat exchanger. 3.2 Heat exchanger model A dual cell model is used to simulate the heat transfer in this study. This model can present the temperature field of both the primary and auxiliary flow and has no limitation of mesh type and heat exchanger geometry. Heat transfer rate is computed for each cell in the two cores (primary and auxiliary) and added as a source term Sh to
the energy equation for the respective flows [24]. For the dual cell model, a mesh cell is considered as a heat exchanger. For each cell, the number of heat transfer units (NTU number) is retained and interpolated from the NTU table, which allows the overall performance of the heat exchanger to be calculated [24]. The flow of the heat exchanger in this paper is considered to be counter flow, since the number of turns in the bundle exceeds four times [26]. The schematic of the dual cell model is shown in Fig. 5. The import and export boundary conditions of auxiliary flow (helium) are mass-flow-inlet and pressure-outlet, respectively. And the interface boundary condition is used in the junction of different auxiliary flow grid zones.
Fig. 5. The dual cell model for primary and auxiliary flow
The equations used in the calculation are given as follows: ππ πππππ,π΄ = πππππ,π΄πππππ,π΄π΄πππππ‘,π΄
(9)
ππ πππππ,π = πππππ,ππππππ,ππ΄πππππ‘,π
(10)
πΆπππ,π πππππ = min [(ππ ππππππΆπππππ)|π,(ππ ππππππΆπππππ)|π΄]
(11)
ππππ πππππ = [πππππ’ππ(ππ πππππ,π,ππ πππππ,π΄)]πππππππππππ‘πππππππ‘πππ
(12)
ππ΄π πππππ = ππππ ππππππΆπππ,π πππππ
(13)
πππππ =
ππ΄π πππππ(πππππ,π΄ β πππππ,π)π πππππ
(14)
The iterative procedure to obtain the overall performance of heat exchanger is shown in Fig. 6.
Fig. 6. Flow chart of the iteration process to calculate the heat exchanger NTU number
The shell-side heat transfer coefficient is calculated using the Kayβs and London empirical correction [25]: h = 0.571GπΆππ π β0.4
(15)
The tube-side heat transfer coefficient for turbulent flow is calculated using the Gnielinski empirical correction [27]: Nu =
(π/8)(π π β 1000)ππ π 8
(ππ
1 + 12.7
2/3
β 1)
π 2/3
[1 + ( π )
π = (1.82log10 π π β 1.64) β2
]πΆ
π‘
(16) (17)
The tube-side heat transfer coefficient for laminar flow is calculated using the empirical formula: Nu = 3.66
(18)
The heat transfer efficiency is given by: π
Ξ΅ = ππππ₯
where ππππ₯ is the theoretical maximum heat transfer rate. The NTU β Ξ΅ relation of counter flow is given by:
(19)
Ξ΅=
1βπ
βπππ(1 β πΆπππ/πΆπππ₯)
1 β (πΆπππ/πΆπππ₯)π
(20)
βπππ(1 β πΆπππ/πΆπππ₯)
In addition, the properties of air and helium vary greatly, and large temperature variation is present on both sides of heat transfer tube. Therefore, the properties of the fluid are defined as a function of temperature to improve the accuracy estimations of heat transfer and pressure drop [28]. 3.3 Numerical simulation method validation A simulation of the heat exchanger in [13] was carried out to investigate the accuracy of the present simulation method. In this section, the simulation results are compared with the experiment results obtained from the reference. In the experiment, the primary flow in shell-side is nitrogen, and the auxiliary flow in the tube-side is helium. Its tube diameter is similar to the tube diameter studied in this paper, so the validation of the method is convincing. According to [13], the boundary conditions are shown in Table 1. Table 1. Boundary conditions in [13]
Helium entrance temperature (K)
Helium entrance mass flow rate (kg/s)
Nitrogen entrance temperature (K)
Nitrogen entrance mass flow rate (kg/s)
223
0.00093
877
0.0259
Table 2 shows the simulation and experimental results for pressure drop and heat transfer rate. It is found that the error between the experimental results and the CFD results is 10.4% in pressure drop and 16.6% in heat transfer rate. This indicates good agreement and satisfies the requirements of the present work [29].
Table 2. Comparison of the experiment results and simulation results
Experiment results Simulation results
Pressure drop (pa) 4600 4120
Heat transfer rate (w) 2560 2985
Percentage error (%)
10.4
16.6
Grid independence study is also performed; the simulation results differences between different computational grids quantities are compared. The quantities of the grid are 3.1 ο΄ 105, 4.8 ο΄ 105, 7.0 ο΄ 105 and 10.0 ο΄ 105, used to simulate the same case respectively. The simulation results are shown as follows:
Total temperature (K)
440 Mesh1 Mesh2 Mesh3 Mesh4
400
360
320
0.0
0.1
0.2
0.3
0.4
Radial location (m)
Fig.7. Radial distributions of total temperature for heat exchanger outlet with different grid quantities (Mesh1: 3.1 ο΄ 105; Mesh2: 4.8 ο΄ 105; Mesh3: 7.0 ο΄ 105; Mesh4: 10.0 ο΄ 105) Table 3. Radial velocity of the heat transfer region entrance with different grid quantities
The quantity of the grid 3.1 ο΄ 105 4.8 ο΄ 105 7.0 ο΄ 105 10.0 ο΄ 105
Radial velocity of the heat transfer region entrance(m/s) 12.84 13.34 13.35 13.38
Table 4. Total pressure recovery of the heat exchanger outlet with different grid quantities
The quantity of the grid 3.1 ο΄ 105 4.8 ο΄ 105 7.0 ο΄ 105 10.0 ο΄ 105
Total pressure recovery of the heat exchanger outlet 0.9567 0.9574 0.9571 0.9572
It can be seen that the quantity of the grid will affect the simulation results in some extent. For the simulation model in this study, the simulation results tend to be stable when the grid quantity reaches 4.8 ο΄ 105. In order to ensure the accuracy of the
simulation and avoid waste of computing resources, the quantity of grid used in this paper is 4.8 ο΄ 105. 4. Results and discussions 4.1 Flow characteristics of the heat exchanger The flow characteristics of the heat exchanger are studied here. The inlet parameters in this section are shown in Table 5. And the Table 6 shows the mass-weighted average simulation results of the heat exchanger. Table 5. The inlet parameters of the flowing medium
Flowing medium
Total pressure (pa)
Total temperature (K)
Mass flow rate (kg/s)
Air
200000
1341
20.73
Helium
2000000
200
4.13
Table 6. The simulation results of the heat exchanger
Heat transfer
Heat transfer
Heat exchanger
region entrance
region exit
outlet
Total pressure recovery
0.998
0.959
0.958
Total pressure distortion
0.0147
0.0114
0.0101
Total temperature (K)
1341
400.89
401.09
Total temperature distortion
0
0.408
0.341
Parameters
The velocity contour of the heat exchanger is shown in Fig. 8. It can be seen that the velocity upstream of the heat transfer region decreases along the axis, the velocity downstream of the heat transfer region increases axially, and this is caused by the flow characteristics of variable mass flow rate channel flow. According to basic laws of gas dynamics, Eq. 21 is applicable in the case of equal section area [30]; when the main flow velocity is subsonic and the additional flow is vertical to the main flow, increasing the mass flow rate will increase the flow velocity until the flow velocity reaches the
speed of sound. Similarly, decreasing the mass flow rate decreases the flow velocity. dΞ½ Ξ½
1
ππ
= 1 β ππ2[(1 + πππ2)] π
(21)
In this study, the flow upstream of the heat exchanger can be seen as a mass flow rate reduction flow with equal section area approximately, because the entrance direction of the heat transfer region is approximately perpendicular to the upstream flow direction; the velocity upstream of the heat transfer region decreases axially. And the flow downstream of the heat exchanger can be seen as an increasing mass flow rate flow with equal section area approximately. As such, the velocity increases axially.
Fig. 8. Velocity contour (m/s)
The axial static pressure distributions at the entrance and exit of the heat transfer region are shown in Fig.9. It can be seen that the static pressure of the heat transfer region entrance increases along the axis. According to the Eq.22 [30], the static pressure increases with the reducing mass flow rate in the upstream of heat exchanger; and the static pressure at the exit of the heat transfer region decreases axially with the increasing mass flow rate in the downstream of heat exchanger. Therefore, the pressure difference between the heat transfer region entrance and exit becomes larger axially. In the heat transfer region, the flow direction changes to become radial flow quickly due to the
large pressure drop in radial direction. This increasing static pressure difference can subsequently lead to an increase in mass flow rate along the axis. This effect can also be verified from Fig. 10, which shows the axial mass flux (multiply density by radial velocity) distributions along the entrance and exit of the heat transfer region. dp p
πππ2
(
= β 1 β ππ2[2 β 1 +
)]πππ
πβ1 2 2 ππ
(22)
220000
Static pressure (pa)
217500 215000 Heat transfer region entrance Heat transfer region exit
212500 210000 207500
0.00
0.25
0.50
0.75
1.00
Axial location (m)
Fig. 9. Axial distributions of static pressure 17.5
Heat transfer region entrance Heat transfer region exit
15.0
Flux (kg/(m2s))
12.5 10.0 7.5 5.0 2.5
0.00
0.25
0.50
0.75
1.00
Axial location (m)
Fig. 10. Axial distributions of flux
The total pressure contour of the heat exchanger is shown in Fig. 11. Combined with the simulation results in Table.6, it illustrates that the total pressure loss of the entire heat exchanger is primarily generated in the heat transfer region; and the total pressure decreases significantly when the air flow through the heat transfer region.
Additionally, the total pressure distribution in the heat transfer region is not uniform, the total pressure loss produced in the heat transfer region increases axially. This is because the mass flow rate in the heat transfer region increases along the axis, which can be seen in Fig.10, and a large mass flow rate results in a high velocity, and then will result in a larger total pressure loss.
Fig. 11. Total pressure contour (pascal)
The total pressure distributions plotted against the dimensionless axial and radial location are shown in Fig.12, including the axial distributions in the heat transfer region with different radial location, expressed as axial position 1-4, the location is evenly distributed between the heat transfer region entrance and exit. It can be seen that the total pressure of heat transfer region entrance increases axially; according to the Eq.23 [30], the total pressure increases with the reducing mass flow rate in the upstream of heat exchanger. In the top right corner before the heat transfer region, the flow direction changes severely and a small recirculation zone is formed, as shown in Fig.8, resulting the total pressure decreasing at the corner. In the heat transfer region, as the flow deepens, the distribution of total pressure along the axial direction changes from the initial increase along the axis to the decrease along the axis. This is caused by the
increasing total pressure loss axially in the heat transfer region. Finally, it results in the decreasing total pressure distribution axially in the heat transfer region exit. ο§
dm dp* ο½ οkMa 2 ο§ * p m
(23)
202000
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region entrance Heat exchanger outlet
Total pressure (pa)
200000 198000 196000 194000 192000 190000 188000
0.00
0.25
0.50
0.75
1.00
Dimensionless location
Fig. 12. Total pressure distributions of dimensionless location (Axial direction: x/L, L=1000mm; Radial direction: r/R, R=350mm)
The air total temperature contour of the heat exchanger is shown in Fig. 13. The air total temperature distributions plotted against the dimensionless axial and radial location are shown in Fig.14. It can be seen that the total temperature sharply decreases from 1341 K to 400 K when the air goes through the heat transfer region and meet the temperature demands of the compressor. But the effect of cooling weakens axially at the same radial location, the total temperature distributions along the axis in the heat transfer region are rising, this can also be seen from the Fig.14, it finally resulting in total temperature distortion at the heat exchanger outlet. This uneven heat transfer rate is affected by the uneven mass flow rate distribution; the cooling effect strengthened where the mass flow rate is small and, is weakened when the mass flow rate is large. Therefore, the total temperature of the heat transfer region
exit increases along the axial direction. The total temperature distortion of the heat transfer region exit is up to 0.408, although it decreased to 0.341 at the heat exchanger outlet for the mixing of the air flow downstream of the heat transfer region, it is still at a very high level. It has a great negative influence on the aerodynamic stability of the compressor, and the engine is more prone to surge [31]. Furthermore, in the heat transfer region, the heat transfer capacity of the former zones is stronger compared with the latter zones, because the heat transfer area in the former zones is larger. Fig.15 shows the axial distributions of total temperature in the heat transfer region for cooling medium helium, it can also reflect this situation.
Fig. 13. Total temperature contour (K)
Total temperature (K)
1400
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region exit Heat exchanger outlet
1200 1000 800 600 400 200
0.00
0.25
0.50
0.75
Dimensionless location
1.00
Fig. 14. Total temperature distributions of dimensionless location (Axial direction: x/L, L=1000mm; Radial direction: r/R, R=350mm)
Total temperature (K)
1400
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region exit
1200 1000 800 600 400 200 0
0.00
0.25
0.50
0.75
Axial location (m)
1.00
Fig.15 Axial distributions of total temperature in the heat transfer region for helium
In summary, the uneven flux distribution caused by the uneven static pressure distribution causes a distortion of total pressure and total temperature. Therefore, the flux distribution is a key factor affecting the characteristics of the heat exchanger. 4.2 The effect of heat transfer region entrance velocity In this section, the effects of entrance velocity are studied, while the total pressure and total temperature of heat exchanger inlet maintain constant. The entrance velocity varies with the mass flow rate controlled by the outlet pressure. The other thing to note is that the target of all cases studied in this paper is to cool the high total temperature air to be 400 K by adjusting the helium mass flow rate. Table 7 presents the simulation results for the total pressure recovery with different heat transfer region entrance velocity conditions. It can be seen from the Table7 that the total pressure recovery decreases when the entrance velocity is increased. From the Eq.6, it can be seen that as the velocity increases, the additional momentum source term
increases, which leads to an increase in total pressure loss. Fig.16 and 17 show the total pressure distortion and total temperature distortion variation with different entrance velocities. The results show that the total pressure distortion and total temperature distortion increase when the entrance velocity increases. The total pressure loss in heat transfer region becomes more uneven axially with the increasing entrance velocity, then the total pressure distortion increases. The variation of total temperature distortion is because the mass flow rate increases when the entrance velocity increases, then the flux distribution becomes more uneven axially. In other words, increasing the heat transfer region entrance velocity has a negative effect on the performance of the heat exchanger, and is unfavorable for the stability of compressors. Table 7. Simulation results with different entrance velocity boundary conditions
Upstream region 0.997 0.996 0.994 0.990
Heat transfer region 0.973 0.966 0.951 0.922
Downstream region 0.9998 0.9997 0.9996 0.9993
0.035
Total pressure distortion
Case 1 Case 2 Case 3 Case 4
Entrance velocity (m/s) 10.66 12.11 14.86 19.03
Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.030 0.025 0.020 0.015 0.010 0.005 10
12
14
16
18
20
Heat transfer region entrance velocity (m/s)
Fig.16. Total pressure distortion for different entrance velocity
Overall region 0.970 0.962 0.945 0.912
Total temperature distortion
0.5 0.4 0.3 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.2 0.1 0.0 10
12
14
16
18
20
Heat transfer region entrance velocity (m/s)
Fig.17. Total temperature distortion for different entrance velocity
4.3 The effect of heat exchanger inlet total temperature In this section, the effect of inlet total temperature on heat exchanger performance is studied. In order to isolate this effect, the inlet total pressure and mass flow rate is maintained constant. The constant inlet mass flow rate is achieved by adjusting the outlet pressure. Table 8 presents the simulation results for the total pressure recovery with different heat exchanger inlet total temperature conditions. It can be seen that the total pressure recovery decreases when the inlet total temperature is increased. The density decreases as the total temperature is increased with total pressure maintains constant, so the velocity increases with the mass flow rate maintains constant, thereby increasing the pressure loss. Fig.18 and 19 show the total pressure distortion and total temperature distortion variation with different inlet total temperatures. It is shown that the total pressure distortion and total temperature distortion increases with the inlet total temperature increase. The variation of total pressure distortion is due to the more uneven total pressure loss axially caused by the increasing entrance velocity, and the
variation of total temperature distortion is caused by the more uneven flux distribution with the entrance velocity increase. This indicates the importance of the entrance velocity on the performance of heat exchanger. Table 8. Simulation results with different inlet total temperature boundary conditions
Case1 Case2 Case3 Case4
Total temperature (K) 900 1100 1500 1900
Upstream region 0.998 0.997 0.993 0.985
Heat transfer region 0.978 0.970 0.948 0.905
Downstream region 0.9994 0.9997 0.9996 0.9991
Total pressure distortion
0.05 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.04 0.03 0.02 0.01 800
1000
1200
1400
1600
1800
2000
Heat exchanger inlet total temperature (K)
Fig.18. Total pressure distortion for different inlet total temperature
Total temperature distortion
0.6 0.5 0.4 0.3 Heat transfer region entrance Heat transfer region outlet Heat exchanger outlet
0.2 0.1 0.0 800
1000
1200
1400
1600
1800
2000
Heat exchanger inlet total temperature (K)
Fig.19. Total temperature distortion for different inlet total temperature
4.4 The effect of heat exchanger inlet total pressure
Overall region 0.975 0.966 0.941 0.891
In this section, the effect of the inlet total pressure on the heat exchanger performance is examined. The inlet total temperature and heat transfer region entrance velocity are held constant. In the simulation process, the heat transfer region entrance velocity is monitored to be consistent by controlling the outlet pressure. Table 9 presents the results of corresponding total pressure recovery with different heat exchanger inlet total pressure conditions. It can be seen that the total pressure recovery of heat transfer region almost unchanged when the inlet total pressure is increased, this is because the entrance velocity is constant, then the pressure loss unchanged. Fig.20 and 21 show the effect of the inlet total pressure on the total pressure distortion and total temperature distortion. It is shown that the total pressure distortion stays nearly constant when the heat exchanger inlet total pressure is changed, this is also because the entrance velocity maintains constant. In addition, the total temperature distortion increases with the inlet total pressure increase, this is because the mass flow rate increases with the inlet total pressure increase, and results in the more uneven flux distribution. Table 9. Simulation results with different inlet total pressure boundary conditions
Case 1 Case 2 Case 3 Case 4
Total pressure (pa) 180000 200000 220000 250000
Upstream region 0.995 0.998 0.995 0.995
Heat transfer region 0.960 0.961 0.962 0.963
Downstream region 0.9996 0.9997 0.9997 0.9997
Overall region 0.955 0.958 0.957 0.958
Total pressure distortion
0.020 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet 0.015
0.010
0.005 160000
180000
200000
220000
240000
260000
Heat exchanger inlet total pressure (pa)
Fig.20. Total pressure distortion for different inlet total pressure
Total temperature distortion
0.5 0.4 0.3 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.2 0.1 0.0 160000
180000
200000
220000
240000
260000
Heat exchanger inlet total pressure (pa)
Fig.21. Total temperature distortion for different inlet total pressure
5. Conclusions In this paper, a porous model and dual cell model are used to study a compact tube heat exchanger for pre-cooled aero-engines. The accuracy of the simulation method was examined through comparison to experiment and was found to be satisfactory. The flow field characteristics of the heat exchanger and the effects of entrance velocity, inlet total temperature, and inlet total pressure on the total pressure recovery, total pressure distortion, and total temperature distortion were studied and discussed. It is found that due to the geometry of the heat exchanger, the flow of upstream and
downstream heat exchanger can be considered as mass flow rate decreasing and increasing flow with equal section area respectively; the static pressure difference between the entrance and exit of the heat transfer region increases axially. This causes an uneven axial flux distribution. The flux of the heat transfer region increases axially and causes a non-uniform total temperature distribution, and then causes severe total temperature distortion at the outlet of the heat exchanger. As well, the uneven flux distribution causes an uneven velocity distribution, which results in a non-uniform total pressure distribution. Therefore, the flux distribution is a key factor affecting the operation of the heat exchanger. The pressure drop and flow distortion will affected by the changes of entrance velocity, inlet total temperature and inlet total pressure. With an increase of the heat transfer region entrance velocity and heat exchanger inlet total temperature, the total pressure distortion and total temperature distortion are significantly increased, and the total pressure recovery is decreased; In addition, with the increase of heat exchanger inlet total pressure, the total pressure recovery and total pressure distortion remains mostly constant, but the total temperature distortion is increased. These effects are predominantly caused by changes in the flux distribution and velocity; the total pressure recovery and total pressure distortion is determined by the entrance velocity, while the total temperature distortion is determined by the flux distribution. References [1] U. Mehta, M. Aftosmis, J. Bowles, et al., Skylon Aerodynamics and SABRE Plumes, in: 20th AIAA International Space Planes and Hypersonic Systems and Technologies
Conference, 2015, 3605. [2] Z.G. Wang, Y. Wang, J.Q. Zhang, et al., Overview of the key technologies of combined cycle engine precooling systems and the advanced applications of microchannel heat transfer, Aerospace Science and Technology. 39 (2014) 31β39. [3] W. Huang, L. Yan, J.G. Tan, Survey on the mode transition technique in combined cycle propulsion systems, Aerospace Science and Technology. 39 (2014) 685β691. [4] W.J.D. Escher, Hydrogen as a transportation fuel, Applied Energy. 47 (2) (1994) 201β226. [5] T. Price, D. Probert, Environmental impacts of air traffic, Applied Energy. 50 (1995) 133β162. [6] A.P. Roskilly, R. Palacin, J. Yan, Novel technologies and strategies for clean transport systems, Applied Energy. 157 (2015) 563β566. [7] Y. Chen, Z. Zou, C. Fu, A study on the similarity method for helium compressors, Aerospace Science and Technology. 90 (2019) 115β126. [8] P. Dong, H. Tang, M. Chen, et al., Overall performance design of paralleled heat release and compression system for hypersonic aeroengine, Applied Energy. 220 (2018) 36-46. [9] C.F. McDonald, Helium turbomachinery operating experience from gas turbine power plants and test facilities, Applied Thermal Engineering. 44 (2012) 108β142. [10] Z. Zou, H. Liu, H. Tang, et al., Precooling technology study of hypersonic aeroengine. Acta Aeronautica et Astronautica Sinica. 36 (8) (2015) 2544β2562. [11] T. Sato, H. Kobayashi, N. Tanatsugu, et al., Development study of the precooler
of ATREX engine, in: 12th AIAA International Space Planes and Hypersonic Systems and Technologies. Norfolk, Virginia, 2003, 6985. [12] P. Hendrick, N. Heintz, D. Bizzarri, et al., Experimental study of air-hydrogen heat exchangers, in: 15th AIAA international space planes and hypersonic systems and technologies conference, 2008, 2502. [13] J.J. Murray, C.M. Hempsell, A. Bond, An experimental precooler for airbreathing rocket engines, Journal of the British Interplanetary Society. 54 (2001) 199β209. [14] R.Varvill, Heat exchanger development at Reaction Engines Ltd, Acta Astronautica. 66 (2010) 1468β1474. [15] H. Lee, S. Ma, Y. Chen, et al., Experimental study on compact heat exchanger for hypersonic aero-engine, in: 21st AIAA international space planes and hypersonic systems and technologies conferences, 2017, 2333. [16] B.W. Lucy, J.A. Reed, A Survey of Turbine Engine Temperature Distortion Generator Requirements and Concept Trade Study, in: AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2011, 5969. [17] J. Kurzke, Effects of inlet flow distortion on the performance of aircraft gas turbines, Journal of Engineering for Gas Turbines & Power. 130 (4) (2006) 117-125. [18] R. A. RUEDY, R. J. ANTL, The effect of inlet temperature distortion on the performance of a turbo-fan engine compressor system, in: 6th Propulsion Joint Specialist Conference, 1970, 625. [19] G. L. Hammock, Cross-flow, staggered-tube heat exchanger analysis for high enthalpy flows. Tennessee Research and Creative Exchanger, United States, North
America Trace, 2011. [20] K. Kritikos, C. Albanakis, D. Missirlis, et al., Investigation of the thermal efficiency of a staggered elliptic-tube heat exchanger for aeroengine applications, Applied Thermal Engineering. 30(2010) 134β142. [21] C. S. An, M. Kim, Thermo-hydraulic analysis of multi-row cross-flow heat exchangers, International Journal of Heat and Mass Transfer. 120(2018) 534-539. [22] X. Zhang, P. Tseng, M. Saeed, et al., A CFD-based simulation of fluid flow and heat transfer in the Intermediate Heat Exchanger of sodium-cooled fast reactor, Annals of Nuclear Energy. 109 (2017) 529β1537. [23] D. Missirlis, S. Donnerhack, O. Seite, et al., Numerical development of a heat transfer and pressure drop porosity model for a heat exchanger for aero engine applications, Applied Thermal Engineering. 30 (2010) 1341β1350. [24] ANSYS Inc., Fluent theory Guide; 2013. [25] W. M. Kays, A. L. London, Compact heat exchangers [M]. McGraw-Hill, 1955. [26] Standards of tubular heat exchanger manufacturer association [S], 6th ed. New York: Tubular Exchanger Manufacturer association, 1978. [27] V. Gnielinski, New equations for heat and mass-transfer in turbulent pipe and channel flow, International Chemical Engineering. 16 (1975) 359-368. [28] L. Gu, J. Min, X. Wu, et al., Airside heat transfer and pressure loss characteristics of bare and finned tube heat exchanger used for aero engine cooling considering variable air properties, International Journal of Heat and Mass Transfer. 108 (2017) 1839-1849.
[29] P. Promoppatum, S. Yao, T. Hultz, et al., Experimental and numerical investigation of the cross-flow PCM heat exchanger for the energy saving of building HVAC, Energy and Buildings. 138 (2017) 468-478. [30] M. J. Zucrow, J. D. Hoffman, et al., Gas Dynamics, Volume 1. New York: Wiley, 1976. [31] Abdelwahab, M., Effects of Temperature Transients at Fan Inlet of a Turbofan Engine, NASA TP-1031, 1977.
Declaration of interests
οThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
βThe authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Highlights: A simplified numerical method for axisymmetric compact heat exchanger is established. The flowfield distortion caused by the heat exchangerβs special geometry is studied. The effects of entrance conditions on the heat exchangerβs performance are analyzed.
S1359-4311(19)34077-3 https://doi.org/10.1016/j.applthermaleng.2020.114977 ATE 114977
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Please cite this article as: W. Ding, Q. Eri, B. Kong, Z. Zhang, Numerical investigation of a compact tube heat exchanger for hypersonic pre-cooled aero-engine, Applied Thermal Engineering (2020), doi: https://doi.org/ 10.1016/j.applthermaleng.2020.114977
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Numerical investigation of a compact tube heat exchanger for hypersonic pre-cooled aero-engine Wenhao Dinga, Qitai Eria*, Bo Konga*, Zhen Zhangb a School of Energy and Power Engineering, Beihang University, Beijing, 100191,China b China Academy of Aerospace Aerodynamics, Beijing, 100074,China * To whom correspondence should be addressed: Qitai Eri, Bo Kong E-mail address of Qitai Eri: [email protected] E-mail address of Bo Kong: [email protected]
Abstract The compact tube heat exchanger is a key component of pre-cooled aero-engine. The pressure drop and flow distortion of the heat exchanger have a crucial effect on the performance characteristics of pre-cooled aero-engines including thrust and stability. However, it is difficult to simulate directly because of its extremely complex geometry. Therefore, a porous model and a dual cell heat exchanger model are utilized in this paper to simulate the pressure drop and heat transfer, respectively. The method is verified by comparing to previous experimental results. The simulation results are in good agreement with that of the experiment. The flow field characteristics of the heat exchanger and the effect of heat exchanger entrance conditions on the performance of the heat exchanger are studied in detail. It is found that uneven mass flux caused by the special geometry of the heat exchanger leads to non-uniform heat transfer and pressure drop along its axis. This subsequently results in flow distortion at the exit of the heat exchanger. Especially for the total temperature distortion, it will result in the reduction of stable work margin of the compressor. In addition, the changes of velocity, total temperature and total pressure affect the pressure drop and flow distortion. These effects are predominantly caused by changes in the flux distribution and velocity. Key words: Compact tube heat exchanger, Pre-cooled aero-engine, Flow
distortion, Porous model, Dual cell model
Nomenclature heat capacity, J/K C πΆπ Specific heat capacity, J/(kgΒ·K) Heat transfer coefficient, w/(m2Β·K) β Ratio of specified heats, π Mass flow rate, kg/s π Pressure, pascal π β Total pressure, pascal π Heat transfer rate, w π Temperature, K π
πβ π£ ΞΌ Ο ππ π π ππ’ ππ
Total temperature, K Velocity, m/s Viscosity, NΒ·s/ m2 Density, kg/m3 Mach number, Reynolds number, Nusselt number, Prandtl number, -
1. Introduction In the development of hypersonic propulsion systems, the pre-cooled aero-engine has become a major focus because of its applicability over wide range of flight conditions including reusable horizontal takeoff and landing [1,2,3]. Hydrogen powered pre-cooled aero-engine can reduce greenhouse gas emissions οΌ this more efficient engine is considered as a main direction of the potential cleaner aviation, which can weaken the effects of aviation on the global atmosphere [4,5,6]. The heatexchange-medium helium having good thermal conductivity is used to cool the hightemperature air flow, which provides high reliability and high compressor efficiency [7,8,9]. The compact tube heat exchanger is a key component of the pre-cooled aeroengine [10]. The performance of the heat exchanger has a major effect on the performance of the engine. The heat exchanger is located between the intake and the compressor. High-temperature air entering the aero-engine flows through the heat exchanger to be cooled under high-speed flight conditions. The air is cooled to a temperature where the compressor can operate normally [11]. The heat exchanger is
usually axisymmetric in order to match the geometry of the aero-engine. The inlet and outlet geometry and size of the heat exchanger are the same as the outlet of the intake and the inlet of the compressor, respectively. Furthermore, the heat exchanger tube bundles are small in diameter, numerous in numbers, and are densely packed to allow the high-temperature air entering the aero-engine to cool rapidly. Experimental studies of the pro-cooled heat exchanger with small bore tubes have been carried out, including studies of design, manufacture, and performance [12,13, 14,15]. Distortion of the air flow through the heat exchanger results in reduced stability of the compression components and decreases the thrust of the aero-engine. In addition, air flow through the heat exchanger may cause large total temperature distortion due to uneven heat transfer. Total temperature distortion has negative impacts on engine operation, resulting in the reduction of the stall margin, and the engine is more tending to surge [16,17]. Among them, the high pressure compressor is most sensitive to temperature distortion [18]. Thus, there is a need to study the flow characteristics and distortion of compact tube heat exchangers used for pre-cooled aero-engines. The simulation of the three-dimensional flow and heat transfer process in compact tube heat exchangers is very difficult due to the large number of tube bundles in the heat exchanger. Therefore, a simplified simulation approach for the flow and heat transfer of compact tube heat exchanger is necessary. Hammock [19] presented a crossflow, staggered-tube heat exchanger analysis for high enthalpy flow. Empirical correction characteristics were presented by comparing the empirical and experimental results. Kritikos et al. [20] investigated the thermal efficiency of a staggered elliptic-
tube heat exchanger for aero-engine applications with two different methods. Namely, the exact geometry cell and the porous medium approaches were used. It was shown that both approaches can be used for the detailed investigation of the thermal performance of the heat exchanger. An et al. [21] studied the thermal and hydraulic characteristics of a cross-flow finned tube heat exchanger using the porous medium model and found the simulation results agreed well with the experimental data. Zhang et al. [22] studied the heat transfer in the intermediate heat exchanger of a sodiumcooled fast reactor with the porous model and heat exchanger model. This approach was able to replicate the pressure drop and heat transfer characteristics of the detailed model. Missirlis et al. [23] studied an aero-engine heat exchanger using the porosity model, and found that this approach could effectively simulate the heat exchanger in the respects of heat transfer and pressure drop. The simplified simulation methods provide the means to numerically simulate the compact tube heat exchanger of a precooled aero-engine. In this paper, a numerical simulation method for axisymmetric compact tube heat exchanger is established. The simulation method is validated with experimental results. A porous model and dual cell model are used to simulate the pressure drop and heat transfer, respectively. The flow characteristics and heat transfer performance of the heat exchanger and the influence of entrance boundary conditions on the performance of the heat exchanger are studied. 2. The compact tube heat exchanger model A schematic of the intake and heat exchanger investigated in this study is shown in
Fig.1. Both the intake and the heat exchanger are axisymmetric. The axial length of the heat exchanger is 1000mm, the external diameter is 1000mm and the internal diameter is 700mm, as shown in Fig.2. The specified structure of heat exchanger tube is shown in Fig.3, and the detailed sizes of the heat exchanger tube bundle are marked. The flow of the shell-side is high-temperature air flow. The flow of the tube-side is lowtemperature supercritical helium.
Fig. 1. Schematic of the intake and heat exchanger
Fig. 2. Typical view of the heat exchanger
Fig. 3. Specified structure of the heat exchanger tube (mm)
As the heat exchanger is axisymmetric and efficient, the temperature variation in the heat exchanger is very large. A temperature difference of 900K is produced when the
air travels through the heat exchanger under high-speed flight conditions. Thus the properties of air vary greatly due to the temperature differences. In view of this situation, the heat transfer zone is divided into five zones in the radial direction and each zone has its own working parameters. The simulation model structure with its boundary conditions is shown in Fig. 4, and the domain was considered as axisymmetric for simulations.
Fig. 4. Simulation model structure of the heat exchanger with boundary conditions
The flow characteristics of the heat exchanger and the effect of entrance conditions on the heat exchanger are studied. The main parameters of interest are the total pressure recovery, total pressure distortion, and total temperature distortion. The equation of total pressure recovery is expressed by Eq. 1. The equation of steady distortion coefficient is expressed by Eq. 2. ο³i ο½ π·=
pi* pin*
πΌ β πππ₯ β πΌ β πππ πΌ β ππ£π
(1)
(2)
where Ξ± represents the respective total pressure and total temperature. 3. Simulation methods The numerical simulations were carried out using the commercial software ANSYS
Fluent 15.0. Porous model and dual cell model were used to simulate the pressure drop and heat transfer, respectively. 3.1 Porous model For the fluid flowing through the compact tube heat exchanger, the flow region is regarded as porous media to estimate the pressure drop. The government equations are presented below for mass, momentum and energy: ο² οΆο² ο« ο ο§( ο² v ) ο½ 0 οΆt
ο² ο²ο² ο΅ο² ο΅ο² οΆο² v ο« οο§( ο² vv) ο½ οοp ο« οο§(ο΄ ) ο« ο² g ο« S οΆt
(3)
(4)
where π is the superficial velocity in porous media, and π is the additional vector momentum source term of porous media. ο² ο² οΆ ( ο² E ) ο« οο§(v( ο² E ο« p )) ο½ οο§(keff οT ο« (ο΄ eff ο v)) ο« S h οΆt
(5)
The first two terms on the right-hand side of energy equation represent energy transfer due to conduction and viscous dissipation, respectively. And Sh represents the heat source term. Finite volume method is used for governing equations, and space discretization using second-order upwind. SIMPLE algorithm is employed to solve equations. The air flow in the simulation domain is considered as compressible flow, although the velocity of air is relatively low after the deceleration in the intake and the Mach number is no more than 0.3. For the porous model, the resistance is regarded as a pressure loss source term [24].Both viscous loss and inertial loss were considered. The viscous loss is the primary mechanism for pressure drop in low velocity magnitude, and the inertial loss is primary
in high velocity magnitude. For a simple porous media, the additional momentum source term is presented as: π
π π = β(πΌππ + 0.5ππ2|π£|ππ)
(6)
where πΌ is the permeability of porous media and c2 is the inertial loss coefficient. In this study, the viscous loss and inertial loss are considered simultaneously. In addition, because the flow is axisymmetric, the loss coefficient is considered in the axial and radial direction. In order to get the viscous and inertial loss coefficient, the empirical correction of Kays & London [25] is used. The specified formula is shown below: βp = πΊ2 β π β π΄π π’ππ,π/(2 β π β π΄πππ) π = 0.55π π β0.18
(7) (8)
where G is the maximum flux, π΄π π’ππ,π is the heat transfer area, π΄πππ is the minimum flow area, π is the friction factor. The relationship of pressure drop and free flow velocity can be obtained using the empirical correction, allowing the loss coefficient to be calculated. And the porosity defined as the ratio of the volume of air flowing through the heat exchanger to the overall volume of the heat exchanger is 0.7328 for this heat exchanger, calculated from the geometry of heat exchanger. 3.2 Heat exchanger model A dual cell model is used to simulate the heat transfer in this study. This model can present the temperature field of both the primary and auxiliary flow and has no limitation of mesh type and heat exchanger geometry. Heat transfer rate is computed for each cell in the two cores (primary and auxiliary) and added as a source term Sh to
the energy equation for the respective flows [24]. For the dual cell model, a mesh cell is considered as a heat exchanger. For each cell, the number of heat transfer units (NTU number) is retained and interpolated from the NTU table, which allows the overall performance of the heat exchanger to be calculated [24]. The flow of the heat exchanger in this paper is considered to be counter flow, since the number of turns in the bundle exceeds four times [26]. The schematic of the dual cell model is shown in Fig. 5. The import and export boundary conditions of auxiliary flow (helium) are mass-flow-inlet and pressure-outlet, respectively. And the interface boundary condition is used in the junction of different auxiliary flow grid zones.
Fig. 5. The dual cell model for primary and auxiliary flow
The equations used in the calculation are given as follows: ππ πππππ,π΄ = πππππ,π΄πππππ,π΄π΄πππππ‘,π΄
(9)
ππ πππππ,π = πππππ,ππππππ,ππ΄πππππ‘,π
(10)
πΆπππ,π πππππ = min [(ππ ππππππΆπππππ)|π,(ππ ππππππΆπππππ)|π΄]
(11)
ππππ πππππ = [πππππ’ππ(ππ πππππ,π,ππ πππππ,π΄)]πππππππππππ‘πππππππ‘πππ
(12)
ππ΄π πππππ = ππππ ππππππΆπππ,π πππππ
(13)
πππππ =
ππ΄π πππππ(πππππ,π΄ β πππππ,π)π πππππ
(14)
The iterative procedure to obtain the overall performance of heat exchanger is shown in Fig. 6.
Fig. 6. Flow chart of the iteration process to calculate the heat exchanger NTU number
The shell-side heat transfer coefficient is calculated using the Kayβs and London empirical correction [25]: h = 0.571GπΆππ π β0.4
(15)
The tube-side heat transfer coefficient for turbulent flow is calculated using the Gnielinski empirical correction [27]: Nu =
(π/8)(π π β 1000)ππ π 8
(ππ
1 + 12.7
2/3
β 1)
π 2/3
[1 + ( π )
π = (1.82log10 π π β 1.64) β2
]πΆ
π‘
(16) (17)
The tube-side heat transfer coefficient for laminar flow is calculated using the empirical formula: Nu = 3.66
(18)
The heat transfer efficiency is given by: π
Ξ΅ = ππππ₯
where ππππ₯ is the theoretical maximum heat transfer rate. The NTU β Ξ΅ relation of counter flow is given by:
(19)
Ξ΅=
1βπ
βπππ(1 β πΆπππ/πΆπππ₯)
1 β (πΆπππ/πΆπππ₯)π
(20)
βπππ(1 β πΆπππ/πΆπππ₯)
In addition, the properties of air and helium vary greatly, and large temperature variation is present on both sides of heat transfer tube. Therefore, the properties of the fluid are defined as a function of temperature to improve the accuracy estimations of heat transfer and pressure drop [28]. 3.3 Numerical simulation method validation A simulation of the heat exchanger in [13] was carried out to investigate the accuracy of the present simulation method. In this section, the simulation results are compared with the experiment results obtained from the reference. In the experiment, the primary flow in shell-side is nitrogen, and the auxiliary flow in the tube-side is helium. Its tube diameter is similar to the tube diameter studied in this paper, so the validation of the method is convincing. According to [13], the boundary conditions are shown in Table 1. Table 1. Boundary conditions in [13]
Helium entrance temperature (K)
Helium entrance mass flow rate (kg/s)
Nitrogen entrance temperature (K)
Nitrogen entrance mass flow rate (kg/s)
223
0.00093
877
0.0259
Table 2 shows the simulation and experimental results for pressure drop and heat transfer rate. It is found that the error between the experimental results and the CFD results is 10.4% in pressure drop and 16.6% in heat transfer rate. This indicates good agreement and satisfies the requirements of the present work [29].
Table 2. Comparison of the experiment results and simulation results
Experiment results Simulation results
Pressure drop (pa) 4600 4120
Heat transfer rate (w) 2560 2985
Percentage error (%)
10.4
16.6
Grid independence study is also performed; the simulation results differences between different computational grids quantities are compared. The quantities of the grid are 3.1 ο΄ 105, 4.8 ο΄ 105, 7.0 ο΄ 105 and 10.0 ο΄ 105, used to simulate the same case respectively. The simulation results are shown as follows:
Total temperature (K)
440 Mesh1 Mesh2 Mesh3 Mesh4
400
360
320
0.0
0.1
0.2
0.3
0.4
Radial location (m)
Fig.7. Radial distributions of total temperature for heat exchanger outlet with different grid quantities (Mesh1: 3.1 ο΄ 105; Mesh2: 4.8 ο΄ 105; Mesh3: 7.0 ο΄ 105; Mesh4: 10.0 ο΄ 105) Table 3. Radial velocity of the heat transfer region entrance with different grid quantities
The quantity of the grid 3.1 ο΄ 105 4.8 ο΄ 105 7.0 ο΄ 105 10.0 ο΄ 105
Radial velocity of the heat transfer region entrance(m/s) 12.84 13.34 13.35 13.38
Table 4. Total pressure recovery of the heat exchanger outlet with different grid quantities
The quantity of the grid 3.1 ο΄ 105 4.8 ο΄ 105 7.0 ο΄ 105 10.0 ο΄ 105
Total pressure recovery of the heat exchanger outlet 0.9567 0.9574 0.9571 0.9572
It can be seen that the quantity of the grid will affect the simulation results in some extent. For the simulation model in this study, the simulation results tend to be stable when the grid quantity reaches 4.8 ο΄ 105. In order to ensure the accuracy of the
simulation and avoid waste of computing resources, the quantity of grid used in this paper is 4.8 ο΄ 105. 4. Results and discussions 4.1 Flow characteristics of the heat exchanger The flow characteristics of the heat exchanger are studied here. The inlet parameters in this section are shown in Table 5. And the Table 6 shows the mass-weighted average simulation results of the heat exchanger. Table 5. The inlet parameters of the flowing medium
Flowing medium
Total pressure (pa)
Total temperature (K)
Mass flow rate (kg/s)
Air
200000
1341
20.73
Helium
2000000
200
4.13
Table 6. The simulation results of the heat exchanger
Heat transfer
Heat transfer
Heat exchanger
region entrance
region exit
outlet
Total pressure recovery
0.998
0.959
0.958
Total pressure distortion
0.0147
0.0114
0.0101
Total temperature (K)
1341
400.89
401.09
Total temperature distortion
0
0.408
0.341
Parameters
The velocity contour of the heat exchanger is shown in Fig. 8. It can be seen that the velocity upstream of the heat transfer region decreases along the axis, the velocity downstream of the heat transfer region increases axially, and this is caused by the flow characteristics of variable mass flow rate channel flow. According to basic laws of gas dynamics, Eq. 21 is applicable in the case of equal section area [30]; when the main flow velocity is subsonic and the additional flow is vertical to the main flow, increasing the mass flow rate will increase the flow velocity until the flow velocity reaches the
speed of sound. Similarly, decreasing the mass flow rate decreases the flow velocity. dΞ½ Ξ½
1
ππ
= 1 β ππ2[(1 + πππ2)] π
(21)
In this study, the flow upstream of the heat exchanger can be seen as a mass flow rate reduction flow with equal section area approximately, because the entrance direction of the heat transfer region is approximately perpendicular to the upstream flow direction; the velocity upstream of the heat transfer region decreases axially. And the flow downstream of the heat exchanger can be seen as an increasing mass flow rate flow with equal section area approximately. As such, the velocity increases axially.
Fig. 8. Velocity contour (m/s)
The axial static pressure distributions at the entrance and exit of the heat transfer region are shown in Fig.9. It can be seen that the static pressure of the heat transfer region entrance increases along the axis. According to the Eq.22 [30], the static pressure increases with the reducing mass flow rate in the upstream of heat exchanger; and the static pressure at the exit of the heat transfer region decreases axially with the increasing mass flow rate in the downstream of heat exchanger. Therefore, the pressure difference between the heat transfer region entrance and exit becomes larger axially. In the heat transfer region, the flow direction changes to become radial flow quickly due to the
large pressure drop in radial direction. This increasing static pressure difference can subsequently lead to an increase in mass flow rate along the axis. This effect can also be verified from Fig. 10, which shows the axial mass flux (multiply density by radial velocity) distributions along the entrance and exit of the heat transfer region. dp p
πππ2
(
= β 1 β ππ2[2 β 1 +
)]πππ
πβ1 2 2 ππ
(22)
220000
Static pressure (pa)
217500 215000 Heat transfer region entrance Heat transfer region exit
212500 210000 207500
0.00
0.25
0.50
0.75
1.00
Axial location (m)
Fig. 9. Axial distributions of static pressure 17.5
Heat transfer region entrance Heat transfer region exit
15.0
Flux (kg/(m2s))
12.5 10.0 7.5 5.0 2.5
0.00
0.25
0.50
0.75
1.00
Axial location (m)
Fig. 10. Axial distributions of flux
The total pressure contour of the heat exchanger is shown in Fig. 11. Combined with the simulation results in Table.6, it illustrates that the total pressure loss of the entire heat exchanger is primarily generated in the heat transfer region; and the total pressure decreases significantly when the air flow through the heat transfer region.
Additionally, the total pressure distribution in the heat transfer region is not uniform, the total pressure loss produced in the heat transfer region increases axially. This is because the mass flow rate in the heat transfer region increases along the axis, which can be seen in Fig.10, and a large mass flow rate results in a high velocity, and then will result in a larger total pressure loss.
Fig. 11. Total pressure contour (pascal)
The total pressure distributions plotted against the dimensionless axial and radial location are shown in Fig.12, including the axial distributions in the heat transfer region with different radial location, expressed as axial position 1-4, the location is evenly distributed between the heat transfer region entrance and exit. It can be seen that the total pressure of heat transfer region entrance increases axially; according to the Eq.23 [30], the total pressure increases with the reducing mass flow rate in the upstream of heat exchanger. In the top right corner before the heat transfer region, the flow direction changes severely and a small recirculation zone is formed, as shown in Fig.8, resulting the total pressure decreasing at the corner. In the heat transfer region, as the flow deepens, the distribution of total pressure along the axial direction changes from the initial increase along the axis to the decrease along the axis. This is caused by the
increasing total pressure loss axially in the heat transfer region. Finally, it results in the decreasing total pressure distribution axially in the heat transfer region exit. ο§
dm dp* ο½ οkMa 2 ο§ * p m
(23)
202000
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region entrance Heat exchanger outlet
Total pressure (pa)
200000 198000 196000 194000 192000 190000 188000
0.00
0.25
0.50
0.75
1.00
Dimensionless location
Fig. 12. Total pressure distributions of dimensionless location (Axial direction: x/L, L=1000mm; Radial direction: r/R, R=350mm)
The air total temperature contour of the heat exchanger is shown in Fig. 13. The air total temperature distributions plotted against the dimensionless axial and radial location are shown in Fig.14. It can be seen that the total temperature sharply decreases from 1341 K to 400 K when the air goes through the heat transfer region and meet the temperature demands of the compressor. But the effect of cooling weakens axially at the same radial location, the total temperature distributions along the axis in the heat transfer region are rising, this can also be seen from the Fig.14, it finally resulting in total temperature distortion at the heat exchanger outlet. This uneven heat transfer rate is affected by the uneven mass flow rate distribution; the cooling effect strengthened where the mass flow rate is small and, is weakened when the mass flow rate is large. Therefore, the total temperature of the heat transfer region
exit increases along the axial direction. The total temperature distortion of the heat transfer region exit is up to 0.408, although it decreased to 0.341 at the heat exchanger outlet for the mixing of the air flow downstream of the heat transfer region, it is still at a very high level. It has a great negative influence on the aerodynamic stability of the compressor, and the engine is more prone to surge [31]. Furthermore, in the heat transfer region, the heat transfer capacity of the former zones is stronger compared with the latter zones, because the heat transfer area in the former zones is larger. Fig.15 shows the axial distributions of total temperature in the heat transfer region for cooling medium helium, it can also reflect this situation.
Fig. 13. Total temperature contour (K)
Total temperature (K)
1400
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region exit Heat exchanger outlet
1200 1000 800 600 400 200
0.00
0.25
0.50
0.75
Dimensionless location
1.00
Fig. 14. Total temperature distributions of dimensionless location (Axial direction: x/L, L=1000mm; Radial direction: r/R, R=350mm)
Total temperature (K)
1400
Heat transfer region entrance Axial position 1 Axial position 2 Axial position 3 Axial position 4 Heat transfer region exit
1200 1000 800 600 400 200 0
0.00
0.25
0.50
0.75
Axial location (m)
1.00
Fig.15 Axial distributions of total temperature in the heat transfer region for helium
In summary, the uneven flux distribution caused by the uneven static pressure distribution causes a distortion of total pressure and total temperature. Therefore, the flux distribution is a key factor affecting the characteristics of the heat exchanger. 4.2 The effect of heat transfer region entrance velocity In this section, the effects of entrance velocity are studied, while the total pressure and total temperature of heat exchanger inlet maintain constant. The entrance velocity varies with the mass flow rate controlled by the outlet pressure. The other thing to note is that the target of all cases studied in this paper is to cool the high total temperature air to be 400 K by adjusting the helium mass flow rate. Table 7 presents the simulation results for the total pressure recovery with different heat transfer region entrance velocity conditions. It can be seen from the Table7 that the total pressure recovery decreases when the entrance velocity is increased. From the Eq.6, it can be seen that as the velocity increases, the additional momentum source term
increases, which leads to an increase in total pressure loss. Fig.16 and 17 show the total pressure distortion and total temperature distortion variation with different entrance velocities. The results show that the total pressure distortion and total temperature distortion increase when the entrance velocity increases. The total pressure loss in heat transfer region becomes more uneven axially with the increasing entrance velocity, then the total pressure distortion increases. The variation of total temperature distortion is because the mass flow rate increases when the entrance velocity increases, then the flux distribution becomes more uneven axially. In other words, increasing the heat transfer region entrance velocity has a negative effect on the performance of the heat exchanger, and is unfavorable for the stability of compressors. Table 7. Simulation results with different entrance velocity boundary conditions
Upstream region 0.997 0.996 0.994 0.990
Heat transfer region 0.973 0.966 0.951 0.922
Downstream region 0.9998 0.9997 0.9996 0.9993
0.035
Total pressure distortion
Case 1 Case 2 Case 3 Case 4
Entrance velocity (m/s) 10.66 12.11 14.86 19.03
Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.030 0.025 0.020 0.015 0.010 0.005 10
12
14
16
18
20
Heat transfer region entrance velocity (m/s)
Fig.16. Total pressure distortion for different entrance velocity
Overall region 0.970 0.962 0.945 0.912
Total temperature distortion
0.5 0.4 0.3 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.2 0.1 0.0 10
12
14
16
18
20
Heat transfer region entrance velocity (m/s)
Fig.17. Total temperature distortion for different entrance velocity
4.3 The effect of heat exchanger inlet total temperature In this section, the effect of inlet total temperature on heat exchanger performance is studied. In order to isolate this effect, the inlet total pressure and mass flow rate is maintained constant. The constant inlet mass flow rate is achieved by adjusting the outlet pressure. Table 8 presents the simulation results for the total pressure recovery with different heat exchanger inlet total temperature conditions. It can be seen that the total pressure recovery decreases when the inlet total temperature is increased. The density decreases as the total temperature is increased with total pressure maintains constant, so the velocity increases with the mass flow rate maintains constant, thereby increasing the pressure loss. Fig.18 and 19 show the total pressure distortion and total temperature distortion variation with different inlet total temperatures. It is shown that the total pressure distortion and total temperature distortion increases with the inlet total temperature increase. The variation of total pressure distortion is due to the more uneven total pressure loss axially caused by the increasing entrance velocity, and the
variation of total temperature distortion is caused by the more uneven flux distribution with the entrance velocity increase. This indicates the importance of the entrance velocity on the performance of heat exchanger. Table 8. Simulation results with different inlet total temperature boundary conditions
Case1 Case2 Case3 Case4
Total temperature (K) 900 1100 1500 1900
Upstream region 0.998 0.997 0.993 0.985
Heat transfer region 0.978 0.970 0.948 0.905
Downstream region 0.9994 0.9997 0.9996 0.9991
Total pressure distortion
0.05 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.04 0.03 0.02 0.01 800
1000
1200
1400
1600
1800
2000
Heat exchanger inlet total temperature (K)
Fig.18. Total pressure distortion for different inlet total temperature
Total temperature distortion
0.6 0.5 0.4 0.3 Heat transfer region entrance Heat transfer region outlet Heat exchanger outlet
0.2 0.1 0.0 800
1000
1200
1400
1600
1800
2000
Heat exchanger inlet total temperature (K)
Fig.19. Total temperature distortion for different inlet total temperature
4.4 The effect of heat exchanger inlet total pressure
Overall region 0.975 0.966 0.941 0.891
In this section, the effect of the inlet total pressure on the heat exchanger performance is examined. The inlet total temperature and heat transfer region entrance velocity are held constant. In the simulation process, the heat transfer region entrance velocity is monitored to be consistent by controlling the outlet pressure. Table 9 presents the results of corresponding total pressure recovery with different heat exchanger inlet total pressure conditions. It can be seen that the total pressure recovery of heat transfer region almost unchanged when the inlet total pressure is increased, this is because the entrance velocity is constant, then the pressure loss unchanged. Fig.20 and 21 show the effect of the inlet total pressure on the total pressure distortion and total temperature distortion. It is shown that the total pressure distortion stays nearly constant when the heat exchanger inlet total pressure is changed, this is also because the entrance velocity maintains constant. In addition, the total temperature distortion increases with the inlet total pressure increase, this is because the mass flow rate increases with the inlet total pressure increase, and results in the more uneven flux distribution. Table 9. Simulation results with different inlet total pressure boundary conditions
Case 1 Case 2 Case 3 Case 4
Total pressure (pa) 180000 200000 220000 250000
Upstream region 0.995 0.998 0.995 0.995
Heat transfer region 0.960 0.961 0.962 0.963
Downstream region 0.9996 0.9997 0.9997 0.9997
Overall region 0.955 0.958 0.957 0.958
Total pressure distortion
0.020 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet 0.015
0.010
0.005 160000
180000
200000
220000
240000
260000
Heat exchanger inlet total pressure (pa)
Fig.20. Total pressure distortion for different inlet total pressure
Total temperature distortion
0.5 0.4 0.3 Heat transfer region entrance Heat transfer region exit Heat exchanger outlet
0.2 0.1 0.0 160000
180000
200000
220000
240000
260000
Heat exchanger inlet total pressure (pa)
Fig.21. Total temperature distortion for different inlet total pressure
5. Conclusions In this paper, a porous model and dual cell model are used to study a compact tube heat exchanger for pre-cooled aero-engines. The accuracy of the simulation method was examined through comparison to experiment and was found to be satisfactory. The flow field characteristics of the heat exchanger and the effects of entrance velocity, inlet total temperature, and inlet total pressure on the total pressure recovery, total pressure distortion, and total temperature distortion were studied and discussed. It is found that due to the geometry of the heat exchanger, the flow of upstream and
downstream heat exchanger can be considered as mass flow rate decreasing and increasing flow with equal section area respectively; the static pressure difference between the entrance and exit of the heat transfer region increases axially. This causes an uneven axial flux distribution. The flux of the heat transfer region increases axially and causes a non-uniform total temperature distribution, and then causes severe total temperature distortion at the outlet of the heat exchanger. As well, the uneven flux distribution causes an uneven velocity distribution, which results in a non-uniform total pressure distribution. Therefore, the flux distribution is a key factor affecting the operation of the heat exchanger. The pressure drop and flow distortion will affected by the changes of entrance velocity, inlet total temperature and inlet total pressure. With an increase of the heat transfer region entrance velocity and heat exchanger inlet total temperature, the total pressure distortion and total temperature distortion are significantly increased, and the total pressure recovery is decreased; In addition, with the increase of heat exchanger inlet total pressure, the total pressure recovery and total pressure distortion remains mostly constant, but the total temperature distortion is increased. These effects are predominantly caused by changes in the flux distribution and velocity; the total pressure recovery and total pressure distortion is determined by the entrance velocity, while the total temperature distortion is determined by the flux distribution. References [1] U. Mehta, M. Aftosmis, J. Bowles, et al., Skylon Aerodynamics and SABRE Plumes, in: 20th AIAA International Space Planes and Hypersonic Systems and Technologies
Conference, 2015, 3605. [2] Z.G. Wang, Y. Wang, J.Q. Zhang, et al., Overview of the key technologies of combined cycle engine precooling systems and the advanced applications of microchannel heat transfer, Aerospace Science and Technology. 39 (2014) 31β39. [3] W. Huang, L. Yan, J.G. Tan, Survey on the mode transition technique in combined cycle propulsion systems, Aerospace Science and Technology. 39 (2014) 685β691. [4] W.J.D. Escher, Hydrogen as a transportation fuel, Applied Energy. 47 (2) (1994) 201β226. [5] T. Price, D. Probert, Environmental impacts of air traffic, Applied Energy. 50 (1995) 133β162. [6] A.P. Roskilly, R. Palacin, J. Yan, Novel technologies and strategies for clean transport systems, Applied Energy. 157 (2015) 563β566. [7] Y. Chen, Z. Zou, C. Fu, A study on the similarity method for helium compressors, Aerospace Science and Technology. 90 (2019) 115β126. [8] P. Dong, H. Tang, M. Chen, et al., Overall performance design of paralleled heat release and compression system for hypersonic aeroengine, Applied Energy. 220 (2018) 36-46. [9] C.F. McDonald, Helium turbomachinery operating experience from gas turbine power plants and test facilities, Applied Thermal Engineering. 44 (2012) 108β142. [10] Z. Zou, H. Liu, H. Tang, et al., Precooling technology study of hypersonic aeroengine. Acta Aeronautica et Astronautica Sinica. 36 (8) (2015) 2544β2562. [11] T. Sato, H. Kobayashi, N. Tanatsugu, et al., Development study of the precooler
of ATREX engine, in: 12th AIAA International Space Planes and Hypersonic Systems and Technologies. Norfolk, Virginia, 2003, 6985. [12] P. Hendrick, N. Heintz, D. Bizzarri, et al., Experimental study of air-hydrogen heat exchangers, in: 15th AIAA international space planes and hypersonic systems and technologies conference, 2008, 2502. [13] J.J. Murray, C.M. Hempsell, A. Bond, An experimental precooler for airbreathing rocket engines, Journal of the British Interplanetary Society. 54 (2001) 199β209. [14] R.Varvill, Heat exchanger development at Reaction Engines Ltd, Acta Astronautica. 66 (2010) 1468β1474. [15] H. Lee, S. Ma, Y. Chen, et al., Experimental study on compact heat exchanger for hypersonic aero-engine, in: 21st AIAA international space planes and hypersonic systems and technologies conferences, 2017, 2333. [16] B.W. Lucy, J.A. Reed, A Survey of Turbine Engine Temperature Distortion Generator Requirements and Concept Trade Study, in: AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2011, 5969. [17] J. Kurzke, Effects of inlet flow distortion on the performance of aircraft gas turbines, Journal of Engineering for Gas Turbines & Power. 130 (4) (2006) 117-125. [18] R. A. RUEDY, R. J. ANTL, The effect of inlet temperature distortion on the performance of a turbo-fan engine compressor system, in: 6th Propulsion Joint Specialist Conference, 1970, 625. [19] G. L. Hammock, Cross-flow, staggered-tube heat exchanger analysis for high enthalpy flows. Tennessee Research and Creative Exchanger, United States, North
America Trace, 2011. [20] K. Kritikos, C. Albanakis, D. Missirlis, et al., Investigation of the thermal efficiency of a staggered elliptic-tube heat exchanger for aeroengine applications, Applied Thermal Engineering. 30(2010) 134β142. [21] C. S. An, M. Kim, Thermo-hydraulic analysis of multi-row cross-flow heat exchangers, International Journal of Heat and Mass Transfer. 120(2018) 534-539. [22] X. Zhang, P. Tseng, M. Saeed, et al., A CFD-based simulation of fluid flow and heat transfer in the Intermediate Heat Exchanger of sodium-cooled fast reactor, Annals of Nuclear Energy. 109 (2017) 529β1537. [23] D. Missirlis, S. Donnerhack, O. Seite, et al., Numerical development of a heat transfer and pressure drop porosity model for a heat exchanger for aero engine applications, Applied Thermal Engineering. 30 (2010) 1341β1350. [24] ANSYS Inc., Fluent theory Guide; 2013. [25] W. M. Kays, A. L. London, Compact heat exchangers [M]. McGraw-Hill, 1955. [26] Standards of tubular heat exchanger manufacturer association [S], 6th ed. New York: Tubular Exchanger Manufacturer association, 1978. [27] V. Gnielinski, New equations for heat and mass-transfer in turbulent pipe and channel flow, International Chemical Engineering. 16 (1975) 359-368. [28] L. Gu, J. Min, X. Wu, et al., Airside heat transfer and pressure loss characteristics of bare and finned tube heat exchanger used for aero engine cooling considering variable air properties, International Journal of Heat and Mass Transfer. 108 (2017) 1839-1849.
[29] P. Promoppatum, S. Yao, T. Hultz, et al., Experimental and numerical investigation of the cross-flow PCM heat exchanger for the energy saving of building HVAC, Energy and Buildings. 138 (2017) 468-478. [30] M. J. Zucrow, J. D. Hoffman, et al., Gas Dynamics, Volume 1. New York: Wiley, 1976. [31] Abdelwahab, M., Effects of Temperature Transients at Fan Inlet of a Turbofan Engine, NASA TP-1031, 1977.
Declaration of interests
οThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
βThe authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Highlights: A simplified numerical method for axisymmetric compact heat exchanger is established. The flowfield distortion caused by the heat exchangerβs special geometry is studied. The effects of entrance conditions on the heat exchangerβs performance are analyzed.