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Effect of fin-endwall fillet on thermal hydraulic performance of airfoil printed circuit heat exchanger
Applied Thermal Engineering 89 (2015) 1087e1095
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Effect of fin-endwall fillet on thermal hydraulic performance of airfoil printed circuit heat exchanger* Ting Ma a, Fei Xin a, Lei Li a, Xiang-yang Xu a, Yi-tung Chen b, Qiu-wang Wang a, * a b
Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China Department of Mechanical Engineering, University of Nevada, Las Vegas, NV 89154, USA
h i g h l i g h t s Fillets are formed in the endwall of airfoil fins during the photochemical etching. Two-fluid model can be replaced by single-fluid model to perform simulation. Fin-endwall fillet can increase heat transfer and pressure drop at zl ¼ 1.63. Effect of fin-endwall fillet decreases as transverse pitch increases at zl ¼ 1.63. Longitudinal pitch has little effect at zl 1.88.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 December 2014 Received in revised form 6 April 2015 Accepted 9 April 2015 Available online 21 April 2015
Printed circuit heat exchanger (PCHE) is recommended to be used for intermediate heat exchanger in Very High Temperature Reactor (VHTR). One of the key features is that it is manufactured by the photochemical etching in order to maintain the internal structure and metal properties. In this paper, a photochemical etching experiment is conducted to manufacture the airfoil PCHE plate. The result indicates that the airfoil fin is not an ideal airfoil profile, but has a fin-endwall fillet. For the purpose of simplifying the numerical model and saving computational time, a validated model with a single fluid is used to further study the effect of fin-endwall fillet on the thermal hydraulic performance of airfoil PCHE. It is found that the fin-endwall fillet can increase the heat transfer and pressure drop in the cases with the non-dimensional longitudinal pitch being 1.63. The effect of fin-endwall fillet on thermal hydraulic performance decreases with the increase of transverse pitch, but the longitudinal pitch has little effect when the non-dimensional longitudinal pitch is greater than 1.88. In the studied cases, the maximum difference of Nusselt number and friction factor between the two models with and without fin-endwall fillet is up to 6.7% and 6.4%. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Printed circuit heat exchanger Endwall fillet Thermal hydraulic High temperature Photochemical etching
1. Introduction The nuclear energy has received considerable attention in many countries due to fossil fuels' exhaustion and environmental terms. To use it with high economy, enhanced safety, minimal waste and proliferation resistant, the U.S. Department of Energy proposed six top candidates for the IV generation nuclear plants,
* Presented at the 17th Conference on Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction PRES 2014, 23e27 August 2014 Prague, Czech Republic. (Original paper title: “Study on Heat Transfer and Pressure Drop Performances of Airfoil-Shaped Printed Circuit Heat Exchanger” and Paper No.: # 370). * Corresponding author. Tel.: þ86 (29) 82665539; fax: þ86 (29) 82663502. E-mail address: [email protected] (Q.-w. Wang).
http://dx.doi.org/10.1016/j.applthermaleng.2015.04.022 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
i.e., Very High Temperature Reactor (VHTR), Supercritical Water Cooled Reactor (SCWR), Sodium Cooled Fast Reactor (SFR), Molten Salt Reactor (MSR), Lead-Cooled Fast Reactor (LFR) and Gas-Cooled Fast Reactor (GFR) [1]. As one of the most promising candidates, the VHTR can supply heat over a range of core outlet temperature between 700 C and 950 C, which can be utilized by the refineries, petrochemistry, metallurgy and hydrogen production through an intermediate heat exchanger [2]. On the other hand, the intermediate heat exchanger in the VHTR needs to withstand ultra high temperature, high pressure, high pressure difference and high heat flux [3,4]. The traditional shell-and-tube heat exchangers are unsuitable to be used for the VHTR due to low heat transfer efficiency, while the traditional plate-fin heat exchangers and plate heat exchangers cannot satisfy the requirement of high pressure and high temperature. Hung et al. [5] used the staggered fin arrays to
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Nomenclature A Amin cp Dh f h Hf k Lf Lp m N Nu p Pl Pt Re
heat transfer area, mm2 minimum cross sectional area, mm2 specific heat, J/(kg K) maximum width of airfoil shaped fin, mm Darcy friction factor heat transfer coefficient, W/(m2 K) height of airfoil shaped fin, mm thermal conductivity, W/(m K) chord length of airfoil shaped fin, mm wave channel pitch along streamwise direction, mm mass flow rate, kg/h row of airfoil shaped fin Nusselt number static pressure, Pa longitudinal pitch of airfoil shaped fin, mm transverse pitch of airfoil shaped fin, mm Reynolds number
enhance the heat transfer performance of concentric tube heat exchanger in VHTR. Recently, a plate heat exchanger called printed circuit heat exchanger (PCHE) is recommended to be used for intermediate heat exchanger in VHTR. Different from the traditional manufacturing methods used for plate heat exchangers, the channels of PCHE are formed in the metal plates by photochemical etching. Then these plates are stacked together and fabricated by diffusion bonding. The PCHE can withstand the high temperature up to 900 C, and high pressure up to 60 MPa because the diffusion bonding can make the strength of bonding joints similar to the parent metal [6]. The channel diameter of plates manufactured by photochemical etching is usually ranged from 0.5 mm to 2.0 mm [7]. Compared to the traditional shell-and-tube heat exchangers with bare tubes, the PCHE only needs 1/30 of volume to achieve the same heat transfer rate in the VHTR [8]. The thermalehydraulic performance of PCHE is determined by the shape of channel manufactured by the photochemical etching. The basic channel of PCHE is a straight semicircular shape. Mylavarapu et al. [9] set up an experimental system to test the PCHE with straight semicircular channels at 790 C and 2.7 MPa, and found that the onset of transition from laminar flow to transition flow regime occurred much earlier than the circular pipe. Lo et al. [10] conducted a numerical simulation of PCHE with straight semicircular channels. The result indicated that the velocity and mass flow rate had significant effects on the performance. But the heat transfer effectiveness of the PCHE with straight semicircular channels was less than 80% when the mass flow rate was greater than 15 kg/h [11]. The zigzag channel could significantly enhance the heat transfer effectiveness of PCHE up to 85% at mass flow rate of 15 kg/h [12]. The arc-shaped ribs were attached to the flow channel of double-faced-type PCHE to enhance the heat transfer performance [13]. Lee et al. [14] used a RANS analysis to perform a multi-objective optimization of a double-faced type PCHE with zigzag channels. However, the pressure drop of zigzag-type PCHE is still too high to be used at the large mass flow rate. To reduce the pressure drop, Tsuzuki et al. [15] proposed a PCHE with an S-shaped channel. It was found that the pressure drop of S-shaped channel was only one-fifth of the zigzag channel with identical heat transfer performance due to the uniform flow velocity profile and less reverse flows and eddies in the S-shaped channel. The experiment conducted by Ngo et al. [16] further confirmed that the S-shaped PCHE was better than the zigzag-type PCHE in reducing the
T umax Wf
temperature, K superficial maximum velocity, m/s maximum thickness of airfoil shaped fin, mm
Greek
r Dp Dpa Dpf m d zl zt
density, kg/m3 total pressure drop, Pa acceleration pressure drop, Pa friction pressure drop, Pa dynamic viscosity, Pa s thickness of substrate plate, mm non-dimensional longitudinal pitch non-dimensional transverse pitch
Subscripts b averaged value in one pitch in inlet in one longitudinal pitch out outlet in one longitudinal pitch w wetted surface
pressure drop. Kim et al. [17] designed an airfoil fin to optimize the thermal hydraulic performance of PCHE. The pressure drop of the airfoil fin could be reduced to one-twentieth of that of zigzag channel but the total heat transfer rate per unit volume was almost the same. Yoon et al. [18] proposed Fanning factor and Nusselt number correlations for an airfoil PCHE with fixed geometrical parameters. Xu et al. [19] modified the profile of airfoil fin to further reduce the flow resistance and recommend the staggered fin arrangement for the airfoil PCHE. Zhou and Catton [20] found that the performances of NACA airfoil and elliptic fins were better compared to dropform and circular fins. However, it is found that the airfoil fin manufactured by the photochemical etching is not an ideal airfoil profile, but has a finendwall fillet. Therefore, the present study focuses on the effect of fin-endwall fillet on the thermal hydraulic performance of PCHE.
2. Photochemical etching experiment of airfoil PCHE The photochemical etching, also known as photochemical machining, employs chemical etching through a photoresist stencil as the method of material removal over selected areas [21]. This corrosive oxidation process does not alter the internal structure of the metal and metal properties such as hardness, grain structure and ductility [7], which is beneficial to be used at high temperature. The aqueous ferric chloride solution is usually selected as an etchant for stainless steel and superalloy. Considering the superalloy is much more expensive than stainless steel, the stainless steel SUS304 is used to conduct the present photochemical etching experiment. However, the process of etching the superalloy is almost the same. The basic chemical reactions are illustrated as follows:
8 < Fe þ 2FeCl3 ¼ 3FeCl2 Cr þ 3FeCl3 ¼ CrCl3 þ 3FeCl2 : Ni þ 2FeCl3 ¼ NiCl2 þ 2FeCl2
(1)
From the above chemical reaction equation set, it can be seen that the concentration of ferric ion has a significant effect on the chemical reactions. As the time increases, the concentration of ferric ion reduces. On the other hand, the Fe(OH)3 may be produced between ferric ion and (OH) ion. Therefore, the hydrochloric acid
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Fig. 1. Cross-sectional shape of channels manufactured by photochemical etching: (a) Sketch of cross-sectional shape of channels; (b) Experimental photo of cross-sectional shape of channels (unit: cm).
and nitric acid are added to main the acidity. The corresponding chemical reactions are shown as follows:
3Fe þ 8HNO3 ¼ 3FeðNO3 Þ2 þ 2NO[ þ 4H2 O 2Ni þ 2HNO3 þ 4HCl ¼ 2NiCl2 þ 2NO[ þ 3H2 O
(2)
The hydrochloric acid can increase the solubility of ferrous ion and rate of etching, while the nitric acid can improve the smooth and uniformity of channels. It was found that the etchant attacked not only downwards into the metal but also sideways beneath the photoresist stencil layer because the etching was isotropic, as shown in Fig. 1(a) [21]. Fig. 1(b) shows the cross-sectional shape of channels manufactured by the photochemical etching experiment. It can be seen that the fillets are formed in the endwalls of channels. Fig. 2 shows the airfoil PCHE plate manufactured by photochemical etching. The airfoil fins are etched in a SUS304 stainless steel plate with thickness of 2 mm. There are fillets in the endwall
Fig. 2. Airfoil PCHE plate manufactured by photochemical etching.
Fig. 3. Micrographs of airfoil PCHE plate obtained by laser microscope: (a) 3D micrograph of airfoil channels (unit: mm); (b) 2D micrograph of airfoil channels.
of airfoil fins. The detailed 3D and 2D micrographs of airfoil PCHE plate are obtained by laser microscope, as shown in Fig. 3. The formed fillets in the endwalls of airfoil fins are clearly indicated in these images. In the following sections, we will discuss about the effect of this formed fin-endwall fillets on the thermal hydraulic performance of airfoil PCHE.
3. Computational modeling of airfoil PCHE 3.1. Numerical model and computational method The NACA0021 airfoil fin is used for the present study, as shown in Fig. 4. It has the maximum thickness of Wf ¼ 0.84 mm and a chord length of Lf ¼ 4 mm with a height of Hf ¼ 1 mm. The thickness of substrate plate is d ¼ 1 mm. There are 12 rows of fins along the streamwise direction in a staggered arrangement. In the baseline model, the transverse pitch Pt is 2 mm and the longitudinal pitch Pl is 6.5 mm. The numerical model with two fluids is described in Fig. 5. Because the hot and cold fluids flow alternately in the channels along the z direction, only one hot-side fluid channel, one cold-side fluid channel and the corresponding substrate plates and fins are selected as the numerical model to simplify the numerical simulation. Here, the top and bottom plates have a half thickness of substrate plate. The periodic boundary is specified to the top and bottom surfaces. In the transverse direction, one full fin and two fins with half of the maximum thickness are used so that the symmetrical boundary is used to the left and right surfaces. In order to support a uniform velocity at the inlet and suppress the backflow at the outlet, the inlet is extended to 5 times of
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Fig. 4. Geometrical parameters of airfoil fins.
at high temperature [27]. The local pitch-averaged Nusselt number is defined by the local temperature, local surface heat flux and local physical properties, which are averaged in a single streamwise pitch rather than an arbitrary position. The local parameters in one longitudinal pitch are defined for the analysis. The local Reynolds number Re in one longitudinal pitch is defined as follows:
Re ¼
rumax Dh mDh ¼ m mAmin
(3)
where umax is the superficial maximum velocity evaluated at the minimum cross section, m is the mass flow rate, Amin is the minimum cross sectional area, Dh is the maximum width of airfoil fin. r is the density of helium and m is the dynamic viscosity of helium, which are evaluated at the average temperature of helium in one longitudinal pitch. The local Nusselt number Nu in one longitudinal pitch is defined as follows:
Nu ¼ Fig. 5. Numerical model with two fluids of airfoil PCHE: (a) 3D view of numerical model; (b) Cross section of numerical model.
channel height while the outlet is extended to 30 times of channel height. The fluids on both sides are helium, whose physical properties are taken from NIST [22]. The material of substrate plates and fins is Alloy 617 [23]. The inlet temperature is 1173.15 K on hot side and 761.96 K on cold side. Pressures are specified at the outlets of the channels, which are 7.59 MPa on the hot side and 7.83 MPa on the cold side. These parameters are taken from the operating condition of a helium cooled pebble bed reactor [24]. In this study, we also give an analysis of thermalehydraulic performance of PCHE with a single fluid to study the feasibility of using this model to replace the model with two fluids. In the model with a single fluid, only the hot-side fluid channel and hot-side fins shown in Fig. 5 are used for the numerical simulation. In this model, the constant temperature of 1123.15 is applied to the top and bottom surfaces of hot-side fluid channel. The inlet temperature is defined as 1173.15 K. The flow in the computational domain is regarded as 3D, incompressible, turbulence and steady. The shear stress transport (SST) kew model developed by Menter [25] is used to perform the turbulent flow. It provides an effective combination of the robust and accurate formulation of the kew model in the near-wall region with the free-stream independence of the ke3 model in the far field, which makes it more accurate and reliable for airfoil flow than the standard kew model [26]. The SST kew model was selected by Xu et al. [19] to evaluate the supercritical CO2 in the Zigzag, S-shaped and airfoil PCHEs. The calculation is carried out in the finite volume method software ANSYS FLUENT 14.5. The convection terms are solved by a second-order upwind discretization. The Semi Implicit Method Pressure Linked Equation (SIMPLE) algorithm is used to resolve the coupling of velocity and pressure. The residual for every variable is required to be less than 106 before solution convergence. It was found that the local pitch-averaged Nusselt number correlation is more appropriate than the global Nusselt number correlation
hDh k
(4)
in which, the heat transfer coefficient h is defined as follows:
mcp ðTin Tout Þ Aw ðTw Tb Þ
h¼
(5)
where Tin, Tout, Tb are the inlet, outlet and average temperature of helium in one longitudinal pitch, respectively. Tw is the temperature of wetted surface in one longitudinal pitch while Aw is the corresponding area. k is the thermal conductivity of helium and cp is the specific heat of helium, which are evaluated at the average temperature of helium in one longitudinal pitch. The local Darcy friction factor f in one longitudinal pitch is defined as follows:
f ¼
2Dpf Dh rumax Pl
(6)
where Pl is the longitudinal pitch of fins, and Dpf is the frictional pressure drop. The frictional pressure drop Dpf can be obtained by:
Dpf ¼ Dp Dpa
(7)
Dpa ¼ rout u2out rin u2in
(8)
where Dp is the total pressure drop, Dpa is the acceleration pressure drop. rin, uin and rout, uout are the density and velocity evaluated at the inlet and outlet of one longitudinal pitch. In order to study the effect of longitudinal pitch and transverse pitch, the non-dimensional longitudinal pitch zl and nondimensional transverse pitch zt are defined as follows:
zl ¼
Pl Lf
(9)
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Table 1 Grid independence test (Re ¼ 2541). Grid 1,169,502 2,110,750 2,985,390 3,667,302
zt ¼
elements elements elements elements
Nu
Relative error
f
Relative error
10.37 10.57 10.69 10.76
e 1.89% 1.12% 0.65%
0.0243 0.0239 0.0240 0.0242
e 1.67% 0.42% 0.83%
Pt Wf
(10)
3.2. Grid independence and code validation Due to the sensitivity of grid on the computational result, it is necessary to find an appropriate grid system. Four grid systems on the baseline model with a single fluid are established to test the grid independence. The four grid systems have 1,169,502 elements, 2,110,750 elements, 2,985,390 elements and 3,667,302 elements, respectively. The result is shown in Table 1. Comparing to the result of the finest grid system with 3,667,302 elements, the deviation of Nu and f of the grid system with 2,985,390 elements is less than 1%. As shown in Fig. 6, very dense grids are established near the wall surfaces of fins and substrate plates to make sure that the yþ is less than 1. Therefore, the grid system with 2,985,390 elements is used for the baseline model with one fluid and the similar grid system is adopted for other models in the later discussion. Because the structure of this model is similar to the plain finand-tube heat exchanger, a numerical model with six tube rows is established to examine the applicability of the present method by comparing with the previous experiment on the plain fin-and-tube heat exchanger [28]. As shown in Fig. 7, the deviation of Nu between the present numerical result and experimental data is less than 8.9% and the deviation of f is less than 11.5%. Therefore, the present numerical method is reliable.
Fig. 6. Selected grid system: (a) 3D view of selected grid system; (b) Top view of selected grid system.
Fig. 7. Method validation with experimental data [28].
4. Results and discussion 4.1. Comparison of numerical models with a single fluid and two fluids In the actual PCHE, the length of plate is more than 500 mm which includes about 100 rows of airfoil fins [18]. However, it is not economic to establish a model with the full length because it needs more than 50 million grid elements. In this section, a simplified numerical method is studied to perform the analysis. Here, the baseline geometrical parameters are used in the two models, whose non-dimensional longitudinal pitch zl is 1.63 and nondimensional transverse pitch zt is 2.38. The thermal hydraulic performance of numerical model with a single fluid along the streamwise direction is described in Fig. 8. In this model, the physical properties of helium are constant so that the Reynolds number in every longitudinal pitch is constant. As shown in Fig. 8(a), the Nusselt number decreases along the streamwise direction and reduces to the minimum in the third row. After that, it increases and achieves approximately fully-developed condition since the 8th row. Here, the fluctuation that less than 4% is regarded as the fully-developed condition. In the last row, there is a little increase in the Nusselt number due to the outlet effect. As shown in Fig. 8(b), a sharp decrease in friction factor occurs between the first and second rows. After that, the friction factor increases, but decreases again since the third row and then gradually becomes steady. The fluctuation in friction factor is smaller than the Nusselt number, which is less than 2% since the 8th row. Because the streamlines in airfoil channel are very smooth, the upstream velocity profile has a significant effect on the heat transfer and pressure drop of downstream airfoil channel, and thus takes a long distance to reach the fully-developed condition. In the studied Reynolds number, both the Nusselt number and friction factor from the 8th row to the 11th can be regarded as the fully-developed condition. Fig. 9 shows the thermal hydraulic performance comparison of numerical simulations with a single fluid and two fluids. It can be seen that the Nusselt number and friction factor obtained by the model with a single fluid match well with those obtained by the model with two fluids. The relative difference between them is less than 2% in Nusselt number and 5.5% in friction factor. It should be noted that these data comes from the 8th to 11th rows because the Nusselt number and friction factor can reach the fully-developed condition, as mentioned in the above discussion. Although the physical properties of helium and the wall temperature are various in the numerical model with two fluids, but the non-dimensional velocity and non-dimensional temperature can achieve a steady
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Fig. 9. Thermal hydraulic performance comparison of numerical simulations with a single fluid and two fluids: (a) Local Nusselt number comparison of numerical simulations with a single fluid and two fluids; (b) Local friction factor comparison of numerical simulations with a single fluid and two fluids.
Fig. 8. Thermal hydraulic performance of numerical model with a single fluid along streamwise direction: (a) Local Nusselt number distribution along streamwise direction; (b) Local friction factor distribution along streamwise direction.
condition and is similar to the behaviors of model with a single fluid [12]. Therefore, both the Nusselt number and friction factor in the two models can match well with each other. The model with a single fluid can be used to replace the model with two fluids to perform the numerical simulation for the purpose of simplifying the numerical model and saving computational time. 4.2. Effect of transverse pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet As mentioned in the photochemical etching experiment of airfoil PCHE, the fillets are found in the endwalls of airfoil fins. In the following sections, the effect of this formed fin-endwall fillets on the performance of airfoil PCHE will be discussed under different transverse and longitudinal pitches. The effect of transverse pitch on the Nusselt number of airfoil PCHE with and without fin-endwall fillet is plotted in Fig. 10(a). The non-dimensional longitudinal pitch in all the cases is fixed at 1.63. The Nusselt number in all the cases increases with the increase of Reynolds number, but decreases with the increases of transverse pitch. The decreasing trend of Nusselt number becomes smaller as the transverse pitch increases in each model with or without finendwall fillets. The Nusselt number of the model with fin-endwall
fillet is bigger than that without fin-endwall fillet. When the nondimensional transverse pitch is 2.38, the difference of Nusselt number between the two models is 6.7% at Reynolds number being 2300. But it becomes smaller and smaller as the Reynolds number increases. When the Reynolds number is greater than 3300, it is less than 3%. It decreases with the increase of transverse pitch. The maximum deviation between the models with and without finendwall fillet is 5.1% for zt ¼ 2.98, and 3.6% for zt ¼ 3.57. The effect of transverse pitch on the friction factor of airfoil PCHE with and without fin-endwall fillet is shown in Fig. 10(b). The friction factor decreases with the increase of Reynolds number and transverse pitch. Under the same transverse pitch, the friction factor of the model with fin-endwall fillet is bigger than that without fin-endwall fillet, but the difference between the two models is almost the same at different Reyonlds numbers. As the transverse pitch increases, the average difference between the two models decreases. The average deviation between the models with and without fin-endwall fillet is 6.4%, 5.1% and 4.3% for zt ¼ 2.38, zt ¼ 2.98 and zt ¼ 3.57, respectively. According to the above analysis, it can be seen that the finendwall fillet can increase the heat transfer and pressure drop. The heat transfer and pressure drop of actual airfoil PCHE may be underestimated if ignoring the fin-enwall fillet. The velocity and streamlines comparison may give an explanation for this phenomenon, as shown in Fig. 11. In the model without fin-endwall fillet, the upper and lower velocity and streamlines are symmetrical based on the transverse central axis. However, more fluids flow across the upper region because the flow area in the upper region is bigger than the lower region in the model with fin-endwall fillet.
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Fig. 12. Temperature comparison of airfoil PCHE with and without fin-endwall fillet (zt ¼ 2.98, zl ¼ 1.63): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: K); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K).
Fig. 10. Effect of transverse pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet: (a) Effect of transverse pitch on local Nusselt number of airfoil PCHE with and without fin-endwall fillet; (b) Effect of transverse pitch on local friction factor of airfoil PCHE with and without fin-endwall fillet.
Fig. 11. Velocity and streamlines comparison of airfoil PCHE with and without finendwall fillet (zt ¼ 2.98, zl ¼ 1.63): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: m/s); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: m/s).
The inclined surfaces in the model with fin-endwall fillet produce small vortices in the leading and trailing edges, which may enhance the turbulent intensity and thus increases the heat transfer and pressure drop. As shown in Fig. 12, the fin-endwall fillet changes the temperature distribution near the airfoil fins. The temperature gradient in the model with fin-endwall fillet is a little bigger than that in the model without fin-endwall fillet so that the heat transfer is enhanced by the fin-endwall fillet.
Fig. 13. Effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet: (a) Effect of longitudinal pitch on local Nusselt number of airfoil PCHE with and without fin-endwall fillet; (b) Effect of longitudinal pitch on local friction factor of airfoil PCHE with and without fin-endwall fillet.
4.3. Effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet The effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet is shown in Fig. 13. Here, the non-dimensional transverse pitch in all the cases is fixed at 2.38. With the increase of Reynolds number,
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using the model with a single fluid to replace the model with two fluids was studied. The effect of fin-endwall fillet on the thermal hydraulic performance of airfoil PCHE was investigated under different transverse and longitudinal pitches. The main conclusions are summarized as follows:
Fig. 14. Velocity and streamlines comparison of airfoil PCHE with and without finendwall fillet (zt ¼ 2.38, zl ¼ 1.88): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: m/s); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: m/s).
Fig. 15. Temperature comparison of airfoil PCHE with and without fin-endwall fillet (zt ¼ 2.38, zl ¼ 1.88): (a) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K).
the Nusselt number in each model increases but the friction factor decreases. The Nusselt number and friction factor decrease as the longitudinal pitch increases under the same Reynolds number. The longitudinal pitch has little effect on the heat transfer and pressure drop when the non-dimensional longitudinal pitch is greater than 1.88. The maximum deviation of Nusselt number between the models with and without fin-endwall fillet is less than 3% while the maximum deviation of friction factor is less than 2% when the non-dimensional longitudinal pitch is greater than 1.88. The fin-endwall fillet may decrease the Nusselt number and friction factor a little at a higher Reynolds number. The critical Reynolds number that changes the effect of fin-endwall fillet from the heat transfer enhancement to the heat transfer reduction reduces as the longitudinal pitch increases. Figs. 14 and 15 show the velocity, streamlines and temperature comparison of airfoil PCHE with and without fin-endwall fillet at zl ¼ 1.88. Although the fin-endwall fillet still affects the flow field near the airfoil fins, but the velocity and temperature distributions in most locations are similar. The effect of fin-endwall fillet at the big longitudinal pitch is much smaller compared to the small longitudinal pitch that shown in Figs. 11 and 12. It is because that the produced small vortices in the leading and trailing edges by the fin-endwall fillets has little effect on the farther downstream flow field at the big longitudinal pitch. 5. Conclusions In this paper, a photochemical etching experiment to manufacture the airfoil PCHE plate was performed and the feasibility of
(1) The fillets are formed in the endwalls of airfoil fins during the photochemical etching because the etching is isotropic. (2) In the studied cases, both the Nusselt number and friction factor can reach the fully-developed condition since the 8th row. In the fully-developed condition region, the Nusselt number and friction factor obtained by the model with a single fluid match well with those obtained by the model with two fluids, whose relative difference is less than 2% in Nusselt number and 5.5% in friction factor. Therefore, the model with a single fluid can be used to perform the numerical simulation for the purpose of simplifying the numerical model and saving computational time. (3) In the cases with non-dimensional longitudinal pitch being 1.63, the fin-endwall fillet can increase the heat transfer and pressure drop because the inclined surfaces produce small vortices in the leading and trailing edges. (4) The difference between the two models with and without fin-endwall fillet decreases with the increase of transverse pitch. The longitudinal pitch has little effect on the heat transfer and pressure drop when the non-dimensional longitudinal pitch is greater than 1.88. However, the fin-endwall fillet may decrease the Nusselt number and friction factor a little at a higher Reynolds number, which occurs at a smaller Reynolds number as the longitudinal pitch increases. In the studied cases, the maximum difference of Nusselt number between the two models with and without fin-endwall fillet is up to 6.7%, and the maximum difference of friction factor is 6.4% at zl ¼ 2.38 and zt ¼ 1.63. Acknowledgements This work is financially supported by the International Cooperation and Exchanges Project of NSFC of China (Grant No. 51120165002), and the Special and First Class Financial Grants from the China Postdoctoral Science Foundation (No. 2014T70919, No. 2013M530423). References [1] U.S. Nuclear Energy Research Advisory Committee (NERAC) and the Generation IV International Forum (GIF), A Technology Roadmap for Generation IV Nuclear Energy Systems, 2002. Washington DC, USA. [2] Nuclear Energy Agency (NEA) of the Organisation for Economic Co-operation and Development (OECD) and the Generation IV International Forum (GIF), Technology Roadmap Update for Generation IV Nuclear Energy Systems, 2014. Washington DC, USA. [3] F. Pra, P. Tochon, C. Mauget, J. Fokkens, S. Willemsen, Promising designs of compact heat exchangers for modular HTRs using the Brayton cycle, Nucl. Eng. Des. 238 (2008) 3160e3173. [4] C.H. Oh, E.S. Kim, M. Patterson, Design option of heat exchanger for the next generation nuclear plant, ASME J. Eng. Gas Turb. Power 132 (2010) 032903. [5] T.C. Hung, H.C. Chen, D.S. Lee, H.H. Fu, Y.T. Chen, G.P. Yu, Optimal design of a concentric heat exchanger for high-temperature systems using CFD simulations, Appl. Therm. Eng. 75 (2015) 700e708. [6] Website of Heatric Division of Meggitt (UK) Ltd, 2008. Available at: www. Heatric.com (accessed 03.12.14). [7] S.K. Mylavarapu, X.D. Sun, R.N. Christensen, R.R. Unocic, R.E. Glosup, M.W. Patterson, Fabrication and design aspects of high-temperature compact diffusion bonded heat exchangers, Nucl. Eng. Des. 249 (2012) 49e56. [8] K. Natesan, A. Moisseytsev, S. Majumdar, Preliminary issues associated with the next generation nuclear plant intermediate heat exchanger design, J. Nucl. Mater. 392 (2009) 307e315. [9] S.K. Mylavarapu, X.D. Sun, R.E. Glosup, R.N. Christensen, M.W. Patterson, Thermal hydraulic performance testing of printed circuit heat exchangers in a high-temperature helium test facility, Appl. Therm. Eng. 65 (2014) 605e614.
T. Ma et al. / Applied Thermal Engineering 89 (2015) 1087e1095 [10] H.P. Lo, C.H. Hung, C.C. Wang, Simulation of velocity distribution and pressure drop in every channel in the printed circuit heat exchanger, ECS Trans. 57 (2013) 393e399. [11] J. Figley, X.D. Sun, S.K. Mylavarapu, B. Hajek, Numerical study on thermal hydraulic performance of a printed circuit heat exchanger, Prog. Nucl. Energy 68 (2013) 89e96. [12] T. Ma, L. Li, X.Y. Xu, Y.T. Chen, Q.W. Wang, Study on local thermo-hydraulic performance and optimization of zigzag-type printed circuit heat exchanger at high temperature, Energy Convers. Manag. (2015), http://dx.doi.org/ 10.1016/j.enconman.2015.03.016. [13] S.M. Lee, K.Y. Kim, Multi-objective optimization of arc-shaped ribs in the channels of a printed circuit heat exchanger, Int. J. Therm. Sci. 94 (2015) 1e8. [14] S.M. Lee, K.Y. Kim, S.W. Kim, Multi-objective optimization of a double-faced type printed circuit heat exchanger, Appl. Therm. Eng. 60 (2013) 44e50. [15] N. Tsuzuki, Y. Kato, T. Ishiduka, High performance printed circuit heat exchanger, Appl. Therm. Eng. 27 (2007) 1702e1707. [16] T.L. Ngo, Y. Kato, K. Nikitin, T. Ishizuka, Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles, Exp. Therm. Fluid Sci. 32 (2007) 560e570. [17] D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermalehydraulic performance of new printed circuit heat exchanger model, Nucl. Eng. Des. 238 (2008) 3269e3276. [18] S.H. Yoon, H.C. No, G.B. Kang, Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermediate heat exchangers of HTGRs and SFRs, Nucl. Eng. Des. 270 (2014) 334e343.
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[19] X.Y. Xu, T. Ma, L. Li, M. Zeng, Y.T. Chen, Y.P. Huang, Q.W. Wang, Optimization of fin arrangement and channel configuration in an airfoil fin PCHE for supercritical CO2 cycle, Appl. Therm. Eng. 70 (2014) 867e875. [20] F. Zhou, I. Catton, Numerical evaluation of flow and heat transfer in plate-pin fin heat sinks with various pin cross-sections, Numer. Heat Transfer Part A: Appl. Int. J. Comput. Methodol. 60 (2011) 107e128. [21] D.M. Allen, Photochemical Machining: from ‘manufacturing's best kept secret’ to a $6 billion per annum, rapid manufacturing process, CIRP Ann. Manuf. Technol. 53 (2004) 559e572. [22] National Institute of Standards and Technology (NIST) Standard Reference Data, USA, 2011. Available at: webbook.nist.gov/chemistry/fluid/ (accessed 03.12.14). [23] Special Metals Corporation, USA, Available at: www.specialmetals.com/ documents/Inconel%20alloy%20617.pdf, 11/04/2014. [24] C. Wang, R.G. Ballinger, P.W. Staphle, Design of a power conversion system for an indirect cycle, helium cooled pebble bed reactor, in: Proceedings of the HTR-2002, Petten, NL, April, 2002, pp. 22e24. [25] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598e1605. [26] ANSYS FLUENT14.5 User's Guide, ANSYS Inc., Canonsburg, PA, USA, 2011. [27] I.H. Kim, H.C. No, J.I. Lee, B.G. Jeon, Thermal hydraulic performance analysis of the printed circuit heat exchanger using a helium test facility and CFD simulations, Nucl. Eng. Des. 239 (2009) 2399e2408. [28] L.H. Tang, M. Zeng, G.N. Xie, Q.W. Wang, Fin pattern effects on air-side heat transfer and friction characteristics of fin-and-tube heat exchangers with large number of large-diameter tube rows, Heat Transfer Eng. 30 (2009) 171e180.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Effect of fin-endwall fillet on thermal hydraulic performance of airfoil printed circuit heat exchanger* Ting Ma a, Fei Xin a, Lei Li a, Xiang-yang Xu a, Yi-tung Chen b, Qiu-wang Wang a, * a b
Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China Department of Mechanical Engineering, University of Nevada, Las Vegas, NV 89154, USA
h i g h l i g h t s Fillets are formed in the endwall of airfoil fins during the photochemical etching. Two-fluid model can be replaced by single-fluid model to perform simulation. Fin-endwall fillet can increase heat transfer and pressure drop at zl ¼ 1.63. Effect of fin-endwall fillet decreases as transverse pitch increases at zl ¼ 1.63. Longitudinal pitch has little effect at zl 1.88.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 December 2014 Received in revised form 6 April 2015 Accepted 9 April 2015 Available online 21 April 2015
Printed circuit heat exchanger (PCHE) is recommended to be used for intermediate heat exchanger in Very High Temperature Reactor (VHTR). One of the key features is that it is manufactured by the photochemical etching in order to maintain the internal structure and metal properties. In this paper, a photochemical etching experiment is conducted to manufacture the airfoil PCHE plate. The result indicates that the airfoil fin is not an ideal airfoil profile, but has a fin-endwall fillet. For the purpose of simplifying the numerical model and saving computational time, a validated model with a single fluid is used to further study the effect of fin-endwall fillet on the thermal hydraulic performance of airfoil PCHE. It is found that the fin-endwall fillet can increase the heat transfer and pressure drop in the cases with the non-dimensional longitudinal pitch being 1.63. The effect of fin-endwall fillet on thermal hydraulic performance decreases with the increase of transverse pitch, but the longitudinal pitch has little effect when the non-dimensional longitudinal pitch is greater than 1.88. In the studied cases, the maximum difference of Nusselt number and friction factor between the two models with and without fin-endwall fillet is up to 6.7% and 6.4%. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Printed circuit heat exchanger Endwall fillet Thermal hydraulic High temperature Photochemical etching
1. Introduction The nuclear energy has received considerable attention in many countries due to fossil fuels' exhaustion and environmental terms. To use it with high economy, enhanced safety, minimal waste and proliferation resistant, the U.S. Department of Energy proposed six top candidates for the IV generation nuclear plants,
* Presented at the 17th Conference on Process Integration, Modelling and Optimisation for Energy Saving and Pollution Reduction PRES 2014, 23e27 August 2014 Prague, Czech Republic. (Original paper title: “Study on Heat Transfer and Pressure Drop Performances of Airfoil-Shaped Printed Circuit Heat Exchanger” and Paper No.: # 370). * Corresponding author. Tel.: þ86 (29) 82665539; fax: þ86 (29) 82663502. E-mail address: [email protected] (Q.-w. Wang).
http://dx.doi.org/10.1016/j.applthermaleng.2015.04.022 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
i.e., Very High Temperature Reactor (VHTR), Supercritical Water Cooled Reactor (SCWR), Sodium Cooled Fast Reactor (SFR), Molten Salt Reactor (MSR), Lead-Cooled Fast Reactor (LFR) and Gas-Cooled Fast Reactor (GFR) [1]. As one of the most promising candidates, the VHTR can supply heat over a range of core outlet temperature between 700 C and 950 C, which can be utilized by the refineries, petrochemistry, metallurgy and hydrogen production through an intermediate heat exchanger [2]. On the other hand, the intermediate heat exchanger in the VHTR needs to withstand ultra high temperature, high pressure, high pressure difference and high heat flux [3,4]. The traditional shell-and-tube heat exchangers are unsuitable to be used for the VHTR due to low heat transfer efficiency, while the traditional plate-fin heat exchangers and plate heat exchangers cannot satisfy the requirement of high pressure and high temperature. Hung et al. [5] used the staggered fin arrays to
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Nomenclature A Amin cp Dh f h Hf k Lf Lp m N Nu p Pl Pt Re
heat transfer area, mm2 minimum cross sectional area, mm2 specific heat, J/(kg K) maximum width of airfoil shaped fin, mm Darcy friction factor heat transfer coefficient, W/(m2 K) height of airfoil shaped fin, mm thermal conductivity, W/(m K) chord length of airfoil shaped fin, mm wave channel pitch along streamwise direction, mm mass flow rate, kg/h row of airfoil shaped fin Nusselt number static pressure, Pa longitudinal pitch of airfoil shaped fin, mm transverse pitch of airfoil shaped fin, mm Reynolds number
enhance the heat transfer performance of concentric tube heat exchanger in VHTR. Recently, a plate heat exchanger called printed circuit heat exchanger (PCHE) is recommended to be used for intermediate heat exchanger in VHTR. Different from the traditional manufacturing methods used for plate heat exchangers, the channels of PCHE are formed in the metal plates by photochemical etching. Then these plates are stacked together and fabricated by diffusion bonding. The PCHE can withstand the high temperature up to 900 C, and high pressure up to 60 MPa because the diffusion bonding can make the strength of bonding joints similar to the parent metal [6]. The channel diameter of plates manufactured by photochemical etching is usually ranged from 0.5 mm to 2.0 mm [7]. Compared to the traditional shell-and-tube heat exchangers with bare tubes, the PCHE only needs 1/30 of volume to achieve the same heat transfer rate in the VHTR [8]. The thermalehydraulic performance of PCHE is determined by the shape of channel manufactured by the photochemical etching. The basic channel of PCHE is a straight semicircular shape. Mylavarapu et al. [9] set up an experimental system to test the PCHE with straight semicircular channels at 790 C and 2.7 MPa, and found that the onset of transition from laminar flow to transition flow regime occurred much earlier than the circular pipe. Lo et al. [10] conducted a numerical simulation of PCHE with straight semicircular channels. The result indicated that the velocity and mass flow rate had significant effects on the performance. But the heat transfer effectiveness of the PCHE with straight semicircular channels was less than 80% when the mass flow rate was greater than 15 kg/h [11]. The zigzag channel could significantly enhance the heat transfer effectiveness of PCHE up to 85% at mass flow rate of 15 kg/h [12]. The arc-shaped ribs were attached to the flow channel of double-faced-type PCHE to enhance the heat transfer performance [13]. Lee et al. [14] used a RANS analysis to perform a multi-objective optimization of a double-faced type PCHE with zigzag channels. However, the pressure drop of zigzag-type PCHE is still too high to be used at the large mass flow rate. To reduce the pressure drop, Tsuzuki et al. [15] proposed a PCHE with an S-shaped channel. It was found that the pressure drop of S-shaped channel was only one-fifth of the zigzag channel with identical heat transfer performance due to the uniform flow velocity profile and less reverse flows and eddies in the S-shaped channel. The experiment conducted by Ngo et al. [16] further confirmed that the S-shaped PCHE was better than the zigzag-type PCHE in reducing the
T umax Wf
temperature, K superficial maximum velocity, m/s maximum thickness of airfoil shaped fin, mm
Greek
r Dp Dpa Dpf m d zl zt
density, kg/m3 total pressure drop, Pa acceleration pressure drop, Pa friction pressure drop, Pa dynamic viscosity, Pa s thickness of substrate plate, mm non-dimensional longitudinal pitch non-dimensional transverse pitch
Subscripts b averaged value in one pitch in inlet in one longitudinal pitch out outlet in one longitudinal pitch w wetted surface
pressure drop. Kim et al. [17] designed an airfoil fin to optimize the thermal hydraulic performance of PCHE. The pressure drop of the airfoil fin could be reduced to one-twentieth of that of zigzag channel but the total heat transfer rate per unit volume was almost the same. Yoon et al. [18] proposed Fanning factor and Nusselt number correlations for an airfoil PCHE with fixed geometrical parameters. Xu et al. [19] modified the profile of airfoil fin to further reduce the flow resistance and recommend the staggered fin arrangement for the airfoil PCHE. Zhou and Catton [20] found that the performances of NACA airfoil and elliptic fins were better compared to dropform and circular fins. However, it is found that the airfoil fin manufactured by the photochemical etching is not an ideal airfoil profile, but has a finendwall fillet. Therefore, the present study focuses on the effect of fin-endwall fillet on the thermal hydraulic performance of PCHE.
2. Photochemical etching experiment of airfoil PCHE The photochemical etching, also known as photochemical machining, employs chemical etching through a photoresist stencil as the method of material removal over selected areas [21]. This corrosive oxidation process does not alter the internal structure of the metal and metal properties such as hardness, grain structure and ductility [7], which is beneficial to be used at high temperature. The aqueous ferric chloride solution is usually selected as an etchant for stainless steel and superalloy. Considering the superalloy is much more expensive than stainless steel, the stainless steel SUS304 is used to conduct the present photochemical etching experiment. However, the process of etching the superalloy is almost the same. The basic chemical reactions are illustrated as follows:
8 < Fe þ 2FeCl3 ¼ 3FeCl2 Cr þ 3FeCl3 ¼ CrCl3 þ 3FeCl2 : Ni þ 2FeCl3 ¼ NiCl2 þ 2FeCl2
(1)
From the above chemical reaction equation set, it can be seen that the concentration of ferric ion has a significant effect on the chemical reactions. As the time increases, the concentration of ferric ion reduces. On the other hand, the Fe(OH)3 may be produced between ferric ion and (OH) ion. Therefore, the hydrochloric acid
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Fig. 1. Cross-sectional shape of channels manufactured by photochemical etching: (a) Sketch of cross-sectional shape of channels; (b) Experimental photo of cross-sectional shape of channels (unit: cm).
and nitric acid are added to main the acidity. The corresponding chemical reactions are shown as follows:
3Fe þ 8HNO3 ¼ 3FeðNO3 Þ2 þ 2NO[ þ 4H2 O 2Ni þ 2HNO3 þ 4HCl ¼ 2NiCl2 þ 2NO[ þ 3H2 O
(2)
The hydrochloric acid can increase the solubility of ferrous ion and rate of etching, while the nitric acid can improve the smooth and uniformity of channels. It was found that the etchant attacked not only downwards into the metal but also sideways beneath the photoresist stencil layer because the etching was isotropic, as shown in Fig. 1(a) [21]. Fig. 1(b) shows the cross-sectional shape of channels manufactured by the photochemical etching experiment. It can be seen that the fillets are formed in the endwalls of channels. Fig. 2 shows the airfoil PCHE plate manufactured by photochemical etching. The airfoil fins are etched in a SUS304 stainless steel plate with thickness of 2 mm. There are fillets in the endwall
Fig. 2. Airfoil PCHE plate manufactured by photochemical etching.
Fig. 3. Micrographs of airfoil PCHE plate obtained by laser microscope: (a) 3D micrograph of airfoil channels (unit: mm); (b) 2D micrograph of airfoil channels.
of airfoil fins. The detailed 3D and 2D micrographs of airfoil PCHE plate are obtained by laser microscope, as shown in Fig. 3. The formed fillets in the endwalls of airfoil fins are clearly indicated in these images. In the following sections, we will discuss about the effect of this formed fin-endwall fillets on the thermal hydraulic performance of airfoil PCHE.
3. Computational modeling of airfoil PCHE 3.1. Numerical model and computational method The NACA0021 airfoil fin is used for the present study, as shown in Fig. 4. It has the maximum thickness of Wf ¼ 0.84 mm and a chord length of Lf ¼ 4 mm with a height of Hf ¼ 1 mm. The thickness of substrate plate is d ¼ 1 mm. There are 12 rows of fins along the streamwise direction in a staggered arrangement. In the baseline model, the transverse pitch Pt is 2 mm and the longitudinal pitch Pl is 6.5 mm. The numerical model with two fluids is described in Fig. 5. Because the hot and cold fluids flow alternately in the channels along the z direction, only one hot-side fluid channel, one cold-side fluid channel and the corresponding substrate plates and fins are selected as the numerical model to simplify the numerical simulation. Here, the top and bottom plates have a half thickness of substrate plate. The periodic boundary is specified to the top and bottom surfaces. In the transverse direction, one full fin and two fins with half of the maximum thickness are used so that the symmetrical boundary is used to the left and right surfaces. In order to support a uniform velocity at the inlet and suppress the backflow at the outlet, the inlet is extended to 5 times of
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Fig. 4. Geometrical parameters of airfoil fins.
at high temperature [27]. The local pitch-averaged Nusselt number is defined by the local temperature, local surface heat flux and local physical properties, which are averaged in a single streamwise pitch rather than an arbitrary position. The local parameters in one longitudinal pitch are defined for the analysis. The local Reynolds number Re in one longitudinal pitch is defined as follows:
Re ¼
rumax Dh mDh ¼ m mAmin
(3)
where umax is the superficial maximum velocity evaluated at the minimum cross section, m is the mass flow rate, Amin is the minimum cross sectional area, Dh is the maximum width of airfoil fin. r is the density of helium and m is the dynamic viscosity of helium, which are evaluated at the average temperature of helium in one longitudinal pitch. The local Nusselt number Nu in one longitudinal pitch is defined as follows:
Nu ¼ Fig. 5. Numerical model with two fluids of airfoil PCHE: (a) 3D view of numerical model; (b) Cross section of numerical model.
channel height while the outlet is extended to 30 times of channel height. The fluids on both sides are helium, whose physical properties are taken from NIST [22]. The material of substrate plates and fins is Alloy 617 [23]. The inlet temperature is 1173.15 K on hot side and 761.96 K on cold side. Pressures are specified at the outlets of the channels, which are 7.59 MPa on the hot side and 7.83 MPa on the cold side. These parameters are taken from the operating condition of a helium cooled pebble bed reactor [24]. In this study, we also give an analysis of thermalehydraulic performance of PCHE with a single fluid to study the feasibility of using this model to replace the model with two fluids. In the model with a single fluid, only the hot-side fluid channel and hot-side fins shown in Fig. 5 are used for the numerical simulation. In this model, the constant temperature of 1123.15 is applied to the top and bottom surfaces of hot-side fluid channel. The inlet temperature is defined as 1173.15 K. The flow in the computational domain is regarded as 3D, incompressible, turbulence and steady. The shear stress transport (SST) kew model developed by Menter [25] is used to perform the turbulent flow. It provides an effective combination of the robust and accurate formulation of the kew model in the near-wall region with the free-stream independence of the ke3 model in the far field, which makes it more accurate and reliable for airfoil flow than the standard kew model [26]. The SST kew model was selected by Xu et al. [19] to evaluate the supercritical CO2 in the Zigzag, S-shaped and airfoil PCHEs. The calculation is carried out in the finite volume method software ANSYS FLUENT 14.5. The convection terms are solved by a second-order upwind discretization. The Semi Implicit Method Pressure Linked Equation (SIMPLE) algorithm is used to resolve the coupling of velocity and pressure. The residual for every variable is required to be less than 106 before solution convergence. It was found that the local pitch-averaged Nusselt number correlation is more appropriate than the global Nusselt number correlation
hDh k
(4)
in which, the heat transfer coefficient h is defined as follows:
mcp ðTin Tout Þ Aw ðTw Tb Þ
h¼
(5)
where Tin, Tout, Tb are the inlet, outlet and average temperature of helium in one longitudinal pitch, respectively. Tw is the temperature of wetted surface in one longitudinal pitch while Aw is the corresponding area. k is the thermal conductivity of helium and cp is the specific heat of helium, which are evaluated at the average temperature of helium in one longitudinal pitch. The local Darcy friction factor f in one longitudinal pitch is defined as follows:
f ¼
2Dpf Dh rumax Pl
(6)
where Pl is the longitudinal pitch of fins, and Dpf is the frictional pressure drop. The frictional pressure drop Dpf can be obtained by:
Dpf ¼ Dp Dpa
(7)
Dpa ¼ rout u2out rin u2in
(8)
where Dp is the total pressure drop, Dpa is the acceleration pressure drop. rin, uin and rout, uout are the density and velocity evaluated at the inlet and outlet of one longitudinal pitch. In order to study the effect of longitudinal pitch and transverse pitch, the non-dimensional longitudinal pitch zl and nondimensional transverse pitch zt are defined as follows:
zl ¼
Pl Lf
(9)
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Table 1 Grid independence test (Re ¼ 2541). Grid 1,169,502 2,110,750 2,985,390 3,667,302
zt ¼
elements elements elements elements
Nu
Relative error
f
Relative error
10.37 10.57 10.69 10.76
e 1.89% 1.12% 0.65%
0.0243 0.0239 0.0240 0.0242
e 1.67% 0.42% 0.83%
Pt Wf
(10)
3.2. Grid independence and code validation Due to the sensitivity of grid on the computational result, it is necessary to find an appropriate grid system. Four grid systems on the baseline model with a single fluid are established to test the grid independence. The four grid systems have 1,169,502 elements, 2,110,750 elements, 2,985,390 elements and 3,667,302 elements, respectively. The result is shown in Table 1. Comparing to the result of the finest grid system with 3,667,302 elements, the deviation of Nu and f of the grid system with 2,985,390 elements is less than 1%. As shown in Fig. 6, very dense grids are established near the wall surfaces of fins and substrate plates to make sure that the yþ is less than 1. Therefore, the grid system with 2,985,390 elements is used for the baseline model with one fluid and the similar grid system is adopted for other models in the later discussion. Because the structure of this model is similar to the plain finand-tube heat exchanger, a numerical model with six tube rows is established to examine the applicability of the present method by comparing with the previous experiment on the plain fin-and-tube heat exchanger [28]. As shown in Fig. 7, the deviation of Nu between the present numerical result and experimental data is less than 8.9% and the deviation of f is less than 11.5%. Therefore, the present numerical method is reliable.
Fig. 6. Selected grid system: (a) 3D view of selected grid system; (b) Top view of selected grid system.
Fig. 7. Method validation with experimental data [28].
4. Results and discussion 4.1. Comparison of numerical models with a single fluid and two fluids In the actual PCHE, the length of plate is more than 500 mm which includes about 100 rows of airfoil fins [18]. However, it is not economic to establish a model with the full length because it needs more than 50 million grid elements. In this section, a simplified numerical method is studied to perform the analysis. Here, the baseline geometrical parameters are used in the two models, whose non-dimensional longitudinal pitch zl is 1.63 and nondimensional transverse pitch zt is 2.38. The thermal hydraulic performance of numerical model with a single fluid along the streamwise direction is described in Fig. 8. In this model, the physical properties of helium are constant so that the Reynolds number in every longitudinal pitch is constant. As shown in Fig. 8(a), the Nusselt number decreases along the streamwise direction and reduces to the minimum in the third row. After that, it increases and achieves approximately fully-developed condition since the 8th row. Here, the fluctuation that less than 4% is regarded as the fully-developed condition. In the last row, there is a little increase in the Nusselt number due to the outlet effect. As shown in Fig. 8(b), a sharp decrease in friction factor occurs between the first and second rows. After that, the friction factor increases, but decreases again since the third row and then gradually becomes steady. The fluctuation in friction factor is smaller than the Nusselt number, which is less than 2% since the 8th row. Because the streamlines in airfoil channel are very smooth, the upstream velocity profile has a significant effect on the heat transfer and pressure drop of downstream airfoil channel, and thus takes a long distance to reach the fully-developed condition. In the studied Reynolds number, both the Nusselt number and friction factor from the 8th row to the 11th can be regarded as the fully-developed condition. Fig. 9 shows the thermal hydraulic performance comparison of numerical simulations with a single fluid and two fluids. It can be seen that the Nusselt number and friction factor obtained by the model with a single fluid match well with those obtained by the model with two fluids. The relative difference between them is less than 2% in Nusselt number and 5.5% in friction factor. It should be noted that these data comes from the 8th to 11th rows because the Nusselt number and friction factor can reach the fully-developed condition, as mentioned in the above discussion. Although the physical properties of helium and the wall temperature are various in the numerical model with two fluids, but the non-dimensional velocity and non-dimensional temperature can achieve a steady
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Fig. 9. Thermal hydraulic performance comparison of numerical simulations with a single fluid and two fluids: (a) Local Nusselt number comparison of numerical simulations with a single fluid and two fluids; (b) Local friction factor comparison of numerical simulations with a single fluid and two fluids.
Fig. 8. Thermal hydraulic performance of numerical model with a single fluid along streamwise direction: (a) Local Nusselt number distribution along streamwise direction; (b) Local friction factor distribution along streamwise direction.
condition and is similar to the behaviors of model with a single fluid [12]. Therefore, both the Nusselt number and friction factor in the two models can match well with each other. The model with a single fluid can be used to replace the model with two fluids to perform the numerical simulation for the purpose of simplifying the numerical model and saving computational time. 4.2. Effect of transverse pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet As mentioned in the photochemical etching experiment of airfoil PCHE, the fillets are found in the endwalls of airfoil fins. In the following sections, the effect of this formed fin-endwall fillets on the performance of airfoil PCHE will be discussed under different transverse and longitudinal pitches. The effect of transverse pitch on the Nusselt number of airfoil PCHE with and without fin-endwall fillet is plotted in Fig. 10(a). The non-dimensional longitudinal pitch in all the cases is fixed at 1.63. The Nusselt number in all the cases increases with the increase of Reynolds number, but decreases with the increases of transverse pitch. The decreasing trend of Nusselt number becomes smaller as the transverse pitch increases in each model with or without finendwall fillets. The Nusselt number of the model with fin-endwall
fillet is bigger than that without fin-endwall fillet. When the nondimensional transverse pitch is 2.38, the difference of Nusselt number between the two models is 6.7% at Reynolds number being 2300. But it becomes smaller and smaller as the Reynolds number increases. When the Reynolds number is greater than 3300, it is less than 3%. It decreases with the increase of transverse pitch. The maximum deviation between the models with and without finendwall fillet is 5.1% for zt ¼ 2.98, and 3.6% for zt ¼ 3.57. The effect of transverse pitch on the friction factor of airfoil PCHE with and without fin-endwall fillet is shown in Fig. 10(b). The friction factor decreases with the increase of Reynolds number and transverse pitch. Under the same transverse pitch, the friction factor of the model with fin-endwall fillet is bigger than that without fin-endwall fillet, but the difference between the two models is almost the same at different Reyonlds numbers. As the transverse pitch increases, the average difference between the two models decreases. The average deviation between the models with and without fin-endwall fillet is 6.4%, 5.1% and 4.3% for zt ¼ 2.38, zt ¼ 2.98 and zt ¼ 3.57, respectively. According to the above analysis, it can be seen that the finendwall fillet can increase the heat transfer and pressure drop. The heat transfer and pressure drop of actual airfoil PCHE may be underestimated if ignoring the fin-enwall fillet. The velocity and streamlines comparison may give an explanation for this phenomenon, as shown in Fig. 11. In the model without fin-endwall fillet, the upper and lower velocity and streamlines are symmetrical based on the transverse central axis. However, more fluids flow across the upper region because the flow area in the upper region is bigger than the lower region in the model with fin-endwall fillet.
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Fig. 12. Temperature comparison of airfoil PCHE with and without fin-endwall fillet (zt ¼ 2.98, zl ¼ 1.63): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: K); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K).
Fig. 10. Effect of transverse pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet: (a) Effect of transverse pitch on local Nusselt number of airfoil PCHE with and without fin-endwall fillet; (b) Effect of transverse pitch on local friction factor of airfoil PCHE with and without fin-endwall fillet.
Fig. 11. Velocity and streamlines comparison of airfoil PCHE with and without finendwall fillet (zt ¼ 2.98, zl ¼ 1.63): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: m/s); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: m/s).
The inclined surfaces in the model with fin-endwall fillet produce small vortices in the leading and trailing edges, which may enhance the turbulent intensity and thus increases the heat transfer and pressure drop. As shown in Fig. 12, the fin-endwall fillet changes the temperature distribution near the airfoil fins. The temperature gradient in the model with fin-endwall fillet is a little bigger than that in the model without fin-endwall fillet so that the heat transfer is enhanced by the fin-endwall fillet.
Fig. 13. Effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet: (a) Effect of longitudinal pitch on local Nusselt number of airfoil PCHE with and without fin-endwall fillet; (b) Effect of longitudinal pitch on local friction factor of airfoil PCHE with and without fin-endwall fillet.
4.3. Effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet The effect of longitudinal pitch on thermal hydraulic performance of airfoil PCHE with and without fin-endwall fillet is shown in Fig. 13. Here, the non-dimensional transverse pitch in all the cases is fixed at 2.38. With the increase of Reynolds number,
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using the model with a single fluid to replace the model with two fluids was studied. The effect of fin-endwall fillet on the thermal hydraulic performance of airfoil PCHE was investigated under different transverse and longitudinal pitches. The main conclusions are summarized as follows:
Fig. 14. Velocity and streamlines comparison of airfoil PCHE with and without finendwall fillet (zt ¼ 2.38, zl ¼ 1.88): (a) Left side of model without fin-endwall fillet between the 8th and 10th fins (unit: m/s); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: m/s).
Fig. 15. Temperature comparison of airfoil PCHE with and without fin-endwall fillet (zt ¼ 2.38, zl ¼ 1.88): (a) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K); (b) Left side of model with fin-endwall fillet between the 8th and 10th fins (unit: K).
the Nusselt number in each model increases but the friction factor decreases. The Nusselt number and friction factor decrease as the longitudinal pitch increases under the same Reynolds number. The longitudinal pitch has little effect on the heat transfer and pressure drop when the non-dimensional longitudinal pitch is greater than 1.88. The maximum deviation of Nusselt number between the models with and without fin-endwall fillet is less than 3% while the maximum deviation of friction factor is less than 2% when the non-dimensional longitudinal pitch is greater than 1.88. The fin-endwall fillet may decrease the Nusselt number and friction factor a little at a higher Reynolds number. The critical Reynolds number that changes the effect of fin-endwall fillet from the heat transfer enhancement to the heat transfer reduction reduces as the longitudinal pitch increases. Figs. 14 and 15 show the velocity, streamlines and temperature comparison of airfoil PCHE with and without fin-endwall fillet at zl ¼ 1.88. Although the fin-endwall fillet still affects the flow field near the airfoil fins, but the velocity and temperature distributions in most locations are similar. The effect of fin-endwall fillet at the big longitudinal pitch is much smaller compared to the small longitudinal pitch that shown in Figs. 11 and 12. It is because that the produced small vortices in the leading and trailing edges by the fin-endwall fillets has little effect on the farther downstream flow field at the big longitudinal pitch. 5. Conclusions In this paper, a photochemical etching experiment to manufacture the airfoil PCHE plate was performed and the feasibility of
(1) The fillets are formed in the endwalls of airfoil fins during the photochemical etching because the etching is isotropic. (2) In the studied cases, both the Nusselt number and friction factor can reach the fully-developed condition since the 8th row. In the fully-developed condition region, the Nusselt number and friction factor obtained by the model with a single fluid match well with those obtained by the model with two fluids, whose relative difference is less than 2% in Nusselt number and 5.5% in friction factor. Therefore, the model with a single fluid can be used to perform the numerical simulation for the purpose of simplifying the numerical model and saving computational time. (3) In the cases with non-dimensional longitudinal pitch being 1.63, the fin-endwall fillet can increase the heat transfer and pressure drop because the inclined surfaces produce small vortices in the leading and trailing edges. (4) The difference between the two models with and without fin-endwall fillet decreases with the increase of transverse pitch. The longitudinal pitch has little effect on the heat transfer and pressure drop when the non-dimensional longitudinal pitch is greater than 1.88. However, the fin-endwall fillet may decrease the Nusselt number and friction factor a little at a higher Reynolds number, which occurs at a smaller Reynolds number as the longitudinal pitch increases. In the studied cases, the maximum difference of Nusselt number between the two models with and without fin-endwall fillet is up to 6.7%, and the maximum difference of friction factor is 6.4% at zl ¼ 2.38 and zt ¼ 1.63. Acknowledgements This work is financially supported by the International Cooperation and Exchanges Project of NSFC of China (Grant No. 51120165002), and the Special and First Class Financial Grants from the China Postdoctoral Science Foundation (No. 2014T70919, No. 2013M530423). References [1] U.S. Nuclear Energy Research Advisory Committee (NERAC) and the Generation IV International Forum (GIF), A Technology Roadmap for Generation IV Nuclear Energy Systems, 2002. Washington DC, USA. [2] Nuclear Energy Agency (NEA) of the Organisation for Economic Co-operation and Development (OECD) and the Generation IV International Forum (GIF), Technology Roadmap Update for Generation IV Nuclear Energy Systems, 2014. Washington DC, USA. [3] F. Pra, P. Tochon, C. Mauget, J. Fokkens, S. Willemsen, Promising designs of compact heat exchangers for modular HTRs using the Brayton cycle, Nucl. Eng. Des. 238 (2008) 3160e3173. [4] C.H. Oh, E.S. Kim, M. Patterson, Design option of heat exchanger for the next generation nuclear plant, ASME J. Eng. Gas Turb. Power 132 (2010) 032903. [5] T.C. Hung, H.C. Chen, D.S. Lee, H.H. Fu, Y.T. Chen, G.P. Yu, Optimal design of a concentric heat exchanger for high-temperature systems using CFD simulations, Appl. Therm. Eng. 75 (2015) 700e708. [6] Website of Heatric Division of Meggitt (UK) Ltd, 2008. Available at: www. Heatric.com (accessed 03.12.14). [7] S.K. Mylavarapu, X.D. Sun, R.N. Christensen, R.R. Unocic, R.E. Glosup, M.W. Patterson, Fabrication and design aspects of high-temperature compact diffusion bonded heat exchangers, Nucl. Eng. Des. 249 (2012) 49e56. [8] K. Natesan, A. Moisseytsev, S. Majumdar, Preliminary issues associated with the next generation nuclear plant intermediate heat exchanger design, J. Nucl. Mater. 392 (2009) 307e315. [9] S.K. Mylavarapu, X.D. Sun, R.E. Glosup, R.N. Christensen, M.W. Patterson, Thermal hydraulic performance testing of printed circuit heat exchangers in a high-temperature helium test facility, Appl. Therm. Eng. 65 (2014) 605e614.
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