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Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Modeling of Cryogenic Liquefied Natural Gas Ambient Air Vaporizers Biao Sun,† Divyamaan Wadnerkar,† Ranjeet P. Utikar,† Moses Tade,† Neil Kavanagh,‡ Solomon Faka,‡ Geoffrey M. Evans,§ and Vishnu K. Pareek*,† †
Department of Chemical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia Woodside Energy Limited, GPO Box D188, Perth, WA 6840, Australia § Department of Chemical Engineering, University of Newcastle, Callaghan, NSW 2308, Australia Downloaded via UNIV OF MINNESOTA on July 10, 2018 at 00:17:19 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
‡
ABSTRACT: The ambient air vaporizer (AAV) technology is a promising option for vaporization of cryogenic fluids including liquefied natural gas (LNG). In this study, the heat transfer between ambient air and cryogenic LNG under supercritical conditions has been studied by using computational fluid dynamics (CFD). The process of regasification was first analyzed from the thermodynamics standpoint. In the absence of actual data for LNG, the empirical correlations and experimental data for supercritical flows of water and carbon dioxide were used to validate the CFD model. The model was then used to investigate the supercritical flow of LNG inside AAV. Operating conditions such as air flow velocity and operating pressure were studied. Furthermore, optimization of fin configurations including the number of fins, fin length, and fin thickness was also investigated. The methodology and results discussed in this study are of critical importance for designing AAV.
1. INTRODUCTION An integral and essential part of liquefied natural gas (LNG) receiving terminals is the vaporizer. The choice of the regasification system in an LNG project is critical, as it has a huge impact on capital expenditure, operating costs, operating flexibility, reliability, emissions, etc. Based on various heat sources, there are mainly three types of regasification systems in the LNG industry, namely, open rack vaporizer (ORV), submerged combustion vaporizer (SCV), and air-heated vaporizer.1,2 ORVs and SCVs are widely used in Asia and Europe.3,4 However, these units are environmentally unsustainable, as they produce large amounts of emission, such as exhaust gas in SCVs and processed cold seawater in ORVs. Most current U.S. LNG terminals utilize SCVs or intermediate fluid vaporizers (IFVs) with fire heaters because it is thought that the released cold and chlorinated seawater from ORV could have a negative impact on the marine environment by killing marine life.5 Increased energy costs and concerns about environmental issues have led to the development of greener vaporization systems. One of the promising alternatives is the air-heated vaporizer. Some large LNG projects have adopted ambient-air based approaches instead of traditional regasification technologies, such as Dahej LNG terminal6 in India and Oregon LNG import terminal7 and Corpus Christi Liquefaction project8 in the USA. Among the different types of airheated vaporizers, the forced-draft ambient air vaporizers (AAVs) (Figure 1a) have a competitive edge over others. The external fans equipped on the top of the AAV unit force warm air through the gaps of compacted finned tubes (Figure 1b) making them less sensitive to ambient air conditions and more efficient compared to natural-draft ones (Figure 1c). One © XXXX American Chemical Society
Figure 1. Two main types of AAVs and compacted finned tubes.
particular concern of using LNG AAVs involves fog formation9,10 as the discharged cold and dry air mixes with ambient warm and humid air, which may significantly affect human activities (such as process operation, transportation, etc.) inside or nearby LNG terminals. Moreover, frost formation on finned tubes11 in LNG regasification process may lead to very large frost loadings which could produce thermal resistance and significantly reduce heat transfer rate. As these phenomena are governed by the heat transfer between ambient air and cryogenic LNG, it is essential to adequately understand the heat transfer process. Since high pressure is required for long-distance pipeline transportation, LNG is first pressurized through an isenthalpic process as shown in Figure 2. This ensures a lower operating cost, as increasing pressure in the liquid phase is significantly Received: Revised: Accepted: Published: A
March 22, 2018 May 31, 2018 June 7, 2018 June 7, 2018 DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
Article
Industrial & Engineering Chemistry Research
Essentially, the critical point is defined as the point where the distinction between liquid and vapor regions disappears. It is characterized by the state parameters tcr and pcr which must be determined experimentally. A fluid with a pressure above the critical pressure but at a temperature below the critical temperature is classified as a compressed fluid.13,14 Studies have been performed to investigate the heat transfer behavior in AAVs. Jeong et al.14 conducted a numerical study on heat transfer from natural-draft AAVs by using liquid nitrogen as working fluid. Heat transfer coefficients of both inside/outside the pipe were compared with empirical correlations. Studies of the different number of fins and the fin length and thickness of the finned tube in natural-draft AAVs have been investigated both experimentally and numerically.11,15 It has been found that increasing the heat transfer area (i.e., increasing fin length and number of fins) could promote heat transfer rate. Liu et al.16 and Liu et al.17 performed studies on heat transfer performance in LNG AAV by using a coupled heat transfer model. The model combined the phase change of LNG boiling with natural convection of air flow to investigate the factors such as air temperature, LNG flow rate, and finned tube distribution in a bundle. Zhao et al.18 and Xu et al.19 studied different types of vaporizers by treating LNG flow as a supercritical flow. However, most of the previous studies were mainly focused on natural-draft AAVs which are normally used in relatively smaller LNG station in terms of operating capacity. In order to improve the efficiency
Figure 2. Vaporization process in methane phase diagram.
cheaper than compressing the vapor. The pressurized LNG is then heated and evaporated in the vaporizers, which involves a typical isobaric process (Figure 2). Based upon different operating pressures inside finned tubes, the “vaporization” of LNG can be characterized as (i) boiling and (ii) supercritical heating. Boiling occurs when operating pressure is below the critical pressure (4.6 MPa for methane), while a supercritical fluid is technically termed as both pressures and temperatures being higher than the thermodynamic critical values.12,13
Figure 3. Temperature-dependent thermal properties of pure methane under different pressures. B
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research Table 1. Correlations for Heat Transfer at Supercritical Conditions characteristic parameters in Nu, Re, Pr ref
flow geometry
T (°C)
length Dhy
0.8
0.33
0
0
tube tube tube
tf = (tb + tw)/2 tb, tpc, or tw tb tb
D D D
0.77 0.8 ∼0.8
0.55, tw 0.8, tb, or tw ∼0.33
0 0 0
tube
tw
D
0.923
tube, annulus tube annulus tube bundle
tb
Dhy
0.8
0.613 based on −0.231, tb/tw cp̅ 0 0
0 0 0 0 0.11, tb/tw −0.33, tb/ tw 0.231, tb/ 0 tw 0 0
tb tb tb tb
D Dhy D Dhy
0.8 0.8 0.85 0.8
0.8, tb, or tw 0.4 0.8 and Prnpc 0.7 based on cp̅
0 0 0 0.2, tb/tin
0 0
McAdams et al.36
annulus
Bringer and Smith37 Shitsman38 Krasnoshchekov and Protopopov39 Swenson et al.40 Kondrat’ev21 Ornatsky et al.41 Ornatsky et al.42 Yamagata et al.22 Dyadyakin and Popov23
m1
m2
m3
−0.3, tb/tw 0 0 −0.45, tb/tw, and 0.1
m4
m5 0
m6
m7
0
1
0 0 0.35
0 0 0
0
0
0
0
0 0 0 0
0 0 0 or n1 0
0 0 0 1
0 0
n2 0
0 0
( ) ρb
ρin
Kirillov et al.20 Gorban et al.43
tube tube
tb tb
D D
∼0.8 0.9
∼0.33 or 0.4 −0.12
x
−n1 0
2. THEORETICAL BASIS 2.1. Thermophysical Properties of Fluids. In order to simplify the fluid properties, the supercritical fluid inside the finned tubes of AAV is assumed to be pure methane. The critical temperature and pressure of methane are 190.56 K and 4.6 MPa, respectively. Thermophysical properties change significantly with pressures and temperatures. A closer observation of physical properties of pure methane under different temperatures and pressures34 (Figure 3) reveals that heat capacity has peak values at the critical and pseudocritical points (pseudocritical points, ppc and tpc, correspond to the maximum value of heat capacity when pressure is above critical pressure). With increasing operating pressure, the pseudocritical points move toward higher temperatures and the peak values of heat capacity decrease. Viscosity and density also increase with pressure. When pressure is above the critical value, all the thermophysical properties become continuous with respect to temperature compared with the sharp change in properties at boiling points in subcritical pressures. Distinct liquid and gas phases do not exist in supercritical conditions, and the fluid can be treated as a continuous single phase.18 2.2. Prediction Methods. Heat transfer coefficient (h, W/ m2·K) is a quantitative characteristic of convective heat transfer between fluid medium and a wall surface over which the fluid flows.35 It is expressed as Q h= A ·(Tw − Tb) (1)
and reduce the footprint of AAVs in large LNG terminals, the forced-draft and air-based vaporizers become more attractive and are obtained with increasing attention. Both experimental and numerical studies to investigate the heat transfer performance and flow behavior of supercritical fluids have been reported.20−25 The main purpose of these studies was to correlate the dimensionless number (i.e., the Nusselt number) and to better predict the heat transfer coefficient. Most of the available experimental studies12,26,27 were mainly restricted to water and carbon dioxide as working fluids under various test conditions (i.e., pressure and temperature), flow conditions (i.e., heat flux and flow rate), and flow geometry (i.e., horizontal/vertical tube, annuli, bundles, etc.). Depending on the operating conditions, three different types of heat transfer mechanism could be involved in supercritical flows, namely, normal heat transfer (when q/G < 0.92, q is heat flux, G is mass flux), deteriorated heat transfer (e.g., high heat flux and low mass flux), and improved heat transfer (closed to the pseudosupercritical point). In recent years, supercritical cryogens, such as liquid helium,28 liquid nitrogen,29,30 and cryogenic propellants,31 have been investigated to explore the injection, mixing, and combustion32 behavior. Numerical studies of supercritical flow based upon phenomenological model and computational fluid dynamics (CFD) codes have received increasing attention.33 The main challenges in CFD modeling relate to turbulence modeling, as the thermophysical properties vary significantly, especially near the pseudocritical point. Empirical correlations for heat transfer coefficient derived from experimental results are preferred for industrial applications. The objective of present study is to investigate the supercritical flow of LNG and evaluate the heat transfer performance flow inside AAVs. However, since experimental data are not available for LNG supercritical flow, supercritical test on water and carbon dioxide is used to validate the CFD model. The validated model is used to predict the heat transfer behavior of LNG AAVs. A parametric study of fin configuration, such as the number of fins and fin length, is presented in order to optimize the fin design.
where Q is heat transfer rate (W); A is heat transfer surface area (m2); Tw and Tb are wall temperature and characteristic bulk fluid temperature (K), respectively. Using the methods of similarity criteria, the dependence of heat transfer coefficient on many factors can be represented by using dimensionless parameters, such as the Nusselt number. The Dittus−Boelter correlation (eq 2) is quite common and particularly useful for many applications when forced convection is the only mode of heat transfer (no boiling, condensation, etc.). Nu = 0.023Re 0.8Pr 0.4 C
(2) DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Industrial & Engineering Chemistry Research where Re is Reynolds number and Pr is Prandtl number. Heat transfer coefficient can be calculated as Nu·k h= l
Table 2. Properties of Methane at 8.0 MPa (1)100−210K Thermal conductivity (W/m·K): k = 3.125 × 10−7 T2 − 1.404× 10−3 T + 0.3449 Specific heat capacity (J/kg·K): cp = 1.614× 10−6 T5 − 1.032 × 10−3 T4 + 0.2613 T3 − 32.64 T2 + 2.011 × 103 T − 4.556 × 104 Viscosity (Pa·S): μ = −1.402 × 10−10 T3 + 7.626 × 10−8 T2 − 1.447 × 10−5 T + 9.917 × 10−4 Density (kg/m3): ρ = −3.120 × 10−6 T4 + 1.717 × 10−3 T3 − 0.3554 T2 + 31.21 T − 5.291 × 102 (1) 210−300K Thermal conductivity (W/m·K): k = −2.317 × 10−11 T5 + 3.144 × 10−8 T4 − 1.706 × 10−5 T3 + 4.631 × 10−3 T2 − 0.6288T + 3.422 Specific heat capacity (J/kg·K): cp = −3.333 × 10−6 T5 + 4.683 × 10−3 T4 − 2.629T3 + 7.376 × 102 T2 − 1.034 × 105 T + 5.805 × 106 Viscosity (Pa·S): μ = 6.055 × 10−13 T4 − 6.482 × 10−10 T3 + 2.599 × 10−7 T2 − 4.625 × 10−5 T + 3.095 × 10−3 Density (kg/m3): ρ = −1.053 × 10−7 T5 + 1.408 × 10−4 T4 − 7.526 × 10−2 T3 + 20.10T2 − 2.685 × 103 T + 1.437 × 105
(3)
where k is thermal conductivity (W/m·K); l is characteristic length (m). However, there is no satisfactory analytical method to calculate heat transfer coefficient near critical and pseudocritical points due to the difficulties in dealing with the steep property variations. The Dittus−Boelter correlation may give unrealistic results under some supercritical flow conditions. Therefore, the correlation has been revised into a general form13 of all derived correlations for calculating supercritical heat transfer, expressed as Nu =
m m m i ρ yz 3ij μ yz 4 ij k yzm5ij c p̅ yz 6 tz j tz j tz j m1 m2 j z j j z C1Ret Prt jjj zzz jjj zzz jj zz jj zz j z j z k ρt { k μt { k kt { k c p, t { m D y 7 ij jj1 + C hy zzz 2 jj L h zz{ k
(4)
where C1, C2, and m1∼ m6 are modified constants; ρ, μ, and cp are density, viscosity, and specific heat, respectively; Dhy is hydraulic-equivalent diameter; Lh is hydraulic heated length; subtitle t represents b(bulk), w(wall), in(inlet), respectively; cp̅ is averaged over cross-sectional specific heat at constant pressure, expressed by c p̅ =
H w − Hb Tw − Tb
ÄÅ ÅÅ Å ∂(ρE) + ∇·[v (⃗ ρE + p)] = ∇·ÅÅÅÅkeff ∇T − ÅÅ ∂t ÅÅÇ ÑÉÑ ÑÑ + (τeff̿ ·v ⃗)ÑÑÑÑ ÑÑ ÑÑÖ
(5)
where Hw and Hb are fluid specific enthalpy at wall and bulk. Some correlations of calculating heat transfer at supercritical pressures are summarized in Table 1. In this study, ANSYS Fluent 17.1 was used to develop the CFD model that offered a comprehensive description of the complex domain, stream properties, and flow mechanism.44,45 In order to better cope with the steep variation of fluid properties in supercritical conditions, piecewise-polynomial temperature profiles involving two ranges (separated at the pseudosupercritical point shown in Table 246) were used to describe the fluid properties in simulations, with the maximum deviation less than 4%. Equations of continuity, momentum, energy, and turbulence are listed as below Continuity equation. ∂ρ + ∇·(ρv ⃗) = 0 ∂t
E=h−
∑ hjJj ⃗ j
p v2 + ρ 2
(9)
(10)
where E is total energy; keff is effective conductivity. The heat balance between the outer and inner regions of the tubes is achieved by heat transfer through finned-tube walls. Therefore, boundary layer effects are critical in selecting appropriate turbulence model. Shear−stress transport (SST) k−ω turbulence model (eq 11) blends the robust and accurate formulation of the standard k−ω model in the near-wall region with the free-stream independence of k−ε model in the far field;47,48 hence, SST k−ω model is used to deal with the turbulence flow. μt = α*
ρk t ω
∂(ρk tuj) ∂(ρk t) ∂ ijjj ∂k t yzzz ı = + jΓk z + Gk − Yk ∂xj ∂xj jj ∂xj zz ∂t k {
(6)
where ρ is the density of the fluid; v⃗ is velocity vector of three dimensions. Momentum equation.
∂(ρωuj) ∂(ρω) ∂ ijjj ∂ω yzzz = + jΓω z + Gω − Yω + Dω ∂xj ∂xj jj ∂xj zz ∂t k {
∂(ρv ⃗) + ∇·(ρvv⃗ ⃗) = −∇p + ∇·(τ ̿ ) + ρg ⃗ + F ⃗ (7) ∂t ÄÅ ÑÉÑ Å 2 τ ̿ = μÅÅÅÅ(∇v ⃗ + ∇v ⃗T ) − ∇·vI⃗ ÑÑÑÑ ÅÅÇ ÑÑÖ (8) 3 where p is pressure; τ̿ is stress tensor; F⃗ is the sum of body forces; ρg⃗ means gravity in the vertical direction; μ is dynamic viscosity. Energy equation.
(11)
(12)
(13)
where μt is turbulent viscosity; α* is a coefficient; kt is turbulent kinetic energy; ω is specific dissipation rate; Γk and Γω are the effective diffusivity of kt and ω; G̃ k and Gω represent the generation of k and ω, respectively; Yk and Yω represent the dissipation of k and ω due to turbulence; Dω is the crossdiffusion term. D
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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3. VALIDATION OF CFD MODELING ON SUPERCRITICAL FLOW As experimental data on supercritical methane is not available, experimental data on water and carbon dioxide in supercritical regime were used to validate the CFD model. Shitsman13,49 used an external-heated vertical tube ((D = 8 mm, L = 1.5 m) to carry out experiments on the supercritical flow of water. The operating pressure in two different cases was 23.3 and 25.3 MPa which is above the critical point of water (22.1 MPa and 547.1 K). Constant heat fluxes and mass fluxes were applied in the experiments, i.e., 1084 kW/m2 and 1500 kg/m2·s in Test 1 and 385 kW/m2 and 449 kg/m2·s in Test 2, respectively. Figure 4 shows the supercritical properties of water at the
The simulation predictions matched closely with experimental data as illustrated in Figure 5. The deviation of temperature between CFD simulation results and experimental data was within 5%. While the predicted heat transfer coefficient (HTC) showed wider deviation (within 30%), it was still better agreement than most of the empirical correlations. The discrepancy in HTC was primarily a result of the significant variations in thermoproperties which are treated locally in CFD model but could only be treated as average values in empirical correlations. Figure 6 illustrated a comparison between CFD prediction and experimental data for the supercritical flow of carbon dioxide. The experimental data are from Chalk River Laboratories, AECL.13 This test was conducted in a vertical tube (D = 8.0 mm, L = 2.208 m) to explore the behavior of CO2 flow under supercritical conditions. The operating pressure was 8.2 MPa, and the critical point of CO2 is 7.38 MPa and 304.13 K. It could be observed in Figure 6 that CFD simulations gave a better agreement with experimental data than available correlations. A particular flat region in temperature curve was observed in the vicinity of pseudocritical point (tpc = 310 K), which is similar to the temperature change in subcritical pressures that a flat region could be observed at boiling temperatures. However, the general trends in supercritical heat transfer still need to be further investigated, and more consistent and systematic experimental studies should be conducted to achieve greater understandings.13
4. SUPERCRITICAL LNG FLOW INSIDE A FINNED TUBE The AAV unit examined in this study had dimensions of 3.66 m (L), 3.66 m (W), and 12.80 m (H).7,50 It comprised 144 finned tubes and was installed vertically. Each tube had 8 aluminum fins with the tube diameter of 0.0254 m (1 in.), fin length of 0.127 m (5 in.), and tube length of 12.80 m (42 ft). The processing capacity and operating pressure of each unit were 15 MMscfd (approx. 17 000 N m3/h) and 8.0 MPa, respectively.7,50 The elevations of AAVs are available in various heights, and one needs to pay special attention in determining
Figure 4. Thermophysical properties of water at supercritical conditions (Tc = 647.1K, Pc = 22.064 MPa).
pressure of 25.3 MPa. The steep variation in properties, particularly near the pseudocritical temperature, was observed in all properties. The significant change of thermophysical properties was accounted for using piecewise-polynomial expressions which were applied in the CFD model.
Figure 5. Comparison of various calculation results with experimental data (water). E
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 6. Comparison of various calculation results with experimental data (carbon dioxide).
significantly larger than the experimental geometries used for validation of the CFD model, it is expected that the underpinning mechanisms of flow and heat transfer will remain the same. Therefore, the same computational parameters as outlined in the detailed validation reported in Section 3 were used to simulate the AAV. To further assert the reliability of the model, preliminary numerical experiments were carried out to make sure that the solution obtained was grid independent and numerically verified. In order to save computational power and obtain a high-resolution mesh, a vertical slice of 1/8 of the finned tube was taken into consideration owing to the rotational periodicity. In the LNG flow domain, a finer mesh was used in the regions with high flow or temperature gradients, such as near the tube-wall surface. In the air flow domain, a relatively finer mesh was used in the region close to the wall surface. The mesh independence was tested that an overall 4.84 million cells were finally used in the total computational domain. The inlets of air flow (shell top) and LNG flow (tube bottom) were defined as velocity inlets. Pressure outlet boundary condition was imposed on the surfaces of shell bottom and tube top. Wall boundary condition was applied to the fin surface and inner surface of the tube. Rotational periodic boundaries were defined on the vertical paired surfaces of LNG flow domain, solid fin domain, and air flow domain, respectively. In the simulation, the base case was set as inlet velocity of LNG 0.1124 m/s, inlet temperature 120 K, and operating pressure 8.0 MPa. The air flow velocity was 3.5 m/s, with air inlet temperature 303.15 K. The simulations were performed on a 3.70 GHz Intel Xeon processor with 32.0 GB RAM which took approximately 24 h to reach a converged solution. The quantitative and qualitative results are shown in Figure 8. The bulk flow temperature is the average flow temperature at a given height. The overall temperature increase and the temperature drop of LNG flow and air flow were approximately 130 and 40 K, respectively. The outlet temperatures of LNG and air were calculated as 247.85 and 263.23 K, respectively. The cross-sectional temperature contours along the tube height showed that the air temperature decreased from top to bottom, while a reverse trend was observed for the LNG flow. The pressure drop of both LNG flow and air flow was 63.32 and 18.75 Pa, respectively. The outlet velocity of LNG was 0.54 m/s which was around four times higher than the velocity at the tube inlet. It was because
the length of these units because it impacts not only the outlet temperature of LNG vapor but also the exit temperature of air. In a relatively longer AAV unit, the temperature of LNG at the outlet would be higher than the AAV unit having a shorter length, but the temperature at air outlet would decrease dramatically in the meanwhile which could also lead to severe problems of frost formation on fin surface and fog formation in the surrounding environment.9,51 The computational domain used to investigate the heat transfer behavior of LNG flow in supercritical pressures is shown in Figure 7. Even though the AAV geometry is
Figure 7. Geometry and mesh of finned tube in CFD model. (a, top) Schematic geometry of finned tube (tube diameter 0.0254 m, tube height 12. 0m, fin length 0.127 m). (b, bottom) Meshes for air flow area (1/8 of the total geometry). F
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 8. Temperature profile of LNG flow and air flow.
Figure 9. Supercritical heat transfer at different air velocities.
the methane density was decreased when the LNG flow was heated by air flow. Figure 9a shows LNG temperature profiles for different air flow rates. According to the U.S. standard of NFPA 59A,52 the temperature of natural gas after regasification should be about 4.0 °C (277.15 K). Supplement heat by an auxiliary heating device should be provided if the required outlet temperature could not be achieved. It was observed that the outlet temperature was satisfied if the air velocity was maintained above 8 m/s. As a result of increased velocity, the fin side pressure drop increases to 80.43 Pa. However, this is not a significant cost driver. In order to understand the effect of the operating pressure on the supercritical heat transfer, CFD simulations were conducted at different pressures of 10, 8, 6, and 5 MPa. The bulk LNG temperature profile along the length of the tube at different pressures is shown in Figure 10. At a higher pressure of 10 MPa, the LNG temperature increased faster than the cases with lower pressures. With the decrease in the operating pressure, it was observed that the bulk fluid temperature profile tended to move toward the typical curve of convective boiling
Figure 10. Temperature profiles of LNG flow at different operating pressures.
G
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 11. Comparison of temperature profile and heat transfer coefficient of different fin numbers.
Figure 12. Temperature profile at air flow outlet of different fin numbers.
Figure 13. Comparison of temperature profile and heat transfer coefficient of different fin lengths.
of the vertical tube, and the curve rise (especially in the middle part of tube length) became flat and even. Essentially, in the boiling curve, liquid region, two-phase region and vapor region could be characterized individually, and the slowing-down stage (or flat curve) occurs in the two-phase boiling region. While in the supercritical flow, although the distinction of liquid and vapor regions disappears, it still undergoes a slowing-down region, and this usually occurs in the vicinity of
pseudocritical points, namely, 192.5 K at 5 MPa, 200.0 K at 6 MPa, 210.0 K at 8 MPa, and 217.5 K at 10 MPa, respectively.
5. STUDY OF FIN CONFIGURATIONS 5.1. Number of Fins. As fin configurations impact heat transfer between ambient air and LNG, the number of fins, fin length, and fin thickness were investigated in this study. Figure 11 illustrated the temperature rise along the tube length and H
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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Figure 14. Comparison of temperature profile and heat transfer coefficient of different fin thickness.
not as significant as the number of fins or fin length. As shown in Figure 14, by increasing the fin thickness from 0.1 to 0.4 in., the temperature and heat transfer coefficient did not rise significantly. This was because the heat transferred from air to LNG was through the fin surface, and the total heat transfer area is the key parameter to impact heat transfer,35 while the surface area was increased slightly with the increase in fin thickness.
total heat transfer coefficient for different fin numbers. With the increase in the number of fins, as shown in Figure 11a, temperature rise became more prominent, and the total heat transfer coefficient also increased in the meanwhile. As illustrated in Figure 11b, the heat transfer coefficient and the outlet temperature increase drastically with the addition of fins. However, the outlet temperature starts to plateau beyond 8 fins, and the effectiveness of adding more fins diminishes. Increasing the number of fins increases the heat transfer area but also increases the resistance offered to the air flow. In this case, beyond 8 or 12 fins there was no significant improvement in the outlet temperature or the heat transfer coefficient. As also demonstrated qualitatively in Figure 12, at lower fin count (e.g., 4−8 fins) steep gradients in air temperature were observed from the tube surface to the bulk, and the heat in the air flow was utilized effectively. Increasing the number of fins (12−16 fins) showed a region of uniform temperature near the tube effectively decreasing the heat transfer from the LNG. By observing the rate of improvement in temperature and heat transfer coefficient, the number of fins could be optimized. In this study, 8 or 12 fins were found to be optimal. 5.2. Fin Length. As fin length is strongly related to the surface area of fins, heat transfer effect on fin length ranging from 0 to 11in was investigated. Figure 13 illustrated the temperature profiles of LNG vapor and total heat transfer coefficients for different fin lengths. As expected, the heat transfer was improved significantly as fin length increased. The effect of fin length was less pronounced as the fin length was extended beyond 7 in. It should, however, be noted that increasing the fin length also means increasing the distance between tubes. Thus, an optimal fin length is a compromise between acceptable heat transfer performance and AAV footprint. As the simulations show marginal improvement (4.1% increase in the outlet temperature from fin length 7 to 11 in.) beyond 5−7 in. fin length, this length could be a starting point in achieving an optimal configuration of the AAV. 5.3. Fin Thickness. The fin thickness is an important parameter relating to the mechanical strength of the AAV tubes. Increasing the fin thickness will strengthen the tubes amd at the same time will also result in increased weight of the AAV. The increased thermal mass as a result of thicker fins will also affect the time required to defrost the AAV after ice formation. The effect of fin thickness on the heat transfer was
6. CONCLUSION In this study, heat transfer performance of supercritical LNG in AAV was investigated. A comparison of thermophysical properties of LNG at supercritical pressures was presented. For the temperature range in question, the fluid had continuous properties and thus was considered as a single phase. A detailed CFD model that offered a comprehensive description of the complex domain, stream properties, and flow mechanism was developed. The CFD model was first validated by empirical mathematical correlations and experimental data on heat transfer using supercritical water and supercritical carbon dioxide. The validated model was then used to investigate the heat transfer performance of AAV. It was found that increasing air flow velocity could largely improve the heat transfer performance. Upon comparing the temperature profile along the tube height under different operating pressures, a slowing-down region was observed in the middle part of the tube where the temperature was around the pseudocritical point. The CFD model was further used to study the configuration of fins (number of fins, fin length, and thickness), and optimized configurations were evolved. The number of fins and fin length dictated the heat transfer efficiency, while fin thickness played a less important role in promoting heat transfer.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +61 8 9266 4687. Fax: +61 8 9266 2681. E-mail address:
[email protected]. ORCID
Biao Sun: 0000-0002-4692-2153 Notes
The authors declare no competing financial interest. I
DOI: 10.1021/acs.iecr.8b01226 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX
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ACKNOWLEDGMENTS We thank Woodside Energy Limited (www.woodside.com.au) for funding the project and A Green Technology for LNG Regasification (Project No. LP130100700). This work is also supported by computing resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia.
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NOMENCLATURE AND ABBREVIATIONS A = heat transfer surface area (m2) AAV = ambient air vaporizer C1, C2 = modified constants in eq 4 cp = specific heat capacity (J/kg·K) CFD = computational fluid dynamics CHF = critical heat flux Dhy = hydraulic-equivalent diameter (m) Dω = cross-diffusion term E = total energy (J) F⃗ = sum of body forces g⃗ = gravity acceleration (m/s2) G̃ k and Gω = generation of k and ω h = heat transfer coefficient (W/m2·K) Hw and Hb = fluid specific enthalpy at wall and bulk (J/kg) k = thermal conductivity (W/m·K) kt = kinetic energy keff = effective conductivity l = characteristic length (m) Lh = hydraulic heated length (m) m1∼m6 = modified constants in eq 4 Nu = Nusselt number ORV = open rack vaporizer p = pressure (Pa) pcr = critical pressure (Pa) Pr = Prandtl number ppr = pseudocritical pressure (Pa) Q = heat transfer rate (W) Re = Reynolds number SCV = submerged combustion vaporizer Sh = energy source Sk and Sω = user-defined source terms Tb = characteristic bulk fluid temperature (K) tcr = critical temperature (K) tpr = pseudocritical temperature (K) Tw = wall temperature (K) v⃗ = velocity vector of three dimension Yk and Yω = dissipation of of k and ω due to turbulence
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GREEK LETTERS α* = coefficient in eq 11 Γk and Γω = effective diffusivity of k and ω μ = dynamic viscosity (Pa·s) μt = turbulent viscosity ρ = density (kg/m3) τ = stress tensor ω = specific dissipation rate
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