Numerical Analysis of Heat Transfer and Pressure Drop in Helically Micro-Finned Tubes
Abstract
:1. Introduction
2. Methodology
2.1. Domain Definition
2.2. Meshing and Boundary Conditions
2.3. Solution
3. Results and Discussion
3.1. Grid Independence Study
3.2. Numerical Procedure Validation
3.3. Effect of Micro Fins on Pressure Drop and Heat Transfer
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
b | fin base width, [m] | turbulence kinetic energy due to buoyancy, [J/kg] | |
c | fin top width, [m] | turbulence kinetic energy due to mean velocity gradients, [J/kg] | |
specific heat, [J/kg.K] | Prandtl number | ||
User defined constants | Reynolds number | ||
tube diameter, [m] | strain tensor | ||
e | fin height, [m] | heat source term, [W/m2] | |
total energy, [J] | , | turbulence source terms, [J/kg] | |
f | friction factor | 3D temperature array, [K] | |
external forces, [N] | T | temperature, [K] | |
gravitational force, [N] | time averaged velocity | ||
heat transfer coefficient, [W/m2.K] | inlet uniform velocity, [m/s] | ||
sensible enthalpy, [J] | velocity vector, [m/s] | ||
diffusion flux, [kg/m2.s] | Cartesian vector | ||
turbulence kinetic energy, [J/kg] | fluctuating dilatation, [J/kg] | ||
thermal conductivity, [W/m.K] | Greek Symbols | ||
effective thermal conductivity, [W/m.K] | helix angle, [deg] | ||
tube length, [m] | turbulence energy dissipation, [J/kg] | ||
mass flow rate, [kg/s] | thermal performance index | ||
helical Fin pitch, [m] | dynamic viscosity, [Pa.s] | ||
number of fins | Eddy viscosity, [Pa.s] | ||
Nusselt number | deviatoric stress tensor | ||
fluid static pressure, [Pa] | kinematic viscosity, [m2/s] | ||
, | turbulence Prandtl numbers | fluid density, [kg/m3] | |
stress tensor | |||
Subscripts | |||
b | bulk fluid | in | inlet |
finned | finned tube | o | outer |
h | hydraulic | out | outlet |
i | inner | w | wall |
References
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Enhancement Technique | Analysis Technique | Working Fluid | Parameters | Observations |
---|---|---|---|---|
Blossom shape internal fins [4] | CFD/Experimental | Air | 3255 ≤ Re ≤ 19,580 0.34 ≤ Pf/Dh ≤ 0.98 0.78 ≤ e/Dh ≤ 1.51 Di = 6 mm, 8 mm, 10 mm | Heat transfer performance of 3- and 4-pieces blossom fin is greater than 2-pieces blossom fin. Numerical correlation had a mean deviation of 8.69% in Nu and 6.76% in f. |
Arc shape fins with Y-shape inserts [5] | Experimental | Water | 4108 ≤ Re ≤ 14,500 e = 0.7 mm, Pf = 0.6 mm, Y-insert L = 30.5 mm Di = 19.05 mm | Nu is 2.1~4.3 times higher than smooth tube. f is 6.89~9.25 time more than smooth tube. Overall thermal performance is 1.02~2.22 times more than smooth tube. |
Internal repeated ring ribs [6] | CFD | Air | 3600 ≤ Re ≤ 16,500 0.29 ≤ Pf/Di ≤ 4.35 0.025 ≤ e/Di ≤ 0.069 Di = 13.8 mm | Highest Nu was obtained using ring type ribs as compared to other rib geometries. Nu was within ±10%, f within ±15% and performance evaluation criterion was within ±15% of experimental results. |
Dimples [7] | Experimental | Water, R-134 a | 300 ≤ Mass flux[kg·m−2·s−1] ≤ 500 10 ≤ Heat flux[kW·m−2] ≤ 20 0.5 mm ≤ Dimple depth ≤ 1.0 mm Di = 8.1 mm, Quality = 0.1–0.8 | 83% and 893% increase recorded in heat transfer coefficient and friction factor respectively. The efficiency index is less than 1 for all configurations, which limits the use of dimpled tubes for special applications. |
Dimples & longitudinal grooves [8] | Experimental | Water, R-410 a | 70 ≤ Mass flux[kg·m−2·s−1] ≤ 150 32.6 ≤ Heat flux[kW·m−2] ≤ 37 Groove pitch = 3.4 mm Di = 11.07 mm, Quality = 0.1–0.9 | Enhanced tubes increase the heat transfer coefficient with increasing mass flux. At constant mass flux, heat transfer coefficient increases by increasing heat flux. |
Twisted tape inserts [9] | Experimental | Water | 400 ≤ Re ≤ 11400 2 ≤ Heat flux[kW·m−2] ≤ 4 3 ≤ Twist ratio ≤ 5 Di = 19.0 mm | As the twist ratio decreased, the Colburn j-factor increased and caused early transition. Increasing twist ratio decreased the friction factor. |
Twisted tape inserts [10] | Experimental | R-134 a | 75 ≤ Mass flux[kg·m−2·s−1] ≤ 1000 5 ≤ Heat flux[kW·m−2] ≤ 250 3 ≤ Twist ratio ≤ 14 Di = 10, 12.7, 15.9 mm, Quality = 0.01–0.95 | Twisted inserts increased heat transfer by causing earlier transition to turbulent flow. Mass fluxes higher than 400 and heat fluxes higher than 100 caused no change in heat transfer coefficient. Improvements in heat transfer were measured for low to moderate mass and heat fluxes. |
Annular metal foam inserts [11] | Experimental | Water Vapor | 20 ≤ Vapor mass flow rate [kg·h−1] ≤ 100 Di = 22 mm, Quality = 0.5–0.8 | Heat transfer unit mass efficiency coefficient is 1.3 times greater than the corresponding micro-fin tube. Increasing metal foam size, increases the pressure drop. |
Metallic foam, circumferential pin fins, twisted pin fins [12] | Experimental | R-134 a | 50 ≤ Mass flux[kg·m−2·s−1] ≤ 150 Saturation pressure = 11.6 bar, 13.4 bar Di = 8.7, 12.7 mm, Quality = 0.3–0.9 | Average increase in heat transfer coefficient for the enhanced tubes is 2 times the plain tube. Head impact flow configuration for eight-fin tube is measured to be the best. |
Twisted tape inserts [13] | Experimental | R-1234 yf | 160 ≤ Mass flux[kg·m−2·s−1] ≤ 310 6 ≤ Twist ratio ≤ 12 Di = 8.7 mm, Quality = 0.12–0.84 | 42% and 235% increase in heat transfer coefficient and pressure drop measured as compared to smooth tube. |
Delta winglet vortex generator [14] | Experimental | Water | 5000 ≤ Re ≤ 25,000 Winglet height = 5 mm, 7.5 mm and 10 mm Di = 52 mm | Nu and f increase by increasing winglet height and attack angle. Maximum of 73% increase in Nu and 2.5 times higher f is measured as compared to smooth tube. |
Micro-finned tube [15] | CFD | Oil | 100 ≤ Re ≤ 1000 0.2 mm < e < 0.5 mm, 5° < α < 45° Di = 8.62 mm | 44% increase in heat transfer and 69% increase in friction factor at 1000 Re. |
Micro-finned tube [16] | Experimental | Water/ CuO nanofluid | 5650 ≤ Re ≤ 17,000 Pf/Di = 0.05 e/Di = 0.019, Di = 8.64 mm | Nu and f increased by 1.5 times and 2 times respectively as compared to plain tube. η was observed to be more than unity across the whole range of Re. |
Micro-finned tube [17] | Experimental | Water | 5725 ≤ Re ≤ 25,353 Pf/Di = 0.045, e/Di = 0.027 Di = 6, 8, 7.48 mm | Pressure drop measured on average to be 2 times more than the smooth tube. |
Micro-finned tube [18] | Experimental | Water | 8000 ≤ Re ≤ 24,000 e/Di = 0.020, Di = 8.92 mm | Heat transfer coefficient increased 33% as compared to smooth tube |
Helical Groove [19] | CFD | Water | 4000 ≤ Re ≤ 20,000 7.1 mm < Groove Pitch < 305 mm Di = 7.1 mm | Maximum η of 1.2 achieved at Re 15,000 and pitch length of 130 mm. |
Micro-finned tube [20] | Experimental | Water | 10,000 ≤ Re ≤ 70,000 0.007 mm < e/Di < 0.085 mm, 0° < α < 45° Di = 21.18–24.41 mm | Increase in Nu was measured 15–180% and f 50–500% more than the smooth tube. |
Micro finned tube [21] | Experimental | Water | 2300 ≤ Re ≤ 20,000 Pf/Di = 0.052, e/Di = 0.022 Di = 9.52 mm | Heat transfer coefficient increased 2.9 times and pressure drop increased 1.7 times as compared to smooth tube for Re >10,000. |
Micro-finned tube [22] | Experimental | Water | 3000 ≤ Re ≤ 40,000 0.12 mm < e < 0.15 mm, 9° < α < 25° Di = 19 mm | Maximum η calculated was 1.35 for Re ≈10,000 η became less than unity for Re > 30,000 |
Micro-finned tube [23] | Experimental | Water, Oil | 2500 ≤ Re ≤ 90,000 e/Di = 0.017, Di = 17.5 mm | Heat transfer coefficient more than twice that of the smooth tube. Friction factor 40–50% more than that of the smooth tube. |
Micro-finned tube [24] | Experimental | Water | 12,000 ≤ Re ≤ 60,000 0.0199 < e/Di < 0.0327, 25° < α < 48° Di = 15.57–15.65 mm | Highest Colburn j-factor achieved for tube with N = 45, α = 48°, e/Di = 0.0244. Lowest friction factor achieved for tube with N = 10, α = 48°, e/Di = 0.0244. |
Micro-finned tube, Corrugated tube [25] | CFD | Water | 12,000 ≤ Re ≤ 57,000 e/Di = 0.024, 25° < α < 48° Di = 15.62–18.0 mm | Highest heat transfer coefficient and friction factor obtained for N = 45, α = 48°, e/Di = 0.024. Corrugated tubes showed intermediate performance between smooth and finned tubes. |
Longitudinal finned tube [26] | Experimental | Fe3O4, Water | 5300 ≤ Re ≤ 49,200 e/Di = 0.15, Di = 26 mm | Heat transfer increase of 80–90% observed as compared to plain tube. Friction factor increased 3–4 times as compared to plain tube. |
Micro-finned coiled tube [27] | Experimental | R-134 a | 75 ≤ Mass flux [kg·m−2·s−1] ≤ 191 1.5 ≤ Heat flux[kW·m−2] ≤ 17.25 e/Di = 0.02, α = 18° Di = 8.58, 8.92 mm, Quality = 0.1–0.8 | Coiled micro-finned tube showed 160–255% and 69–155% higher heat transfer coefficient and pressure drop respectively, as compared to straight smooth tube. |
Micro-finned tube with porous copper fiber insert [28] | Experimental | Water | 4000 ≤ Re ≤ 14,000 e/Di = 0.052, Di = 19 mm | Heat transfer coefficient increase measured 6.4 times than that of smooth tube. η value of 2.29 evaluated. |
Micro-finned tube [29] | Experimental | R410 A | 100 ≤ Mass flux [kg·m−2·s−1] ≤ 450 10 ≤ Heat flux[kW·m−2] ≤ 20 e/Di = 0.033, Di = 7.4 mm, Quality = 0.1–0.9 | Heat transfer coefficient and pressure drop increased on average of 1.34 and 1.23 times respectively as compared to the smooth tube. |
Micro-finned tube [30] | Experimental | R22 | 130 ≤ Mass flux [kg·m−2·s−1] ≤ 550 Saturation Temperature = 45 °C e/Di = 0.026, Di = 5.98 mm, Quality = 0.1–0.8 | Heat transfer coefficient increased from 46.3–63.6% as compared to the smooth tube. |
Micro-finned tube [31] | CFD | R410A | 500 ≤ Mass flux [kg·m−2·s−1] ≤ 700 Saturation Temperature = 47 °C e/Di = 0.032, Di = 4.6 mm, Quality = 0.45–1.0 | Enhanced heat transfer coefficient in healically micro-finned tubes as compared to stratight finned tubes. The heat transfer coefficient shows maximum increase for vapor quality <0.6 |
Mirco-finned tube [32] | Experimental | R1234 yf | 500 ≤ Mass flux [kg·m−2·s−1] ≤ 1000 Saturation Temperature = 40 °C, 43 °C, 45 °C e/Di = 0.057, 0.071, Di = 3.5 mm, Quality = 0.2–0.8 | Heat transfer coefficient and pressure drop of micro-finned tubes increased 2.53–3.67 times and 1.95–2.49 times respectively as compared to smooth tube. |
Tubes/ Specifications | L [mm] | Do [mm] | Di [mm] | e [mm] | b [mm] | c [mm] | α [deg] | Pf [mm] | N | |
---|---|---|---|---|---|---|---|---|---|---|
Smooth | 2740 | 18.82 | 15.64 | - | - | - | - | - | - | - |
Equal fin height | 2740 | 18.82 | 15.64 | 0.38 | 0.48 | 0.2 | 25 | 102 | 10 | 0.024 |
Alternating fin height | 2740 | 18.82 | 15.64 | 0.19–0.38 | 0.48 | 0.2 | 25 | 102 | 10 | 0.012–0.024 |
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Ammar Ali, M.; Sajid, M.; Uddin, E.; Bahadur, N.; Ali, Z. Numerical Analysis of Heat Transfer and Pressure Drop in Helically Micro-Finned Tubes. Processes 2021, 9, 754. https://doi.org/10.3390/pr9050754
Ammar Ali M, Sajid M, Uddin E, Bahadur N, Ali Z. Numerical Analysis of Heat Transfer and Pressure Drop in Helically Micro-Finned Tubes. Processes. 2021; 9(5):754. https://doi.org/10.3390/pr9050754
Chicago/Turabian StyleAmmar Ali, Muhammad, Muhammad Sajid, Emad Uddin, Niaz Bahadur, and Zaib Ali. 2021. "Numerical Analysis of Heat Transfer and Pressure Drop in Helically Micro-Finned Tubes" Processes 9, no. 5: 754. https://doi.org/10.3390/pr9050754
APA StyleAmmar Ali, M., Sajid, M., Uddin, E., Bahadur, N., & Ali, Z. (2021). Numerical Analysis of Heat Transfer and Pressure Drop in Helically Micro-Finned Tubes. Processes, 9(5), 754. https://doi.org/10.3390/pr9050754