Published in: Proceedings of the th EUROSIM Congress on Modelling and Simulation

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1 Aalborg Universitet Parametric CFD Analysis to Study the Inluence o Fin Geometry on the Perormance o a Fin and Tube Heat Exchanger Singh, Shobhana; Sørensen, Kim; Condra, Thomas Joseph Published in: Proceedings o the 016 9th EUROSIM Congress on Modelling and Simulation DOI (link to publication rom Publisher): /EUROSIM Publication date: 016 Document Version Accepted author manuscript, peer reviewed version Link to publication rom Aalborg University Citation or published version (APA): Singh, S., Sørensen, K., & Condra, T. J. (016). Parametric CFD Analysis to Study the Inluence o Fin Geometry on the Perormance o a Fin and Tube Heat Exchanger. In Proceedings o the 016 9th EUROSIM Congress on Modelling and Simulation (pp ). IEEE Computer Society Press. DOI: /EUROSIM General rights Copyright and moral rights or the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition o accessing publications that users recognise and abide by the legal requirements associated with these rights.? Users may download and print one copy o any publication rom the public portal or the purpose o private study or research.? You may not urther distribute the material or use it or any proit-making activity or commercial gain? You may reely distribute the URL identiying the publication in the public portal? Take down policy I you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access to the work immediately and investigate your claim. Downloaded rom vbn.aau.dk on: maj 09, 018

2 016 9th EUROSIM Congress on Modelling and Simulation Parametric CFD Analysis to Study the Inluence o Fin Geometry on the Perormance o a Fin and Tube Heat Exchanger Shobhana Singh, Kim Sørensen, Thomas J. Condra Department o Energy Technology Pontoppidanstræde 90 Aalborg East, Denmark ssi@et.aau.dk; kso@et.aau.dk; tc@et.aau.dk Abstract Heat transer and pressure loss characteristics o a in and tube heat exchanger are numerically investigated based on parametric in geometry. The cross-low type heat exchanger with circular tubes and rectangular in proile is selected as a reerence design. The in geometry is varied using a design aspect ratio as a variable parameter in a range o to predict the impact on overall perormance o the heat exchanger. In this paper, geometric proiles with a constant thickness o in base are studied. Threedimensional, steady state CFD model is developed using commercially available Multiphysics sotware COMSOL v5.. The numerical results are obtained or Reynolds number in a range rom 5000 to and veriied with the experimentally developed correlations. Dimensionless perormance parameters such as Nusselt number, Euler number, eiciency index, and area-goodness actor are determined. The best perormed geometric in proile based on the higher heat transer and lower pressure loss is predicted. The study provides insights into the impact o in geometry on the heat transer perormance which help escalate the understanding o heat exchanger designing and manuacturing at a minimum cost. Keywords Fin and tube heat exchanger; numerical modelling; in proile; conjugate heat transer; turbulent low; pressure loss. I. INTRODUCTION Fins are the extended suraces used in heat exchangers to enhance the heat transer rate between heat transer suraces and the lowing luid [1]. The increment in the heat transer perormance through in suraces is widely employed in many industrial applications. Application o waste heat recovery systems has received tremendous attention during the last decade due to the resulting saving o primary uel, increased energy eiciency and lower greenhouse gas emissions. Heat exchangers are one o the important components o these waste heat recovery systems. During past ew years, H-type inned and tube heat exchangers have been studied both experimentally [- 4] and numerically [5-7]. The studies mainly ocused on examining the heat transer and low resistance characteristics or a reerence design o the H-type inned tube bundles. In addition, combined heat and mass transer analysis on H-type design with three types o inned tube namely-dimple inned tube, longitudinal vortex generators (LVGs) inned tube, and inned tube with compound dimples and LVGs together was conducted [8, 9]. The implementation o ins on the primary heat surace enhances the complexity, volume and weight which make the design and construction o in suraces o vital importance in heat exchanger applications. Very limited research on dierent in types or geometry proiles is available due to restricted experimental conditions and numerical challenges. This limitation overshadows the current knowledge o design actors that has an inluence on the heat transer and pressure loss characteristics. Hence, it becomes imperative to study the dierent in geometric proiles in order to determine the optimal in design or a given H-type in and tube heat exchanger application. In this paper, we used Computational Fluid Dynamics (CFD) to obtain the solution o governing equations o physical phenomena in a cross-low type in and tube heat exchanger. The parametric study o in geometry is conducted using air as a working luid considering the rectangular in as reerence geometric proile. Heat transer and pressure loss characteristics in a in and tube heat exchanger with dierent geometric in proiles are predicted and compared with the reerence in proile geometry. II. NUMERICAL MODEL DEVELOPMENT A. Heat exchanger geometry The heat exchanger used in the present study is in and tube type. The design entails circular tubes and rectangular ins which are attached to the set o two tubes with a ixed gap in between. This particular design is also called Htype inned tube heat exchanger due to the typical arrangement o ins on tubes resembling the letter H. An orderly arrangement o the single unit results in the complete heat exchanger coniguration which can be scaled or desired applications based on the heat transer rate and allowable pressure loss. Fig. 1 shows the pictorial view o in and tube heat exchanger coniguration used in the present study. The design typically used in waste heat recovery applications such as marine boilers, where hot exhaust gas lows over the inned tube bundle and cold water lows inside the tubes as can be seen in Fig.1. The heat transers rom hot exhaust gases, by convection through ins and conduction within in and tube thickness, to the water inside the tubes or steam generation or other application purposes B. Computational geometry The geometry o the in and tube heat exchanger simulated in the present study is shown in Fig.. In order to save the computational eort, the geometry to be studied is reduced to one-hal o the single unit /16 $ IEEE DOI /EUROSIM

3 Gas low Water low = 1.0 = 0.7 = 0.5 = 0.3 = 0.1 t,r b,r Figure 1. Double in and tube (or H-type) heat exchanger coniguration. The computational geometry is divided into three domains- in, tube and gas; and boundaries- inlet, outlet, and symmetry. The geometric dimensions o the heat exchanger design are given in Table I. C. Formulation o the in geometric proile In the present work, the geometry o the in is varied deined as the ratio o thickness o in tip ( t )to the thickness o in base ( b ) and can be expressed as- t (1) b, r In order to simpliy the analysis and geometric complexity, rectangular geometry o the in is considered as a reerence geometric proile and the thickness o in base is kept constant as o reerence rectangular in ( b,r ) while the thickness o the in tip is subjected to a variation (Fig. 3) transorming the reerence rectangular in proile (at which eventually resembles a triangu =0.1). With the change in aspect ratio, total heat transer area, the thermal contact area between the in and tubes and, the weight o the heat exchanger unit (computational geometry) changes as shown in Fig. 4. Figure 3. Schematic view o reerence rectangular in (on let) and dierent in geometric proiles (on right) investigated in the present study TABLE I. DESIGN PARAMETERS AND OPERATING CONDITIONS FOR A SINGLE UNIT OF THE EXCHANGER Parameter Symbol Value Unit Length o the in L m Width o the in W m Thickness o the reerence in base b,r 0.00 m Thickness o the reerence in tip t,r 0.00 m Width o the gap between ins a m Inner diameter o the tube D i m Outer diameter o the tube D o m Tube pitch p t m Length o the gas domain L g m Width o the gas domain W g m Fin pitch p m Temperature at gas inlet T in K Pressure at gas outlet p out 0.0 Pa Temperature o inner tube wall T w K D. Governing equations 3D CFD model is developed using commercially available Multiphysics sotware COMSOL v5.. Following assumptions are made in the present model- Steady state low and heat transer Incompressible low Negligible thermal contact resistance Inlet Gas domain Fin domain Symmetry Symmetry Symmetry Tube domain Outlet Figure. Computational geometry used in the present investigation Figure 4. Variation o geometric proile parameters with respect to the aspect ratio o the in 11

4 Temperature dependent luid property Constant inner tube wall temperature No periodic boundary condition (i.e. model is valid or the irst unit o the heat exchanger as shown in Fig.1). The mass and momentum balance or low in the gas domain and energy balance in terms o heat transer are given as- u 0 () T ( u) u[ pi( u( u) )] F (3) CpuT qq (4) where, q kt Based on the mass low rate and the heat exchanger coniguration, Shear Stress Transport (SST) model is adopted. The governing equations o two-equation SST - k k P ok (( k T) k) t u (5) u P (( T ) ) t (6) T (1 ) k v1 The deault model parameters used to solve the governing equations are deined in the Appendix. Table II lists initial conditions or a steady state simulation [11] and boundary conditions used to numerically solve the computational model and achieving preliminary results. III. MODEL VALIDATION A. Experimental validation The validation o numerical results is perormed using the experimentally developed correlations by Chen et al. [4] and a comparison is shown in Fig. 5. Correlations or Nusselt number and Euler number given by (7) and (8) are valid or Reynolds number range o with a relative error o.79% and 3.70%, respectively. The average percent deviation o numerically predicted Nusselt and Euler numbers rom the correlation values is calculated to be 5.61% and 5.7%, respectively. The deviation accounts or the assumptions in the present study or and the experimental errors in developing the correlations. TABLE II. DESIGN PARAMETERS AND OPERATING CONDITIONS FOR A SINGLE UNIT OF THE EXCHANGER Initial Condition Gas domain 3/ 10 Ck init k u 0 ; p 0 ; k ; ; init (0.1 l ) 0.1l 0.1l All domains T K Boundary Condition Inlet T T ; u 0, vu, w0 init re re re in in Wall 3/4 3/ C ke un 0; ke n0 ; v w Inner tube wall T T w Outlet p p, nq 0 ; k n0 ; n0 out Symmetry un 0 ; nq 0 ; k n0 ; n0 e e Figure 5. Comparison o numerical and correlation results These deviations are in acceptable range and hence, the results are assumed accurate enough to predict the physical behavior. Nu D L W o 0.053Re p p p B. Mesh independence test (7) 1.3 L 0.57 Eu 19.14Re Do (8) Mesh independence test is made on the reerence in using temperature dierence across the gas domain as an objective property. Five dierent meshes with , , 9977, and elements are used in the simulation. The test result suggests the mesh with elements as a good choice in relation to accuracy and computational time. IV. RESULTS AND DISCUSSION The results predicted rom the present study are discussed in this section. Table III expresses the dimensionless parameters used to evaluate the perormance o the heat exchanger design. The Nusselt number and Euler number are used to assess the heat transer and pressure loss characteristics o the heat exchanger with dierent in geometric proile. TABLE III. Perormance parameter Nusselt number, Nu Euler number, Eu Eiciency index, Area-goodness actor, j/ PERFORMANCE PARAMETERS Expression hdo k p 1 u g max Nu p 1 gu in Nu 1 RePr 3 pd o 1 guinl g 113

5 Figure 6. Variation o Nusselt number with respect to Reynolds number As observed rom Fig. 6, Nusselt number increases with the Reynolds number which shows thermal perormance increases as the low velocity increases. to 0.1 where the in geometric proile becomes nearly triangular. This eect results rom the decreasing low the convective heat transer. Variation in Euler number with Reynolds number or dierent in geometric proiles can be seen rom Fig to 0.1, which is a clear demonstration o reduced pressure loss on a In order to evaluate the overall perormance o the heat exchanger in terms o both, heat transer and pressure loss, eiciency index (Table III) is calculated. Fig. 8 shows a variation in eiciency index with respect to Reynolds number or dierent in geometric proiles. The eiciency index increases with the Reynolds number and so thus the overall perormance o the heat exchanger design. As 1.0 to 0.1 which dictates that the in with tapered geometric proile perorms better in comparison to the conventional rectangular in geometric proile. Figure 7. Variation o Euler number with respect to Reynolds number Eiciency index, Reynolds number, Re Figure 8. Variation o eiciency number with respect to Reynolds number rom 1.0 to 0.1, the pressure reduction is dominant than that o increment in thermal perormance. In addition, the equivalent perormance. For instance, at Re=13000 Heat transer through the in can be predicted rom the temperature gradients on the in surace. = 0.1 = 0.3 = 0.5 = 0.7 = 1.0 Figure 9. Temperature gradients on the in surace o dierent geometric proiles 114

6 To investigate the most suitable geometric in proile, the reduction in the weight o the heat exchanger unit as determined and is shown in Fig. 11 the weight o the heat exchanger unit (considered one-hal in the present study, Fig. ) reduces and accounts or results and discussion, it can be observed that in geometric proile shows better perormance with less weight than the reerence rectangular in geometry at Figure 10. Perormance comparison o dierent geometric in proile Fig. 9 shows temperature gradients on the in surace o dierent geometric proiles. The dissipation o the heat rom hot gas to the in is evident rom the higher temperatures away rom in and tube interace where the heat is conducted rom the in to the tube wall resulting in lower temperatures in those regions. Relatively, higher evident o lower heat transer rate due to the lower temperature dierence between the gas and the in which urther reduces the heat transer perormance. To determine the impact o dierent in proiles on the overall perormance at the equitable basis, a dimensionless parameter called area-goodness actor is used. It is deined as a ratio o Colburn j actor to the riction actor, o the heat exchanger design with respect to the reerence in geometry (Table III). Fig. 10 shows the comparative perormance o the heat exchanger with dierent in geometric proiles at Reynolds number range geometric proile) has the highest perormance actor in comparison to the other in proiles under similar operating conditions. In many industrial applications o in and tube heat exchangers such as waste heat recovery, aerospace, airconditioning, automobile radiator, marine vessels etc., the available volume space and heat exchanger unit weight is a primary design consideration. Figure 11. Comparison o the change in weight o heat exchanger unit with dierent geometric in proile V. CONCLUSION In the present study, the impact o dierent in geometric proiles on the heat transer perormance and pressure loss in a in and tube heat exchanger design are analyzed. The numerical study concludes that the in with with reduced pressure loss in comparison to the exchanger weight up to 8 % which is always desirable in the industrial applications o in and tube heat exchangers. The work presented in this paper encourages the urther investigation on dierent possible in geometric proiles in order to optimize the material and manuacturing cost which are the main controlling actors in designing a in and tube heat exchangers at the industrial scale. ACKNOWLEDGMENT This work is a part o the research project: THERMCYC- Advanced thermodynamic cycles utilising low-temperature heat sources (Project No B). NOMENCLATURE D diameter o the tube, m Eu Euler number F body orce vector, N/m 3 h Convective heat transer coeicient, W/m.K K thermal conductivity, W/m.K k turbulent kinetic energy, m /s L length, m Nu Nusselt Number p pressure, Pa p pressure dierence across the gas domain, Pa Pr Prandtl number Q heat lux vector, W/m Re Reynolds number T temperature, K Q heat source or sink, W/m 3 u low velocity, m/s u average velocity vector, m/s Symbols Speciic dissipation rate, 1/s density, kg/m 3 dynamic viscosity o the gas, Pa.s Subscripts g gas or gas domain l liquid in w inner tube wall i inner tube 115

7 o outer tube max maximum r reerence in geometric proile REFERENCES [1] Y. A. Cengel, J. M. Cimbala and R. H. Turner. Fundamentals o thermal-luid sciences, ourth edition in SI units. McGraw-Hill, 01. [] X. Yu, Y. Yuan, Y. Ma, and H. Liu, Experimental tests and numerical simulation on heat transer and resistance characteristics o H-type inned tube banks, J. Power Eng., vol. 30, pp , June 010. [3] H.T. Chen and J.R. Lai, Study o heat-transer characteristics on the in o two-row plate inned-tube heat exchangers, Int. J. Heat Mass Tran., vol. 55, pp , July 01. [4] H. Chen, Y. Wang, Q. Zhao, H. Ma, Y. Li, and Z. Chen, Experimental Investigation o Heat Transer and Pressure Drop Characteristics o H-type Finned Tube Banks, Energies, vol.7, pp , November 014. [5] L. Tong, 3D numerical analysis o heat transer characteristics or H-type inned tube, Mech. Electr. Eng. Mag., vol.15, pp , October 007. [6] Z. Zhang, Y. Wang, and Q. Zhao, Numerical study on perormance optimization o H-type inned tubes, J. Power Eng., vol. 30, pp , December 010. [7] Y. Jin, G.H. Tang, Y.L. He, and W.Q. Tao, Parametric study and ield synergy principle analysis o H-type inned tube bank with 10 rows, Int. J. Heat Mass. Tran., vol. 60, 41 51, February 013. [8] Y.C. Wang and G.H. Tang, Acid condensation and heat transer characteristics on H-type in surace with bleeding dimples and longitudinal vortex generators, Chin. Sci. Bull., vol. 59(33), pp , August 014. [9] X.B. Zhao, G.H. Tang, X.W. Ma, Y. Jin, and W.Q. Tao. Numerical investigation o heat transer and erosion characteristics or H-type inned oval tube with longitudinal vortex generators and dimples. Appl. Energy, vol. 17, pp , August 014. [10] F.R.Menter, Two-Equation Eddy-Viscosity Turbulence Models or Engineering Applications, AIAA Journal, vol. 38(8), pp , August [11] F.R. Menter, M. Kuntz, and R. Langtry. Ten years o industrial experience with the SST Turbulence Model. Turbulence Heat and Mass Transer, 003. [1] J.V. Pira., C. W. Bullard, and A. M Jacobi., An Evaluation o Heat Exchangers Using System Inormation and PEC, ACRC TR- 175, Project Report, 000. [13] VDI Heat Atlas, Springer Heidelberg Dordrecht London New York, Second Edition, ISBN , 010. APPENDIX In (5), P min( Pk,10 ok) (i) T (ii) where, Pk T( u: ( u( u) ) ( u) ku 3 3 ak 1 The turbulent viscosity is, T (iii) max( a, S ) 1 v S ij S ij S (iv) The other model constants are given in terms o interpolation unctions as, 4 v 11(1 v 1) or =,, k, and v 1 tanh( 1) k k (iv) 1 min max,, o l l CDkl where, lw is the distance to the closest wall. 10 CDk max k,10 k 500 v tanh( ) and max, o l l The other deault model parameter values are, , 1 5 / 9, k1 0.85, 1 0.5, 0.088, 0.44, k 1.0, 0.856, 0.09, a 0.31 (vii) o 1 The Reynolds number calculated as: (viii) umaxdo Re The gas-side convective heat transer coeicient is determined by overall heat transer coeicient as [17]: 1 1 A t 1 ( Do Di) (ix) U hg Ai hl K On urther simpliication, (x) UAt hgat hlai KAi ( Do D i) Since the heat transer coeicient inside the tube is high (~10 4 W/m.K), the second term in (x) is omitted. The above equation can be urther simpliied without losing accuracy as the tubes being analyzed are o small thickness (~10-3 m) and higher thermal conductivity (~50 W/m.K) which makes the third term very small and hence negligible. This results in a much simpler expression, 1 1 (xi) UAt hgat U h g (xii) Overall heat transer coeicient can be determined as: U Qt (xiii) A T t lm ( Tw Tin) ( Tw Tout ) (xiv) where, Tlm ( Tw Tin) ln ( Tw Tout ) (v) (vi) where, S is the characteristic magnitude o the mean velocity gradients, 116