energies Article Numerical Investigation Effect Variable Baffle Spacing on Thermal Performance a Shell Tube Heat Exchanger Halil Bayram 1,2 Gökhan Sevilgen 1, * 1 Faculty Engineering, Department Automotive Engineering, Uludağ University, Görükle, Bursa 16059, Turkey; halilbayram@uludag.edu.tr or halil.bayram@amasya.edu.tr 2 Faculty Technology, Department Automotive Engineering, Amasya University, Amasya 05100, Turkey * Correspondence: gsevilgen@uludag.edu.tr; Tel.: +90-224-294-2648 Received: 23 June 2017; Accepted: 1 August 2017; Published: 7 August 2017 Abstract: In this present study, oretical analysis were both used to investigate effect variable baffle spacing on rmal characteristics a small tube heat exchanger. The study was performed by using a three dimensional computational fluid dynamics (CFD) method computations were performed under steady-state conditions. We employed five different cases where first had equal baffle spacing ors had variable ones conring different configurations for balancing pressure drop on. Theoretical calculations were run using Bell-Delaware Kern methods which are most commonly used methods in available literature. We show that rmal performance a tube heat exchanger can be improved by evaluating toger results CFD Bell-Delaware methods. From results, we can say that variable spacing with centered baffle spacing scheme can be proposed as an alternative construction layout compared to an equal baffle spacing scheme. The results were in good agreement with oretical data in available literature. Keywords: heat exchanger; baffle spacing; CFD 1. Introduction Heat exchangers are devices made for efficient heat transfer from one zone to anor in order to transfer energy y are widely used in different industries like automotive, heating, ventilation air conditioning (HVAC), chemical food industry so on [1,2]. The tube heat exchanger is an indirect contact type heat exchanger re are conrable reasons to prefer tube heat exchanger, such as relatively simple manufacturing, multi-purpose applicability, robust geometry construction, easy maintenance, etc. Certain stards correlations proposed by Tubular Exchanger Manufacturers Association (TEMA) have to be conred when a well-designed tube heat exchanger is desired for industrial applications. In tube heat exchanger re are two main fluid flows, one fluid flow that goes through tubes while or flows on [3 5]. In a baffled tube heat exchanger, baffles are used for different reasons such as providing support for tubes, obtaining a desirable fluid velocity to be maintained for - fluid flow, preventing tubes from vibrating. They also direct flow to enhance heat transfer coefficient but ir usage conversely produces an increased pressure drop [6]. Therefore, ir dimensions locations have to be optimized or y have to be replaced with or types which have better heat transfer efficiency lower pressure drops [7 10]. There are numerous studies on impact baffle cut, number baffles, baffle type, etc. on rmal performance tube heat exchanger in available literature, Energies 2017, 10, 1156; doi:10.3390/en10081156 www.mdpi.com/journal/energies
Energies 2017, 10, 1156 2 19 however re is a limited amount research on effect variable baffle spacing schemes on heat transfer rate pressure drop a small tube heat exchanger. Baffle spacing is one most important parameters used in design tube heat exchangers. Closer spacing causes a higher heat transfer rate pressure drop. On or h, a higher baffle spacing reduces both heat transfer rate pressure drop [11]. In this study, we investigated impact variable baffle spacing on rmal characteristics a tube heat exchanger. As default tube heat exchanger an E type was selected which is most commonly used due to its low cost simplicity. The tube heat exchanger used in this study had one one pass with 19 tubes seven baffles. In oretical calculations for predicting overall heat transfer coefficient, convective heat transfer coefficients for tube s are needed. On tube, well known correlations have to be selected according to flow conditions. On or h, analysis is more complex than tube one because several additional parameters that affect flow. On heat exchanger, Kern Bell-Delaware methods are common methods used in literature to calculate heat transfer coefficient pressure drop. Comparing se two methods, Kern method is also only suitable for preliminary sizing whereas Bell-Delaware method is a very detailed method that takes into account effects various leakage bypass streams on. The Bell-Delaware method gives also most reliable results for analysis [1,12,13]. However, while all se oretical calculations indicate deficiencies design in general se methods do not give any information about location se weaknesses. On or h, a well designed built computational fluid dynamics (CFD) model can be a useful tool to obtain flow heat transfer characteristics a tube heat exchanger. The CFD method with se common correlations can be utilized to get appropriate flow heat transfer characteristics taking into account desired heat transfer rate pressure drop. The CFD method can be used both in rating iteratively in sizing heat exchangers [14]. On or h, to get a successful CFD simulation for a detailed heat exchanger model, in computations, we chose a small tube heat exchanger to evaluate effect variable baffle spacing on heat transfer coefficient also pressure drop that can be compared with correlation-based ones. 2. Materials Methods 2.1. Theoretical Study The total heat transfer rate between two different fluid streams can be easily calculated by using Equations (1) (2) under steady-state conditions assuming negligible heat transfer between heat exchanger its surroundings: Q h = (. m c p )h (T h,1 T h,2 ), (1) Q c = (. m c p )c (T c,2 T c,1 ). (2) On or h difference in heat exchanger varies with location in both tube s. Thus, for design process, total heat transfer rate can be written by using logarithmic mean difference (LMTD) shown in Equation (3): Q = U A T lm. (3) where U f is overall heat transfer coefficient described in Equation (5) conring fouling resistance, A is total heat transfer area a heat exchanger T lm can be calculated as a function inlet outlet s both hot cold fluids by using Equation (4): T lm = T 1 T 2 ln( T 1 / T 2 ), (4)
Energies 2017, 10, 1156 3 19 1 = 1 + 1 + t + R U f h h h c k f,h + R f,c, (5) w 1 U = d o 1 + d o ln(d o /d i ) + 1. (6) d i h i 2k h o In this study, fouling resistance is assumed negligible in oretical calculations, thus Equation (5) can be rewritten for cylindrical geometries final form overall heat transfer coefficient based on outer diameter tube which is used in this study is described in Equation (6) for clean surfaces. The use Equation (6) requires convective heat transfer coefficients for tube s. In this study, heat transfer coefficient pressure drop for various baffle spacings were calculated by using Kern Bell-Delaware methods described below. The heat transfer coefficient tube was calculated by using appropriate correlation known as Petukhov-Kirillov method flow was assumed as turbulent (Equations (7) (10)): Re = ρ U m d i µ (7) Nu = (f/2) Re Pr 1.07 + 12.7 (f/2) 1/2 ( ) (8) Pr 2/3 1 f = (1.58lnRe 3.28) 2 (9) h i = Nu k d i (10) 2.1.1. Shell Side Heat Transfer Coefficient Pressure Drop Using Kern Method In Kern method, all results are based on a constant baffle cut (Bc) ratio which is taken as 25% in this study. The heat transfer coefficient can be calculated with correlation suggested by Mc Adams expressed by Equation (11), where h o is - heat transfer coefficient, De is equivalent diameter on is calculated by using Equation (12) G s is mass velocity which is ratio mass flow rate to bundle crossflow area at center that can be calculated from Equation (13) [15]. The bundle crossflow area can be calculated using inner diameter (D s ), clearance between adjacent tubes (C), distance between two successive baffles (B) pitch size (P t ) (Equation (14)): h o D e k = 0.36 ( ) De G s 0.55 µ D e = ( cp µ k ) ( ) 0.14 µb 1/3, (11) µ w ( ) P 4 3 T 3 4 π d2 o 8, (12) G s = π d o 2. m A s, (13) A s = D s C B P T. (14) In this method, pressure drop for can be calculated with Equation (15), where N b is number baffles, φ s is calculated from Equation (16) where µ is dynamic viscosity friction factor (f) for can be calculated from Equation (17) conring range Reynolds number described: p s = f G2 s (N b + 1) D s 2 ρ D e φ s, (15)
Energies 2017, 10, 1156 4 19 φ s = (µ b /µ w ) 0.14, (16) f = exp(0.576 0.19 ln(re s ), 400 < Re s = G s D e Energies 2017, 10, 1156 < 1 10 6. (17) µ 4 18 2.1.2. Shell Side Heat Transfer Coefficient Pressure Drop Using Bell-Delaware Method The Bell-Delaware method method is more is more complicated complicated than than Kern method Kern because method because some additional some parameters additional parameters that are involved that are in involved calculations. in These calculations. parameters These concern parameters various concern leakages various bypass leakages streams bypass on streams on ir effect onir effect on ideal heat transfer ideal coefficient heat transfer is described coefficient by is Equation described (18): by Equation The ideal(18): heatthe transfer ideal coefficient heat transfer (h id ) coefficient described (hid) in described Bell-Delaware in method Bell-Delaware for pure method crossflow for pure in ancrossflow ideal tube in bank ideal tube is calculated bank is from calculated Equation from (19), Equation where (19), J i is Colburn where Ji j-factor is Colburn j-factor it can be found it can as abe function found as a function Reynolds number, Reynolds A s is number, cross-flow As is area cross-flow at centerline area at centerline for one cross-flow for between one cross-flow two baffles. between J c is two correction baffles. factor Jc is for baffle correction cut factor spacing, for baffle J l is cut correlation spacing, factorjl for is baffle correlation leakage effects factor including for baffle tube-to-baffle leakage effects -to-baffle including tube-to-baffle leakage, J b is -to-baffle correction factor leakage, for bundle Jb is bypassing correction effects factor for Jbundle s is correction bypassing factor effects for variable Js is baffle correction spacing at factor inlet for variable outlet. baffle J r is only spacing appropriate at inlet if Re is less outlet. than Jr 100. is This only factor appropriate can beif selected Re is less as 1.00 than if100. Re > This 100. factor Bafflecan leakage be selected effectsas were 1.00 not if Re conred > 100. Baffle in leakage CFD model effects so were not J l factor conred was assumed in CFD as 1. model J s is a so correction Jl factor factor was if assumed baffle as spacing 1. Js is length a correction is different factor inif inlet baffle spacing outletlength fluid zones. is different In this in study, inlet value outlet this fluid length zones. was In equal this study, to each or value for se this zones, length thus was equal J s factor each was or assumed for se as zones, 1. The details thus Js this factor method was assumed can be found as 1. The in [1]: details this method can be found in [1]: h o = h id J c J l J b J s J r, (18) h =h J J J J J, (18) (. ) ( ) ( ) m 0.14 s ks µs h id = j i c p,s Φ 2/3 (19) h = j c, Φ A m / k s c p,s µ s µ s,w μ. (19) A c, μ μ, For For Reynolds Reynolds number number we we used used Equation Equation (20) (20) where where d o is outer diameter one do is outer diameter a one tube tube A s is crossflow bundle area described in Equation (14). The Reynolds number is computed As is crossflow bundle area described in Equation (14). The Reynolds number is to computed be about to 2773, be about thus 2773, thus flow is assumed flow is as assumed turbulent: as turbulent: Re s d o G s Re = d G.. (20) µ s μ In this method total pressure drop for (Δps) is calculated conring entering In this method total pressure drop for ( p s ) is calculated conring entering leaving (Δpe), internal cross-flow (Δpc) baffle window (Δpw) nozzle (Δpn) regions, leaving ( p e ), internal cross-flow ( p c ) baffle window ( p w ) nozzle ( p n ) regions, detailed information about se calculations can be found in references [16] [17] (Equation detailed information about se calculations can be found in references [16] [17] (Equation (21)). (21)). These pressure drop regions are shown in 1 for tube heat exchangers in These pressure drop regions are shown in 1 for tube heat exchangers in general: general: pδp s = =Δp p c + +Δp p win + +Δp p e + +Δp p n (21) 2.2. Numerical Study 1. Pressure drop regions in in a tube heat exchanger. 2.2.1. CAD Model Heat Exchanger We conred three different locations that can be taken as a reference point for comparison rmal performance. These locations were selected at inlet, outlet center heat exchanger. This can be also examined in different configurations but five different baffle spacing schemes were selected for simulations to evaluate effect variable baffle spacing on heat transfer characteristics in terms using se reference locations.
Energies 2017, 10, 1156 5 19 2.2. Numerical Study 2.2.1. CAD Model Heat Exchanger We conred three different locations that can be taken as a reference point for comparison rmal performance. These locations were selected at inlet, outlet center heat exchanger. This can be also examined in different configurations but five different baffle spacing Energies schemes 2017, 2017, were 10, 10, 1156 selected 1156 for simulations to evaluate effect variable baffle spacing 5 5 on 18 18 heat transfer characteristics in terms using se reference locations. In In first first case case heat heat exchanger had had equal baffle spacing length or or cases cases it it had had a a variable a one. one. On On or or h, h, in in second case, baffle spacing length decreases when approaching center line line heat heat exchanger. The The third case case had had an an opposite structure to to second case. For For fourth fifth fifth cases, a a baffle spacing length which decreases from centerline to to inlet inlet outlet zones, respectively, was was selected. These variable baffle spacing schemes dimensions are are shown in in s 2 2 33 3 Table 1. 1. We 1. We We selected se se five five five different schemes schemes for for for comparison results results in view in in view pressure pressure drops drops heat heat transfer heat transfer rates. rates. The The CAD model tube tube heat heat exchanger is is shown in in 4. 4. The The tube tube had had a a triangular pitch layout dimensional properties tube tube tube heat heat heat exchanger used used in in in simulations are are listed are listed in Table in in Table 2. 2. 2. 2. 2. 2. The The dimensions baffle spacing lengths for for all all cases. 3. 3. Baffle spacing scheme for for all all cases. Table 1. 1. The The dimensions baffle spacing lengths for for all all cases. Spacing Length Case-I (mm) Case-II (mm) Case-III (mm) Case-IV (mm) Case-V (mm) L1 L1 26.75 26.75 26.75 26.75 26.75 26.75 26.75 26.75 26.75 26.75 L2 L2 26.75 26.75 41.25 41.25 16.00 16.00 16.00 16.00 38.50 38.50 L3 L3 26.75 26.75 26.00 26.00 26.00 26.00 21.00 21.00 34.00 34.00
Energies 2017, 10, 1156 6 19 Table 1. The dimensions baffle spacing lengths for all cases. Spacing Length Case-I (mm) Case-II (mm) Case-III (mm) Case-IV (mm) Case-V (mm) L1 26.75 26.75 26.75 26.75 26.75 L2 26.75 41.25 16.00 16.00 38.50 L3 26.75 26.00 26.00 21.00 34.00 L4 26.75 16.00 41.25 26.00 31.00 L5 26.75 16.00 41.25 31.00 26.00 L6 26.75 26.00 26.00 34.00 21.00 L7 26.75 41.25 16.00 38.50 16.00 Energies 2017, L810, 1156 26.75 26.75 26.75 26.75 26.75 6 18 4. 4. CAD CAD model model tube tube heat heat exchanger exchanger used used in in this this study. study. Table Table 2. 2. The The dimensions dimensions tube tube heat heat exchanger. exchanger. Shell Side Dimensions Shell internal diameter diameter 44 mm 44 mm Shell wall thickness 3 mm 3 mm Baffle plate wall thickness 1 mm 1 mm Number baffle plates 7 Number baffle plates 7 Tube Side Dimensions Tube internal diameter 4 mm 4 mm Tube wall wall thickness 1 mm 1 mm Effective tube length 221 mm Effective tube length 221 mm Number tubes in tube bundle 19 Number tubes in tube bundle 19 2.2.2. Mesh Structure Boundary Conditions Numerical Calculations for Shell Tube Heat 2.2.2. Exchanger Mesh Structure Boundary Conditions Numerical Calculations for Shell Tube Heat Exchanger In calculations all cases, computational domain had eight fluid zones in In for getting comparative calculations all cases, detailed computational results ( domain 5). had The eight multi-zone fluid zones approach in was used to for model getting comparative heat exchanger all detailed se zones results had ( tetrahedral 5). The mesh multi-zone elements approach due to was complexity used to model CAD heat exchanger model. The number all se zones total had elements tetrahedral was about mesh 6.0 elements million due to mesh complexity should be well CAD designed model. to The resolve number important total elements flow features was about which 6.0 are million dependent upon mesh flow condition should be parameters. well designed to resolve important flow features which are dependent upon flow condition In parameters. calculations, mesh generation is very crucial for getting accurate predicted results reducing computation time [9,12,14,18,19]. The mesh structure surfaces computational domain view this domain are shown in 6. Today, re are many computer stware packages for flow field heat transfer analysis. For mesh generation solution, Ansys Fluent package stware program was used. In this stware flow fields were computed by a three dimensional CFD method. This stware solves continuum, energy transport equations ly coupled algorithm was chosen for pressure-velocity
Shell internal diameter 44 mm Shell wall thickness 3 mm Baffle plate wall thickness 1 mm Number baffle plates 7 Energies 2017, 10, 1156 Tube Side Dimensions 7 19 Tube internal diameter 4 mm coupling, k-ε realizable model was Tube used wall for thickness turbulence modeling this model 1 mm was used for such calculations due to stability precision Effective tube length results in available 221 literature mm [6,12,18 22]. The governing equations for steady Number state tubes conditions in tube are bundle shown below: 19 2.2.2. Mesh Structure Boundary Conditions Numerical Calculations for Shell Tube Conservationmass : (ρ V) = 0, (22) Heat Exchanger x-momentum : (ρu ( ) [ )] [ )] V) = p x + x 2µ u x + λdivv + y µ( u y + v x + z µ( w In calculations all cases, computational domain had eight x fluid + u zzones, in (23) for getting comparative y-momentum : (ρv [ detailed )] results [ ( 5). ] The multi-zone [ )] approach V) = ρg y p y + x µ( v x + u y + y 2µ v y + λdivv + z µ( v z + w y, (24) Energies was used 2017, to 10, model 1156 heat exchanger all se zones had tetrahedral mesh elements due to 7 18 complexity CAD model. z-momentum : (ρw The number [ total )] elements [ was about )] 6.0 ( million mesh V) = p z + x µ( w x + u z + y µ( v should be well designed solution, to resolve Ansys Fluent important package flow stware features z + program w y which + was z are 2µ dependent used. w z ), + In λdivv this upon stware flow (25) flow condition parameters. fields were computed Energy : (ρ e by a three V) = p dimensional CFD method. This stware solves V + (k T) + q + Φ. continuum, energy transport equations ly coupled algorithm was chosen (26) for pressure-velocity coupling, k-ε realizable model was used for turbulence modeling this model was used for such calculations due to stability precision results in available literature [6,12,18 22]. The governing equations for steady state conditions are shown below: x-momentum: ρuv = + y-momentum: ρvv =ρg z-momentum: ρwv = Conservation mass: ρ V =0, (22) 2μ + λdivv + μ + + μ +, (23) + + μ + + 2μ + λdivv + μ +, (24) μ + + μ + + 2μ + λdivv, (25) 5. Energy: Separated ρ fluid e V zones = p V on + k T +q+φ. heat exchanger. (26) In calculations, mesh generation is very crucial for getting accurate predicted results reducing computation time [9,12,14,18,19]. The mesh structure surfaces computational domain view this domain are shown in 6. Today, re are many computer stware packages for flow field heat transfer analysis. For mesh generation 6. Mesh structure heat exchanger. In Equation (22), Φ is dissipation function that can be calculated from: Φ = μ 2 u x + v y + w z + v x + u y + w y + v z + u z + w [ ( ) 2 ( ) 2 ( ) ] 2 ( ) 2 ( ) 2 ( ) ] 2 ( x ) 2 Φ = µ 2[ u x + v y + w z + v x + u y + w y + v z + u z + w x + λ u x + v y + w z (27) + λ u x + v y + w (27) All calculations were performed z under steady state conditions in calculations, water was selected as both tube fluid in model All calculations were performed under steady state conditions in heat exchanger. The mass flow rates hot cold water were set to 0.3 kg/s 0.2 kg/s calculations, water was selected as both tube fluid in model values se zones were set to 50 C 10 C, respectively. The detailed solver heat exchanger. The mass flow rates hot cold water were set to 0.3 kg/s 0.2 kg/s settings boundary conditions used in this study are shown in Table 3. values se zones were set to 50 C 10 C, respectively. The detailed solver settings boundary conditions used in this study are shown in Table 3. The flow chart simulation used in this study is shown in 7. In first stage, 3D CFD analysis a tube heat exchanger was achieved by using a commercial CFD solver. When entire fluid domain is modeled as a single continuum zone, data can be obtained only for this zone getting computed values, velocity pressure between baffles becomes difficult. We used a multi-zone approach in which entire fluid
Energies 2017, 10, 1156 8 19 Table 3. Solver settings boundary conditions used in simulations. Solver Settings Solver Pressure-based Time Steady-state conditions Equations Combined simulation flow energy Flow type k-epsilon realizable turbulence model Shell Side Supply cold water 10 C Mass flow rate 0.2 kg s 1 Shell outer surfaces Adiabatic conditions Outlet nozzle Gauge pressure equals to 0 Pa Tube-Side Supply hot water 50 C Mass flow rate 0.3 kg s 1 Outlet surfaces tube Gauge pressure equals to 0 Pa Thermal Properties Water at Mean Temperature Thermal conductivity 0.6 W m 1 K 1 Specific heat Cold : 4180 j kg 1 K 1, Hot : 4186.5 j kg 1 K 1 Density 998.2 kg m 3 Dynamic viscosity 0.001003 kg m 1 s 1 The flow chart simulation used in this study is shown in 7. In first stage, 3D CFD analysis a tube heat exchanger was achieved by using a commercial CFD solver. When entire fluid domain is modeled as a single continuum zone, data can be obtained only for this zone getting computed values, velocity pressure between baffles becomes difficult. We used a multi-zone approach in which entire fluid domain for CFD analysis was divided into sub-zones as shown in s 5 6. These sub-zones can helpful to get solution data between two successive fluid zones compared to single zone. These sub-zones were used to obtain rmal characteristics pressure drop in an efficient way. In this content, we can easily say that multi-zone solution scheme including solid fluid zones can be used to evaluate heat transfer characteristics pressure drop in a more detailed way compared to single zone approach because multi-zone approach enables one to investigate each fluid zone individually in view heat transfer coefficient, pressure drop, velocity distributions. On or h, this approach can be used to evaluate results such as weaknesses (different leakage flow paths, bypass streams for different flow zones, velocity distribution for each zone etc.) on for different operating conditions. Moreover, using a 3D CFD model, effect main important parameters such as baffle spacing length baffle cut on heat transfer pressure drop in can be obtained easily in this stage. The validation results can be achieved by comparison with oretical results common methods like Kern Bell-Delaware methods. Thus multi-zone CFD approach used toger with common oretical methods can be useful for getting better design solution conring maximum pressure drop limit desired heat transfer rate heat exchanger. The desired configuration based on ly obtained flow fields can be achieved iteratively this solution procedure is shown in 7. In calculations, 3D model heat exchanger was obtained conring inlet outlet plenums, whereas in literature, some investigations were performed by applying a constant mass flow rate for each tube individually constant boundary conditions were applied to tube surfaces in general, but in this study, we also conred effect velocity distribution inlet outlet regions (plenum) on flow in tubes
Tube-Side Supply hot water 50 C Mass flow rate 0.3 kg s 1 Outlet surfaces tube Gauge pressure equals to 0 Pa Thermal Properties Water at Mean Temperature Energies 2017, 10, 1156 9 19 1 1 Thermal conductivity 0.6 W m K Specific heat Cold : 4180 j kg 1 K 1, Hot : 4186.5 j kg 1 K 1 tube flows were both solved simultaneously with energy equations [5,12]. On Density 998.2 kg m 3 or h, we also employed solid zones such as tube walls, body, baffles inlet outlet Dynamic viscosity 0.001003 kg m 1 s 1 nozzles etc. to include conjugate heat transfer in this study. Energies 2017, 10, 1156 9 18 The validation results can be achieved by comparison with oretical results common methods like Kern Bell-Delaware methods. Thus multi-zone CFD approach used toger with common oretical methods can be useful for getting better design solution conring maximum pressure drop limit desired heat transfer rate heat exchanger. The desired configuration based on ly obtained flow fields can be achieved iteratively this solution procedure is shown in 7. In calculations, 3D model heat exchanger was obtained conring inlet outlet plenums, whereas in literature, some investigations were performed by applying a constant mass flow rate for each tube individually constant boundary conditions were applied to tube surfaces in general, but in this study, we also conred effect velocity distribution inlet outlet regions (plenum) on flow in tubes tube flows were both solved simultaneously with energy equations [5,12]. On or h, we also employed solid zones such asanalysis tube walls, forfor desired solution rmal a body, 7.7. Flow Flowchart chart method method desired solution rmal analysis a baffles inlet outlet nozzles etc. to include conjugate heat transfer in this study. tube heat heat exchanger suggested in this tube exchanger suggested instudy. this study. 3. Results Results Discussion Discussion 3. For getting getting comparative comparative results, defined in different For results, we we defined eighteight in different zones zones ( 8). The first end are located at mid-center nozzles ( 8). The first end are located at mid-center nozzles or or ones are located at middle center each fluid zone. To evaluate data in ones are located at middle center each fluid zone. To evaluate data in terms terms multi-zone each had outlet inlet outlet faces, separately. These faces multi-zone approach,approach, each fluid zonefluid had zone inlet faces, separately. These faces (window, (window, inlet outlet faces) are shown in 9. inlet outlet faces) are shown in 9. 8. 8. Schematic view defined for comparative results results for for..
Energies 2017, 10, 1156 10 19 8. Schematic view defined for comparative results for. 9. Window surfaces located between two adjacent fluid zones. Energies 2017, 10, 1156 9. Window surfaces located between two adjacent fluid zones. 10 18 The predicted are are shown in s 10 14.10 14. The predicted values valuesatatse se shown in s calculated maximum difference was about 2.5 C in first plane for all cases. The calculated maximum difference was about 2.5 C in first plane for all On On or h,h, predicted values increased with cases. or predicted values increased with z-coordinate z-coordinate maximum values valueswere werecomputed computed at location which had dense baffle spacing construction at location which had dense baffle spacing construction because because this leads structure to an increase in predictedvalues sethus this structure to anleads increase in predicted in se values in. we. we can say that transfer rate on strictly depends on baffle spacing length. can say Thus that heat transfer rateheat strictly depends baffle spacing length. From calculated calculated values middle center fluid each fluid zone values at atmiddle center each zone valuesthan were than ors aligned for region aligned with forwindow for all values were lower lower ors for region with window area all casesarea in general cases in 10 14). general The (s 10 14). The maximum between first were end (s maximum difference betweendifference first end were computed at about 9 C for Case-I Case-II. In se, computed at about 9 C for Case-I Case-II. In se, calculated maximum calculated maximum value was obtained Case-II about it 23 wasccomputed about 23 C value was obtained for Case-II it was for computed at z = 0.173 m at z = which 0.173 m which is located close to planeasa heat As a plane is located plane close to middle plane heatmiddle exchanger. result exchanger. se result se data, we can easily say that different baffle spacing scheme has a great data, we can easily say that different baffle spacing scheme has a great effect on effect on distribution results heat transfer rate. These results can distribution also heat transfer rate.also These can be used for getting better be used for getting better designs in terms heat transfer characteristics. designs in terms heat transfer characteristics. 10. Prediction Prediction ( C) ( C) distribution at defined in (Case-I).
Energies 2017, 10, 1156 11 19 10. Prediction ( C) distribution at defined in (Case-I). 11. Prediction ( ( C) distribution at in in (Case-II). 11.10, Prediction C) distribution defined defined (Case-II). Energies 2017, 1156 11 18 Energies 2017, 10, 1156 11 18 C) distribution 12.12. Prediction distributionatat defined in (Case-III). Prediction (( C) defined in (Case-III). 12. Prediction ( C) distribution at defined in (Case-III). 13. Prediction ( C) distribution at defined in (Case-IV). C) distribution Prediction (( C) defined in (Case-IV). 13.13. Prediction distributionatat defined in (Case-IV).
Energies 2017, 10, 1156 12 19 13. Prediction ( C) distribution at defined in (Case-IV). C) distribution at 14. 14.Prediction Prediction (( C) defined definedin in (Case-V). (Case-V). These computed data for each zone is shown in Tables 4 5. From obtained results, calculated pressure drop changed between 893 Pa 1210 Pa for each zone. Due to assignation zero gauge pressure for outlet surface to obtain relative pressure drop between inlet outlet s, maximum pressure drop was calculated from win-7 to cold outlet surfaces. One reasons for this situation is that, contraction at outlet nozzle leads to a higher pressure drop. The maximum pressure drop that occurred in a single fluid zone was calculated at about 1600 Pa for Case-II. However, in this case, this leads to an increase in values also heat transfer rate compared to Case-III, Case-IV Case-V. On or h difference between cold inlet outlet surfaces was predicted at about 7.2 C for Case-III, Case-IV Case-V. This value was computed as 8.1 C 8.0 C for Case-I Case-II, respectively. Thus, Case-I Case-II have similar rmal properties in view heat transfer rate pressure drop was calculated to be nearly equal, but pressure drop should be adopted conring best design configuration by changing baffle spacing length for Case-II. Table 4. Computed pressure values at different surfaces (i). Case-I Case-II Case-III Surface Name Pressure (Pa) Temperature ( C) Pressure (Pa) Temperature ( C) Pressure (Pa) Temperature ( C) Cold-inlet Win-1 Win-2 Win-3 Win-4 Win-5 Win-6 Win-7 Cold-outlet 20,832 19,622 18,729 17,588 16,484 15,361 14,269 13,147 0 10.00 11.78 12.82 13.91 14.89 15.86 16.76 17.63 18.11 21,340 20,194 19,356 18,243 16,754 15,183 14,023 12,986 0 10.00 11.83 13.22 14.13 14.82 15.43 16.37 17.49 17.98 21,312 20,128 18,934 17,756 16,759 15,768 14,709 13,230 0 10.00 11.50 12.20 13.20 14.36 15.41 16.27 16.67 17.16 The predicted heat transfer rates for each zone total heat transfer rate for all cases are shown in Table 6. From obtained results, calculated total heat transfer rates for Case-I Case-II were about equal to 6.5 kw se cases had similar properties in terms rmal performance. The ratio total heat transfer rate to computed heat transfer rate for Case-I was defined as a dimensionless number (Rh ) this value was computed as 0.98. These results shown that
Energies 2017, 10, 1156 13 19 Case-II which had variable spacing with centered baffle spacing scheme had similar rmal properties compared to Case-I but more experimental investigation about this scheme has to be performed conring practical problems. The predicted total heat transfer rates for Case-III, Case-IV Case-V were about 5.9 kw, thus se baffle spacing schemes had lower rmal performance than ors. The minimum predicted heat transfer rate was obtained for Case-III Case-V. Surface Name Table 5. Computed pressure values at different surfaces (ii). Case-IV Case-V Pressure (Pa) Temperature ( C) Pressure (Pa) Temperature ( C) Cold-inlet 20,907 10.00 21,196 10.00 Win-1 19,759 11.51 19,852 11.64 Win-2 18,602 12.22 19,021 12.83 Win-3 17,308 12.97 17,938 13.87 Win-4 16,195 13.83 16,944 14.71 Win-5 15,103 14.79 15,851 15.56 Win-6 14,125 15.77 14,661 16.24 Win-7 13,130 16.75 13,132 16.67 Cold-outlet 0 17.22 0 17.16 Shell Side Fluid Zones Table 6. Predicted heat transfer rates on for all cases. CFD Results Heat Transfer Rates for All Cases (Watt) Case-I Case-II Case-III Case-IV Case-V Fluid zone-1 1460.59 1501.61 1230.83 1239.04 1345.71 Fluid zone-2 853.38 1140.57 574.39 582.59 976.46 Fluid zone-3 894.40 746.70 820.55 615.42 853.38 Fluid zone-4 804.14 566.18 951.84 705.68 689.27 Fluid zone-5 795.94 500.54 861.58 787.73 697.47 Fluid zone-6 738.50 771.32 705.68 804.14 557.98 Fluid zone-7 713.88 919.02 328.22 804.14 352.84 Fluid zone-8 393.87 402.07 402.07 385.66 402.07 Total 6654.69 6548.02 5875.17 5924.40 5875.17 R h 1 0.98 0.88 0.89 0.88 The computed overall heat transfer coefficients, total heat transfer rates pressure drops for all cases are shown in Table 7. For pressure drop calculations, we only used Bell-Delaware method because Kern method is just suitable for initial sizing problems but Bell-Delaware method estimates heat transfer coefficients pressure drops more precisely. The baffle cut ratio was selected as 25% which is reference value Kern method. From results given in Table 7, computed overall heat transfer coefficient by using Kern CFD methods were calculated to be 2533 W m 2 K 1 2347 W m 2 K 1, respectively, but this computed value was about 2270 W m 2 K 1 from Bell-Delaware method. In CFD method, effects various leakage bypass streams on were ignored, thus computed value was higher than that one obtained from Bell-Delaware method. The outlet, pressure drop overall heat transfer coefficient were directly computed from CFD results difference between heat transfer rates for tube s was nearly about 0.5 Watt, thus we can easily say that steady-state conditions were achieved for CFD results. The calculated total pressure drop for Case-I was about 21 kpa 18 kpa by using CFD Bell-Delaware methods, respectively.
Energies 2017, 10, 1156 14 19 Table 7. Results analytical calculations for all cases. Thermal properties Heat Transfer Characteristics Case-I Case-II Case-III Case-IV Case-V CFD Kern Bell-Delaware CFD U (W m 2 K 1 ) 2533.06 2346.74 2269.00 2485.00 2175.54 2199.57 2177.83 Q cold (W) 6654.69 6164.72 5960.51 6548.02 5875.17 5924.40 5875.17 Q hot (W) 6654.18 6164.72 5960.51 6551.76 5871.48 5925.51 5876.63 P s (Pa) Pressure Drop Calculations CFD Bell-Delaware CFD 20,832 17,769 21,340 21,312 20,907 21,196 We also defined a horizontal plane parallel to flow direction in middle center tube heat exchanger calculated distributions throughout flow direction for all cases are shown in 15. These results may be used to evaluate heat transfer characteristics between cold hot fluid streams. As expected, maximum difference between tube outer wall fluid were predicted in first fluid zone for all cases. This value decreased along tubes minimum value was computed for end zone. The higher values were predicted in second half heat exchanger we can easily say that baffle spacing length scheme directly affected distribution in center plane heat exchanger. The predicted velocity distribution in all fluid zones is shown in 16 for all cases. The computed velocity value was obtained between 1.1 m s 1 2.25 m s 1 in general but maximum value was computed about 4.5 m s 1 near nozzle regions due to contraction in inlet outlet regions. The calculated mass average velocity values for all fluid zones are shown in Table 8. The predicted mass average velocity values varied between 0.4 m s 1 2.25 m s 1 in general, however maximum calculated value was 0.662 m s 1 in fluid-zone 5 for Case-II due to effect dense baffle spacing scheme for that zone. The computed mass average velocity value in first end fluid zones was calculated at about 0.6 m s 1 0.5 m s 1, respectively, for all cases. It can be observed that a decrease in baffle spacing length leads to higher velocity values heat transfer rate will be higher with increasing velocity values. Table 8. CFD results velocity distribution for each fluid zone (m/s). Shell Side Fluid Zones Case-I Case-II Case-III Case-IV Case-V Fluid zone-1 0.62 0.62 0.62 0.62 0.62 Fluid zone-2 0.44 0.37 0.61 0.60 0.37 Fluid zone-3 0.50 0.50 0.52 0.57 0.46 Fluid zone-4 0.50 0.65 0.41 0.52 0.46 Fluid zone-5 0.49 0.66 0.40 0.47 0.50 Fluid zone-6 0.50 0.52 0.50 0.44 0.55 Fluid zone-7 0.49 0.41 0.65 0.41 0.66 Fluid zone-8 0.58 0.57 0.59 0.57 0.59 Average 0.51 0.51 0.51 0.51 0.51
Energies 2017, 10, 1156 15 19 Energies 2017, 10, 1156 14 18 15. 15. Temperature Temperature distribution distribution at at center center plane plane heat heat exchanger exchanger (a) (a) Case-I Case-I (b) (b) Case-II Case-II (c) (c) Case-III (d) Case-IV (e) Case-V. Case-III (d) Case-IV (e) Case-V. Table 8. CFD results velocity distribution for each fluid zone (m/s). Shell Side Fluid Zones Case-I Case-II Case-III Case-IV Case-V Fluid zone-1 0.62 0.62 0.62 0.62 0.62 Fluid zone-2 0.44 0.37 0.61 0.60 0.37 Fluid zone-3 0.50 0.50 0.52 0.57 0.46 Fluid zone-4 0.50 0.65 0.41 0.52 0.46 Fluid zone-5 0.49 0.66 0.40 0.47 0.50 Fluid zone-6 0.50 0.52 0.50 0.44 0.55 Fluid zone-7 0.49 0.41 0.65 0.41 0.66 Fluid zone-8 0.58 0.57 0.59 0.57 0.59 Average 0.51 0.51 0.51 0.51 0.51
Energies 2017, 10, 1156 16 15 19 18 16. Prediction velocity (m s -1 ) distribution flow (a) Case-I (b) Case-II (c) Case-III (d) Case-IV 16. Prediction (e) Case-V. velocity (m s -1 ) distribution flow (a) Case-I (b) Case-II (c) Case-III (d) Case-IV (e) Case-V. 4. Conclusions 4. Conclusions In this study, oretical analysis were both used to investigate effect variable bafflein spacing this study, on rmal characteristics oretical analysis a small were both tube used heat to exchanger. investigate As a result effect se variable baffle spacing computations, on rmal we can say characteristics that correlation-based a small approaches tube indicate heat exchanger. deficiencies As a result a se tube heat exchanger computations, but we location can say that se correlation-based weaknesses is not approaches used in any indicate se methods. deficiencies By using a a well tube designed heat exchanger builtbut multi-zone location CFD se model, weaknesses flow is not heat used transfer in any characteristics se methods. a By using tube a well heat designed exchanger can built be changed multi-zone CFD improved. model, Anor flow important heat result transfer is that characteristics Case-I which a had equal tube baffle heat spacing exchanger configuration can be changed had smallest improved. pressure Anor drop important highestresult rmal is performance that Case-I among which all had schemes. equal baffle On spacing or h, configuration predicted had smallest difference pressure drop between highest cold rmal inlet performance outlet surfaces among was all about 8schemes. C for Case-I On or Case-II. h, Thus, predicted difference between cold inlet outlet surfaces was about 8 C for
Energies 2017, 10, 1156 17 19 we conclude that rmal performance Case-II was close to that Case-I but using variable baffle spacing scheme in practical applications may cause difficulties such as manufacturing maintenance problems, etc. More experimental investigations about this scheme have to be performed conring industrial applications. However, using a centered baffle spacing scheme leads to an increase in pressure drop also heat transfer rates, so design parameters have to be determined for best configuration conring maximum pressure drop limit desired heat transfer rate heat exchanger. We can easily say that different baffle spacing schemes have a great effect on distribution also heat transfer rate. These results can be used for getting best design in terms heat transfer characteristics a tube heat exchanger. Moreover, using CFD model toger with correlation-based approaches not only indicates weaknesses, but also predicts location maximum pressure drop, variation heat transfer rate flow field effects different baffle spacing schemes on heat transfer characteristics tube heat exchanger in a more detailed way. In this study, simulation results are compared with results from Kern Bell Delaware methods results were in good agreement with oretical data, although in this study, data from CFD solution were more compatible with oretical results calculated with Kern method. However, more complicated parameters such as by-pass leakage streams various factors existing in Bell-Delaware method leads to underestimated rmal performance results. We plan to investigate transient rmal performance a tube heat exchanger in future studies conring different baffle spacing schemes or design configurations. Author Contributions: Halil Bayram Gökhan Sevilgen prepared this article Gökhan Sevilgen analysed research data to contribute design configurations Halil Bayram Gökhan Sevilgen wrote this paper. Conflicts Interest: The authors declare no conflicts interest. Nomenclature A total heat transfer rate area [m 2 ] As bundle crossflow area [m 2 ] B baffle spacing [m] c p specific heat at constant pressure [J kg 1 K 1 ] C clearance between adjacent tubes [m] d i tube in diameter [m] d o tube out diameter [m] D e equivalent diameter [m] D s inner diameter [m] f friction factor - g gravitational acceleration [m s 2 ] G s mass velocity [kg m 2 s 1 ] h convection heat transfer coefficient [W m 2 K 1 ] j i Colbum j-factor for an ideal tube bank - J b bundle bypass correction factor for heat transfer - J c segmental baffle window correction factor for heat transfer - J l baffle leakage correction factor for heat transfer - J r laminar flow heat transfer correction factor - J s heat transfer correction factor for unequal end baffle spacing - k kinetic energy turbulent fluctuations per unit mass - k rmal conductivity [W m 1 K 1 ]. m mass flow rate [kg s 1 ] N b number baffles - Nu Nusselt number - t thickness [m] T [K]
Energies 2017, 10, 1156 18 19 p pressure [Pa] Pr Prl number - P T pitch size [m] q heat flux as a source term [W m 2 ] Q total heat transfer rate [W] R fouling resistance [m 2 K W 1 ] Re Reynolds number - R h Heat transfer ratio - u, v, w velocity components [m s 1 ] U overall heat transfer coefficient [W m 2 K 1 ] U f overall heat transfer coefficient with fouilng [W m 2 K 1 ] V velocity vector - x, y, z position coordinates - p s total pressure drop [Pa] p e pressure drop in entering leaving [Pa] p c pressure drop in cross flow [Pa] p win pressure drop in window [Pa] p n pressure drop in nozzle region [Pa] λ viscosity coefficient - ρ density [kg m 3 ] τ shear stress [N m 2 ] φ s viscosity correction factor for - fluids - Φ dissipation function - µ dynamic viscosity [N s m 2 ] µb viscosity evaluated at bulk mean [N s m 2 ] µw viscosity evaluated at wall [N s m 2 ] µs fluid dynamic viscosity at average [N s m 2 ] µs,w fluid dynamic viscosity at wall [N s m 2 ] Subscript b c f h i id lm m o s w bulk mean cold fouling factor hot inner ideal logarithmic mean mean outer wall delta operator Laplacian operator References 1. Kakac, S.; Liu, H.; Pramuanjaroenkij, A. Heat Exchangers: Selection, Rating, Thermal Design; CRC Press: Boca Raton, FL, USA, 2012; pp. 361 425. ISBN 978-1-4398-4991-0. 2. Raj, K.T.R.; Ganne, S. Shell analysis a tube heat exchanger conring effects baffle inclination angle on fluid flow using CFD. Therm. Sci. 2012, 16, 1165 1174. [CrossRef] 3. Yang, J.; Ma, L.; Bock, J.; Jacobi, A.M.; Liu, W. A comparison four modeling approaches for enhanced --tube heat exchangers with experimental validation. Appl. Therm. Eng. 2014, 65, 369 383. [CrossRef]
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