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Numerical optimization of location of ‘common flow up’ delta winglets for inline aligned finned tube heat exchanger
Applied Thermal Engineering 82 (2015) 329e340
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Numerical optimization of location of ‘common flow up’ delta winglets for inline aligned finned tube heat exchanger Amit Arora*, P.M.V. Subbarao, R.S. Agarwal Department of Mechanical Engineering, Indian Institute of Technology, Delhi, India
h i g h l i g h t s Optimal location of winglets for maximum thermal compactness of the heat exchanger. Optimal location has helped in cooling down the fin. Augmentation of average Nusselt number of the fin at the same Reynolds number. Magnitude of the Nusselt number peaks is gradually decreasing in the flow direction.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2014 Accepted 24 February 2015 Available online 5 March 2015
Heat transfer augmentation of a fin and tube heat exchanger by the winglet type vortex generator strongly depends on the location of the winglet w.r.t. tube centre. This study was aimed at optimizing the location of the ‘common flow up’ delta winglets for the maximum thermal compactness of a given inline aligned fin and tube heat exchanger. The winglets were erected with a conservative attack angle to avoid severe increase in the pressure drop. This work also attempts to first time model the contact resistance between the fins and the tube as a hypothetical conduction resistance. Beginning with the selection of all promising locations of the winglets, an optimal location was identified that allows maximum augmentation of the thermal performance on the fin side. This numerical study clearly shows that the optimally located ‘common flow up’ delta winglets have improved the average thermal performance of both the fins and the tubes at the same Reynolds number. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Delta winglets Optimal location Thermal compactness Finned tube heat exchanger
1. Introduction Finned tube heat exchangers find wide applications in the areas like process heat transfer, air conditioning, automobiles etc. In these exchangers, the fin side is cursed with high thermal resistance by virtue of low heat transfer coefficients [1,2]. Enhancement of heat transfer coefficients on the fin side is crucial to the compact design of such heat exchangers. Methods for improving heat transfer on the fin side can be classified as active, passive or compound [2,3]. Employing longitudinal vortex generators (LVGs) on the fin side is one of the widely studied passive enhancement technique. The longitudinal vortices shed by the LVG(s) constitute three dimensional swirling flows that facilitate better mixing of the cold and the hot fluid by destabilizing the flow, and result in the boundary layer modification [4,5]. The secondary flow created
* Corresponding author. Tel.: þ91 9250272551. E-mail address: [email protected] (A. Arora). http://dx.doi.org/10.1016/j.applthermaleng.2015.02.071 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
by the vortices disrupts the thermal boundary layer, and consequently causes augmentation of the local heat transfer coefficients on the fin. Initially, the longitudinal vortices were used for boundary layer control, but later they were extensively studied for modifying the flows in the plain channels and for the thermal management of the tube wakes in the fin-and-tube heat exchangers [3,6e8]. The LVG(s) can be of two types, the wings and the winglets [6]. The thermo-hydraulic performance of the winglets is better than the wing type vortex generators [9]. Heat transfer enhancement due to the secondary flow generated by the vortices is effective when the winglets are erected in pairs. Literature recommends that the delta winglets vortex generators (DVG) are found to be more effective than the rectangular winglets for improving heat transfer. Based on the orientation, a DVG pair can be classified as ‘common flow down’ and ‘common flow up’ configuration [8,10,11]. These two configurations are also addressed as ‘toe-in’ and ‘toe-out’ or ‘common downwash’ and ‘common upwash’ respectively [11,12]. For the thermal
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management of tube wake, DVG(s) in ‘common flow down’ configuration are characteristically placed as a pair behind the tube with the transverse distance between the leading edges smaller than the trailing edges [13,14] whereas the ‘common flow up’ configuration calls for placing them adjacent to the tube with the transverse distance between the trailing edges being smaller than the leading edges [10,14]. The longitudinal vortices generated by DVG(s) in ‘common flow down’ configuration displace the fluid in the direction normal to the flow, thereby facilitate contraction of the tube wake due to the momentum transfer and improves the heat transfer coefficients in the wake region. In contrast, apart from displacing the fluid in the normal direction, acute angle made by the ‘common flow up’ configuration with the upstream flow makes it kinematically different from the ‘common flow down’ configuration, because such an orientation of winglets guides the accelerated upstream flow in the tube's recirculation region [4], which helps in imparting large motion to the fluid with otherwise low mobility. A lot of work has been reported so far on the winglets with ‘common flow down’ configuration, but lately ‘common flow up’ configuration is emerging as another lucrative configuration for the thermal management of the tube wakes in the fin-and-tube heat exchangers [5,8,10,12,14]. Experimental study [12] compared the heat transfer enhancement by ‘toe-out’ delta winglets in an inline and staggered finned tube bank. It was reported that compared to the single row of winglets in the staggered tube bank, two rows arrangement increased the heat transfer by 6e15% and pressure loss by 61e117% over the range of Reynolds number being studied. Corresponding increase for inline tube bank were 7e9% and 3e9% respectively. Another experimental study [15] reported that increasing the number of ‘common flow up’ winglet rows yield better heat transfer performance; but also results in higher friction factor, which was found to decrease rapidly with increasing Reynolds number. Similar study about the effect of the number of ‘common flow up’ winglet rows on thermal performance of an inline finned tube heat exchanger was pursued numerically [4], and similar conclusions were drawn. Effect of the attack angle of the winglets on a fin and tube heat exchanger was studied numerically [10,14,16e18] and it was reported that both heat transfer coefficient and friction factor are the direct functions of the attack angle, but increasing the attack angle causes much faster increase in friction factor compared to the heat transfer. Experimental study [19] investigated the effect of the number of tube rows on thermal and hydraulic performances of a finned staggered tube bundle in the presence of ‘common flow up’ delta winglets behind the leading tube only. It was reported that the scaled Colburn's factor is almost independent of the tube rows. Numerical study [20] found that increase in the thermal performance of a finned oval tube heat exchanger is the direct function of the attack angle of ‘toe-in’ winglets, and the delta winglets are found to deliver better thermal performance than the rectangular winglets. Effect of the shape of longitudinal vortex generators on the thermal and hydraulic performance in a channel flow was investigated numerically [21]. This study reported that when the area of LVG is fixed, delta winglets are found to be more effective than the rectangular winglets for improving the heat transfer. Numerical investigation [22] reported that both heat transfer coefficient and pressure loss of an inline finned tube heat exchanger are the direct functions of attack angle and number of rows of ‘toe-out’ winglets. It is also stated that the attack angle leads to rapid increase in pressure loss compared to the heat transfer coefficient. While studying the effect of staggering of the winglets, it is found that the staggered arrangement of winglets delivered thermal performance same as the inline arrangement, but helped in reducing the pressure loss by 4.5e8.3% over the studied range of Reynolds number.
Placement of DVG(s) for the maximum thermal compactness of a fin-and-tube heat exchanger requires its spatial optimization. A few studies have been published regarding the optimization of the position and geometry of ‘toe-in’ configuration of delta winglets in a finned tube bank [13,23], but literature on the optimization of ‘toe-out’ configuration is inadequate. So, this study attempts to identify the optimal location of ‘toe-out’ delta winglets for the maximum augmentation of heat transfer in an inline aligned fin and tube heat exchanger. Though the literature says that the augmentation of average heat transfer coefficient is a direct function of attack angle and length of the winglets, but it is also known that the pressure loss increases much rapidly with the attack angle and the length of winglets compared to the heat transfer coefficient [10,14,22e25]. Based on these conclusions, the aspect ratio (AR) of ‘toe-out’ delta winglets is subjectively kept equal to unity and they are placed with the most widely studied conservative attack angle of 15 to pursue the optimization of location w.r.t. tube centre [4,10,15,26]. 2. Experimental apparatus Experiments were conducted on the existing in-house experimental facility [13] to validate the preliminary (single tube) numerical model. The preliminary model is validated only to cut down the cost of the experiments, which was later extended (as per Section 3) for the numerical optimization of the winglet's location in a three rows inline aligned fin and tube heat exchanger. Quantities being measured were local temperature distribution in the fin and the pressure drop across the heat exchanger. The test section of the wind tunnel has a cross-section of 300 300 mm2 and its schematic is shown in Fig. 1. Air flow in the tunnel was maintained by a variable speed induced draft axial flow fan. Heat exchanger prototype being tested was made from flat aluminium fins fitted centrally but tightly on a thick walled copper tube as shown in Fig. 2(a). Dimensions of the said prototype were as follows: tube's external diameter (D), tube's effective length, fin pitch, fin thickness, fin length and fin width were 38.1 mm, 300 mm, 13 mm, 1 mm, 210 mm and 300 mm respectively. Copper tube was heated by the resistance heating element housed in it. Temperature distribution was measured in only one of the fins, which was placed at the middle of the tube length; and rest of the fins were meant to maintain the flow periodicity in the normal direction of the flow. The fin under study was constructed by joining two aluminium sheets as a sandwich with embedded thermocouples to obtain the temperature distribution in the fin. A total of sixteen T-type thermocouples (0.2 mm core) were embedded symmetrically in the grooves (around the tube in a rectangular array) cut in the fin. Spatial locations of all the thermocouples and schematic of the fin are shown in Fig. 2(b). A thermally conducting (silicone) gel was applied at all the locations of temperature measurement to limit the error due to the contact resistance between the thermocouple junction and the fin. Tube wall temperature was measured by the thermocouple attached to its wall and the temperature of the far field upstream air was measured by a resistance temperature detector. Temperature was measured with a resolution of ±0.1 C and maximum statistical uncertainty in the measurement of local excess temperature was ±9.35% with the confidence level of 95.45%. Far field upstream mean flow velocity was measured by the Thermal velocity probe (Testo 435®), which had a resolution of 0.01 m/s and maximum statistical uncertainty of ±3.25% with the confidence level same as for temperature measurement. The static pressure drop across the heat exchanger was measured by the digital differential pressure meter (Testo 512®). Resolution of the said pressure meter and maximum statistical uncertainty in the pressure
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Fig. 1. Schematic of experimental set-up.
drop measurement were 0.1 Pa and ±9.61% respectively. It is always recommended to repeat the experiments to ensure the reliability of the results. Such an exercise is called ‘repeatability test’. The results of the repeatability test of apparent friction factor over a range of
Reynolds number obtained from two different test runs are shown in Fig. 3. 3. Model description & mathematical formulation 3.1. Computational domain Schematic of the fins of three rows inline modified fin and tube heat exchanger is shown in Fig. 4. Dimensions of the said heat exchanger are as follow: tube's external diameter (D) is 38.1 mm, fin pitch is 13 mm, fin thickness is 1 mm, transverse and longitudinal pitches of the tubes (i.e. PT & PL) are 2.6D, attack angle (a) of the delta winglets is 15 and height of the winglets is same as the fin spacing. Array of all the possible locations of winglets modelled in this numerical study are discussed in Section 4. The winglets are modelled as adiabatic bodies to restrict heat transfer augmentation only due to the enhanced turbulence, and the thickness of the winglets is kept same as the fins. Only a spanwise symmetric section of the periodic fin-space (with half fin thickness) is modelled to restrict the computational expense of the simulation as shown in Fig. 5. The computational domain is extended by 10H and 30H at the inlet and the exit to allow the application of uniform velocity and outflow boundary conditions respectively [24,27,28]. In the presence of the extended regions at the inlet and the exit, computational domain is constituted by three major regions viz. upstream, downstream and fin-tube region.
Fig. 2. (a) Fin and tube heat exchanger prototype. (b) Array of thermocouples in the fin under study.
Fig. 3. Repeatability of apparent friction factor (fapp).
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Transport equations for Turbulent kinetic energy (k) and dissipation rate (ε):
3.2. Governing equations and boundary conditions Flow through the computational domain was assumed steady turbulent, incompressible with no viscous dissipation, and was simulated by solving the three dimensional continuity, momentum (RANS) and energy equations. By virtue of small change in the bulk temperature of the air over the fin length, its thermo-physical properties were assumed constant. The effect of the turbulence on the mean flow was modelled by using the famous RNG (keε) turbulence model, as it is well suited for wall bounded turbulent flows [27,29,30]. Buoyancy effects were neglected by virtue of the Richardson number being smaller than 0.1. Temperature distribution in the fins was predicted by solving fluidesolid conjugate heat transfer problem at the fluidesolid interface, solid was assumed isotropic, and the thermal contact resistance between the tube and the fins is modelled as a hypothetical conduction resistance. The tube wall was assumed to be at constant temperature [4,5,22e24,29], and rests of all the relevant boundary conditions are mentioned below. For the convenience of the readers, most of the boundary conditions are also shown in the figure depicting the schematic of the computational domain (Fig. 5). Governing equations with indexed notations are shown below: Continuity equation:
(1)
" !# v rui uj vp v vui vuj 2 vuk v ru0i u0j ¼ þ þ dij m þ vxj vxi vxi vxj vxi 3 vxk vxi (2) Reynolds stress term is the above equation is calculated using ‘Boussinesq’ hypothesis as follows,
ru0i u0j ¼ mt
vui vuj þ vxj vxi
2 vu rk þ mt k dij 3 vxk
(3)
(6)
1. Upstream (fluid inlet) region Inlet boundary
u ¼ const;
v ¼ w ¼ 0;
T ¼ const
Turbulent intensity at the flow inlet is prescribed as per the correlation suggested in the literature [27,30]. Upper & lower boundaries
Uup ¼ Udown ;
Tup ¼ Tdown
Front & back boundaries
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
2. Downstream (fluid exit) region Upper & lower boundaries
Uup ¼ Udown ;
Tup ¼ Tdown
Front & back boundaries
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
vu vv vw vT ¼ ¼ ¼ ¼0 vx vx vx vx 3. Fin & tube region Upper & lower boundaries
u ¼ v ¼ w ¼ 0;
(4)
where ‘E’ is the total energy and keff is the effective thermal conductivity.
Tup ¼ Tdown
DVG surface
u ¼ v ¼ w ¼ 0;
Energy equation:
v½ui ðrE þ pÞ v vT keff ¼ vxi vxi vxi
v v vε ε ε2 aε meff þ C1ε mt S2 C2ε r Rε ðrεui Þ ¼ vxi vxi vxi k k
Exit boundary
Momentum (RANS) equation:
!
(5)
where (ak and aε) are inverse effective Prandtl numbers for (k and ε) respectively, (S) is the modulus of the mean rate of strain tensor, (mt) is turbulent (or eddy) viscosity, (meff) is effective viscosity, (C1ε, C2ε) are model constants and (Rε) is the rate of strain term. Refer [27,29,30] for the definition/value of these terms/constants. Boundary conditions in the three major regions of the computational domain of three rows inline aligned finned tube heat exchanger are defined below. The term ‘Front boundary’ refers to the boundary falling on the plane passing through the tube centre i.e. at Z ¼ 0, and the term ‘Back boundary’ refers to the boundary falling on the plane at Z ¼ 0.5 PT.
Fig. 4. Fins of modified fin and tube heat exchanger.
vðrui Þ ¼0 vxi
v v vk ak meff þ mt S2 rε ðrkui Þ ¼ vxi vxi vxi
vT ¼0 vn
Front & back boundaries of the fluid
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
Front & back boundaries of the fin
333
Fig. 5. Computational domain.
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A. Arora et al. / Applied Thermal Engineering 82 (2015) 329e340
u ¼ v ¼ w ¼ 0;
vT ¼0 vz
Tube surface
u ¼ v ¼ w ¼ 0;
T ¼ const:
3.3. Numerical method & grid independence Commercial CFD code ANSYS Fluent 14.0 was used to solve the governing equations in conjunction with boundary conditions. Computational domain was created by using GAMBIT 2.2.3 as the pre-processor. The computational domain was split into several sub-domains to control the quality of the mesh. The upstream and the downstream extended regions were meshed with hexahedral elements, and rest of the domain was meshed with hex-wedge elements. Near-wall regions were resolved through the Enhanced wall treatment [30], which demands placing the wall adjacent nodes at yþ value less than unity. The wall effects of the fins and the tubes were resolved by generating graded mesh in the direction normal to the wall as shown in Fig. 6. Periodic surfaces were appropriately linked before applying the periodic boundary condition. Finite volume method was used for the discretization of the governing equations. Coupling between the velocity and pressure is done through the SIMPLE algorithm, and convective terms in the governing equations are discretized by the second order upwind scheme [27,30]. Convergence was concluded on the basis of two criterion viz. magnitude of the normalized residuals of the governing equations as well as the net imbalance in the mass and heat transfer rates. Order of normalized residuals of the energy equation and rest of the equations at convergence were 108 and 105 respectively; and net imbalance in the mass and heat transfer rates was 0.02%. An iterative grid independence test was carried out to choose the mesh density. As the difference in results obtained from the highest and the second highest mesh densities was less than 1.5%, so the second highest mesh density was chosen, which had approximately 45.9 105 and 45.7 105 mesh volumes in the computational domains of the plain and the modified single tube heat exchangers respectively. Simulated performances of the plain heat exchanger with three different mesh densities at the highest Reynolds number are tabulated in Table 1.
computational domain [4,5,22e24,29]. This work attempts to first time model the said contact resistance as a hypothetical conduction resistance, whose thermal resistance is varied by changing the thermal conductivity in discrete steps until the ‘Root mean squared’ error in the predicted local fin temperatures attains minima (Fig. 7). When the contact resistance between the fins and the tube wall was ignored, r.m.s. error in the local fin temperatures of the plain fin was 7.02 C at the Reynolds number of 4245. Modelling of the said contact resistance has helped in reducing the r.m.s. error to 1.51 C. This act of reducing the error in temperature distribution based on the minimization of r.m.s. error may be addressed as the tuning of the numerical model. Later, experimental validation of the tuned model was carried out based on the dimensionless local excess temperature of the plain fin at the highest Reynolds number; and apparent friction factor over the Reynolds number range from 1415 to 7075 (Fig. 8). The corresponding far field upstream air velocity range was from 1 to 5 m/s. It is found that the r.m.s. error in the temperatures of the plain fin was 1.57 C at the highest Reynolds number. Also, it is evident that the numerically predicted apparent friction factor is always smaller than the actual over the whole range of Reynolds number. After validating the preliminary model, the same model was later extended for pursuing the numerical study of the three rows inline aligned finned tube heat exchanger, which was aimed at optimizing the location of ‘common flow up’ delta winglets for the maximum augmentation of the heat transfer.
3.5. Parameter definitions Heat transfer coefficient and the pressure drop across the heat exchanger can be defined in the non-dimensional forms by the Nusselt number (Nu), Colburn's factor (j) and the apparent friction factor (fapp). The characteristic dimension for defining the Reynolds number (Re) and Nusselt number is taken as twice the fin-space [8,12]. Far field upstream uniform inlet flow velocity is taken to define the Reynolds number. Local fin temperature (Tf) is expressed as the dimensionless excess temperature (q*), which is the ratio of local excess temperature on the fin (qf) and excess temperature on the tube wall (qtube). Definitions of the relevant dimensionless parameters are given below:
Re ¼
r Lc U∞ ; m
Nu ¼
h Lc ; kf
3.4. Tuning & validation of numerical model Numerical studies in the past have ignored the thermal contact resistance between the fins and tube wall while modelling the
j¼
q ¼
2 h Pr 3 ; rU∞ Cp
=
334
f app ¼
qf T T∞ ¼ f qtube Ttube T∞
Fig. 6. Graded mesh for resolving the wall effects (a) Fins. (b) Tube.
2$Dp Amin $ rU2∞ Ao
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Table 1 Grid independence test. Mesh volumes
53.7 105
45.9 105
35.5 105
Nu Dp (Pa)
47.51 11.53
47.07 11.41
45.43 11.22
where U∞ is the free-stream flow velocity (m/s), Lc is the characteristic dimension of the channel (m), Amin is the minimum flow area of the channel (m2), Ao is the total heat transfer area of the channel (m2), Dp is the pressure drop across the heat exchanger (Pa) and h is the average heat transfer coefficient (W/m2 K). 4. Numerical results & discussions Selection of all promising locations of the ‘common flow up’ delta winglets precedes the task of identification of the optimal location that allows maximum thermal compactness of the heat exchanger. Selection of all promising locations is done numerically by modelling the winglets at all possible locations in the rectangular fin lamina around the tube. The extends of the said lamina are determined from the maximum order of the longitudinal & transverse tube pitches recommended in the literature [2,31]. A total of twenty discrete locations of the delta winglets were possible to model in the solution domain as shown in Fig. 9. The locations in the said figure represent the position of the trailing edge of the winglets. Array of all the possible locations of the winglets was created such that the nearest location in the streamwise and the spanwise direction is at 0.1D from the tube centre, and the successive locations were created at discrete steps of 0.2D in both the directions. The effect of the winglets on the change in thermal performance of the fin is characterized in terms of the ‘Scaled Colburn's factor’ (SCF), which is defined as the ratio of the Colburn's factor of the fin with and without winglets (jVG/jO). A given location of the delta winglet was treated promising when the ‘Scaled Colburn's factor’ (SCF) was greater than the unity. After numerically solving the flow with all physically possible locations of the winglets, locations with serial numbers (1e17) are identified as the promising and locations with serial numbers (aec) are identified as the counter-productive ones (Fig. 9). Optimization of the location that allows maximum thermal compactness of the heat exchanger is accomplished by plotting the scaled Colburn's factor (SCF) of all promising locations against the location number and the scaled friction factor (SFF) as shown in Fig. 10(a) and (b) respectively. It is found that the relation between the Colburn's factor (SCF) and the friction factor (SFF) of all promising locations of DVG is best described by the second order
Fig. 7. Minimization of r.m.s. error in fin temperature for tuning of numerical model.
Fig. 8. Validation of numerical model (a) Non-dimensional local excess temperature of the fin. (b) Apparent friction factor.
polynomial fit. It is also evident from the said figure that each promising location is delivering different augmentation of the thermal performance. Further, it is observed that though a correlation between SCF & SFF do exists but the R-squared value of the said correlation is small, which can be attributed to the large scatter in the plot. The R-squared value is found to improve dramatically from 0.66 to 0.93, when the location with the highest SCF among all the locations with closely scattered friction factors is retained and discarding the rest (Fig. 10(c)). Fitting a second order polynomial correlation to the SCF & SFF of such selected locations result in a drooping curve with a maxima for the SCF. The winglet's location that delivers maximum SCF bears serial number (12) and the coordinates of this location in the plane of the fin are (x ¼ 0.1D, z ¼ ±0.9D) w.r.t. tube centre. The ‘Common flow up’ delta winglets at this optimal location are expected to modify the mean flow such
Fig. 9. Array of all possible and promising locations of winglets.
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why the ‘toe-out’ orientation of a delta winglet pair is also called ‘common upwash’ configuration. The swirling (or secondary) flow created by the longitudinal vortices facilitates bulk mixing of the fluid in the core and near wall regions. The said flow modification results in the disruption of the thermal boundary layer on the confining walls, and consequently causes dramatic rise in the heat transfer coefficients. The velocity vectors of the secondary flow created by each winglet are drawn on the planes at five discrete streamwise locations ‘X’ w.r.t. tube centre as shown in Fig. 11. The coordinates of the five planes are 0.2D, 0.5D, 0.8D, 1.1D and 1.5D from the tube centre. This figure also shows the enlarged view of the velocity vectors on the planes at X ¼ 0.2D, 0.8D and 1.5D for better appreciation of the flow structures. It is evident from the figure that each winglet is essentially shedding two vortices, namely the main vortex and the corner vortex. The main vortex is generated due to the flow separation at the leading edge of the winglet whereas the mechanism of corner vortex generation is similar to the horse shoe vortex generated in case of flow over a cylinder. The corner vortex is generated at the junction between the fin and the stagnation line on the pressure side of the winglet. The corner vortex first wraps around the winglet and later travels with the main flow. Both the vortices accompany the main flow after the trailing edge of the winglet to travel in the streamwise direction, but the strength of these vortices decreases in the direction of the flow. It is evident from the figure that both the vortices are vanishing in the direction of the flow, which is attributed to the viscous dissipation. The direction of rotation of the main vortex generated by the left winglet is anti-clockwise when seen from the side from which flow is entering the finspace, and the corner vortex rotates in the direction opposite to the main vortex which is clockwise. In contrast, direction of rotation of the main and corner vortex generated by the right winglet is clockwise and anti-clockwise respectively. The secondary flow created by the winglets displaces the fluid in the transverse direction, hence facilitates contraction of the tube wake due to the momentum transfer and improves the heat transfer coefficients in the wake region. 4.2. Effect on fin temperature
Fig. 10. (a) Thermal performance augmentation by all promising locations of DVG. (b) R-squared value of correlation for all promising locations. (c) R-squared value of correlation for selected promising locations.
that the heat transfer on the fin side of the heat exchanger will undergo maximum augmentation. A discussion on the modification of the flow structure and the consequent heat transfer augmentation due to the incorporation of winglets at the said optimal location is narrated below.
4.1. Effect on flow structure A discussion on the modification of the mean flow structure due to the optimally located winglet becomes inevitable because the augmentation of heat transfer resulted due to the vortices generated by the winglets. The pressure difference across the ‘common flow up’ delta winglets cause intentional generation of two corotating longitudinal (or streamwise) vortices due to the flow separation at the leading edge of the winglets. The fluid confined between the two vortices is washed away from the fin, which is
Temperature of the plain and modified fins is plotted along the lines at discrete spanwise and streamwise locations to appreciate the favourable effect of the winglets. The winglets were placed at above identified optimal location. The locations of the said lines on the fin are shown in Fig. 12. It can be easily appreciated from Figs. 13 and 14 that presence of the winglets at the identified optimal location has helped in cooling down the fin (in both streamwise and spanwise directions). The figures are superimposed with the rectangles showing the location and diameter of the tubes. Fig. 13 also shows that the fin temperature along the streamwise line close to the tubes is experiencing oscillations of higher amplitude compared to the fin temperature away from the tubes. This oscillating behaviour of temperature distribution is attributed to the varying fin length in the radial direction (i.e. radial distance between the tube wall and the points falling on the streamwise line) available for the conduction heat transfer. Further inspection of Fig. 14 tells that the winglets at the said optimal location are delivering same order of drop in the fin temperature in the downstream of each tube. 4.3. Effect on heat transfer coefficient Positive effect of said delta winglets on the improvement in thermal performance of the fin can be recognized by plotting the Nusselt number. Fig. 15 shows the scaled Nusselt number (NuVG/ NuO) of the upper fin face in the streamwise direction at Re ¼ 4245.
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Fig. 11. Velocity vectors of secondary flow in the downstream of ‘toe out’ delta winglet.
Spanwise symmetric section of the modified fin is aligned with the plot for better appreciation of the variation in the Nusselt number. Scaling of the Nusselt number is done w.r.t. plain fin, and the Nusselt number is averaged over the span. The scaled Nusselt number being greater than unity is treated as the improvement in the thermal performance of the fin. As evident from the figure, scaled Nusselt number is either greater than or equal to unity over the whole fin length, which clearly implies that the presence of winglets at the identified optimal location has helped in augmenting average Nusselt number of the fin at the same Reynolds number. Further careful inspection of the figure tells that the distribution of the Nusselt number in the streamwise direction upto the leading point of the leading winglet pair is almost same for the plain and the modified fins. Later, the scaled Nusselt number distribution exhibits periodically occurring three sharp peaks, one adjacent to each tube, where each peak is succeeded by a small hump. Magnitude of the peaks is observed to be gradually decreasing in the flow direction, but nevertheless is always greater than the unity. Each pair of the sharp peak and the small hump is attributed to the turbulence imparted due to the combined effect of the acceleration and deceleration of the flow through the nozzle like constricted passage created by the combination of tube aft surface and the winglet pair, and formation of the complex three dimensional vortex system behind each winglet pair. The said vortex system is primarily constituted by two co-rotating longitudinal
vortices. These longitudinal vortices facilitate better fluid mixing, and augment local heat transfer coefficients by modifying the thermal boundary layer. Maximum increase in the span averaged Nusselt number is 60.4% whereas increase at the trailing edge of the fin is 9% at Re ¼ 4245. In nutshell, average Nusselt number of the upper fin side and the three tubes increased by 17.8%, 1.6%, 7.8% and 13.1% respectively. 4.4. Effect on bulk temperature rise Augmentation of the heat transfer coefficients on the surfaces of the fin and the tubes should result in more convective heat transfer from the same surface area on the gas side, when operating constraints are fixed. Increase in the net heat transfer will lead to increase in the bulk temperature rise (i.e. qb, x ¼ Tb,x T∞) on the gas side. The bulk temperature rise of the modified heat exchanger can also be expressed as a scaled value (qb,VG/qb, O), where scaling is done w.r.t. the plain fin. It is evident from Fig. 16 that the bulk temperature rise in the streamwise direction upto the leading point of the leading winglet pair is almost same for the plain and the modified fins. Later, the scaled bulk temperature rise is undergoing a stair-case increase (at every successive winglet pair) in the flow direction due to the incorporation of the optimally located delta winglets. Maximum increase in the mass averaged bulk temperature rise is 9.7% whereas increase at the trailing edge of the fin is 9.4% at Re ¼ 4245.
Fig. 12. Arrangement of lines in streamwise and spanwise directions for computing fin temperature.
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Fig. 15. Span averaged scaled Nusselt number of upper fin face.
5. Conclusions
Fig. 13. Fin temperature in streamwise direction at Re ¼ 4245 (a) At Z ¼ 25 mm. (b) At Z ¼ 45 mm.
A three dimensional numerical study was performed to optimize the location of ‘common flow up’ delta winglets in an inline aligned fin and tube heat exchanger. Also, a single tube heat exchanger prototype was fabricated to experimentally validate the numerical model over the Reynolds number range from 1415 to 7075. The effect of the turbulence was modelled by RNG (keε) model and the temperature distribution in the fins was predicted by solving fluidesolid conjugate heat transfer problem. This numerical study also attempts to first time model the thermal contact resistance between the tube and the fins, which is modelled as a hypothetical conduction resistance. Modelling of the said contact resistance has helped in reducing the r.m.s. error in the fin
Fig. 14. Fin temperature in spanwise direction at Re ¼ 4245 (a) At X ¼ 75 mm. (b) At X ¼ 175 mm. (c) At X ¼ 125 mm. (d) At X ¼ 225 mm.
A. Arora et al. / Applied Thermal Engineering 82 (2015) 329e340
Fig. 16. Scaled bulk temperature rise of coolant in streamwise direction.
temperature from 7.02 C to 1.51 C. A total of twenty locations of the winglets were simulated. The effect of the winglets on the change in the thermal performance of the fin is quantified as ‘Scaled Colburn's factor’ (SCF), which is defined as the ratio of the Colburn's factor of the fin with and without winglets (jVG/jO). A given location with SCF greater than the unity was treated promising. Starting from identifying all the promising locations, location that allowed maximum augmentation of heat transfer coefficient is identified as optimal for the maximum thermal compactness of the heat exchanger. The major conclusions drawn from this study are summarized below: 1. Out of the twenty possible locations, seventeen were found to be promising and the rest three turn out to be counter-productive. It is observed that each promising location is delivering different augmentation of the thermal performance. The relation between the Colburn's factor and friction factor of all promising locations of DVG is best described by the second order polynomial fit. The coordinates of winglet's location that delivers maximum augmentation of heat transfer in the plane of the fin are (x ¼ 0.1D, z ¼ ±0.9D) w.r.t. tube centre. 2. Velocity vectors of the secondary flow created by the winglet reveals that each winglet is shedding two vortices, namely the main vortex and the corner vortex. Both the vortices are observed to be vanishing in the direction of the flow, which is attributed to the viscous dissipation. 3. Decaying fin temperature in both streamwise and spanwise directions clearly reflects improved heat transfer from the fin at the same Reynolds number. Likewise, distribution of the scaled Nusselt number of the fin over whole flow length also shows that presence of winglets at the optimal location has helped in augmenting average Nusselt number of the fin at the same Reynolds number. Maximum increase in the span averaged Nusselt number is 60.4% at Re ¼ 4245. Acknowledgement The authors thank the Mechanical Engineering department of the Indian Institute of Technology, Delhi, India for financially supporting this work. Nomenclature AR cp D
aspect ratio, 2H/L specific heat (kJ/kg C) tube diameter (m)
DVG fapp h H j k kf LVG L Lc Nu Dp PL PT Pr Re SFF SCF T Tf Ttube T∞ Tw U∞ u, v, w VG X Y Z
339
delta winglet vortex generator apparent friction factor heat transfer coefficient (W/m2 K) fin-space or height of DVG Colburn's factor turbulent kinetic energy (m2/s2) thermal conductivity of fluid (W/m K) longitudinal vortex generator length of DVG (m) characteristic length (m) Nusselt number pressure drop (Pa) longitudinal tube pitch (m) transverse tube pitch (m) Prandtl number Reynolds number f VG scaled friction factor, app; fapp;o scaled Colburn's factor, jjVG O temperature ( C) fin temperature ( C) tube temperature ( C) far upstream air temperature ( C) tube wall temperature ( C) far upstream air velocity (m/s) x, y, z velocity components (m/s) vortex generator coordinate in streamwise direction coordinate normal to the fin coordinate in spanwise direction
Greek symbols a attack angle ( ) ε turbulent energy dissipation rate (m2/s3) r density (kg/m3) q* non-dimensional excess temperature qb bulk mean temperature rise ( C)
References [1] F. Incropera, D. Dewitt, Fundamentals of Heat and Mass Transfer, fifth ed., Wiley, 2006. [2] R.L. Webb, N.H. Kim, Principles of Enhanced Heat Transfer, second ed., Taylor & Francis, New York, 2005. [3] A.M. Jacobi, R.K. Shah, Heat transfer surface enhancement through the use of longitudinal vortices: a review of recent progress, Exp. Therm. Fluid Sci. 11 (1995) 295e309. [4] A. Joardar, A.M. Jacobi, A numerical study of flow and heat transfer enhancement using an array of delta-winglet vortex generators in a fin-andtube heat exchanger, J. Heat Transfer 129 (2007) 1156e1167. [5] A. Jain, G. Biswas, D. Maurya, Winglet-type vortex generators with commonflow-up configuration for fin-tube heat exchangers, Numer. Heat Transfer Part A 43 (2003) 201e219. [6] M. Fiebig, Embedded vortices in internal flow: heat transfer and pressure loss enhancement, Int. J. Heat Fluid Flow 16 (1995) 376e388. [7] M. Fiebig, A. Valencia, N.K. Mitra, Wing-type vortex generators for fin-andtube heat exchangers, Exp. Therm. Fluid Sci. 7 (1993) 287e295. [8] K. Torii, K.M. Kwak, K. Nishino, Heat transfer enhancement accompanying pressure-loss reduction with winglet-type vortex generators for fin-tube heat exchangers, Int. J. Heat Mass Transfer 45 (2002) 3795e3801. [9] P. Chu, Y.L. He, Y.G. Lei, L.T. Tian, R. Li, Three-dimensional numerical study on fin-and-oval-tube heat exchanger with longitudinal vortex generators, Appl. Therm. Eng. 29 (2009) 859e876. [10] A. Pal, D. Bandyopadhyay, G. Biswas, Enhancement of heat transfer using delta-winglet type vortex generators with a common-flow-up arrangement, Numer. Heat Transfer Part A (2012) 37e41. [11] C.S. Subramaniam, P.M. Ligrani, M.F. Tuzzolo, Surface heat transfer and flow properties of vortex arrays induced artificially and from centrifugal instabilities, Int. J. Heat Fluid Flow 13 (1992) 210e223. [12] K.M. Kwak, K. Torii, K. Nishino, Simultaneous heat transfer enhancement and pressure loss reduction for finned-tube bundles with the first or two transverse rows of built-in winglets, Exp. Therm. Fluid Sci. 29 (2005) 625e632.
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[13] S.M. Pesteei, P.M.V. Subbarao, R.S. Agarwal, Experimental study of the effect of winglet location on heat transfer enhancement and pressure drop in fin-tube heat exchangers, Appl. Therm. Eng. 25 (2005) 1684e1696. [14] Y. Lei, Y. He, L. Tian, P. Chu, W. Tao, Hydrodynamics and heat transfer characteristics of a novel heat exchanger with delta-winglet vortex generators, Chem. Eng. Sci. 65 (2010) 1551e1562. [15] A. Joardar, A.M. Jacobi, Heat transfer enhancement by winglet-type vortex generator arrays in compact plain-fin-and-tube heat exchangers, Int. J. Refrig. 31 (2008) 87e97. [16] J.Y. Jang, L.F. Hsu, J.S. Leu, Optimization of the span angle and location of vortex generators in a plate-fin and tube heat exchanger, Int. J. Heat Mass Transfer 67 (2013) 432e444. [17] J.S. Leu, Y.H. Wu, J.Y. Jang, Heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with a pair of block shape vortex generators, Int. J. Heat Mass Transfer 47 (2004) 4327e4338. [18] H. Huisseune, C. T'Joen, P.D. Jaeger, B. Ameel, S.D. Schampheleire, M.D. Paepe, Influence of the louver and delta winglet geometry on the thermal hydraulic performance of a compound heat exchanger, Int. J. Heat Mass Transfer 57 (2013) 58e72. [19] K.M. Kwak, K. Torii, K. Nishino, Heat transfer and pressure loss penalty for the number of tube rows of staggered finned-tube bundles with a single transverse row of winglets, Int. J. Heat Mass Transfer 46 (2003) 175e180. [20] V. Prabhakar, G. Biswas, V. Eswaran, Numerical prediction of heat transfer in a channel with a built-in oval tube and two different shaped vortex generators, Numer. Heat Transfer Part A 41 (2002) 307e329. [21] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a channel with longitudinal vortex generator. Part B: parametric study of major influence factors, Int. J. Heat Mass Transfer 51 (2008) 3683e3692.
[22] Y. He, P. Chu, W. Tao, Y. Zhang, T. Xie, Analysis of heat transfer and pressure drop for fin-and-tube heat exchangers with rectangular winglet-type vortex generators, Appl. Therm. Eng. 61 (2013) 770e783. [23] Y. Chen, M. Fiebig, N. Mitra, Conjugate heat transfer of a finned oval tube with a punched longitudinal vortex generator in form of a delta winglet-parametric investigations of the winglet, Int. J. Heat Mass Transfer 41 (1998) 2850e2867. [24] Y. He, H. Han, W. Tao, Y. Zhang, Numerical study of heat-transfer enhancement by punched winglet-type vortex generator arrays in fin-and-tube heat exchangers, Int. J. Heat Mass Transfer 55 (2012) 5449e5458. [25] M. Zeng, L.H. Tang, M. Lin, Q.W. Wang, Optimization of heat exchangers with vortex-generator fin by Taguchi method, Appl. Therm. Eng. 30 (2010) 1775e1783. [26] A. Sinha, K. Ashoke Raman, H. Chattopadhyay, G. Biswas, Effects of different orientations of winglet arrays on the performance of plate-fin heat exchangers, Int. J. Heat Mass Transfer 57 (2013) 202e214. [27] L. Tian, Y. He, Y. Tao, W. Tao, A comparative study on the air-side performance of wavy fin-and-tube heat exchanger with punched delta winglets in staggered and in-line arrangements, Int. J. Therm. Sci. 48 (2009) 1765e1776. [28] J.M. Wu, W.Q. Tao, Investigation on laminar convection heat transfer in finand-tube heat exchanger in aligned arrangement with longitudinal vortex generator from the viewpoint of field synergy principle, Appl. Therm. Eng. 27 (2007) 2609e2617. [29] M. Gorji, H. Mirgolbabaei, A. Barari, G. Domairry, N. Nadim, Numerical analysis on longitudinal location optimization of vortex generator in compact heat exchangers, Int. J. Numer. Methods Fluids 66 (2011) 705e713. [30] FLUENT Incorporated, FLUET 6.2 User's Guide, Fluent Incorporated Lebanon, NH, USA, 2004. [31] W.M. Kays, A.L. London, Compact Heat Exchangers, McGraw-Hill, New York, 1994.
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Research paper
Numerical optimization of location of ‘common flow up’ delta winglets for inline aligned finned tube heat exchanger Amit Arora*, P.M.V. Subbarao, R.S. Agarwal Department of Mechanical Engineering, Indian Institute of Technology, Delhi, India
h i g h l i g h t s Optimal location of winglets for maximum thermal compactness of the heat exchanger. Optimal location has helped in cooling down the fin. Augmentation of average Nusselt number of the fin at the same Reynolds number. Magnitude of the Nusselt number peaks is gradually decreasing in the flow direction.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2014 Accepted 24 February 2015 Available online 5 March 2015
Heat transfer augmentation of a fin and tube heat exchanger by the winglet type vortex generator strongly depends on the location of the winglet w.r.t. tube centre. This study was aimed at optimizing the location of the ‘common flow up’ delta winglets for the maximum thermal compactness of a given inline aligned fin and tube heat exchanger. The winglets were erected with a conservative attack angle to avoid severe increase in the pressure drop. This work also attempts to first time model the contact resistance between the fins and the tube as a hypothetical conduction resistance. Beginning with the selection of all promising locations of the winglets, an optimal location was identified that allows maximum augmentation of the thermal performance on the fin side. This numerical study clearly shows that the optimally located ‘common flow up’ delta winglets have improved the average thermal performance of both the fins and the tubes at the same Reynolds number. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Delta winglets Optimal location Thermal compactness Finned tube heat exchanger
1. Introduction Finned tube heat exchangers find wide applications in the areas like process heat transfer, air conditioning, automobiles etc. In these exchangers, the fin side is cursed with high thermal resistance by virtue of low heat transfer coefficients [1,2]. Enhancement of heat transfer coefficients on the fin side is crucial to the compact design of such heat exchangers. Methods for improving heat transfer on the fin side can be classified as active, passive or compound [2,3]. Employing longitudinal vortex generators (LVGs) on the fin side is one of the widely studied passive enhancement technique. The longitudinal vortices shed by the LVG(s) constitute three dimensional swirling flows that facilitate better mixing of the cold and the hot fluid by destabilizing the flow, and result in the boundary layer modification [4,5]. The secondary flow created
* Corresponding author. Tel.: þ91 9250272551. E-mail address: [email protected] (A. Arora). http://dx.doi.org/10.1016/j.applthermaleng.2015.02.071 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
by the vortices disrupts the thermal boundary layer, and consequently causes augmentation of the local heat transfer coefficients on the fin. Initially, the longitudinal vortices were used for boundary layer control, but later they were extensively studied for modifying the flows in the plain channels and for the thermal management of the tube wakes in the fin-and-tube heat exchangers [3,6e8]. The LVG(s) can be of two types, the wings and the winglets [6]. The thermo-hydraulic performance of the winglets is better than the wing type vortex generators [9]. Heat transfer enhancement due to the secondary flow generated by the vortices is effective when the winglets are erected in pairs. Literature recommends that the delta winglets vortex generators (DVG) are found to be more effective than the rectangular winglets for improving heat transfer. Based on the orientation, a DVG pair can be classified as ‘common flow down’ and ‘common flow up’ configuration [8,10,11]. These two configurations are also addressed as ‘toe-in’ and ‘toe-out’ or ‘common downwash’ and ‘common upwash’ respectively [11,12]. For the thermal
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management of tube wake, DVG(s) in ‘common flow down’ configuration are characteristically placed as a pair behind the tube with the transverse distance between the leading edges smaller than the trailing edges [13,14] whereas the ‘common flow up’ configuration calls for placing them adjacent to the tube with the transverse distance between the trailing edges being smaller than the leading edges [10,14]. The longitudinal vortices generated by DVG(s) in ‘common flow down’ configuration displace the fluid in the direction normal to the flow, thereby facilitate contraction of the tube wake due to the momentum transfer and improves the heat transfer coefficients in the wake region. In contrast, apart from displacing the fluid in the normal direction, acute angle made by the ‘common flow up’ configuration with the upstream flow makes it kinematically different from the ‘common flow down’ configuration, because such an orientation of winglets guides the accelerated upstream flow in the tube's recirculation region [4], which helps in imparting large motion to the fluid with otherwise low mobility. A lot of work has been reported so far on the winglets with ‘common flow down’ configuration, but lately ‘common flow up’ configuration is emerging as another lucrative configuration for the thermal management of the tube wakes in the fin-and-tube heat exchangers [5,8,10,12,14]. Experimental study [12] compared the heat transfer enhancement by ‘toe-out’ delta winglets in an inline and staggered finned tube bank. It was reported that compared to the single row of winglets in the staggered tube bank, two rows arrangement increased the heat transfer by 6e15% and pressure loss by 61e117% over the range of Reynolds number being studied. Corresponding increase for inline tube bank were 7e9% and 3e9% respectively. Another experimental study [15] reported that increasing the number of ‘common flow up’ winglet rows yield better heat transfer performance; but also results in higher friction factor, which was found to decrease rapidly with increasing Reynolds number. Similar study about the effect of the number of ‘common flow up’ winglet rows on thermal performance of an inline finned tube heat exchanger was pursued numerically [4], and similar conclusions were drawn. Effect of the attack angle of the winglets on a fin and tube heat exchanger was studied numerically [10,14,16e18] and it was reported that both heat transfer coefficient and friction factor are the direct functions of the attack angle, but increasing the attack angle causes much faster increase in friction factor compared to the heat transfer. Experimental study [19] investigated the effect of the number of tube rows on thermal and hydraulic performances of a finned staggered tube bundle in the presence of ‘common flow up’ delta winglets behind the leading tube only. It was reported that the scaled Colburn's factor is almost independent of the tube rows. Numerical study [20] found that increase in the thermal performance of a finned oval tube heat exchanger is the direct function of the attack angle of ‘toe-in’ winglets, and the delta winglets are found to deliver better thermal performance than the rectangular winglets. Effect of the shape of longitudinal vortex generators on the thermal and hydraulic performance in a channel flow was investigated numerically [21]. This study reported that when the area of LVG is fixed, delta winglets are found to be more effective than the rectangular winglets for improving the heat transfer. Numerical investigation [22] reported that both heat transfer coefficient and pressure loss of an inline finned tube heat exchanger are the direct functions of attack angle and number of rows of ‘toe-out’ winglets. It is also stated that the attack angle leads to rapid increase in pressure loss compared to the heat transfer coefficient. While studying the effect of staggering of the winglets, it is found that the staggered arrangement of winglets delivered thermal performance same as the inline arrangement, but helped in reducing the pressure loss by 4.5e8.3% over the studied range of Reynolds number.
Placement of DVG(s) for the maximum thermal compactness of a fin-and-tube heat exchanger requires its spatial optimization. A few studies have been published regarding the optimization of the position and geometry of ‘toe-in’ configuration of delta winglets in a finned tube bank [13,23], but literature on the optimization of ‘toe-out’ configuration is inadequate. So, this study attempts to identify the optimal location of ‘toe-out’ delta winglets for the maximum augmentation of heat transfer in an inline aligned fin and tube heat exchanger. Though the literature says that the augmentation of average heat transfer coefficient is a direct function of attack angle and length of the winglets, but it is also known that the pressure loss increases much rapidly with the attack angle and the length of winglets compared to the heat transfer coefficient [10,14,22e25]. Based on these conclusions, the aspect ratio (AR) of ‘toe-out’ delta winglets is subjectively kept equal to unity and they are placed with the most widely studied conservative attack angle of 15 to pursue the optimization of location w.r.t. tube centre [4,10,15,26]. 2. Experimental apparatus Experiments were conducted on the existing in-house experimental facility [13] to validate the preliminary (single tube) numerical model. The preliminary model is validated only to cut down the cost of the experiments, which was later extended (as per Section 3) for the numerical optimization of the winglet's location in a three rows inline aligned fin and tube heat exchanger. Quantities being measured were local temperature distribution in the fin and the pressure drop across the heat exchanger. The test section of the wind tunnel has a cross-section of 300 300 mm2 and its schematic is shown in Fig. 1. Air flow in the tunnel was maintained by a variable speed induced draft axial flow fan. Heat exchanger prototype being tested was made from flat aluminium fins fitted centrally but tightly on a thick walled copper tube as shown in Fig. 2(a). Dimensions of the said prototype were as follows: tube's external diameter (D), tube's effective length, fin pitch, fin thickness, fin length and fin width were 38.1 mm, 300 mm, 13 mm, 1 mm, 210 mm and 300 mm respectively. Copper tube was heated by the resistance heating element housed in it. Temperature distribution was measured in only one of the fins, which was placed at the middle of the tube length; and rest of the fins were meant to maintain the flow periodicity in the normal direction of the flow. The fin under study was constructed by joining two aluminium sheets as a sandwich with embedded thermocouples to obtain the temperature distribution in the fin. A total of sixteen T-type thermocouples (0.2 mm core) were embedded symmetrically in the grooves (around the tube in a rectangular array) cut in the fin. Spatial locations of all the thermocouples and schematic of the fin are shown in Fig. 2(b). A thermally conducting (silicone) gel was applied at all the locations of temperature measurement to limit the error due to the contact resistance between the thermocouple junction and the fin. Tube wall temperature was measured by the thermocouple attached to its wall and the temperature of the far field upstream air was measured by a resistance temperature detector. Temperature was measured with a resolution of ±0.1 C and maximum statistical uncertainty in the measurement of local excess temperature was ±9.35% with the confidence level of 95.45%. Far field upstream mean flow velocity was measured by the Thermal velocity probe (Testo 435®), which had a resolution of 0.01 m/s and maximum statistical uncertainty of ±3.25% with the confidence level same as for temperature measurement. The static pressure drop across the heat exchanger was measured by the digital differential pressure meter (Testo 512®). Resolution of the said pressure meter and maximum statistical uncertainty in the pressure
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Fig. 1. Schematic of experimental set-up.
drop measurement were 0.1 Pa and ±9.61% respectively. It is always recommended to repeat the experiments to ensure the reliability of the results. Such an exercise is called ‘repeatability test’. The results of the repeatability test of apparent friction factor over a range of
Reynolds number obtained from two different test runs are shown in Fig. 3. 3. Model description & mathematical formulation 3.1. Computational domain Schematic of the fins of three rows inline modified fin and tube heat exchanger is shown in Fig. 4. Dimensions of the said heat exchanger are as follow: tube's external diameter (D) is 38.1 mm, fin pitch is 13 mm, fin thickness is 1 mm, transverse and longitudinal pitches of the tubes (i.e. PT & PL) are 2.6D, attack angle (a) of the delta winglets is 15 and height of the winglets is same as the fin spacing. Array of all the possible locations of winglets modelled in this numerical study are discussed in Section 4. The winglets are modelled as adiabatic bodies to restrict heat transfer augmentation only due to the enhanced turbulence, and the thickness of the winglets is kept same as the fins. Only a spanwise symmetric section of the periodic fin-space (with half fin thickness) is modelled to restrict the computational expense of the simulation as shown in Fig. 5. The computational domain is extended by 10H and 30H at the inlet and the exit to allow the application of uniform velocity and outflow boundary conditions respectively [24,27,28]. In the presence of the extended regions at the inlet and the exit, computational domain is constituted by three major regions viz. upstream, downstream and fin-tube region.
Fig. 2. (a) Fin and tube heat exchanger prototype. (b) Array of thermocouples in the fin under study.
Fig. 3. Repeatability of apparent friction factor (fapp).
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Transport equations for Turbulent kinetic energy (k) and dissipation rate (ε):
3.2. Governing equations and boundary conditions Flow through the computational domain was assumed steady turbulent, incompressible with no viscous dissipation, and was simulated by solving the three dimensional continuity, momentum (RANS) and energy equations. By virtue of small change in the bulk temperature of the air over the fin length, its thermo-physical properties were assumed constant. The effect of the turbulence on the mean flow was modelled by using the famous RNG (keε) turbulence model, as it is well suited for wall bounded turbulent flows [27,29,30]. Buoyancy effects were neglected by virtue of the Richardson number being smaller than 0.1. Temperature distribution in the fins was predicted by solving fluidesolid conjugate heat transfer problem at the fluidesolid interface, solid was assumed isotropic, and the thermal contact resistance between the tube and the fins is modelled as a hypothetical conduction resistance. The tube wall was assumed to be at constant temperature [4,5,22e24,29], and rests of all the relevant boundary conditions are mentioned below. For the convenience of the readers, most of the boundary conditions are also shown in the figure depicting the schematic of the computational domain (Fig. 5). Governing equations with indexed notations are shown below: Continuity equation:
(1)
" !# v rui uj vp v vui vuj 2 vuk v ru0i u0j ¼ þ þ dij m þ vxj vxi vxi vxj vxi 3 vxk vxi (2) Reynolds stress term is the above equation is calculated using ‘Boussinesq’ hypothesis as follows,
ru0i u0j ¼ mt
vui vuj þ vxj vxi
2 vu rk þ mt k dij 3 vxk
(3)
(6)
1. Upstream (fluid inlet) region Inlet boundary
u ¼ const;
v ¼ w ¼ 0;
T ¼ const
Turbulent intensity at the flow inlet is prescribed as per the correlation suggested in the literature [27,30]. Upper & lower boundaries
Uup ¼ Udown ;
Tup ¼ Tdown
Front & back boundaries
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
2. Downstream (fluid exit) region Upper & lower boundaries
Uup ¼ Udown ;
Tup ¼ Tdown
Front & back boundaries
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
vu vv vw vT ¼ ¼ ¼ ¼0 vx vx vx vx 3. Fin & tube region Upper & lower boundaries
u ¼ v ¼ w ¼ 0;
(4)
where ‘E’ is the total energy and keff is the effective thermal conductivity.
Tup ¼ Tdown
DVG surface
u ¼ v ¼ w ¼ 0;
Energy equation:
v½ui ðrE þ pÞ v vT keff ¼ vxi vxi vxi
v v vε ε ε2 aε meff þ C1ε mt S2 C2ε r Rε ðrεui Þ ¼ vxi vxi vxi k k
Exit boundary
Momentum (RANS) equation:
!
(5)
where (ak and aε) are inverse effective Prandtl numbers for (k and ε) respectively, (S) is the modulus of the mean rate of strain tensor, (mt) is turbulent (or eddy) viscosity, (meff) is effective viscosity, (C1ε, C2ε) are model constants and (Rε) is the rate of strain term. Refer [27,29,30] for the definition/value of these terms/constants. Boundary conditions in the three major regions of the computational domain of three rows inline aligned finned tube heat exchanger are defined below. The term ‘Front boundary’ refers to the boundary falling on the plane passing through the tube centre i.e. at Z ¼ 0, and the term ‘Back boundary’ refers to the boundary falling on the plane at Z ¼ 0.5 PT.
Fig. 4. Fins of modified fin and tube heat exchanger.
vðrui Þ ¼0 vxi
v v vk ak meff þ mt S2 rε ðrkui Þ ¼ vxi vxi vxi
vT ¼0 vn
Front & back boundaries of the fluid
vu vv ¼ ¼ 0; vz vz
w ¼ 0;
vT ¼0 vz
Front & back boundaries of the fin
333
Fig. 5. Computational domain.
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A. Arora et al. / Applied Thermal Engineering 82 (2015) 329e340
u ¼ v ¼ w ¼ 0;
vT ¼0 vz
Tube surface
u ¼ v ¼ w ¼ 0;
T ¼ const:
3.3. Numerical method & grid independence Commercial CFD code ANSYS Fluent 14.0 was used to solve the governing equations in conjunction with boundary conditions. Computational domain was created by using GAMBIT 2.2.3 as the pre-processor. The computational domain was split into several sub-domains to control the quality of the mesh. The upstream and the downstream extended regions were meshed with hexahedral elements, and rest of the domain was meshed with hex-wedge elements. Near-wall regions were resolved through the Enhanced wall treatment [30], which demands placing the wall adjacent nodes at yþ value less than unity. The wall effects of the fins and the tubes were resolved by generating graded mesh in the direction normal to the wall as shown in Fig. 6. Periodic surfaces were appropriately linked before applying the periodic boundary condition. Finite volume method was used for the discretization of the governing equations. Coupling between the velocity and pressure is done through the SIMPLE algorithm, and convective terms in the governing equations are discretized by the second order upwind scheme [27,30]. Convergence was concluded on the basis of two criterion viz. magnitude of the normalized residuals of the governing equations as well as the net imbalance in the mass and heat transfer rates. Order of normalized residuals of the energy equation and rest of the equations at convergence were 108 and 105 respectively; and net imbalance in the mass and heat transfer rates was 0.02%. An iterative grid independence test was carried out to choose the mesh density. As the difference in results obtained from the highest and the second highest mesh densities was less than 1.5%, so the second highest mesh density was chosen, which had approximately 45.9 105 and 45.7 105 mesh volumes in the computational domains of the plain and the modified single tube heat exchangers respectively. Simulated performances of the plain heat exchanger with three different mesh densities at the highest Reynolds number are tabulated in Table 1.
computational domain [4,5,22e24,29]. This work attempts to first time model the said contact resistance as a hypothetical conduction resistance, whose thermal resistance is varied by changing the thermal conductivity in discrete steps until the ‘Root mean squared’ error in the predicted local fin temperatures attains minima (Fig. 7). When the contact resistance between the fins and the tube wall was ignored, r.m.s. error in the local fin temperatures of the plain fin was 7.02 C at the Reynolds number of 4245. Modelling of the said contact resistance has helped in reducing the r.m.s. error to 1.51 C. This act of reducing the error in temperature distribution based on the minimization of r.m.s. error may be addressed as the tuning of the numerical model. Later, experimental validation of the tuned model was carried out based on the dimensionless local excess temperature of the plain fin at the highest Reynolds number; and apparent friction factor over the Reynolds number range from 1415 to 7075 (Fig. 8). The corresponding far field upstream air velocity range was from 1 to 5 m/s. It is found that the r.m.s. error in the temperatures of the plain fin was 1.57 C at the highest Reynolds number. Also, it is evident that the numerically predicted apparent friction factor is always smaller than the actual over the whole range of Reynolds number. After validating the preliminary model, the same model was later extended for pursuing the numerical study of the three rows inline aligned finned tube heat exchanger, which was aimed at optimizing the location of ‘common flow up’ delta winglets for the maximum augmentation of the heat transfer.
3.5. Parameter definitions Heat transfer coefficient and the pressure drop across the heat exchanger can be defined in the non-dimensional forms by the Nusselt number (Nu), Colburn's factor (j) and the apparent friction factor (fapp). The characteristic dimension for defining the Reynolds number (Re) and Nusselt number is taken as twice the fin-space [8,12]. Far field upstream uniform inlet flow velocity is taken to define the Reynolds number. Local fin temperature (Tf) is expressed as the dimensionless excess temperature (q*), which is the ratio of local excess temperature on the fin (qf) and excess temperature on the tube wall (qtube). Definitions of the relevant dimensionless parameters are given below:
Re ¼
r Lc U∞ ; m
Nu ¼
h Lc ; kf
3.4. Tuning & validation of numerical model Numerical studies in the past have ignored the thermal contact resistance between the fins and tube wall while modelling the
j¼
q ¼
2 h Pr 3 ; rU∞ Cp
=
334
f app ¼
qf T T∞ ¼ f qtube Ttube T∞
Fig. 6. Graded mesh for resolving the wall effects (a) Fins. (b) Tube.
2$Dp Amin $ rU2∞ Ao
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Table 1 Grid independence test. Mesh volumes
53.7 105
45.9 105
35.5 105
Nu Dp (Pa)
47.51 11.53
47.07 11.41
45.43 11.22
where U∞ is the free-stream flow velocity (m/s), Lc is the characteristic dimension of the channel (m), Amin is the minimum flow area of the channel (m2), Ao is the total heat transfer area of the channel (m2), Dp is the pressure drop across the heat exchanger (Pa) and h is the average heat transfer coefficient (W/m2 K). 4. Numerical results & discussions Selection of all promising locations of the ‘common flow up’ delta winglets precedes the task of identification of the optimal location that allows maximum thermal compactness of the heat exchanger. Selection of all promising locations is done numerically by modelling the winglets at all possible locations in the rectangular fin lamina around the tube. The extends of the said lamina are determined from the maximum order of the longitudinal & transverse tube pitches recommended in the literature [2,31]. A total of twenty discrete locations of the delta winglets were possible to model in the solution domain as shown in Fig. 9. The locations in the said figure represent the position of the trailing edge of the winglets. Array of all the possible locations of the winglets was created such that the nearest location in the streamwise and the spanwise direction is at 0.1D from the tube centre, and the successive locations were created at discrete steps of 0.2D in both the directions. The effect of the winglets on the change in thermal performance of the fin is characterized in terms of the ‘Scaled Colburn's factor’ (SCF), which is defined as the ratio of the Colburn's factor of the fin with and without winglets (jVG/jO). A given location of the delta winglet was treated promising when the ‘Scaled Colburn's factor’ (SCF) was greater than the unity. After numerically solving the flow with all physically possible locations of the winglets, locations with serial numbers (1e17) are identified as the promising and locations with serial numbers (aec) are identified as the counter-productive ones (Fig. 9). Optimization of the location that allows maximum thermal compactness of the heat exchanger is accomplished by plotting the scaled Colburn's factor (SCF) of all promising locations against the location number and the scaled friction factor (SFF) as shown in Fig. 10(a) and (b) respectively. It is found that the relation between the Colburn's factor (SCF) and the friction factor (SFF) of all promising locations of DVG is best described by the second order
Fig. 7. Minimization of r.m.s. error in fin temperature for tuning of numerical model.
Fig. 8. Validation of numerical model (a) Non-dimensional local excess temperature of the fin. (b) Apparent friction factor.
polynomial fit. It is also evident from the said figure that each promising location is delivering different augmentation of the thermal performance. Further, it is observed that though a correlation between SCF & SFF do exists but the R-squared value of the said correlation is small, which can be attributed to the large scatter in the plot. The R-squared value is found to improve dramatically from 0.66 to 0.93, when the location with the highest SCF among all the locations with closely scattered friction factors is retained and discarding the rest (Fig. 10(c)). Fitting a second order polynomial correlation to the SCF & SFF of such selected locations result in a drooping curve with a maxima for the SCF. The winglet's location that delivers maximum SCF bears serial number (12) and the coordinates of this location in the plane of the fin are (x ¼ 0.1D, z ¼ ±0.9D) w.r.t. tube centre. The ‘Common flow up’ delta winglets at this optimal location are expected to modify the mean flow such
Fig. 9. Array of all possible and promising locations of winglets.
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why the ‘toe-out’ orientation of a delta winglet pair is also called ‘common upwash’ configuration. The swirling (or secondary) flow created by the longitudinal vortices facilitates bulk mixing of the fluid in the core and near wall regions. The said flow modification results in the disruption of the thermal boundary layer on the confining walls, and consequently causes dramatic rise in the heat transfer coefficients. The velocity vectors of the secondary flow created by each winglet are drawn on the planes at five discrete streamwise locations ‘X’ w.r.t. tube centre as shown in Fig. 11. The coordinates of the five planes are 0.2D, 0.5D, 0.8D, 1.1D and 1.5D from the tube centre. This figure also shows the enlarged view of the velocity vectors on the planes at X ¼ 0.2D, 0.8D and 1.5D for better appreciation of the flow structures. It is evident from the figure that each winglet is essentially shedding two vortices, namely the main vortex and the corner vortex. The main vortex is generated due to the flow separation at the leading edge of the winglet whereas the mechanism of corner vortex generation is similar to the horse shoe vortex generated in case of flow over a cylinder. The corner vortex is generated at the junction between the fin and the stagnation line on the pressure side of the winglet. The corner vortex first wraps around the winglet and later travels with the main flow. Both the vortices accompany the main flow after the trailing edge of the winglet to travel in the streamwise direction, but the strength of these vortices decreases in the direction of the flow. It is evident from the figure that both the vortices are vanishing in the direction of the flow, which is attributed to the viscous dissipation. The direction of rotation of the main vortex generated by the left winglet is anti-clockwise when seen from the side from which flow is entering the finspace, and the corner vortex rotates in the direction opposite to the main vortex which is clockwise. In contrast, direction of rotation of the main and corner vortex generated by the right winglet is clockwise and anti-clockwise respectively. The secondary flow created by the winglets displaces the fluid in the transverse direction, hence facilitates contraction of the tube wake due to the momentum transfer and improves the heat transfer coefficients in the wake region. 4.2. Effect on fin temperature
Fig. 10. (a) Thermal performance augmentation by all promising locations of DVG. (b) R-squared value of correlation for all promising locations. (c) R-squared value of correlation for selected promising locations.
that the heat transfer on the fin side of the heat exchanger will undergo maximum augmentation. A discussion on the modification of the flow structure and the consequent heat transfer augmentation due to the incorporation of winglets at the said optimal location is narrated below.
4.1. Effect on flow structure A discussion on the modification of the mean flow structure due to the optimally located winglet becomes inevitable because the augmentation of heat transfer resulted due to the vortices generated by the winglets. The pressure difference across the ‘common flow up’ delta winglets cause intentional generation of two corotating longitudinal (or streamwise) vortices due to the flow separation at the leading edge of the winglets. The fluid confined between the two vortices is washed away from the fin, which is
Temperature of the plain and modified fins is plotted along the lines at discrete spanwise and streamwise locations to appreciate the favourable effect of the winglets. The winglets were placed at above identified optimal location. The locations of the said lines on the fin are shown in Fig. 12. It can be easily appreciated from Figs. 13 and 14 that presence of the winglets at the identified optimal location has helped in cooling down the fin (in both streamwise and spanwise directions). The figures are superimposed with the rectangles showing the location and diameter of the tubes. Fig. 13 also shows that the fin temperature along the streamwise line close to the tubes is experiencing oscillations of higher amplitude compared to the fin temperature away from the tubes. This oscillating behaviour of temperature distribution is attributed to the varying fin length in the radial direction (i.e. radial distance between the tube wall and the points falling on the streamwise line) available for the conduction heat transfer. Further inspection of Fig. 14 tells that the winglets at the said optimal location are delivering same order of drop in the fin temperature in the downstream of each tube. 4.3. Effect on heat transfer coefficient Positive effect of said delta winglets on the improvement in thermal performance of the fin can be recognized by plotting the Nusselt number. Fig. 15 shows the scaled Nusselt number (NuVG/ NuO) of the upper fin face in the streamwise direction at Re ¼ 4245.
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Fig. 11. Velocity vectors of secondary flow in the downstream of ‘toe out’ delta winglet.
Spanwise symmetric section of the modified fin is aligned with the plot for better appreciation of the variation in the Nusselt number. Scaling of the Nusselt number is done w.r.t. plain fin, and the Nusselt number is averaged over the span. The scaled Nusselt number being greater than unity is treated as the improvement in the thermal performance of the fin. As evident from the figure, scaled Nusselt number is either greater than or equal to unity over the whole fin length, which clearly implies that the presence of winglets at the identified optimal location has helped in augmenting average Nusselt number of the fin at the same Reynolds number. Further careful inspection of the figure tells that the distribution of the Nusselt number in the streamwise direction upto the leading point of the leading winglet pair is almost same for the plain and the modified fins. Later, the scaled Nusselt number distribution exhibits periodically occurring three sharp peaks, one adjacent to each tube, where each peak is succeeded by a small hump. Magnitude of the peaks is observed to be gradually decreasing in the flow direction, but nevertheless is always greater than the unity. Each pair of the sharp peak and the small hump is attributed to the turbulence imparted due to the combined effect of the acceleration and deceleration of the flow through the nozzle like constricted passage created by the combination of tube aft surface and the winglet pair, and formation of the complex three dimensional vortex system behind each winglet pair. The said vortex system is primarily constituted by two co-rotating longitudinal
vortices. These longitudinal vortices facilitate better fluid mixing, and augment local heat transfer coefficients by modifying the thermal boundary layer. Maximum increase in the span averaged Nusselt number is 60.4% whereas increase at the trailing edge of the fin is 9% at Re ¼ 4245. In nutshell, average Nusselt number of the upper fin side and the three tubes increased by 17.8%, 1.6%, 7.8% and 13.1% respectively. 4.4. Effect on bulk temperature rise Augmentation of the heat transfer coefficients on the surfaces of the fin and the tubes should result in more convective heat transfer from the same surface area on the gas side, when operating constraints are fixed. Increase in the net heat transfer will lead to increase in the bulk temperature rise (i.e. qb, x ¼ Tb,x T∞) on the gas side. The bulk temperature rise of the modified heat exchanger can also be expressed as a scaled value (qb,VG/qb, O), where scaling is done w.r.t. the plain fin. It is evident from Fig. 16 that the bulk temperature rise in the streamwise direction upto the leading point of the leading winglet pair is almost same for the plain and the modified fins. Later, the scaled bulk temperature rise is undergoing a stair-case increase (at every successive winglet pair) in the flow direction due to the incorporation of the optimally located delta winglets. Maximum increase in the mass averaged bulk temperature rise is 9.7% whereas increase at the trailing edge of the fin is 9.4% at Re ¼ 4245.
Fig. 12. Arrangement of lines in streamwise and spanwise directions for computing fin temperature.
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Fig. 15. Span averaged scaled Nusselt number of upper fin face.
5. Conclusions
Fig. 13. Fin temperature in streamwise direction at Re ¼ 4245 (a) At Z ¼ 25 mm. (b) At Z ¼ 45 mm.
A three dimensional numerical study was performed to optimize the location of ‘common flow up’ delta winglets in an inline aligned fin and tube heat exchanger. Also, a single tube heat exchanger prototype was fabricated to experimentally validate the numerical model over the Reynolds number range from 1415 to 7075. The effect of the turbulence was modelled by RNG (keε) model and the temperature distribution in the fins was predicted by solving fluidesolid conjugate heat transfer problem. This numerical study also attempts to first time model the thermal contact resistance between the tube and the fins, which is modelled as a hypothetical conduction resistance. Modelling of the said contact resistance has helped in reducing the r.m.s. error in the fin
Fig. 14. Fin temperature in spanwise direction at Re ¼ 4245 (a) At X ¼ 75 mm. (b) At X ¼ 175 mm. (c) At X ¼ 125 mm. (d) At X ¼ 225 mm.
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Fig. 16. Scaled bulk temperature rise of coolant in streamwise direction.
temperature from 7.02 C to 1.51 C. A total of twenty locations of the winglets were simulated. The effect of the winglets on the change in the thermal performance of the fin is quantified as ‘Scaled Colburn's factor’ (SCF), which is defined as the ratio of the Colburn's factor of the fin with and without winglets (jVG/jO). A given location with SCF greater than the unity was treated promising. Starting from identifying all the promising locations, location that allowed maximum augmentation of heat transfer coefficient is identified as optimal for the maximum thermal compactness of the heat exchanger. The major conclusions drawn from this study are summarized below: 1. Out of the twenty possible locations, seventeen were found to be promising and the rest three turn out to be counter-productive. It is observed that each promising location is delivering different augmentation of the thermal performance. The relation between the Colburn's factor and friction factor of all promising locations of DVG is best described by the second order polynomial fit. The coordinates of winglet's location that delivers maximum augmentation of heat transfer in the plane of the fin are (x ¼ 0.1D, z ¼ ±0.9D) w.r.t. tube centre. 2. Velocity vectors of the secondary flow created by the winglet reveals that each winglet is shedding two vortices, namely the main vortex and the corner vortex. Both the vortices are observed to be vanishing in the direction of the flow, which is attributed to the viscous dissipation. 3. Decaying fin temperature in both streamwise and spanwise directions clearly reflects improved heat transfer from the fin at the same Reynolds number. Likewise, distribution of the scaled Nusselt number of the fin over whole flow length also shows that presence of winglets at the optimal location has helped in augmenting average Nusselt number of the fin at the same Reynolds number. Maximum increase in the span averaged Nusselt number is 60.4% at Re ¼ 4245. Acknowledgement The authors thank the Mechanical Engineering department of the Indian Institute of Technology, Delhi, India for financially supporting this work. Nomenclature AR cp D
aspect ratio, 2H/L specific heat (kJ/kg C) tube diameter (m)
DVG fapp h H j k kf LVG L Lc Nu Dp PL PT Pr Re SFF SCF T Tf Ttube T∞ Tw U∞ u, v, w VG X Y Z
339
delta winglet vortex generator apparent friction factor heat transfer coefficient (W/m2 K) fin-space or height of DVG Colburn's factor turbulent kinetic energy (m2/s2) thermal conductivity of fluid (W/m K) longitudinal vortex generator length of DVG (m) characteristic length (m) Nusselt number pressure drop (Pa) longitudinal tube pitch (m) transverse tube pitch (m) Prandtl number Reynolds number f VG scaled friction factor, app; fapp;o scaled Colburn's factor, jjVG O temperature ( C) fin temperature ( C) tube temperature ( C) far upstream air temperature ( C) tube wall temperature ( C) far upstream air velocity (m/s) x, y, z velocity components (m/s) vortex generator coordinate in streamwise direction coordinate normal to the fin coordinate in spanwise direction
Greek symbols a attack angle ( ) ε turbulent energy dissipation rate (m2/s3) r density (kg/m3) q* non-dimensional excess temperature qb bulk mean temperature rise ( C)
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