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3D CFD analysis of the effect of inlet air flow maldistribution on the fluid flow and heat transfer performances of plate-fin-and-tube laminar heat exchangers
International Journal of Heat and Mass Transfer 74 (2014) 490–500
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
3D CFD analysis of the effect of inlet air flow maldistribution on the fluid flow and heat transfer performances of plate-fin-and-tube laminar heat exchangers Wahiba Yaïci ⇑, Mohamed Ghorab, Evgueniy Entchev Renewables and Integrated Energy Systems Laboratory, CanmetENERGY Research Centre/Natural Resources Canada, 1 Haanel Drive, Ottawa, Ontario K1A 1M1, Canada
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 7 March 2014 Accepted 12 March 2014 Available online 11 April 2014 Keywords: 3D CFD simulation Maldistribution Non-uniformity Heat exchanger Heat transfer Fluid flow Hydrodynamics Thermal performance
a b s t r a c t Plate fin-and-tube heat exchangers are widely used in several areas such as heating, ventilating, air conditioning and refrigeration systems. Nonuniformity of the inlet air flow in heat exchangers is first order importance and has decisive influence on their efficiency because it can intensify longitudinal wall heat conduction and the maldistribution of interior temperature. This study presents the results of three-dimensional (3D) Computational Fluid Dynamics (CFD) simulations aim to investigate the effect of inlet air flow maldistribution on the thermo-hydraulic performance of heat exchangers. Validation of the computation results with experimental data found in the literature has shown a very good agreement. Different computation test cases with a variety of inlet air flow distributions on in-line and staggered plate-fin-and-tube heat exchangers were run to systematically analyse their effects on system performance. The CFD results confirmed the importance of the influence of inlet fluid flow nonuniformity on heat exchanger efficiency. Results indicate that up to 50% improvement or deterioration in the Colburn j-factor are found compared to the baseline case of a heat exchanger with a uniform inlet air velocity profile. Moreover, the present investigation with respect to inlet flow maldistribution demonstrates that 3D CFD simulation is a useful tool for analysing, designing and optimising heat exchangers. Finally, the results of this study can be also of significant value for the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
1. Introduction Plate fin-and-tube heat exchangers are widely used in several areas such as HVACR systems. They have a high degree of surface compactness. Substantial heat transfer enhancement is obtained as a result of the periodic starting and development of laminar boundary layers over interrupted channels formed by the fins and their dissipation in the fin wakes. This is however accompanied by an increase in the pressure drop due to increased friction and form-drag contribution from the finite thickness of the interrupted fins [1–5]. The governing thermal resistance for these heat exchangers is usually on the air side which may account for 85% or more of the total resistance. The effect of fluid flow nonuniformity on heat exchanger efficiency is of first order importance because it can intensify longitudinal wall heat conduction and the ⇑ Corresponding author. Tel.: +1 613 996 3734; fax: +1 613 947 0291. E-mail address: [email protected] (W. Yaïci). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.034 0017-9310/Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
maldistribution of interior temperature. In the design of platefin-and-tube heat exchanger, it is usually assumed that the inlet flow and temperature distribution across the exchanger core are uniform and steady. However, the assumption is generally not realistic under real operating conditions due to various reasons. One of these reasons is mainly related to the flow nonuniformity. In fact, the flow nonuniformity is usually divided into two types: gross maldistribution and passage-to-passage maldistribution. The gross flow maldistribution in plate-fin heat exchangers is mainly associated with improper heat exchanger entrance configuration, such as poor design of header and distributor configuration. The passage-to-passage flow maldistribution occurs in a highly compact heat exchanger caused by various manufacturing tolerances, frosting of condensable impurities, etc. [6–9]. Considerable research has been dedicated on the study on the effects of flow maldistribution on heat exchangers performance. Most of these studies in heat exchangers have only been investigated experimentally and analytically due to their complexity.
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Nomenclature BC Cp D Fp Ft f H HVACR h j k L Ll Lt Nu Pin P p Pr Re
boundary condition specific heat of the fluid at constant pressure, J/kg K tube diameter, m fin pitch, m fin thickness, m fanning friction factor fin spacing, m heating, ventilating, air conditioning and refrigeration average heat transfer coefficient, W/m2 K Colburn factor thermal conductivity, W/m K flow length, m longitudinal tube pitch, m transverse tube pitch, m Nusselt number inlet or upstream pressure, Pa pressure, Pa local pressure, Pa Prandtl number Reynolds number based on fin spacing
Most of previous works mainly investigated the effect of flow nonuniformity on heat exchangers performance deterioration based on their own flow maldistribution model [9–32]. For example, Fleming [6] set up a flow maldistribution model in paired-channel heat exchangers and investigated the effect of flow maldistribution on the performance deterioration. Based on the experimental data obtained from wind tunnel experiments, Chiou [8,9] set up a continuous flow distribution model and studied the thermal performance deterioration in cross-flow heat exchangers. Mueller [12] and Mueller and Chiou [11] summarised various types of flow maldistribution in heat exchangers and discussed the reason leading to flow maldistribution. Thermal performance reduction in air-cooled heat exchangers due to nonuniform flow and temperature distributions was investigated by Beiler and Kroger [13]. The results showed that nonuniform air velocity distribution to a tube row leaves the row with a distorted temperature profile. The temperature non-uniformity was found to increase as the air passes through subsequent tube rows. Ranganayakulu et al. [15] and Ranganayakulu and Seetharamu [16,17] investigated the combined effects of wall longitudinal heat conduction, inlet flow uniformity and temperature nonuniformity on the thermal performance of a two fluid cross-flow plate-fin heat exchanger using finite element method. The results showed that the performance may be reduced by 30% under non-uniform operating conditions. Computational investigations into flow maldistribution effects on heat exchanger performance are becoming more common as the capabilities of commercial CFD codes and the cost of computing power improves [33–40]. Lalot et al. [33] used CFD to study the gross flow maldistribution in an electrical heater. They presented the effect of flow non-uniformity on the performance of heat exchangers, based on the study of flow maldistribution in an experimental electrical heater. They found that reverse flows would occur for the poor header design and the perforated grid can improve the fluid flow distribution. Their results indicated also that the flow maldistribution leads to a loss of effectiveness of about 25% for cross-flow exchangers. Ng et al. [34] used CFD modelling to generate the velocity profiles for the numerical e-NTU thermal performance analysis, but no hydrodynamics performance effects were presented. The main focus has been on header design with authors such as Zhang and Li [35], Wen and Li [36] and Sheik
T Tin Twall U, V, W u u uin u, v, w x, y, z
temperature, °C inlet temperature, °C wall temperature, °C dimensionless velocity in x, y, z directions velocity vector, m/s velocity, m/s inlet frontal velocity, m/s velocity in x, y, z directions, m/s direction coordinates
Greek symbols h dimensionless temperature r vector operator l dynamic viscosity, Pa s q density, kg/m3 Subscripts in inlet r ratio
Ismail et al. [37] using CFD to design various flow dispersion baffles in order to improve flow distribution into the heat exchanger. 3D CFD simulation method can provide the flexibility to construct realistic computational models that are easily adapted to a wide variety of physical conditions without constructing expensive test rigs or large-scale prototypes. Therefore, CFD can provide an effective platform where various design options can be tested and an optimal design can be determined at a relatively low cost. The results of the literature studies showed the importance of considering the flow maldistribution for better design of plate heat exchangers [40]. It must be noted that all of the above works mainly concentrated on the effect of flow nonuniformity on the heat exchanger performance using simplified 2D or 3D modelling. The focus with these designs is on flow uniformity entering the heat exchanger with the goal to maximise the thermal performance but the hydrodynamics aspect was not always presented, such as the pressure drop penalties associated with the baffle design or the effect of flow maldistribution on the performance taking into account the coupling of fluid flow and heat transfer. The objective of this work is to predict the influence of different inlet air velocity profiles simulating inlet flow maldistribution on the thermo-hydraulic performance of heat exchangers using 3D CFD. The results will help in suggesting a way of modifying, improving or optimising the design of header configurations for heat exchangers in order to minimise the effect of flow maldistribution on the heat exchanger performance. The work involves 3D CFD modelling, validation and simulation for two types of platefin-and-tube heat exchangers to demonstrate it. The results of this investigation are expected to be valuable for the improvement and the optimum design of this heat exchanger type.
2. CFD model details 2.1. Physical model Fig. 1 illustrates the geometric models of the plain-fin-and-tube heat exchangers considered in the present work. Fig. 2 shows the nomenclature used for the in-line and staggered arrangements, with the geometrical values listed in Table 1. Fig. 3 presents the
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W. Yaïci et al. / International Journal of Heat and Mass Transfer 74 (2014) 490–500 Table 1 Geometrical parameters for the plain-fin-and-tube heat exchanger models.
Fig. 1. Schematic of typical plain fin-and-tube compact heat exchanger (staggered arrangement).
Parameters
Values
Tube diameter fin collar outside diameter, D (mm) Longitudinal tube pitch, Ll (mm) Transverse pitch, Lt (mm) Fin pitch, Fp (mm) Fin thickness, Ft (mm) Number of tube row, N Fin-and-tube arrangements
9.97 27.50 31.75 3.21 0.20 4 In-line, staggered
computational domain with the co-ordinate system of the two heat exchanger types. 3D steady flow models of plate-fin-and-tube heat exchangers with four rows for in-line and staggered arrangements were built in the CFD commercial software COMSOL [41]. It was used as the grid generator and the CFD solver, respectively. The following assumptions were considered in the flow models: the working fluid is air within the laminar regime on the external side (100 < Re 6 1200); it is assumed to be Newtonian, incompressible with constant inlet properties; the flow is assumed to be threedimensional and steady state; water at high velocity is assumed to flow inside the tubes, resulting in a constant tube-surface temperature; the viscous dissipation and viscous work are neglected; there are no body forces.
(a)
(b) Fig. 2. Modelled heat exchangers: (a) nomenclature and simulation domain; (b) computational domain with boundary conditions.
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temperature and energy transport are coupled. Eqs. (1) and (2) are solved together with an energy balance in steady-state 3D. Conservation of energy:
qC p ðu rÞT ¼ kr2 T
ð3Þ
2.3. Boundary conditions This section describes boundary conditions used in the present study with reference to Figs. 2 and 3. Assuming symmetry conditions on the mid-plane between two fins, the bottom and top boundaries simulate the fin and the mid-plane respectively. This symmetry of the problem was used to model only one half of the domain for the computational purposes. The boundary conditions used are as follows: At the upstream inlet boundary, Dirichlet boundary conditions, uniform flow with constant velocity uin and constant temperature Tin are assumed.
u ¼ uin ;
Fig. 3. Comparison of present CFD results with experimental results of Wang et al. [2] and CFD results of Bhuiyan et al. [46] in the heat exchanger for validation study: (a) friction factor f; (b) Colburn factor j.
In order to better predict the air flow field behaviour, the optimised solution-adaptive mesh refinement is used. More cells were added at locations where significant flow changes are expected, for example near the walls. The resulting mesh enabled the features of the flow field to be better represented. The symmetric solver selected here accounts for the three-dimensional effects, and the calculation domain was half of the physical body, based on symmetry considerations. Mixed topology of unstructured grids was used, and the final mesh was composed around 9 105 elements for the in-line and staggered configurations. The cells close to inlet and outlet ports and walls are small enough to capture the complex flow structure. Details on the grid system and selected mesh elements are provided in Section 2.4. 2.2. Governing equations
v ¼ w ¼ 0;
T in ¼ 20o C
ð4Þ
At the downstream end of the computational domain or outlet, the Neumann boundary condition is applied, i.e. stream wise gradients for all the variables are set to zero. No-slip boundary condition is used at the fin and tube surfaces. These surfaces are assumed to be solid walls with no slip wall boundary condition; the velocity of the fluid at the wall is zero and constant wall temperature is assumed. This indicates that the fin efficiency, which is a function of the wall temperature (tube wall and fins), is assumed to be equal to 1. In other words, this simplification corresponds to isothermal wall boundary condition. The fin and tubes are assumed to be made of aluminium. Since aluminium is a relatively high thermal conductivity material, constant wall temperature boundary condition can be safely assumed over the surfaces. The condition prescribes:
u ¼ v ¼ w ¼ 0;
T wall ¼ 80 C
ð5Þ
Free stream planes (top and bottom planes of the extended surface areas):
@u ¼ 0; @z
@v ¼ 0; @z
w ¼ 0;
@T ¼0 @z
ð6Þ
Symmetry boundary conditions are prescribed at the centre plane, tube centre plane and the top symmetry plane (mid-plane between two fins) as shown in Fig. 2. At these planes zero normal velocity and zero normal gradients of all variables are assumed. Side planes (symmetry planes):
@u ¼ 0; @y
@w ¼ 0; @y
v ¼ 0;
@T ¼0 @y
ð7Þ
The Fanning f-friction factor (ratio of wall shear stress to the flow kinetic energy), which is related to pressure drop in tubeand-fin heat exchangers is expressed as:
ðPin PÞH 1 qu2in 4L 2
The Navier–Stokes and energy equations in three-dimensional form were used to solve for the steady-state hydrodynamics and thermal fields. Therefore, the resulting governing equations without consideration of body forces and viscous dissipation can be written in Cartesian vector form as follows: Conservation of mass:
The Colburn j-factor (ratio of convection heat transfer per unit duct surface area) to the amount virtually transferable (per unit of cross-sectional flow area) is defined as:
ru¼0
ð1Þ
j¼
ð2Þ
where Reynolds Re and average Nusselt numbers are defined as follows:
Conservation of momentum:
qðu rÞu ¼ rp þ lr2 u
The coupled heat transfer and laminar flow is used to model slow-moving flow (Re = 100–1200) in the heat exchanger where
f ¼
Nu RePr1=3
Re ¼
quin H l
ð8Þ
ð9Þ
ð10Þ
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Nu ¼
W. Yaïci et al. / International Journal of Heat and Mass Transfer 74 (2014) 490–500
hH k
ð11Þ
Given that the improvements in heat transfer are also accompanied by increases in the pressure drops, it is necessary to evaluate the net enhancement or degradation obtained in the heat exchangers with the effect of air flow distribution. One way of assessing the relative thermal–hydraulic performance enhancement, among many others is to consider the London area goodness factor or efficiency index, which is defined as the ratio of the Colburn j-factor over the friction f-factor. It is a commonly used metric because it examines the intrinsic link and trade-off between heat transfer enhancement and increased frictional forces in air flow over surfaces, and is given by [42–44]:
j=f ¼
Nu f RePr1=3
ð12Þ
2.4. Numerical procedure The governing equations of mass, momentum and energy conservation were solved by using the finite element method, based on the assumptions listed in Section 2.1. The governing equations are discretised on the computational domain, linearised in an implicit manner and solved by the finite element method using a pressure based solver. SIMPLEC (SIMPLE-Consistent) algorithm is employed for the pressure– velocity coupling, the second order upwind discretisation scheme is used for the convection terms and each governing equation is solved using QUICK scheme [45]. It is necessary to carry out independency verification of the grid system before CFD computation. The mesh independence study is investigated by using three different mesh sizes (coarse, normal, fine and finest meshes) of 159,864, 330,721, 901,685 and 2,965,847, and 126,237, 279,691, 897,857 and 2,960,748 for the in-line and staggered arrangements respectively are adopted for computation for the baseline case with the uniform inlet air velocity profile. The difference in the Fanning friction f-factor and the Colburn j-factor between the last two mesh sizes are less than 2% for both cases, before settling to a fine mesh for half of the geometry of the computational in-line or staggered heat exchanger cases. Computations were then run for a mesh containing about 901,685 and 897,857 elements for the in-line and staggered arrangements respectively, which was considered to be acceptable in terms of accuracy and efficiency. Furthermore, the solution is iterated until convergence is achieved, that is, residual for each equation achieves values less than 106 and 108, and changes in flow field temperature and energy, respectively become negligible. A workstation with 2 (R) Xeon processors of 2.4 Hz and an installed memory (RAM) of 16 GB, which took between 1 and 24 h of CPU time depending on the case study, was used to perform the required duty. 3. Model validation Experimental data by Wang et al. [2] are used to validate the present CFD model. The geometrical parameters for the plain fin staggered arrangement used by experiments of Wang et al. [2] and the present numerical study for model validation purpose are the same reported here: Ll = 22 mm, Lt = 25.4 mm, Fp = 3.00 mm, Ft = 0.13 mm, and D = 9.5 mm. Validation is performed with air and wall temperatures of 25 and 100 °C, respectively. Air is used as working fluid assuming constant properties (q = 1.185 kg/m3, l = 1.831 105 Pa s, k = 0.0261 W/m K, Pr = 0.736).
The values of the Fanning friction factor f and Colburn factor j as a function of Reynolds numbers in the range of 100–2000 are used to compare the predicted results by the present study with experimental data [2], as shown in Fig. 4. The authors [2] reported maximum uncertainties of 0.31%, 0.1 °C and 0.5% in the primary measurements for air flow, air temperature and heat exchanger pressure drop, respectively. The maximum uncertainties in the reported experimental derived values of the friction f factor and Colburn j factor were in the order of ±17.7% and ±9.4% at Re = 600. Very good agreement is obtained between the experimental and the CFD simulation results, which are within less than 5% of discrepancy. Also, the present CFD results have been compared with CFD results of Bhuiyan et al. [46] obtained using FLUENT software. A good agreement can be observed between CFD predictions using different CFD codes, with a deviation within 7%, as can be seen in Fig. 4. This numerical model was then used for further heat exchanger analysis with supporting reliability of the computation.
4. Results and discussion A numerical study was performed to predict the influence of the inlet air flow distribution on the performance of heat exchangers. Table 1 presents the ranges and values of the geometry of the heat exchangers studied for the CFD simulation. The effect of inlet air flow non-uniformity on the governing independent parameters influencing the hydrodynamics and heat transfer on the heat exchanger performance are the Reynolds number (Re), Prandtl number (Pr), the geometrical parameters of the heat exchanger, the tube arrangement and other parameters such as circuitry, variety of working fluids. Table 2 shows the summary of the simulation matrix for the parametric study. Each case is studied for different combination of the Reynolds numbers, Re = 100, 300, 600, 900 and 1200 and six inlet air velocity profiles to mimic the inlet airflow non-uniformity including a uniform air flow velocity, which case corresponds to the baseline. The inlet air velocity profiles were chosen based on the possible cases that could be encountered in real heat exchangers of air handling units for example. This approach allows simulating the air flow maldistribution case by case in order to be able to make a quantitative assessment of its effect on the system performance. The ultimate objective is to use CFD tool for the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution. The geometrical factors considered in this investigation are the tube alignments of the heat exchangers as described in the previous section; while the seven inlet air velocity profiles considered are Uniform, Linear-up, Linear-down, Linear-down with the Velocity at the centre, Parabolic, Half-parabolic, and an expression of velocity profile [47] as presented in Fig. 4. These numerical results cover the operating conditions for the laminar flow regime with inlet frontal velocities ranging from 2 and 6 m/s. These correspond to 70 cases investigated. Effect of inlet airflow maldistribution on hydrodynamics and thermal performance results for the heat exchangers are presented in details following the conditions shown in Table 2. Possible ways were identified to eliminate it or improve the heat exchanger performance. CFD results for both the in-line and staggered tube heat exchangers presented in the form of the Colburn factor j, Fanning friction factor f, and the efficiency index j/f as a function the Reynolds number Re for the seven inlet air velocity profiles are shown in Figs. 5–7. As mentioned earlier, the uniform inlet airflow velocity profile is considered as the baseline case in this investigation.
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y
y
y u = u in
u = C1 ⋅ uin ⋅ y /(Lt / 2)
u = 2 ⋅ uin − C1 ⋅ uin ⋅ y /(Lt / 2)
C1 = 1.23485
u Uniform
C1 = 1.1854
u Linear-down
u Linear-up
u = uin ⋅ C1 ⋅ sin(2 ⋅ π ⋅ y / Lt)
y
y
u = uin ⋅ C1 ⋅ sin(π ⋅ y / Lt)
C1 = 1.7358
y
C1 = 1.5772
u =1.59117⋅ uin −C1 ⋅ uin ⋅ y /(Lt/ 2) C1 = 0.73
u Linear-down with velocity at the center
u Parabolic
u Half-parabolic
u = uin ⋅ C1 ⋅ C2 + ( y ⋅ uin ⋅ C2 ⋅ 4⋅ (1− C1) / Lt) C1 = 0.5 & C2 = 0.6578
y
u Velocity profile [47] Fig. 4. Inlet air velocity profiles used in CFD simulations.
Table 2 Summary of the simulation matrix with the input data of the heat exchangers. Simulations
Computational cases
Figures
Heat exchanger arrangements
Velocity profilesa
Re (–)
Sim 3D.1
Case Case Case Case Case Case Case Case Case Case Case Case Case Case
Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs.
In-line
V1 V2 V3 V4 V5 V6 V7 V1 V2 V3 V4 V5 V6 V7
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100,
Sim 3D.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b
Staggered
300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300,
600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600,
900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900,
1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200
Tw (°C)
Tini (°C)
80
20
80
20
V1: uniform; V2: linear-up; V3: linear-down; V4: linear-down with velocity at centre; V5: parabolic; V6: half-parabolic; V7: equation [47]. a Fig. 4.
Fig. 5a and b show the variation of the Colburn factor j as a function of Reynolds number, Re for the different inlet air velocity profiles and for the in-line and staggered arrangements, respectively. As expected, it can be seen from the figure that the j factor decreases as the Reynolds number increases. In the case of the thermal performance of the in-line heat exchanger, as shown in Fig. 5a, the Linear-up velocity profile has 58% and 40% lower j values for Re numbers of 100 and 1200 respectively, when compared with the Uniform velocity profile. For the same Re values and relative to the Uniform velocity profile, the Linear-down velocity profile has 49% and 30% higher j values. Furthermore, the Parabolic velocity profile has j values lower of
9.5% and 6%, when compared with the baseline Uniform velocity profile results at Re numbers of 100 and 1200, respectively. Similarly, it is observed the same trend for the staggered arrangement, as illustrated in Fig. 5b, the Linear-up velocity profile has 55% and 28% lower j values for Re numbers of 100 and 1200 respectively, when compared with the Uniform velocity profile. For the same Re values and relative to the Uniform velocity profile, the Linear-down velocity profile has 51% and 17% higher j values. Furthermore, the parabolic velocity profile has lower j values of about 7% and 5%, when compared with the baseline Uniform velocity profile results at Re numbers of 100 and 1200, respectively.
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Fig. 6. Effect of inlet air velocity profiles on friction f factor at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
Fig. 5. Effect of inlet air velocity profiles on Colburn factor j at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
As expected and known, the tube arrangement plays a vital role in the heat transfer and pressure drop characteristics. In staggered arrangements, there is better flow mixing due to staggered tube layouts and thus provides higher heat transfer and pressure drop characteristics than the in-line arrangements. More importantly, the numerical results show that the inlet air flow distribution has a significant impact on the fluid flow and heat transfer characteristics and on the thermo-hydraulic performance due to different inlet air velocity profiles. It is found that this variation in thermal performance is more pronounced at low Re and tends to diminish at high Re. Accordingly, even if the operating and geometrical parameters play an important role on the heat exchanger efficiency, the airflow distribution has a strong impact on the degradation or enhancement of the thermal performance. Consequently, the heat exchanger header and distributor should be appropriately and accurately designed taking into account the inlet airflow characteristics and distribution. Figs. 6a and b, 7a and b present the variation of the friction factor f and the efficiency index j/f as a function of Reynolds number Re for the seven inlet air velocity profiles of in-line and staggered arrangements. As expected, given that the improvement in heat transfer is also accompanied by increases in the frictional losses, the same trend is observed in the results for f and j/f. These figures show that the friction factor f decreases with the increase in the Reynolds number. Moreover, the Linear-up velocity profile has 68% lower f and 85% higher j/f values for Re number of 1200, respectively, when compared to the Uniform velocity profile. However, for the same Re value and relative to the Uniform velocity
profile, the Linear-down velocity profile has 78% higher and 27% lower j/f values. Furthermore, the Parabolic velocity profile has f and j/f values of about 6% and 3% lower values, when compared with the baseline Uniform velocity profile results at Re number of 1200, respectively. Furthermore, it is observed the same trends for the staggered configuration, as shown in Figs. 6b and 7b. The Linear-up velocity profile has 66% lower f and 100% higher j/f values for Re number of 1200, respectively, when compared to the Uniform velocity profile. For the same Re value and relative to the Uniform velocity profile, the Linear-down velocity profile has 86% higher and 37% lower j/f values. Also, the Parabolic velocity profile has f and j/f value of about 6% lower and 1% higher values, when compared with the baseline Uniform velocity profile results at Re number of 1200, respectively. From the CFD results, it can be noted again the strong influence in the inlet air velocity distribution that may result in significant variations in fluid flow and heat transfer characteristics and hence on the heat exchanger performance. With the seven inlet air velocity distributions, simulating the influence of inlet air flow non-uniformity for the two types of heat exchangers considered in this study, it is found that the improvement or deterioration in heat transfer may be up to 50% compared to the baseline Uniform velocity distribution. Given the improvement or degradation in heat transfer are also accompanied by increase or decrease in f and j/f factors, there is consequently a trade-off in the thermo-hydraulic parameters to take into account in the design of the heat exchanger in order to achieve its optimal performance. Figs. 8–10 show the effect of the inlet air flow distributions on the dimensionless velocity, temperature and pressure ratio contours for both the in-line (Figs. 8a, 9a, 10a) and staggered
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(a)
Fig. 7. Effect of inlet air velocity profiles on efficiency index j/f at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
(Figs. 8b, 9b, 10b) arrangements taken on the x–y planes at the mid-plane z = 0 for Re = 1000, respectively. The dimensionless velocity, temperature, and pressure are defined as follows:
U¼
u uin
ð13Þ
h¼
T T in T w T in
ð14Þ
pr ¼ 1 2
p
qu2in
ð15Þ
For the present analysis as shown in Table 2, the inlet air temperature was kept constant at 20 °C and the fin and the tube surfaces were kept as wall boundary with a constant temperature of 80 °C and outlet pressure was assumed to be zero. Fig. 8a and b present the velocity distribution normalised by the value of the uniform inlet velocity (Eq. (13)) for different inlet air velocity profiles and for both the in-line and staggered arrangements. It can be seen from the figures the remarkable stream wise developing velocity profiles along the heat exchanger for the Linear-down, Linear-down with velocity at the centre and the Parabolic velocity profiles. The velocity profile is nearly symmetric and repeats itself, except at the inlet of the heat exchanger; the flow is not fully developed, due to entrance effect. The difference between the staggered and in-lined configuration can be observed from the figure. For the staggered configuration, it can be seen that stronger recirculation zones are formed compared to the in-line
(b) Fig. 8. Velocity ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
arrangement. Flow gets disturbed only by the tubes and a flow recirculation zone is observed at the trailing edge of the tubes. Fig. 9a and b illustrate the effect of the inlet velocity profiles on the normalised temperature lines (isotherms). All isotherms range from 0 to 1, which represents a low fluid temperature at the inlet to higher fluid temperature as it reaches the hot tube surface. Based on the previous velocity field patterns, as the velocity increases, specifically for the Linear-down, Linear-down with velocity at the centre profiles, and Parabolic velocity profile cases, the lower value isotherms penetrate deeper, which means the colder fluid is getting closer to the hot surface. As a result of this behaviour, the heat transfer is increased, as has been demonstrated in the computed Colburn j factor as a function of Re. As shown in
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(a) (a)
(b) Fig. 9. Temperature ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
the case of the V1, V2, V6 and V7 velocity profiles, a non-uniform air flow accentuates the cold isotherms, which penetrates farther downstream and hence results in lower heat transfer. The influence of the hydrodynamics upon the transfer of energy is shown in Fig. 9. Specifically, the influence of the inlet velocity at the entrance of the heat exchanger has a direct effect on the temperature field. Larger temperature changes are achieved upstream and over the tubes, where recirculation bubbles behind the tubes can be seen. Similar behaviour is observed for the staggered configuration, but the patterns alternate due to the tube arrangement; this allows improving mixing in the fluid and increasing the heat transfer. Fig. 10a and b show the influence of the inlet air flow distribution on the normalised pressure drop at fixed Reynolds number of 1000 for the in-line and staggered configurations, respectively. It can be seen that as expected, the pressure decreases monotonically along the heat exchanger. It can be noticed, however, that the inlet
(b) Fig. 10. Pressure ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
air distribution has a strong effect on the heat transferred within the heat exchanger as seen with the velocity and temperature ratio distributions in Figs. 8 and 9. It can be noticed that depending of the inlet air velocity distribution, corresponds a pressure profile impacting on the hydrodynamics and heat rate of the system. The pressure drop increases with the inlet velocity of the air flowing into the channel of the heat exchanger. The inlet airflow distribution can be used as a mechanism to enhance the local heat rate or to improve the heat exchanger design. Moreover shown in the figure is the fact that, regardless of the velocity profiles, there is a rapid decrease in the amount of heat transferred within the system, specifically in the case of the in-line arrangement as the air temperature rapidly attains the wall temperature. Finally, this study with respect to inlet flow malditribution shows that 3D CFD simulation is a valuable tool for analysing,
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designing and optimising heat exchangers. Moreover, the present results can also be of considerable importance on the optimum design of header and distributor configurations to minimise maldistribution and optimise the heat exchanger performance.
We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from: wahiba.yaici@nrcan. gc.ca.
5. Conclusions
Acknowledgments
Nonuniformity of the inlet airflow in heat exchangers is of first order importance and has crucial influence on their efficiency because it can intensify longitudinal wall heat conduction and the maldistribution of interior temperature. In this study, 3D CFD simulations have been carried out to investigate the effect of the inlet airflow maldistribution on the thermo-hydraulic performance in heat exchangers used in air handling units. The CFD model was first validated against the experimental data available in the literature. Very good agreement between the numerical results and the experiments was found. This implies that the model used in the present study is reliable and can predict the thermal performance satisfactorily for heat exchangers. The CFD simulations have been then conducted for in-line and staggered plate-fin-and-tube heat exchangers with seven inlet air flow distributions for steady-state laminar flow conditions to systematically analyse their effects on the system performance. The CFD results confirmed the importance of the effect of inlet fluid flow nonuniformity on heat exchanger efficiency. Results indicate that up to 50% improvement or deterioration in the Colburn j and friction f factors are found compared to the baseline case of a heat exchanger with a uniform inlet velocity profile. Given the improvement or degradation in heat transfer are also accompanied by increase or decrease in f and j/f factors, there is consequently a trade-off in the thermo-hydraulic parameters to take into account in the design of the heat exchanger in order to achieve its optimal performance. The inlet airflow distribution can be used as a mechanism to enhance the local heat rate or to improve the heat exchanger design. Moreover, the present investigation with respect to inlet flow maldistribution demonstrates that 3D CFD simulation is a valuable tool for analysing, designing and optimising heat exchangers. Finally, the results of this study have significant contribution on the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution.
Funding for this work was provided by Natural Resources Canada through the Program of Energy Research and Development.
Conflict of interest We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration due to the protection of intellectual property associated with this work and there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He/she is responsible for communicating with the other authors about progress, submissions of revisions and final approval of proofs.
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[26] R.B. Prabhakara, B. Sunden, S.K. Das, An experimental and theoretical investigation of the effect of flow maldistribution on the thermal performance of plate heat exchangers, ASME J. Heat Transfer 127 (2005) 332–343. [27] A. Jiao, S. Baek, Effects of distributor configuration on flow maldistribution in plate-fin heat exchangers, Heat Transfer Eng. 26 (2005) 19–25. [28] N. Srihari, R.B. Prabhakara, B. Sunden, S.K. Das, Transient response of plate heat exchangers considering effect of flow maldistribution, Int. J. Heat Mass Transfer 48 (2005) 3231–3243. [29] R.B. Prabhakara, B. Sunden, S.K. Das, An experimental investigation of the port flow maldistribution in small and large plate package heat exchanger, Appl. Therm. Eng. 26 (2006) 1919–1926. [30] R.B. Prabhakara, B. Sunden, S.K. Das, Thermal analysis of plate condensers in presence of flow maldistribution, Int. J. Heat Mass Transfer 49 (2006) 4966– 4977. [31] F.A. Tereda, N. Srihari, B. Sunden, S.K. Das, Experimental investigation on portto-channel flow maldistribution in plate heat exchangers, Heat Transfer Eng. 28 (2007) 435–443. [32] C. T’joen, A. Willockx, H.J. Steeman, M. De Paepe, Performance prediction of compact fin-and-tube heat exchangers in maldistributed airflow, Heat Transfer Eng. 28 (2007) 986–996. [33] S. Lalot, P. Florent, S.K. Lang, A.E. Bergles, Flow maldistribution in heat exchangers, Appl. Therm. Eng. 19 (1999) 847–863. [34] E.Y. Ng, P.W. Johnson, S. Watkins, An analytical study on heat transfer performance of radiators with non-uniform airflow distribution, Proc. Inst. Mech. Eng. Part D: J. Automobile Eng. 219 (2005) 1451–1467. [35] Z. Zhang, Y. Li, CFD simulation on inlet configuration of plate-fin heat exchangers, Cryogenics 43 (2003) 673–678. [36] J. Wen, Y. Li, Study of flow distribution and its improvement on the header of plate-fin heat exchanger, Cryogenics 44 (2004) 823–831.
[37] L.S. Ismail, C. Ranganayakulu, R.K. Shah, Numerical study of flow patterns of compact plate-fin heat exchangers and generation of design data for offset and wavy fins, Int. J. Heat Mass Transfer 52 (2009) 3972–3983. [38] M.A. Habib, R. Ben-Mansour, S.A.M. Said, M.S. Al-Qahtani, J.J. Al-Bagawi, K.M. Al-Mansour, Evaluation of flow maldistribution in air-cooled heat exchangers, Comput. Fluids 38 (2009) 677–690. [39] J. Hoffmann-Vocke, J. Neale, M. Walmsley, The effect of inlet conditions on the air side hydraulic resistance and flow maldistribution in industrial air heaters, Int. J. Heat Fluid Flow 32 (2011) 834–845. [40] M.M.A. Bhutta, N. Hayat, M.H. Bashir, A.R. Khan, K.N. Ahmad, S. Khan, CFD applications in various heat exchangers design: a review, Appl. Therm. Eng. 32 (2012) 1–12. [41] COMSOL Multiphysics, CFD, Heat Transfer modules, Version 4.3b, COMSOL Inc, May 2013. [42] R.K. Shah, A.L. London, Laminar Forced Convection in Ducts, a Source Book for Compact Heat Exchanger Analytical Data, Academic Press, New York, 1978. [43] R.L. Webb, Principles of Enhanced Heat Transfer, Wiley, New York, 1994. [44] A.E. Bergles, Techniques to enhance heat transfer, in: W.M. Rohsenow, J.P. Hartnett, Y.I. Cho (Eds.), Handbook of Heat Transfer, third ed., McGraw-Hill, New York, 1998. chapter 11. [45] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington DC, 1980. [46] A.A. Bhuiyan, M.R. Amin, A.K.M.S. Islam, Three-dimensional performance analysis of plain fin tube heat exchangers in transitional regime, Appl. Therm. Eng. 50 (2013) 445–454. [47] M.R. Kaern, T. Tiedemann, Compensation of airflow maldistribution in fin-andtube evaporators, in: International Refrigeration and Air Conditioning Conference, Purdue, USA, 2012.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
3D CFD analysis of the effect of inlet air flow maldistribution on the fluid flow and heat transfer performances of plate-fin-and-tube laminar heat exchangers Wahiba Yaïci ⇑, Mohamed Ghorab, Evgueniy Entchev Renewables and Integrated Energy Systems Laboratory, CanmetENERGY Research Centre/Natural Resources Canada, 1 Haanel Drive, Ottawa, Ontario K1A 1M1, Canada
a r t i c l e
i n f o
Article history: Received 8 January 2014 Received in revised form 7 March 2014 Accepted 12 March 2014 Available online 11 April 2014 Keywords: 3D CFD simulation Maldistribution Non-uniformity Heat exchanger Heat transfer Fluid flow Hydrodynamics Thermal performance
a b s t r a c t Plate fin-and-tube heat exchangers are widely used in several areas such as heating, ventilating, air conditioning and refrigeration systems. Nonuniformity of the inlet air flow in heat exchangers is first order importance and has decisive influence on their efficiency because it can intensify longitudinal wall heat conduction and the maldistribution of interior temperature. This study presents the results of three-dimensional (3D) Computational Fluid Dynamics (CFD) simulations aim to investigate the effect of inlet air flow maldistribution on the thermo-hydraulic performance of heat exchangers. Validation of the computation results with experimental data found in the literature has shown a very good agreement. Different computation test cases with a variety of inlet air flow distributions on in-line and staggered plate-fin-and-tube heat exchangers were run to systematically analyse their effects on system performance. The CFD results confirmed the importance of the influence of inlet fluid flow nonuniformity on heat exchanger efficiency. Results indicate that up to 50% improvement or deterioration in the Colburn j-factor are found compared to the baseline case of a heat exchanger with a uniform inlet air velocity profile. Moreover, the present investigation with respect to inlet flow maldistribution demonstrates that 3D CFD simulation is a useful tool for analysing, designing and optimising heat exchangers. Finally, the results of this study can be also of significant value for the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
1. Introduction Plate fin-and-tube heat exchangers are widely used in several areas such as HVACR systems. They have a high degree of surface compactness. Substantial heat transfer enhancement is obtained as a result of the periodic starting and development of laminar boundary layers over interrupted channels formed by the fins and their dissipation in the fin wakes. This is however accompanied by an increase in the pressure drop due to increased friction and form-drag contribution from the finite thickness of the interrupted fins [1–5]. The governing thermal resistance for these heat exchangers is usually on the air side which may account for 85% or more of the total resistance. The effect of fluid flow nonuniformity on heat exchanger efficiency is of first order importance because it can intensify longitudinal wall heat conduction and the ⇑ Corresponding author. Tel.: +1 613 996 3734; fax: +1 613 947 0291. E-mail address: [email protected] (W. Yaïci). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.034 0017-9310/Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.
maldistribution of interior temperature. In the design of platefin-and-tube heat exchanger, it is usually assumed that the inlet flow and temperature distribution across the exchanger core are uniform and steady. However, the assumption is generally not realistic under real operating conditions due to various reasons. One of these reasons is mainly related to the flow nonuniformity. In fact, the flow nonuniformity is usually divided into two types: gross maldistribution and passage-to-passage maldistribution. The gross flow maldistribution in plate-fin heat exchangers is mainly associated with improper heat exchanger entrance configuration, such as poor design of header and distributor configuration. The passage-to-passage flow maldistribution occurs in a highly compact heat exchanger caused by various manufacturing tolerances, frosting of condensable impurities, etc. [6–9]. Considerable research has been dedicated on the study on the effects of flow maldistribution on heat exchangers performance. Most of these studies in heat exchangers have only been investigated experimentally and analytically due to their complexity.
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Nomenclature BC Cp D Fp Ft f H HVACR h j k L Ll Lt Nu Pin P p Pr Re
boundary condition specific heat of the fluid at constant pressure, J/kg K tube diameter, m fin pitch, m fin thickness, m fanning friction factor fin spacing, m heating, ventilating, air conditioning and refrigeration average heat transfer coefficient, W/m2 K Colburn factor thermal conductivity, W/m K flow length, m longitudinal tube pitch, m transverse tube pitch, m Nusselt number inlet or upstream pressure, Pa pressure, Pa local pressure, Pa Prandtl number Reynolds number based on fin spacing
Most of previous works mainly investigated the effect of flow nonuniformity on heat exchangers performance deterioration based on their own flow maldistribution model [9–32]. For example, Fleming [6] set up a flow maldistribution model in paired-channel heat exchangers and investigated the effect of flow maldistribution on the performance deterioration. Based on the experimental data obtained from wind tunnel experiments, Chiou [8,9] set up a continuous flow distribution model and studied the thermal performance deterioration in cross-flow heat exchangers. Mueller [12] and Mueller and Chiou [11] summarised various types of flow maldistribution in heat exchangers and discussed the reason leading to flow maldistribution. Thermal performance reduction in air-cooled heat exchangers due to nonuniform flow and temperature distributions was investigated by Beiler and Kroger [13]. The results showed that nonuniform air velocity distribution to a tube row leaves the row with a distorted temperature profile. The temperature non-uniformity was found to increase as the air passes through subsequent tube rows. Ranganayakulu et al. [15] and Ranganayakulu and Seetharamu [16,17] investigated the combined effects of wall longitudinal heat conduction, inlet flow uniformity and temperature nonuniformity on the thermal performance of a two fluid cross-flow plate-fin heat exchanger using finite element method. The results showed that the performance may be reduced by 30% under non-uniform operating conditions. Computational investigations into flow maldistribution effects on heat exchanger performance are becoming more common as the capabilities of commercial CFD codes and the cost of computing power improves [33–40]. Lalot et al. [33] used CFD to study the gross flow maldistribution in an electrical heater. They presented the effect of flow non-uniformity on the performance of heat exchangers, based on the study of flow maldistribution in an experimental electrical heater. They found that reverse flows would occur for the poor header design and the perforated grid can improve the fluid flow distribution. Their results indicated also that the flow maldistribution leads to a loss of effectiveness of about 25% for cross-flow exchangers. Ng et al. [34] used CFD modelling to generate the velocity profiles for the numerical e-NTU thermal performance analysis, but no hydrodynamics performance effects were presented. The main focus has been on header design with authors such as Zhang and Li [35], Wen and Li [36] and Sheik
T Tin Twall U, V, W u u uin u, v, w x, y, z
temperature, °C inlet temperature, °C wall temperature, °C dimensionless velocity in x, y, z directions velocity vector, m/s velocity, m/s inlet frontal velocity, m/s velocity in x, y, z directions, m/s direction coordinates
Greek symbols h dimensionless temperature r vector operator l dynamic viscosity, Pa s q density, kg/m3 Subscripts in inlet r ratio
Ismail et al. [37] using CFD to design various flow dispersion baffles in order to improve flow distribution into the heat exchanger. 3D CFD simulation method can provide the flexibility to construct realistic computational models that are easily adapted to a wide variety of physical conditions without constructing expensive test rigs or large-scale prototypes. Therefore, CFD can provide an effective platform where various design options can be tested and an optimal design can be determined at a relatively low cost. The results of the literature studies showed the importance of considering the flow maldistribution for better design of plate heat exchangers [40]. It must be noted that all of the above works mainly concentrated on the effect of flow nonuniformity on the heat exchanger performance using simplified 2D or 3D modelling. The focus with these designs is on flow uniformity entering the heat exchanger with the goal to maximise the thermal performance but the hydrodynamics aspect was not always presented, such as the pressure drop penalties associated with the baffle design or the effect of flow maldistribution on the performance taking into account the coupling of fluid flow and heat transfer. The objective of this work is to predict the influence of different inlet air velocity profiles simulating inlet flow maldistribution on the thermo-hydraulic performance of heat exchangers using 3D CFD. The results will help in suggesting a way of modifying, improving or optimising the design of header configurations for heat exchangers in order to minimise the effect of flow maldistribution on the heat exchanger performance. The work involves 3D CFD modelling, validation and simulation for two types of platefin-and-tube heat exchangers to demonstrate it. The results of this investigation are expected to be valuable for the improvement and the optimum design of this heat exchanger type.
2. CFD model details 2.1. Physical model Fig. 1 illustrates the geometric models of the plain-fin-and-tube heat exchangers considered in the present work. Fig. 2 shows the nomenclature used for the in-line and staggered arrangements, with the geometrical values listed in Table 1. Fig. 3 presents the
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W. Yaïci et al. / International Journal of Heat and Mass Transfer 74 (2014) 490–500 Table 1 Geometrical parameters for the plain-fin-and-tube heat exchanger models.
Fig. 1. Schematic of typical plain fin-and-tube compact heat exchanger (staggered arrangement).
Parameters
Values
Tube diameter fin collar outside diameter, D (mm) Longitudinal tube pitch, Ll (mm) Transverse pitch, Lt (mm) Fin pitch, Fp (mm) Fin thickness, Ft (mm) Number of tube row, N Fin-and-tube arrangements
9.97 27.50 31.75 3.21 0.20 4 In-line, staggered
computational domain with the co-ordinate system of the two heat exchanger types. 3D steady flow models of plate-fin-and-tube heat exchangers with four rows for in-line and staggered arrangements were built in the CFD commercial software COMSOL [41]. It was used as the grid generator and the CFD solver, respectively. The following assumptions were considered in the flow models: the working fluid is air within the laminar regime on the external side (100 < Re 6 1200); it is assumed to be Newtonian, incompressible with constant inlet properties; the flow is assumed to be threedimensional and steady state; water at high velocity is assumed to flow inside the tubes, resulting in a constant tube-surface temperature; the viscous dissipation and viscous work are neglected; there are no body forces.
(a)
(b) Fig. 2. Modelled heat exchangers: (a) nomenclature and simulation domain; (b) computational domain with boundary conditions.
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temperature and energy transport are coupled. Eqs. (1) and (2) are solved together with an energy balance in steady-state 3D. Conservation of energy:
qC p ðu rÞT ¼ kr2 T
ð3Þ
2.3. Boundary conditions This section describes boundary conditions used in the present study with reference to Figs. 2 and 3. Assuming symmetry conditions on the mid-plane between two fins, the bottom and top boundaries simulate the fin and the mid-plane respectively. This symmetry of the problem was used to model only one half of the domain for the computational purposes. The boundary conditions used are as follows: At the upstream inlet boundary, Dirichlet boundary conditions, uniform flow with constant velocity uin and constant temperature Tin are assumed.
u ¼ uin ;
Fig. 3. Comparison of present CFD results with experimental results of Wang et al. [2] and CFD results of Bhuiyan et al. [46] in the heat exchanger for validation study: (a) friction factor f; (b) Colburn factor j.
In order to better predict the air flow field behaviour, the optimised solution-adaptive mesh refinement is used. More cells were added at locations where significant flow changes are expected, for example near the walls. The resulting mesh enabled the features of the flow field to be better represented. The symmetric solver selected here accounts for the three-dimensional effects, and the calculation domain was half of the physical body, based on symmetry considerations. Mixed topology of unstructured grids was used, and the final mesh was composed around 9 105 elements for the in-line and staggered configurations. The cells close to inlet and outlet ports and walls are small enough to capture the complex flow structure. Details on the grid system and selected mesh elements are provided in Section 2.4. 2.2. Governing equations
v ¼ w ¼ 0;
T in ¼ 20o C
ð4Þ
At the downstream end of the computational domain or outlet, the Neumann boundary condition is applied, i.e. stream wise gradients for all the variables are set to zero. No-slip boundary condition is used at the fin and tube surfaces. These surfaces are assumed to be solid walls with no slip wall boundary condition; the velocity of the fluid at the wall is zero and constant wall temperature is assumed. This indicates that the fin efficiency, which is a function of the wall temperature (tube wall and fins), is assumed to be equal to 1. In other words, this simplification corresponds to isothermal wall boundary condition. The fin and tubes are assumed to be made of aluminium. Since aluminium is a relatively high thermal conductivity material, constant wall temperature boundary condition can be safely assumed over the surfaces. The condition prescribes:
u ¼ v ¼ w ¼ 0;
T wall ¼ 80 C
ð5Þ
Free stream planes (top and bottom planes of the extended surface areas):
@u ¼ 0; @z
@v ¼ 0; @z
w ¼ 0;
@T ¼0 @z
ð6Þ
Symmetry boundary conditions are prescribed at the centre plane, tube centre plane and the top symmetry plane (mid-plane between two fins) as shown in Fig. 2. At these planes zero normal velocity and zero normal gradients of all variables are assumed. Side planes (symmetry planes):
@u ¼ 0; @y
@w ¼ 0; @y
v ¼ 0;
@T ¼0 @y
ð7Þ
The Fanning f-friction factor (ratio of wall shear stress to the flow kinetic energy), which is related to pressure drop in tubeand-fin heat exchangers is expressed as:
ðPin PÞH 1 qu2in 4L 2
The Navier–Stokes and energy equations in three-dimensional form were used to solve for the steady-state hydrodynamics and thermal fields. Therefore, the resulting governing equations without consideration of body forces and viscous dissipation can be written in Cartesian vector form as follows: Conservation of mass:
The Colburn j-factor (ratio of convection heat transfer per unit duct surface area) to the amount virtually transferable (per unit of cross-sectional flow area) is defined as:
ru¼0
ð1Þ
j¼
ð2Þ
where Reynolds Re and average Nusselt numbers are defined as follows:
Conservation of momentum:
qðu rÞu ¼ rp þ lr2 u
The coupled heat transfer and laminar flow is used to model slow-moving flow (Re = 100–1200) in the heat exchanger where
f ¼
Nu RePr1=3
Re ¼
quin H l
ð8Þ
ð9Þ
ð10Þ
494
Nu ¼
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hH k
ð11Þ
Given that the improvements in heat transfer are also accompanied by increases in the pressure drops, it is necessary to evaluate the net enhancement or degradation obtained in the heat exchangers with the effect of air flow distribution. One way of assessing the relative thermal–hydraulic performance enhancement, among many others is to consider the London area goodness factor or efficiency index, which is defined as the ratio of the Colburn j-factor over the friction f-factor. It is a commonly used metric because it examines the intrinsic link and trade-off between heat transfer enhancement and increased frictional forces in air flow over surfaces, and is given by [42–44]:
j=f ¼
Nu f RePr1=3
ð12Þ
2.4. Numerical procedure The governing equations of mass, momentum and energy conservation were solved by using the finite element method, based on the assumptions listed in Section 2.1. The governing equations are discretised on the computational domain, linearised in an implicit manner and solved by the finite element method using a pressure based solver. SIMPLEC (SIMPLE-Consistent) algorithm is employed for the pressure– velocity coupling, the second order upwind discretisation scheme is used for the convection terms and each governing equation is solved using QUICK scheme [45]. It is necessary to carry out independency verification of the grid system before CFD computation. The mesh independence study is investigated by using three different mesh sizes (coarse, normal, fine and finest meshes) of 159,864, 330,721, 901,685 and 2,965,847, and 126,237, 279,691, 897,857 and 2,960,748 for the in-line and staggered arrangements respectively are adopted for computation for the baseline case with the uniform inlet air velocity profile. The difference in the Fanning friction f-factor and the Colburn j-factor between the last two mesh sizes are less than 2% for both cases, before settling to a fine mesh for half of the geometry of the computational in-line or staggered heat exchanger cases. Computations were then run for a mesh containing about 901,685 and 897,857 elements for the in-line and staggered arrangements respectively, which was considered to be acceptable in terms of accuracy and efficiency. Furthermore, the solution is iterated until convergence is achieved, that is, residual for each equation achieves values less than 106 and 108, and changes in flow field temperature and energy, respectively become negligible. A workstation with 2 (R) Xeon processors of 2.4 Hz and an installed memory (RAM) of 16 GB, which took between 1 and 24 h of CPU time depending on the case study, was used to perform the required duty. 3. Model validation Experimental data by Wang et al. [2] are used to validate the present CFD model. The geometrical parameters for the plain fin staggered arrangement used by experiments of Wang et al. [2] and the present numerical study for model validation purpose are the same reported here: Ll = 22 mm, Lt = 25.4 mm, Fp = 3.00 mm, Ft = 0.13 mm, and D = 9.5 mm. Validation is performed with air and wall temperatures of 25 and 100 °C, respectively. Air is used as working fluid assuming constant properties (q = 1.185 kg/m3, l = 1.831 105 Pa s, k = 0.0261 W/m K, Pr = 0.736).
The values of the Fanning friction factor f and Colburn factor j as a function of Reynolds numbers in the range of 100–2000 are used to compare the predicted results by the present study with experimental data [2], as shown in Fig. 4. The authors [2] reported maximum uncertainties of 0.31%, 0.1 °C and 0.5% in the primary measurements for air flow, air temperature and heat exchanger pressure drop, respectively. The maximum uncertainties in the reported experimental derived values of the friction f factor and Colburn j factor were in the order of ±17.7% and ±9.4% at Re = 600. Very good agreement is obtained between the experimental and the CFD simulation results, which are within less than 5% of discrepancy. Also, the present CFD results have been compared with CFD results of Bhuiyan et al. [46] obtained using FLUENT software. A good agreement can be observed between CFD predictions using different CFD codes, with a deviation within 7%, as can be seen in Fig. 4. This numerical model was then used for further heat exchanger analysis with supporting reliability of the computation.
4. Results and discussion A numerical study was performed to predict the influence of the inlet air flow distribution on the performance of heat exchangers. Table 1 presents the ranges and values of the geometry of the heat exchangers studied for the CFD simulation. The effect of inlet air flow non-uniformity on the governing independent parameters influencing the hydrodynamics and heat transfer on the heat exchanger performance are the Reynolds number (Re), Prandtl number (Pr), the geometrical parameters of the heat exchanger, the tube arrangement and other parameters such as circuitry, variety of working fluids. Table 2 shows the summary of the simulation matrix for the parametric study. Each case is studied for different combination of the Reynolds numbers, Re = 100, 300, 600, 900 and 1200 and six inlet air velocity profiles to mimic the inlet airflow non-uniformity including a uniform air flow velocity, which case corresponds to the baseline. The inlet air velocity profiles were chosen based on the possible cases that could be encountered in real heat exchangers of air handling units for example. This approach allows simulating the air flow maldistribution case by case in order to be able to make a quantitative assessment of its effect on the system performance. The ultimate objective is to use CFD tool for the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution. The geometrical factors considered in this investigation are the tube alignments of the heat exchangers as described in the previous section; while the seven inlet air velocity profiles considered are Uniform, Linear-up, Linear-down, Linear-down with the Velocity at the centre, Parabolic, Half-parabolic, and an expression of velocity profile [47] as presented in Fig. 4. These numerical results cover the operating conditions for the laminar flow regime with inlet frontal velocities ranging from 2 and 6 m/s. These correspond to 70 cases investigated. Effect of inlet airflow maldistribution on hydrodynamics and thermal performance results for the heat exchangers are presented in details following the conditions shown in Table 2. Possible ways were identified to eliminate it or improve the heat exchanger performance. CFD results for both the in-line and staggered tube heat exchangers presented in the form of the Colburn factor j, Fanning friction factor f, and the efficiency index j/f as a function the Reynolds number Re for the seven inlet air velocity profiles are shown in Figs. 5–7. As mentioned earlier, the uniform inlet airflow velocity profile is considered as the baseline case in this investigation.
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y
y
y u = u in
u = C1 ⋅ uin ⋅ y /(Lt / 2)
u = 2 ⋅ uin − C1 ⋅ uin ⋅ y /(Lt / 2)
C1 = 1.23485
u Uniform
C1 = 1.1854
u Linear-down
u Linear-up
u = uin ⋅ C1 ⋅ sin(2 ⋅ π ⋅ y / Lt)
y
y
u = uin ⋅ C1 ⋅ sin(π ⋅ y / Lt)
C1 = 1.7358
y
C1 = 1.5772
u =1.59117⋅ uin −C1 ⋅ uin ⋅ y /(Lt/ 2) C1 = 0.73
u Linear-down with velocity at the center
u Parabolic
u Half-parabolic
u = uin ⋅ C1 ⋅ C2 + ( y ⋅ uin ⋅ C2 ⋅ 4⋅ (1− C1) / Lt) C1 = 0.5 & C2 = 0.6578
y
u Velocity profile [47] Fig. 4. Inlet air velocity profiles used in CFD simulations.
Table 2 Summary of the simulation matrix with the input data of the heat exchangers. Simulations
Computational cases
Figures
Heat exchanger arrangements
Velocity profilesa
Re (–)
Sim 3D.1
Case Case Case Case Case Case Case Case Case Case Case Case Case Case
Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs. Figs.
In-line
V1 V2 V3 V4 V5 V6 V7 V1 V2 V3 V4 V5 V6 V7
100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100,
Sim 3D.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5a–10a 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b 5b–10b
Staggered
300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300,
600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600,
900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900,
1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200
Tw (°C)
Tini (°C)
80
20
80
20
V1: uniform; V2: linear-up; V3: linear-down; V4: linear-down with velocity at centre; V5: parabolic; V6: half-parabolic; V7: equation [47]. a Fig. 4.
Fig. 5a and b show the variation of the Colburn factor j as a function of Reynolds number, Re for the different inlet air velocity profiles and for the in-line and staggered arrangements, respectively. As expected, it can be seen from the figure that the j factor decreases as the Reynolds number increases. In the case of the thermal performance of the in-line heat exchanger, as shown in Fig. 5a, the Linear-up velocity profile has 58% and 40% lower j values for Re numbers of 100 and 1200 respectively, when compared with the Uniform velocity profile. For the same Re values and relative to the Uniform velocity profile, the Linear-down velocity profile has 49% and 30% higher j values. Furthermore, the Parabolic velocity profile has j values lower of
9.5% and 6%, when compared with the baseline Uniform velocity profile results at Re numbers of 100 and 1200, respectively. Similarly, it is observed the same trend for the staggered arrangement, as illustrated in Fig. 5b, the Linear-up velocity profile has 55% and 28% lower j values for Re numbers of 100 and 1200 respectively, when compared with the Uniform velocity profile. For the same Re values and relative to the Uniform velocity profile, the Linear-down velocity profile has 51% and 17% higher j values. Furthermore, the parabolic velocity profile has lower j values of about 7% and 5%, when compared with the baseline Uniform velocity profile results at Re numbers of 100 and 1200, respectively.
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Fig. 6. Effect of inlet air velocity profiles on friction f factor at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
Fig. 5. Effect of inlet air velocity profiles on Colburn factor j at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
As expected and known, the tube arrangement plays a vital role in the heat transfer and pressure drop characteristics. In staggered arrangements, there is better flow mixing due to staggered tube layouts and thus provides higher heat transfer and pressure drop characteristics than the in-line arrangements. More importantly, the numerical results show that the inlet air flow distribution has a significant impact on the fluid flow and heat transfer characteristics and on the thermo-hydraulic performance due to different inlet air velocity profiles. It is found that this variation in thermal performance is more pronounced at low Re and tends to diminish at high Re. Accordingly, even if the operating and geometrical parameters play an important role on the heat exchanger efficiency, the airflow distribution has a strong impact on the degradation or enhancement of the thermal performance. Consequently, the heat exchanger header and distributor should be appropriately and accurately designed taking into account the inlet airflow characteristics and distribution. Figs. 6a and b, 7a and b present the variation of the friction factor f and the efficiency index j/f as a function of Reynolds number Re for the seven inlet air velocity profiles of in-line and staggered arrangements. As expected, given that the improvement in heat transfer is also accompanied by increases in the frictional losses, the same trend is observed in the results for f and j/f. These figures show that the friction factor f decreases with the increase in the Reynolds number. Moreover, the Linear-up velocity profile has 68% lower f and 85% higher j/f values for Re number of 1200, respectively, when compared to the Uniform velocity profile. However, for the same Re value and relative to the Uniform velocity
profile, the Linear-down velocity profile has 78% higher and 27% lower j/f values. Furthermore, the Parabolic velocity profile has f and j/f values of about 6% and 3% lower values, when compared with the baseline Uniform velocity profile results at Re number of 1200, respectively. Furthermore, it is observed the same trends for the staggered configuration, as shown in Figs. 6b and 7b. The Linear-up velocity profile has 66% lower f and 100% higher j/f values for Re number of 1200, respectively, when compared to the Uniform velocity profile. For the same Re value and relative to the Uniform velocity profile, the Linear-down velocity profile has 86% higher and 37% lower j/f values. Also, the Parabolic velocity profile has f and j/f value of about 6% lower and 1% higher values, when compared with the baseline Uniform velocity profile results at Re number of 1200, respectively. From the CFD results, it can be noted again the strong influence in the inlet air velocity distribution that may result in significant variations in fluid flow and heat transfer characteristics and hence on the heat exchanger performance. With the seven inlet air velocity distributions, simulating the influence of inlet air flow non-uniformity for the two types of heat exchangers considered in this study, it is found that the improvement or deterioration in heat transfer may be up to 50% compared to the baseline Uniform velocity distribution. Given the improvement or degradation in heat transfer are also accompanied by increase or decrease in f and j/f factors, there is consequently a trade-off in the thermo-hydraulic parameters to take into account in the design of the heat exchanger in order to achieve its optimal performance. Figs. 8–10 show the effect of the inlet air flow distributions on the dimensionless velocity, temperature and pressure ratio contours for both the in-line (Figs. 8a, 9a, 10a) and staggered
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(a)
Fig. 7. Effect of inlet air velocity profiles on efficiency index j/f at different Reynolds numbers for heat exchanger arrangements: (a) in-line; (b) staggered.
(Figs. 8b, 9b, 10b) arrangements taken on the x–y planes at the mid-plane z = 0 for Re = 1000, respectively. The dimensionless velocity, temperature, and pressure are defined as follows:
U¼
u uin
ð13Þ
h¼
T T in T w T in
ð14Þ
pr ¼ 1 2
p
qu2in
ð15Þ
For the present analysis as shown in Table 2, the inlet air temperature was kept constant at 20 °C and the fin and the tube surfaces were kept as wall boundary with a constant temperature of 80 °C and outlet pressure was assumed to be zero. Fig. 8a and b present the velocity distribution normalised by the value of the uniform inlet velocity (Eq. (13)) for different inlet air velocity profiles and for both the in-line and staggered arrangements. It can be seen from the figures the remarkable stream wise developing velocity profiles along the heat exchanger for the Linear-down, Linear-down with velocity at the centre and the Parabolic velocity profiles. The velocity profile is nearly symmetric and repeats itself, except at the inlet of the heat exchanger; the flow is not fully developed, due to entrance effect. The difference between the staggered and in-lined configuration can be observed from the figure. For the staggered configuration, it can be seen that stronger recirculation zones are formed compared to the in-line
(b) Fig. 8. Velocity ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
arrangement. Flow gets disturbed only by the tubes and a flow recirculation zone is observed at the trailing edge of the tubes. Fig. 9a and b illustrate the effect of the inlet velocity profiles on the normalised temperature lines (isotherms). All isotherms range from 0 to 1, which represents a low fluid temperature at the inlet to higher fluid temperature as it reaches the hot tube surface. Based on the previous velocity field patterns, as the velocity increases, specifically for the Linear-down, Linear-down with velocity at the centre profiles, and Parabolic velocity profile cases, the lower value isotherms penetrate deeper, which means the colder fluid is getting closer to the hot surface. As a result of this behaviour, the heat transfer is increased, as has been demonstrated in the computed Colburn j factor as a function of Re. As shown in
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(a) (a)
(b) Fig. 9. Temperature ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
the case of the V1, V2, V6 and V7 velocity profiles, a non-uniform air flow accentuates the cold isotherms, which penetrates farther downstream and hence results in lower heat transfer. The influence of the hydrodynamics upon the transfer of energy is shown in Fig. 9. Specifically, the influence of the inlet velocity at the entrance of the heat exchanger has a direct effect on the temperature field. Larger temperature changes are achieved upstream and over the tubes, where recirculation bubbles behind the tubes can be seen. Similar behaviour is observed for the staggered configuration, but the patterns alternate due to the tube arrangement; this allows improving mixing in the fluid and increasing the heat transfer. Fig. 10a and b show the influence of the inlet air flow distribution on the normalised pressure drop at fixed Reynolds number of 1000 for the in-line and staggered configurations, respectively. It can be seen that as expected, the pressure decreases monotonically along the heat exchanger. It can be noticed, however, that the inlet
(b) Fig. 10. Pressure ratio contours for different inlet air velocity profiles at Re = 1000 for heat exchanger arrangements: (a) in-line; (b) staggered.
air distribution has a strong effect on the heat transferred within the heat exchanger as seen with the velocity and temperature ratio distributions in Figs. 8 and 9. It can be noticed that depending of the inlet air velocity distribution, corresponds a pressure profile impacting on the hydrodynamics and heat rate of the system. The pressure drop increases with the inlet velocity of the air flowing into the channel of the heat exchanger. The inlet airflow distribution can be used as a mechanism to enhance the local heat rate or to improve the heat exchanger design. Moreover shown in the figure is the fact that, regardless of the velocity profiles, there is a rapid decrease in the amount of heat transferred within the system, specifically in the case of the in-line arrangement as the air temperature rapidly attains the wall temperature. Finally, this study with respect to inlet flow malditribution shows that 3D CFD simulation is a valuable tool for analysing,
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designing and optimising heat exchangers. Moreover, the present results can also be of considerable importance on the optimum design of header and distributor configurations to minimise maldistribution and optimise the heat exchanger performance.
We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from: wahiba.yaici@nrcan. gc.ca.
5. Conclusions
Acknowledgments
Nonuniformity of the inlet airflow in heat exchangers is of first order importance and has crucial influence on their efficiency because it can intensify longitudinal wall heat conduction and the maldistribution of interior temperature. In this study, 3D CFD simulations have been carried out to investigate the effect of the inlet airflow maldistribution on the thermo-hydraulic performance in heat exchangers used in air handling units. The CFD model was first validated against the experimental data available in the literature. Very good agreement between the numerical results and the experiments was found. This implies that the model used in the present study is reliable and can predict the thermal performance satisfactorily for heat exchangers. The CFD simulations have been then conducted for in-line and staggered plate-fin-and-tube heat exchangers with seven inlet air flow distributions for steady-state laminar flow conditions to systematically analyse their effects on the system performance. The CFD results confirmed the importance of the effect of inlet fluid flow nonuniformity on heat exchanger efficiency. Results indicate that up to 50% improvement or deterioration in the Colburn j and friction f factors are found compared to the baseline case of a heat exchanger with a uniform inlet velocity profile. Given the improvement or degradation in heat transfer are also accompanied by increase or decrease in f and j/f factors, there is consequently a trade-off in the thermo-hydraulic parameters to take into account in the design of the heat exchanger in order to achieve its optimal performance. The inlet airflow distribution can be used as a mechanism to enhance the local heat rate or to improve the heat exchanger design. Moreover, the present investigation with respect to inlet flow maldistribution demonstrates that 3D CFD simulation is a valuable tool for analysing, designing and optimising heat exchangers. Finally, the results of this study have significant contribution on the optimum design of header and distributor configurations of heat exchangers to minimise maldistribution.
Funding for this work was provided by Natural Resources Canada through the Program of Energy Research and Development.
Conflict of interest We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration due to the protection of intellectual property associated with this work and there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He/she is responsible for communicating with the other authors about progress, submissions of revisions and final approval of proofs.
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