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water nanofluid
Accepted Manuscript Title: Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO 2/water nanofluid Author: Mostafa Mahmoudi, Mohammad Reza Tavakoli, Mohamad Ali Mirsoleimani, Arash Gholami, Mohammad Reza Salimpour PII: DOI: Reference:
S0140-7007(16)30383-8 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.11.014 JIJR 3482
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
11-6-2016 13-11-2016 19-11-2016
Please cite this article as: Mostafa Mahmoudi, Mohammad Reza Tavakoli, Mohamad Ali Mirsoleimani, Arash Gholami, Mohammad Reza Salimpour, Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid, International Journal of Refrigeration (2016), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid Mostafa Mahmoudi1, Mohammad Reza Tavakoli*,2, Mohamad Ali Mirsoleimani3, Arash Gholami4, Mohammad Reza Salimpour5 1 M.Sc student, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 2 Assist. Professor, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 3 M.Sc student, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 4 M.Sc, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111 5 Professor, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] * Corresponding author, Email: [email protected] Highlights
A 30% enhancement in heat transfer coefficient was achieved.
Increasing the Dean number at fixed Reynolds number increases the heat transfer.
The friction factor is an ascending function of nanoparticles concentration.
Four general correlations for the Nusselt number and friction factor were proposed.
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Abstract: In the present article, forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid as working fluid were investigated experimentally and numerically. The aim is to investigate and provide additional insight about the effects of physical and geometrical properties on heat transfer augmentation and pressure drop in helically coiled tubes. The experiments were conducted in the range of Reynolds number from 3000 to 18000 and in the nanoparticle concentrations of 0.1, 0.2, and 0.5% for five different curvature ratios. In numerical simulations the thermophysical properties of the working fluid were assumed to be a function of nanofluid temperature and concentration. For turbulent regime the standard k model was used to simulate the turbulent flow characteristics. The numerical results were in a good agreement with the experimental data. The results showed that utilization of nanofluid instead of distilled water leads to an enhancement in the Nusselt number up to 30%. Also, four formulas were introduced to obtain the average Nusselt number and friction factor in helically coiled tubes under constant wall temperature condition for both laminar and turbulent flow regimes. Keywords: Nanofluid; Heat transfer enhancement; Pressure drop; Helically coiled pipe; Turbulent flow.
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Nomenclature Parameter
Symbol
Helix surface area [m2]
Ap
Heat capacity [kg.m2/s2.K]
Cp
Coil inner diameter [m]
d
Helix diameter [m]
D
Friction factor
f
Heat transfer coefficient [W/m2.K]
h
Turbulence kinetic energy [m2/s2]
k
Coil length [m]
lh
Mass flow rate [kg/s]
m
Pressure [pa]
p
Volumetric flow rate [m3/s]
Q
Temperature [K]
T
Logarithmic temperature difference
Δ TLM TD
Velocity component [m/s]
ui
Velocity fluctuation component [m/s]
u i
Greek symbols Thermal conductivity ratio
Turbulence dissipation [m2/s3]
Nanoparticles concentration (%)
Φ
Molecular thermal diffusivity
Γ k / C p
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Curvature ratio
Dynamic viscosity [kg/m.s]
Kinematic viscosity [m2/s]
Density [kg/m3]
Non-dimensional parameters Reynolds number
Re u b d /
Dean number
D e Re d / D
Nusselt number
Nu hd / k
Subscripts Bulk property
b
Base fluid property
f
Nanofluid property
nf
Nanoparticle property
p
Reference parameter
ref
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1- Introduction The development of techniques that allow more effective heat transfer augmentation is a growing need in many technologies and has drawn lots of attention in the field of nanofluids [1-3]. From heat transfer point of view, common fluids such as water and oil have low thermal conductivity in comparison with metals. Nanofluids show a notable potential to enhance the heat transfer rate. On the other hand, the configuration of pipes might increase the heat transfer rate. Due to the presence of secondary flow in these geometries, in comparison with the straight pipes, the flow field and convective heat transfer distribution in helically coiled pipes are complicated. The secondary flow motion induced by curvature of pipes and the resultant centrifugal force makes a pair of longitudinal vortices which results in increase in the heat transfer coefficient [4]. With increasingly development of processes that need high heat transfer rates, the necessity of utilizing high performance heat exchangers, e.g. the ones work with nanofluids, get importance in various industries. Helical coiled heat exchangers are used in a very wide range of industrial applications such as compact heat exchanger, condensers and evaporators, environmental engineering, waste heat recovery, cryogenic processes, etc. Comprehensive review articles about the applications of nanofluid in heat transfer have been published by several researchers [5-8]. The literature related to heat transfer enhancements in forced convection with different nanofluids is very rich and researchers have studied different aspects of this field. Although these works provide important information about momentum and heat transfer in nanofluids, the majority has been focused on forced convection under laminar flow regime in heat exchangers and less attention has been paid to turbulent flow and heat transfer in helically coiled pipes using nanofluids. Salimpour [9] has performed an experimental investigation on heat transfer characteristic of temperature dependent-property engine-oil inside shell and coiled tube heat exchangers. He presented an empirical correlation to predict the heat transfer coefficient inside these kinds of heat exchangers. Salimpour [10] in another work has experimentally studied the effect of coil pitch on heat transfer rate in helically coiled tube heat exchangers. He found that the coils with larger pitches have higher heat
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transfer rates in comparison with ones with smaller pitch. Shokouhmand et al. [11] have conducted an experimental investigation to study the shell and helically coiled tube heat exchangers. They considered both parallel flow and counter flow configurations to study the effects of various pitches and curvature ratios on the heat transfer rate. They found that using the counter flow configuration instead of parallel one increases the overall heat transfer coefficient up to 40%. Reddy and Rao [12] have conducted an experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluids in double pipe heat exchanger. They found that for the case of nanofluid at 0.02% volume concentration, the heat transfer coefficient and friction factor get enhanced by 13.85% and 10.69%, respectively. Jamishidi et al. [13] have presented an experimental study of heat transfer rate enhancement in shell and helical tube heat exchangers. They used the Taguchi method to obtain the optimum condition according to the overall heat transfer coefficient for whole heat exchanger. In another work, Jamshidi et al. [14] have studied the effect of adding nanoparticles in thermal-hydraulic performance of helical tubes. They used Taguchi method to find the optimum condition for the desired parameters. Their results indicated that using nanofluids results in improvement of the thermal-hydraulic performance of helical pipes. Akhavan-Behabadi et al. [15] have simultaneously utilized the helical coiled tubes and nanofluids and investigated their effects on the heat transfer during the experiments. Based on their experimental results, utilizing helical coiled tubes enhances the heat transfer rate remarkably. San et al. [16] have performed an experimental investigation on heat transfer performance of a helical heat exchanger. They used Reynolds numbers in the range 307 to 2547 and found that increasing number of turns of the heat exchanger increases its effectiveness Park et al. [17] have carried out a combined experimental and numerical case study of the heat transfer around the helical ground heat exchanger. Kahani et al. [18] have experimentally studied the heat transfer behavior of metal oxide nanofluid flows inside helical coiled tube. They found that the convection heat transfer coefficient and pressure drop are increased considerably because of the tube curvature. Huminic and Huminic [19] have used a three dimensional analysis to study the heat transfer and laminar flow characteristics in a helical heat exchangers using nanofluids. They investigated the effects of nanoparticles concentration
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level and Dean number on the heat transfer rates. They found that increasing the flow rate and Dean number leads to increase in heat transfer coefficient. Kumar et al. [20] have conducted experimental as well as numerical simulations to study the heat transfer characteristics in helically coiled heat exchangers. Bahremand et al. [21] have investigated the turbulent flow in helically coiled tubes under constant heat flux using both numerical and experimental methods. Their results showed that the nanoparticles tend to increase the axial velocity slightly and suppress the turbulent kinetic energy. Akbaridoust et al. [22] have investigated the laminar flow regime through helically coiled pipes using experimental and numerical methods. They have considered a constant wall temperature condition. Their results showed that using base fluid in helically coiled pipe instead of using nanofluid in straight pipes enhances the heat transfer more effectively. Hashemi and Akhavan-Behabadi [23] have experimentally studied the problem of heat transfer and pressure drop through horizontal helical tube under constant heat flux using nanofluids. Their results showed that utilization of nanofluid leads to increase in the heat transfer coefficient and pressure drop. Our literature review revealed that the previous studies have been restricted mostly to the laminar flow condition and the effects of Dean number at different Reynolds number get paid less attention. In the present paper, a comprehensive numerical and experimental study of turbulent flow and heat transfer of TiO2 nanofluids in helically coiled tubes with constant wall temperature condition were carried out. The experimental and numerical simulations were performed for three nanoparticles concentration of 0.1%, 0.2%, and 0.3%. Also the effect of helix curvature ratio in turbulent flow regime on heat transfer augmentation and pressure drop was investigated. A standard k turbulent model was used to simulate the turbulent flow and heat transfer regime. The main objective of this study is to investigate and provide additional insight about the effects of physical and geometrical properties on heat transfer augmentation in helically coiled tubes using nanofluid.
2. Experiments and Measurements 2.1. Preparation and Property of Nanofluid
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Water was used as the base fluid and nanofluids with nanoparticles concentration of 0.1% and 0.5% were prepared by dispersing TiO2 nanoparticles. The solid particles used in this study were TiO2 nanoparticles. The nanoparticles have been produced with an average particle size in range of 1015nm and 99.986% pureness by means of chemical analysis method. Table 1 shows the physical and thermophysical properties of nanoparticles used in the experiments. A UP200S ultrasonic mixer was used to disperse the coagulated nanoparticles and leads to a uniform dispersion of nanoparticles throughout the nanofluid. The resulted nanofluids were stable for about 24 hours. The sedimentation was observed after 5 days with naked eyes. However, According to the literature review for TiO2/water and other nanofluids with low nanoparticle concentrations, i.e. less than 0.5%, the complete sedimentation occurred after a week. For example, Kedzierski and Gong [24] used the low nanofluid concentration in order to avoid rapid sedimentation. Hashemi and Akhavan-Behabadi [23] have observed with naked eyes that the complete sedimentation occurred after a week. Kahani et al. [25] have observed no sedimentation after 48 hours of prepration. Thus, because the experiments have been performed during the next 24 hours after preparation of the nanofluid, the possibility of sedimentation was quite low.
Due to the thermophysical differences between the base fluid and nanofluid, it is necessary to compute the thermophysical properties of nanofluid for numerical simulations. Two classical formulas are used to obtain effective density and thermal capacity of the nanofluid [26 and 27]: nf 1 f + p
C p
nf
1 C p C p f
(1) (2) p
where the subscripts nf, f, and p are indicating that quantity is related to the nanofluid, base fluid, and nanoparticles, respectively. Rea et al. [28] and Karimi et al. [29] have presented the following experimental formula for nanofluid viscosity as a function of temperature and volumetric concentration:
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nf T , Φ f T exp 4.91Φ 0.2092 Φ f T ref
T T ref
n
1 1 exp B T T ref
(3)
where B 4700, n 8.9, T ref 295 K , and ref 9.59 10 4 N .s / m 2 . These formulas are valid for the nanoparticle volumetric concentration less than 6% and temperature range of 290-350K. In the case of calculation of the thermal conductivity of nanofluid the Maxwell model [30], which is one of the oldest and well-known formula to compute the thermal conductivity of the solid-fluid mixture, is used,
k nf kf
2 2 1
(4)
2 1
where k p / k f is defined as the ratio of the thermal conductivity of nanoparticles to thermal conductivity of the base fluid.
2.2. Measurement of Heat Transfer Coefficient Rate of net heat transfer from the vapor bath to the working fluid flowing through the test section depends on the measurements of inlet and outlet temperature as well as the mass flow rate of nanofluid in the test section. In order to compute the overall heat transfer coefficient at constant wall temperature condition, following relation can be used: m C p Tout Tin hA p Δ T L M T D
(5)
where m is the nanofluid mass flow rate, Tin and Tout are the bulk fluid temperature at inlet and outlet of test section, respectively. A p is the surface area of the helical coiled pipe which has a direct contact with the hot fluid, h is the overall heat transfer coefficient, and Δ T L M T D is the logarithmic temperature difference which is defined as
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Δ TLM TD
Δ Tin Δ Tou t
(6)
Tin ln Tou t
where Δ Tin Ts Tin and Δ Tin Ts Tout and T s is the temperature of helical coiled tube. Finally, the overall heat transfer coefficient after some simplifications becomes,
h
C p Q Tout Tin
(7)
d ilh Δ TLM TD
where Q is the volumetric flow rate, d i the inner diameter of pipe, and l h is the length of helical coiled tube. Therefore, the non-dimensional heat transfer coefficient is given by
Nu
(8)
hd k
where k is the effective thermal conductivity of the nanofluid. To validate the experimental data, we carried out some experiments for a straight tube and compared the results with the Saider-Tate equation for the laminar regime and with Dittus-Boelter equaion and Gnielinski relation for the turbulence flow regime [31]: Saider-Tate equation:
Gnielinski equation:
Dittus-Boelter equation:
N u 1.86 R e P r d / l
Nu
f
1/ 3
b s
0 .14
/ 8 R e 1000 P r
1 12.7 f / 8
1/ 2
Nu 0.023 Re
0.8
Pr Pr
2/3
0.4
1
(9)
(10)
(11)
2.3. Measurement of Friction Factor Experimental friction factor is determined using the measurements of pressure drop along the helical coiled pipe. A U-shaped manometer is used to measure the pressure drop along the pipe Δ P . The axial pressure drop of fluid flow inside the coil can be read as [12, 32]:
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Δ p d i
2
32 l Q
2
5
f exp
(12)
In order to validate our experimental data, the experimental data were compared with Blasius equation [31] for laminar regime and with Petukhov equation for turbulent regime [31]:
f
(13)
64 Re
f
(14)
1
0.79 ln R e 1.64
2
Eq. (13) for laminar flow and Eq. (14) is Petukhov equation for turbulent flow through straight tube which is valid on Reynolds number range of 3 10 3 Re 5 10 6 .
2.4. Experimental Setup One of the common apparatus which is used to enhance the heat transfer rate is helical coiled pipes. Due to the curvature of the pipe, the fluid experiences a centrifugal force while it is flowing in the helical coiled pipes. The centrifugal force exerted to the fluid causes secondary flows inside the pipe and this secondary flows leads to heat transfer augmentation in these apparatus. Figure 1 shows a schematic of helical coiled tubes and its geometrical properties. The pipe has a diameter of (d) and the diameter of the helical coil is illustrated by (D). The distance between two successive turns (b) is called the pitch. An experimental setup is designed to study the behavior of convection heat transfer and pressure drop in helically coiled pipes under constant wall temperature using nanofluids as working fluid. The schematic diagram of the experimental setup is shown in Fig. 2. In order to obtain the constant wall temperature condition, a steam bath has been used. The experimental apparatus is included of a main loop for the base/nanoluid which is comprised of different equipment such as the nanofluid reservoir, pump, test section, heat exchanger, a U-shaped manometer, flow meter, thermocouples, and a data logger.
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The nanofluid is pumped from the reservoir to the test section using by a centrifugal pump. The test section is included of a copper helical tube with various outer diameters in range of 65 to 112 mm. The geometrical properties of the coils are shown in table 2. All the helical pipes used in current work have 8 turns. Four 2000 W electric heaters are considered to generate the steam and then to reach a stable condition in the vapor bath, just two of them will stay in the circuit. The working fluid flows inside the test section while the vapor bath is full of saturated vapor. To reduce the heat losses from the steam bath to the surroundings, it is thermally insulated. The nanofluid temperature is measured at the inlet and outlet of the test section using two calibrated K-type thermocouples. Also, in order to measure the outer wall temperature of the helically coiled pipe, four other K-type thermocouples are provided. The temperatures of these points showed that the variation of surface temperature can be neglected (the uncertainty in wall temperature measurements was ±0.5℃). After that the warmed nanofluid enters the heat exchanger and loses its temperature using the cooling water to the initial temperature and then drains to the reservoir. To make sure that the experiment apparatus were working correctly and they have an acceptable accuracy, before performing the experiments on helical coiled pipes using nanofluid, a test for a straight pipe using water as working fluid was conducted. The data obtained for different Reynolds number is compared with the Eqs. (9-11) and Eqs. (12 and 13). Figure 3(a) demonstrates the variation of friction factor in both laminar and turbulent regimes. The data shows that there is a maximum 4.1% deviation from the Blasius equation in laminar flow and a maximum 6.3% error compared with Petukhov equation for turbulent regime. Figure 3(b) illustrates the average Nusselt number as a function of Reynolds number. As it is understood from Fig. 3(b) there is a good agreement between Dittus-Boelter equation, Gnielinski equation, Saider-Tate equation and present experimental data.
3. Numerical Simulation 3.1. Governing Equations The steady state forced convection heat transfer through helical coiled piped using nanofluid was studied. The helical coil is assumed to remain at constant temperature of T w that is greater than the
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bulk fluid temperature T . In numerical simulations the heat transfer and pressure drop in turbulent flow regime was studied. The effects of presence of nanoparticles on the viscosity, heat capacity, thermal conductivity, and density of working fluid are modeled using the proper correlations. The reason is that to model the interactions between the nanoparticles and the fluid numerically, it is necessary to use discrete phase models and consider the effects of flow field on the particle such as Saffman’s lift force, drag force, and the effect of gravity on particles. In addition, it is necessary to consider the effect of particle motions on the flow field which results in a transient problem. Furthermore, the thermal effects of the presence of nanoparticles on the heat transfer rate should be modeled. Therefore, due to the large number of meshes and the turbulent nature of flow at the investigated Reynolds numbers, considering the interactions between nanoparticles and the water will lead to increase in computational and time costs. Thus, it is convenient to model the effects of presence of nanoparticles on the flow field and the heat transfer using a single phase model and the proper correlations for density, thermal capacity, viscosity, and thermal conductivity. The governing equations for the conservation of mass, momentum and energy have been solved in the Cartesian coordinate system [29]; the mass conservation (continuity) is: ui xi
(12)
0
And the momentum equation can be written as
x j
u u i
j
xi x j 1 p
u u j i x xi j
u iu j x j
(13)
where and are the effective density and kinematic viscosity of the nanofluid, respectively.
The energy equation reads as follows:
x j
u iT
T Γ Γ t x j x j
(14)
where Γ and Γ t are the molecular thermal diffusivity and turbulent thermal diffusivity, respectively and defined as follows:
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Γ / Pr , Γ t t / Prt
The Reynolds stress term in momentum equation, i.e. u iu j , is modeled using by the k turbulence model in conjugate with Boussinesq hypothesis [32]: u u j i u iu j t x xi j
(15)
where t is the eddy viscosity and can be achieved by, t C k / 2
The kinematic energy of turbulence and the dissipation rate of the turbulence kinetic energy can be written as [33]
uj
uj
x j
k x j
C 1
ui
ij
k
x j
ij
ui x j
C 2
(16)
t k x j k x j
2
k
t x j x j
(17)
where the closure coefficients read as follows: C 1 1.44,
C 2 1.92,
1.3,
k 1.0,
Prt 0.9
3.2. Numerical Method, Boundary and Initial Conditions Finite Volume Method was used to solve Eqns. (12)-(17). SIMPLE algorithm was employed to couple pressure and momentum and the second-order upwind scheme was utilized for spatial discretization in all equations. The dependent variables (pressure, velocities, temperature, turbulence kinetic energy, and turbulence dissipation rate) are under relaxed by the factors of 0.3, 0.7, 0.5, 0.7, and 0.7 for P, U, T, k, and respectively. A preconditioned bi-Conjugate Gradient (PBiCG) solver was used for the governing equations. The PBiCG method is used when the system of equations are not necessary
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symmetric. It should be noted that the convergence criterion is defined as the maximum relative error between of variables in two successive iterations to be less than 10 7 .
In the case of boundary conditions a constant mass flow rate with uniform temperature T is specified as inlet boundary conditions of inlet extended pipe. The helical coiled tube wall is assumed to be in constant temperature T w and the flow exits to ambient at the outlet surface of the outlet extended pipe. At inlet the turbulent intensity, turbulence kinetic energy and turbulence dissipation rate are given by [33],
I
u
2
Ue
k
0.16 R e D
3 2
U e I
C
3/ 4
k
1/ 8
2
3/ 2
l
where C 0.09 and the length scale l is defined as l 0.07 D .
3.3. Grid-Independent Study and Validation Different sizes of numerical mesh were studied to investigate the dependency of solution to the computational grid (Table 3). Figs. 4(a, b) show the averaged non-dimensional heat transfer coefficient and friction factor at Re 9000 . These figures show that the variation of averaged Nusselt number and friction factor while using a grid number of 1095850 (or greater) is just 0.03%. Variation of average Nusselt number and friction factor from grid 1 to grid 2 is significant, because the resolution of the viscous sublayer in grid 2 was increased. By reducing the size of meshes, especially near the coil wall, the wall effect can be calculated more accurately and therefore, the variation of friction factor inside the helically coiled pipe becomes smaller. An asymptotic tendency of the friction factor values to converge with increasing the number of meshes, i.e. from 897248 (grid
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1) to 2154923 (grid 6), can be observed. The results suggest that a grid-independent solution is obtained when using a mesh number larger than 1.1 10 6 ; thus, we used a computational grid with the 1.6 10 cells. As it is demonstrated in Fig. 5, the grids in vicinity of the wall were refined due to 6
reach a more accurate velocity and temperature gradient in this region. Figure 4 illustrates the grid which was used in this study and Table 4 shows the total elements used in numerical simulations for different geometries.
As a benchmark comparison, simulation for forced convection heat transfer of nanofluid in a straight pipe has been carried out at different Reynolds numbers (see Figure 6). This problem was studied previously by Fotukian and Nasr Esfahani [34], Maiga et al. [35], Pak and Cho [26], and Xuan and Li [36] numerically and experimentally. It can be seen that the results of current numerical simulation are in a good agreement with their works. In Fig. 7(a), the results of the averaged Nusselt numbers in helically coiled pipes for distilled water in laminar and turbulent flows have been compared with the well-known experimental correlation of Schmidt [37] and the analytical formula of Mori and Nakayama [38], respectively: Schmidt [37]:
(18)
Mori and Nakayama [38]:
(19)
where
is the curvature ratio. The Schmidt correlation is valid for
in which
[37]. The Mori and Nakayama formula is valid for and
[38].
In order to validate the friction factor results, the results of Ito’s correlations (Eqs. 20 and 21) [39] for helically coiled pipes were compared with the current experimental data (figure 7(b)). The Ito’s correlations for laminar and turbulent flows are as follows, respectively: (20)
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(21) where
[39]. As it can be seen in Fig. 7, the present experimental data are in a
good agreement with the well-known previous correlations.
The uncertainty analysis was carried out using the procedure proposed by Beckwith et al. [40], and it was found that the expected experimental error for the Reynolds number, friction factor, heat transfer coefficient, and the Nusselt number were ±0.6%, ±7.1%, ±2.64, and ±2.64%, respectively.
4. Results and discussions The following sections are devoted on the effects of Dean number and nanoparticles concentration on overall heat transfer coefficient and friction factor in helical coiled tubes. The figures clearly show the positive effect of the presence of nanoparticles on heat transfer rate in helical coiled heat exchangers. Also, four formulas are introduced to obtain the averaged Nusslet number and friction factor in helical coiled tubes under constant wall temperature condition for both laminar and turbulent flow regimes. Then the capability and reliability of numerical simulation is discussed in order to find the characteristics of heat transfer and fluid flow behavior of nanofluids in other geometries.
4.1. Heat transfer coefficient Figure 8(a-c) shows the variation of overall non-dimensional heat transfer coefficient as a function of Dean number for different helical coiled pipes. As it is demonstrated in Fig. 8 and 9, with adding the nanoparticles to the distillated water, the heat transfer rate increases. The experiments were performed for the nanoparticle concentration of Φ 0.1 and 0.5 , while the numerical simulations were conducted for Φ 0.1, 0 .2 and 0.5 to obtain additional insight about the effects of nanoparticle concentration on heat transfer rate. Increasing the Dean number at a constant curvature ratio leads to change in flow regime, in other words, the transition of laminar flow to turbulent one. As it is seen in
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Fig. 8, at higher Dean numbers, adding nanoparticles to the base fluid results in enhancing the heat transfer rate more than in lower Dean numbers, i.e. laminar flow. This difference in increasing the Nusselt number in helical coiled pipes is related to the fact that in higher Dean numbers the secondary flows, which are developed in the cross section of the pipe, are stronger than secondary flows at lower Dean numbers. Therefore, the momentum transfer from the wall of the pipe increases and as a result of having higher momentum exchange rate near the wall, the heat transfer rate increases. Fig. 8(a-c) and Fig 9(a-c) indicate that with increasing the curvature ratio, the slope of variation of Nusselt number with Dean number decreases. For example, the non-dimensional heat transfer rate in Coil 1 (Fig. 8(a)) has a value of Nu 140 at De 3600 , while in coil 5, Fig. 8(c), this value occurs at De 6300 . As it is seen in Figure 8, with increasing the concentration of nanoparticles from Φ 0.1 to 0.5 the overall heat transfer rate in the pipes increases. That is due to the increasing in the viscosity of nanofluid when adding more nanoparticles. This increase can be seen in the Eq. 3 which the viscosity of nanofluid in the aforementioned range of nanoparticles concentration is an ascending function of Φ.
Figure 10 demonstrates the average non-dimensional heat transfer coefficient as a function of Dean number at various values of Reynolds numbers. As it is seen in Fig. 10(a-c) with increasing the Reynolds number from Re 3000 to Re 10500 , a dramatic increase in heat transfer rate occurs. That is due to the transition from the laminar flow regime to turbulence one which possesses higher momentum transfer rate. Also, with increasing the Reynolds number from Re 10500 to Re 18000 , the overall heat transfer coefficient increases. Another point in Fig. 10(a) is that by
increasing the concentration of nanoparticles from 0.1 to 0.5, at lower Reynolds number such as , the average Nusselt number is increased, considerably. For example, at
and
, increasing the nanoparticle concentration leads to increase in non-dimensional heat transfer coefficient up to 30%.
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At constant Reynolds number the effects of Dean number on heat transfer and factors which lead to the increase in heat transfer rate were investigated in the past sections. But Fig. 10 refers to another point that with increasing the Reynolds number till the flow regime turns to turbulence one, the effect of nanoparticles concentration approximately tarnishes. On the other hand, at lower Reynolds numbers, e.g. Re 3000 , nanoparticles concentration has an intense impact on average Nusselt number. At Re 3000 and De 1250 , increasing the concentration of nanoparticles from Φ 0.1 to Φ 0.5 results in a 70% enhancement in heat transfer rate. But this increase at higher Reynolds numbers, e.g. Re 18000 and De 4450 , is just 1.87% . This trend in heat transfer rate, in other words vanishing the effects of particles concentration on heat transfer rate, can be explained as follows: enhancing the momentum transfer rate with increasing the Reynolds number, i.e. increase in velocities fluctuations, may prevail the growth in momentum exchange rate between the particleparticle and particle-fluid. In this situation adding more amount of nanoparticles probably leads to a decrease in overall heat transfer coefficient, because it is possible increasing the nanoparticles concentration causes higher pressure drop, both frictional and axial pressure drop, along the coiled pipe which as a result, the heat transfer rate decreases. Figure 11 shows the variation of numerical values with experimental values for average Nusselt number. As it is seen, the deviation of numerical solution data from the experimental data is within 13% and 28% .
Finally, to calculate the average Nusselt number in coiled pipes with nanofluid as the working fluid, using the least-squares method the following relations are fitted to the experimental data: Laminar regime:
N u lam 0.043 R e
0.812
Pr
0.35
0.045
0.038
(22)
Turbulent regime
N u turb 0.028 R e
0.854
Pr
0.38
0.039
0.041
(23)
Equation (22) predicts the overall heat transfer rate with maximum error of +5.1% and minimum error of -6.7% in laminar flow regimes. For turbulent flows the equation (23) predicts +3.6% and -11.2%
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for maximum and minimum error, respectively. It should be noted that Eqs(22) and (23) are valid for the Reynolds numbers in range of 2346 Re 18563 , Prantdl numbers in 2.7 Pr 3.51 , curvature ratio in 0.0375 0.123 , and nanoparticles volumetric concentration in 10
3
3
5 10 .
4.2. Friction factor Figure 12(a-c) illustrates the variation of friction factor along the helical coiled pipes for different values of Dean numbers at various curvature ratios. From classic fluid mechanics it is expected that increasing the Reynolds number leads to having lower friction factor. That is because of changes in the velocity profiles when the Reynolds number increases. In the case of helical coiled pipes the Dean number plays the main rule in measuring the friction factor along the coiled pipes. As it is shown in Figs. 12 and 13, with increasing the Dean number at constant curvature ratio, the friction factor increases, too. At higher Dean numbers, the secondary flows get stronger and lead to enhancing the momentum transfer rate in the helical coiled pipes. Also, the enhancement of secondary flows causes the maximum velocity in the pipe happens closer to the coiled pipe wall which increases the velocity gradient in vicinity of the wall.
Fig. 12 also demonstrates that with increasing the nanoparticles concentration the pressure drop through the coiled pipe increases. That is due to the fact that with increasing the solid content of nanofluid, the density and viscosity of the fluid increases. Therefore, as a result of increasing in fluid thermophysical properties the friction factor through the pipe increases. On the other hand, at higher Dean numbers, the chaotic motion and migration of nanoparticles are higher than for lower Dean number which increases the momentum exchange rate in the fluid. This transport of momentum between the solid-solid and solid-fluid phases causes an increase in pressure drop, too.
Page 20 of 40
It should be noted that according to the literature, there is a critical Reynolds number ( helically coiled pipes which the flows at higher Reynolds number than
) in
are considered as
turbulent flows. Table 5 provides the proposed value of these critical Reynolds numbers by various researchers for the coils used in our paper. According to the data of Table 5 and the heat transfer and friction factor curves, the Reynolds numbers in which the flow is transiting to the turbulence flow from the laminar one can be determined. Thus, at Reynolds numbers higher than
, the turbulent
regime in the coil is achieved and the proper equations were used to simulate the heat transfer and flow field, numerically. Accurate simulation of the secondary flows in helically coiled pipes is crucial for prediction of the heat transfer and friction factor in these geometries. The contour lines of non-dimensional axial velocity and secondary flows at Reynolds numbers of 10500 and 18000 for the coil 5 and nanoparticle concentration of 0.1% are presented in Figure 14. As it can be seen in this figure, due to the turbulent nature of flow at these Reynolds numbers, the secondary flow pattern has more than two vortexes. Figure 15 demonstrates the variation of numerical values with experimental values of friction factor. Fig. 15 indicates that the deviation of numerical solution data from the experimental data is within 13% and 20% .
A least-squares method was used to obtain the relationship between the friction factor and Reynolds number, curvature ratio, and nanoparticles concentration in helically coiled pipes under constant wall temperature. Laminar regime:
f lam 10.145 R e
Turbulent regime
f turb 0.302 R e
0.530
0.177
0.012
(24)
0.013
(25)
0.241
0.116
Equation (24) predicts the friction factor in helically coiled tubes for laminar flow regime with maximum and minimum error of 3.6% and 4.6% , respectively. For turbulence flow the Eq. (25) gives the friction factor in coiled pipes with maximum error of 5.5% and minimum error of 9.6%
Page 21 of 40
relative to the experimental data. The above relations are valid for the Reynolds number in range of 2346 Re 18563 , curvature ratio in 0.0375 0.123 , and volumetric concentration in 10
3
3
5 10 .
5. Conclusion In this paper the forced convection heat transfer and pressure drop in helical coiled pipes using TiO2/water nanofluid as the working fluid were investigated experimentally and numerically. The numerical simulations were performed using finite volume method. The effects of curvature ratio, Reynolds number, and nanoparticles concentration was studied broadly. The experiments were conducted for laminar, transitional and turbulence flow regimes, But the numerical simulations were carried out only for turbulent flow regime. There was a good agreement between experimental and numerical data. The results showed that using nanofluid as the working fluid in helical coiled heat exchangers, leads to a noticeably enhancement in heat transfer rate. The main highlights of current research are summarized as follows:
Utilization of nanofluid instead of the distillated water leads to considerable heat transfer enhancement. In some cases an enhancement up to 30% can be achieved by using the TiO2/water nanofluid with 0.5% nanoparticles concentration.
Increasing the Dean number (curvature ratio) at fixed Reynolds number results in an increase in heat transfer.
Using nanofluids as the base fluid in helical coiled heat exchangers leads to higher friction factor than using distillated water. The friction factor is an ascending function of nanoparticles concentration.
General correlations of Nusselt number and friction factor is obtained to predict these parameters in helical coiled heat exchangers under constant wall temperature in laminar flow regime:
Page 22 of 40
N u lam 0.043 R e
0.812
f lam 10.145 R e
Pr
0.530
0.35
0.045
0.241
0.038
0.012
Also, general correlations for Nusselt number and friction factor are obtained in turbulence flow regime: N u turb 0.028 R e
0.854
f turb 0.302 R e
Pr
0.177
0.38
0.039
0.116
0.041
0.013
applicable ranges are: 2346 Re 18563 , 2.7 Pr 3.51 , 0.0375 0.123 , 10
3
3
5 10 .
Page 23 of 40
References [1] X.Q. Wang, A.S. Mujumdar, Review on nanofluids. Part II: experiments and applications, Braz J Chem Eng 25 (2008) 631–48. [2] K.D. Sarit, Nanofluids-the cooling medium of the future. Heat Transfer Eng 27(10) (2006) 1– 2. [3] S. Lee, S.U.S. Choi, Application of metallic nanoparticle suspensions in advanced cooling systems, Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition; Atlanta, GA, USA (1997) 227–234. [4] J.S. Jayakumar, S.M. Mahajani, J.C. Mandal, P.K. Vijayan, Rohidas Bhoi, Experimental and CFD estimation of heat transfer in helically coiled heat exchangers, Chemical engineering research and design 86 (2008) 221–232. [5] G. Huminic, A. Huminic, Application of nanofluids in heat exchangers: A review, Renewable and Sustainable Energy Reviews 16 (2012) 5625–5638. [6] R. Saidur, K.Y. Leong, H.A. Mohammad, A review on applications and challenges of nanofluids, Renewable and Sustainable Energy Reviews 15 (2011) 1646–1668. [7] D. Wen, G. Lin, S. Vafaei, K. Zhang, Review of nanofluids for heat transfer applications, Particuology 7 (2009) 141–150. [8] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer 52 (2009) 3187–3196. [9] M.R. Salimpour, Heat transfer characteristics of a temperature-dependent-property fluid in shell and coiled tube heat exchangers, International Communications in Heat and Mass Transfer 35 (2008) 1190–1195. [10] M.R. Salimpour, Heat transfer coefficients of shell and coiled tube heat exchangers, Experimental Thermal and Fluid Science 33 (2009) 203–207. [11] H. Shokouhmand, M.R. Salimpour, M.A. Akhavan-Behabadi, Experimental investigation of shell and coiled tube heat exchangers using wilson plots, International Communications in Heat and Mass Transfer 35 (2008) 84–92.
Page 24 of 40
[12] M. Chandra Sekhara Reddy, V.V. Rao, Experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluid in double pipe heat exchanger with and without helical coil inserts, International Communications in Heat and Mass Transfer 50 (2014) 68–76. [13] N. Jamshidi, M. Farhadi, K. Sedighi, D. Domeiry Ganji, Optimization of design parameters for nanofluids flowing inside helical coils, International Communications in Heat and Mass Transfer 39 (2012) 311–317 [14] N. Jamshidi, M. Farhadi, D.Domeiry Ganji, K. Sedighi, Experimental analysis of heat transfer enhancement in shell and helical tube heat exchangers, Applied Thermal Engineering 51 (2013) 644-652. [15] M.A. Akhavan-Behabadi, M. Fakoor Pakdaman, M. Ghazvini, Experimental investigation on the convective heat transfer of nanofluid flow inside vertical helically coiled tubes under uniform wall temperature condition, International Communications in Heat and Mass Transfer 39 (2012) 556–564. [16] J.Y. San, C.H. Hsu, S.H. Chen, Heat transfer characteristics of a helical heat exchanger, Applied Thermal Engineering 39 (2012) 114-120. [17] H. Park, S.R. Lee, S. Yoon, H. Shin, D.S. Lee, Case study of heat transfer behavior of helical ground heat exchanger, Energy and Buildings 53 (2012) 137–144. [18] M. Kahani, S. Zeinali Heris, S.M. Mousavi, Comparative study between metal oxide nanopowders on thermal characteristics of nanofluid flow through helical coils, Powder Technology 246 (2013) 82–92. [19] G. Huminic, A. Huminic, Heat transfer characteristics in double tube helical heat exchangers using nanofluids, International Journal of Heat and Mass Transfer 54 (2011) 4280–4287. [20] V. Kumar, S. Saini, M. Sharma, K.D.P. Nigam, Pressure drop and heat transfer study in tube-in-tube helical heat exchanger, Chemical Engineering Science 61 (2006) 4403–4416. [21] H. Bahremand, A. Abbassi, M. Saffar-Avval, Experimental and numerical investigation of turbulent nanofluid flow in helically coiled tubes under constant wall heat flux using Eulerian–Lagrangian approach, Powder Technology 269 (2015) 93–100.
Page 25 of 40
[22] F. Akbaridoust, M. Rakhsha, A. Abbassi, M. Saffar-Avval, Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model, International Journal of Heat and Mass Transfer 58 (2013) 480–491. [23] S.M. Hashemi, M.A. Akhavan-Behabadi, An empirical study on heat transfer and pressure drop characteristics of CuO–base oil nanofluid flow in a horizontal helically coiled tube under constant heat flux, International Communications in Heat and Mass Transfer 39 (2012) 144– 151. [24] M.A. Kedzierski, M. Gong, Effect of CuO nanolubricant on R134a pool boiling heat transfer, International Journal of Refrigeration 32 (2009) 791–799. [25] M. Kahani, S. Zeinali Heris, and S. M. Mousavi, Effects of Curvature Ratio and Coil Pitch Spacing on Heat Transfer Performance of Al2O3/Water Nanofluid Laminar Flow through Helical Coils, Journal of Dispersion Science and Technology 34 (2013) 1704–1712. [26] B.C. Pak, Y. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle, Experimental Heat Transfer 11 (1998) 151-170. [27] Y.M. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701-3707. [28] T.M. Rea, L. Hu, J. Buongiorno, Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids, Int. J. Heat Mass Transfer 52(7-8) (2009) 2042-2048. [29] M. Karimi, E. Shirani, A. Avara, Analysis of entropy generation, pumping power, and tube wall temperature in aqueous suspensions of alumina particles, Heat Transfet Res 43(4) (2012) 327-342. [30] J.C.A. Maxwell, Treatise electricity magnetism. Second ed., Clarendon Press, Oxford, UK, 1881. [31] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Introduction of heat transfer, sixth ed., John Wiley & Sons, USA, 2011.
Page 26 of 40
[32] M. Kahani, S. Zeinali Heris, and S. M. Mousavi, Effects of Curvature Ratio and Coil Pitch Spacing on Heat Transfer Performance of Al2O3/Water Nanofluid Laminar Flow through Helical Coils, Journal of Dispersion Science and Technology 34 (2013) 1704–1712. [33] D.C. Wilcox, Turbulence modeling for CFD. Third ed., Birmingham Press, Inc., San Diego, California, USA, 2006. [34] S.M. Fotukian, M. Nasr Esfahany, Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube, International Communications in Heat and Mass Transfer 37 (2010) 214–219. [35] S.E.B. Maiga, C.T. Nguyen, N. Galanis, G. Roy, T. Mare, M. Coqueux, Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, International Journal of Numerical Methods for Heat and Fluid Flow 16 (3) (2006) 275–292. [36] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151–155. [37] E.F. Schmidt, Warmeubergang and Druckverlust in Rohrschbugen, Chemical Engineering Technology 13 (1967) 781–789. [38] Y. Mori, W. Nakayama, Study on forced convective heat transfer in curved pipes, Int J Heat Mass Transfer 8 (1965) 67–82. [39] H. Ito, Friction factors for turbulent flow in curved pipes, J. Basic Engineering 81 (1959) 123–134. [40] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements. New York, Addison-Wesley Publishing Company, Fifth Ed. (1990). [41] P.S. Srinivas, S.S. Nandapur, F.A. Holland, Pressure drop and heat transfer in coils. Transactions of the Institution of Chemical Engineers and the Chemical Engineer 46 (1968): c113.
Page 27 of 40
Figure 1. Schematic of the studied problem and the geometrical parameters
Tout
T4
T3 T2
Data Logger
T1
Tin
Test Section
Cooling Water out
Reservoir Cooling Water in
Flow-meter
Main Line
Heat Exchanger
Reflux Line
Drain
U-tube Manometer
Figure 2. Schematic diagram of experimental setup
Page 28 of 40
(a)
(b) Figure 3. Validation of current experimental work with the theoretical equations in straight tube using water as the working fluid (a) Friction factor and (b) Averaged Nusslet number
Page 29 of 40
(a)
(b) Figure 4. Effect of computational grid size on (a) the average nondimensional heat transfer coefficient and (b) the friction factor
Page 30 of 40
Figure 5. The grids used for finite volume solution
Figure 6. Validation of our numerical solution with References [26, 32-36].
Page 31 of 40
(a)
(b) Figure 7. (a) Comparison of present experimental Nusselt number with Schmidt [37] and Mori and Nakamaya [38] correlations for laminar and turbulent flow regimes, respectively, and (b) Comparison of present experimental friction factor with Ito’s correlations [39].
Page 32 of 40
(a)
(b)
Page 33 of 40
(c) Figure 8. Variation of averaged Nusselt number as a function of Dean number for (a) 0.0375 (coil 1), (b) 0.0784 (coil 4), and (c) 0.1231 (coil 5)
Figure 9. Variation of averaged Nusselt number for different values of Dean number and for (a) 0.05 (coil 2), (b) 0.064 (coil 3), and (c) 0.1778 (coil 6)
Page 34 of 40
Figure 10. variation of average Nusselt number for different Dean numbers at (a) Re 3000 , (b) Re 10500 , and (c) Re 18000
Figure 11. Comparison between numerical simulations and experimental data for Nusselt number in all geometries and Reynolds numbers in Range of 3000 Re 18000
Page 35 of 40
(a)
(b)
Page 36 of 40
(c) Figure 12. Variation of friction factor as a function of Dean number for (a) 0.0375 (coil 1), (b) 0.0784 (coil 4), and (c) 0.1231 (coil 5)
Figure 13. Variation of friction factor along the helical coiled pipe for different values of Dean number and for (a) 0.05 (coil 2), (b) 0.064 (coil 3), and (c) 0.1778 (coil 6)
Page 37 of 40
Figure 14. The dimensionless axial velocity and secondary flow for coil 5 at (a)
and (b)
.
Figure 15. Comparison between numerical simulations and experimental data of friction factor in all geometries and Reynolds numbers in Range of 3000 Re 18000
Page 38 of 40
Table 1. physical and thermophysical properties of nanoparticles Chemical Formula
TiO2
color
white
Particle shape
Spherical
Purity
99.986%
Average particle
10-15
diameter (nm) Density (kg/m3)
3840
Specific heat (J/kg.K)
710
Thermal conductivity
11.7
(W/m.K)
Table 2. physical properties of different geometries used in this study Inner
Outer
Helix
diameter
diameter
diameter
(mm)
(mm)
(mm)
8
10
-
-
930
-
4.2
5.2
112
0.0375
2937.08
30
Coil 2
8
-
160
0.05
4140.39
30
Coil 3†
8
-
125
0.064
3262.74
30
Coil 4
8
10
102
0.0784
2699.26
30
Coil 5
8
10
65
0.1231
1763.16
30
Coil 6†
8
-
45
0.1778
1268.16
30
Coil
Straight tube Coil 1 †
†
Curvature
Helix pipe
ratio
length
Pitch (mm)
(mm)
The sign means that there is no experimental data for this coil.
Table 3. number of elements used in different grids for grid-dependency analysis for coil 4 Grid
grid 1
grid 2
grid 3
grid 4
grid 5
grid 6
grid 7
Total
201728
349948
741132
1095850
1603440
2072296
2741932
elements
Page 39 of 40
Table 4. total elements used in numerical simulations for different geometries Coil
coil 1
coil 2
coil 3
coil 4
coil 5
coil 6
Total
897248
921366
1497420
1603440
1789571
2154923
elements
Table 5. Comparison of the experimental critical Reynolds number with previous proposed correlations. Coil
Experimental
[39]
[37]
[41]
interval of Coil 1
6943-7981
6994
6813
6980
Coil 4
7779-9577
8579
8315
8815
Coil 5
9362-12128
10228
10003
10938
According to the Table 5, it is clear that the predicted critical Reynolds numbers are in the obtained experimental critical Reynolds number interval. The predicted critical Reynolds number by Schmidt [37] is slightly lower than the experimental critical Reynolds number interval.
Page 40 of 40
S0140-7007(16)30383-8 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.11.014 JIJR 3482
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
11-6-2016 13-11-2016 19-11-2016
Please cite this article as: Mostafa Mahmoudi, Mohammad Reza Tavakoli, Mohamad Ali Mirsoleimani, Arash Gholami, Mohammad Reza Salimpour, Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid, International Journal of Refrigeration (2016), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.11.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Experimental and numerical investigation on forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid Mostafa Mahmoudi1, Mohammad Reza Tavakoli*,2, Mohamad Ali Mirsoleimani3, Arash Gholami4, Mohammad Reza Salimpour5 1 M.Sc student, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 2 Assist. Professor, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 3 M.Sc student, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] 4 M.Sc, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111 5 Professor, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 65148-61111, Email: [email protected] * Corresponding author, Email: [email protected] Highlights
A 30% enhancement in heat transfer coefficient was achieved.
Increasing the Dean number at fixed Reynolds number increases the heat transfer.
The friction factor is an ascending function of nanoparticles concentration.
Four general correlations for the Nusselt number and friction factor were proposed.
Page 1 of 40
Abstract: In the present article, forced convection heat transfer and pressure drop in helically coiled pipes using TiO2/water nanofluid as working fluid were investigated experimentally and numerically. The aim is to investigate and provide additional insight about the effects of physical and geometrical properties on heat transfer augmentation and pressure drop in helically coiled tubes. The experiments were conducted in the range of Reynolds number from 3000 to 18000 and in the nanoparticle concentrations of 0.1, 0.2, and 0.5% for five different curvature ratios. In numerical simulations the thermophysical properties of the working fluid were assumed to be a function of nanofluid temperature and concentration. For turbulent regime the standard k model was used to simulate the turbulent flow characteristics. The numerical results were in a good agreement with the experimental data. The results showed that utilization of nanofluid instead of distilled water leads to an enhancement in the Nusselt number up to 30%. Also, four formulas were introduced to obtain the average Nusselt number and friction factor in helically coiled tubes under constant wall temperature condition for both laminar and turbulent flow regimes. Keywords: Nanofluid; Heat transfer enhancement; Pressure drop; Helically coiled pipe; Turbulent flow.
Page 2 of 40
Nomenclature Parameter
Symbol
Helix surface area [m2]
Ap
Heat capacity [kg.m2/s2.K]
Cp
Coil inner diameter [m]
d
Helix diameter [m]
D
Friction factor
f
Heat transfer coefficient [W/m2.K]
h
Turbulence kinetic energy [m2/s2]
k
Coil length [m]
lh
Mass flow rate [kg/s]
m
Pressure [pa]
p
Volumetric flow rate [m3/s]
Q
Temperature [K]
T
Logarithmic temperature difference
Δ TLM TD
Velocity component [m/s]
ui
Velocity fluctuation component [m/s]
u i
Greek symbols Thermal conductivity ratio
Turbulence dissipation [m2/s3]
Nanoparticles concentration (%)
Φ
Molecular thermal diffusivity
Γ k / C p
Page 3 of 40
Curvature ratio
Dynamic viscosity [kg/m.s]
Kinematic viscosity [m2/s]
Density [kg/m3]
Non-dimensional parameters Reynolds number
Re u b d /
Dean number
D e Re d / D
Nusselt number
Nu hd / k
Subscripts Bulk property
b
Base fluid property
f
Nanofluid property
nf
Nanoparticle property
p
Reference parameter
ref
Page 4 of 40
1- Introduction The development of techniques that allow more effective heat transfer augmentation is a growing need in many technologies and has drawn lots of attention in the field of nanofluids [1-3]. From heat transfer point of view, common fluids such as water and oil have low thermal conductivity in comparison with metals. Nanofluids show a notable potential to enhance the heat transfer rate. On the other hand, the configuration of pipes might increase the heat transfer rate. Due to the presence of secondary flow in these geometries, in comparison with the straight pipes, the flow field and convective heat transfer distribution in helically coiled pipes are complicated. The secondary flow motion induced by curvature of pipes and the resultant centrifugal force makes a pair of longitudinal vortices which results in increase in the heat transfer coefficient [4]. With increasingly development of processes that need high heat transfer rates, the necessity of utilizing high performance heat exchangers, e.g. the ones work with nanofluids, get importance in various industries. Helical coiled heat exchangers are used in a very wide range of industrial applications such as compact heat exchanger, condensers and evaporators, environmental engineering, waste heat recovery, cryogenic processes, etc. Comprehensive review articles about the applications of nanofluid in heat transfer have been published by several researchers [5-8]. The literature related to heat transfer enhancements in forced convection with different nanofluids is very rich and researchers have studied different aspects of this field. Although these works provide important information about momentum and heat transfer in nanofluids, the majority has been focused on forced convection under laminar flow regime in heat exchangers and less attention has been paid to turbulent flow and heat transfer in helically coiled pipes using nanofluids. Salimpour [9] has performed an experimental investigation on heat transfer characteristic of temperature dependent-property engine-oil inside shell and coiled tube heat exchangers. He presented an empirical correlation to predict the heat transfer coefficient inside these kinds of heat exchangers. Salimpour [10] in another work has experimentally studied the effect of coil pitch on heat transfer rate in helically coiled tube heat exchangers. He found that the coils with larger pitches have higher heat
Page 5 of 40
transfer rates in comparison with ones with smaller pitch. Shokouhmand et al. [11] have conducted an experimental investigation to study the shell and helically coiled tube heat exchangers. They considered both parallel flow and counter flow configurations to study the effects of various pitches and curvature ratios on the heat transfer rate. They found that using the counter flow configuration instead of parallel one increases the overall heat transfer coefficient up to 40%. Reddy and Rao [12] have conducted an experimental investigation of heat transfer coefficient and friction factor of ethylene glycol water based TiO2 nanofluids in double pipe heat exchanger. They found that for the case of nanofluid at 0.02% volume concentration, the heat transfer coefficient and friction factor get enhanced by 13.85% and 10.69%, respectively. Jamishidi et al. [13] have presented an experimental study of heat transfer rate enhancement in shell and helical tube heat exchangers. They used the Taguchi method to obtain the optimum condition according to the overall heat transfer coefficient for whole heat exchanger. In another work, Jamshidi et al. [14] have studied the effect of adding nanoparticles in thermal-hydraulic performance of helical tubes. They used Taguchi method to find the optimum condition for the desired parameters. Their results indicated that using nanofluids results in improvement of the thermal-hydraulic performance of helical pipes. Akhavan-Behabadi et al. [15] have simultaneously utilized the helical coiled tubes and nanofluids and investigated their effects on the heat transfer during the experiments. Based on their experimental results, utilizing helical coiled tubes enhances the heat transfer rate remarkably. San et al. [16] have performed an experimental investigation on heat transfer performance of a helical heat exchanger. They used Reynolds numbers in the range 307 to 2547 and found that increasing number of turns of the heat exchanger increases its effectiveness Park et al. [17] have carried out a combined experimental and numerical case study of the heat transfer around the helical ground heat exchanger. Kahani et al. [18] have experimentally studied the heat transfer behavior of metal oxide nanofluid flows inside helical coiled tube. They found that the convection heat transfer coefficient and pressure drop are increased considerably because of the tube curvature. Huminic and Huminic [19] have used a three dimensional analysis to study the heat transfer and laminar flow characteristics in a helical heat exchangers using nanofluids. They investigated the effects of nanoparticles concentration
Page 6 of 40
level and Dean number on the heat transfer rates. They found that increasing the flow rate and Dean number leads to increase in heat transfer coefficient. Kumar et al. [20] have conducted experimental as well as numerical simulations to study the heat transfer characteristics in helically coiled heat exchangers. Bahremand et al. [21] have investigated the turbulent flow in helically coiled tubes under constant heat flux using both numerical and experimental methods. Their results showed that the nanoparticles tend to increase the axial velocity slightly and suppress the turbulent kinetic energy. Akbaridoust et al. [22] have investigated the laminar flow regime through helically coiled pipes using experimental and numerical methods. They have considered a constant wall temperature condition. Their results showed that using base fluid in helically coiled pipe instead of using nanofluid in straight pipes enhances the heat transfer more effectively. Hashemi and Akhavan-Behabadi [23] have experimentally studied the problem of heat transfer and pressure drop through horizontal helical tube under constant heat flux using nanofluids. Their results showed that utilization of nanofluid leads to increase in the heat transfer coefficient and pressure drop. Our literature review revealed that the previous studies have been restricted mostly to the laminar flow condition and the effects of Dean number at different Reynolds number get paid less attention. In the present paper, a comprehensive numerical and experimental study of turbulent flow and heat transfer of TiO2 nanofluids in helically coiled tubes with constant wall temperature condition were carried out. The experimental and numerical simulations were performed for three nanoparticles concentration of 0.1%, 0.2%, and 0.3%. Also the effect of helix curvature ratio in turbulent flow regime on heat transfer augmentation and pressure drop was investigated. A standard k turbulent model was used to simulate the turbulent flow and heat transfer regime. The main objective of this study is to investigate and provide additional insight about the effects of physical and geometrical properties on heat transfer augmentation in helically coiled tubes using nanofluid.
2. Experiments and Measurements 2.1. Preparation and Property of Nanofluid
Page 7 of 40
Water was used as the base fluid and nanofluids with nanoparticles concentration of 0.1% and 0.5% were prepared by dispersing TiO2 nanoparticles. The solid particles used in this study were TiO2 nanoparticles. The nanoparticles have been produced with an average particle size in range of 1015nm and 99.986% pureness by means of chemical analysis method. Table 1 shows the physical and thermophysical properties of nanoparticles used in the experiments. A UP200S ultrasonic mixer was used to disperse the coagulated nanoparticles and leads to a uniform dispersion of nanoparticles throughout the nanofluid. The resulted nanofluids were stable for about 24 hours. The sedimentation was observed after 5 days with naked eyes. However, According to the literature review for TiO2/water and other nanofluids with low nanoparticle concentrations, i.e. less than 0.5%, the complete sedimentation occurred after a week. For example, Kedzierski and Gong [24] used the low nanofluid concentration in order to avoid rapid sedimentation. Hashemi and Akhavan-Behabadi [23] have observed with naked eyes that the complete sedimentation occurred after a week. Kahani et al. [25] have observed no sedimentation after 48 hours of prepration. Thus, because the experiments have been performed during the next 24 hours after preparation of the nanofluid, the possibility of sedimentation was quite low.
Due to the thermophysical differences between the base fluid and nanofluid, it is necessary to compute the thermophysical properties of nanofluid for numerical simulations. Two classical formulas are used to obtain effective density and thermal capacity of the nanofluid [26 and 27]: nf 1 f + p
C p
nf
1 C p C p f
(1) (2) p
where the subscripts nf, f, and p are indicating that quantity is related to the nanofluid, base fluid, and nanoparticles, respectively. Rea et al. [28] and Karimi et al. [29] have presented the following experimental formula for nanofluid viscosity as a function of temperature and volumetric concentration:
Page 8 of 40
nf T , Φ f T exp 4.91Φ 0.2092 Φ f T ref
T T ref
n
1 1 exp B T T ref
(3)
where B 4700, n 8.9, T ref 295 K , and ref 9.59 10 4 N .s / m 2 . These formulas are valid for the nanoparticle volumetric concentration less than 6% and temperature range of 290-350K. In the case of calculation of the thermal conductivity of nanofluid the Maxwell model [30], which is one of the oldest and well-known formula to compute the thermal conductivity of the solid-fluid mixture, is used,
k nf kf
2 2 1
(4)
2 1
where k p / k f is defined as the ratio of the thermal conductivity of nanoparticles to thermal conductivity of the base fluid.
2.2. Measurement of Heat Transfer Coefficient Rate of net heat transfer from the vapor bath to the working fluid flowing through the test section depends on the measurements of inlet and outlet temperature as well as the mass flow rate of nanofluid in the test section. In order to compute the overall heat transfer coefficient at constant wall temperature condition, following relation can be used: m C p Tout Tin hA p Δ T L M T D
(5)
where m is the nanofluid mass flow rate, Tin and Tout are the bulk fluid temperature at inlet and outlet of test section, respectively. A p is the surface area of the helical coiled pipe which has a direct contact with the hot fluid, h is the overall heat transfer coefficient, and Δ T L M T D is the logarithmic temperature difference which is defined as
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Δ TLM TD
Δ Tin Δ Tou t
(6)
Tin ln Tou t
where Δ Tin Ts Tin and Δ Tin Ts Tout and T s is the temperature of helical coiled tube. Finally, the overall heat transfer coefficient after some simplifications becomes,
h
C p Q Tout Tin
(7)
d ilh Δ TLM TD
where Q is the volumetric flow rate, d i the inner diameter of pipe, and l h is the length of helical coiled tube. Therefore, the non-dimensional heat transfer coefficient is given by
Nu
(8)
hd k
where k is the effective thermal conductivity of the nanofluid. To validate the experimental data, we carried out some experiments for a straight tube and compared the results with the Saider-Tate equation for the laminar regime and with Dittus-Boelter equaion and Gnielinski relation for the turbulence flow regime [31]: Saider-Tate equation:
Gnielinski equation:
Dittus-Boelter equation:
N u 1.86 R e P r d / l
Nu
f
1/ 3
b s
0 .14
/ 8 R e 1000 P r
1 12.7 f / 8
1/ 2
Nu 0.023 Re
0.8
Pr Pr
2/3
0.4
1
(9)
(10)
(11)
2.3. Measurement of Friction Factor Experimental friction factor is determined using the measurements of pressure drop along the helical coiled pipe. A U-shaped manometer is used to measure the pressure drop along the pipe Δ P . The axial pressure drop of fluid flow inside the coil can be read as [12, 32]:
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Δ p d i
2
32 l Q
2
5
f exp
(12)
In order to validate our experimental data, the experimental data were compared with Blasius equation [31] for laminar regime and with Petukhov equation for turbulent regime [31]:
f
(13)
64 Re
f
(14)
1
0.79 ln R e 1.64
2
Eq. (13) for laminar flow and Eq. (14) is Petukhov equation for turbulent flow through straight tube which is valid on Reynolds number range of 3 10 3 Re 5 10 6 .
2.4. Experimental Setup One of the common apparatus which is used to enhance the heat transfer rate is helical coiled pipes. Due to the curvature of the pipe, the fluid experiences a centrifugal force while it is flowing in the helical coiled pipes. The centrifugal force exerted to the fluid causes secondary flows inside the pipe and this secondary flows leads to heat transfer augmentation in these apparatus. Figure 1 shows a schematic of helical coiled tubes and its geometrical properties. The pipe has a diameter of (d) and the diameter of the helical coil is illustrated by (D). The distance between two successive turns (b) is called the pitch. An experimental setup is designed to study the behavior of convection heat transfer and pressure drop in helically coiled pipes under constant wall temperature using nanofluids as working fluid. The schematic diagram of the experimental setup is shown in Fig. 2. In order to obtain the constant wall temperature condition, a steam bath has been used. The experimental apparatus is included of a main loop for the base/nanoluid which is comprised of different equipment such as the nanofluid reservoir, pump, test section, heat exchanger, a U-shaped manometer, flow meter, thermocouples, and a data logger.
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The nanofluid is pumped from the reservoir to the test section using by a centrifugal pump. The test section is included of a copper helical tube with various outer diameters in range of 65 to 112 mm. The geometrical properties of the coils are shown in table 2. All the helical pipes used in current work have 8 turns. Four 2000 W electric heaters are considered to generate the steam and then to reach a stable condition in the vapor bath, just two of them will stay in the circuit. The working fluid flows inside the test section while the vapor bath is full of saturated vapor. To reduce the heat losses from the steam bath to the surroundings, it is thermally insulated. The nanofluid temperature is measured at the inlet and outlet of the test section using two calibrated K-type thermocouples. Also, in order to measure the outer wall temperature of the helically coiled pipe, four other K-type thermocouples are provided. The temperatures of these points showed that the variation of surface temperature can be neglected (the uncertainty in wall temperature measurements was ±0.5℃). After that the warmed nanofluid enters the heat exchanger and loses its temperature using the cooling water to the initial temperature and then drains to the reservoir. To make sure that the experiment apparatus were working correctly and they have an acceptable accuracy, before performing the experiments on helical coiled pipes using nanofluid, a test for a straight pipe using water as working fluid was conducted. The data obtained for different Reynolds number is compared with the Eqs. (9-11) and Eqs. (12 and 13). Figure 3(a) demonstrates the variation of friction factor in both laminar and turbulent regimes. The data shows that there is a maximum 4.1% deviation from the Blasius equation in laminar flow and a maximum 6.3% error compared with Petukhov equation for turbulent regime. Figure 3(b) illustrates the average Nusselt number as a function of Reynolds number. As it is understood from Fig. 3(b) there is a good agreement between Dittus-Boelter equation, Gnielinski equation, Saider-Tate equation and present experimental data.
3. Numerical Simulation 3.1. Governing Equations The steady state forced convection heat transfer through helical coiled piped using nanofluid was studied. The helical coil is assumed to remain at constant temperature of T w that is greater than the
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bulk fluid temperature T . In numerical simulations the heat transfer and pressure drop in turbulent flow regime was studied. The effects of presence of nanoparticles on the viscosity, heat capacity, thermal conductivity, and density of working fluid are modeled using the proper correlations. The reason is that to model the interactions between the nanoparticles and the fluid numerically, it is necessary to use discrete phase models and consider the effects of flow field on the particle such as Saffman’s lift force, drag force, and the effect of gravity on particles. In addition, it is necessary to consider the effect of particle motions on the flow field which results in a transient problem. Furthermore, the thermal effects of the presence of nanoparticles on the heat transfer rate should be modeled. Therefore, due to the large number of meshes and the turbulent nature of flow at the investigated Reynolds numbers, considering the interactions between nanoparticles and the water will lead to increase in computational and time costs. Thus, it is convenient to model the effects of presence of nanoparticles on the flow field and the heat transfer using a single phase model and the proper correlations for density, thermal capacity, viscosity, and thermal conductivity. The governing equations for the conservation of mass, momentum and energy have been solved in the Cartesian coordinate system [29]; the mass conservation (continuity) is: ui xi
(12)
0
And the momentum equation can be written as
x j
u u i
j
xi x j 1 p
u u j i x xi j
u iu j x j
(13)
where and are the effective density and kinematic viscosity of the nanofluid, respectively.
The energy equation reads as follows:
x j
u iT
T Γ Γ t x j x j
(14)
where Γ and Γ t are the molecular thermal diffusivity and turbulent thermal diffusivity, respectively and defined as follows:
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Γ / Pr , Γ t t / Prt
The Reynolds stress term in momentum equation, i.e. u iu j , is modeled using by the k turbulence model in conjugate with Boussinesq hypothesis [32]: u u j i u iu j t x xi j
(15)
where t is the eddy viscosity and can be achieved by, t C k / 2
The kinematic energy of turbulence and the dissipation rate of the turbulence kinetic energy can be written as [33]
uj
uj
x j
k x j
C 1
ui
ij
k
x j
ij
ui x j
C 2
(16)
t k x j k x j
2
k
t x j x j
(17)
where the closure coefficients read as follows: C 1 1.44,
C 2 1.92,
1.3,
k 1.0,
Prt 0.9
3.2. Numerical Method, Boundary and Initial Conditions Finite Volume Method was used to solve Eqns. (12)-(17). SIMPLE algorithm was employed to couple pressure and momentum and the second-order upwind scheme was utilized for spatial discretization in all equations. The dependent variables (pressure, velocities, temperature, turbulence kinetic energy, and turbulence dissipation rate) are under relaxed by the factors of 0.3, 0.7, 0.5, 0.7, and 0.7 for P, U, T, k, and respectively. A preconditioned bi-Conjugate Gradient (PBiCG) solver was used for the governing equations. The PBiCG method is used when the system of equations are not necessary
Page 14 of 40
symmetric. It should be noted that the convergence criterion is defined as the maximum relative error between of variables in two successive iterations to be less than 10 7 .
In the case of boundary conditions a constant mass flow rate with uniform temperature T is specified as inlet boundary conditions of inlet extended pipe. The helical coiled tube wall is assumed to be in constant temperature T w and the flow exits to ambient at the outlet surface of the outlet extended pipe. At inlet the turbulent intensity, turbulence kinetic energy and turbulence dissipation rate are given by [33],
I
u
2
Ue
k
0.16 R e D
3 2
U e I
C
3/ 4
k
1/ 8
2
3/ 2
l
where C 0.09 and the length scale l is defined as l 0.07 D .
3.3. Grid-Independent Study and Validation Different sizes of numerical mesh were studied to investigate the dependency of solution to the computational grid (Table 3). Figs. 4(a, b) show the averaged non-dimensional heat transfer coefficient and friction factor at Re 9000 . These figures show that the variation of averaged Nusselt number and friction factor while using a grid number of 1095850 (or greater) is just 0.03%. Variation of average Nusselt number and friction factor from grid 1 to grid 2 is significant, because the resolution of the viscous sublayer in grid 2 was increased. By reducing the size of meshes, especially near the coil wall, the wall effect can be calculated more accurately and therefore, the variation of friction factor inside the helically coiled pipe becomes smaller. An asymptotic tendency of the friction factor values to converge with increasing the number of meshes, i.e. from 897248 (grid
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1) to 2154923 (grid 6), can be observed. The results suggest that a grid-independent solution is obtained when using a mesh number larger than 1.1 10 6 ; thus, we used a computational grid with the 1.6 10 cells. As it is demonstrated in Fig. 5, the grids in vicinity of the wall were refined due to 6
reach a more accurate velocity and temperature gradient in this region. Figure 4 illustrates the grid which was used in this study and Table 4 shows the total elements used in numerical simulations for different geometries.
As a benchmark comparison, simulation for forced convection heat transfer of nanofluid in a straight pipe has been carried out at different Reynolds numbers (see Figure 6). This problem was studied previously by Fotukian and Nasr Esfahani [34], Maiga et al. [35], Pak and Cho [26], and Xuan and Li [36] numerically and experimentally. It can be seen that the results of current numerical simulation are in a good agreement with their works. In Fig. 7(a), the results of the averaged Nusselt numbers in helically coiled pipes for distilled water in laminar and turbulent flows have been compared with the well-known experimental correlation of Schmidt [37] and the analytical formula of Mori and Nakayama [38], respectively: Schmidt [37]:
(18)
Mori and Nakayama [38]:
(19)
where
is the curvature ratio. The Schmidt correlation is valid for
in which
[37]. The Mori and Nakayama formula is valid for and
[38].
In order to validate the friction factor results, the results of Ito’s correlations (Eqs. 20 and 21) [39] for helically coiled pipes were compared with the current experimental data (figure 7(b)). The Ito’s correlations for laminar and turbulent flows are as follows, respectively: (20)
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(21) where
[39]. As it can be seen in Fig. 7, the present experimental data are in a
good agreement with the well-known previous correlations.
The uncertainty analysis was carried out using the procedure proposed by Beckwith et al. [40], and it was found that the expected experimental error for the Reynolds number, friction factor, heat transfer coefficient, and the Nusselt number were ±0.6%, ±7.1%, ±2.64, and ±2.64%, respectively.
4. Results and discussions The following sections are devoted on the effects of Dean number and nanoparticles concentration on overall heat transfer coefficient and friction factor in helical coiled tubes. The figures clearly show the positive effect of the presence of nanoparticles on heat transfer rate in helical coiled heat exchangers. Also, four formulas are introduced to obtain the averaged Nusslet number and friction factor in helical coiled tubes under constant wall temperature condition for both laminar and turbulent flow regimes. Then the capability and reliability of numerical simulation is discussed in order to find the characteristics of heat transfer and fluid flow behavior of nanofluids in other geometries.
4.1. Heat transfer coefficient Figure 8(a-c) shows the variation of overall non-dimensional heat transfer coefficient as a function of Dean number for different helical coiled pipes. As it is demonstrated in Fig. 8 and 9, with adding the nanoparticles to the distillated water, the heat transfer rate increases. The experiments were performed for the nanoparticle concentration of Φ 0.1 and 0.5 , while the numerical simulations were conducted for Φ 0.1, 0 .2 and 0.5 to obtain additional insight about the effects of nanoparticle concentration on heat transfer rate. Increasing the Dean number at a constant curvature ratio leads to change in flow regime, in other words, the transition of laminar flow to turbulent one. As it is seen in
Page 17 of 40
Fig. 8, at higher Dean numbers, adding nanoparticles to the base fluid results in enhancing the heat transfer rate more than in lower Dean numbers, i.e. laminar flow. This difference in increasing the Nusselt number in helical coiled pipes is related to the fact that in higher Dean numbers the secondary flows, which are developed in the cross section of the pipe, are stronger than secondary flows at lower Dean numbers. Therefore, the momentum transfer from the wall of the pipe increases and as a result of having higher momentum exchange rate near the wall, the heat transfer rate increases. Fig. 8(a-c) and Fig 9(a-c) indicate that with increasing the curvature ratio, the slope of variation of Nusselt number with Dean number decreases. For example, the non-dimensional heat transfer rate in Coil 1 (Fig. 8(a)) has a value of Nu 140 at De 3600 , while in coil 5, Fig. 8(c), this value occurs at De 6300 . As it is seen in Figure 8, with increasing the concentration of nanoparticles from Φ 0.1 to 0.5 the overall heat transfer rate in the pipes increases. That is due to the increasing in the viscosity of nanofluid when adding more nanoparticles. This increase can be seen in the Eq. 3 which the viscosity of nanofluid in the aforementioned range of nanoparticles concentration is an ascending function of Φ.
Figure 10 demonstrates the average non-dimensional heat transfer coefficient as a function of Dean number at various values of Reynolds numbers. As it is seen in Fig. 10(a-c) with increasing the Reynolds number from Re 3000 to Re 10500 , a dramatic increase in heat transfer rate occurs. That is due to the transition from the laminar flow regime to turbulence one which possesses higher momentum transfer rate. Also, with increasing the Reynolds number from Re 10500 to Re 18000 , the overall heat transfer coefficient increases. Another point in Fig. 10(a) is that by
increasing the concentration of nanoparticles from 0.1 to 0.5, at lower Reynolds number such as , the average Nusselt number is increased, considerably. For example, at
and
, increasing the nanoparticle concentration leads to increase in non-dimensional heat transfer coefficient up to 30%.
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At constant Reynolds number the effects of Dean number on heat transfer and factors which lead to the increase in heat transfer rate were investigated in the past sections. But Fig. 10 refers to another point that with increasing the Reynolds number till the flow regime turns to turbulence one, the effect of nanoparticles concentration approximately tarnishes. On the other hand, at lower Reynolds numbers, e.g. Re 3000 , nanoparticles concentration has an intense impact on average Nusselt number. At Re 3000 and De 1250 , increasing the concentration of nanoparticles from Φ 0.1 to Φ 0.5 results in a 70% enhancement in heat transfer rate. But this increase at higher Reynolds numbers, e.g. Re 18000 and De 4450 , is just 1.87% . This trend in heat transfer rate, in other words vanishing the effects of particles concentration on heat transfer rate, can be explained as follows: enhancing the momentum transfer rate with increasing the Reynolds number, i.e. increase in velocities fluctuations, may prevail the growth in momentum exchange rate between the particleparticle and particle-fluid. In this situation adding more amount of nanoparticles probably leads to a decrease in overall heat transfer coefficient, because it is possible increasing the nanoparticles concentration causes higher pressure drop, both frictional and axial pressure drop, along the coiled pipe which as a result, the heat transfer rate decreases. Figure 11 shows the variation of numerical values with experimental values for average Nusselt number. As it is seen, the deviation of numerical solution data from the experimental data is within 13% and 28% .
Finally, to calculate the average Nusselt number in coiled pipes with nanofluid as the working fluid, using the least-squares method the following relations are fitted to the experimental data: Laminar regime:
N u lam 0.043 R e
0.812
Pr
0.35
0.045
0.038
(22)
Turbulent regime
N u turb 0.028 R e
0.854
Pr
0.38
0.039
0.041
(23)
Equation (22) predicts the overall heat transfer rate with maximum error of +5.1% and minimum error of -6.7% in laminar flow regimes. For turbulent flows the equation (23) predicts +3.6% and -11.2%
Page 19 of 40
for maximum and minimum error, respectively. It should be noted that Eqs(22) and (23) are valid for the Reynolds numbers in range of 2346 Re 18563 , Prantdl numbers in 2.7 Pr 3.51 , curvature ratio in 0.0375 0.123 , and nanoparticles volumetric concentration in 10
3
3
5 10 .
4.2. Friction factor Figure 12(a-c) illustrates the variation of friction factor along the helical coiled pipes for different values of Dean numbers at various curvature ratios. From classic fluid mechanics it is expected that increasing the Reynolds number leads to having lower friction factor. That is because of changes in the velocity profiles when the Reynolds number increases. In the case of helical coiled pipes the Dean number plays the main rule in measuring the friction factor along the coiled pipes. As it is shown in Figs. 12 and 13, with increasing the Dean number at constant curvature ratio, the friction factor increases, too. At higher Dean numbers, the secondary flows get stronger and lead to enhancing the momentum transfer rate in the helical coiled pipes. Also, the enhancement of secondary flows causes the maximum velocity in the pipe happens closer to the coiled pipe wall which increases the velocity gradient in vicinity of the wall.
Fig. 12 also demonstrates that with increasing the nanoparticles concentration the pressure drop through the coiled pipe increases. That is due to the fact that with increasing the solid content of nanofluid, the density and viscosity of the fluid increases. Therefore, as a result of increasing in fluid thermophysical properties the friction factor through the pipe increases. On the other hand, at higher Dean numbers, the chaotic motion and migration of nanoparticles are higher than for lower Dean number which increases the momentum exchange rate in the fluid. This transport of momentum between the solid-solid and solid-fluid phases causes an increase in pressure drop, too.
Page 20 of 40
It should be noted that according to the literature, there is a critical Reynolds number ( helically coiled pipes which the flows at higher Reynolds number than
) in
are considered as
turbulent flows. Table 5 provides the proposed value of these critical Reynolds numbers by various researchers for the coils used in our paper. According to the data of Table 5 and the heat transfer and friction factor curves, the Reynolds numbers in which the flow is transiting to the turbulence flow from the laminar one can be determined. Thus, at Reynolds numbers higher than
, the turbulent
regime in the coil is achieved and the proper equations were used to simulate the heat transfer and flow field, numerically. Accurate simulation of the secondary flows in helically coiled pipes is crucial for prediction of the heat transfer and friction factor in these geometries. The contour lines of non-dimensional axial velocity and secondary flows at Reynolds numbers of 10500 and 18000 for the coil 5 and nanoparticle concentration of 0.1% are presented in Figure 14. As it can be seen in this figure, due to the turbulent nature of flow at these Reynolds numbers, the secondary flow pattern has more than two vortexes. Figure 15 demonstrates the variation of numerical values with experimental values of friction factor. Fig. 15 indicates that the deviation of numerical solution data from the experimental data is within 13% and 20% .
A least-squares method was used to obtain the relationship between the friction factor and Reynolds number, curvature ratio, and nanoparticles concentration in helically coiled pipes under constant wall temperature. Laminar regime:
f lam 10.145 R e
Turbulent regime
f turb 0.302 R e
0.530
0.177
0.012
(24)
0.013
(25)
0.241
0.116
Equation (24) predicts the friction factor in helically coiled tubes for laminar flow regime with maximum and minimum error of 3.6% and 4.6% , respectively. For turbulence flow the Eq. (25) gives the friction factor in coiled pipes with maximum error of 5.5% and minimum error of 9.6%
Page 21 of 40
relative to the experimental data. The above relations are valid for the Reynolds number in range of 2346 Re 18563 , curvature ratio in 0.0375 0.123 , and volumetric concentration in 10
3
3
5 10 .
5. Conclusion In this paper the forced convection heat transfer and pressure drop in helical coiled pipes using TiO2/water nanofluid as the working fluid were investigated experimentally and numerically. The numerical simulations were performed using finite volume method. The effects of curvature ratio, Reynolds number, and nanoparticles concentration was studied broadly. The experiments were conducted for laminar, transitional and turbulence flow regimes, But the numerical simulations were carried out only for turbulent flow regime. There was a good agreement between experimental and numerical data. The results showed that using nanofluid as the working fluid in helical coiled heat exchangers, leads to a noticeably enhancement in heat transfer rate. The main highlights of current research are summarized as follows:
Utilization of nanofluid instead of the distillated water leads to considerable heat transfer enhancement. In some cases an enhancement up to 30% can be achieved by using the TiO2/water nanofluid with 0.5% nanoparticles concentration.
Increasing the Dean number (curvature ratio) at fixed Reynolds number results in an increase in heat transfer.
Using nanofluids as the base fluid in helical coiled heat exchangers leads to higher friction factor than using distillated water. The friction factor is an ascending function of nanoparticles concentration.
General correlations of Nusselt number and friction factor is obtained to predict these parameters in helical coiled heat exchangers under constant wall temperature in laminar flow regime:
Page 22 of 40
N u lam 0.043 R e
0.812
f lam 10.145 R e
Pr
0.530
0.35
0.045
0.241
0.038
0.012
Also, general correlations for Nusselt number and friction factor are obtained in turbulence flow regime: N u turb 0.028 R e
0.854
f turb 0.302 R e
Pr
0.177
0.38
0.039
0.116
0.041
0.013
applicable ranges are: 2346 Re 18563 , 2.7 Pr 3.51 , 0.0375 0.123 , 10
3
3
5 10 .
Page 23 of 40
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[22] F. Akbaridoust, M. Rakhsha, A. Abbassi, M. Saffar-Avval, Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model, International Journal of Heat and Mass Transfer 58 (2013) 480–491. [23] S.M. Hashemi, M.A. Akhavan-Behabadi, An empirical study on heat transfer and pressure drop characteristics of CuO–base oil nanofluid flow in a horizontal helically coiled tube under constant heat flux, International Communications in Heat and Mass Transfer 39 (2012) 144– 151. [24] M.A. Kedzierski, M. Gong, Effect of CuO nanolubricant on R134a pool boiling heat transfer, International Journal of Refrigeration 32 (2009) 791–799. [25] M. Kahani, S. Zeinali Heris, and S. M. Mousavi, Effects of Curvature Ratio and Coil Pitch Spacing on Heat Transfer Performance of Al2O3/Water Nanofluid Laminar Flow through Helical Coils, Journal of Dispersion Science and Technology 34 (2013) 1704–1712. [26] B.C. Pak, Y. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle, Experimental Heat Transfer 11 (1998) 151-170. [27] Y.M. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701-3707. [28] T.M. Rea, L. Hu, J. Buongiorno, Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids, Int. J. Heat Mass Transfer 52(7-8) (2009) 2042-2048. [29] M. Karimi, E. Shirani, A. Avara, Analysis of entropy generation, pumping power, and tube wall temperature in aqueous suspensions of alumina particles, Heat Transfet Res 43(4) (2012) 327-342. [30] J.C.A. Maxwell, Treatise electricity magnetism. Second ed., Clarendon Press, Oxford, UK, 1881. [31] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Introduction of heat transfer, sixth ed., John Wiley & Sons, USA, 2011.
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[32] M. Kahani, S. Zeinali Heris, and S. M. Mousavi, Effects of Curvature Ratio and Coil Pitch Spacing on Heat Transfer Performance of Al2O3/Water Nanofluid Laminar Flow through Helical Coils, Journal of Dispersion Science and Technology 34 (2013) 1704–1712. [33] D.C. Wilcox, Turbulence modeling for CFD. Third ed., Birmingham Press, Inc., San Diego, California, USA, 2006. [34] S.M. Fotukian, M. Nasr Esfahany, Experimental study of turbulent convective heat transfer and pressure drop of dilute CuO/water nanofluid inside a circular tube, International Communications in Heat and Mass Transfer 37 (2010) 214–219. [35] S.E.B. Maiga, C.T. Nguyen, N. Galanis, G. Roy, T. Mare, M. Coqueux, Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension, International Journal of Numerical Methods for Heat and Fluid Flow 16 (3) (2006) 275–292. [36] Y. Xuan, Q. Li, Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151–155. [37] E.F. Schmidt, Warmeubergang and Druckverlust in Rohrschbugen, Chemical Engineering Technology 13 (1967) 781–789. [38] Y. Mori, W. Nakayama, Study on forced convective heat transfer in curved pipes, Int J Heat Mass Transfer 8 (1965) 67–82. [39] H. Ito, Friction factors for turbulent flow in curved pipes, J. Basic Engineering 81 (1959) 123–134. [40] T.G. Beckwith, R.D. Marangoni, J.H. Lienhard, Mechanical Measurements. New York, Addison-Wesley Publishing Company, Fifth Ed. (1990). [41] P.S. Srinivas, S.S. Nandapur, F.A. Holland, Pressure drop and heat transfer in coils. Transactions of the Institution of Chemical Engineers and the Chemical Engineer 46 (1968): c113.
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Figure 1. Schematic of the studied problem and the geometrical parameters
Tout
T4
T3 T2
Data Logger
T1
Tin
Test Section
Cooling Water out
Reservoir Cooling Water in
Flow-meter
Main Line
Heat Exchanger
Reflux Line
Drain
U-tube Manometer
Figure 2. Schematic diagram of experimental setup
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(a)
(b) Figure 3. Validation of current experimental work with the theoretical equations in straight tube using water as the working fluid (a) Friction factor and (b) Averaged Nusslet number
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(a)
(b) Figure 4. Effect of computational grid size on (a) the average nondimensional heat transfer coefficient and (b) the friction factor
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Figure 5. The grids used for finite volume solution
Figure 6. Validation of our numerical solution with References [26, 32-36].
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(a)
(b) Figure 7. (a) Comparison of present experimental Nusselt number with Schmidt [37] and Mori and Nakamaya [38] correlations for laminar and turbulent flow regimes, respectively, and (b) Comparison of present experimental friction factor with Ito’s correlations [39].
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(a)
(b)
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(c) Figure 8. Variation of averaged Nusselt number as a function of Dean number for (a) 0.0375 (coil 1), (b) 0.0784 (coil 4), and (c) 0.1231 (coil 5)
Figure 9. Variation of averaged Nusselt number for different values of Dean number and for (a) 0.05 (coil 2), (b) 0.064 (coil 3), and (c) 0.1778 (coil 6)
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Figure 10. variation of average Nusselt number for different Dean numbers at (a) Re 3000 , (b) Re 10500 , and (c) Re 18000
Figure 11. Comparison between numerical simulations and experimental data for Nusselt number in all geometries and Reynolds numbers in Range of 3000 Re 18000
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(a)
(b)
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(c) Figure 12. Variation of friction factor as a function of Dean number for (a) 0.0375 (coil 1), (b) 0.0784 (coil 4), and (c) 0.1231 (coil 5)
Figure 13. Variation of friction factor along the helical coiled pipe for different values of Dean number and for (a) 0.05 (coil 2), (b) 0.064 (coil 3), and (c) 0.1778 (coil 6)
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Figure 14. The dimensionless axial velocity and secondary flow for coil 5 at (a)
and (b)
.
Figure 15. Comparison between numerical simulations and experimental data of friction factor in all geometries and Reynolds numbers in Range of 3000 Re 18000
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Table 1. physical and thermophysical properties of nanoparticles Chemical Formula
TiO2
color
white
Particle shape
Spherical
Purity
99.986%
Average particle
10-15
diameter (nm) Density (kg/m3)
3840
Specific heat (J/kg.K)
710
Thermal conductivity
11.7
(W/m.K)
Table 2. physical properties of different geometries used in this study Inner
Outer
Helix
diameter
diameter
diameter
(mm)
(mm)
(mm)
8
10
-
-
930
-
4.2
5.2
112
0.0375
2937.08
30
Coil 2
8
-
160
0.05
4140.39
30
Coil 3†
8
-
125
0.064
3262.74
30
Coil 4
8
10
102
0.0784
2699.26
30
Coil 5
8
10
65
0.1231
1763.16
30
Coil 6†
8
-
45
0.1778
1268.16
30
Coil
Straight tube Coil 1 †
†
Curvature
Helix pipe
ratio
length
Pitch (mm)
(mm)
The sign means that there is no experimental data for this coil.
Table 3. number of elements used in different grids for grid-dependency analysis for coil 4 Grid
grid 1
grid 2
grid 3
grid 4
grid 5
grid 6
grid 7
Total
201728
349948
741132
1095850
1603440
2072296
2741932
elements
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Table 4. total elements used in numerical simulations for different geometries Coil
coil 1
coil 2
coil 3
coil 4
coil 5
coil 6
Total
897248
921366
1497420
1603440
1789571
2154923
elements
Table 5. Comparison of the experimental critical Reynolds number with previous proposed correlations. Coil
Experimental
[39]
[37]
[41]
interval of Coil 1
6943-7981
6994
6813
6980
Coil 4
7779-9577
8579
8315
8815
Coil 5
9362-12128
10228
10003
10938
According to the Table 5, it is clear that the predicted critical Reynolds numbers are in the obtained experimental critical Reynolds number interval. The predicted critical Reynolds number by Schmidt [37] is slightly lower than the experimental critical Reynolds number interval.
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