HEAT TRANSFER IN A DIRECT-CONTACT TURBULENT HEAT EXCHANGER
Cédric Durandal1, Thierry Lemenand, Dominique Della Valle, Hassan Peerhossaini Thermofluids, Complex Flows and Energy Group
Laboratoire de Thermocinétique de Nantes, CNRS UMR 6607, Ecole Polytechnique de l’Université de Nantes,
Rue Christian Pauc, BP 50609, 44306 Nantes Cedex 3 - France
cedric.durandal@polytech.univ-nantes.fr, thierry.lemenand@polytech.univ-nantes.fr, dominique.della-valle@polytech.univ-nantes.fr, hassan.peerhossaini@polytech.univ-nantes.fr
ABSTRACT
Heat transfer between two concurrent immiscible liquid flows is of great interest for improving the characteristic time, compactness, and energy cost of cooling and heating processes. A high-efficiency vortex (HEV) static mixer is investigated as a direct-contact heat exchanger (DCE). This new type of mixer generates coherent large-scale structures, enhancing momentum and heat transfer in the bulk flow and thus providing favorable conditions for phase dispersion and quick temperature homogenization in the mean phase. Experiments involved injection of a mineral oil into a continuous flow of water; the two fluids are immiscible. The inlet water temperature ranged from 11 to 13°C, the inlet oil temperature ranged from 40 to 48°C, and the Reynolds number varied between 7500 and 15000. This DCE produces an in situ dispersion of the oil phase in the continuous water phase with no external energy input, and thus is energetically more efficient than other DCEs for an identical emulsion production. Experimental results are compared to an algebraic 1D thermal model taking into account the axial development of the specific dispersion area for heat transfer. The efficiency of this heat exchanger is compared with that of a simple duct of equal hydraulic diameter.
KEYWORDS
Heat exchanger, Interfacial area, Direct contact heat exchanger, Sauter diameter, Static mixer, Two- phase flow, Liquid/liquid dispersion.
1. INTRODUCTION
Direct contact heat exchangers (DCEs) are based on direct heat transfer between the main flow and a dispersed phase (particles, drops, bubbles). A DCE is a relatively simple design that provides cost- effective heat transfer due to its large contact area, and is thus suitable for preheating and evaporating a working fluid using thermal energy at low temperatures. These devices are recommended for water desalination (Sideman et al., 1966; Letan, 1988), crystallization (Letan, 1988; Core et al., 1990), energy recovery from industrial waste (Shimizu et al., 1988), and thermal energy storage (Core et al., 1990; Wright, 1988).
The object of the present study is to characterize the heat transfer with a new static mixer commonly called HEV (high-efficiency vortex) used as a DCE. In this case, the dispersion of the oil in the water flow is achieved in the HEV, so that no extra energy is needed to produce the dispersed phase.
The design of the HEV is based on curved baffles fixed on tube walls that generate large-scale longitudinal vortices, substantially increasing heat transfer phenomena over those in the simple pipe.
Various aspects of this heat exchanger have been previously studied: heat transfer (Mokrani et al.,
1Corresponding author.
1995) and the turbulent structure; and droplet formation (Lemenand et al., 2003 and Lemenand et al., 2005). The well established properties of HEV flow are used in modeling the heat transfer and interpreting the measurements.
2. EXPERIMENTAL APPARATUS AND METHODS
2.1 Hydraulic loop
Two-phase flow experiments were performed by injecting the oily phase into the turbulent water flow.
The experimental setup is composed of two feed loops, as shown in Figure 1. The oil, pumped by a centrifugal pump (Grunfos CHV2-50), is injected in the center of the HEV section by the mean of a pipe of 3 mm diameter. The water is supplied by a constant-level feed tank where the free-surface buffer tank configuration avoids transmission of pump vibrations that might induce fluctuations into the flow. The oil and water flow rates are controlled by valves and measured with rotameters. The test section is connected to a preconditioner and postconditioner, which are 300 mm straight transparent tubes of circular cross-section of 20 mm inner diameter.
Oil tank B
Static mixer
Réservoir A
Pump Flowmeters
Water Oil
Flowmeters Storage of the produced emulsion
Water tank A
Figure 1: Hydrodynamic loop.
2.2 Hydrodynamic properties of the static mixer HEV
The geometry to be tested is a static mixer consisting of a straight tube of circular cross section (inner diameter 20 mm) in which several arrays of tabs are inserted in the cross section. These tabs play the role of vortex generators able to enhance the mixing capacities of the heat exchanger. As shown on Figure 2, the tabs are trapezoidal baffles fixed to the tube wall at a 30° angle. The standard size of the tabs is 7 mm long and 7 mm and 5 mm at the base, respectively, on the wall and at the end of the trapezoid. The hydraulic diameter DH of the duct equipped with the baffles is 17.1 mm.
Figure 2: Four tabs in one section of the HEV and tab dimensions
Figure 3: Over all view of HEV.
Typical vortices generated by the baffles are visualized by the Laser-Induced Fluorescence (LIF) technique (Peerhossaini and Wesfreid, 1988) in single-phase water flow for transitional Reynolds numbers of 1500 (see Figure 4). However, this flow qualitatively represents the flow pattern at higher Reynolds numbers. The mushroom-shaped vortices visible in the cross section are enhanced as the Reynolds number increases. Four pairs of vortices are generated at each section and the succession of baffles along the longitudinal axis of the static mixer creates a complex combination of whirls.
Detailed information on the flow pattern and turbulence structure of single-phase flow in a static mixer can be found in Lemenand et al. (2003), Mokrani et al. (1995) and Phillips et al. (1997).
(a) (b)
(c) (d)
Figure 4: Photographs of cross-section of longitudinal vortices downstream of (a) first, (b) second, (c) third and (d) fourth baffle array for Re = 1500.
Vortices generated by the baffles contribute to intensify heat and mass transfers in the cross section of the HEV, especially between the “high shear zone” in the wake of the baffles and the “bulk flow”. In fact, the breakup efficiency is due to this high shear zone, and the macro-mixing role of the vortices allows a homogeneous residence time of the oil droplets to realize a complete breakup (Lemenand et al., 2003). Concerning the heat transfer, the homogeneity in reasonably well ensured in the whole section of the pipe.
Figure 5: Location of the longitdinal vortices.
2.3 Working fluids
The working fluids are water for the continuous phase and a technical vaseline oil, without additives, for the dispersed phase; the physical properties of the oil are given in Table 1.
Property (20°C) Value Measurement method
Kinematic viscosity 30.0 10-6 m2 s-1 Mettler RM180 rheometer Specific heat 2300 J K-1 kg-1 Differential scanning calorimeter
Density 850 kg m-3 Technical data
Thermal conductivity 0.15 W m-1 K-1 Technical data
Interfacial tension with water 30.8 10-3 N m-1 Krüss (K12) tensiometer by the ring method Table 1: Physical properties of oil.
The specific heat of the oil was measured by a differential scanning calorimeter for temperatures between 10 °C and 60 °C, and the following expression is proposed to compute this physical property, with a relative error less than 1%:
T . (T)
Cpo = 2238+297 (T in °C) (1)
Since the water temperature varies between 11 and 15 °C during the experiments, the specific heat of water is taken constant at 4181 J K-1 kg-1.
2.4 Temperature probing
The continous phase temperature along the axis is measured by five thermocouples of type K (K1 to K5), with 80 µm wire diameter. The accuracy is about 0.1 °C after calibration . As seen on Figure 6, two of them (K3 and K4) are located near the wall, at x=0.09 m (after the third tab) and at x=0.17 m (after the seventh tab). K1 and K2 respectively give the water and oil inlet temperatures.
Thermocouple K5, in the same end section as K4 (x=0.17 m), allows the measurement of the temperature profile thanks to a micrometeric traversing mechanism. The latter shows that the wall temperature is close to the average temperature of the water, hence the temperature can be assumed uniform in the cross section.
Figure 6: Location of the thermocouples.
3. ONE-DIMENSIONAL HEAT TANSFER MODEL
3.1 Enthalpic model
A global one-dimensional model is developed in order to obtain the mean axial temperature profile in the two phases. Three main assumptions ground the establishment of the thermal balance in the present form:
- the water (continuous phase) temperature is constant in the tube cross-section (see Sec. 2.4), so that the axial dispersion term vanishes (plug flow model) ;
- the oil temperature is homogeneous in each drop, so that the wall temperature used to compute the heat flux is the drop average temperature ;
- the effect of the peculiarities due to the tabs are not taken into account, longitudinal gradients are modeled globally.
The dispersed phase is assumed to be of uniform droplet size equal to the Sauter diameter, so that the interphase contact surface is the same as for the real size distribution. The heat transfer between an oil droplet and the water phase is modeled by a convective heat transfer coefficient hx.
Figure 7: Heat transfer on the droplets surface
The enthalpic balance on the two phases over a length dx along the axis x (Figure 7) yields:
(
xdx x) (
x x)
w w w x x o w
p w
wQ C T T hS T T
ρ + − = − (2)
(
xdx x) (
x x)
o o o x x o w
p o
oQC T + −T =−h S T −T
ρ (3)
with
ρ
w andρ
o respectively the water and oil density, Qw and Qo respectively the water and oil flow rate, Cpw and Cpo respectively the water and oil specific heat, and Tw and T0 respectively the water and oil temperatures.This system of two ordinary differential equations is coupled through the heat transfer term
(
ox wx)
x
xS T T
h −
ρ
, where Sx is the interfacial area. Hence, the heat transfer term needs two modeling steps: the heat transfer coefficient h, and the interfacial area S linked to the droplet diameter.3.2 Modeling of heat transfer coefficient
Droplets are assumed to be transported by the main water flow with zero slip velocity between the two phases. The heat transfer coefficient hx corresponding to the heat transfer between the droplets and the continuous phase flow is given by a Nusselt number value of 2 for a static environment, which is the case here if it is considered that the droplets behave like passive particles in the main flow (see Bricard et al., 1996 or Whitaker, 1972):
32 =2
=
w xd Nu h
λ , (4)
where λw is the water thermal conductivity.
3.3 Modeling of droplet size
The contact surface Sx is related to the Sauter diameter of the size distribution by the volume/surface definition of d32. Over a differential volume of length dx:
32
6 d
dx Sx = ϕA
, (5)
where ϕ is the oil volume fraction and A the HEV section area.
The evolution of d32 is described by two alternative models:
- the “constant-drop-diameter model”, which implies the same value for interfacial area along the heat exchanger ;
- the “kinetic model for drop-breakup”, where the progressive dispersion along the tube is taken into account.
For the first case, which can be predicted by the general breakup model in a turbulent flow (adapted to the HEV), see Lemenand et al. (2003). If U is the flow velocity and
σ
the oil/water interfacial tension, the final maximum droplet diameter dmax,f is given for the HEV by the mean turbulence kinetic energy dissipation rate ε :25 max, 0.379 −
= ε
ρ σ 35
w
d f (6)
The Sauter diameter d32 is proportional to the maximum droplet diameter dmax (Lemenand et al., 2003):
max 32 0.48d
d = (7)
The previous diameter determination approach states that equilibrium conditions are reached, i.e.
the drops are submitted to the break-up mechanism for a time period equal or longer than the characteristic break-up time. This has been verified by evaluating the present breakup frequency in the flow, using the approach of Martinez-Bazan et al. (1999). This criterion shows that the drop size stabilizes in the middle of its travel in the heat exchanger, so that breakup kinetics in the device could well be pertinent.
A kinetic model for droplet break-up can be developed from the following observations. At the injection zone, the order of magnitude of the droplets is given by the injector diameter, which is the boundary condition for the drop diameter . The droplet size reduces along the flow by the effect of the turbulent stresses until it reaches an equilibrium value. The break-up model is based on the evaluation of the break-up frequency n of the droplet by turbulence in the HEV; this frequency n is given in terms of a critical diameter dc (Martinez-Bazan et al., 1999):
f max,
c= d
d 1.63 (8)
If dmax at the current section is greater than dc, inertial forces dominate, so that:
3 2 max 3
1 −
d
=
n ε (9)
Conversely, if the typical dmax is smaller than dc, thensurface forces dominate and:
d 1
= d n
f max, 5 max 3 3 -2
w
−
ε
ρ σ
(10)
This model is consistent within the limit of dmax at dmax,f .
The number of division Nx of the droplets between two axial positions x and x+dx during the residence time
U
dx is hence given by:
U dx
Nx =n (11)
Considering a “mother” droplet that breaks up into two “daughter” droplets, the evolution of diameter between two axial positions x and x+dx is given by:
U ndx
N d e
d d
x x x dx
x
23 . 0 max 3
max max
2
= −
+ = (12)
The mean turbulence kinetic energy dissipation rate is evaluated in both cases by the global pressure drop:
L P U
ρ
wε
= ∆ (13)The entry zone is taken into account by a pressure drop evaluated as in a smooth straight duct, in order to avoid overestimating the heat flux in the first centimeters (up to 0.04m). The dispersion model is considered independent of the temperature evolution; then the evolution of the d32 diameter in the axial direction follows the curve shown on Figure 8.
Figure 8: Axial evolution of Sauter diameter d32 as a function of Reynolds number Re.
4. EXPERIMENTAL VALIDATION OF THE DISPERSION/THERMAL MODEL AND DISCUSSION
The results of the one-dimensional thermal model for temperature are compared with experimental measurements on water (continuous phase) temperature (note that the oil droplet temperature is not accessible to the thermocouples).
In all experiments, the volume oil fraction is maintained at 15% and the Reynolds number based on the hydraulic diameter of the HEV is fixed between 7500 and 15000. Four runs were made for each Reynolds number to ensure reproducibility. Unfortunately, the experimental device does not let us fix thermal inlet conditions precisely because the pump heats up the oil, and the water temperature follows the reservoir temperature, which is equal to the ambient temperature. Thus the inlet water temperature is around 12 °C and oil inlet temperature is between 40 and 48 °C; experiments are numbered from 1 to 16. Table 2 summarizes the experimental conditions and water temperature measurements. The wall insulation is assure by a 3 cm of Plexiglas thickness and by a weak difference between water and room temperature.
The dimensionless temperature is defined as follows:
inlet , w eq
inlet , w
* w
w T T
T T T
−
= − , (14)
where Teq is the water and oil temperature when the heat transfer process is completed, i.e. the temperature at the thermal equilibrium of the two phase flow when Tw=To=Teq. Thanks to the dimensionless temperature Tw
*, all runs for a given Reynolds number fall on a single curve.
N° Re U (m s-1) Qw (l h-1) Qo (l h-1) Tw,inlet To,inlet Tw,x=0.09 Tw,x=0.17
1 15000 0.75 721 127 12.5 46.7 14.5 14.8
2 12.5 44.7 14.2 14.5
3 11.7 47.6 13.9 14.2
4 12.8 43.1 14.3 14.6
5 12500 0.63 601 106 12.5 45.1 14.2 14.5
6 12.6 45 14.1 14.4
7 11.7 47.5 13.6 13.9
8 12.9 42 13.9 14.3
9 10000 0.5 481 85 11.4 44.9 13 13.4
10 12.6 43.1 13.9 14.2
11 11.8 45.2 13.3 13.7
12 12.8 40.4 13.7 14.1
13 7500 0.38 360 64 11.4 43.8 12.5 13
14 12.7 42.4 13.5 13.9
15 11.8 45.9 13.2 13.7
16 13 41.2 13.9 14.3
Table 2: Operating conditions and experimental results.
Despite the care taken in flow measurement, the relative error in the oil flow rate is about 11%
and 3% for the water flow rate. The error in the oil flow rate measurement explains the dispersion of the experimental results.
The discrepancy between the curves for the two droplet break-up models given in Figures 9 to 12 shows the decisive importance of the dispersion mode. The “constant-drop-diameter model” gives a higher heat transfer rate than the “kinetics model for drop break-up”, where the water temperature increase is “delayed” because of a coarser dispersion.
Examples of oil temperature profiles computed with the kinetic model are presented in Figure 13.
The oil temperature decrease is more pronounced than the water temperature increase due to the volume fraction and the specific heat ratio between oil and water. Even though the model slightly overestimates the heat transfer, the agreement seems satisfactory to the extent that no fitting parameter has been introduced to improve the model. Actually, in this exclusively phenomenological approach, the relative error in the dimensionless water temperature is between 15 and 25 %.
Figure 9: Water temperature, Re = 7 500. Figure 10: Water temperature, Re = 10 000.
Figure 11: Water temperature, Re = 12 500. Figure 12: Water temperature, Re = 15 000.
Figure 13: Typical oil temperature profiles obtained from the drop breakup kinetics model for the case of Tw,inlet=13°C and To,inlet=47°C.
Some aspects of the basic hypotheses underlying the model should be reappraised. No great improvement is expected in the break-up model nor in the global heat transfer coefficient h, which
could increase only if boundary layers are considered. With regard to the effects of dimensionless numbers, the model’s overestimate of the heat transfer can be explained, in particular, by the effect of Biot number Bi of the oil droplet, which is considered constant along the axis and independent of the Reynolds and Weber numbers:
d Nu Bi h
o w o
x x
λ λ λ
0.48max =
= (15)
Following the literature (Bricard et al., 1996), if the Biot number is below 0.1, the temperature of the droplet can be assumed uniform. In this study, the Biot number is 3.8, so the hypothesis of uniform temperature droplets is not fulfilled ; it is probably this issue that contributes the most to the overestimation of heat transfer in the model.
5. COMPARISON WITH A DOUBLE-JACKETED HEAT EXCHANGER
The use of the HEV as a DCE can be examined via the one-dimensional thermal model. The efficiency of this DCE was compared to a smooth duct heat exchanger of equal length and hydraulic diameter, at the same flow rate, and under the most favorable conditions for a double-jacketed heat exchanger: a constant wall temperature equal to the oil inlet temperature over the whole heat exchanger surface (this case is, of course, unrealistic). The Colburn correlation is used to evaluate heat transfer in the pipe:
13 8 .
0 Pr
Re 023 .
=0
Nu (16)
The global performance is evaluated by the energy efficiency rate R, the ratio of thermal power transferred over the pumping (pressure drop) energy lost in the pipe and in the HEV:
P
nged PowerExcha
R= ∆ (17)
Figure 14 shows the superiority of the DCE with respect to pressure loss: the ratio R for the HEV used as DCE is at least 20% better than for the classical double-jacketed heat exchanger.
Figure 14: Energy efficiency rate of the HEV and double-jacketed exchanger.
6. CONCLUSIONS
Experimental data on heat transfer in a HEV used as a DCE for oil droplets in a turbulent water flow are presented. It is shown that this direct contact heat exchanger is more efficient than a double-pipe heat exchanger even under the most favorable conditions for the latter. Moreover, compared with other DCEs, the HEV produces simultaneous droplet breakup, according a considerable advantage in terms of energy cost. Because of the difficulties encountered in fixing the operating conditions precisely, more experimental data are needed in order to produce statistically valid results. These measurements will be the focus of future work.
The one-dimensional model developed here can be used as a sizing tool for heat transfer in liquid/liquid two-phase operations with concomitant break-up, for instance in energy salvage and storage in thermal plants. This model, not yet sufficiently precise, can be improved by taking into account the temperature non-uniformity inside the droplet, an issue that will be the focus of future work.
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