- Email: [email protected]
Determination of representative and instantaneous process side heat transfer coefficients in agitated vessel using heat flux sensors
Chemical Engineering and Processing 44 (2005) 993–998
Determination of representative and instantaneous process side heat transfer coefficients in agitated vessel using heat flux sensors G. Delaplace ∗ , J.-F. Demeyre, R. Gu´erin, P. Debreyne, J.-C. Leuliet a INRA-LGPTA,
369 Rue Jules Guesde, B.P. 39, 59651 Villeneuve d’Ascq, France
Received 15 May 2004; received in revised form 3 June 2004; accepted 16 November 2004 Available online 25 February 2005
Abstract In this work, process side heat transfer coefficients were determined through the use of a heat flux sensor and compared to those using conventional thermocouples and heat balance technique. A local heat fluxmeter was mounted on the inner wall of a rounded bottom vessel equipped with an atypical helical ribbon impeller supported by two vertical arms. A detailed analysis of the variations of instantaneous heat flux with impeller positions is also presented. It is shown that the heat flux sensor is able to monitor the thermal boundary layer thickness and its renewal with the impeller rotation. © 2005 Elsevier B.V. All rights reserved. Keywords: Heat flux sensors; Mixing; Heat transfer; Helical ribbon impeller; Newtonian fluid
1. Introduction The use of heat flux sensors is now widespread in a number of application fields, for instance to determine local heat transfer coefficients in process equipment [1], to measure heat losses through walls, floors and roofs [2,3], to measure heat losses from insulated pipes [2] or to in-line monitor fouling due to deposit of whey protein in a process equipment [4,5]. Although heat flux sensors allow to measure the instantaneous local heat transfer coefficient and consequently provide useful information about heat transfer mechanisms in process equipment, relatively little attention has been addressed on this issue. For example, according to us there are very few works [6] which emphasizes the change of the heat flux with the impeller rotation in an agitated vessel. This is a great pity since such information allow us to gain understanding about the renewal of the thermal boundary layer and thus to select the best suited mixing system in terms of heat performances. Major restrictions to perform such works or to determine process side heat transfer coefficients using heat flux sensors are related to implementation and calibration. Note that ∗
Corresponding author. Tel.: +33 20435437; fax: +33 20435426. E-mail address: [email protected] (G. Delaplace).
0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.11.005
implementation problems mainly concern the maximum temperature that the cement can withstand. The aim of this work is two fold: - to show that the use of the heat flux sensors embedded on the tank wall would be a useful and a viable means to obtain both representative average process side heat transfer coefficients avoiding arduous time consuming experiments with conventional thermocouples and heat balance technique. - To show that instantaneous heat flux measured directly with fluxmeter can provide very useful information to understand mechanism of heat transfer.
2. Materials and methods 2.1. Experimental equipment The mixing vessel is a jacketed stainless steel tank of 0.346 m diameter equipped with a double helical ribbon supported by two vertical arms (Fig. 1). The wall clearance is equal to 0.01 m. The mixing equipment used in this investigation was driven by an electric motor equipped with a variable-speed drive. A tachometer and a torquemeter were
994
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
The new sensitivity obtained by in situ calibration was equal to 2.71 V W−1 m2 . Depending on the targets of the experiments: (i) determination of representative process side heat transfer coefficients or (ii) measurements of heat flux variations with impeller rotational speed, the frequency data acquisition system (Agilent Technologies 34970A) was respectively equal to 15 s and 50 ms.
Fig. 1. Picture of the mixing system investigated (Paravisc® —Ekato).
used to monitor respectively the rotational speed of the impeller and the torque. 2.2. Experimental procedure Process side heat transfer coefficients were obtained using two different experimental approaches: - by conventional thermocouples and heat balance technique. Eleven thermocouples located at various axial and radial positions were simultaneously used to measure the average bulk fluid and vessel wall temperatures. Temperature accuracy of copper–constantin thermocouples used is ±0.3 ◦ C. Bulk temperature measurements are located in a well-mixed region and so can be properly used to determine film heat transfer coefficient [7]. - By a heat flux sensor (Fig. 2) mounted on the inside tank wall (CAPTEC, France). This heat flux sensor exhibits a potential directly proportional to the heat flow through its surface area, J. Typical sensitivity of the heat flux sensor given by the manufacturer is equal to 4.19 V W−1 m2 . However, this value was corrected due to mounting procedure adopted which strain the area of the sensor. Indeed sticking and varnishing treatments required to correctly embedded the fluxmeter on the process side of the vessel contribute to decrease sensitivity of the sensor.
Fig. 2. Heat flux sensor—CAPTEC, France.
The calibration procedure consisted in covering the flux sensor with a resistance which had the same area than the fluxmeter and to measure the voltage signal when a known electrical power provided by the resistance is dissipated through the flux sensor. Process side heat transfer coefficients of the mixing system were measured experimentally for both heating and cooling procedures. Temperature at the vessel wall was maintained at a constant value by introducing into the jacketed vessel hot water at 60 ◦ C or glycol ethylene at 5 ◦ C. Heat transfer experiments were carried out (i) at constant impeller rotational speed. The range of rotational speed investigated varied from 10 to 70 rpm, (ii) with a glucose syrup/water solution of viscosity ranging from 2.3 Pa s at 60 ◦ C to 164 Pa s at 20 ◦ C. In this work, thermal dependence of physical and rheological properties of the agitated fluid (ρ, Cp , µ, λ) was taken into account. Note that (ρ, Cp , µ, λ) were systematically estimated at average bulk fluid temperature. 2.3. Determination of process side heat transfer coefficients 2.3.1. Using a fluxmeter Process side heat transfer coefficients hJ were determined from the local heat flux J measured through the surface area of the sensor: hJ =
J (θw − θb )
(1)
In Eq. (1), θ w and θ b refer respectively to the tank wall and bulk temperature. The integer time for heat flux density J measurements was set up to 200 ms. The reliability of process side heat transfer coefficients deduced from the sensor measurements was ascertained by comparing their values to those determined by conventional thermocouples (located at bulk and at wall) and heat balance technique. This comparison is based on the assumption that local measurements of heat flux were representative of the average heat flux exchanged through the wall of the jacketed vessel. This was partly proved for this study since the additional thermocouple integrated in the sensor provide a wall temperature which was in agreement with the 6 wall temperatures measured by conventional thermocouples. 2.3.2. Using conventional thermocouples Process side heat transfer coefficients h measured by conventional thermocouples and heat balance technique were
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
obtained as follow: Φt − Φv − Φl h= A(θw − θb )
(2)
In Eq (2), A is the heat transfer area of the jacketed vessel. Φt , Φv , Φl are respectively the overall heat flux supplied to the agitated medium, the additional calorific power due to viscous dissipation and heat flux losses. Using the fact that (i) Φt = mCp (dθ b /dt) with (dθ b /dt) the bulk temperature derivative and m the mass of the agitated fluid and assuming that (ii) heat losses are negligible (iii) the additional calorific power due to viscous dissipation is equal to the power consumption required for mixing Pmec , Eq. (2) is reduced to: h=
mCp (dθb /dt) − Pmec A(θw − θb )
995
(3)
For each heat transfer experiments, (dθ b /dt) was evaluated at various bulk temperatures (15, 20, 25, 30, 35, 40, 50, 55 and 60 ◦ C) and Pmec was determined using torque and rotational speed of the impeller measurements as previously described [7]. Note that the uncertainties related on process side heat transfer coefficient determination are closely linked to heat loss and hypothesis assumed on viscous dissipation. Consequently such uncertainties are very difficult to estimate. For instance, Chabbra [9] mentions that an error to 25–60% in the value of process side heat transfer is not all bad in view of the complexity of the flow in an agitated vessel. In this work, a rough estimation of the error should be at a maximum of 15%.
3. Results and discussion 3.1. Process side heat transfer coefficient results Fig. 3 illustrates process side heat transfer coefficients obtained using Eqs. (1) and (3). It is shown that instantaneous process side heat transfer coefficients (determined from direct measurement with flux sensor) averaged within a period
Fig. 3. Comparison of process side heat transfer coefficients deduced from heat flux sensor measurements (hJ ) and from conventional thermocouples located at bulk and wall (h). Process side heat transfer values have been obtained when mixing Newtonian liquids at various impeller rotational speeds (3 < Reynolds number < 3974, 2289 < Cp < 2563, 1337 < ρ < 1412, 0.16 < µ < 33.93, 0.23 < λ < 0.47).
close to the process time (=1/N) are close to global heat transfer coefficients obtained by measurements with conventional thermocouples for both heating and cooling procedures. These preliminary results clearly demonstrate that using appropriate calibration procedure for sensitivity heat flux sensor is a viable mean to determine representative process side heat transfer coefficients. 3.2. Heat flux variations with time Evolution with time of the instantaneous heat flux signal measured by the fluxmeter is shown on Fig. 4. For this run, the integer time for J measurements and the rotational impeller speed were respectively set equal to 16.7 ms and is largely inferior to the process time (=1/N with N = 10 rpm). Note that other heat transfer experiments carried out with various impeller rotational speeds also give similar plots. Heat flux seems to describe a sustained oscillatory signal. Close inspection of the heat flux signal shows that a periodic variation exists. It can be noted that two hollows of the heat
Fig. 4. Heat flux evolution with time obtained for highly viscous fluid when mixing at 10 rpm with helical ribbon impeller.
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G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
Fig. 5. Sketch of variations of the heat flux with impeller position.
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
997
flux signal corresponds to one impeller revolution (Fig. 5a). A Fast Fourier Transform procedure allows us to obtain the way energy of the signal is distributed over its various component frequencies. It appears from the frequency spectrum obtained by this approach that the heat flux is associated both with the helical blades and vertical arms passages opposite the fluxmeter. These observations allow us to make hypothesis about particular position of the impeller relative to the characteristic periodic variations of the heat flux signal (Fig. 5a and b): - the minimum absolute value of the heat flux (Fig. 5a – position 1) corresponds to the instant where the helical blade is the most distant from the heat flux sensor (Fig. 5b – position 1). Indeed, when the helical blade was keep away from the fluxmeter for a long time, the material in the immediate vicinity of the wall was not removed and the transfer between the jacketed vessel and the adjacent liquid film becomes weak. - When the helical blade come close to the heat flux sensor, the heat flux starts to increase since the material in the immediate vicinity of the wall is removed completely. It is assumed that the change of the slope for the increasing heat flux signal (Fig. 5a – position 2) is due to the helical blade passage (Fig. 5b – position 2). As the helical impeller blade had passed, the liquid on the tank wall close to the sensor carries on to be removed due to suction effect (Fig. 5a). Consequently, the heat flux signal carries on increasing. When heat flux sensor gives up to be reached by fresh liquid, the heat flux stop to increase and reaches a maximum value (Fig. 5b – position 3). At this time, the two helical blade are too far away from the blade (Fig. 5b – middle left) to remove the fluid in the vicinity of the sensor, consequently the heat flux decreases. As the vertical arm passes (Fig. 5b – position 4), the heat flux increases slightly since the arm manage to wipe a part of the liquid from the surface area of the sensor. Note that the scraping effect of the vertical arm are largely inferior to the upward flow observed for the helical blade. Moreover it is shown that the trail effect due to the arms is a very brief life time. The slight upward flow generated by the arms compare to those of the helical blade was already observed in [8]. - Following the vertical arm passage, the heat flux decreases again till the second helical blade is able to remove fluid from the heat flux sensor (Fig. 5b – bottom left). - After that, a new period starts. Note that the amplitude of heat flux fluctuation of the second helical blade is not so important than the first one. This phenomenon may be explained by a secondary flow or slight geometry difference between the two helical blades. The instantaneous heat flux measured in previous experiments are very interesting since it leads to a better understanding about renewal of the thermal boundary layer with the impeller passage. Indeed assuming that during one impeller revolution thermal conductivity λ and both wall and bulk temperatures are constant and using Nusselt theory, an
Fig. 6. Variations of the thermal boundary layer thickness with time and impeller position. Impeller positions which appears corresponds to sketch given on Fig. 5.
hypothetical thermal boundary layer thickness ε can be deduced from heat flux density measurements J as follow: ε=
λ (θw − θb ) J
(4)
Fig. 6 shows temporal variations of the hypothetical thermal boundary layer thickness deduced from Eq. (4). Note that results presented for the hypothetical thermal boundary layer thickness were normalized using the wall clearance in order to make it independent of the scale. This thickness varies with the helical blades positions. Fig. 6 clearly shows that thickness is maximum when the helical blades are the most distant of the sensor. Thickness values are always lower than the wall clearance of the mixing system. At this state, it is clear that the choice of the reference temperature (here the bulk temperature) for the calculation of the hypothetical thermal boundary layer thickness influences considerably the values obtained; however these results shown that flux sensor are tools which allowing a better understanding in heat exchange mechanisms.
4. Conclusions Process side heat transfer coefficients in agitated vessel have been investigated using heat flux sensor. It is shown that heat transfer coefficients obtained by fluxmeter are in agreement with those obtained from experiments with conventional thermocouples and heat balance technique. However, the meaningfulness of the measurements carried out with fluxmeters is dependent on its correct installation and in situ calibration. Using a rapid data acquisition system, instantaneous heat flux variations with impeller rotation have also been monitoring during a heat transfer process. It is shown that the heat flux sensor is able to monitor an hypothetical
998
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
thermal boundary layer thickness and its renewal with the impeller rotation. These results shown that fluxmeters are instruments that offer valuable information in complement to temperature data, allowing a better understanding of heat exchange. Note that, the understanding of the renewal of the thermal boundary layer with impeller rotational speed pointed out in this work is very interesting since such information can lead to a better classification of heat transfer performances of mixing equipments based on heat flux variations with impeller rotational speed. Of course, it would be interesting to carry out heat transfer experiments with other mixing systems. This will be tackle in a future work.
Appendix A. Nomenclature
A c Cp h J m P
area of the jacketed vessel (m2 ) wall clearance (m) specific heat at constant pressure (J kg−1 K−1 ) film heat transfer coefficient (W m−2 K−1 ) heat flux per square meter (W m−2 ) mass (kg) power (W)
Greek letters ε thermal boundary layer thickness (m) λ thermal conductivity (W m−1 K−1 ) µ Newtonian viscosity (Pa s) θ temperature (◦ C) ρ density (kg m−3 )
Subscripts b bulk w wall
References [1] S. Azoory, T.R. Bott, Local heat transfer coefficients in a model “Falling Film” scraped surface exchanger, Canadian J. Chem. Eng. 48 (1970) 373–377. [2] Van der Graaf F., Heat Flux sensors, in: T. Ricolfi, J. Scholz (Eds.), Thermal Sensors, vol. 4 (8), 1990. [3] W.K.P. Van Loon, H.M.H. Bastings, E.J. Moors, Calibration of soil heat flux sensors, Agric. Forest Meteorol. 92 (1998) 1–8. [4] T.J. Davies, S.C. Henstridge, C.R. Gillham, D.I. Wilson, Investigation of whey protein deposit properties using heat flux sensors, Trans IChemE. 75 (1997) 106–110. [5] T. Truong, S. Anema, K. Kirkpatrick, H. Chen, The use of heat flux sensor for in-line monitoring of fouling of non-heated surfaces, Trans IChemE. 80 (2002) 1–10. [6] S. Haam, R.S. Brodkey, J.B. Fasano, Local heat transfer in a mixing vessel using heat flux sensors, Ind. Eng. Chem. Res. 31 (1992) 1384–1391. [7] G. Delaplace, C. Torrez, J.-C. Leuliet, N. Belaubre, C. Andre, Experimental and CFD simulation of heat transfer to highly viscous fluids in an agitated vessel equipped with a non standard helical ribbon impeller, Trans IChemE. 79 (2001) 927–937. [8] G. Delaplace, C. Torrez, C. Andr´e, N. Belaubre, P. Loisel, Numerical simulation of flow of Newtonian fluids in an agitated vessel equipped with a non standard helical ribbon impeller, in: H.E.A. van den Akker, J.J. Derksen (Eds.), Proceedings of the 10th European Conference on Mixing, Elselvier Science B.V, Delf, The Netherlands, 2000, pp. 289–296. [9] R.P. Chhabra, Fluid mechanics and heat transfer with non-Newtonian liquids in mechanically agitated vessels, Adv. Heat Transfer 37 (2003) 77–178.
Determination of representative and instantaneous process side heat transfer coefficients in agitated vessel using heat flux sensors G. Delaplace ∗ , J.-F. Demeyre, R. Gu´erin, P. Debreyne, J.-C. Leuliet a INRA-LGPTA,
369 Rue Jules Guesde, B.P. 39, 59651 Villeneuve d’Ascq, France
Received 15 May 2004; received in revised form 3 June 2004; accepted 16 November 2004 Available online 25 February 2005
Abstract In this work, process side heat transfer coefficients were determined through the use of a heat flux sensor and compared to those using conventional thermocouples and heat balance technique. A local heat fluxmeter was mounted on the inner wall of a rounded bottom vessel equipped with an atypical helical ribbon impeller supported by two vertical arms. A detailed analysis of the variations of instantaneous heat flux with impeller positions is also presented. It is shown that the heat flux sensor is able to monitor the thermal boundary layer thickness and its renewal with the impeller rotation. © 2005 Elsevier B.V. All rights reserved. Keywords: Heat flux sensors; Mixing; Heat transfer; Helical ribbon impeller; Newtonian fluid
1. Introduction The use of heat flux sensors is now widespread in a number of application fields, for instance to determine local heat transfer coefficients in process equipment [1], to measure heat losses through walls, floors and roofs [2,3], to measure heat losses from insulated pipes [2] or to in-line monitor fouling due to deposit of whey protein in a process equipment [4,5]. Although heat flux sensors allow to measure the instantaneous local heat transfer coefficient and consequently provide useful information about heat transfer mechanisms in process equipment, relatively little attention has been addressed on this issue. For example, according to us there are very few works [6] which emphasizes the change of the heat flux with the impeller rotation in an agitated vessel. This is a great pity since such information allow us to gain understanding about the renewal of the thermal boundary layer and thus to select the best suited mixing system in terms of heat performances. Major restrictions to perform such works or to determine process side heat transfer coefficients using heat flux sensors are related to implementation and calibration. Note that ∗
Corresponding author. Tel.: +33 20435437; fax: +33 20435426. E-mail address: [email protected] (G. Delaplace).
0255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2004.11.005
implementation problems mainly concern the maximum temperature that the cement can withstand. The aim of this work is two fold: - to show that the use of the heat flux sensors embedded on the tank wall would be a useful and a viable means to obtain both representative average process side heat transfer coefficients avoiding arduous time consuming experiments with conventional thermocouples and heat balance technique. - To show that instantaneous heat flux measured directly with fluxmeter can provide very useful information to understand mechanism of heat transfer.
2. Materials and methods 2.1. Experimental equipment The mixing vessel is a jacketed stainless steel tank of 0.346 m diameter equipped with a double helical ribbon supported by two vertical arms (Fig. 1). The wall clearance is equal to 0.01 m. The mixing equipment used in this investigation was driven by an electric motor equipped with a variable-speed drive. A tachometer and a torquemeter were
994
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
The new sensitivity obtained by in situ calibration was equal to 2.71 V W−1 m2 . Depending on the targets of the experiments: (i) determination of representative process side heat transfer coefficients or (ii) measurements of heat flux variations with impeller rotational speed, the frequency data acquisition system (Agilent Technologies 34970A) was respectively equal to 15 s and 50 ms.
Fig. 1. Picture of the mixing system investigated (Paravisc® —Ekato).
used to monitor respectively the rotational speed of the impeller and the torque. 2.2. Experimental procedure Process side heat transfer coefficients were obtained using two different experimental approaches: - by conventional thermocouples and heat balance technique. Eleven thermocouples located at various axial and radial positions were simultaneously used to measure the average bulk fluid and vessel wall temperatures. Temperature accuracy of copper–constantin thermocouples used is ±0.3 ◦ C. Bulk temperature measurements are located in a well-mixed region and so can be properly used to determine film heat transfer coefficient [7]. - By a heat flux sensor (Fig. 2) mounted on the inside tank wall (CAPTEC, France). This heat flux sensor exhibits a potential directly proportional to the heat flow through its surface area, J. Typical sensitivity of the heat flux sensor given by the manufacturer is equal to 4.19 V W−1 m2 . However, this value was corrected due to mounting procedure adopted which strain the area of the sensor. Indeed sticking and varnishing treatments required to correctly embedded the fluxmeter on the process side of the vessel contribute to decrease sensitivity of the sensor.
Fig. 2. Heat flux sensor—CAPTEC, France.
The calibration procedure consisted in covering the flux sensor with a resistance which had the same area than the fluxmeter and to measure the voltage signal when a known electrical power provided by the resistance is dissipated through the flux sensor. Process side heat transfer coefficients of the mixing system were measured experimentally for both heating and cooling procedures. Temperature at the vessel wall was maintained at a constant value by introducing into the jacketed vessel hot water at 60 ◦ C or glycol ethylene at 5 ◦ C. Heat transfer experiments were carried out (i) at constant impeller rotational speed. The range of rotational speed investigated varied from 10 to 70 rpm, (ii) with a glucose syrup/water solution of viscosity ranging from 2.3 Pa s at 60 ◦ C to 164 Pa s at 20 ◦ C. In this work, thermal dependence of physical and rheological properties of the agitated fluid (ρ, Cp , µ, λ) was taken into account. Note that (ρ, Cp , µ, λ) were systematically estimated at average bulk fluid temperature. 2.3. Determination of process side heat transfer coefficients 2.3.1. Using a fluxmeter Process side heat transfer coefficients hJ were determined from the local heat flux J measured through the surface area of the sensor: hJ =
J (θw − θb )
(1)
In Eq. (1), θ w and θ b refer respectively to the tank wall and bulk temperature. The integer time for heat flux density J measurements was set up to 200 ms. The reliability of process side heat transfer coefficients deduced from the sensor measurements was ascertained by comparing their values to those determined by conventional thermocouples (located at bulk and at wall) and heat balance technique. This comparison is based on the assumption that local measurements of heat flux were representative of the average heat flux exchanged through the wall of the jacketed vessel. This was partly proved for this study since the additional thermocouple integrated in the sensor provide a wall temperature which was in agreement with the 6 wall temperatures measured by conventional thermocouples. 2.3.2. Using conventional thermocouples Process side heat transfer coefficients h measured by conventional thermocouples and heat balance technique were
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
obtained as follow: Φt − Φv − Φl h= A(θw − θb )
(2)
In Eq (2), A is the heat transfer area of the jacketed vessel. Φt , Φv , Φl are respectively the overall heat flux supplied to the agitated medium, the additional calorific power due to viscous dissipation and heat flux losses. Using the fact that (i) Φt = mCp (dθ b /dt) with (dθ b /dt) the bulk temperature derivative and m the mass of the agitated fluid and assuming that (ii) heat losses are negligible (iii) the additional calorific power due to viscous dissipation is equal to the power consumption required for mixing Pmec , Eq. (2) is reduced to: h=
mCp (dθb /dt) − Pmec A(θw − θb )
995
(3)
For each heat transfer experiments, (dθ b /dt) was evaluated at various bulk temperatures (15, 20, 25, 30, 35, 40, 50, 55 and 60 ◦ C) and Pmec was determined using torque and rotational speed of the impeller measurements as previously described [7]. Note that the uncertainties related on process side heat transfer coefficient determination are closely linked to heat loss and hypothesis assumed on viscous dissipation. Consequently such uncertainties are very difficult to estimate. For instance, Chabbra [9] mentions that an error to 25–60% in the value of process side heat transfer is not all bad in view of the complexity of the flow in an agitated vessel. In this work, a rough estimation of the error should be at a maximum of 15%.
3. Results and discussion 3.1. Process side heat transfer coefficient results Fig. 3 illustrates process side heat transfer coefficients obtained using Eqs. (1) and (3). It is shown that instantaneous process side heat transfer coefficients (determined from direct measurement with flux sensor) averaged within a period
Fig. 3. Comparison of process side heat transfer coefficients deduced from heat flux sensor measurements (hJ ) and from conventional thermocouples located at bulk and wall (h). Process side heat transfer values have been obtained when mixing Newtonian liquids at various impeller rotational speeds (3 < Reynolds number < 3974, 2289 < Cp < 2563, 1337 < ρ < 1412, 0.16 < µ < 33.93, 0.23 < λ < 0.47).
close to the process time (=1/N) are close to global heat transfer coefficients obtained by measurements with conventional thermocouples for both heating and cooling procedures. These preliminary results clearly demonstrate that using appropriate calibration procedure for sensitivity heat flux sensor is a viable mean to determine representative process side heat transfer coefficients. 3.2. Heat flux variations with time Evolution with time of the instantaneous heat flux signal measured by the fluxmeter is shown on Fig. 4. For this run, the integer time for J measurements and the rotational impeller speed were respectively set equal to 16.7 ms and is largely inferior to the process time (=1/N with N = 10 rpm). Note that other heat transfer experiments carried out with various impeller rotational speeds also give similar plots. Heat flux seems to describe a sustained oscillatory signal. Close inspection of the heat flux signal shows that a periodic variation exists. It can be noted that two hollows of the heat
Fig. 4. Heat flux evolution with time obtained for highly viscous fluid when mixing at 10 rpm with helical ribbon impeller.
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G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
Fig. 5. Sketch of variations of the heat flux with impeller position.
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
997
flux signal corresponds to one impeller revolution (Fig. 5a). A Fast Fourier Transform procedure allows us to obtain the way energy of the signal is distributed over its various component frequencies. It appears from the frequency spectrum obtained by this approach that the heat flux is associated both with the helical blades and vertical arms passages opposite the fluxmeter. These observations allow us to make hypothesis about particular position of the impeller relative to the characteristic periodic variations of the heat flux signal (Fig. 5a and b): - the minimum absolute value of the heat flux (Fig. 5a – position 1) corresponds to the instant where the helical blade is the most distant from the heat flux sensor (Fig. 5b – position 1). Indeed, when the helical blade was keep away from the fluxmeter for a long time, the material in the immediate vicinity of the wall was not removed and the transfer between the jacketed vessel and the adjacent liquid film becomes weak. - When the helical blade come close to the heat flux sensor, the heat flux starts to increase since the material in the immediate vicinity of the wall is removed completely. It is assumed that the change of the slope for the increasing heat flux signal (Fig. 5a – position 2) is due to the helical blade passage (Fig. 5b – position 2). As the helical impeller blade had passed, the liquid on the tank wall close to the sensor carries on to be removed due to suction effect (Fig. 5a). Consequently, the heat flux signal carries on increasing. When heat flux sensor gives up to be reached by fresh liquid, the heat flux stop to increase and reaches a maximum value (Fig. 5b – position 3). At this time, the two helical blade are too far away from the blade (Fig. 5b – middle left) to remove the fluid in the vicinity of the sensor, consequently the heat flux decreases. As the vertical arm passes (Fig. 5b – position 4), the heat flux increases slightly since the arm manage to wipe a part of the liquid from the surface area of the sensor. Note that the scraping effect of the vertical arm are largely inferior to the upward flow observed for the helical blade. Moreover it is shown that the trail effect due to the arms is a very brief life time. The slight upward flow generated by the arms compare to those of the helical blade was already observed in [8]. - Following the vertical arm passage, the heat flux decreases again till the second helical blade is able to remove fluid from the heat flux sensor (Fig. 5b – bottom left). - After that, a new period starts. Note that the amplitude of heat flux fluctuation of the second helical blade is not so important than the first one. This phenomenon may be explained by a secondary flow or slight geometry difference between the two helical blades. The instantaneous heat flux measured in previous experiments are very interesting since it leads to a better understanding about renewal of the thermal boundary layer with the impeller passage. Indeed assuming that during one impeller revolution thermal conductivity λ and both wall and bulk temperatures are constant and using Nusselt theory, an
Fig. 6. Variations of the thermal boundary layer thickness with time and impeller position. Impeller positions which appears corresponds to sketch given on Fig. 5.
hypothetical thermal boundary layer thickness ε can be deduced from heat flux density measurements J as follow: ε=
λ (θw − θb ) J
(4)
Fig. 6 shows temporal variations of the hypothetical thermal boundary layer thickness deduced from Eq. (4). Note that results presented for the hypothetical thermal boundary layer thickness were normalized using the wall clearance in order to make it independent of the scale. This thickness varies with the helical blades positions. Fig. 6 clearly shows that thickness is maximum when the helical blades are the most distant of the sensor. Thickness values are always lower than the wall clearance of the mixing system. At this state, it is clear that the choice of the reference temperature (here the bulk temperature) for the calculation of the hypothetical thermal boundary layer thickness influences considerably the values obtained; however these results shown that flux sensor are tools which allowing a better understanding in heat exchange mechanisms.
4. Conclusions Process side heat transfer coefficients in agitated vessel have been investigated using heat flux sensor. It is shown that heat transfer coefficients obtained by fluxmeter are in agreement with those obtained from experiments with conventional thermocouples and heat balance technique. However, the meaningfulness of the measurements carried out with fluxmeters is dependent on its correct installation and in situ calibration. Using a rapid data acquisition system, instantaneous heat flux variations with impeller rotation have also been monitoring during a heat transfer process. It is shown that the heat flux sensor is able to monitor an hypothetical
998
G. Delaplace et al. / Chemical Engineering and Processing 44 (2005) 993–998
thermal boundary layer thickness and its renewal with the impeller rotation. These results shown that fluxmeters are instruments that offer valuable information in complement to temperature data, allowing a better understanding of heat exchange. Note that, the understanding of the renewal of the thermal boundary layer with impeller rotational speed pointed out in this work is very interesting since such information can lead to a better classification of heat transfer performances of mixing equipments based on heat flux variations with impeller rotational speed. Of course, it would be interesting to carry out heat transfer experiments with other mixing systems. This will be tackle in a future work.
Appendix A. Nomenclature
A c Cp h J m P
area of the jacketed vessel (m2 ) wall clearance (m) specific heat at constant pressure (J kg−1 K−1 ) film heat transfer coefficient (W m−2 K−1 ) heat flux per square meter (W m−2 ) mass (kg) power (W)
Greek letters ε thermal boundary layer thickness (m) λ thermal conductivity (W m−1 K−1 ) µ Newtonian viscosity (Pa s) θ temperature (◦ C) ρ density (kg m−3 )
Subscripts b bulk w wall
References [1] S. Azoory, T.R. Bott, Local heat transfer coefficients in a model “Falling Film” scraped surface exchanger, Canadian J. Chem. Eng. 48 (1970) 373–377. [2] Van der Graaf F., Heat Flux sensors, in: T. Ricolfi, J. Scholz (Eds.), Thermal Sensors, vol. 4 (8), 1990. [3] W.K.P. Van Loon, H.M.H. Bastings, E.J. Moors, Calibration of soil heat flux sensors, Agric. Forest Meteorol. 92 (1998) 1–8. [4] T.J. Davies, S.C. Henstridge, C.R. Gillham, D.I. Wilson, Investigation of whey protein deposit properties using heat flux sensors, Trans IChemE. 75 (1997) 106–110. [5] T. Truong, S. Anema, K. Kirkpatrick, H. Chen, The use of heat flux sensor for in-line monitoring of fouling of non-heated surfaces, Trans IChemE. 80 (2002) 1–10. [6] S. Haam, R.S. Brodkey, J.B. Fasano, Local heat transfer in a mixing vessel using heat flux sensors, Ind. Eng. Chem. Res. 31 (1992) 1384–1391. [7] G. Delaplace, C. Torrez, J.-C. Leuliet, N. Belaubre, C. Andre, Experimental and CFD simulation of heat transfer to highly viscous fluids in an agitated vessel equipped with a non standard helical ribbon impeller, Trans IChemE. 79 (2001) 927–937. [8] G. Delaplace, C. Torrez, C. Andr´e, N. Belaubre, P. Loisel, Numerical simulation of flow of Newtonian fluids in an agitated vessel equipped with a non standard helical ribbon impeller, in: H.E.A. van den Akker, J.J. Derksen (Eds.), Proceedings of the 10th European Conference on Mixing, Elselvier Science B.V, Delf, The Netherlands, 2000, pp. 289–296. [9] R.P. Chhabra, Fluid mechanics and heat transfer with non-Newtonian liquids in mechanically agitated vessels, Adv. Heat Transfer 37 (2003) 77–178.