- Email: [email protected]
EHD enhanced heat transfer in a vertical annulus
International Communications in Heat and Mass Transfer 32 (2005) 748 – 757 www.elsevier.com/locate/ichmt
EHD enhanced heat transfer in a vertical annulusB Walter GrassiT, Daniele Testi, Mario Saputelli LOTHAR (LOw gravity and THermal Advanced Research laboratory), Department of Energetics bL. Poggi Q, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy Available online 17 March 2005
Abstract The preliminary experimental results of the effect of an electrostatic field on turbulent aided mixed convection in a short vertical annulus are reported herein. A dielectric liquid (FC-72 by 3M) is used as working fluid. The local heat transfer improvement is obtained by inserting appropriate points on the inner surface of the annulus, generally acting as the positive electrode, while the surrounding pipe is grounded. A high voltage (up to 22 kV) is established between the two surfaces. The heat exchange revealed to be highly enhanced by this technique, thus providing encouraging indications for practical applications. D 2005 Elsevier Ltd. All rights reserved. Keywords: EHD; Enhanced heat transfer; Vertical annulus
1. Introduction The material presented herein represents the very beginning of a broader research work aimed at performing a feasibility study of an EHD (electrohydrodynamic) enhanced high efficiency compact heat exchanger for space applications. In particular we, at first, confined our interest to the rather weak flow typical of a cold plate. Before starting a very systematic investigation, we checked the existence of the foreseen effects and their real extent in terms of heat transfer enhancement. As this initial step provided us with very encouraging indications, we decided to immediately communicate them. In the meantime we started performing a very detailed experimental campaign, as required by the complexity of the involved matter and by the high potentiality of this technique. With the above aim in mind, we will not B
Communicated by J.W. Rose and A. Briggs. T Corresponding author. E-mail addresses: [email protected] (W. Grassi)8 [email protected] (D. Testi). 0735-1933/$ - see front matter D 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2004.10.011
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
749
deal with the complex fluid dynamics implied by the studied regime, only stressing that the Richardson number (Gr/Re 2 ) ranges from 0.1 to 10, thus identifying a mixed convection regime, which is turbulent, according to the map proposed by Metais and Eckert [1]. Neither we will treat the fundamentals of the interaction of an electric field with an insulating fluid, simply illustrating the main features relevant to the following discussion. In the presence of an electric field, a body force f E arises in a dielectric medium, given by [2]: 1 2 1 2 Be f E ¼ qE E E je þ j qE ð1Þ 2 2 Bq T The first RHS term, the electrophoretic component, is the Coulomb force exerted by an electric field, E, upon the free charge, with density q E . The second term represents the dielectrophoretic body force, related to a local change of medium permittivity, e, in an electric field. The third term, the electrostrictive component, acts on the dielectric, with density q, in a non-uniform electric field. The last two terms represent the forces acting on polarisation charges. This electric force has to be inserted in the momentum equation. The whole set of equations to be used to solve any EHD problem is, thus, composed by the momentum, mass continuity and energy equations, plus the complete set of Maxwell equations. Although several alternative hypotheses have been formulated [3,4], there is a general agreement that the EHD phenomenon of heat transfer augmentation is of convective nature [5]. The expression of the vorticity balance assumes particular importance, showing which conditions lead to a convective motion. In the Boussinesq approximation [6], taking the curl of the momentum equation, we obtain (x = j 1 u): Bx 1 eb þ ujx ¼ xjuþvj2 x þ bg ^ jT þ jqE ^ E þ e jE2 jT Bt q 2q
ð2Þ
Electrostriction does not generate vorticity, while dielectrophoresis needs both a temperature gradient and a non-uniform electric field (b e = (1/e)(de/dT) represents the temperature coefficient of permittivity). A free charge gradient instead is necessary for the Coulomb force to produce a vortical flow. Two main mechanisms can generate free charge in a liquid, namely: thermal gradients, producing what is commonly known as electrothermal convection, and ion injection at the electrode/liquid interface via electrochemical reactions. This latter phenomenon will be dealt with in the following. Of particular importance for our purposes is the expression of the current density: j¼
n X i¼1
jqðEiÞ jK ðiÞ E þ qE u þ BðBteEÞ DcjqE
ð3Þ
n species of charge carriers of density q E(i) being present in the medium, each one with its own mobility, K (i). Eq. (3) uses a very general constitutive model for the dielectric, taking into account respectively: ion-drift, charge convection, displacement and diffusion currents. Bulk space charge can be created in dielectric liquids by injection of ions at the metal/liquid interface. The injected charges are homocharges [7], i.e. of the same polarity as the injecting electrode, called the emitter. This phenomenon most often occurs at one electrode only (the sharper one) [8] and is mainly controlled by electrochemical reactions at the interface, critically depending on the composition, geometry and polarity of the electrode [9] and on the chemical nature of the dielectric fluid. The injected space charge gives rise to a jet-like motion towards the facing electrode [10]. In liquids of low enough
750
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
electrical conductivity, the mechanism of ion injection gives the dominant contribution to the current [11] and the magnitude of the Coulomb force may be considered, to a first approximation, as being independent of temperature gradients. Assuming a unipolar injection (i.e. injection of only one species of charge carriers), Eq. (3) can be simplified as: j ¼ jqE jKE þ qE u
ð4Þ
Tabulated values of K are available only for the more common liquids. However, this parameter can be related to the dynamic viscosity, according to the so-called Walden’s rule [12], which rarely fails by an order of magnitude, as K = 2 1011/g, in SI units. In the absence of a forced flow, the problem of charge transfer bears an analogy with thermal convection [13], where the advection of hot and cold blobs in the fluid increases the heat transfer rate. In the unipolar injection problem, fingers of highly charged liquid coming from the injector boundary layer move across the inter-electrode space, while weakly charged liquid flows back to the injector due to mass continuity. In order to interpret the phenomenon, it is convenient to introduce a dimensionless parameter, known as the mobility parameter, M = e 1/2q 1/2 K1, which is the ratio of the hydrodynamic mobility and the true ion mobility. An order of magnitude of the induced fluid velocity can be obtained by balancing the fluid kinetic energy and the electrostatic one: rffiffiffiffi 1 2 1 2 u e qu ~ eE Z ~ ð5Þ 2 2 E q The hydrodynamic mobility is usually in the order of 107 H 108 m2 V1 s1 and typical velocities are in the range 0.1 H1 m s1. For Mb1, the fluid motion only slightly affects the trajectories of charge carriers, which are practically the electric field lines (this behaviour is typical of gases). Instead, for high enough values of the mobility parameter, which is the case of most liquids, the induced fluid velocity is higher than the ion drift velocity. Then, the charge distribution depends drastically on the motion it induces [11]. In a weakly forced flow, even in the turbulent regime, when a strong electroconvection by ion injection is established (a current density in the order of 104 H 105 A m2 is needed), the Nusselt number is controlled by the current alone [13,14], regardless of the Reynolds number and with negligible influence of buoyancy forces. A high heat transfer enhancement via ion injection can be obtained with fluids of low viscosity and low electrical conductivity [15], like the one used in these experiments.
2. Experimental apparatus and procedure In this work we examine the effect of a d.c. electric field on turbulent aided mixed convection in a heated vertical annulus with sharp points added to the inner electrode. The dielectric fluid chosen for the experiments is the Fluorinertk Electronic Liquid FC-72 (manufactured by 3M, St. Paul, MN, USA). FC-72 is thermally and chemically stable, compatible with sensitive materials, non-flammable, nontoxic, colourless and has no ozone depletion potential. This combination of properties makes FC-72 suitable even for applications with strict safety specifications, like spacecrafts. The physical properties of the fluid at 25 8C are given in Table 1. FC-72 has a low viscosity and an extremely low electrical conductivity, thus being really suitable for this kind of process.
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
751
Table 1 FC-72 Physical properties at 25 8C (Courtesy of 3M ) Chemical formula Electrical conductivity Dielectric strength Relative permittivity Boiling point (at 1 atm)
C6F14 1013 V1 m1 15 MV m1 1.75 56 8C
density kinematic viscosity specific heat thermal conductivity coefficient of cubic expansion
1680 kg m3 0.38 cSt 1100 J kg1 K1 0.057 W m1 K1 0.00156 K1
A test loop was built as shown in the schematic of Fig. 1. A peristaltic pump made the working fluid circulate through the test specimen at volume flow rates in the range 0.25 H 1.25 lt min1. After calibration for FC-72, an asameter could measure the flow rate with an accuracy of F 0.011 lt min1. The fluid, uniformly heated in its upward flow along the test section, was cooled to the desired inlet temperature using a shell-tube heat exchanger. The annular test specimen was connected to a 0 H 30 kV d.c. high voltage power supply. An expansion vessel was used to compensate the volume increase in the fluid loop due to temperature variations and to set the pressure of the position it was mounted on. An absolute pressure transducer was placed right upstream of the peristaltic pump, in order to check that the lowest pressure in the loop was still above the room pressure, thus avoiding air from being sucked in by the pump. All the tests were performed at an absolute pressure of about 2 bars. A detailed schematic of the test section is shown in Fig. 2. The inner cylinder was made of stainless steel and had a diameter of 1.6 mm, while the diameter of the point was estimated at 0.6 mm. The points were made of tin-coated copper and were welded to the inner cylinder by a silver alloy. The outer electrode, also made of stainless steel, had an inner diameter of 17 mm and a wall thickness of 2 mm. The fluid was warmed up by an electrical resistance heater applied to the outer wall for a length (L) of 50 cm. Also 20 thermocouples were stuck on the outer wall at five cross sections, 12.5 cm apart along the
Fig. 1. Schematic of the test loop.
752
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 2. Detail of the EHD test section (distances are expressed in mm).
heated length. Each section had four thermocouples, placed one every 908. To minimise heat losses, the entire specimen was covered with a 35 mm thick thermal insulator (k ~ 40 mW m1 K1). Two more thermocouples were placed at the fluid inlet and outlet, to check the power supplied to the test section in steady state through an energy balance. Since the differences between the measured and the theoretical values for the temperature increase across the test section were within the experimental uncertainty of the thermocouples, heating losses were assumed to be negligible. All the thermocouples were type-T and used a zero-point reference cell, whose temperature was controlled by a reference resistance thermometer. The overall accuracy of each thermocouple after calibration in the 15 H 60 8C range was F0.3 K. In another configuration of the test section, a single metallic point was moved in different tests from 11 cm upstream to 4 cm downstream of section C. The bulk temperature of the fluid at the various axial positions was calculated considering a temperature of adiabatic mixing for each cross section, with a linear increase from the inlet to the outlet. The inner wall temperatures were obtained from the ones measured on the outer wall properly corrected for the conduction within the tube wall thickness. The dimensionless numbers describing mixed convection (i.e. Re, Gr and Nu) were calculated with reference to the hydraulic diameter of the annulus and with the physical properties taken at film temperature. The values of volumetric flow rate 0.25, 0.50, 0.75, 1.00, 1.25 lt min1, power 30.5, 54.0, 85.0 W and high voltage 0, F 10, 22 kV were tested. Even at
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
753
Fig. 3. Sketch of equipotential contours and electric field vectors in the vicinity of the point electrode.
the highest heat flux, the fluid temperature at the inner wall was fairly below the boiling point, never reaching 50 8C. In a preliminary operation, we tested the dielectric strength of the medium. We applied a voltage ramp till reaching electrical breakdown, which occurred at 24 kV. Therefore, we decided that it was unsafe to perform the tests of the campaign at high voltage values higher than 22 kV. A sketch of the equipotential contours and electric field vectors in the vicinity of the point electrode is presented in Fig. 3. Although the space charge free solution of the electric field can be expressed approximately in closed form if the shape of the point is a hyperboloid of revolution [16], injection of charge would distort this distribution significantly. In fact, the presence of homocharges would lower the electric field near the point and enhance it near the non-injecting electrode [17]. Every test was run under constant flow rate and heat flow. The thermocouples’ signals were acquired by a scanner mounted on a digital multimeter (Model 2000, manufactured by Keithley, Cleveland, OH); then the data were sent to a PC in order to be processed and recorded by the program Labviewk (a trademark of National Instruments, Austin, TX), using MatlabR (a registered product of The MathWorks, Natick, MA) as the interface for mathematical calculations. Once a steady state condition was reached, we started recording wall and fluid temperatures, with an acquisition every 2 s. After 200 s of data recording, a 700 s high voltage step was applied to the electrodes. In every test, 600 s have always been sufficient for obtaining a new steady state condition, so the last 50 measurements with the electric field on were averaged and used for analysis purposes.
3. Discussion of results As already said, these tests were essentially focused on verifying the gross effect of a point on the heat transfer. Fig. 4 shows the steep decrease of the local surface temperature in section B (x = L/4), caused by the application of a high voltage step (HV = 22 kV) for 700 s. The fluid temperature, represented by the dotted line in the figure, keeps constant around 23 8C during this test, while the wall temperature starts from around 39 8C with no field and drops to about 26 8C a short time after the electric field is switched on. It keeps constant at this value during the whole duration of the step, to recover the initial value once the field is switched off. Thus, there is an absolutely clear evidence of the remarkable influence of the electric phenomena on the thermal ones. A similar phenomenon occurs for the wall superheat DTwall-bulk in sections B, C and D, as shown in Fig. 5. Results with zero and 22 kV high voltage are reported. With no electric field, a strong dependence on the Reynolds number is detectable. For example, with reference to the measurement section placed at
754
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 4. Wall temperature steep decrease due to the application of an electric field (E on) with: heating power P T = 85 W, volumetric flow rate G V = 0.25 lt min1, high voltage HV = 22 kV.
Fig. 5. Wall superheat with respect to the fluid bulk temperature DTwall-bulk vs. x/L at various Re and with HV = 0 and HV = 22 kV (P T = 85 W).
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
755
section C (x = L/2), the wall superheats roughly go from 14 K at Re = 736 to 22 K at Re = 2841. In addition a different local dependence of the superheat on Re has to be expected, as we are in a developing flow region of turbulent aided mixed convection, with laminarisation effects [18]. On the contrary, when the field is on, the wall superheats at section C range between 4.5 K and 5.5 K in correspondence of the same Reynolds numbers as before, thus showing a negligible effect of Re. Also a marked different local dependence on the Reynolds number has not been evidenced at this high voltage value. Since the electrohydrodynamic phenomenon is localised in the vicinity of the emitter, a thorough analysis of the Nusselt number distribution upstream and downstream of the point was needed, in order to find the optimum gap to set between the points and examine the effect of the flow rate. A series of experiments was carried out in which a single metallic point was moved from 11 cm upstream to 4 cm downstream of section C, where Nu was calculated. The same results could reasonably be obtained by fixing the point in section C (n = 0) and moving the thermocouple along the wall in the axial direction. Doing this, a surface distribution of the Nusselt number is obtained, interpreting the co-ordinate n as the thermocouple’s position on the heating wall with respect to the point, made dimensionless by means of the hydraulic diameter. For positive values of n, roughly above 1, the Nusselt number slightly increases with the Reynolds number and decreases with increasing n. Actually the different curves end almost at the same value (Nu a little below 60). At smaller co-ordinate values, i.e. closer to the point, this trend is reversed. In fact the Nusselt number still increases with decreasing n, but its augmentation decreases at increasing Re. As expected, the maximum Nu occurs when the point is in correspondence of the measurement section. The asymmetry of the curve, with steeper Nu gradients upstream of the point, is absolutely evident as well as its larger sharpness for lower Re.
Fig. 6. Nusselt number distribution on the wall in the proximity of a point (section C, P T = 85 W, HV = 22 kV).
756
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 6 clearly shows also how an increase in Re causes a more significant propagation of the effect of the point in the flow direction. A numerical calculation of the curves’ areas has been performed dividing the wall co-ordinate into two intervals: the upstream ( 3 V n V 0) and the downstream (0 V n V 7) ones: n¼7 Z
Nudn ¼
n¼3
n¼0 Z
Nudn þ
n¼3
n¼7 Z
Nudn
ð6Þ
n¼0
This revealed that the area of the curve on the right of the maximum has almost the same value independently of the Reynolds number. It means that the average Nusselt number is the same downstream of the point, no matter of the flow velocity. This latter parameter only affects the wall uniformity of Nu, which is larger at the highest flow rates. Conversely, the area upstream of the point is larger at lower Reynolds numbers and a possible interpretation could be the existence of an EHD induced backflow at weaker main flow rates, which would cause a greater mixing in the fluid, with corresponding higher heat transfer rates.
4. Concluding remarks EHD convection was shown to yield remarkable heat transfer enhancement. The phenomenon is localised in the proximity of the emitter, decaying more rapidly upstream than downstream of the point. Electrohydrodynamic heat transfer augmentation may yield large reductions in weight and volume of heat exchangers, making this technique very attractive for industrial applications, especially in the space environment, where the absence of gravity makes natural convection by buoyancy forces inapplicable and where size and power reductions are highly regarded. It will be desirable to keep the Reynolds number as low as possible, obtaining laminar flow conditions, in order to minimise the pressure drop through the compact heat exchanger. In fact, as experimentally demonstrated in [14] and [15], the electrohydrodynamic induced flow does not produce the large pressure drops and the resulting increase in pump size and power associated with conventional methods introducing turbulence. As long as pure FC-72 is utilised, electrically generated heat will be negligible, due to the outstanding insulation given by the fluid, under electric fields below its dielectric strength.
Acknowledgements The continuous and effective collaboration of Mr. Roberto Manetti in setting up the electronics and the measurement devices is gratefully acknowledged.
References [1] [2] [3] [4]
B. Metais, E.R.G. Eckert, J. Heat Transfer, Trans. ASME 86 (1964) 295. W. Grassi, Notes on electric fields in fluids, Dept. of Energetics, University of Pisa (unpublished). N.F. Baboi, M.K. Bologa, K.N. Semenov, Elect. Treat. Mater. 1 (1965) 57. T.B. Jones, Adv. Heat Transf. 14 (1978) 107.
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757 [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
B.R. Lazarenko, F.P. Grosu, M.K. Bologa, Int. J. Heat Mass Transfer 18 (1975) 1433. D.J. Tritton, Physical Fluid Dynamics, Oxford University Press, 1988. P. Atten, IEEE Trans. Dielectr. Electr. Insul. 3 (1) (1996) 1. N. Felici, Dir. Curr. 2 (1971) 90. A. Richter, A. Plettner, K.A. Hotmann, H. Sandmaier, Sens. Actuators, A 29 (2) (1991) 159. P. Atten, B. Malraison, M. Zahn, IEEE Trans. Dielectr. Electr. Insul. 4 (6) (1997) 710. P. Atten, L. Elouadie, J. Electrost. 34 (1995) 279. J.M. Crowley, G.S. Wright, J.C. Chato, IEEE Trans. Ind. Appl. 26 (1) (1990) 42. P. Atten, F.M.J. McCluskey, A.T. Perez, IEEE Trans. Electr. Insul. 23 (4) (1988) 659. J.L. Ferna´ndez, R. Poulter, Int. J. Heat Mass Transfer 30 (10) (1987) 2125. J.S. Paschkewitz, D.M. Pratt, Exp. Therm. Fluid Sci. 21 (2000) 187. R. Coelho, J. Debeau, J. Phys. D: Appl. Phys. 4 (1971) 1266. M. Zahn, IEEE Trans. Dielectr. Electr. Insul. 5 (5) (1998) 627. T. Aicher, H. Martin, Int. J. Heat Mass Transfer 40 (15) (1997) 3617.
757
EHD enhanced heat transfer in a vertical annulusB Walter GrassiT, Daniele Testi, Mario Saputelli LOTHAR (LOw gravity and THermal Advanced Research laboratory), Department of Energetics bL. Poggi Q, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy Available online 17 March 2005
Abstract The preliminary experimental results of the effect of an electrostatic field on turbulent aided mixed convection in a short vertical annulus are reported herein. A dielectric liquid (FC-72 by 3M) is used as working fluid. The local heat transfer improvement is obtained by inserting appropriate points on the inner surface of the annulus, generally acting as the positive electrode, while the surrounding pipe is grounded. A high voltage (up to 22 kV) is established between the two surfaces. The heat exchange revealed to be highly enhanced by this technique, thus providing encouraging indications for practical applications. D 2005 Elsevier Ltd. All rights reserved. Keywords: EHD; Enhanced heat transfer; Vertical annulus
1. Introduction The material presented herein represents the very beginning of a broader research work aimed at performing a feasibility study of an EHD (electrohydrodynamic) enhanced high efficiency compact heat exchanger for space applications. In particular we, at first, confined our interest to the rather weak flow typical of a cold plate. Before starting a very systematic investigation, we checked the existence of the foreseen effects and their real extent in terms of heat transfer enhancement. As this initial step provided us with very encouraging indications, we decided to immediately communicate them. In the meantime we started performing a very detailed experimental campaign, as required by the complexity of the involved matter and by the high potentiality of this technique. With the above aim in mind, we will not B
Communicated by J.W. Rose and A. Briggs. T Corresponding author. E-mail addresses: [email protected] (W. Grassi)8 [email protected] (D. Testi). 0735-1933/$ - see front matter D 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2004.10.011
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
749
deal with the complex fluid dynamics implied by the studied regime, only stressing that the Richardson number (Gr/Re 2 ) ranges from 0.1 to 10, thus identifying a mixed convection regime, which is turbulent, according to the map proposed by Metais and Eckert [1]. Neither we will treat the fundamentals of the interaction of an electric field with an insulating fluid, simply illustrating the main features relevant to the following discussion. In the presence of an electric field, a body force f E arises in a dielectric medium, given by [2]: 1 2 1 2 Be f E ¼ qE E E je þ j qE ð1Þ 2 2 Bq T The first RHS term, the electrophoretic component, is the Coulomb force exerted by an electric field, E, upon the free charge, with density q E . The second term represents the dielectrophoretic body force, related to a local change of medium permittivity, e, in an electric field. The third term, the electrostrictive component, acts on the dielectric, with density q, in a non-uniform electric field. The last two terms represent the forces acting on polarisation charges. This electric force has to be inserted in the momentum equation. The whole set of equations to be used to solve any EHD problem is, thus, composed by the momentum, mass continuity and energy equations, plus the complete set of Maxwell equations. Although several alternative hypotheses have been formulated [3,4], there is a general agreement that the EHD phenomenon of heat transfer augmentation is of convective nature [5]. The expression of the vorticity balance assumes particular importance, showing which conditions lead to a convective motion. In the Boussinesq approximation [6], taking the curl of the momentum equation, we obtain (x = j 1 u): Bx 1 eb þ ujx ¼ xjuþvj2 x þ bg ^ jT þ jqE ^ E þ e jE2 jT Bt q 2q
ð2Þ
Electrostriction does not generate vorticity, while dielectrophoresis needs both a temperature gradient and a non-uniform electric field (b e = (1/e)(de/dT) represents the temperature coefficient of permittivity). A free charge gradient instead is necessary for the Coulomb force to produce a vortical flow. Two main mechanisms can generate free charge in a liquid, namely: thermal gradients, producing what is commonly known as electrothermal convection, and ion injection at the electrode/liquid interface via electrochemical reactions. This latter phenomenon will be dealt with in the following. Of particular importance for our purposes is the expression of the current density: j¼
n X i¼1
jqðEiÞ jK ðiÞ E þ qE u þ BðBteEÞ DcjqE
ð3Þ
n species of charge carriers of density q E(i) being present in the medium, each one with its own mobility, K (i). Eq. (3) uses a very general constitutive model for the dielectric, taking into account respectively: ion-drift, charge convection, displacement and diffusion currents. Bulk space charge can be created in dielectric liquids by injection of ions at the metal/liquid interface. The injected charges are homocharges [7], i.e. of the same polarity as the injecting electrode, called the emitter. This phenomenon most often occurs at one electrode only (the sharper one) [8] and is mainly controlled by electrochemical reactions at the interface, critically depending on the composition, geometry and polarity of the electrode [9] and on the chemical nature of the dielectric fluid. The injected space charge gives rise to a jet-like motion towards the facing electrode [10]. In liquids of low enough
750
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
electrical conductivity, the mechanism of ion injection gives the dominant contribution to the current [11] and the magnitude of the Coulomb force may be considered, to a first approximation, as being independent of temperature gradients. Assuming a unipolar injection (i.e. injection of only one species of charge carriers), Eq. (3) can be simplified as: j ¼ jqE jKE þ qE u
ð4Þ
Tabulated values of K are available only for the more common liquids. However, this parameter can be related to the dynamic viscosity, according to the so-called Walden’s rule [12], which rarely fails by an order of magnitude, as K = 2 1011/g, in SI units. In the absence of a forced flow, the problem of charge transfer bears an analogy with thermal convection [13], where the advection of hot and cold blobs in the fluid increases the heat transfer rate. In the unipolar injection problem, fingers of highly charged liquid coming from the injector boundary layer move across the inter-electrode space, while weakly charged liquid flows back to the injector due to mass continuity. In order to interpret the phenomenon, it is convenient to introduce a dimensionless parameter, known as the mobility parameter, M = e 1/2q 1/2 K1, which is the ratio of the hydrodynamic mobility and the true ion mobility. An order of magnitude of the induced fluid velocity can be obtained by balancing the fluid kinetic energy and the electrostatic one: rffiffiffiffi 1 2 1 2 u e qu ~ eE Z ~ ð5Þ 2 2 E q The hydrodynamic mobility is usually in the order of 107 H 108 m2 V1 s1 and typical velocities are in the range 0.1 H1 m s1. For Mb1, the fluid motion only slightly affects the trajectories of charge carriers, which are practically the electric field lines (this behaviour is typical of gases). Instead, for high enough values of the mobility parameter, which is the case of most liquids, the induced fluid velocity is higher than the ion drift velocity. Then, the charge distribution depends drastically on the motion it induces [11]. In a weakly forced flow, even in the turbulent regime, when a strong electroconvection by ion injection is established (a current density in the order of 104 H 105 A m2 is needed), the Nusselt number is controlled by the current alone [13,14], regardless of the Reynolds number and with negligible influence of buoyancy forces. A high heat transfer enhancement via ion injection can be obtained with fluids of low viscosity and low electrical conductivity [15], like the one used in these experiments.
2. Experimental apparatus and procedure In this work we examine the effect of a d.c. electric field on turbulent aided mixed convection in a heated vertical annulus with sharp points added to the inner electrode. The dielectric fluid chosen for the experiments is the Fluorinertk Electronic Liquid FC-72 (manufactured by 3M, St. Paul, MN, USA). FC-72 is thermally and chemically stable, compatible with sensitive materials, non-flammable, nontoxic, colourless and has no ozone depletion potential. This combination of properties makes FC-72 suitable even for applications with strict safety specifications, like spacecrafts. The physical properties of the fluid at 25 8C are given in Table 1. FC-72 has a low viscosity and an extremely low electrical conductivity, thus being really suitable for this kind of process.
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
751
Table 1 FC-72 Physical properties at 25 8C (Courtesy of 3M ) Chemical formula Electrical conductivity Dielectric strength Relative permittivity Boiling point (at 1 atm)
C6F14 1013 V1 m1 15 MV m1 1.75 56 8C
density kinematic viscosity specific heat thermal conductivity coefficient of cubic expansion
1680 kg m3 0.38 cSt 1100 J kg1 K1 0.057 W m1 K1 0.00156 K1
A test loop was built as shown in the schematic of Fig. 1. A peristaltic pump made the working fluid circulate through the test specimen at volume flow rates in the range 0.25 H 1.25 lt min1. After calibration for FC-72, an asameter could measure the flow rate with an accuracy of F 0.011 lt min1. The fluid, uniformly heated in its upward flow along the test section, was cooled to the desired inlet temperature using a shell-tube heat exchanger. The annular test specimen was connected to a 0 H 30 kV d.c. high voltage power supply. An expansion vessel was used to compensate the volume increase in the fluid loop due to temperature variations and to set the pressure of the position it was mounted on. An absolute pressure transducer was placed right upstream of the peristaltic pump, in order to check that the lowest pressure in the loop was still above the room pressure, thus avoiding air from being sucked in by the pump. All the tests were performed at an absolute pressure of about 2 bars. A detailed schematic of the test section is shown in Fig. 2. The inner cylinder was made of stainless steel and had a diameter of 1.6 mm, while the diameter of the point was estimated at 0.6 mm. The points were made of tin-coated copper and were welded to the inner cylinder by a silver alloy. The outer electrode, also made of stainless steel, had an inner diameter of 17 mm and a wall thickness of 2 mm. The fluid was warmed up by an electrical resistance heater applied to the outer wall for a length (L) of 50 cm. Also 20 thermocouples were stuck on the outer wall at five cross sections, 12.5 cm apart along the
Fig. 1. Schematic of the test loop.
752
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 2. Detail of the EHD test section (distances are expressed in mm).
heated length. Each section had four thermocouples, placed one every 908. To minimise heat losses, the entire specimen was covered with a 35 mm thick thermal insulator (k ~ 40 mW m1 K1). Two more thermocouples were placed at the fluid inlet and outlet, to check the power supplied to the test section in steady state through an energy balance. Since the differences between the measured and the theoretical values for the temperature increase across the test section were within the experimental uncertainty of the thermocouples, heating losses were assumed to be negligible. All the thermocouples were type-T and used a zero-point reference cell, whose temperature was controlled by a reference resistance thermometer. The overall accuracy of each thermocouple after calibration in the 15 H 60 8C range was F0.3 K. In another configuration of the test section, a single metallic point was moved in different tests from 11 cm upstream to 4 cm downstream of section C. The bulk temperature of the fluid at the various axial positions was calculated considering a temperature of adiabatic mixing for each cross section, with a linear increase from the inlet to the outlet. The inner wall temperatures were obtained from the ones measured on the outer wall properly corrected for the conduction within the tube wall thickness. The dimensionless numbers describing mixed convection (i.e. Re, Gr and Nu) were calculated with reference to the hydraulic diameter of the annulus and with the physical properties taken at film temperature. The values of volumetric flow rate 0.25, 0.50, 0.75, 1.00, 1.25 lt min1, power 30.5, 54.0, 85.0 W and high voltage 0, F 10, 22 kV were tested. Even at
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
753
Fig. 3. Sketch of equipotential contours and electric field vectors in the vicinity of the point electrode.
the highest heat flux, the fluid temperature at the inner wall was fairly below the boiling point, never reaching 50 8C. In a preliminary operation, we tested the dielectric strength of the medium. We applied a voltage ramp till reaching electrical breakdown, which occurred at 24 kV. Therefore, we decided that it was unsafe to perform the tests of the campaign at high voltage values higher than 22 kV. A sketch of the equipotential contours and electric field vectors in the vicinity of the point electrode is presented in Fig. 3. Although the space charge free solution of the electric field can be expressed approximately in closed form if the shape of the point is a hyperboloid of revolution [16], injection of charge would distort this distribution significantly. In fact, the presence of homocharges would lower the electric field near the point and enhance it near the non-injecting electrode [17]. Every test was run under constant flow rate and heat flow. The thermocouples’ signals were acquired by a scanner mounted on a digital multimeter (Model 2000, manufactured by Keithley, Cleveland, OH); then the data were sent to a PC in order to be processed and recorded by the program Labviewk (a trademark of National Instruments, Austin, TX), using MatlabR (a registered product of The MathWorks, Natick, MA) as the interface for mathematical calculations. Once a steady state condition was reached, we started recording wall and fluid temperatures, with an acquisition every 2 s. After 200 s of data recording, a 700 s high voltage step was applied to the electrodes. In every test, 600 s have always been sufficient for obtaining a new steady state condition, so the last 50 measurements with the electric field on were averaged and used for analysis purposes.
3. Discussion of results As already said, these tests were essentially focused on verifying the gross effect of a point on the heat transfer. Fig. 4 shows the steep decrease of the local surface temperature in section B (x = L/4), caused by the application of a high voltage step (HV = 22 kV) for 700 s. The fluid temperature, represented by the dotted line in the figure, keeps constant around 23 8C during this test, while the wall temperature starts from around 39 8C with no field and drops to about 26 8C a short time after the electric field is switched on. It keeps constant at this value during the whole duration of the step, to recover the initial value once the field is switched off. Thus, there is an absolutely clear evidence of the remarkable influence of the electric phenomena on the thermal ones. A similar phenomenon occurs for the wall superheat DTwall-bulk in sections B, C and D, as shown in Fig. 5. Results with zero and 22 kV high voltage are reported. With no electric field, a strong dependence on the Reynolds number is detectable. For example, with reference to the measurement section placed at
754
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 4. Wall temperature steep decrease due to the application of an electric field (E on) with: heating power P T = 85 W, volumetric flow rate G V = 0.25 lt min1, high voltage HV = 22 kV.
Fig. 5. Wall superheat with respect to the fluid bulk temperature DTwall-bulk vs. x/L at various Re and with HV = 0 and HV = 22 kV (P T = 85 W).
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
755
section C (x = L/2), the wall superheats roughly go from 14 K at Re = 736 to 22 K at Re = 2841. In addition a different local dependence of the superheat on Re has to be expected, as we are in a developing flow region of turbulent aided mixed convection, with laminarisation effects [18]. On the contrary, when the field is on, the wall superheats at section C range between 4.5 K and 5.5 K in correspondence of the same Reynolds numbers as before, thus showing a negligible effect of Re. Also a marked different local dependence on the Reynolds number has not been evidenced at this high voltage value. Since the electrohydrodynamic phenomenon is localised in the vicinity of the emitter, a thorough analysis of the Nusselt number distribution upstream and downstream of the point was needed, in order to find the optimum gap to set between the points and examine the effect of the flow rate. A series of experiments was carried out in which a single metallic point was moved from 11 cm upstream to 4 cm downstream of section C, where Nu was calculated. The same results could reasonably be obtained by fixing the point in section C (n = 0) and moving the thermocouple along the wall in the axial direction. Doing this, a surface distribution of the Nusselt number is obtained, interpreting the co-ordinate n as the thermocouple’s position on the heating wall with respect to the point, made dimensionless by means of the hydraulic diameter. For positive values of n, roughly above 1, the Nusselt number slightly increases with the Reynolds number and decreases with increasing n. Actually the different curves end almost at the same value (Nu a little below 60). At smaller co-ordinate values, i.e. closer to the point, this trend is reversed. In fact the Nusselt number still increases with decreasing n, but its augmentation decreases at increasing Re. As expected, the maximum Nu occurs when the point is in correspondence of the measurement section. The asymmetry of the curve, with steeper Nu gradients upstream of the point, is absolutely evident as well as its larger sharpness for lower Re.
Fig. 6. Nusselt number distribution on the wall in the proximity of a point (section C, P T = 85 W, HV = 22 kV).
756
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757
Fig. 6 clearly shows also how an increase in Re causes a more significant propagation of the effect of the point in the flow direction. A numerical calculation of the curves’ areas has been performed dividing the wall co-ordinate into two intervals: the upstream ( 3 V n V 0) and the downstream (0 V n V 7) ones: n¼7 Z
Nudn ¼
n¼3
n¼0 Z
Nudn þ
n¼3
n¼7 Z
Nudn
ð6Þ
n¼0
This revealed that the area of the curve on the right of the maximum has almost the same value independently of the Reynolds number. It means that the average Nusselt number is the same downstream of the point, no matter of the flow velocity. This latter parameter only affects the wall uniformity of Nu, which is larger at the highest flow rates. Conversely, the area upstream of the point is larger at lower Reynolds numbers and a possible interpretation could be the existence of an EHD induced backflow at weaker main flow rates, which would cause a greater mixing in the fluid, with corresponding higher heat transfer rates.
4. Concluding remarks EHD convection was shown to yield remarkable heat transfer enhancement. The phenomenon is localised in the proximity of the emitter, decaying more rapidly upstream than downstream of the point. Electrohydrodynamic heat transfer augmentation may yield large reductions in weight and volume of heat exchangers, making this technique very attractive for industrial applications, especially in the space environment, where the absence of gravity makes natural convection by buoyancy forces inapplicable and where size and power reductions are highly regarded. It will be desirable to keep the Reynolds number as low as possible, obtaining laminar flow conditions, in order to minimise the pressure drop through the compact heat exchanger. In fact, as experimentally demonstrated in [14] and [15], the electrohydrodynamic induced flow does not produce the large pressure drops and the resulting increase in pump size and power associated with conventional methods introducing turbulence. As long as pure FC-72 is utilised, electrically generated heat will be negligible, due to the outstanding insulation given by the fluid, under electric fields below its dielectric strength.
Acknowledgements The continuous and effective collaboration of Mr. Roberto Manetti in setting up the electronics and the measurement devices is gratefully acknowledged.
References [1] [2] [3] [4]
B. Metais, E.R.G. Eckert, J. Heat Transfer, Trans. ASME 86 (1964) 295. W. Grassi, Notes on electric fields in fluids, Dept. of Energetics, University of Pisa (unpublished). N.F. Baboi, M.K. Bologa, K.N. Semenov, Elect. Treat. Mater. 1 (1965) 57. T.B. Jones, Adv. Heat Transf. 14 (1978) 107.
W. Grassi et al. / International Communications in Heat and Mass Transfer 32 (2005) 748–757 [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
B.R. Lazarenko, F.P. Grosu, M.K. Bologa, Int. J. Heat Mass Transfer 18 (1975) 1433. D.J. Tritton, Physical Fluid Dynamics, Oxford University Press, 1988. P. Atten, IEEE Trans. Dielectr. Electr. Insul. 3 (1) (1996) 1. N. Felici, Dir. Curr. 2 (1971) 90. A. Richter, A. Plettner, K.A. Hotmann, H. Sandmaier, Sens. Actuators, A 29 (2) (1991) 159. P. Atten, B. Malraison, M. Zahn, IEEE Trans. Dielectr. Electr. Insul. 4 (6) (1997) 710. P. Atten, L. Elouadie, J. Electrost. 34 (1995) 279. J.M. Crowley, G.S. Wright, J.C. Chato, IEEE Trans. Ind. Appl. 26 (1) (1990) 42. P. Atten, F.M.J. McCluskey, A.T. Perez, IEEE Trans. Electr. Insul. 23 (4) (1988) 659. J.L. Ferna´ndez, R. Poulter, Int. J. Heat Mass Transfer 30 (10) (1987) 2125. J.S. Paschkewitz, D.M. Pratt, Exp. Therm. Fluid Sci. 21 (2000) 187. R. Coelho, J. Debeau, J. Phys. D: Appl. Phys. 4 (1971) 1266. M. Zahn, IEEE Trans. Dielectr. Electr. Insul. 5 (5) (1998) 627. T. Aicher, H. Martin, Int. J. Heat Mass Transfer 40 (15) (1997) 3617.
757