Influence of ultrasonic treatment on heat transfer in the heat exchanger

This paper deals with the influence of guided ultrasonic waves on heat transfer. Two piezoelectric transducers, whose structure can be vibrated at different powers and at their resonant frequency in the ultrasonic range of 27–45 kHz, were placed on the plates of a heat exchanger to inhibit the formation of a mineral deposit. These waves were set to diffuse only into the metal plates of the exchanger. During these tests, an increase in the heat transfer between the two fluids was directly observed on the continuous recording of the outlet temperature, on the calculations of the global exchange coefficient, and on the flow exchanged between the two fluids in the laminar regime. Tests are presented in this article, tests in the presence of the 45 kHz transducer, another with a 27 kHz transducer, and which combines the two have a different positioning on the exchanger. The results obtained from the ultrasonic guided waves are similar to the classical ultrasonic waves.


Abstract
This paper deals with the influence of guided ultrasonic waves on heat transfer. Two piezoelectric transducers, whose structure can be vibrated at different powers and at their resonant frequency in the ultrasonic range of 27-45 kHz, were placed on the plates of a heat exchanger to inhibit the formation of a mineral deposit. These waves were set to diffuse only into the metal plates of the exchanger. During these tests, an increase in the heat transfer between the two fluids was directly observed on the continuous recording of the outlet temperature, on the calculations of the global exchange coefficient, and on the flow exchanged between the two fluids in the laminar regime. Tests are presented in this article, tests in the presence of the 45 kHz transducer, another with a 27 kHz transducer, and which combines the two have a different positioning on the exchanger. The results obtained from the ultrasonic guided waves are similar to the classical ultrasonic waves.

Introduction
In industrial companies, the heat exchanger is an essential element of any energy management policy, 90% of the thermal energy used in industrial processes passes through a heat exchanger at least once [1]. The main problems encountered by heat exchanger users are related to fouling phenomena that reduce heat transfer.
Research is currently conducted on two completely different, but complementary, fronts for fouling detection [1].
The first method was developed by Zeljka Ujevic Andrijic et al it is a method based on neural network and nonlinear finite impulse response models, using the number of transfer units method, these models effectively detect fouling formation in an industrial heat exchanger [2]. The other model was created by C. B. Panchal and Ehr-Ping Huangfu, it is a model based on the calculation of the rate of the transfer resistance as a function of time to detect fouling [3].
And the second study, which we wish to join, concerns the products allowing the cleaning of these deposits, either during operation or during the maintenance sequence. Several experimental studies address the intensification of heat transfer by ultrasonic waves [4,5].
Nakayama tested ultrasonic energy of 140 W with a frequency of 20 kHz on a 20 mm thick plate immersed in distilled water. He found up to four times an increase in heat transfer coefficient [6].
Y. Tisseau, P. Boldo, N. Gondexon, and A. Bontemps tested the effect of ultrasound on a beam-type heat exchanger, the results obtained showed that ultrasound systematically increases the overall heat transfer coefficient. However, this improvement is very sensitive to the hydrodynamic configuration chosen and does not vary with the power of the ultrasound field [7].
According to Nomura et al when ultrasonic vibration of 28 and 45 kHz was applied to water, the heat transfer coefficient increased significantly due to cavitation bubbles. However, when the ultrasonic vibration was close to 100 kHz, the increase in heat transfer coefficient became small compared to those of 28 and 45 kHz [8].
The same author tested the application of sound energy generated by a 60.7 kHz transducer on three types of the plate (acrylic, aluminum, and polystyrene) of different thicknesses, he found that the heat transfer coefficient decreased as the thickness of the flat plate increased. And that the heat transfer coefficient was highest for the acrylic plate, then the aluminum plate, and lowest for the polystyrene plate [9].
In another study by the same author, a horizontal downward-facing heating surface with ultrasonic vibrations from below was performed in a natural convection region. Up to ten times more, heat transfer coefficient was obtained by applying 20 W in tap water and degassed water in the presence of a fixed horn transducer on resonance frequency 60.7 kHz [10].
An experimental investigation was conducted to investigate the effects of ultrasonic waves on heat transfer by Bartoli and Baffigi, under subcooled boiling conditions of distilled water. The acoustic flow influences the kinematic field and thus increases the heat transfer coefficient [11].
Monnot et al performed experiments using a specific experimental setup involving a high-frequency ultrasonic reactor equipped with a helical cooling coil, to study the effect of ultrasound at different frequencies on the heat transfer between the water contained in the reactor and the cooling water flowing through the coil. The results obtained show that the ultrasonic field leads to an increase in the cooling rate due to an increase in the overall heat transfer coefficient of the coil up to 100% [12].
In the same context, Gondrexon et al applied the low-frequency ultrasonic field on a shell and tube heat exchanger, the results show that under ultrasonic conditions, the overall heat transfer coefficient can be increased from 123 to 257% [13].
Experimental studies were carried out by Hoshino and Yakawa on a 28KHz standing ultrasonic wave applied to a sonoexchanger type heat exchanger. The results obtained show a good temperature distribution and a good heat transfer by free convection. The authors explained the heat transfer mechanism in an ultrasonic standing wave field by an acoustic radiation pressure theory (Hoshino and Yukawa 1979) [14].
A study by Komarov and Hirasawa aims to show the enhancement of heat transfer between solids and ambient gas by the application of strong acoustic fields. The experiments are carried out on a frequency range of 6.9 to 17.2 kHz. Examination of the Nusselt number with and without acoustic field shows that the heat transfer rate is improved with the intensity of the acoustic field. And the higher the gas flow velocity, the lower the effect of the sound wave on the heat transfer enhancement [15].
This heat transfer enhancement is different from one fluid to another, and depends on the substances present in the medium as well. The heat transfer enhancement for brine shows a different variation from that of sugar water, and the heat transfer enhancement ratio always increases with increasing sugar water concentration [16]. This is confirmed by Bonekamp and Bier in a study to show the effect of 40 kHz ultrasound on the freeboiling heat transfer of the refrigerant mixture R23 and R134a over a wide range of heat flows and saturation pressures. The improvement of the heat transfer coefficient, which can be achieved by 40 kHz ultrasound, is much more pronounced for mixtures than for single bodies, especially at medium saturation pressures. However, this improvement is limited to rather low heat flows (q<10 kW m −2 ) [17].
The impact of ultrasound on heat transfer is related to the operating parameter. According to Bulliard-Sauret, the laminar regime is characterized by a remarkable difference between the overall exchange coefficients obtained without and with ultrasound, as shown in the figure below for a frequency of 35 kHz [4]. Figure 1 below shows two graphs. The first one deals with the variation of the global exchange coefficient in different flow regimes, and the second one gathers several points, each one representing a bibliographic reference. And this is also a study that shows an increase in heat transfer as a function of ultrasound frequency. Most of these studies deal with low frequency ultrasound and give roughly the same results.
On the other hand, Markov has performed experiments which show that the heat transfer coefficient can be up to double. In the case of a forced flow of a melt at high temperature under elastic oscillations at a frequency of 20 kHz [20]. In a previous study, our research team investigated the impact of ultrasonic guided waves on the formation of calcium carbonate within a heat exchanger. During experimental tests, an improvement in heat transfer was noticed [21]. In the classical ultrasonic techniques mentioned before, the waves propagate as mass waves. Mass waves can be in the form of compressional or shear motion of particles in the medium. They usually travel at a constant speed and the pulses are launched with a wide frequency spectrum. Conversely, a scattered acoustic wave can be defined as a guided acoustic wave transmitted by a process that limits the physical dispersion along the direction of propagationThe most important difference between conventional ultrasound and guided waves is the variation in velocity with the change in frequency The objective of our study is to compare the heat transfer realized in a heat exchanger with insulated plates and joints, in the presence or not of guided ultrasonic waves at a fixed frequency, at two different ultrasonic powers. And to realize the two temperature profiles in real time with the casteminus and to approve the effectiveness of these waves to improve the thermal transfer. The most important difference between conventional ultrasound and guided waves is the variation of speed with the change of frequency.

Materials and methods
Operating protocol First, it is necessary to describe the experimental pilot studied and the quantities involved in the heat balances.

The experimental pilot
To study the effect of ultrasonic guided waves associated with the heterodyne effect of multiple frequencies on the formation of a mineral deposit 〈calcium and magnesium carbonate〉, an experimental pilot is designed 〈see figure 2〉. It includes: a plate and gasket heat exchanger, see figure 4, with an exchange surface of 0,38 m 2 〈10 plates, 5 compartments〉, perfectly insulated with a cover based on glass wool.
a cold circuit in which circulates, the scaling water 〈total hardness of 30°F〉, stored in a tank 〈100 l〉, with a flow rate of 1.16 l.min −1 and an inlet temperature close to 25°C, the hot circuit with 20 liters of ultrapure water at 50°C and circulating at a flow rate of 16 l.min −1 .
thermocouples are installed at each inlet and outlet of the exchanger in order to follow the heat exchange between the two fluids [21].  [18], and Influence of ultrasonic frequency on the exchange coefficient h [19].

The exchanger plates
The plates of this exchanger are 316 L steel plates separated by a nitrile gasket. The plate is 460 mm long, 200 mm wide, and has a spline angle of approximately 60°, as shown in figure 3. The thickness of the plate is 0.5 mm and the space between the plates varies between 5 and 6 mm [22].

The ultrasonic transducer
In the present case, ultrasound is generated by a piezoelectric transducer of the Langevin type. In this kind of transducer, two polarized ferroelectric ceramics convert electrical energy into kinetic energy. The upper part of the ceramic is the counter mass, and the lower part is the horn 'transducer head' [23], as shown in figure 4. When the two 'piezo' disks of the transducer absorb electrical energy through two electrodes, they convert it into kinetic energy, which causes a deformation/expansion of the piezoelectric materials. This expansion/ displacement is transmitted to the radiant heat of the 'transverse vibration' transducer. And the larger the displacement amplitude of the radiating head, the higher the voltage [4].
In conventional ultrasonic techniques, the waves propagate as mass waves in the whole of the ultrasound scanner, whereas the ultrasound waveguides propagate mainly in the metal plates of the scanner. The objective of this approach is not to generate high levels of acoustic pressure, leading to cavitation, but rather to maximize  In past research studies, both 45 kHz and 27 kHz at medium power have shown encouraging results in inhibiting tartar formation. In this paper, the effect of two piezo-electric transducers, 45 kHz and 27 kHz, programmed on different ultrasonic powers will be tested to show the influence of ultrasound on heat transfer.
Method of evaluating the impact of scaling on the overall exchange coefficient Two methods are considered in this manuscrite to estimate the influence of scaling on heat exchange performance.
The first method consists in considering the hydrodynamic behavior of the exchanger. For the same flow rate, the reduction of the hydraulic diameter of the exchanger resulting from the formation of a deposit creates an increase in the head losses [24]. In our case, no increase in pressure drop is detected: the operating mode 〈closed-circuit〉 and the duration of the experiment do not allow the formation of a sufficient scale thickness.
The second method is based on the measurement of the global heat transfer coefficient from a heat balance: With, f, the flow exchanged between the two fluids (W); H, the overall heat transfer coefficient (W.m −2 .K −1 ); S, the exchange surface of the exchanger (m 2 ); DT , ml the logarithmic mean temperature difference between the fluids (K).
The heat flux lost by the hot fluid is written:  With, C , ph the heat capacity of the hot fluid (J.kg −1 .K −1 ) ;  m , h mass flow rate of the hot fluid (kg.s −1 ); T hi , the inlet temperature of the hot fluid; T ho , the outlet temperature of the hot fluid.
The system being insolated, it can be considered as adiabatic. Thus, the heat flow lost by the hot fluid is recovered by the cold fluid according to the following equation.
With, C , pc the mass heat capacity of the cold fluid (J.kg −1 .K −1 );  m , c the mass flow rate of the cold fluid (kg.s −1 ); T ci , the inlet temperature of the cold fluid; T co , the outlet temperature of the cold fluid.
The overall thermal exchange coefficient, H (W.m −2 .K −1 ), reflects the capacity of the exchanger to transfer heat from the hot fluid to the cold fluid, as shown in the equation below: Note that the exchanger operates in counter-current and thus, ΔT ml is calculated from the outlet and inlet temperatures of the hot and cold fluids according to the following equation: The overall heat transfer coefficient H can also be calculated for plate heat exchangers using the following formula: However, the heat transfer coefficients on the hot and cold sides of the heat exchanger can vary over time [25]. Therefore, the uncertainty of the overall heat transfer coefficient has been calculated by the following relationship [26]: The proposed correlations for calculating the hot and cold side heat coefficients depend primarily on the plate geometry and corrugation angle. In this case, the plate surface is nonlinear, the wall temperature is assumed to be uniform, the spline shape is an 'obtuse' chevron with a corrugation angle α of 60°, and the overall exchange area is 0.38 m 2 . The flow regime is determined from the Reynolds number Re:  The calculation of the density of water was done by the following relation [29] : With, ρL, in kg.m −3 ; T in K with 273 K<T<648 K. Table 4 collects the coefficients A, B, C and D.

Logarithmic mean temperature difference (LMTD)
To know the temperature Th and Tc in an interval dx inside the exchanger and at time t, an equation has been developed for plotting the temperature profiles. Figure 6 shows the flow of both hot and cold fluids between the plates. The differential heat balance is expressed by the following relationship: With, (x) the infinitesimal heat flux transferred to the point of abscissa x (W); dS, the infinitesimal area (m 2 ).
The exchange surface is 0.38 m 2 , distributed over 10 plates. The distance between the first plate and the last plate is represented by a ratio of distance between 0 and L, as shown in the figure 7: The equation (20) becomes: Figure 6. Heat transfer between the two fluids cold and hot throughout the plate assembly. Therefore, the equation of the temperature profile curve from (T h and T c ) 0 becomes: for a distance ratio of: < < x L 0

Results and discussion
Fluid temperature monitoring Temperature profiles To better follow the heat exchange between the two compartments of the exchanger, a temperature profile was made for both fluids according to the following equation: The following equation was plotted based on the temperature recording at each inlet and outlet of the exchanger for 72 h: Without ultrasonic treatment Figure 8 show the temperature recording at the cold and hot sides of the heat exchanger for 72 h without ultrasonic treatment.
The equation for the evolution of the final temperature in the absence of ultrasound is as follows, [19]: The same author approved that the factor responsible for the final temperature increase is defined by the following relationship: The analysis of the temperature profiles shows that in the presence of the 30 W ultrasound, the final temperature is higher than that without ultrasound. The ultrasonic power contributes to the decrease of the gap between the two curves T h and T c , and thus contributes to the increase of the heat transfer.

Influence of scaling on the overall exchange coefficient
The results for the two compartments with and without ultrasonic treatment are shown in tables 5 and 6. The variation of the logarithmic mean between the two fluids is 13.61 K. Therefore, the heat flux exchanged between the two fluids in the presence of the deposit is around: 3518 W, with an average thickness of about 9 μm.
The thickness of the deposit was measured experimentally with a 3D digital microscope after the dismantling of the exchanger [21], but the analysis of the scaled plates shows that the thickness of the deposit is not homogeneous since there are places that are sensitive to scale formation [22].    The energy balance of the two tests is simply the equality of the hot and cold flows. In this study, even if the exchanger is protected by an insulating cover, it is never perfectly adiabatic. Therefore, the energy balance becomes: With, q h , the amount of heat released by the hot circuit; q c , the amount of heat acquired by the cold circuit; q , env the amount of heat lost to the environment.
In the presence of ultrasound, the ultrasonic power is counted positive in the direction entering the system, the balance becomes: With, q h , the amount of heat released by the hot circuit; P , us the amount of heat generated by the ultrasonic power; q c , the amount of heat acquired by the cold circuit; q , env the amount of heat lost to the environment. Figures 11 and 12 show the variation of the exchanged fluxes and of the global thermal exchange coefficient in the presence and absence of ultrasound.
The results presented show that in the presence of ultrasound, an increase in the overall exchange coefficient and the heat flux exchanged between the two fluids is observed. Therefore, there is an intensification of heat transfer in the presence of low power ultrasound, regardless of the ultrasonic frequency of 45 kHz or 27 kHz. This is confirmed by Tisseau et al a systematic increase of the global heat transfer coefficient in the presence of ultrasound which can reach 250% for a tube bundle/calendar type heat exchanger coupled to an ultrasonic field. This improvement does not vary with the power of the ultrasonic field but is very sensitive to the hydrodynamic configuration chosen [30].
This improvement in heat transfer is independent of the thickness of the fouling. At the end of each test, a deposition protocol has been programmed and based on the Ca 2+ and Mg 2+ dosage of the washing solution, we can estimate the amount deposited on all the cold compartments of the exchanger. For the transducers, and whatever the power tested, the quantity of deposited limestone does not exceed 1.5±0.2 grams distributed over 10 plates. In order to show the influence of the addition of frequencies on the heat transfer, another series of tests was carried out, but this time in the presence of two transducers programmed on two different frequencies and same ultrasonic power, and which functions at the same time. The applied ultrasonic power is of the order of 15 W. The two transducers were tested at different locations of the exchanger as shown in figure 13.
The variation of the global co-efficient of the exchanger during 72 h operating in multi-frequency and the same power is gathered in figure 14.
To ensure proper operation of the transducers at the same time, the distance between the transducers must be equal to or greater than λ/2. In our case, for the 27 kHz transducer this ratio is close to 15, and for 45 kHz is about 17. Therefore, the distance between the two transducers is about 17.8 cm. According to the comparison of the obtained results, the best position to expect a better heat transfer is position number 2. This has been confirmed by a study carried out by a study by Nakayama et al who indicated that the improvement in heat transfer depended on the positioning of the transducer and also on the flux. According to the authors, the case of low heat flux was better than the case of high heat flux (Nakayama and Kano, n.d.).
On the other hand, this improvement does not exceed the rate of the global exchange coefficient obtained by a single 45 kHz-15 W transducer. This improvement in the transfer is independent of the transfer resistance of    the fouling. The scale deposited on the total exchange surface, which is about 0.38 m 2 , does not exceed 0.98±0.05 grams distributed over 10 plates, in all the multi-frequency tests.
The results obtained show that ultrasound can improve heat transfer at different frequencies, at different powers, or in multi-frequency mode. We also found that the overall exchange coefficient is doubled for a frequency of 45 kHz and an ultrasonic power of 15 W. It is well known that the rate of heat transfer from a solid surface to a fluid is increased in an ultrasonic field, but the mechanism of heat transfer enhancement with ultrasound has not been sufficiently elucidated. In order to clarify the mechanism of heat transfer by ultrasonic irradiation.
When emitted ultrasound in liquid several can be induced. First, the liquid can be heated because of the acoustic energy. The dissipation of ultrasound in the liquid can create a momentum gradient, which causes a movement of the fluid, called acoustic current. It can appear micro-bubbles of vapor in the liquid medium, and agitate the liquid at the microscopic level, this phenomenon is called acoustic cavitation. Finally, a fourth phenomenon that can appear, at high frequency only, is the nebulization or the acoustic fountain [19]. Figure 15 shows all these phenomena.
In the presence of ultrasound, the phenomenon of acoustic cavitation is capable of triggering a turbulent transition, which makes ultrasound more apt to intensify heat transfer in the laminar regime [4]. As shown in figure 16.
For the purpose of observing cavitation and thermal bubble behavior using a high-speed video imaging system, Kim et al conducted tests that show that the effects of ultrasonic vibrations on flow behavior are very different depending on the heat transfer regime and the amount of dissolved gas. In the natural convection and subcooled boiling regimes, the behavior of cavitation bubbles strongly affects the degree of heat transfer