Experimental Evaluation and Kinetic Analysis of Direct-Contact Ultrasonic Fabric Drying Process

Clothes drying is one of the most frequently and widely utilized operating processes in our daily life. Since its first marketing in 1938, clothes dryers have become a standard feature in nearly 85% of American homes [1]. The typical electric conventional dryer consumes 600–1000 kWh/year, which makes it one of the most energy-intensive appliances in US, after space conditioning and water heating [2]. In total, clothes dryers now represent a $9 billion annual energy bill and approximately 6% of residential electricity consumption [3].

About 80% of clothes dryers in the US use an electrical resistance heater to heat the air from the ambient [4]. The other 20% of the clothes dryer in the US are gas dryers, which use a gas burner to produce the heat used to warm up the air. The warmed air is directed into a rotational drum in which the wet clothes are tumbling. The air collects the moisture in fabrics and leaves the drum [5]. Although the conventional clothes drying process is effective, simple, and reliable, it is not energy efficient since much electricity is consumed to overcome the latent heat of vaporization of water in wet fabrics. During the past 25 years, major appliances like clothes washers, refrigerators, and air conditioners have undergone significant energy efficiency improvements. However, clothes dryers have almost made no progress in improving energy efficiency during the same period [6]. In the context of growing awareness about climate change and increasing energy bills, it becomes crucial to promote the energy efficiency of clothes dryers.

In order to reduce the energy consumption of residential clothes dryers, a variety of physical mechanisms have been exploited to dry fabrics, including vapor-compression heat pump dryer [7–9], microwave dryer [10,11], infrared (IR) dryer [12,13], vacuum dryer [14,15], and thermoelectric dryer [16–18]. In 2016, a direct-contact ultrasonic clothes drying technique was first reported by us, which emerges as a promising method for reducing the energy use and drying time of the fabric drying process [19–26]. In this technology, an ultrasonic transducer is utilized to generate high-frequency (>20 kHz) mechanical vibrations which are able to extract the water moisture in fabric pores (placed in direct contact with the transducer surface) as a fine mist of very small droplets. Because the fabric drying process in this technique lacks thermal evaporation, i.e., bypassing the latent heat of evaporation, it is much more energy efficient than the traditional drying techniques. The world’s first benchtop direct-contact ultrasonic clothes dryer has been developed by us using metal mesh-based ultrasonic transducers [19]. Based on our initial performance evaluation results, compared with a typical electrical resistance dryer, this novel fabric drying technique consumes 90% less energy; compared with a typical heat pump-based clothes dryer, the energy consumption of this technique is 80% less.

While our previous investigations on direct-contact ultrasonic fabric drying have got several important findings, such as the kinematic and thermal mechanisms of the fabric dewatering process, one of the most important of which is the selection of the metal mesh-based ultrasonic transducer [19,20,23]. A metal mesh-based ultrasonic transducer uses an annular piezoelectric ring to excite the vibration of a metal mesh which is attached to the piezoelectric ring. Dissimilar to the traditional ultrasonic transducers using a whole piece of piezoelectric ceramic as a working area, the piezoelectric ring excited metal mesh breaks water droplets on the top surface and transported the fine mist through mesh pores to the bottom surface, which reduce the drying time. Our results have shown that the metal mesh-based transducer consumes 90% less energy than the traditional piezoelectric ceramic transducer [20]. While our prior studies have obtained many important findings about direct-contact ultrasonic fabric drying based on experimental analysis, which can contribute to the advancement in the development of the direct-contact ultrasonic clothes dryer, there is still a lack of the modeling technique which encompasses the performance characteristics of the ultrasonic dryer in terms of the operating parameters, such as transducer frequency and power, as well as the nature of fabric. Similar to all the existing drying technologies, modeling of the drying processes is one of the most important aspects of this new drying technique. The purpose of modeling is to allow the engineers to select the most proper method of drying for a given fabric as well as to select appropriate operating conditions.

Therefore, this work aims to investigate the drying performance of various fabrics under different direct-contact ultrasonic drying conditions experimentally and analytically. First, the drying processes of four kinds of fabrics under various transducer vibration frequency and input power combinations were experimentally tested. Then, five different kinetic drying models were applied to model the fabric drying process under various drying conditions. Both the ultrasonic transducer related parameters and the parameters related to the nature of fabric were incorporated in the models. Finally, the modeling performances using different models were evaluated.

An experimental setup utilized for testing the wet fabric drying performance on a metal mesh-based transducer was built, which is similar with Peng et al. [19,20] and Peng and Moghaddam [22] (Fig. 1). A function generator (AFG2021; Tektronix Inc.) was tuned to supply an electrical signal with certain voltage and frequency to a radio frequency (RF) power amplifier (A-303; A.A. Lab Systems Ltd, Ramat-Gan, Israel). The power amplifier output was connected to a metal mesh-based ultrasonic transducer and drove the transducer with desired power for fabric drying studies. During the drying process, a microbalance (AL104; Mettler Toledo) was utilized to measure the mass of wet fabrics with a 0.1 mg resolution until the recorded mass came back to the mass of dry fabric.

A metal mesh-based ultrasonic transducer was utilized in this study for fabric drying studies, as illustrated in Fig. 2(a). A structural diagram of the transducer is shown in Fig. 2(b), consisting of a thin stainless-steel disk mesh sandwiched by two annular piezoelectric rings which excite the vibration of the thin disk. The resonant frequency of the transducer is ∼135 kHz.

In this study, four different types of fabrics (F1, F2, F3, and F4) were tested according to the US Department of Energy (DOE) standard, as shown in Fig. 3. F1 consists of partially cotton/partially synthetic (50% cotton/50% polyester) with an area density of 111.4 g/m². F2 consists of 65% cotton/35% polyester with an area density of 190.9 g/m². F3 consists of 80% cotton/20% polyester with an area density of 193.9 g/m². F4 consists of 100% cotton with an area density of 300.1 g/m². The thicknesses of fabrics F1, F2, F3, and F4 were 0.27, 0.40, 0.53, and 0.91 mm, respectively. As shown in Fig. 3, fabrics F3 and F4 illustrate denser structures and smaller pores than fabrics F1 and F2. That is, the porosity of fabrics F3 and F4 are less than that of fabrics F1 and F2.

For the fabric drying tests in this study, the experimental method was similar to the method of Peng et al. [19,20] and Peng and Moghaddam [22]. The mass of the dry fabric sample was measured by using the microbalance before the drying test. The dry fabric sample placed on the transducer surface was then wetted with a certain volume of water, which was in order to saturate the sample. After 5 s driving the transducer, the mass of the fabric sample was checked again by using the microbalance. The wet fabric sample was completely dried for retests next time after the measurement. With this method, the mass of an originally saturated fabric sample was measured continuously after driving the transducer in increments of 5–10 s until the saturated fabric sample was completely dried. Considering the different properties of fabrics including thickness, density, and porosity as well as the transducer-fabric vibration resonant frequency shift while adding various saturated fabrics to the transducer surface, three different transducer driving frequencies (115, 135, and 155 kHz) and input powers (1.2, 2.5 and 4.4 W) were supplied to the transducer during the fabric drying process. For each combination of the transducer vibration frequency and the input power, the measurement of fabric mass was repeated for at least three times for each time interval. The measurements were conducted until the mass of the fabric was less than 5% of the initially saturated fabric.

For modeling drying behavior of various materials, such as food and agricultural materials [27–31] as well as fabrics [32–34], thin-layer drying equations are the most popularly utilized ones. According to different assumptions and simplifications, thin-layer drying models can be divided as theoretical models, semi-theoretical models, as well as empirical models. For the theoretical models, the most widely studied model is derived from the solution of Fick’s second law [27]. Nevertheless, the main limitation of theoretical models is that they are typically established based on certain assumptions, which makes these models unreliable and results in great errors for the predicted results. In addition, theoretical models always include many unknown parameters, which is inconvenient for the real applications. Thus, theoretical models are usually simplified as semi-theoretical ones for the convenience of real applications. Furthermore, the stuff drying process is a complex process in which various heat and mass transfer mechanisms may occur and interact with each other and we do have little knowledge about them. In view of this, in this study, semi-theoretical models and empirical models were adopted for demonstrating the wet fabric drying process assisted by direct-contact ultrasonic vibration.

The Weibull distribution function [42,43] (Table 1, Eq. (4)) which mathematically describes the drying process as a succession of probabilistic incidents is one of the empirical models. The other widely utilized empirical model is the Gaussian function which describes the normal distribution [44–46] (Table 1, Eq. (5)). Gaussian functions have been successfully utilized to establish different kinds of artificial neutral networks which have demonstrated good performances in predicting drying processes [45,46].

The drying behaviors of four different types of saturated fabrics (F1, F2, F3, and F4) 4 mm × 4 mm in size on the transducer were illustrated in Fig. 4. The fabric size was chosen for considering the working area of the transducer. The water contents required to wet through the selected fabric samples were ∼4.4, ∼6.5, ∼8.6, and ∼14.6 µl, respectively. The fabric drying process shown in Fig. 4 consists of two distinct regions:

• An initial non-linear region in which the water contents in the four fabrics decreased ∼70–80% in 5 s;

• Followed by a linear region in which the water contents in the four fabrics decreased linearly with time.

These two distinct regions of the drying curve are developed as a result of the kinematic and thermal effects of the ultrasonic transducer and consist of mechanical vibration and thermal evaporation regimes which determine the energy consumption and drying time of the fabric drying process [19]. The detailed physical mechanisms of the fabric drying process have been reported by us, as shown in Ref. [19]. For the four fabric samples shown in Fig. 3, the pores in each kind of fabric can be divided into large pores between the fabric threads, where the transducer vibrational force was larger than the water capillary force, and small pores within the fabric threads, where the transducer vibrational force was smaller than the water capillary force. Immediately after the transducer was actuated, overcoming the capillary force, the water in the large fabric pores was ejected by the transducer vibrational force. Besides, the amount of water extracted in the non-linear region rises, with the number of such pores increases. According to the drying date illustrated in Fig. 4, it can be induced that fabrics F1 and F2 had larger fractions of such pores than fabrics F3 and F4, which resulted in a larger reduction of water contents in the non-linear region. This conclusion can also be derived from Fig. 3, in which fabrics F3 and F4 demonstrate denser structures and smaller pores than fabrics F1 and F2. At the end of the non-linear region, the only pores still containing water were those with the capillary force larger than the vibrational force. Due to the viscous dissipation, the water temperature in such pores increased and the temperature rise induced thermal evaporation of the water in the fabric (shown in Fig. 5), which resulted in a linear decrease of water content in the fabric.

Using the non-linear least squares curve fitting tool in matlab, the parameters in each model were calculated by using the experimental data under different combinations of driving frequency and input power conditions. The result of each parameter was expressed as X ± σ, where X indicated the average of model parameter and σ denoted the 95% confidence interval. The parameters in each model under different ultrasonic fabric drying conditions were summarized in Table 2.

In the three semi-theoretical models, i.e., the Lewis model, Henderson and Pabis model, and logarithmic model, the parameter K was directly related to the direct-contact ultrasonic fabric drying rate. The higher drying rate at each drying condition corresponded to a larger magnitude of parameter K in these three models, as illustrated in Fig. 6. Based on the fabric drying tests for different conditions discussed in Sec. 3.1, the fabric drying time increased from F1 to F4 when the transducer vibration frequency and input power kept the same. Accordingly, the parameter value K reduced from F1 to F4. Referring to the nature of different fabrics (Fig. 3), F1 consists of the least portion of cotton (50%), while F4 consists of the largest portion of cotton (100%). Thus, F1 illustrated the least value of density, and F4 showed the largest value of density among the four kinds of fabrics. Among the four fabrics, F1 had the smallest fabric thickness and F4 had the largest thickness. For the same area of fabric samples, F1 would hold the least volume of water, while F4 would hold the largest volume of water. Furthermore, as discussed in the last section, since F4 consists of 100% cotton, it showed the densest structure, i.e., the smallest porosity, and largest portion of small pores within the fabric threads among the four kinds of fabrics. Therefore, F4 showed the longest drying time and F1 showed the shortest drying time during the fabric dewatering process according to the direct-contact ultrasonic fabric drying mechanism analysis discussed in the last section.

In addition, comparing different transducer vibration frequencies, the parameter K had the largest value at frequency 135 kHz. This is due to that the 135 kHz driving frequency was closer to the resonant frequency of the transducer. Thus, the transducer had the largest vibration amplitude (i.e., acceleration) at 135 kHz. As demonstrated in Fig. 6, keeping the vibration frequency at 135 kHz and input power at 2.5 W, for the Lewis model, the drying rate of fabric F1 was 1.6 times faster than that of F4; for the Henderson and Pabis model, the drying rate of F1 was 5.5 times faster than that of F4; for the logarithmic model, the drying rate of F1 was 0.6 times faster than that of F4.

Contrary to the semi-theoretical models, as illustrated in Fig. 7, the magnitude of parameter β in the Weibull model was inversely related to the direct-contact ultrasonic fabric drying rate. The value of β increased with the reduction of fabric drying rate from F1 to F4. Besides, at 135 kHz transducer vibration frequency, the drying rate was the largest compared with the 115 and 155 kHz. That is because the 135 kHz driving frequency was closer to the resonant frequency of the transducer. As illustrated in Fig. 7(a), when the driving frequency was 135 kHz and input power was 1.2 W, the drying rate of F1 was ∼5 times faster than that of F4. Furthermore, compared different input power conditions in Fig. 7, for the same driving frequency and fabric sample, the drying rate was improved with the increase of input power. For the 135 kHz driving frequency, the drying rate of F1 was increased about 1 time from input power 1.2–4.4 W. That is because more energy was utilized for the direct-contact ultrasonic fabric drying when the input power was increased.

Similar to the Weibull model, the magnitude of parameter c in the Gaussian model was also inversely related to the direct-contact ultrasonic fabric drying rate (Fig. 8). Based on the fabric drying test results, from F1 to F4, the drying rate increased. The reason of which has been discussed in Sec. 3.1. The effect of transducer vibration frequency and input power on the value of parameter c was also similar to the Weibull model parameter.

To evaluate the goodness of fit for each model, coefficient of determination (R²), root mean square error (RMSE), as well as relative percentage error (PE) were assessed by using both the anticipated data and the experimental data. The results of R², RMSE, and PE were shown in Table 3 for the five different models for each drying condition. Especially, the PE values obtained by these five models for each drying condition were compared, as shown in Figs. 9–11. Based on the comparison of PE for these five models, the results illustrated that the three semi-theoretical models had larger PE values than the two empirical models, the Weibull model and the Gaussian model. As discussed previously, the semi-theoretical models are derived from the theoretical models, which are usually utilized to model the thermal drying process of food and agricultural materials. For the application of direct-contact ultrasonic fabric drying, they may not suitable. Compared with the semi-theoretical models, the capability of empirical models to anticipate the drying process mainly relies on the soundness of historical data rather than the drying mechanisms. Thus, in view of this, the empirical models can attain better anticipation results than the semi-theoretical models when the real heat and mass transfer mechanism is unknown.

The Weibull model and the Gaussian model are superior to the three semi-theoretical models to describe the drying kinetics under direct-contact ultrasonic fabric drying. Furthermore, although the model prediction performance of the Weibull model and the Gaussian model is comparable, considering the number of model parameters (2 versus 3), the Weibull model is simpler than the Gaussian model for the applications. Therefore, based on this reason, the Weibull model is the most suitable model to predict the drying kinetics of fabrics under direct-contact ultrasonic drying.

In this study, for the first time, the direct-contact ultrasonic fabric drying processes were experimentally tested and kinetically analyzed. The drying processes of four kinds of DOE standard fabrics under different combinations of ultrasonic transducer vibration frequency (115, 135, 155 kHz) and input power (1.2, 2.5, 4.4 W) conditions were experimental tested, the results of which showed that the process consists of a mechanical vibration dominated non-linear drying region and a thermal evaporation dominated linear drying region. The drying rate differences of different kinds of fabrics were attributed to the nature of fabrics, such as composition, thickness, and porosity.

Three semi-theoretical (the Lewis model, the Henderson and Pabis model, and the logarithmic model) and two empirical (the Weibull model and the Gaussian model) kinetic drying models were employed to assess the direct-contact ultrasonic fabric drying processes. The kinetic models not only included the ultrasonic transducer parameters, such as vibration frequency and input power but also the parameters related to the nature of fabric. The kinetic modeling results demonstrated that the magnitude of parameter K in the three semi-theoretical models was increased with the improvement of fabric drying rate which was directly associated with the drying conditions, such as the power input, transducer vibration frequency, and the nature of fabric. However, the magnitude of parameter β in the Weibull model and the magnitude of parameter c in the Gaussian model were inversely related to the increase of fabric drying rate. According to the model prediction evaluation results, the Weibull model and the Gaussian model were superior to the three semi-theoretical models for anticipating the drying kinetics of fabrics under direct-contact ultrasonic drying. Furthermore, the Weibull model was more suitable for real direct-contact ultrasonic fabric drying applications compared with the Gaussian model.

Based on the findings in this study, the proper approach of drying a given fabric as well as the suitable operating conditions can be chosen in order to reduce the energy use of direct-contact ultrasonic fabric drying. In addition, the improvement of ultrasonic transducer design can also benefit from this study for the advancement of direct-contact ultrasonic drying technology.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper. No data, models, or code were generated or used for this paper.