Material

Mature melons of the yellow variety (Cucumis melo L.) purchased in the local market (Recife, PE, Brazil) were used. The previously selected, washed and peeled raw material was sliced into rectangles (5.0 cm×3.0 cm×0.5 cm). The initial moisture (X₀) of the melon, determined by the oven method at 105 °C/24 h (23), was 88.61%.

Ultrasound pretreatment

Melon samples were weighed, placed in 100-mL beakers containing distilled water, and placed in an ultrasonic bath (model USC-2580A; Unique, Indaiatuba, Brazil), without mechanical agitation, at approx. 25 °C. Ultrasound application time was 10, 20 and 30 min. The sample/distilled water mass ratio used was 1:4, and the ultrasound frequency was 25 kHz (154 W), according to the literature (24). Tests with samples without the application of ultrasonic pretreatment (W/O US) were performed as a control. After predetermined times, the samples were taken from the distilled water, placed on absorbent paper for 10 s to remove excess water, and weighed. After that, water loss (WL) and solid gain (SG) were calculated using the following equations, respectively:

where m_W0 is the initial water content in the product (g), m_Wt is the water content in the product at time t (g), and m₀ is the initial mass of the product (g), and

where m_S0 is the initial dry mass (g), m_St is the dry mass at time t (g), and m₀ the initial mass of the product (g).

The moisture content of the samples without ultrasound treatment (W/O US) was 88.16%. Sample moisture content increased to 90.19% after a 10-minute pretreatment with ultrasound (US10), 90.74% after 20-minute ultrasound (US20), and 90.94% after 30-minute ultrasound (US30).

Drying kinetics

Convective drying of melon slices with and without (control treatment) ultrasound pretreatment was performed at 50, 60 and 70 °C, using a stainless-steel fixed bed dryer (tray dryer) with a fixed air velocity of 2.0 m/s. The choice of the temperature range in this study was to avoid very long drying time (temperatures below 50 °C) and high temperatures, which would cause the loss of nutritional components (temperatures above 70 °C).

Samples were weighed using a semi-analytical balance. The time intervals used for weighing were 15 min during the first hour of drying and 30 min until the equilibrium condition was reached (10). The drying kinetics study was performed using dimensionless moisture data. The diffusion model based on Fick’s law was used to estimate the effective diffusivity:

where X is the moisture content (g of water per g of dry mass), t is the time (s), y is the coordinated direction and D_eff is the effective diffusivity of water (m²/s).

The following equation presents the solution to Eq. 3 proposed by Crank (25), considering an infinite flat plate, where the effect of shrinkage is not considered, assuming instantaneous thermal equilibrium and moisture on the surface.

where X_θ is the dimensionless moisture, X₀, X_t and X_e are initial, mean at time t and moisture content at equilibrium (in g of water per g of dry mass), and δ is half of the slab thickness (m).

The linear dependence of the Arrhenius equation, which is a linear function of the logarithm of the diffusivity and the inverse of the temperature, was tested during the drying process using the following equation:

where E_a is the activation energy (kJ/mol), A is a drying constant, R is the universal gas constant (kJ/(mol∙K)), and T is the absolute drying temperature (K).

Modelling of drying kinetics and estimation of thermal properties

Three empirical models were used for drying data fit (26):

where a, k, n and w are the empirical constants in drying models, and t is time (min).

The fit of all the models to the experimental data and their parameters was verified with TIBCO Statistica v. 10.0 (27). The error (E) in percentage between the values observed and predicted by the empirical models was determined according to the following equation:

where V_P is the expected value, V_O is the observed value, and N the number of points considered in the curve.

To simulate the temperature profile during the melon drying, the thermal conductivity (k_p/(W/m∙K)) and specific heat capacity (C_p/(J/kg∙K)) were estimated using the equations presented below (19). The density (ρ), necessary for solving the mass, energy and momentum transport equations, was calculated using the mass-volume relationship.

Simulation of the temperature profile by computational fluidodynamics

The computational domain was solved using the finite volume method, responsible for solving the Navier-Stokes equations based on conservative principles (28). To better observe the current lines acting directly on the heat transfer coefficient, which affects the temperature profile, and considering the geometric domain simplicity, the refining mesh was of high relevance, bringing better precision to the results. The mass transfer study was not possible because the melon (solid domain in this study) should be characterized as a porous domain and this could not be performed. The computational cost to create a mesh that reproduces the pores present in the melon would be too high, making it impractical. Thus, only the simulation for energy and momentum was performed.

The greatest concentration of mesh elements occurred in the wall and contact regions (interface) due to the choice of ‘curvature and proximity’ as criteria to be considered when generating the mesh for the domains. The nodes in the mesh elements were generated by the drop method, which does not generate nodes between the vertices of the geometric element. Due to the importance of the fluid (air) domain, the unstructured mesh was chosen for this domain, which is generated through the Delaunay triangulation and which provides more details for the results. However, the solid domain (melon slice) was represented by a structured mesh, because of its geometric simplicity (29, 30), as shown in Fig. 1.

Fig. 1

Schematic representation of: a) melon slice (I) and simplified dryer body (II), b) structured and unstructured mesh zones used in the XY plane, and c) denser unstructured zone around the melon (I), structured mesh zone used to represent the melon (II) and less dense mesh area, representing the external fluid medium (drying air) (III)

Since the trays used here consisted of a network of fine stainless-steel wires, instead of using perforated plates which would affect the airflow into the dryer, they were not considered in the geometric domain used for simulations. Such presumption was necessary since the computational cost associated with the mesh refining would be higher. Also, the wires are very thin, so their interference with the airflow can be neglected.

Regarding the presumptions made, the effect of shrinkage, generation of heat inside the product, and radiation effects may be neglected. Thermal properties were considered constant. For the turbulence, medium intensity (5%) and eddy (turbulent) viscosity ratio 10, as its use is recommended when there is no information on the turbulence at the entrance, were considered (30). The turbulence model used was the shear-stress transport (SST) k–ω (16, 19, 28), justified due to the high-Re simulation (>10⁴). In the air-dryer and air-slice interfaces, the conservative heat flux was necessary to give stability to the interface model. The selected flow regime was subsonic, due to the low velocities. This work considered transient regime and incompressible fluid, resulting in the following equations:

Conservation of mass (law of continuity):

Conservation of momentum (Newton's second law of motion):

Conservation of energy (first principle of thermodynamics):

where T is the temperature (K), v_i is the speed (m/s) in direction i and τ_ij is the stress tensor in the plane i with the flow in direction j, g is gravity acceleration (m/s²), ρ is the melon density (kg/m³), p is pressure (Pa), t is time (s) and C_p is specific heat capacity (J/kg∙K).

The generalized energy equation (Eq. 16) had its velocity terms zeroed, a necessary condition when used for solids.

The software used to build the geometry, production of the mesh, resolution of the equations, and obtaining the results was the Ansys CFX® 17.0 (31). The solutions were considered to have converged at the time when the normalizing residue was less than 10^-4 (28).

Drying kinetics

The drying kinetics data, obtained at different temperatures, are shown in Fig. 2, where the Y-axis (X_θ) is in the logarithmic scale. At 50 °C (Fig. 2a), the treatments US20 and US30 required a shorter time to reach the equilibrium condition (180 min), followed by the US10 treatment (210 min). These values represent a reduction in comparison with time obtained in the W/O US treatment (240 min). This reduction is 25% for the US20 and US30 treatments and 12.5% for the US10 treatment. Concerning the kinetics at 60 °C (Fig. 2b), the data presented a similar tendency, where the treatments US20 and US30 also had the shortest time to reach equilibrium (120 min) followed by US10 (150 min) and WUS (180 min). At 70 °C (Fig. 2c), the equilibrium was reached in 90 min (US20 and US30), 120 min (US10) and 150 min (W/O US).

Fig. 2

Melon drying kinetics data at: a) 50 °C, b) 60 °C, and c) 70 °C for different treatments, and d) reduction of drying time with the increase of temperature in different treatments. W/O US=drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively. X_ϴ=is the dimensionless moisture

Fig. 2d shows the reductions in drying time in US10 and US20 treatments compared to the W/O US treatment at the different temperatures studied. A synergistic effect was observed between the type of treatment (W/O US, US10, US20 and US30) and the temperature (50, 60 and 70 ° C), so that the reduction in drying time was greater when the temperature and time exposure to ultrasonic waves were also higher. Nowacka et al. (32) reported similar results, obtaining reductions of 31-40% in the apple drying time at 70 °C, air velocity of 1.5 m/s, frequency of 35 kHz and ultrasound for 10, 20 and 30 min. However, it is also possible to find studies in which the increase in temperature promotes a reduction in drying time (8, 33). This difference, linked to the chaos of the microstructural rearrangement of the product, is best explained below.

Empirical modelling of experimental kinetics

Table 1 shows the results of the adjustment of the empirical models (Page, two-term exponential, and Henderson and Pabis) to the obtained experimental data. The models gave satisfactory R² values under all the studied conditions, with the two-term exponential and Page models being those that had the best fit. The best suitability of one model over another in the empirical modelling of drying kinetics can be explained by their dependence on operating conditions and characteristics of the material matrix, as observed in different works reported in the literature (7, 34-37).

Despite the high R² obtained in the Henderson and Pabis model, it presented errors varying 35.46-58.16%, which is explained by the distribution of the data along the regression line since the error variance is constant throughout the studied range, that is, the observed responses show homoscedasticity (38). Such behaviour was not observed in the Two-term exponential and Page models, which presented low percentage errors. Fig. 3 shows the fitting of the Two-term exponential model, which had the smallest error.

Fig. 3

Empirical modelling of experimental data for melon drying: a) without ultrasound (W/O US), and with ultrasound (US) treatment for: b) 10, c) 20 and d) 30 min. The continuous lines represent the best adjusted model, two-term exponential model (TT), for the different temperatures. X_ϴ = is the dimensionless moisture

Mass transfer in terms of effective diffusivity

The values referring to the variation of the effective diffusivity (D_eff) with the change of temperature, obtained through Eq. 3, are given in Table 2. The increase of the ultrasound exposure time caused an increase in the diffusivity under all conditions. The application of ultrasound facilitates the removal of water, increasing its diffusivity, as emphasized by Zhang et al. (37), who analyzed the effect of ultrasound on mass transfer and water removal from mushroom slices. However, this effect did not occur when drying US30 samples at 60 °C. The increase in ultrasound time from 20 (US20) to 30 (US30) min at 60 °C reduced the diffusivity by 4.42%. This particular phenomenon, associated with the different temperature effects on the drying time observed in the literature, shows that the microstructural rearrangement of the product is chaotic after exposure to the ultrasonic waves. Thus, the consequences on the effective diffusivity can be unpredictable, depending on the operating temperature range, since the structure can be organized in a way that will benefit or hinder the water transport from the interior to the external part of the product. Other research studies reported similar behaviour. Nowacka et al. (32), evaluating the effect of ultrasound application on apple drying, found that the application of ultrasound for 10 min resulted in a higher diffusivity coefficient than the treatment for 20 min, generating a difference of 5.07%. Romero and Yépez (39), studying the effect of ultrasound as a pretreatment of Andean blackberry (Rubus glaucus Benth) to convective drying, noticed that at an air velocity of 3 m/s and 50 °C, the increase of the ultrasound application time from 10 to 30 min caused a reduction of the effective diffusivity of the water of 1.25%. Corrêa et al. (6), studying the influence of ultrasound application on osmotic pretreatment and subsequent drying of pineapple, also observed a decrease in diffusivity as the time of exposure to the ultrasound increased at 40 °C (6.70%) and 70 °C (2.86%).

Fig. 4 shows the linear profile of the diffusivity with the reciprocal value of temperature, based on Table 2. The data presented a good fit, obtaining R²>0.994 for W/O US and US10 treatments, and R²>0.977 for treatments US20 and US30. Tzempelikos et al. (19) found similar R² values, around 0.98.

Fig. 4

Dependence of the diffusivity on the reciprocal value of temperature W/O US=drying without ultrasound, US10, US20 and US30=drying with ultrasound pretreatment for 10, 20 and 30 min, respectively

Mass transfer in terms of water loss and solid gain

Two parameters used to determine the conditions for CFD simulation were analyzed: water loss and solid gain, and their obtained values are given in Table 2. The obtained negative water loss values indicated a water gain in all the treatments. As regarding solid gain, the values obtained were also negative, that is, there was a loss of solids. These behaviours corroborate the findings in other studies involving ultrasonic pretreatment for fruit dehydration. Fernandes et al. (24), for sapota (Achras sapota L.) drying, found values of water loss and solid gain ranging from -4.0 to -5.2% and -2.7 to -7.8%, respectively. Garcia-Noguera et al. (40) obtained values of water loss ranging from -2.7 to -3.9% and of solid gain from -0.1 to -0.7% for strawberry dehydration. Silva et al. (10), when drying melon slices, obtained values for water loss and solid gain in the range from -8.51 to -10.59% and -0.07 to -1.45%, respectively.

The treatments US20 and US30 resulted in higher reductions in drying time than W/O US. As these reductions were similar between the two treatments, the use of water loss and solid gain parameters was important for determining adequate conditions. The conditions used for simulation were treatment US20 at 60 °C since water gain (negative water loss) was lower in the US20 treatment than in the US30, and this was the determining factor for the choice, as solid gain values for the two treatments were closer and relied on the dry basis of the product, representing a small fraction of the total mass. The kinetic and diffusion data (Table 2) also corroborated the choice of the US20 treatment at 60 °C as the conditions for simulation.

Simulation via CFD of the temperature profile of the melon slice

The values of the properties used in the temperature profile simulation of the melon slice were: k_p=0.5849 (W/O US) and 0.5953 (US20) W/(m∙K), C_p=3891.830 (W/O US) and 3954.830 (US20) J/(kg∙K), ρ=2028.467 (W/O US) and 2055.224 (US20) kg/m³.

Fig. 5 shows the temperature profile of the solid phase of the moist melon over time for US20 treatment at 60 °C. There was also a simulation of W/O US treatment at 60 °C. However, the obtained profile was similar to that of the US20 at 60 ºC (not shown). The geometry was considered unchanged throughout the two processes, and there was only a small difference between the local temperatures when comparing the two treatments since the values ​​of C_p, k_P and ρ were subtly smaller in W/O US at 60 °C.

Fig. 5

Temperature profile of the melon slice pretreated with ultrasound for 20 min after: a) 30, b) 60 and c) 90 min of drying at 60 °C

The results in Fig. 5 show that the temperature is higher at the edges since the proposed geometry generates turbulence in these regions, which in turn increases the local heat transfer coefficient. As it moves away from the lateral zones towards the centre, a decrease in temperature is observed. This occurs through the formation of low-pressure regions above the melon (Fig. 6a), a consequence of the vortexes generated by the lateral air flows (Fig. 6b), reducing the local heat transfer coefficients (41). Temperature profiles of fruits and moist objects generated by numerical methods found in the literature are similar to those obtained in this study (19-21).

Fig. 6

Relative pressure of the: a) YX (I) and YZ (II) planes, and b) current lines in YX (I) and YZ (II) planes