Evaluation and Modeling of the Aerodynamic Characteristics of Watermelon Seed of Different Varieties

Abstract

In this study, the aerodynamic properties of three varieties of watermelon seeds as a function of moisture content were evaluated and modeled. The watermelon seed varieties used were Charleston grey, Kaolack, and Sugar baby, and their moisture content ranged from 8.61 to 24.26, 10.30 to 26.11, and 7.78 to 23.23% wet basis (wb), respectively. The results showed that the terminal velocity of the Charleston grey, Kaolack, and Sugar baby varieties increased from 5.27 to 6.67, 4.40 to 6.23, and 4.00 to 6.60 ms^–1, respectively, as the moisture content increased. The Reynolds number of the three watermelon seed varieties increased with the increasing seed moisture content, while the drag coefficient generally decreased as the seed moisture content increased. Analysis of variance showed that the moisture content of the three watermelon seed varieties had significant effects on all the aerodynamics properties (p < 0.05). Mathematical models were developed to relate the moisture content of watermelon seeds with the values of the aerodynamic properties investigated.

Keywords:

• Aerodynamic properties
• Models
• Moisture content
• Seeds

INTRODUCTION

Watermelon (Citrullus lanatus) is a member of the cucurbit family (Cucurbitaceae) and it is grown commercially in the tropical and semi-tropical areas. Its fruit is usually large, oval, or oblong in shape, having a smooth skin with dark green rind.^[1] The seeds are usually extracted from the fruit by manual maceration. There are about 50 common varieties of watermelon throughout the world generally classified into five categories namely, all sweet, ice-box, seedless, crimson, and yellow flesh.^[2] Watermelon seed plays an important role in people’s diet due to its high nutritive value.^[1,^2] It has been reported that the seed consists of about 31.9% protein, 4.4% carbohydrates, 57.1% fat, 8.2% fiber, 6.2% ash, 130 mg calcium, 456 mg phosphorus, and 7.5 mg iron.^[2] Furthermore, the seeds have also been reported to contain amino acids which act as an antioxidant during body metabolism.^[3] The kernels are sometimes used as dressings in confectioneries in place of almonds and pistachios, or used as a flavor enhancer.

In the handling and processing of biomaterials, air or water is often used as a carrier in the transportation and separation of desirable products from unwanted ones.^[4] The characteristics of biomaterials in an air stream greatly depend on their aerodynamic properties.^[5] Aerodynamic properties of materials are important pre-requisite in the design of pneumatic separators, screen cleaners, gravity tables, harvesters, conveyors, and general pneumatic equipment.^[6,^7] The transportation and separation of a mixture of particles in a pneumatic system is only possible when the aerodynamic characteristics of the particles are known. Knowledge of the aerodynamic properties of the material of interest is, therefore, essential in the proper design of separating, conveying, and cleaning equipment. Several studies have been carried out on the aerodynamic properties of biomaterials such as cheat seed,^[8] rice, corn, wheat and barley,^[9] pine nuts,^[10] wheat kernel,^[11] makhana,^[12] Turgenia latifolia seeds and wheat kernels,^[6] flax seed,^[13] Makhobeli, triticale and wheat seeds,^[7] and mung bean seed.^[14] However, at the moment there is no published data on the aerodynamic properties of watermelon seeds. It was noted by^[15] that fruit seeds, including watermelon seeds, are usually thrown out as waste during processing or after human consumption, necessitating research on the properties of the seeds. The objective of this study was to evaluate and model the aerodynamic properties of three different varieties of watermelon seeds namely, Charleston grey, Kaolack, and Sugar baby, as a function of moisture content. The properties of biomaterials have been evaluated as a function of moisture content by some researchers.^[16–18] The aerodynamic properties of the seed varieties investigated were terminal velocity, drag coefficient, and Reynolds number.

MATERIALS AND METHODS

Sample Preparation

Three major watermelon seed varieties widely cultivated and consumed in Nigeria were selected for the study. The varieties were Charleston grey, Kaolack, and Sugar baby (Fig. 1). The seeds of these watermelon varieties were obtained from a local market in Enugu, south eastern Nigeria, free of foreign matters, immature, and broken seeds. The initial moisture content of the seeds was determined using the oven dry method set at 103 ± 2°C until a constant weight was reached.^[19] The initial moisture content of the seed varieties were 8.61 ± 0.01, 10.3 ± 0.03, and 7.78 ± 0.02 % (wb) for Charleston grey, Kaolack, and Sugar baby, respectively. In view of the importance of moisture in biomaterial handling, the aerodynamic properties of the watermelon seeds were assessed at five moisture content levels. The watermelon seeds were conditioned to four higher moisture content levels of 12, 16, 20, and 24% (wb) for Charleston grey; 14, 18, 22, and 26% (wb) for Kaolack; and 11, 15, 19, and 23% (wb) for Sugar baby in addition to the earlier determined initial moisture content levels. The seeds were conditioned by adding calculated amount of distilled water to the seeds, sealing them in polyethylene bags, and storing in a refrigerator at 3°C for about 2 weeks for proper moisture distribution.^[20] Before each experiment was conducted, the required seed sample was taken out to equilibrate with the ambient environment and the moisture content verified.^[21] The selected moisture content levels span the range commonly observed for stored watermelon seeds and the seeds freshly extracted from the fruit.

FIGURE 1 Watermelon seed varieties.

Seed Dimensions, Mass, and Density

From the different varieties of watermelon seeds conditioned to different moisture levels, 20 seeds were randomly selected from each moisture level for the determination of seed dimensions. In determining the average size of the seed varieties at each moisture level, the methodology described by^[1] was adopted. Measurement of the major dimensions of the seed, namely length (L, mm), width (W, mm), and thickness (T, mm) were carried out using a digital vernier caliper (SKOLE) measuring to accuracy of 0.001 mm. The length was the highest dimension of the biggest surface of the seed; the width was the shortest dimension of the biggest surface of the seed while the thickness was the shortest dimension of the smallest surface of the seed.^[22] The mass of the seed varieties at different moisture levels was measured using a digital electronic balance (Mettler Toledo JL620-GLA01) measuring to accuracy of 0.001 g. The true density (ρ_t) defined as the ratio of the mass to the volume of a particle was determined for the watermelon seed varieties at different moisture content levels using the toluene displacement method.^[23,24]

Measuring Equipment

The terminal velocity of the different varieties of watermelon seeds at different moisture content levels was measured with equipment which consists of a vertical cylindrical wind tunnel made of Plexiglas, connected to a 1 hp motor-powered centrifugal fan to supply air flow into the wind tunnel. A wire screen was positioned in the top section of the vertical wind tunnel to prevent the seed from falling down to the bottom. The air flow rate of the fan was controlled at the bottom section of the wind tunnel using an adjustable diaphragm. A perforation was made on the Plexiglas just above the wire screen where the hot-wire probe of a digital anemometer (TPI 565C1) measuring to accuracy of 0.1 ms^–1 was inserted to measure the terminal velocity of the seeds.

Terminal Velocity, Drag Coefficient, and Reynolds Number

To measure the terminal velocity of the watermelon seed varieties at each moisture content level, seed samples were placed on the wire screen within the cylindrical wind tunnel. The air flow from the centrifugal fan was then increased until the seed was suspended in the air stream within the wind tunnel. At the point when the rotational movement of the seed was lowest, the air velocity was measured using the digital anemometer.^[7] The probe of the hot-wire anemometer was inserted into the air stream through the perforation on the wind tunnel to measure the air velocity near the location of the suspended seed.

For an object in a free fall, the object will attain a constant terminal velocity (V_t) at which the net gravitational accelerating force (F_g) will equal the resisting upward drag force (F_r).^[4] To derive a general expression for the terminal velocity, the gravitational force (F_g) is set equal to the resisting drag force (F_r) and the velocity V, equaled to the terminal velocity, . The expression for the terminal velocity will be as follows:

(1)

The drag coefficient can be derived as follows:

(2)

And the projected area,

(3)

where is the projected area of the seed (m²), is the drag coefficient (dimensionless), g is acceleration due to gravity (9.81 ms^–2), is the seed length (m), is the mass of seed (kg), is terminal velocity (ms^–1), is the seed width (m), is the density of air (1.206 kgm^–3 at room temperature), is the density of the seed (kgm^–3).

Reynolds number is an important aerodynamic attribute that represents the ratio of inertial effects (i.e., the product of the particle’s velocity and length scale) to viscous effects (i.e., viscosity of the medium/fluid in which the particle is moving—in this case, air).^[25] The Reynolds number (Re) was calculated using the terminal velocity of each seed sample from the following relationship:^[26]

(4)

(5)

where is the geometric mean diameter of the seed (m), T is the seed thickness (m), μ is air viscosity (1.816 × 10^–5 Nsm² at room temperature).

Statistical Procedure

The experiment was setup as a completely randomized design (CRD) with four replicates. The mean values of the aerodynamic properties of the watermelon seed varieties at different moisture levels were compared at p < 0.05 using the Duncan multiple range test. The means were fitted to linear and non-linear models, and the models evaluated according to the statistical criterion, determination coefficient (R²) for verifying the adequacy of fit.^[7] The model with the highest R² was selected as the best model for predicting the aerodynamic properties of the seeds as a function of moisture content. The data were analyzed using GenStat analytical software.

RESULTS AND DISCUSSIONS

The aerodynamic characteristics of three varieties of watermelon seeds namely, Charleston grey, Kaolack, and Sugar baby, were investigated. Prior to the experimental study, the moisture content (wb) of the conditioned seed varieties were verified using oven dry method to ascertain the exact moisture content of the seeds as follows: Charleston grey: 8.61, 12.21, 16.34, 20.11 and 24.26%; Kaolack: 10.30, 14.34, 18.41, 22.13, and 26.11%; and Sugar baby: 7.78, 11.33, 15.06, 19.42, and 23.23%.

Terminal Velocity, Drag Coefficient, and Reynolds Number

The mean values and the corresponding standard deviation of the major dimensions, projected area, mass, and true density recorded for the watermelon seed varieties at different moisture content levels are presented in Table 1. The physical properties were required in calculating the aerodynamic properties of the seeds. The results of the aerodynamic properties of the seed varieties at different moisture content levels are shown in Table 2. For Charleston grey, the terminal velocity and Reynolds number increased from 5.27 to 6.67 ms^–1, and 2054.21 to 2956.16, respectively, as the moisture content increased from 8.61 to 24.26% (wb). An inverse relationship was however observed for the drag coefficient as it decreased from 0.83 to 0.72 as the moisture content increased from 12.21 to 24.26% (wb). Charleston grey had the highest mean value for both the terminal velocity and the Reynolds number at the 24.26% (wb) moisture content level, while the highest mean value for the drag coefficient was recorded at the 12.12% (wb) moisture level. Analysis of variance carried out revealed that the mean values of the terminal velocity, drag coefficient, and the Reynolds number for Charleston grey variety were significantly influenced by moisture content at p < 0.05.

TABLE 1 Mean values of dimensions, projected area, mass, and true density of seed varieties (± standard deviation)

Moisture contentMC (% wet basis)	LengthL (mm)	WidthW (mm)	ThicknessT (mm)	Projected area (mm^2)	Geometric meandiameter, (mm)	Mass m (g)	True density (kg/m^3)
Charleston grey
8.61	12.33 ± 0.45	7.90 ± 0.37	2.09 ± 0.20	76.58 ± 5.43	5.87 ± 0.23	0.10 ± 0.00	867.24 ± 10.20
12.21	12.55 ± 0.64	7.90 ± 0.46	2.36 ± 0.11	78.06 ± 7.77	6.16 ± 0.24	0.13 ± 0.00	912.50 ± 17.67
16.34	12.74 ± 0.62	8.10 ± 0.46	2.53 ± 0.14	81.17 ± 8.12	6.39 ± 0.31	0.15 ± 0.00	920.31 ± 20.11
20.11	13.10 ± 0.68	8.02 ± 0.34	2.71 ± 0.26	82.52 ± 5.26	6.57 ± 0.25	0.15 ± 0.00	854.09 ± 24.17
24.26	12.97 ± 0.58	8.10 ± 0.33	2.84 ± 0.13	82.54 ± 6.41	6.68 ± 0.18	0.16 ± 0.00	902.78 ± 10.38
Kaolack
10.30	8.38 ± 0.65	5.30 ± 0.39	2.11 ± 0.25	35.01 ± 4.74	4.54 ± 0.32	0.05 ± 0.01	761.91 ± 12.23
14.34	8.89 ± 0.47	5.87 ± 0.30	2.29 ± 0.15	41.05 ± 3.46	4.92 ± 0.17	0.06 ± 0.00	809.38 ± 10.35
18.41	8.65 ± 0.59	5.73 ± 0.30	2.40 ± 0.12	38.96 ± 3.65	4.92 ± 0.22	0.07 ± 0.00	859.38 ± 10.93
22.13	9.02 ± 0.55	5.64 ± 0.50	2.54 ± 0.23	40.05 ± 4.97	5.05 ± 0.29	0.07 ± 0.00	967.41 ± 16.71
26.11	8.73 ± 0.52	5.68 ± 0.35	2.64 ± 0.40	38.99 ± 3.81	5.06 ± 0.25	0.08 ± 0.00	1000.00 ± 0.00
Sugar baby
7.78	7.91 ± 0.40	5.10 ± 0.21	2.15 ± 0.13	31.73 ± 2.43	4.43 ± 0.18	0.04 ± 0.00	666.67 ± 14.83
11.33	8.27 ± 0.45	5.13 ± 0.31	2.34 ± 0.14	33.33 ± 2.81	4.62 ± 0.21	0.05 ± 0.01	656.25 ± 6.50
15.06	8.07 ± 0.50	5.36 ± 0.36	2.30 ± 0.18	34.02 ± 4.11	4.63 ± 0.29	0.05 ± 0.00	904.17 ± 8.33
19.42	8.22 ± 0.37	5.31 ± 0.30	2.45 ± 0.16	34.34 ± 2.78	4.75 ± 0.17	0.06 ± 0.01	781.25 ± 6.50
23.23	8.55 ± 0.43	5.45 ± 0.21	2.47 ± 0.15	36.63 ± 2.75	4.86 ± 0.16	0.07 ± 0.00	1179.17 ± 8.33

TABLE 2 Aerodynamic properties of seed varieties (± standard deviation)

Moisture content MC (% wet basis)	Terminal velocity (m/s)	Drag coefficient	Reynolds number
Charleston grey
8.61	5.27 ± 0.06a	0.78 ± 0.00a	2054.21 ± 2.98a
12.21	5.67 ± 0.06b	0.83 ± 0.00b	2317.98 ± 4.30b
16.34	6.20 ± 0.05c	0.77 ± 0.00c	2629.53 ± 3.00c
20.11	6.33 ± 0.06d	0.74 ± 0.00d	2764.21 ± 4.31d
24.26	6.67 ± 0.07e	0.72 ± 0.00e	2956.16 ± 5.50e
Kaolack
10.30	4.40 ± 0.06a	1.14 ± 0.00a	1325.33 ± 3.48a
14.34	5.43 ± 0.05b	0.87 ± 0.00b	1775.74 ± 2.45b
18.41	5.63 ± 0.06c	0.90 ± 0.00c	1839.76 ± 1.55c
22.13	5.80 ± 0.02d	0.90 ± 0.00d	1944.72 ± 1.40d
26.11	6.23 ± 0.05e	0.86 ± 0.00e	2094.82 ± 2.45e
Sugar baby
7.78	4.00 ± 0.00a	1.28 ± 0.00a	1175.60 ± 4.86a
11.33	4.90 ± 0.03b	1.07 ± 0.00b	1505.40 ± 4.02b
15.06	5.60 ± 0.01c	0.83 ± 0.00c	1722.80 ± 3.97c
19.42	6.10 ± 0.00d	0.80 ± 0.00d	1922.40 ± 3.97d
23.23	6.60 ± 0.03e	0.72 ± 0.00e	2131.80 ± 3.57e

Means for each watermelon seed varieties at different moisture content in each column having different letters are significantly different at p < 0.05 using Duncan multiple range test.

TABLE 3 Regression models of aerodynamic properties of seed varieties

Regression models	R^2
Charleston grey
	0.98
	1.00
	0.99
Kaolack
	0.99
	1.00
	1.00
Sugar baby
	0.99
	0.98
	1.00

: terminal velocity; : drag coefficient; : Reynolds number; : moisture content; R²: determination coefficient.

Trends similar to those observed in the aerodynamic properties of Charleston grey were also observed for Kaolack. The terminal velocity and Reynolds number increased from 4.40 to 6.23 ms^–1, and 1325.33 to 2094.82, respectively, while the drag coefficient decreased from 1.14 to 0.86 as the moisture content increased from 10.10 to 26.11% (wb). Mean values recorded for the aerodynamic properties of Kaolack were significantly influenced by the seed moisture content at p < 0.05 as was revealed by the analysis of variance carried out. For the Sugar baby variety, the drag coefficient decreased from 1.28 to 0.72 as the moisture content increased from 7.78 to 23.23% (wb) while the terminal velocity and Reynolds number increased from 4.00 to 6.60 ms^–1, and 1175.60 to 2131.80, respectively. Similar to the results of the analysis of variance carried out on the mean values of the aerodynamic properties of Charleston grey and Kaolack varieties, the means of the aerodynamic properties of Sugar baby variety were also significantly affected by the seed moisture content at p < 0.05. As was noted by,^[7] the increase in the terminal velocity of the seeds with an increase in the moisture content may be attributed to the increased mass of the seeds per unit frontal area presented to the air stream. In the design of pneumatic equipment for the seed varieties, it is important that the source of the air stream be designed such that the air velocity could be adjusted according to the moisture content of the seeds.

The results of the terminal velocity for the different varieties of watermelon seeds obtained in this study agree with published data for some seeds. As the moisture content of shelled sunflower seeds of four different cultivars increased from 6.2 to 14.4% dry basis (d.b.), the terminal velocity increased from 2.36 to 3.16, 2.22 to 3.06, 2.14 to 2.98, and 2.28 to 3.20 ms⁻¹ for NSFH-36, PSFH-118, GKSFH-2002, and SH-3322 cultivars, respectively.^[27] It was reported by^[7] that as moisture content of Makhobeli, triticale, and wheat seeds increased from 7 to 27% (wb), the measured terminal velocity increased from 4.52 to 5.07, 5.37 to 6.42, and 6.31 to 8.02 ms^–1, respectively. Furthermore,^[28] reported an increase in the terminal velocity of mung bean from 4.86 to 5.29 ms^–1 as the moisture content increased from 7.28 to 17.77% (d.b). Aerodynamic properties of pistachio nut was investigated by^[29] and it was reported that as the moisture content of the nut increased from 5.83 to 30.73% (wb), the terminal velocity also increased from 5.51 to 6.29 ms⁻¹; while^[30] reported that the terminal velocity of sunflower, soybean and canola seeds increased from 5.34 to 5.91, 10.16 to 10.38, and 5.10 to 5.32 ms^–1 as the seeds moisture content increased from 7.35 to 23.7, 9.52 to 24.64, and 7.11 to 25.72% (wb), respectively.

Previous studies by different researchers reported an inverse relationship between the drag coefficient and the moisture content of seeds which agrees with the result from this study. The inverse relationship may be due to differences in surface properties, true densities, shapes, and sizes of the seeds as the moisture content increased. It was reported by^[7] that the drag coefficient of Makhobeli, triticale, and wheat seeds decreased as moisture content increased; while^[27] reported a decrease in the drag coefficient of four different cultivars of unshelled sunflower seeds from 0.23 to 0.18, 0.31 to 0.20, 0.27 to 0.16, and 0.36 to 0.12 as the moisture content increased from 6.2 to 14.4% (d.b) for NSFH-36, PSFH-118, GKSFH-2002, and SH-3322 cultivars, respectively. For mung bean seed,^[14] reported that the drag coefficient decreased as moisture content increased while^[31] reported that the drag coefficient of coffee cherries (cv. Catual) decreased from 0.05 to 0.03 as moisture content increased from 10.7 to 53.9% (d.b).

The trend observed in the Reynolds number of the three varieties of the watermelon seeds investigated in this study as the moisture content increased was similar to that reported by^[30] for sunflower and soybean seeds. It was reported that the Reynolds number of sunflower and soybean seeds increased from 2226–2571 and 4379–4652, with increase in the seeds moisture content from 7.35 to 23.7 and 9.52 to 24.64% (wb), respectively. The Reynolds number of mung bean seeds also increased from 1494 to 2937 as the moisture content increased from 7.8 to 25% (d.b).^[14] Similar results were reported by^[32] on the terminal velocity, drag coefficient, and Reynolds number of sunflower seeds and kernels as the moisture content increased from 3 to 14% (d.b).

Regression Models

The data obtained from the investigation of the aerodynamic properties of the three varieties of the watermelon seeds at different moisture content levels were fitted into linear and non-linear models and the best fit was selected. Table 3 presents the models developed for the terminal velocity, drag coefficient, and Reynolds number of the seed varieties as a function of moisture content. The R² ranged from 0.98 to 1.00. Regression models in the form of polynomials were selected as the suitable models for predicting the aerodynamic properties of the seed varieties as a function of moisture content. In the study by,^[14] polynomial models were developed for the terminal velocity of mung bean seeds as a function of moisture content while linear models were developed for the drag coefficient and Reynolds number. A polynomial relationship was reported by^[6] to exist between the terminal velocity of wheat kernel and its moisture content;^[7] also developed a polynomial model to predict the terminal velocity of Makhobeli seeds as a function of moisture content. A linear relationship was reported by^[33] between the terminal velocity of Tef grain and its moisture content while^[31] developed a non-linear equation for the terminal velocity of coffee cherry and bean as a function of their moisture content and true density. A linear equation was used by^[34] to describe the relationship between the terminal velocity of pistachio nut and its kernel as a function of moisture content.

CONCLUSIONS

The aerodynamic characteristics of three varieties of watermelon seeds namely, Charleston grey, Kaolack, and Sugar baby, as a function of moisture content were evaluated and modeled. The terminal velocity and the Reynolds number generally increased with increasing moisture content while the drag coefficient decreased as the moisture content of the three varieties of the seeds increased. For Charleston grey, Kaolack, and Sugar baby varieties, the terminal velocity increased from 5.27 to 6.67, 4.40 to 6.23, and 4.00 to 6.60 ms⁻¹, while the Reynolds number increased from 2054.21 to 2956.16, 1325.33 to 2094.82, and 1175.60 to 2131.80, respectively. The drag coefficient however decreased from 0.83 to 0.72, 1.14 to 0.86, and 1.28 to 0.72 for Charleston grey, Kaolack, and Sugar baby, respectively, as the moisture level increased. Analysis of variance showed that the aerodynamic properties of the seed varieties were significantly affected by the moisture content (p < 0.05). Mathematical models with high determination coefficient ranging from 0.98–1.00 were developed to predict the aerodynamic properties of the three varieties of the seed as a function of moisture content. The results from the study suggest that the aerodynamic characteristics of the three varieties of the watermelon seeds can be significantly influenced by variation in the moisture content following a polynomial relationship.