Figure 1 shows the relation between the drying time and ambient temperature for a typical epoxy (ET5660) and vinyl-acrylic based paint (VINALITE 531) [3]. The drying-time, which forms a large portion of the time duration for the painting process, decreases with increase in air temperature in the painting space. In addition, the surface to be painted usually requires a relative humidity of less than 80%; if this condition is not satisfied, the paint develops problems such as wrinkling, peeling, bubbling, and cracking.

Figure 1: 
Variation in drying time of epoxy ET5660 and vinyl-acrylic based paint VINALITE 531, according to surface temperature

Figure 2 shows a psychrometric chart of the mean daily temperatures and humidity for workspace locations in the Gunsan area for the year 2013. The average temperature ranges from −5 °C with a relative humidity greater than 50% in winter to 30 °C with a relative humidity greater than 80% in summer. Therefore, the air in the painting spaces needs to be heated in the winter, spring, and autumn, and dehumidified in the summer.

Figure 2: 
Average daily temperatures and humidity in the Gunsan area in 2013.

Table 1 compares the costs of energy sources that were generally used in the Gunsan area during the year 2015: electricity, LNG, LPG, diesel, and kerosene. Kerosene, which is the most expensive, is 2.38 times as expensive as electricity, which is the cheapest, for the same thermal energy. Electricity also has advantages over gas and oil in terms of safety, system simplicity, and system management. Therefore, electricity is a strong candidate among the available energy sources for controlling the environment in the present system.

The average energy i_r needed to heat and dehumidify a unit of the painting space air from the environmental to the desired conditions during a period is obtained as follows:

where i_t and i_d are the target and environment enthalpies of the air, respectively, and n is the number of days considered in the period.

Figure 3 shows the average monthly heating load required to reduce the drying time of epoxy ET5660 by 20% in winter in the Gunsan area. The load Δi varies monthly in small increments, and the maximum is about 2.45 kJ/kg in July. In summer, the relative humidity can be reduced by heating or dehumidifying the air.

Figure 3: 
Comparison of energy required to control the temperature of the workspace to reduce the drying time of epoxy ET5660 by 20% in the Gunsan area in 2013.

Figure 4 shows the average monthly heating and dehumidifying energy loads that was needed to satisfy the 80% relative humidity requirement during the year 2013. The loads for the air vary monthly, and the maximum load required for dehumidifying was 5.86 kJ/kg in July. The energy needed for heating the air, to meet the requirements of the painting process from June to September, is about 40% of that for dehumidifying the air. Heating is useful for warming the air in all the seasons and for decreasing the relative humidity in summer. Therefore, electric heating devices are a very good choice from the perspectives of saving energy and capital costs as well as for mobility in the present system.

Figure 4: 
Comparison of energy required to control the humidity of the workspace by heating and dehumidifying, in order to satisfy the relative humidity requirement of 80% in the Gunsan area in 2013.

Impinging jets are widely used to control the temperature of surfaces exposed to an open space, because they provide high heat transfer coefficients. In the present case, the thickness of a steel sheet for a ship block is approximately 20 mm, and the thickness of the paint is approximately 0.1 mm. Therefore, the heat capacity of the paint layer is negligible compared to the steel sheet. Figure 5 shows the lumped thermal model of the present study for painting an object, usually a steel sheet, which is heated on one side and exposed to open space on the other. It is assumed that a cold steel sheet of thickness t_s [m] in air at ambient temperature T_o is fed at a constant rate A˙s [m²/s], and the impinging jet heats it to the target temperature T_t uniformly. This process requires thermal loads on the moving steel sheet and impinging jet. The net thermal energy q_s needed to heat the sheet to the target temperature can be calculated as follows:

Figure 5: 
Schematic diagram of the thermal model for painting an object using convection on both sides.

where ρ_s and c_p,s are the density and heat capacity of the steel sheet, respectively.

As shown in Figure 5, the ambient air at temperature T_o is heated to temperature T_i by applying q_i , and the air with velocity u is ejected from the nozzle of the impinging jet with diameter D onto the steel sheet. The air from the jet on one side of the steel sheet, and the still air on the other side, have heat transfer coefficients h_n and h_o, respectively. The thermal resistances include the convection thermal resistance caused by the impinging jet, the conduction resistance of the steel sheet, and the natural convection thermal resistance on the opposite side. The Biot number of the steel sheet based on the thickness, h_nt/2k_s, is about 0.004 for heat transfer coefficient h_n = 100 W/m²·K, even under severe conditions. Therefore, the steel may be considered as a lumped system whose temperature is almost constant along the thickness direction, i.e., T_s,1 ≈ T_s,2 ≈ T_s. The steel sheet is heated continuously from the ambient temperature T_o to the target temperature T_t, and therefore the average temperature of the steel sheet is assumed to be an arithmetic average in the present work:

The heat transfer coefficient for natural convection in stagnant air is about 5 W/m²·K. Therefore, the configuration of the impinging jet is very important to the heating speed of a steel sheet, and hence, the drying speed of the paint. The energy balance and heat transfer equations are given below:

where q_n and q_o are the heat transfers from the impinging jet to the steel sheet and from the steel sheet to the ambient air, respectively. If we assume natural convection for the air on a vertical disk with radius R, which is a specified heated zone, the heat transfer coefficient on the open space side can be expressed by the Churchill and Chu correlation [7]:

where Nu_o, Ra_o, and Pr are the Nusselt, Rayleigh, and Prandtl numbers, respectively, and ρ_a, β_a, κ_a, μ_a, and R are the density, thermal expansion coefficient, thermal conductivity, viscosity of the air, and radius of the steel respectively.

The thermal load at the nozzle achieves the desired impinging jet temperature from the ambient air, as given below:

where D and u are the nozzle diameter and air velocity of the impinging jet, respectively.

In the present work, the energy efficiency is defined as the ratio of the heat transferred to the steel sheet over the thermal load at the nozzle:

The efficiency depends strongly on the thermal resistance, i.e., the convection heat transfer coefficient between the impinging jet and the painting surface.

The heat transfer coefficient of the impinging jet is a major parameter in the thermal resistance. Goldstein [8] expressed the average Nusselt number of the normal impinging jet on a steel sheet as

where A = 24, B = 533, C = 44, n = 1.285, and L, D, and R are the distance between the nozzle and object, nozzle diameter, and radius of the object (a steel sheet in the present work), respectively. The Nusselt and Reynolds numbers for the nozzle are defined as

where h_n is the average heat transfer coefficient on the surface of the object.

There are various shapes of ship blocks; therefore, the model ship block to be painted is considered to be a steel disk with a 20 mm thickness and 1 m radius (R). Figure 6 shows the graph of the heat transfer coefficient versus the distance between the nozzle and object for various nozzle diameters and air velocities. The heat transfer coefficient is a function of the distance, diameter, and velocity, and shows a maximum value at a certain distance. The maximum heat transfer occurs at L/D = 7.78, as expressed in Equation (12).

Figure 6: 
Heat transfer coefficient versus distance between the nozzle and object for various nozzle diameters and air velocities for a 1 m-radius disk.

Figure 7 shows the net heat transfer rate as a function of the nozzle diameter and air velocity of the impinging jet. In this comparison, the ambient and nozzle temperatures and the ratio of the distance to the object over the nozzle diameter are fixed as 10 °C, 70 °C, and L/D = 7.76. The assumed steel feeding rate is 0.04 m²/s, which is estimated from the surface area that is painted monthly in the field. From the figure, the net heat transfer rate increases as the nozzle diameter and velocity increase, and the maximum net heat transfer rate is obtained at a nozzle diameter of 0.3 m. Figure 8 shows the graph of energy efficiency versus the nozzle diameter for different velocities. In fact, the efficiency increases as the nozzle diameter and velocity decrease. For given operating conditions of steel-feeding velocity and air and steel target temperatures, a small diameter and low velocity, with L/D ≈ 7.76, are recommended for maximum efficiency in the present study.

Figure 7: 
Net heat transfer versus nozzle diameter for 3 nozzle velocities under conditions of T_o = 10℃, T_n = 90℃ , A˙ = 0.04m², t_s = 0.02m, and L/D = 7.76

Figure 8: 
Energy efficiency versus nozzle diameter for 3 nozzle velocities under conditions of T_o = 10℃ , T_n = 90℃ , A˙ = 0.04m², t_s = 0.02m, and L/D = 7.76