A Parametric Study of a Multi-Slot Air Knife for Coating Thickness Reduction

Abstract

This paper presents an investigation of the gas jet wiping process, which is used in the continuous galvanizing line to control the Zn-alloy coating thickness on steel substrates. In this study, a novel configuration of a multi-slot air knife was used as the wiping actuator in a parametric study of the gas jet wiping process. The main goal of the study was to identify the operating window in which lighter coating weights can be achieved with the multi-slot air knife at higher strip velocities. A laboratory scale wiping apparatus was designed and manufactured and the effects of various operating conditions, such as: main and auxiliary jet Reynolds numbers, strip velocity and jet-to-substrate distances on the final coating thickness were determined. Numerical simulations of multi-slot jet wiping were also performed under the same operating conditions using computational fluid dynamics modeling to estimate the pressure and shear stress profiles along with analytical models of the coating thickness to compare with the experimental measurements.

It was observed that the experimental measurements, under different operating conditions for the multi-slot air knives, agreed with the coating weight predictions of analytical models available from the literature. The results showed that the coating weight produced by the multi-slot air knife, with a relatively low flow for the auxiliary jet (i.e. Re_a/Re_m ≤ 0.5), was lower than the final coating weight under similar main jet Reynolds from a single slot nozzle. Conversely, when Re_a/Re_m ~ 1, lower pressure gradient distribution found in the wiping region and consequently increasing the coating thickness.

1. Introduction

In the steel manufacturing industry, ferrous substrates are protected against corrosion by applying a sacrificial layer of zinc to the steel surface through continuous hot dip galvanizing. In this process, the substrate is continuously immersed in a bath of molten zinc at 460°C¹⁾ and, when it is withdrawn from the bath, the strip will be covered with a relatively thick liquid film. In order to reduce the coating thickness of the film to the target thickness, a pair of impinging slot gas jets (or air knives) are located above the bath to remove the excess zinc from the steel strip (Fig. 1). The pressure gradient (dp/dx) and shear stress (τ) applied to the liquid film by the gas jets controls the final film thickness above the air knife, and most of the liquid returns to the bath as a runback flow. The gas jet wiping process leads to a relatively thin coating thickness – typically on the order of 10–20 μm in the case of automotive applications - with a relatively smooth surface. The final coating thickness, h_f, depends on the steel strip velocity (V_s), wiping pressure (P_s), nozzle exit to strip standoff distance (Z), the nozzle slot width (D) and liquid properties such as density (ρ_cL) and viscosity (μ).^{2,3,4,5,6,7,8)}

Fig. 1.

Schematic of the gas jet wiping process. (Online version in color.)

Thin steel sheet products are generally used by the automotive industry for either structural members or closure panels. A recent trend within the automotive industry has been to reduce the zinc coating weights applied to the thin sheets, as part of industry efforts to reduce the overall mass of the body-in-white and reduce costs.⁹⁾ Currently, a single slot air knife configuration is commonly used as the wiping actuator in continuous galvanizing lines (CGLs) for controlling the film coating thicknesses. There are numerous experimental and numerical studies available in the literature to model and characterize the wiping ability of the conventional single slot impinging jet.^2,3,4,6,7,8) The wiping pressure must be increased significantly to obtain lower coating weights using the single slot air knife at reasonable strip velocities. However, increasing the pressure can cause some industrial difficulties such as higher tonal noise generation,^13,14) splashing¹⁵⁾ and coating non-uniformity.⁹⁾ Currently, to cope with such problems, the steel strip velocity is limited to lower values in the CGL, which can adversely affect CGL productivity and costs.

As an alternative approach, the multi-slot air knife, has been recently investigated as the wiping actuator in the CGL instead of the traditional single slot jet. In order to modify the final coating quality and stabilize the substrate to lessen lateral vibrations between the jets, Tu¹⁶⁾ filed a patent and proposed a variety of new air knife designs with dual nozzles for application in the CGL. In all instances, the apparatus comprised a primary stripping jet for wiping and an adjacent smoothing jet. In this patent, the smoothing jet stream impinged on the coating at a low pressures sufficient to smooth the coating whereas the stripping jet impinged at higher pressures sufficient to reduce the thickness of the smoothed layer to a desired target thickness.

Two of the proposed configurations, a main jet with an inclined auxiliary impinging slot jet and two parallel impinging slot jets,¹²⁾ were studied numerically by Tamadonfar et al.¹⁷⁾ The maximum wall pressure gradient and shear stress distribution profiles were obtained for these two configurations. These were then implemented in the coating model developed by Elsaadawy et al.¹⁸⁾ in order to calculate the final coating thickness. Tamadonfar et al.’s numerical results¹⁷⁾ did not show any advantage in using these novel configurations over the single slot air knife in term of coating thickness reduction.

Kim et al.¹⁹⁾ subsequently proposed an innovative multi-slot jet design for application in the CGL to address the splashing problem and reduce surface irregularities due to jet fluctuations. The proposed air knife consisted of one main jet and four symmetrically situated, inclined auxiliary jets discharging air at lower velocities versus the main slot jet. The intent of the patent claim was that, in the proposed multi-slot design, the gas discharged from the main and auxiliary jets provided the necessary force for wiping excess molten zinc from the sheet, where the auxiliary jets were used to prevent splashing by mixing the gas streams of the main jet and auxiliary jets, resulting in a lower speed of the jet wall along the length direction of the substrate. Tamadonfar et al.²⁰⁾ subsequently numerically simulated a multi-slot jet composed of a main jet and two symmetrically situated auxiliary jets adjacent to the main jet. The range of simulated flow conditions in the studies of Tamadonfar et al.²⁰⁾ were limited to one slot jet gap, and one main and auxiliary jet Reynolds number (Re = 11000). In this case, no significant benefits with respect to coating weight reduction were realized as this configuration decreased both the maximum pressure gradient and maximum wall shear stress applied to the coating.

Alibeigi et al.²¹⁾ experimentally investigated the wall pressure distribution of the multi-slot jet configuration of Tamadonfar et al.¹⁶⁾ under wider variety of operating conditions (Re_m, Re_a, Z/D) and compared the results with the numerical simulations of Tamadonfar et al.,^17,20) where appropriate. The comparison showed some disagreements on the maximum wall pressure and pressure distribution between the two studies. The simulated stagnation pressure was higher than the experimentally derived value and the simulated maximum pressure gradient was also higher than the experimental result.

Finnerty et al.,²²⁾ experimentally studied the effect of auxiliary jets on tonal noise reduction originating from aeroacoustics feedback using the multi-slot air knife geometry of Alibeigi et al.²¹⁾ In this study, the main jet velocity was held at 250 m/s for all experiments and auxiliary jet flows were varied between zero and 60 m/s in 20 m/s intervals. The authors showed that the prototype multi-slot air knife was able to decrease the magnitude of the tonal noise to the point of near complete suppression when the auxiliary jet velocity was set at 0.25 V_m or greater.²²⁾ They also showed that the auxiliary jets also introduced broadband noise at low frequencies which was not of sufficient magnitude to present a hazard to CGL workers.

Yahyaee Soufiani et al.²³⁾ investigated the fluid flow of the prototype multi-slot jet configuration of Alibeigi et al.²¹⁾ discharging air on a moving substrate. Computational fluid dynamics were applied to predict the wall pressure and wall shear stress distributions of the multi-slot air knife, and the results were then used in the analytical model of Elsaadawy et al.¹⁸⁾ to estimate the final liquid zinc thickness on the substrate. Takeda et al.^24,25) also investigated the gas wiping process using a three-slot air knife. This study focused on the mixing process of the jets and the distribution of the impinging pressure of the mixed jet. Both studies determined that, at high auxiliary jet velocities, the impinging pressure gradient became more moderate and the wiping performance deteriorated. However, the wall pressure gradient for the Alibeigi et al.¹⁷⁾ multi-slot nozzle using low auxiliary jet velocities (35% of the main jet velocity) increased and made it possible to reduce the coating weight versus the single slot jet configuration.^23,24) A similar trend was reported for shear stress distribution in the wiping region with lower auxiliary jet velocities which reduced the final coating thickness.^23,24)

More recently, Yahyaee Soufiani et al.²⁶⁾ experimentally investigated the applicability of the Elsaadawy et al.¹⁸⁾ analytical coating weight model for wiping via the multi-slot jet geometry and examined the effects of the multi-jet geometry process variables on the final coating thickness. The experimental measurements, under different knife geometries and process conditions, agreed with the coating weight predictions of the analytical model of Elsaadawy et al.¹⁸⁾ Under the investigated operating conditions, it was determined that decreasing the auxiliary jet width such that D_a/D ≤ 1 and operating the auxiliary and main jets such that Re_a/Re_m 0.5, increased the pressure gradient through providing a higher pressure gradient while the maximum pressure remained constant and resulted in a lower final coating thicknesses for the multi-slot air knife wiping versus the single slot geometry.

As mentioned above, the multi-slot jet proposed by Alibeigi et al.²¹⁾ has been shown to be a promising design alternative to overcome some of the limitations of the single slot air knife. However, the effect of operating conditions for the proposed multi-slot jet air knife on final coating thickness have not been determined. The current research focuses on determining effect of the operating conditions of the multi-slot jet on the final coating weight. In this study, the conventional single slot jet geometry was used as a base case for comparing the coating weight data on a moving substrate with those obtained using the multi-slot air knife configuration.

2. Film Thickness Model

The final film thickness can be predicted based on lubrication theory, in which the inertia term in the momentum equation is assumed negligible compared to pressure, gravity and viscosity.²⁾ The Navier-Stokes equation can be then further simplified based on the following assumptions:

The coating flow can be assumed to be incompressible, steady state and with constant viscosity.^2,3) The effects of oxidation, surface tension and surface roughness are also assumed to be negligible¹⁸⁾ and the no-slip condition for the liquid on the steel strip is assumed applicable. The simplified momentum equation, as a result, balances viscous forces with pressure and gravity forces (Eq. (1))   

$$\mu \frac{{\partial }^{2}u}{\partial y^2}-\left(\rho g+\frac{dp}{dx}\right)=0$$(1)

By applying the no slip condition at the strip and the jet shear stress at the liquid surface as the boundary conditions, the velocity profile of the coating liquid can be written as:   

$$u=\frac{1}{2}\frac{\rho g}{\mu }{y}^2-\frac{\rho gh}{\mu }y+V_s$$(2)

By introducing the non-dimensional film thickness $\left(H=h\sqrt{\frac{\rho g}{\mu V_S}}\right)$, non-dimensional shear stress, $\left(S=\frac{\tau }{\sqrt{\rho \mu V_{S}g}}\right)$, and non-dimensional pressure gradient, $\left(G=1+\frac{1}{\rho g}\frac{dp}{dx}\right)$, the non-dimensional liquid volumetric flux, Q, can be derived as:²³⁾   

$$Q=-\frac{G{H}^3}{3}+\frac{S{H}^2}{2}+H$$(3)

The non-dimensional film thickness, H, corresponding to the maximum withdrawal flux (Q_max) can be determined by setting $\frac{dQ}{dH}=0$ and employing the quadratic formula⁵⁾ to solve for H, such that:   

$$H=\frac{S\pm \sqrt{S^2+4G}}{2G}$$(4)

Upon solidification of the coating liquid, the film velocity is equal to the substrate velocity (V_s) and the final coating thickness, h_f, is given by:   

$$h_f={\displaystyle \frac{q}{V_S}}={\displaystyle \frac{Q_{max}}{\sqrt{{\displaystyle \frac{\rho g}{\mu V_S}}}}}$$(5)

The shear stress distribution and pressure gradient along the wall can be used with Eqs. (4) and (5) to estimate the final coating thickness on a moving substrate. In the present work, the pressure gradient and shear stress distributions induced in a static wall by a conventional single-slot and the prototype multi-slot air knife designs were predicted through numerical simulations. The predicted final coating thickness was then compared with experimental measurements, to be described in section 6.

3. Numerical Modeling

For determination of the air flow through the slot jets, the Reynolds-Averaged Navier-Stokes (RANS) equations (Eqs. (6) and (7)) were used with the pressure-based solver and the SIMPLE method for pressure-velocity coupling.   

$$\frac{\partial \left(\rho {\overline{u}}_i\right)}{\partial x_i}=0$$(6)

  

$$\frac{\partial \rho {\overline{u}}_i{\overline{u}}_j}{\partial x_i}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_i}\left[\mu \left(\frac{\partial {\overline{u}}_i}{\partial x_j}+\frac{\partial {\overline{u}}_j}{\partial x_i}\right)-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right]$$(7)

The Reynolds stress $-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ was modeled using the Boussinesq hypothesis, and the two-equation model for the standard k-ε model was used to determine the turbulent viscosity, μ_t. The discretized equations were iterated until the root-mean-square (RMS) residuals for all governing equations were less than 10⁻⁶.

Schematics of the single and multi-slot nozzle geometries used are illustrated in Fig. 2. In order to validate the numerical modelling results with the experimental measurements of Tu and Wood¹¹⁾ and the previous multi-slot jet experiments of Alibeigi et al.,²¹⁾ the following geometric parameters were fixed: auxiliary jet width (D_a) at 3 mm, the distance between the exit of the main and auxiliary jets (s) at 20 mm, and the main jet slot width (D) at 1.5 mm. The inclination of the auxiliary jets relative to the main jet centerline was 20°. The boundary conditions were the no slip condition at the impingement surface and nozzle walls, a pressure inlet at the nozzle inlets and a pressure outlet at the exit of the computational domain. The inlet pressure (P_s), was used to estimate the flow velocity of the jet exiting the nozzle using Eq. (8).²⁷⁾   

$$U=c\sqrt{\frac{2}{\gamma -1}\left[{\left(\frac{P_s+P_{\infty }}{P_{\infty }}\right)}^{\raisebox{1ex}{$\gamma -1$}\!\left/ \!\raisebox{-1ex}{$\gamma $}\right.}-1\right]}$$(8)

Fig. 2.

Schematic of the single slot (left) and multi-slot air knife (right) with definitions for the jet geometric parameters.

Where P_∞ is the ambient pressure, γ is the ratio of specific heats of air, and c is the speed of sound (343 m/s).

The mesh used for the impinging jets was comprised of a mixture of quadrilaterals and triangles. Grid clustering was used adjacent to the wall and around the jet centerline, where large gradients in the velocity field, pressure field and turbulent parameters were expected. Four grids with 252000 to 393000 nodal points, depending on the nozzle plate-to-main jet width (Z/D, Fig. 2) ratio,²³⁾ were tested to verify the mesh independence of the numerical results. In the near wall region, the mesh was refined such that the first node was located in the viscous sub-layer (y+~1) and the mesh size near the wall was approximately 4 μm. The computational domain size was defined as –85 ≤ X/D ≤ +85.

Numerical simulations were benchmarked against experimental wall pressure distribution for different wall to jet ratios (4 ≤ Z/D ≤ 12) at Re_m = 11000. Figure 3 presents a comparison of numerical non-dimensional wall pressure profiles versus the experimental data of Tu and Wood¹¹⁾ for a single-slot planar impinging jet as function of Z/D. It can be seen that the predicted pressure distributions were in good agreement with the experimental data. Figure 4 shows a comparison of the numerical wall pressure profile versus the experimental data of Alibeigi et al.²¹⁾ for a the multi-slot impinging jet where Re_m = Re_a = 11000. From Fig. 4, it can be seen that the numerical models of the multi-slot jet geometry also agreed with the experimental measurements.

Fig. 3.

Comparison of numerical non-dimensional wall pressure profiles at Re = 11000 and 4 ≤ Z/D ≤ 12 with the experimental measurements of Tu and Wood.⁷⁾

Fig. 4.

Comparison of numerical wall pressure distributions with experimental measurements of Alibeigi¹⁷⁾ for multi-slot air knife at Re_m = 11000, Re_a = 11000 and 4 ≤ Z/D ≤ 12.

4. Experimental Facility

A schematic of the prototype multi-slot air knife used in the experimental measurements is presented in Fig. 5. The multi-slot air knife consists of three jets, one main jet and two auxiliary jets symmetrically located on each side of the main jet. The main jet was situated perpendicular to the moving strip and the auxiliary jets were inclined at 20° from the main jet centerline. The prototype multi-slot air knife had three separate chambers and each had an individual plenum and valve to allow independent control of the plenum pressure of each nozzle. Compressed air from a 550 kPa blower was used to feed the auxiliary jets and the main nozzle was supplied with a resident 550 kPa compressed air line. For the main jet, air was passed through a regulator and two filters to prevent any particulates entering the main nozzle. An electric valve was also used immediately after the filter to adjust the main jet pressure. In the case of the auxiliary jets, the air supply was passed through a 5 cm regulator valve, a 5 cm ball valve and a 5 cm gate valve prior to entering a T manifold, where three 2.5 cm globe valves were used to adjust the pressure for each of the auxiliary nozzles. For all of the nozzles, air entered each plenum via a 25.4 mm diameter pipe at the top of the plenum, passed through a flow distributor tube (Fig. 5) and then passed through a series of mesh screens located upstream of the nozzle contraction in order to break up any large-scale turbulent structures (Fig. 5), where the screens comprised stainless steel cloth with a density of 28 wires/cm. Finally, the air exited the nozzle at 90° to its inlet direction. To adjust the distance between the nozzle and the plate – i.e. the Z/D ratio – the prototype multi-slot air knife was mounted on a computer controlled traverse system consisting of a VXM-3 Velmex™ power supply with a Slo-syn stepper motor with a minimum step division of 5 μm. Validyne DP-15 pressure transducers were used to measure the plenum pressure upstream of each jet centreline and prior to the nozzle contraction (Fig. 5) and the data logged using a conventional data acquisition system and a LabVIEW program.

Fig. 5.

Isometric view of the prototype multi-slot air knife.

A cold laboratory-scale model of the continuous galvanizing gas jet wiping process was designed and manufactured (Fig. 6) with the objective of validating the numerically modelled coating weights for the prototype multi-slot air knife.

Fig. 6.

Schematic diagram of the experimental setup. (Online version in color.)

The experimental gas jet wiping apparatus consisted of a vertical stainless steel strip, 50 cm long and 5 cm wide, stretched between two rolls. An electric motor connected to the upper shaft and the upper roll provided the strip motion. The strip velocity was adjusted in the range of 0.5–3.5 m/s by means of an AC to DC speed controller connected to the electric motor. The strip velocity was measured by means of optical and mechanical tachometers with an accuracy of ± 0.05% and a resolution of 0.1 rpm (for the test range of 2 to 9999.9 rpm). The lower roll was designed to be adjustable to allow for the provision of adequate strip tension. The lower roll was immersed in the model working fluid, mineral oil, the properties of which are documented in Table 1. Table 2 compares the range of non-dimensional parameters characteristic of the molten Zn used in the continuous galvanizing line²⁸⁾ versus the apparatus used in the current study. It can be seen that the range of parameters are in satisfactory agreement and, thus, sufficient dynamic similarity was thought to have been established between the laboratory apparatus and the continuous galvanizing line.

Table 1. Working liquid properties in the experimental facility.³⁰⁾

Liquid	Density (kg/m3)	Kinematic Viscosity (m2/s)	Surface Tension (N/m)
Mineral Oil	865	10−5	0.0323

Table 2. Non-dimensional characteristic parameters for the experimental working fluid and the molten Zn alloy used in industrial CGLs.

Similarity Parameters	Continuous Galvanizing Line23)	Experimental Apparatus
G	35–200	77–296
S	1–10	3.9–6.7
h/ho	0.02–0.06	0.019–0.055
Refilm	20–100	1.9–10.2
We	0.3–1.5	0.51–1.48

The gas jet wiping devices tested using this apparatus were the single and multi-slot air knife discussed in the previous section and pictured in Figs. 5 and 6. The multi-slot air knife was positioned 75 cm above the free surface of the liquid bath perpendicular to the strip. Based on the conducted numerical simulations (Figs. 3, 4, 9 and 10), the air knife impingement zone region is in the range of 5 ≤ X/D ≤ 15 which is equal to 7.5 ≤ X ≤ 22.5 mm. Beyond this region, the wall jet pressure profile and the wall shear stress distribution go all the way down to zero, In all the experiments, the air knife was positioned high enough (75 cm) above the free surface of the liquid bath to make sure it has no effect on the free surface of the oil and the belt viscous drag.

Fig. 9.

Non-dimensional wall pressure distributions for different Re_a, with Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Fig. 10.

Non-dimensional a) wall pressure gradient distributions and b) shear stress distribution for different Re_a, with Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

The air knife width was 5 cm longer than the strip width to avoid edge effects. The mineral oil was wiped on only one side of the strip, as pictured in Fig. 6. The main jet to substrate distances and strip velocities used in the experiments were 8 ≤ Z/D ≤ 12 and 0.25 ≤ V_s ≤ 1.5 m/s.

After the substrate passed the through the wiping region, the liquid film remaining on the steel strip was removed by two inclined rubber blades or “squeegees” (Fig. 6). Once steady state was stablished, a digital balance with an accuracy of ± 0.01 g measured the mass of the collected liquid during the 300 s collection period, as measured by a chronometer. The mean liquid film thickness, h_f, was determined through the mass flow rate of liquid removed from the strip during the collection period using Eq. (9):   

$$h_f={\dot{m}}_{cl}/({\rho }_{cl}{L}_s{V}_s)$$(9)

Each experiment was repeated four times. According to Coleman and Steels,²⁹⁾ the overall uncertainty of a discrete dependent variable (r), which is function of j independent measured variable X_i can be found using the Kline and McClintok method given as:   

$$\delta r=\sqrt{\sum _{i=1}^j{\left({\theta }_i\left(\delta X_i\right)\right)}^2}$$(10)

where ${\theta }_i=\frac{\partial r}{\partial X_i}$ and δX_i are the uncertainty for each measured variable. The uncertainty in the mean value of a measured X_i is given by $U_{X_i}=\sqrt{B_{X_i}^2+P_{X_i}^2}$ where B is the instrumental bias error and P is precision (random) error. The random error of the mean was calculated through the student t-distribution at the 95% confidence level and instrumental error was found through manufacturers’ specifications.

5. Results and Discussion

In this section, the properties of the prototype multi-slot air knife shown in Fig. 5 were experimentally determined. The effect of the plate-to-nozzle ratio (Z/D), which ranged between 8 and 12, the main jet Reynolds number of between 7000 and 11000, and the auxiliary jets Reynolds number of between 3000 and 11000, on the final coating weight will be discussed. The main jet width (D), auxiliary jet width (D_a) and the auxiliary jet offset (s) were fixed at D = 1.5 mm, D_a = 1.5 mm (i.e. D_a/D = 1) and s = 10 mm, respectively, as it had been previously shown by the present authors that this configuration of the multi-slot air knife led to lighter coating weights compared to the traditional single slot air knife.²⁶⁾ By adjusting the pressure of the jet nozzles, P_s, the velocity of main jet was changed from 70 m/s to 110 m/s, and the velocity of auxiliary jets were changed from 30 to 110 m/s. The total wiping energy per unit time and unit length of strip, E_w (Eq. (11)), was used for comparing the different case studies.   

$$E_w=P_s{q}_a=P_s{V}_{j}A$$(11)

where A is the nominal jet exit cross sectional area, V_j is the jet exit velocity and q_a is the volumetric air flow rate for each jet. The energy taken into account for the multi-slot air knife (E_total) is the algebraic sum of the energies of the main and the auxiliary jets.

5.1. Effect of Auxiliary Jet Reynolds Number (Re_a)

The effect of Re_a on the coating weight was investigated experimentally and results are compared with analytical model developed by Elsaadawy et al.¹⁸⁾ Re_a was varied between 3000 and 9000 whilst the main slot jet Reynolds number was fixed at Re_m = 11000. According to Fig. 7, the Elsaadawy et al.¹⁸⁾ model predicted the trends seen in the experimental measurements. The slight discrepancy between the model and the experimental measurements (especially at higher strip velocities) can be attributed to two sources of systematic errors; 1) the inefficiency of the wiping scrapers in removing all of the oil from the belt and 2) the splashing of oil from the belt, particularly at the upper pulley (Fig. 6). The latter source of error was observed for strip velocities of V_s ≥ 0.75 m/s. Based on a comparison of the free meniscus coating measurements versus the analytical model developed by Thornton and Graff,²⁾ it was estimated that 1.8% of the oil was left behind due to scraper inefficiency and that the contribution of splashing was 3.2%–5.8% (depending on the strip velocity) to the observed discrepancies between of the experimental measurements versus the analytical model.

Fig. 7.

Effect of auxiliary jet Reynolds number on final coating weight at Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm for a) Re_a = 3000, b) Re_a = 5000, c) Re_a = 7000 and d) Re_a = 9000.

Figure 8 shows the non-dimensional predicted final coating thickness (h_m/h_s) using the Elsaadawy et al. model¹⁸⁾ as a function of Re_a for the experimental range of strip velocities (V_s). In Fig. 8, h_m and h_s represents the predicted final coating thickness for the multi-slot and single jets, respectively. According to the shaded area shown in Fig. 8, there was an operating window at lower auxiliary jet Reynolds numbers, -i.e. Re_a/Rem ≤ 0.5 which resulted in lower coating weights compared to the single slot jet (i.e. h_m/h_s < 1) for the same main jet Reynolds number and the same main jet slot width. It should also be noted that this trend was insensitive to changes in strip velocity within the range explored experimentally (Fig. 8).

Fig. 8.

Predicted final coating weight using the Elsaadawy et al. model¹⁴⁾ as a function of Re_a for Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm and 0.5 ≤ V_s ≤ 1.5 m/s.

This can be explained by examining Figs. 9 and 10, which compare the wall pressure profiles the wall pressure gradient and the wall shear stress distributions for the single and multi-slot air knife at different Re_a, respectively. It can be seen that, at higher Re_a, a greater value for the maximum non-dimensional pressure can be achieved for the multi-slot air knife (Fig. 9). However, by increasing Re_a the wall pressures for (X/D ≥ 1) also increased and led to a wider pressure profile (Fig. 9). Thus, the value of the wall pressure profile gradient was decreased in the vicinity of the wiping region at higher Re_a (Fig. 10(a)). The same trend can be observed in Fig. 10(b) for the wall shear stress distribution. Conversely, at the lower Re_a of 3000, the auxiliary jets contributed to the wiping action by increasing of the maximum pressure while the pressure profile gradient was very similar to that of the single jet profile for the X/D ≥ 1 region (Fig. 10). Furthermore, Fig. 10 shows that a higher maximum pressure gradient and maximum wall shear stress were be achieved for lower values of Re_a (Fig. 10) and, therefore, lower coating weights would be expected.

In order to elaborate the spreading of the multi slot jets at higher auxiliary jet Reynolds numbers (Re_a), the turbulent kinetic energy distribution of the multi-slot air knife is compared in Fig. 11 for Re_a = 3000 and Re_a = 9000 while the main jet Reynolds number and the jet to strip distance were fixed at Re_m = 11000 and Z/D = 12, respectively. According to Fig. 11, at higher auxiliary jet Reynolds number (i.e. Re_a = 9000), due to considerable velocity difference between the auxiliary jets and the stationary ambient air, higher turbulent kinetic energy was observed in vicinity of the auxiliary jets. As a result the width of multi-slot air knife increased for Re_a = 9000 (−5 ≤ X/D ≤ 5) compared with Re_a = 3000 (−1.5 ≤ X/D ≤ 1.5). Therefore, at lower auxiliary jet Reynolds numbers, the diffusion of the main jet can be suppressed and a sharper pressure profile with higher pressure gradient could be obtained, as it illustrated in Figs. 9 and 10.

Fig. 11.

Turbulent kinetic distribution of multi-slot air knife at Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm, s = 10 mm for a) Re_a = 3000 and b) Re_a = 9000. (Online version in color.)

Figure 12 compares the experimentally measured coating weights at different strip velocities as a function of auxiliary jet Reynolds number (Re_a) for Re_m = 11000 and Z/D = 12. Figure 12 also confirms that lower coating weights can be obtained with a relatively low Re_a. Conversely, when the auxiliary jet Reynolds numbers approached that of main jet, the wiping ability of the multi-slot jet decreased and, consequently, the final coating weight increased versus the single slot jet configuration. This can be attributed to the higher pressure gradient and the higher wall shear stress in the wiping region for Re_a/Re_m ≤ 0.5 which was observed in Fig. 10. It can also be seen from Fig. 12 that for all Re_a the coating weight increased with increasing substrate velocity.

Fig. 12.

Effect of auxiliary jet Reynolds number on experimentally measured coating weights at Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm, s = 10 mm and 3000 ≤ Re_a ≤ 9000.

Figure 13 shows the experimentally measured coating weights on the moving strip as a function of strip velocity (V_s) and auxiliary jet Reynolds number, Re_a, for Re_m = 11000 and Z / D = 12. According to Fig. 13, the experimentally measured coating weight data also confirmed that, for the lower auxiliary jet Reynolds number of Re_a = 3000, at higher strip velocities (V_s = 1.5 m/s), lighter coating weight can be achieved compared to the single slot air knife.

Fig. 13.

Comparison of experimentally measured coating weight for multi-slot jet at different strip velocities, Re_m = 11000, Re_a = 3000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm with single slot jet at Re_m = 11000, D = 1.5 mm and Z/D = 12.

The coating thickness reduction observed at the low auxiliary jet Reynolds number can be discussed from the energy point of view. Figure 14 shows the final coating weight versus the non-dimensional total input wiping energy in the multi-slot air knife calculated using Eq. (12). In this figure, the main jet Reynolds number was fixed at Re_m = 11000 while the auxiliary jet Reynolds number was varied between 3000 to 11000. The total energy of the multi-slot air knife was normalized to that of the main jet. The results of Fig. 14 show that coating weight reductions can be realized by having the input energy of the auxiliary jets being less than 5% of the main jet wiping energy (i.e. E_total/E_main < 1.05) compared to the single slot air knife (i.e. E_total/E_main = 1).

Fig. 14.

Final coating weight as a function of the total input energy of the multi-slot air knife for Re_m = 11000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm, 0.5 ≤ V_s ≤ 1.5 m/s and 3000 ≤ Re_a ≤ 11000.

5.2. Effect of Main Jet Reynolds Number (Re_m)

The effect of the main jet Reynolds number (Re_m) on the final coating weight is presented in this section. Re_m was varied between 7000 and 11000 while Re_a was fixed at 3000 for these experiments. That is, the main jet velocity changed from 70 to 110 m/s, whereas the auxiliary jet velocity was fixed at 30 m/s. The main jet width (D), auxiliary jet width (D_a), jet to strip distance (Z/D) and the auxiliary jet offset (s) were fixed at D = 1.5 mm, D_a = 1.5 mm (i.e. D_a/D = 1), Z/D=12 and s = 10 mm, respectively. The experimentally measured final coating weight for the multi-slot jet as a function of strip velocity at different Re_m is shown in Fig. 15. According to this figure, the predicted values of the final coating thickness using the Elsaadawy et al. model¹⁸⁾ agreed with the experimental measurements at each Re_m. Figure 16 compares the coating weights for the multi-slot air knife with the single slot jet coating weight data for 7000 ≤ Re_m ≤ 11000 at fixed Re_a = 3000 and Z/D = 12. According to Fig. 16, at higher strip velocities the coating weight from the multi-slot jet configuration was lower compared to that of the single slot jet for the investigated range of main jet Reynolds numbers. Coating weight estimates from the Elsaadawy et al.¹⁸⁾ model also confirmed this trend for coating thickness reduction (Fig. 17), where the highest difference was observed at V_s=1.5 m/s for all of investigated main jet Reynolds numbers (7000 ≤ Re_m ≤ 11000).

Fig. 15.

Final coating weight for the multi-slot jet at different strip velocities and Re_m, with Re_a = 3000, Z/D = 12, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Fig. 16.

Comparison of experimentally measured coating weight for the single and multi-slot air knife at a) Re_m = 7000, b) Re_m = 9000, c) Re_m = 11000 for Z/D = 12, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Fig. 17.

Comparison of predicted final coating weight for the single and multi-slot air knife using the Elsaadawy et al. model¹⁴⁾ at 7000 ≤ Re_m ≤ 11000 for Z/D = 12, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Figure 18 shows the CFD derived wall pressure gradient distribution at Z/D = 12 and Re_a = 3000 for both the single and multi-slot air knives. It can be seen that adding lower velocity auxiliary jets beside the main jet led to an increase in the maximum non-dimensional pressure gradient and also increased the wiping region pressure gradient for this configuration versus the single-impinging slot jet case. A similar trend can be seen in Fig. 19 for the wall shear stress profile for Re_m = 9000 and Re_m = 11000 while Re_a = 3000 and Z/D = 12.

Fig. 18.

Comparison of non-dimensional wall pressure gradient for the single and multi-slot air knife at a) Re_m = 9000 and b) Re_m = 11000 for Z/D = 12, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Fig. 19.

Comparison of non-dimensional wall shear stress distribution for single and multi-slot air knife at a) Re_m = 9000 and b) Re_m = 11000 for Z/D = 12, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

5.3. Effect of Z/D

The effect of the strip to nozzle ratio (Z/D) on the coating weight on a moving substrate was investigated at Re_m = 11000, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm, s = 10 mm and 0.5 ≤ V_s ≤ 1.5. The results were compared with the results of the conventional single slot jet working at the same main jet Reynolds number. Figure 20 represents the final coating thickness for the multi-slot jet wiping as a function Z/D for Re_m = 11000, Re_a = 3000 and 0.5 ≤ V_s ≤ 1.5. It is shown that the predicted coating weight was sensitive to the Z/D ratio and increased with increasing Z/D. Figure 20 compares the predicted coating weight by the Elsaadawy et al. model¹⁸⁾ as a function of V_s and (Z/D) ratio for the single jet working at Re_m = 11000 versus the multi-slot jet working at Re_m = 11000 and Re_m = 3000. According to Fig. 21, for Z/D ≥ 10, the coating weight for the multi-slot configuration was lower than the single slot jet case for all strip velocities (0.5 ≤ V_s ≤ 1.5), with the largest difference being about 4.7% for V_s = 1.5 m/s.

Fig. 20.

Experimental measurements of final coating thickness as a function of Z/D at different strip velocities, Re_m = 11000, Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

Fig. 21.

Comparison of coating weight predicted by Elsaadawy et al. model¹⁴⁾ for a single jet working at Rem = 11000, D = 1.5 mm and multi-slot jet wiping working at Re_m = 11000 and Re_a = 3000, D = 1.5 mm, D_a = 1.5 mm and s = 10 mm.

For the single slot jet at Z/D = 12, since the potential core was absorbed before impingement, there would be a significant decrease in the maximum wall pressure versus the low Z/D case where the potential core was impinging on the wall. By using the multi-slot configuration under the specific arrangement in this study, the momentum loss of the main jet could be decreased as the auxiliary jet flow merged with that of the main jet without affecting the jet width. The merged jet with higher momentum and with the same width resulted in higher pressure gradient and shear stresses at the coating surface and, consequently, the coating thickness decreased for the multi-slot jet. However, at lower (Z/D), since the potential core of the main jet impinged on the strip, the additional flow coming from the auxiliary jet did not have a significant effect on the pressure gradient or shear stress and no significant coating thickness reduction was observed.

6. Conclusions

The final coating weight during gas jet wiping in the continuous galvanizing process by means of a novel prototype multi-slot air knife over a variety of operating conditions was measured experimentally in this study. Numerical simulations for the same operating conditions were also carried out in this study to estimate the wall pressure and shear stress profiles for the purpose of predicting the coating weight on the moving substrate using a 2-D steady-state analytical model. Based on the previous study of the authors,²⁶⁾ the geometrical of the multi-slot jet was set such that D_a/D = 1 and s = 10 mm for the experimental measurements and numerical simulations.

The sensitivity of the final coating weight to the main and auxiliary jet Reynolds numbers were investigated. It was observed that at higher strip velocities, slightly lighter coating weights could be achieved by using the multi-slot air knife such that the auxiliary jets were operated at a fraction of main jet Reynolds number (i.e. Re_a/Re_m ≤ 0.5). It was also shown that the experimentally measured coating weights were in good agreement with the predicted coating weights using the analytical liquid film coating weight model of Elsaadawy et al.¹⁸⁾ at different auxiliary jet Reynolds number (3000 ≤ Re_a ≤ 9000) for a fixed main jet Reynolds number of Re_m = 11000 and Z/D = 12.

The effect of the main jet Reynolds number (7000 ≤ Re_m ≤ 11000) at fixed auxiliary jet Reynolds number (Re_a = 3000) and jet to strip distance of Z/D = 12 was also experimentally investigated in this paper. The measurements were benchmarked against analytical model of Elsaadawy et al.¹⁸⁾ and the comparisons showed that experimental data agreed with the predicted results. Moreover, for each main jet Reynolds number (7000 ≤ Re_m ≤ 11000), it was confirmed that with D_a/D = 1 and Re_a = 3000, slightly lighter coating weight at higher strip velocities could be achieved using the multi-slot air knife.

In the last part of this paper, senility of coating weight to the jet to wall ratio (Z/D) was investigated for D_a/D = 1, Re_m = 11000 and Re_a = 3000. The experimental results showed the effectiveness of using multi slot air knife for Z/D ≥ 10, as the flow of auxiliary jets reduced the momentum loss of the main without increasing the jet width. Therefore, the higher wall pressure gradient and shear stress upon impingement at the coating surface resulted in lighter coating weights.

Acknowledgment

The authors gratefully acknowledge the financial support of the International Zinc Organization Galvanized Autobody Partnership (IZA-GAP) members, Dofasco Global R&D Hamilton and the Natural Sciences and Engineering Research Council of Canada (NSERC, grant CRDPJ 446105-2012).

Nomenclature

c: Speed of sound (m/s)

D: Main jet width (m)

D_a: Auxiliary jet width (m)

g: Gravitational acceleration (m/s²)

G: Non-dimensional pressure gradient

h_f: Final film thickness (m)

h: Local film thickness (m)

h_o: Free meniscus film coating (m)

h_m: Final film thickness of multi-slot jet (m)

h_m: Final film thickness of single jet (m)

H: Non-dimensional film thickness

L: Computational domain length (m)

L_s: Strip width (m)

$\dot{m}$: Mass flow rate of removed oil (kg/s)

P: Static pressure (Pa)

P_s: Nozzle static pressure (Pa)

P_∞: Ambient pressure (Pa)

q: Withdrawal flux (m²/s)

q_a: Air volume flow rate (m³/s)

Q: Non-dimensional withdrawal flux

R: Universal gas constant (J/mol.K)

Re: Jet Reynolds number ($Re={\displaystyle \frac{\rho uD}{\mu }}$)

S: Non-dimensional shear stress

s: Auxiliary jet offset distance (m)

T: Temperature (K)

U: Fluid velocity (m/s)

V_s: Strip velocity (m/s)

We: Weber number ($We={\displaystyle \frac{{\rho }_{cl}{u}_{cl}^2{h}_f}{\sigma }}$)

Z: Main jet exit to wall distance (m)

μ: Fluid dynamic viscosity (kg/m.s)

μ_t: Turbulent viscosity (kg/m.s)

ρ_cl: Coating liquid density (kg/m³)

γ: Ratio of specific heats of air

τ: Shear stress (Pa)

ρ: Density of gas (kg/m³)

ρ_cl: Density of coating liquid (kg/m³)

σ: Surface tension (N/m)

References

• 1)   A. R.  Marder: Prog. Mater. Sci., 45 (2000), 191.
• 2)   J. A.  Thornton and  H. F.  Graff: Metall. Trans. B, 7 (1976), 607.
• 3)   C. H.  Ellen and  C. V.  Tu: J. Fluids Eng., 106 (1984), 399.
• 4)   P.  Naphade,  A.  Mukhopadhyay and  S.  Chakrabarti: ISIJ Int., 45 (2005), 209.
• 5)   E. O.  Tuck: Phys. Fluids, 26 (1983), 2352.
• 6)   E. O.  Tuck and  J.-M.  Vanden Broeck: AIChE J., 30 (1984), 808.
• 7)   Y.  Takeishi and  T.  Aoki: Tetsu-to-Hagané, 81 (1995), 135 (in Japanese).
• 8)   Y.  Takeishi,  A.  Yamauchi and  S.  Miyauchi: Tetsu-to-Hagané, 81 (1995), 643 (in Japanese).
• 9)   M.  Dubois: Proc. 8th Int. Conf. on Zinc and Zinc Alloy Coated Steel Sheet (Galvatech 2011), AIM, Milano, (2011), 1847.
• 10)   A. N.  Hrymak,  E. A.  Elsaadawy,  G.  Hanumanth,  J. R.  McDermid and  F. E.  Goodwin: Proc. Iron & Steel Technology Conf. (AISTech 2005), Vol. II, Warrendale, PA, (2006), 393.
• 11)   C. V.  Tu and  D. H.  Wood: Exp. Therm. Fluid Sci., 13 (1996), 364.
• 12)   D.  Lacanette,  A.  Gosset,  S.  Vincent,  J. M.  Buchlin and  E.  Arquis: Phys. Fluids, 18 (2006), 042103.
• 13)   J.-R.  Park: Ironnmaking Steelmaking, 28 (2001), 53.
• 14)   D.  Arthurs and  S.  Ziada: Can. Acoust., 35 (2007), 28.
• 15)   K.  Myrillas,  A.  Gosset,  P.  Rambaud,  M.  Anderhuber,  J. M.  Mataigne and  J. M.  Buchlin: Chem. Eng. Process. Process Intensif., 50 (2011), 466.
• 16)   C. V.  Tu: Stripping Liquid Coatings, U.S. Patent US005360641A, (1994).
• 17)   P.  Tamadonfar,  J. R.  McDermid,  A. N.  Hrymak and  F. E.  Goodwin: Proc. Iron & Steel Technology Conf. (AISTech 2010), Warrendale, PA, (2010), 517.
• 18)   E. A.  Elsaadawy,  G. S.  Hanumanth,  A. K. S.  Balthazaar,  J. R.  McDermid,  A. N.  Hrymak and  J. F.  Forbes: Metall. Mater. Trans. B, 38 (2007), 413.
• 19)   G. Y.  Kim,  H. D.  Park,  D. E.  Lee and  W. C.  Chung: Gas Wiping Apparatus Having Multiple Nozzles, U.S. Patent US0031879A1, (2008).
• 20)   P.  Tamadonfar,  J. R.  McDermid,  A. N.  Hrymak and  F. E.  Goodwin: Proc. 8th Int. Conf. on Zinc and Zinc Alloy Coated Steel Sheet (GalvaTech 2011), AIM, Milano, (2011), 846.
• 21)   S.  Alibeigi,  J. R.  McDermid,  S.  Ziada and  F. E.  Goodwin: Proc. Galvatech 2013: 9th Int. Conf. on Zinc and Zinc Alloy Coated Steel Sheet & 2nd Asia-Pacific Galvanizing Conf., Metallurgical Industry Press, Beijing, (2013), 437.
• 22)   D.  Finnerty,  J. R.  McDermid,  F.  Goodwin and  S.  Ziada: Proc. 11th Int. Conf. on Zinc and Zinc Alloy Coated Steel Sheet (Galvatech 2017), ISIJ, Tokyo, (2017), 307.
• 23)   A.  Yahyaee Soufiani,  J. R.  McDermid,  A. N.  Hrymak and  F. E.  Goodwin: J. Coat. Technol. Res., 14 (2017), 1015.
• 24)   G.  Takeda,  H.  Takahashi and  K.  Kabeya: Tetsu-to-Hagané, 102 (2016), 576 (in Japanese).
• 25)   G.  Takeda,  H.  Takahashi,  M.  Miyake and  N.  Nakata: Asia Steel Int. Conf. 2015 Proc., ISIJ, Tokyo, (2015), 124.
• 26)   A.  Yahyaee Soufiani,  J. R.  McDermid,  A. N.  Hrymak and  F. E.  Goodwin: Metall. Mater. Trans. B, 50 (2019), 2523. https://doi.org/10.1007/s11663-019-01666-1
• 27)   F. M.  White: Fluid Mechanics, 4th ed., McGraw-Hill, Boston, (2003), 866.
• 28)   J. M.  Buchlin: Thin Liquid Films and Coating Processes, Von-karman Institute, Waterloo, Belgium, (1997), 141.
• 29)   H. W.  Coleman and  W. G.  Steele: Experimentation and Uncertainity Analysis for Engineers, 2nd ed., John Wiley & Sons Inc., New York, (1999), 271.
• 30)   M. J.  Neale: The Tribology Handbook, 2nd ed., Butterworth-Heinemann, Oxford, (1995), 640.