Experimental and Numerical Study of Coating Thickness Using Multi-slot Air Knives

Abstract

Gas-jet wiping is a widely employed production technology for controlling the final zinc coating thickness on a moving substrate during continuous hot-dip galvanizing. This paper presents an experimental investigation and numerical analysis of a prototype multi-slot air knife, which offers an increase in wiping efficiency relative to the traditional single-slot jet geometry in the continuous galvanizing process. The applicability of the analytical coating weight model of Elsaadawy et al. (Metall Mater Trans B, 38:413-424, 2007) to predict the final coating weight was determined for the multi-slot geometry, where particular focus was devoted to the effect of geometric parameters. Experimental measurements under a variety of knife geometry and process conditions agreed with the coating weight predictions of the analytical model. It was also shown that the air-knife geometric parameters had a significant effect on the pressure profile and shear stress distribution applied by the air knives to the moving substrate. It was determined that the final coating thickness was significantly affected by the auxiliary jet width, Da, where lighter coating weights at higher strip velocities (up to 5.4 pct at Vs = 1.5 m/s) could be achieved by using the multi-slot air-knives prototype vs. the conventional single-slot configuration.

Introduction

In the steel industry, the continuous hot-dip galvanizing (CHDG) process is broadly used in order to protect the underlying steel substrate from the effects of environmental degradation. The CHDG process includes a molten zinc (Zn) bath, usually held at 733 K (460 °C), in which the steel substrate is constantly submerged, resulting in deposition of the liquid Zn-Al-Fe alloy on the steel substrate.[2] Upon exiting the bath, the substrate is coated with a rather thick layer of liquid zinc because of viscous drag forces.[3] In order to control the coating layer thickness on the steel, a pair of impinging gas jets (referred to as air knives in the industry), generally in the single-slot configuration, is located above the bath (Figure 1). These air knives remove the excess zinc by applying a pressure gradient (dp/dx) and shear stress (τ) to the coating layer and return the excess molten Zn liquid to the bath.[3] In this manner, the desired final film thickness (hf), which is a function of the nozzle pressure Ps, the strip velocity Vs, the nozzle-to-moving sheet distance Z, the jet width D, and the viscosity and density of the liquid zinc,[4] can be obtained after the wiping action of the air knives.

Fig. 1
figure1

Schematic of the conventional single-slot gas-jet wiping process for coating control

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 Zn coating weight applied to the steel sheet in order to reduce the overall mass of the automotive body-in-white, thereby increasing fuel efficiency and reducing costs.[5] Furthermore, the industry is motivated to reduce the local variability of the zinc coating thickness in order to mitigate the practice of “over-coating,” also with the objective of reducing costs. There are several studies available in the literature on using a single-slot turbulent impinging gas jet for controlling the liquid zinc coating thickness on the metal strip during continuous galvanizing.[3,4,6,7,8] The early work on modeling the gas-jet wiping process to predict final coating thicknesses—usually expressed as coating weights (e.g., g/m2)—assumed a decoupled model—i.e., a thin liquid coating film with boundary conditions on the surface that related to the impinging flow field (i.e., pressure profile gradient and shear stress gradient).

A fundamental analytical coating weight model has been presented by Thornton and Graff[3] to predict the coating film thickness after wiping by a single-slot air knife. They postulated that only the maximum wall pressure gradient played a significant role in determining the final film thickness. The proposed model predicted the final coating thickness as a function of nozzle-to-substrate distance, strip velocity, momentum flux of the jet, and jet width. In a later modification to the Thornton and Graff[3] coating weight model, Ellen and Tu[4] employed the shear stress applied on the film surface by the jet in their analysis of the gas-jet wiping process. Their model improved the prediction of final coating thickness and correlated well with coating thickness measurements taken from an industrial continuous galvanizing line, CGLs.[3] Subsequent studies on the influence of zinc liquid surface tension on the predicted coating weight showed a negligible contribution of surface tension with the pressure gradients typical of continuous galvanizing gas-jet wiping as the jet action overcame the capillary force on the coating liquid.[7,9] Through their experimental measurements, Tu and Wood[8] studied the effect of jet Reynolds number (3000 ≤ Re ≤ 11,000) and jet-to-wall standoff distances (2 ≤ Z/D ≤ 20) on the wall pressure profile and wall shear stress distribution under an impinging jet. The experimental correlations of wall shear stress and wall pressure gradient[8] were then used in the coating weight model developed by Ellen and Tu[4] to successfully predict the final Zn coating thickness on the moving substrate. Hrymak et al.[10] subsequently used computational methods to develop a coating weight model to optimize operating conditions for a targeted coating weight. The coating weights studied lay between 45 and 75 g/m2 while the jet Z/D ratios ranged from 2 ≤ Z/D ≤ 6. The computational results were benchmarked against industrial coating weight data and excellent agreement was found between the model and the line data with the highest deviation being approximately 8 pct. Gosset et al.[11] studied the properties of a gas jet at small standoff distances (i.e., Z/D ≤ 8) and observed that the final coating thickness remained relatively constant for Z/D < 7, i.e., in the jet potential core. Elsaadawy et al.,[1] proposed a coating weight model based on the work of Ellen and Tu[4] as a function of gas-jet operating conditions, where improved correlations of shear stress and pressure gradient were found by Elsaadawy et al.[1] by employing both experimental measurements and numerical analysis using the kε turbulence model in (FLUENT™). The model predictions were in good agreement with industrial CGL data for coating weights of less than 75 g/m2 for which the average error between the model predictions and measured coating thicknesses was about 8 pct.

Although single-slot jets are widely used in CGLs to control the coating thickness, the current configuration of single-slot jet air knives is very close to their limit with respect to having the capability of wiping to coating weights of less than 40 g/m2 at higher line speeds.[5] In order to lower coating weights using single-slot air knives at reasonable strip velocities, the wiping pressure could be significantly increased. However, higher wiping pressures can lead to industrial difficulties such as higher noise generation,[12,13] splashing,[14] and coating non-uniformity.[5] Currently, to cope with such problems and achieve the desired lower coating weights, the steel strip typically moves at lower speeds, which adversely affects the productivity of the line.

In order to address some of these challenges, Kim et al.[15] proposed a multi-slot air knife design to mitigate the splashing problem and enhance coating quality. Their multi-slot configuration consisted of one main jet and four side jets blowing air at reduced velocities relative to the main jet. However, the effects of the proposed configuration on the wall pressure profile and wall shear stress distribution, and consequently the final coating thickness, were not determined.

Tamadonfar et al.[16,17] numerically simulated a multi-slot jet composed of a main jet and two symmetrically inclined jets adjacent to the main jet. The range of simulated flow conditions in the studies of Tamadonfar et al.[16,17] was limited to one slot jet gap and one specific geometry of the multiple slot jet. For the range of operating parameters explored, the multi-slot air knives did not produce a thinner coating thickness in comparison to a single-slot air knife. Alibeigi et al.[18] later experimentally investigated the wall pressure distribution of the multi-slot jet design under different operating conditions (i.e., Rem, Rea, Z/D) and compared the results with the numerical simulations of Tamadonfar et al.[16,17] The comparisons showed some disagreement on the maximum wall pressure and pressure distribution between the two studies. Finnerty et al.,[19] through the acoustic measurements, later showed that the auxiliary jets of the Tamadonfar et al.[16] design had the ability to eliminate the high-intensity acoustic tones associated with aeroacoustic feedback, implying that the main jet had been stabilized by the action of the auxiliary jets. McDermid et al.[20] later showed via PIV measurements that, when operating the auxiliary jets such that the auxiliary jet velocity was approximately 40 pct of the main jet velocity did, indeed, stabilize the main jet by significantly reducing main jet flapping associated with the aeroacoustic feedback relative to that observed for the single jet design[21] by largely eliminating the vortical structures associated with the high shear gradients between the main jet and bulk environment.

More recently, Yahyaee Soufiani et al.[22] investigated the fluid flow for the prototype multi-slot configuration. Computational fluid dynamics were applied to predict the wall pressure profile and wall shear stress distributions arising from the multi-slot air knives, and the results were then used in the analytical coating weight model developed by Elsaadawy et al.[1] to predict the liquid zinc coating thickness on the moving strip. The authors showed that a specific arrangement for the multiple slot air knife, where the main and auxiliary jet centerlines coincided at a same point on the impingement wall (i.e., the steel strip), led to lower coating weights compared to a single-slot air knife working under the same operating conditions. The coating weight results of Yahyaee Soufiani et al.[22] for the multiple slot air knives were not, however, verified by experimental measurements.

The current contribution focuses on determining the applicability of the Elsaadawy et al.[1] coating weight model for gas-jet wiping using the prototype multi-slot air knife and to determine the effects of jet geometry and jet operating parameters on the final coating weight. In this study, the conventional single-slot jet design was used as a base case for comparing the coating weight data to those derived from the multi-slot air knives.

Analytical Model of Film Thickness

For the convenience of the reader, the key equations and concepts of the analytical coating weight model used in the present work are reviewed below. The final coating thickness is determined by solving the simplified two-dimensional momentum equation for a liquid film. The pressure across the liquid film was assumed to be constant as the film velocity perpendicular to the plate was negligible in comparison with the velocity parallel to the substrate.[4] Using the above assumptions and the xy co-ordinate system specified in Figure 1, the film momentum equation was reduced to

$$ \mu \frac{{\partial^{2} u}}{{\partial y^{2} }} - \left( {\rho g + \frac{{{\text{d}}p}}{{{\text{d}}x}}} \right) = 0, $$
(1)

where the boundary conditions for the solution of Eq. [1] were

$$ u = V_{\text{s}} \quad {\text{at}}\;y = 0, $$
(2)
$$ \mu \left( {\frac{\partial u}{\partial y}} \right) = \tau \quad {\text{at}}\;y = h. $$
(3)

The velocity profile can then be obtained through Eqs. [1] through [3] such that

$$ u = V_{\text{s}} \left[ {1 + \frac{y}{h}SH - \frac{y}{h}\left( {2 - \frac{y}{h}} \right)\frac{{GH^{2} }}{2}} \right], $$
(4)

where \( H = h\sqrt {\frac{\rho g}{{\mu V_{\text{s}} }}} ,\;S = \frac{\tau }{{\sqrt {\rho \mu V_{\text{s}} g} }} \) and \( G = 1 + \frac{1}{\rho g}\frac{{{\text{d}}p}}{{{\text{d}}x}}. \) Integrating Eq. [4] yields the volumetric flux of the liquid, q, as

$$ q = \int_{0}^{h} {u{\text{d}}y = V_{\text{s}} h\left( {1 + \frac{SH}{2} - \frac{{GH^{2} }}{3}} \right)} , $$
(5)

where the non-dimensional withdrawal flux, \( Q = \frac{q}{{V_{\text{s}} }}\sqrt {\frac{\rho g}{{\mu V_{\text{s}} }}} , \) can be derived from Eq. [5] such that

$$ Q = - \frac{{GH^{3} }}{3} + \frac{{SH^{2} }}{2} + H. $$
(6)

The non-dimensional film thickness, H, then can be determined by setting \( \frac{{{\text{d}}Q}}{{{\text{d}}H}} = 0 \)[6] and solving for H such that

$$ H = \frac{{S \pm \sqrt {S^{2} + 4G} }}{2G}. $$
(7)

Upon solidification of the liquid Zn alloy, the film velocity is equal to the strip velocity (Vs) and the coating thickness, hf, can be determined via

$$ h_{\text{f}} = \frac{q}{{V_{\text{s}} }} = \frac{{Q_{\hbox{max} } }}{{\sqrt {\frac{\rho g}{{\mu V_{\text{s}} }}} }}. $$
(8)

The pressure profile gradient and shear stress profile can be used with Eqs. [7] and [8] in predicting the final coating weight. An examination of Eqs. [6] through [8] will show that higher maximum values for the dp/dx and τ distributions near the wiping region will result in lighter coating weights. Thus, in the present work, the wall shear stress and pressure gradient distributions applied by a conventional single-slot and from the prototype multi-slot gas-jet designs were predicted through numerical simulations. The predicted final coating thickness on a moving substrate was then compared with experimental measurements, as will be described in Section VI.

Numerical Modeling

Numerical simulation of the impinging slot jets—both in the single-slot and multi-slot geometries—on a flat plate were performed using FLUENT 15.0. For all simulations, a double precision pressure-based solver was used while for the pressure–velocity coupling the SIMPLE method was applied. The Reynolds-Averaged Navier–Stokes (RANS) equations (Eqs. [9] and [10]) were used for the air flow determination.

$$ \frac{\partial \rho }{\partial t} + \frac{{\partial (\rho \bar{u}_{i} )}}{{\partial x_{i} }} = 0, $$
(9)
$$ \frac{{\partial \rho \bar{u}_{i} }}{\partial t} + \frac{{\partial \rho \bar{u}_{i} \bar{u}_{j} }}{{\partial x_{i} }} = - \frac{\partial p}{{\partial x_{i} }} + \frac{\partial }{{\partial x_{i} }}\left[ {\mu \left( {\frac{{\partial \bar{u}_{i} }}{{\partial x_{j} }} + \frac{{\partial \bar{u}_{j} }}{{\partial x_{i} }}} \right) - \rho \overline{{u^{\prime}_{i} u^{\prime}_{j} }} } \right]. $$
(10)

The Reynolds stress was modeled using the Boussinesq hypothesis, which relates it to the mean velocity gradient via the turbulent viscosity, µt (Eq. [11]):

$$ - \rho \overline{{u^{\prime}_{i} u^{\prime}_{j} }} = \mu_{\text{t}} \left( {\frac{{\partial \bar{u}_{i} }}{{\partial x_{j} }} + \frac{{\partial \bar{u}_{j} }}{{\partial x_{i} }}} \right). $$
(11)

In the present study, the two-equation model of the standard kε turbulence model was used to determine the turbulent viscosity, µt. In this model, two transport equations are required to be solved for turbulent kinetic energy and rate of turbulent dissipation. The transport equations are as follows:

$$ \frac{\partial \rho k}{\partial t} + \frac{{\partial \rho ku_{i} }}{{\partial x_{i} }} = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\mu + \frac{{\mu_{\text{t}} }}{{\sigma_{k} }}} \right)\frac{\partial k}{{\partial x_{j} }}} \right] + G_{k} - \rho \varepsilon , $$
(12)
$$ \frac{\partial \rho \varepsilon }{\partial t} + \frac{{\partial \rho \varepsilon u_{i} }}{{\partial x_{i} }} = \frac{\partial }{{\partial x_{j} }}\left[ {\left( {\mu + \frac{{\mu_{\text{t}} }}{{\sigma_{\varepsilon } }}} \right)\frac{\partial \varepsilon }{{\partial x_{j} }}} \right] + C_{1\varepsilon } \frac{\varepsilon }{k}(G_{k} ) - C_{2\varepsilon } \rho \frac{{\varepsilon^{2} }}{k}, $$
(13)
$$ \mu_{\text{t}} = \rho C_{\mu } k^{2} /\varepsilon , $$
(14)

where Cμ is a model constant. For the pressure term, the standard method for the pressure and a first-order winding-up method was used to determine the turbulent dissipation rate (ε), the turbulent kinetic energy (k), and the momentum. The discretized equations were iterated until the root-mean-square residuals for all governing equations were less than 10 −6.

Schematics of the single-slot and multi-slot nozzle configurations are shown in Figure 2. The pressure profile and shear stress CFD results were validated via the experimental measurements of Ritcey et al.[23] and Alibeigi.[24] The CFD boundary conditions were a defined pressure inlet at the nozzle inlets, the no slip condition at the nozzle walls and at the impingement surface, and a defined pressure outlet at the edge of the computational domain. The inlet pressure (Ps) was used to estimate the flow velocity at the nozzle exit using Eq. [15][25]:

$$ U = c\sqrt {\frac{2}{\gamma - 1}\left[ {\left( {\frac{{P_{\text{s}} + P_{{_{\infty } }} }}{{P_{{_{\infty } }} }}} \right)^{\gamma - 1/\gamma } - 1} \right]} , $$
(15)

where c is the speed of sound (343 m/s), γ is the ratio of specific heats of air, and P is the ambient pressure. A combination of quadrilateral and triangular meshes was used for the jet simulation. The mesh was refined near the wall region and grid clustering was also performed along the jet centerline. Four grids with 252,000 to 393,000 nodal points, depending on the plate-to-main jet width (Z/D, Figure 2) ratio, were examined to ensure mesh independence of the results. Mesh refinement along the wall was such that the first grid was placed in the viscous sub-layer (y + ∼ 1) where the mesh dimension near the wall was on the order of 4 µm.

Fig. 2
figure2

Schematic of (a) the single-slot and (b) multi-slot air-knife geometries

The numerical simulations in the current study were benchmarked against the experimental wall pressure distributions of Alibeigi[24] and Ritcey et al.[23] for 4 < Z/D < 12 at Rem = 11,000. Figure 3 compares the numerically derived non-dimensional wall pressure profiles from the present study vs. the experimental data of Ritcey et al.[23] for the single-slot jet configuration as a function of jet-to-wall distance. Figure 3 illustrates that the numerically simulated pressure profile matches well with the experimental measurements. Figure 4 shows a similar comparison of several numerically derived wall pressure profiles from this work vs. the experimental data of Alibeigi[24] for the multi-slot air knives, where Rem = Rea = 11,000. According to Figure 4, the predicted non-dimensional wall pressure profiles agree, within experimental error, with experiment.

Fig. 3
figure3

Comparison of non-dimensional wall pressure profiles at Re = 11,000 and 4 < Z/D < 12 with the experimental measurements of Ritcey et al.[23]

Fig. 4
figure4

Comparison of numerical wall pressure distribution results with the experimental measurements of Alibeigi[24] for the multi-slot air knife geometry (Fig. 2) at Rem = 11,000, Rea = 11,000 and (a) Z/D = 4, (b) Z/D = 6, (c) Z/D = 8, and (d) Z/D = 12

Test Facility

Air Knives

A schematic of the prototype multi-slot impinging jet used in the experimental measurements is presented in Figure 5. The multi-slot air knives consist of three jets, one main jet and two inclined auxiliary jets symmetrically located on each side of the main jet. The main jet was perpendicular to the moving strip and the auxiliary jets were inclined at 20 deg from the main jet centerline. The prototype multi-slot air knives have three separate inlet chambers and each has an individual plenum and valve to allow independent control of the plenum pressure for each nozzle. Compressed air from a 550 kPa blower was used to feed the auxiliary jets and the main jet was fed 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 jet plenum and nozzle. An electric valve was also used immediately after the filter to adjust the main jet pressure using an in-house computer program. 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 into the applicable plenum via a 25.4-mm-diameter pipe at the top of the plenum, was passed through a flow distributor tube (Figure 5), and then through a series of mesh screens located upstream of the nozzle contraction in order to break up any large-scale turbulent structures (Figure 5). The screens comprised stainless steel cloth with 28 wires/cm. Finally, air exited the nozzle at 90 deg to its inlet direction. To adjust the distance between the nozzle and the plate—i.e., the Z/D ratio—the prototype multi-jet 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 least division of 5 μm. A Validyne DP-15 pressure transducer was used to measure the plenum pressures and the data were logged using a conventional data acquisition system and LabVIEW software. The plenum pressure was measured at the centerline of each jet, upstream of the nozzle contraction.

Fig. 5
figure5

Isometric view of the multi-slot air knives

Wiping Apparatus

The molten zinc temperature commonly employed in the industrial continuous galvanizing process is 733 K (460 °C). A cold laboratory-scale model of the continuous galvanizing gas-jet wiping process was designed and manufactured (Figure 6) with the objective of verifying the numerically modeled coating weights for the prototype multi-jet air knife.

Fig. 6
figure6

Schematic of the experimental multi-slot jet wiping apparatus

The apparatus consists of a vertical stainless steel strip, 75 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 to 3.5 m/s by means of an AC to DC speed controller connected to an electric motor. The strip velocity was measured by means of optical and mechanical tachometers with an accuracy of ± 0.05 m/s and a resolution of 0.1 rpm (for the test range of 2 to 999.9 rpm). The lower roll was designed to be adjustable to allow for the provision of adequate tension of the strip. The lower roll was immersed in the model working fluid, mineral oil, with density of 865 kg/m3 and kinematic viscosity of 10 cSt. The gas-jet wiping devices tested using this apparatus were the single-slot and multi-slot air knives shown schematically in Figure 5 and discussed in the previous section. The multi-slot air knives were positioned 50 cm above the free surface of the liquid bath perpendicular to the strip. The air knives were 5 cm longer than the strip width to avoid edge effects. The wiping mechanism was studied on one side of the strip only. To ensure good stability of the strip in the jet impingement region, the rear face of the strip slid on a rubber damper lubricated by the mineral oil liquid coating. The main jet-to-substrate distances and strip velocities used in the experiments were 8 ≤ Z/D ≤ 12 and 0.25 ≤ Vs ≤ 1.5 m/s.

After the substrate passed the wiping region, the liquid film was removed by two inclined rubber blades or “squeegees.” A digital balance with an accuracy of ± 0.01 g measured the mass of the collected liquid while the collection period was measured by a chronometer. The mean liquid film thickness, hf, was determined through the mass flow rate of liquid removed from the strip during the 300-second collection period using Eq. [16]:

$$ h_{\text{f}} = \dot{m}_{\text{cl}} /(\rho_{\text{cl}} L_{\text{s}} V_{\text{s}} ). $$
(16)

Each experiment was repeated four times and the results reported are an average of these four experimental runs. According to Coleman and Steels,[26] the overall uncertainty of a dependent variable r (∂r), which is function of j independently measured variables Xi can be found by using the Kline and McClintock method, given by

$$ \partial r = \sqrt {\sum\limits_{i = 1}^{j} {\left( {\theta_{i} \left( {\partial X_{i} } \right)} \right)^{2} } } , $$
(17)

where \( \theta_{i} = \frac{\partial r}{{\partial X_{i} }} \) and ∂Xi are the uncertainty for each measured variable. The uncertainty in the mean value of a measured Xi 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 the precision (random) error. The random error was calculated through the Student t-distribution at the 95 pct confidence level and the instrumental bias error was determined through the manufacturer’s specifications. Moreover, two additional sources of bias error were observed for the wiping apparatus depicted in Figure 6, namely (1) inefficiency of the wiping scrapers in removing all the oil from the belt and (2) splashing of oil from the belt, largely at the belt upper roll turnover. The latter source of error was not observed for the lower strip velocities of Vs = 0.25 and 0.5 m/s. It was estimated that 1.8 pct of the mineral oil was left behind on the strip due to scraper inefficiency and the contribution of splashing was 3.2 to 5.8 pct (depending on the strip velocity) to the discrepancy between the experimental measurements vs. the analytical model.

Results and Discussion

In order to assess the viability of the wiping apparatus (Figure 6), experimental measurements were first benchmarked against the analytical coating model of Thornton and Graff[3] and the Elsaadawy et al. model[1] for a free meniscus coating and single gas-jet wiping, respectively.

Free Meniscus Coating

An analytical solution for the free meniscus coating thickness can be determined by solving Eqs. [1] through [5] and setting dp/dx = 0 as there is no gas jet acting on the liquid film.[3]

Figure 7 presents a comparison of the free meniscus experimental data vs. the analytical model of Thornton and Graff.[3] From this, it can be seen that the measured values of the free meniscus coating weight compare favorably with the corresponding predictions of the analytical model. It can be seen that there was a slight under-prediction in the experimental measurements vs. the analytical model for Vs ≥ 0.75 m/s. This discrepancy is attributed to two sources of bias error, discussed previously: (1) inefficiency of the wiping scrapers in removing all the oil from the belt and (2) splashing of oil from the belt, particularly at the belt turnover.

Fig. 7
figure7

Comparison of experimental measurements of coating thickness for free meniscus coatings with the analytical model of Thornton and Graff.[3]

Single Jet Wiping

Figure 8 compares the experimentally measured coating weights with the predictions of the Elsaadawy et al.[1] model for single-slot gas-jet wiping as a function of strip velocity (Vs) for Z/D = 12, Re = 9000, and 11,000. From Figure 8, it can be seen that the predicted coating weight was, generally, in agreement with the experimental measurements for all strip velocities for a main jet Re = 9000. However, it can be seen that the measured final coating weight was slightly lower than the predicted values for Re = 11,000, especially at higher strip velocities (Vs). This is due to the fact that splashing inevitably increased as the strip speed increased. Experiments were also run at a variety of strip-to-knife distances (Z/D) and strip speeds such that 8 ≤ Z/D ≤ 12 and 0.25 ≤ Vs ≤ 1.5 m/s, respectively, for Re = 9000 and 11,000. According to Gosset et al.,[11] coating thickness for the single jet wiping strongly depends on the nozzle-to-strip distance for Z/D ≥ 7. That is mainly because for Z/D ≤ 6, the potential core of the jet would impinge to the strip. For multi-slot jet wiping, the numerical investigation of Yahyaee Soufiani et al.[22] also showed that for Z/D ≥ 8, a lighter coating weight can be achieved through the use of multi-slot jet. In the other hand, in the galvanizing industry, the upper Z/D ratio is usually limited to Z/D = 12; because for a given coating thickness, increasing Z/D results in increasing plenum pressure which causes industrial difficulties such as higher noise generation, splashing, and coating non-uniformity.[5] In terms of strip velocity, Dubois[5] showed that the main reason leading to non-uniform coating was the high strip velocity of Vs ≥ 100 m/min (~ Vs > 1.5 m/s), when Z/D ≥ 7. In the other hand, lower line speeds (Vs ≤ 1 m/s) in the galvanizing industry typically occur for high-temperature annealing or thick strip sheet.[5]

Fig. 8
figure8

Comparison of measured and predicted measurements for single jet wiping with the Elsaadawy et al.[9] coating weight model for Z/D = 12, (a) Re = 9000, and (b) Re = 11,000

The results of these experiments in comparison to the predictions of the Elsaadawy et al.[1] model are shown in Figure 9. It can be seen that for all Z/D and Vs explored, the measured coating weight values agreed with the predictions of the Elsaadawy et al.[1] model.

Fig. 9
figure9

Comparison of measured and predicted coating weights using the Elsaadawy et al.[1] model at 0.25 ≤ Vs ≤ 1.5 m/s for 8 ≤ Z/D ≤ 12, (a) Re = 9000, and (b) Re = 11,000

Multiple Slot Jet Wiping

In this section, the multi-slot jet configuration, shown in Figure 5, was applied as the wiping actuator in the experimental setup and the effect of varying its geometry on the final coating thickness was determined. Figure 10 shows the experimental vs. predicted final coating weight per Elsaadawy et al.[1] for different values of the auxiliary jet width, Da, for a constant main jet Reynolds number of Rem = 11,000, auxiliary jet Reynolds number of Rea = 5000, D = 1.5 mm, and Z/D = 12. According to Figure 10, the predicted coating thickness using the Elsaadawy et al. model[1] agreed with the experimental measurements. It can be also seen that reducing the auxiliary jet width reduced the coating weight. This can be explained by studying the effect of the auxiliary jet width, Da, on the pressure, pressure gradient (i.e., dp/dx), and shear stress profiles applied by the multi-slot air knife. It can be seen that the pressure profile (Figure 11) was broader and possessed a distinct shoulder for Da/D = 3 vs. the Da/D ≤ 1 pressure profiles. This sharper pressure distribution for Da/D ≤ 1 resulted in a greater wall pressure gradient and wall shear stress compared with the Da/D = 3 case, as shown in Figure 12. Thus, lower coating weights can be achieved by decreasing the auxiliary jet width, Da, such that Da/D ≤ 1. This can also be seen in Figure 13, where the predicted coating weights are enumerated as function Da for strip velocities of 0.25 ≤ Vs ≤ 1.5 m/s. It can be seen that, at each strip velocity, the multi-slot jets having Da/D ≤ 1 resulted in lower coating weights compared to the single-slot jet configuration (i.e., Da/D = 0).

Fig. 10
figure10

Comparison of experimental and predicted measurements using the Elsaadawy et al.[1] model for the multi-slot jet where Z/D = 12, Rem = 11,000, Rea = 5000, D = 1.5 mm, and s = 10 mm for (a) Da/D = 1, (b) Da/D = 2, (c) Da/D = 3, and (d) comparison of experimental measurements for 1 ≤ Da/D ≤ 3

Fig. 11
figure11

Non-dimensional wall pressure distribution for 0.67 ≤ Da/D ≤ 3 with Rem = 11,000, Rea = 5000, Z/D = 12, D = 1.5 mm, and s = 10 mm

Fig. 12
figure12

Non-dimensional (a) wall pressure gradient and (b) wall shear stress for 0.67 ≤ Da/D ≤ 3, with Rem = 11,000, Rea = 5000, Z/D = 12, D = 1.5 mm, and s = 10 mm

Fig. 13
figure13

Effect of auxiliary jet width on final coating thickness as a function of strip velocity for Z/D = 12, Rem = 11,000, Rea = 5000, and s = 10 mm

The effect of auxiliary jet offset distance, s, on the final coating thickness was investigated for s = 10 and 0 mm for D = Da = 1.5 mm (i.e., Da/D = 1), Rem = 11,000, Rea = 5000, and Z/D = 12. Figure 14 provides the experimentally measured coating weights vs. the predicted coating weights using the Elsaadawy et al. model.[1] It can be seen that the experimental coating weights agreed well with the predictions of the Elsaadawy et al. model[1] for all values of s explored. Figure 15 shows the compiled coating weight variations as a function of strip velocity for 0 ≤ s ≤ 10 mm. From Figure 15, it can be seen that the final coating weight was not a significant function of the auxiliary jet offset, s, for 0 ≤ s ≤ 10 mm. Comparison of the wall pressure gradient and wall shear stress (Figure 16) also confirmed the negligible effect of changing the auxiliary jet offset on the resultant coating weight.

Fig. 14
figure14

Comparison of coating weight model with experimental measurements for (a) s = 0 mm, (b) s = 5 mm, and (c) s = 10 mm with Z/D = 12, Rem = 11,000, Rea = 5000, and Da = 1.5 mm

Fig. 15
figure15

Effect of auxiliary jet offset, s, on the final coating thickness for different strip velocities where Z/D = 12, Rem = 11,000, Rea = 5000, and D = Da = 1.5 mm

Fig. 16
figure16

Non-dimensional (a) wall pressure gradient and (b) wall shear distribution for different s with Rem = 11,000, Rea = 5000, Z/D = 12, and Da = 1.5 mm

Figure 17 shows a comparison of the coating weights for the single jet and multi-slot jets as a function of strip velocity, Vs, with Z/D = 12, D = Da = 1.5 mm (i.e., D/Da = 1), Rem = 11,000, and Rea = 5000 held constant. According to Figure 17, by increasing the strip velocity, the coating weight increased significantly and it was shown that, for each strip velocity Vs, the predicted coating weight for this multi-slot air knife geometry was lower than the traditional single-slot jet configuration, with the largest difference being about 5.4 pct for Vs = 1.5 m/s.

Fig. 17
figure17

Comparison of (a) experimentally measured and (b) predicted final coating weight of single jet wiping with Rem = 11,000, Z/D = 12, and D = 1.5 mm with the multi-slot jet wiping at different strip velocities with Rem = 11,000, Rea = 5000, Z/D = 12, and D = Da = 1.5 mm

Conclusions

A novel configuration for a multi-slot air knife, which can be effectively used in the continuous galvanizing gas-jet wiping process, was investigated through experiments and computational fluid dynamics simulations. The experimental measurements of the final coating weights were compared with previously developed models for single gas-jet wiping and free meniscus coating.

It was determined that the experimental coating weight measurements agreed with the predictions of the Ellen and Tu[3] and Elsaadawy et al.[1] models. Experiments were also conducted for different geometries of the multi-slot configuration and, in all cases, the experimental coating weight measurements agreed with the predicted values by the Elsaadawy et al.[1] model. It was observed that the final coating thickness was not sensitive to the auxiliary jet standoff distance. However, the auxiliary jet width had a significant impact on the wall pressure gradient, the wall shear stress distribution, and, consequently, on the final coating weight. Results showed that, for Da/D ≤ 1, the width of wall pressure distribution decreased while the maximum pressure remained constant. This resulted in higher values of the wall pressure gradient and shear stress in the vicinity of wiping zone and lower final coating thicknesses for the multi-slot air-knife vs. the single-slot geometries under the same operating conditions, particularly at higher strip velocities (with the highest difference of 5.4 pct at Vs = 1.5 m/s).

Abbreviations

c :

Speed of sound (m/s)

R :

Universal gas constant (J/mol K)

D :

Main jet width (m)

Re :

Jet Reynolds number \( \left( {\text{Re} = \frac{\rho uD}{\mu }} \right) \)

D a :

Auxiliary jet width (m)

S :

Non-dimensional shear stress

g :

Gravitational acceleration (m/s2)

s :

Auxiliary jet offset distance (m)

G :

Non-dimensional pressure gradient

T :

Temperature (K)

h f :

Final film thickness (m)

U :

Fluid velocity (m/s)

h :

Local film thickness (m)

V s :

Strip velocity (m/s)

H :

Non-dimensional film thickness

Z :

Main jet exit-to-wall distance (m)

L :

Computational domain length (m)

μ :

Fluid dynamic viscosity (kg/m s)

L s :

Strip width (m)

μ t :

Turbulent viscosity (kg/m s)

\( \dot{m} \) :

Mass flow rate of removed oil (kg/s)

ρ cl :

Coating liquid density (kg/m3)

P :

Static pressure (Pa)

γ :

Ratio of specific heats of air

P s :

Nozzle static pressure (Pa)

τ :

Shear stress (Pa)

P :

Ambient pressure (Pa)

ρ :

Density of gas (kg/m3)

q :

Withdrawal flux (m2/s)

ρ cl :

Density of coating liquid (kg/m3)

Q :

Non-dimensional withdrawal flux

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Acknowledgments

The authors gratefully acknowledge the financial contributions of the International Zinc Association Galvanized Autobody Partnership (IZA-GAP) Members and the Natural Sciences and Engineering Research Council of Canada (NSERC, Grant CRDPJ 446105-2012) to the success of this research.

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Yahyaee Soufiani, A., McDermid, J.R., Hrymak, A.N. et al. Experimental and Numerical Study of Coating Thickness Using Multi-slot Air Knives. Metall Mater Trans B 50, 2523–2535 (2019). https://doi.org/10.1007/s11663-019-01666-1

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