1　Introduction

Hot dip galvanized steel strip has excellent corrosion resistance,weldability,formability,and other properties;therefore,it is widely used in automobiles,home appliances,ships,construction,and other fields[1-2].Current development activities have caused an increase in the demand for surface quality.Many scholars have conducted research on factors influencing the surface quality of strip steel,and generally believe that the greatest factor influencing the surface quality of the strip is slag adhesion[3].Slag is unavoidable and controlling the quantity of slag is very important for improving the surface quality of hot dip galvanized steel sheet[4].In the study of the flow field in the zinc pot,the method of simulating the experiment equipment was adopted in the early stage.In order to understand the flow and heat transfer of zinc liquid,Toussaint et al.[5] measured the flow in the experimental model of zinc pot firstly by the method of experimental research.Lee et al.[6] established a transparent water model to analyze the flow field distribution of the zinc pot in different strip speed,induction heater flow rate and baffle installation mode.However,this method has great limitation on accuracy.On one hand,zinc solution and water have gigantic differences which lie in fluidity,density,and so on;on the other hand,this method ignores many factors,such as tem-perature field and concentration field.In recent years,the application of numerical simulation has made people have an intuitive understanding of the state of zinc liquid in zinc pot.Ilinca et al.[7] used the experiment and numerical method respectively to analyze the aluminum concentration of zinc ingots with different aluminum content,and the cal-culated results were in good agreement with the experimental results.In the domestic,Zhu Yichun found that raising the zinc pot temperature could effectively reduce the generation of slag through numerical simulation investigation with regard to the formation of slag in the zinc pot[8].Lai Huanxin found that increasing the belt speed resulted in the decrease of the zinc pot temperature in an uneven manner and increased the slag attachment possibilities through the numerical study of flow and hot galvani-zing pot heat transfer.While different strip widths exert a certain influence on the quality of zinc layer,their effect is not obvious[9].Guo Fangfang found that strip temperature exerted a greater influence on the quantity of slag generated in the zinc pot when it entered the zinc pot[10].However,current research only considers one or two factors and has focused mainly on the study of flow field distribution and variation,and temperature field.Therefore,zinc pot roll size,inter mesh,and the position of the induction heater have not yet been considered,and the consideration of multiple factors at the same time is also lacking.The orthogonal experiment method can be used as an efficient optimization method to obtain the optimal process parameters during hot dip galvanizing.Thus,based on the hot dip galvanizing process in a steel enterprise,we con-sidered the slag height and quantity as evaluating indicators,and proceeded to investigate the effect of strip speed v,sink roll diameter S,back stabilizing roll diameter D,stabilizing roll inter mesh L,and position of induction heater P,toward the surface quality of a hot galvanized plate on the basis of previous studies.We designed a hybrid orthogonal experimental scheme L18(61×34) according to the range of each factor.Then,we simulated each experiment with FLUENT software and obtained the optimal combination of hot dip galvanizing process parameters.

2　Model structure

2.1　Physical model

The geometric structure of the hot dip galvanizing zinc pot physical model was simulated by FLUENT software,according to the actual size of the zinc pot at a steel plant,as shown in Fig.1.Zinc was simplified as a heat absorbing surface,placed into the liquid level according to the actual position.The induction heater was simplified as the heating surface and placed into two sides of the hot dip galvanizing pot,according to the actual size and position.The strip entered the zinc liquid at an angle of 60° to the liquid zinc level.Then,it passed through the sink roll,rear stabilizing roll,and front stabilizing roll.Finally,it got out in a direction nearly vertical to the liquid level.The geometric dimensions of the zinc pot were 5 300 mm×3 600 mm×3 136 mm(length×width×height).The size of the front stabilizing roll was 350 mm in diameter and 2 100 mm in length.The size of the rear stabilizing roll was 250 mm in diameter and 2 100 mm in length.The horizontal distance between the center of the front and rear stabilizing rolls was 300 mm.The position of the front stabilizing roll remained unchanged and the rear stabilizing roll could be moved along the horizontal direction;that is,the horizontal distance between the front and the rear stabilizing rolls could be adjusted.This adjusted distance is called the inter mesh.The size of the sink roll was 795 mm in diameter and 2 100 mm in length.We divided the geometric structure of the hot galvanizing pot into grids using a tetrahedron element.To ensure the accurate calculation of the flow field and temperature field of liquid zinc,the mesh of the strip and the area between the sink roll and the two stabilizing rolls were made relatively small.Due to the symmetry of the zinc pot model,only one half of the calculation area needs to be considered when calculating.The initial temperature of zinc pot is 460 ℃,and the surface temperature of zinc ingot is 420 ℃.

2.2　Mathematical model

We considered the zinc liquid in the zinc pot as an incompressible Newton fluid.At the same time,by considering that the zinc pot could be affected by temperature and concentration,the Businne Silk(Boussinesq) approximation should be used.The Navier-Stokes equation is as follows:

(1)

(2)

where,T0 is reference temperature;c0 is reference aluminum concentration; ρ0 is density at T0 and c0;u is flow velocity; t is time; p is pressure; μ is dynamic viscosity coefficient;g is gravity acceleration;T is temperature;c is aluminum concentration;and βT and βAl are the diffusion coefficients of temperature and aluminum concentration.

where v0is the velocity of body-reference system,er and eu are the tensor representations of r and u.

We divided cadmia into slag and dross according to its morphology.The theoretical basis for calcu-lating the quantity of zinc is the Fe-Zn-Al phase diagram.The composition and quantity of the zinc pot were determined by the composition of the Fe-Zn-Al contents and the temperature of the zinc liquid.

·(ρuΦ-ΓΦΦ)=SΦ

(3)

(1) Range analysis

The flow of zinc in a zinc bath is turbulent.Here the SST k-ω model was adopted.The governing equation of the numerical simulation is written in the general form,as expressed in Equation(3):

The concentration of aluminum and iron was derived from the mass transfer equation:

由表2中的柴油凝点检测数据可知，在激励信号频率为32kHz的条件下的差值相比于激励信号频率为16kHz的条件下的差值要大，说明在频率32kHz的条件下检测误差更小。分析原因，可能是高频率激励下的油样电容信号更加稳定，波动较小，从而导致柴油油样的凝点大小更加接近于标准值。

·[(D+DT)ci]

(4)

where,ci is fluid concentration;D is the molecular diffusion coefficient;and DT is the turbulent diffusion coefficient.

The initial concentrations of aluminum and iron were set to 0.14% and 0.027 7%,respectively.In this study,the formulas provided by Ajersch[11] for the limit solubility of aluminum and and used.According to the concentration of Al,we could assess the relationship between cAl and as follows:

(5)

The excessive Fe in the zinc liquid precipitated in the form of Fe3Zn24Al.

The excessive Fe in the zinc liquid precipitated in the form of Fe2Al5.

(6)

and

考虑到通信部分需要使用UART0，本文通过修改运行模式时钟配置寄存器，使用精度更高的外部振荡器作为系统时钟源。外部晶振使用的是6.0 MHz的晶振。

(7)

(8)

where,cFe is the concentration of Fe in the zinc liquid;cAl is the concentration of Al in the zinc liquid.

In actual production,there are many factors influencing the distribution of slag,such as the arc bottom pot radius,strip specification,strip speed,sink roll diameter,front roll diameter,rear roll diameter,zinc liquid temperature,inductor position,inductor power,and inter mesh,among others.Based on previous research results and production practice,we chose v,S,D,L,and P,as the influencing factors.In addition,other factors were fixed.According to the range of each factor,v takes 6 levels,while the other 4 factors take 3 levels,respectively,as shown in Table 1.An orthogonal experiment table for the mixed levels of 5 factors L18(61×34) was designed.

3　Hot dip galvanizing orthogonal experiment

3.1　Orthogonal experimental scheme design

By calculating and comparing the values of cFe and could obtain the quantity of excessive Fe in the zinc liquid.With the quantity of excessive Fe,we could calculate the quantity of cadmia.

3.2　Experimental results

In the process cycle of galvanized steel sheets,the zinc pot was filled with high temperature zinc liquid.Thus,it was difficult to understand the specific distribution of zinc and to collect data.Since it is expensive and difficult to conduct each experiment through actual production,we used numerical simulation to obtain the slag height and quantity in each experiment.In the process of numerical simulation by FLUENT software,the height and quantity of the zinc slag in the zinc pot related to the parameters,e.g.,bottom slag density and simulation time,are set in each experiment.Besides,the higher the bottom slag density,the lower the slag height and the longer the simulation time,the more the slag quantity.In the paper,the bottom slag density was 3 000 kg/m3,the simulation time was 5 days,and the orthogonal experiment results are shown in Table 2.

3.3　Result analysis

In the study of this paper,range analysis and variance analysis were applied to optimize the combination of process parameters.Firstly,the parameters of the optimum surface roughness were determined by the extreme difference analysis,and the difference of the experimental results was caused by different factors.Then,variance analysis was used to determine the significance of each experimental parameter to the experimental results.

There are two common analysis methods of orthogonal experimental result,i.e.,range analysis and variance analysis.Using the method of range analysis,we can obtain the influence degree and the change trend of each factor level.Also we can get the optimal condition of the best experimental index.The analysis of variance can analyze the interaction influence between various factors and find out the main influencing factors,namely whether it is significant for the influence of each experimental parameter on the experimental index and how significant it is.

As shown in Fig.2,the line graph of slag height and quantity was drawn,according to the results presented in Table 2.From Fig.2,we can see that the changing trends of slag quantity and slag height are consistent.In other words,the slag quantity increases as the slag height grows.This is the same as in actual production.Since the changing trend of slag height is relatively large,we only need to consider slag height to analyze the orthogonal experiment results.

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where,ρ is density;u is flow velocity;Φ is a general variable;ΓΦ is the generalized diffusion coefficient;and SΦ is generalized sources.

Range analysis was applied to analyze the result of the bottom slag height.We obtained the mean response table,as shown in Table 3,and the trend of each factor level as shown in Fig.3.

From Table 3 and Fig.3,we can see that the influence order of the factors is:v>L>S>D>P.Since the slag height should be as low as possible,v should take level 3,L should take level 2,S should take level 2,D should take level 1,and P should take level 1.When v=95 m/min,L=12 mm,S=795 mm,D=250 mm,and P is on the high position,each factor is optimal.

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(2) Variance analysis

Variance analysis was applied to analyze the experimental results.The calculation results are shown in Table 4.

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Let us consider the test level of α as 0.05.From Table 4,for hot dip galvanizing,we can see that v had the most significant influence on the quality of galvanized steel and that the order of other factors was L,S,D, and P.The result was the same as the result obtained from range analysis.

4　Conclusion

Through the orthogonal experimental design of the hot dip galvanizing process,and after considering various factors,under the condition that v,L,S,D,and P are the chosen experimental factors,we find that v is the most significant factor,and that the optimal process parameters are:v=95 m/min,L=12 mm,S=795 mm,D=250 mm,and P is on the high position.

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