CN106092020A - The method of testing of melt cinder film thickness in a kind of continuous cast mold - Google Patents

Abstract

The present invention relates to the method for testing of melt cinder film thickness in a kind of continuous cast mold, belong to continuous casting of iron and steel technical field；First the present invention carries out small-sized continuous casting experiment, utilizes thermocouple gather the temperature in continuous casting experimentation and preserve in a computer, goes out the heat flow density of the crystallizer hot side along throwing directional spreding with the temperature inverse of actual measurement；Initial solidification strand measure the green shell thickness along throwing direction after cutting experiment, utilizes slab thickness inverse to go out the temperature along throwing directional spreding and the heat flow density on green shell surface；On this basis, the physical parameter of join protection slag, calculate the thickness distribution of liquid slag film between crystallizer wall and casting billet surface；In the present invention utilizes continuous cast mold, solidification simulation device combined mathematical module accurately calculates the thickness distribution of liquid slag film between the crystallizer wall under specific continuous-casting conditions and casting billet surface, provides infallible data for the calculating of the lubrication of covering slag, heat transfer and liquid frictional force in accurate assurance crystallizer.

Description

The method of testing of melt cinder film thickness in a kind of continuous cast mold

Technical field

The present invention relates to the method for testing of melt cinder film thickness in a kind of continuous cast mold, belong to continuous casting of iron and steel technical field.

Background technology

The lubrication of crystallizer and heat transfer are control slab qualities, improve the two big factors that production efficiency is the most key.Pass through The vibration of crystallizer, the space that the liquid covering slag on molten steel upper strata is pumped between crystallizer wall and casting billet surface, form solid-state Slag film and liquid slag film, slag film plays the effect of Heat Transfer Control；Liquid slag film also has the effect of lubrication, reduces resistance of billet withdrawal, anti- Stop cohering of green shell crystallizer wall.If liquid slag film is the thinnest, covering slag greasy property can be caused to be deteriorated, increase crystallizer wall and casting Frictional force between base surface, is easily caused strand and produces the face crack even generation of bleed-out phenomenon；If liquid slag film is blocked up, meeting Increase the thermal resistance between crystallizer wall and casting billet surface, hinder the transmission of molten steel heat so that production efficiency reduces, and makes to draw knot simultaneously The strand of brilliant device is the thinnest, is easily caused bleed-out；If liquid slag film skewness, cause the heat transfer between solidification strand and crystallizer Medium is inconsistent, owing to the difference of its thermal characteristics makes casting blank surface temperature skewness, produces bigger on solidification strand Thermal stress, once exceed the allowable stress of high temperature green shell, the generation of strand crackle can be caused.Therefore, the thickness of melt cinder film and The uniformity of distribution has extremely important impact to heat transfer and lubrication, and then has influence on surface quality and the continuous casting production effect of strand Rate.

In crystallizer, lubrication state generally represents by frictional force, and the frictional force between crystallizer wall and casting billet surface is continuous The significant process parameter that should be closely monitored and control in cast steel, especially near meniscus, liquid between liquid slag and strand is rubbed Wiping power is bigger on the impact of initial solidification cc billet surface quality.The method of testing of frictional force mainly has at present: (1) force cell Directly method of testing；(2) experimental model method of testing；(3) mathematical model calculates method.Wherein most in the middle of mathematical model method are Newtonian fluid model: f_i=η_i(v_m-v_c)/d_l, wherein, f_iFor unit area liquid friction force, Pa；η_iFor liquid slag viscosity, Pa·s；v_mFor mold oscillation speed, m/s；v_cCasting speed, m/s；d_lMelt cinder film thickness, m；This computation model is simple and convenient, But requiring melt cinder film thickness accurately, melt cinder film thickness is then very difficult to accurately determine, current research only can prove that liquid The slag film thickness order of magnitude is 10^-5～10^-4M scope.Therefore, a kind of method of melt cinder film thickness in Accurate Prediction continuous cast mold Slab quality for continuous casting actual production controls and improves continuous casting production efficiency have great directive significance.Owing to high temperature is disliked Bad environment is difficult to directly measure melt cinder film thickness；The mainly liquid covering slag slag of its lubrication between crystallizer and green shell Film, it is considered that liquid slag film thickness is about 0.1mm；Jenkins(Jenkins M S.Heat transfer in the Continuous casting mold.Ph.D thesis Clayton, Monash University, 1999.) think melt cinder Film average thickness is 1/ (3V_c ^0.5), it is wherein V_cPulling speed of continuous casting.Japan NKK engineering institute Tsutsumi etc., Kawakami etc. (Tsutsumi K,Murakami H,Nishioka S I,et al:Tetsu-to-Hagane 84,no.9(1998):617- 624.Kawakami K,Kitagawa T,Mizukami H,et al:Tetsu-to-Hagané 67,no.8(1981): Mold simulator 1190-1199.) is used to measure the consumption of different continuous casting technique covering slag；But do not survey Amount is to the melt cinder film thickness along throwing direction.

Summary of the invention

For the deficiencies in the prior art, the present invention provides the method for testing of melt cinder film thickness in a kind of continuous cast mold, makes With initial solidification analog in crystallizer, based on the temperature of actual measurement and the slab thickness of actual measurement, inverse goes out crystallizer heat The heat flow density in face, the temperature of casting billet surface and the heat flow density of casting billet surface；On this basis, join protection slag physical property ginseng Number, wherein the crystallization temperature of covering slag is recorded by SHTT experiment, calculates liquid slag thickness, for protecting in accurate assurance crystallizer The calculating protecting the lubrication of slag, heat transfer and liquid frictional force provides infallible data.

In a kind of continuous cast mold of the present invention, the method for testing of melt cinder film thickness, comprises the steps:

Step one

Based on laboratory room small-sized continuous casting experimental simulation factory continuous casting of iron and steel process；Thermocouple measurement in collection crystallizer Temperature data, and pass to data handling equipment；

Step 2

The temperature data being collected is substituted into Billet mathematical model by data handling equipment, calculates by crystallization in real time Heat flow density q of device hot side each point_int；

Step 3

Initial solidification green shell measure the green shell thickness along throwing direction after cutting experiment, utilizes shell thickness, molten steel Thermal conduction study physical function parameter (density, thermal capacitance, heat conductivity and the heat content) inverse of cast temperature and steel goes out green shell surface along drawing Temperature T of base directional spreding_shellWith heat flow density q along throwing directional spreding_shell；

Step 4

Measure crystallization temperature T of covering slag_sol；

Step 5

Calculate the melt cinder film thickness d between the crystallizer wall and strand of throwing directional spreding_l；

Heretofore described Temperature sampler is preferably thermocouple.

In the present invention, data handling equipment is preferably computer, and other equipment that can process data are used equally to this certainly Bright.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step one, described continuous casting is tested, and uses Solidification simulation device in continuous cast mold, sets continuous casting parameter, and described parameter includes frequency of vibration, Oscillation Amplitude, cast temperature Degree, firing test device, carry out continuous casting experiment according to the described parameter set；Described frequency of vibration is 1-5Hz, is preferably industry The actual vibration frequency of continuous crystalizer during application；Oscillation Amplitude is 1-6mm, pouring temperature is more than the liquidus temperature of steel 10-50℃。

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 2, in described crystallizer, along Short transverse (throwing direction), in the crystallizer wall of vertical mold hot side in vertical section, installs two groups of thermocouples, first group Thermocouple is arranged on same vertical curve；Second group of heat it is provided with between first group of thermocouple and its corresponding crystallizer hot side Galvanic couple, second group of thermocouple can not be on same vertical curve.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, two groups of thermocouples, first group of thermocouple sets Put on same vertical curve；It is provided with second group of thermocouple between first group of thermocouple and its corresponding crystallizer hot side, the Two groups of thermocouples can not be on same vertical curve.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 2, described q_intFor along throwing side To, two heat extraction galvanic couples the heat flow density set of each point on parallel crystallizer hot side.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 2, described mathematical Model of Heat Transfer For Two-Dimensional Heat mathematical model.2DIHCP for mold heat flux software (registration number it is preferably when industrial applications 2016SR067373) process the data collected.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 3, by utilizing solidification rhetorical question Topic Levenberg-Marquardt method algorithm solves green shell surface temperature T along throwing directional spreding_shellDraw with edge Heat flow density q of base directional spreding_shell.Described solidification indirect problem Levenberg-Marquardt method algorithm sees Kei " the OPTIMAL NUMERICAL METHODS FOR INVERSE HEAT CONDUCTION AND INVERSE of Okamoto DESIGN SOLIDIFICATION PROBLEMS " the 21-33 page.

In a kind of continuous cast mold of the present invention, the method for testing of melt cinder film thickness, in step 4, is tested by SHTT, records Crystallization temperature T of liquid covering slag_sol.Wherein the cooling rate of liquid covering slag is by calculated strand real-time in step 3 The temperature on surface i.e. green shell surface temperature T_shellDetermining, the covering slag cooldown rate in crystallizer is approximately equal to casting billet surface Cooldown rate.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 5, described d_lFor along throwing side To, the data acquisition system of diverse location liquid covering slag slag film thickness between crystallizer wall and strand.

The method of testing of melt cinder film thickness in a kind of continuous cast mold of the present invention, in step 5, calculates and divides along throwing direction Melt cinder film thickness d between crystallizer wall and the strand of cloth_lTime, it is the physical parameter of join protection slag, described physical parameter bag Include liquid slag heat conductivity, radiation coefficient, covering slag crystallization temperature and crystallizer heat flow density q_int, green shell surface temperature T_shell, Calculate.It optimizes calculating and formula used is as follows:

$R_l=\frac{T_{shell}-T_{sol}}{q_{\mathrm{int}}}---\left(1\right)$

$R_l=\frac{1}{1/R_{lc}+h_{lr}}---\left(2\right)$

$R_{lc}=\frac{d_l}{k_{sl}}---\left(3\right)$

$\frac{1}{h_{lr}}=\frac{0.75a_l{d}_l+{\mathrm{\ϵ}}_{sh}^{-1}+{\mathrm{\ϵ}}_{cry}^{-1}-1}{m^2{\mathrm{\σ}}_B(T_{shell}^2+T_{sol}^2)(T_{shell}+T_{sol})}---\left(4\right)$

In above-mentioned formula, R_lFor melt cinder film entire thermal resistance m²·K/W；R_lcFor melt cinder film thermal conduction resistance, m²·K/W；h_lrFor liquid Slag film radiation heat transfer coefficient, W/m²·K；k_slFor liquid slag heat conductivity, W/m K；a_lAbsorptance m for liquid slag^-1；ε_sh Emissivity for strand；ε_cryEmissivity for crystalline state covering slag；M is reflection factor；σ_BNormal for Stefan-Boltzmann Number, W/ (m²·K⁴)；

Wherein k_sl、a_l、ε_sh、ε_cry、m、σ_BFor known parameter (can draw by consulting handbook)；More than simultaneous several Formula can obtain the melt cinder film thickness d between crystallizer wall and strand_l。

Other calculate along the melt cinder film thickness d between the crystallizer wall and strand of throwing directional spreding_lMethod also can use In the present invention.

Advantages of the present invention:

Use continuous cast mold initial solidification analog (ZL201110301430.3), it is possible to arrange very easily with real The casting parameters that border commercial production is close, simultaneously with industrial protection slag and iron and steel as raw material, therefore experimentation can be very The initial solidification behavior of Mold in the actual casting process of good reduction；With temperature in the crystallizer of actual measurement and actual measurement strand Based on thickness, can more accurately inverse to go out the heat flow density of crystallizer hot side, casting blank surface temperature and casting billet surface hot-fluid close Degree；Join protection slag physical parameter, wherein the crystallization temperature of covering slag is recorded by SHTT experiment, calculates liquid slag thickness, Infallible data is provided for the calculating of the lubrication of covering slag, heat transfer and liquid frictional force in accurate assurance crystallizer.

Accompanying drawing explanation

Fig. 1 is position of thermocouple, flux film distribution and shell growth generalized section；

Fig. 2 is speed and the displacement of a vibration period interior crystallizer；

Fig. 3 is the heat flow density of the crystallizer hot side along throwing directional spreding calculated；

Fig. 4 is the slab thickness measured；

Fig. 5 is the temperature of the casting billet surface along throwing directional spreding calculated；

Fig. 6 is the heat flow density of the casting billet surface along throwing directional spreding calculated；

Fig. 7 is the distribution of melt cinder thickness between crystallizer wall and casting billet surface；

Fig. 1 is position of thermocouple, flux film distribution and shell growth generalized section；Thermocouple is arranged in bent moon In crystallizer arm near face, rectangle ABCD is the zoning of Two-Dimensional Heat mathematical model, and AB, BC, CD, AD are respectively border Position；Near meniscus, molten steel contact water mold arm solidification forms initial solidification green shell, along with throwing down thickness not Break and grow up；Simultaneously under mold oscillation, liquid covering slag penetrates into the gap between crystallizer wall and green shell surface, at crystallizer wall Cooling effect under be formed close to the Solidified Flux Film of crystallizer wall and near the liquid slag film of casting billet surface, slag film plays control and passes The effect of heat, makes green shell heat transfer uniformly, and melt cinder film plays the effect of lubrication, reduces frictional resistance during throwing；Last liquid State slag film thickness the most thinning most zero；Z-direction is the direction of throwing, X slag film thickness direction.

Each moment during one vibration period T=0.5s interior crystallizer of crystallizer moves up and down as can be seen from Figure 2 Corresponding speed and displacement.

The most calculated hot-fluid corresponding along the crystallizer hot side AB every bit of throwing directional spreding is close Degree q_int, the wherein tip of corresponding strand at Z=0mm.

Measure the slab thickness of gained as can be seen from Figure 4；Its embodiment is after experiment terminates, and intercepts along throwing direction The longitudinal section of strand, then records the strand thickness along throwing direction.

Can be seen that utilization solidification indirect problem Levenberg-Marquardt method algorithm is solved from Fig. 5 and Fig. 6 The green shell surface gone out is along temperature T of throwing directional spreding_shellHeat flow density q along throwing directional spreding_shell。

As can be seen from Figure 7 along melt cinder thickness d between the crystallizer wall and casting billet surface in throwing direction_lRelation with position Z.

Detailed description of the invention

Below by specific embodiment, in conjunction with accompanying drawing, the present invention is described in further detail.

In the present embodiment, in order to calculate the covering slag slag consumption during mold oscillation, specifically include following steps:

Step 1, get out experiment steel and experiment covering slag；

In the embodiment of the present invention, steel grade used is ultra-low-carbon steel, and composition is as shown in table 1 below；Covering slag basicity used is 0.96, composition is as shown in table 2；

Table 1 ultra-low-carbon steel composition (wt%).

Table 2 covering slag composition (wt%).

In step 2, employing continuous cast mold, solidification simulation device is tested, and sets continuous casting parameter, described parameter bag Include frequency of vibration, Oscillation Amplitude, pouring temperature and cooling condition, firing test device, carry out even according to the described parameter set Casting experiment；

In the present embodiment, in continuous cast mold, solidification simulation device uses the continuous casting of Patent No. ZL201110301430.3 Mold solidification simulation device, this device discloses structure in the patent, belongs to common knowledge；The concrete company set Casting parameter is: pulling rate 10mm/s, frequency of vibration 2Hz (i.e. vibration period T=0.5s), Oscillation Amplitude 3mm, pouring temperature 1555 DEG C, cooling water flow 3.0L/min, water temperature 24 DEG C；According to set parameter, the vibration speed of a vibration period interior crystallizer Degree V_mAnd vibration displacement D_mAs shown in Figure 2；

Step 3, experimentation utilize the thermocouple being imbedded in copper plate of crystallizer gather casting process with given pace In temperature and be stored in computer, based on actual measurement temperature, inverse obtains the heat flow density of crystallizer hot side；

(1) copper plate of crystallizer median plane installs the thermocouple that two row's depths are different, and the distance of distance crystallizer wall is respectively 3mm and 8mm, thermocouple has eight row, from top to bottom, the distance between row be respectively 3mm, 3mm, 3mm, 3mm, 3mm, 6mm, 10mm, as shown in Figure 1；

(2) the thermometric frequency of fast thermocouple is set to 60Hz, and the software collection that by data collecting card and matches also is deposited The temperature that heat accumulation galvanic couple records；

(3) temperature based on actual measurement, substitutes into crystallizer Two-Dimensional Heat mathematical model 2DIHCP for mold by temperature data Heat flux software, obtains heat flow density q of crystallizer hot side (AB)_intAs it is shown on figure 3, strand tip position Z= 0mm, most advanced and sophisticated above Z value is negative, and most advanced and sophisticated following Z value is just；

Step 4, cut experiment after initial solidification strand measure the green shell thickness along throwing direction, utilize slab thickness Inverse goes out green shell surface along the temperature of throwing directional spreding and heat flow density；

(1) after casting process completes, solidification strand is taken off from crystallizer, use contourograph to measure strand along throwing Thickness distribution upwards, as shown in Figure 4；

(2) based on the slab thickness measured, one-dimensional solidification and heat transfer inverse problem model (1DITPS) inverse is used to go out green shell table Face is along the temperature of throwing directional spreding and heat flow density, casting blank surface temperature T_shellAs it is shown in figure 5, casting billet surface heat flow density q_shellAs shown in Figure 6；

Step 5, the physical parameter of join protection slag, described physical parameter includes liquid slag heat conductivity, radiation coefficient, guarantor Protect slag crystallization temperature, on the basis of step 2 and step 3, calculate between the crystallizer wall and strand of throwing directional spreding Melt cinder film thickness d_l；

(1) fall off rate equal to casting blank surface temperature of covering slag cooldown rate approximation:

(1800K-1600K)/2.0s=100K/s

(2) under the cooldown rate of 100K/s, single Thermocouples Technology (SHTT) is used to measure covering slag crystallization temperature T_sol, It it is 1050 DEG C；

(3) heat transfer between crystallizer, slag film and strand is regarded for the one dimensional heat transfer on x direction, based on preservation of energy, in conjunction with guarantor Protecting slag physical parameter, crystallizer heat flow density, casting blank surface temperature, the calculating of liquid slag film thickness can simultaneous below equation:

$R_l=\frac{T_{shell}-T_{sol}}{q_{\mathrm{int}}}---\left(1\right)$

$R_l=\frac{1}{1/R_{lc}+h_{lr}}---\left(2\right)$

$R_{lc}=\frac{d_l}{k_{sl}}---\left(3\right)$

$\frac{1}{h_{lr}}=\frac{0.75a_l{d}_l+{\mathrm{\ϵ}}_{sh}^{-1}+{\mathrm{\ϵ}}_{cry}^{-1}-1}{m^2{\mathrm{\σ}}_B(T_{shell}^2+T_{sol}^2)(T_{shell}+T_{sol})}---\left(4\right)$

In above-mentioned formula, R_lFor melt cinder film entire thermal resistance m²·K/W；R_lcFor melt cinder film thermal conduction resistance, m²·K/W；h_lrFor liquid Slag film radiation heat transfer coefficient, W/m²·K；k_slFor liquid slag heat conductivity, W/m K；a_lAbsorptance m for liquid slag^-1；ε_sh Emissivity for strand；ε_cryEmissivity for crystalline state covering slag；M is reflection factor；σ_BNormal for Stefan-Boltzmann Number, W/ (m²·K⁴)；

In aforementioned four equation, have four unknown quantity R_l、R_lc、h_lrAnd d_lIt is, more than simultaneous that four equations can obtain liquid The distribution of slag film thickness, as shown in Figure 7.

Claims (10)

1. the method for testing of melt cinder film thickness in a continuous cast mold, it is characterised in that comprise the steps:

Step one

Based on laboratory room small-sized continuous casting experimental simulation factory continuous casting of iron and steel process；The temperature of the thermocouple measurement in collection crystallizer Data, and pass to data handling equipment；

Step 2

The temperature data being collected is substituted into Billet mathematical model by data handling equipment, calculates in real time by crystallizer heat Heat flow density q of face each point_int；

Step 3

Initial solidification green shell measure the green shell thickness along throwing direction after cutting experiment, utilizes shell thickness, molten steel casting The thermal conduction study physical function parameter inverse of temperature and steel goes out green shell surface temperature T along throwing directional spreding_shellWith along throwing side Heat flow density q to distribution_shell；

Step 4

Measure crystallization temperature T of covering slag_sol；

Step 5

Calculate the melt cinder film thickness d between the crystallizer wall and strand of throwing directional spreding_l。

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In one, described continuous casting is tested, and uses solidification simulation device in continuous cast mold, sets continuous casting parameter, and described parameter includes shaking Dynamic frequency, Oscillation Amplitude, pouring temperature, firing test device, carry out continuous casting experiment according to the described parameter set；Described vibration Above 10-50 DEG C of the liquidus temperature that frequency is 1-5Hz, Oscillation Amplitude is 1-6mm, pouring temperature is steel.

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In two, in described crystallizer, two heat extraction galvanic couples are installed along throwing direction；Described two heat extraction galvanic couples are each parallel to the warm of crystallizer Face.

4. according to the method for testing of melt cinder film thickness in claim 3 continuous cast mold, it is characterised in that: along height side To, in the crystallizer wall of vertical mold hot side in vertical section, two groups of thermocouples are installed, first group of thermocouple is arranged on same On bar vertical curve；Second group of thermocouple, second group of thermoelectricity it is provided with between first group of thermocouple and its corresponding crystallizer hot side Occasionally can not be on same vertical curve.

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In two, described q_intFor along throwing direction, two heat extraction galvanic couples the heat flow density set of each point on parallel crystallizer hot side.

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In two, described mathematical Model of Heat Transfer is Two-Dimensional Heat mathematical model.

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In three, solidification indirect problem Levenberg-Marquardt method algorithm is utilized to solve green shell surface along throwing directional spreding Temperature T_shellWith heat flow density q along throwing directional spreding_shell。

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In four, tested by SHTT, record crystallization temperature T of covering slag_sol。

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In five, described d_lFor along throwing direction, the data acquisition system of diverse location liquid covering slag slag film thickness between crystallizer wall and strand.

The method of testing of melt cinder film thickness in a kind of continuous cast mold the most according to claim 1, it is characterised in that: step In rapid five, the melt cinder film thickness computing formula between the crystallizer wall and strand of throwing directional spreding is as follows:

$R_l=\frac{T_{shell}-T_{sol}}{q_{\mathrm{int}}}---\left(1\right)$

$R_l=\frac{1}{1/R_{lc}+h_{lr}}---\left(2\right)$

$R_{lc}=\frac{d_l}{k_{sl}}---\left(3\right)$

$\frac{1}{h_{lr}}=\frac{0.75a_l{d}_l+{\mathrm{\ϵ}}_{sh}^{-1}+{\mathrm{\ϵ}}_{cry}^{-1}-1}{m^2{\mathrm{\σ}}_B(T_{shell}^2+T_{sol}^2)(T_{shell}+T_{sol})}---\left(4\right)$

In above-mentioned formula, R_lFor melt cinder film entire thermal resistance m²·K/W；R_lcFor melt cinder film thermal conduction resistance, m²·K/W；h_lrFor melt cinder film spoke Penetrate heat transfer coefficient, W/m²·K；k_slFor liquid slag heat conductivity, W/m K；a_lAbsorptance m for liquid slag^-1；ε_shFor strand Emissivity；ε_cryEmissivity for crystalline state covering slag；M is reflection factor；σ_BFor Stefan-Boltzmann constant, W/ (m²·K⁴)；

Wherein k_sl、a_l、ε_sh、ε_cry、m、σ_BFor known parameter；It is more than simultaneous that several formulas can obtain crystallizer wall and strand Between melt cinder film thickness d_l。