CN109960835A - The method for establishing continuous cast mold heat flux distribution model - Google Patents
The method for establishing continuous cast mold heat flux distribution model Download PDFInfo
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Abstract
The present invention relates to a kind of method for establishing continuous cast mold heat flux distribution model, the method is as follows: step 1: under conticaster normal operating conditions, acquiring along the crystallizer heat flow density value suitable for reading started along multiple positions of throwing short transverse；Step 2: carried out in entire data area primary " cubic spline interpolation ", step 3: the function of judgment curves is exponential distribution function, use form for
Description
Technical field
The present invention relates to a kind of methods, and in particular to a method of continuous cast mold heat flux distribution model is established, is belonged to
Continuous casting technology field.
Background technique
Conticaster crystallizer is the initial solidification equipment that liquid metal is changed into the slab with certain cross sectional shape, is
The core equipment of conticaster.In crystallizer, the heat of molten steel conducted heat through green shell, protection slag blanket, air gap, copper plate of crystallizer etc.
Journey, finally cooled water with.
In order to carry out the computer simulation analysis of Billet it is necessary to defining the heat transfer perimeter strip in the hot face of copper plate of crystallizer
Part.According to forefathers' experimental study it is known that in crystallizer copper plate surface, along the top-down heat of the short transverse of throwing
Current density distribution be it is nonlinear, basic law is that hot-fluid steeply rises near meniscus, and quickly reduces, finally
Slowly varying in remaining height, the peak value and average value of heat flux increase with the increase of pulling rate.
Crystallizer copper plate surface can be divided into three regions: 1. free area by the characteristic distributions of heat flow density from top to bottom,
The general molten steel identity distance crystallizer free space suitable for reading for having about 50~100mm, the section copper sheet heat flow density close to 0；
It is copper sheet heat flow density 2. high-temperature region, molten steel face and the following section 200~300mm molten steel and copper plate of crystallizer are in close contact
Peak region；3. descending area, from high-temperature region with the mouth under crystallizer, the heat flow density in the region gradually subtracts from top to bottom
It is small.
In the actual production process, since the parameters such as pulling rate, liquid steel temperature are in always in lasting change procedure, knot
Continuous casting billet surface and copper sheet surface temperature and heat flow density are also among lasting variation in brilliant device, but heat flux distribution
Basic model remains unchanged, and peak value size persistently changes in other words, but its relative position remains unchanged.
The regularity of distribution math equation of heat flow density is accurately expressed and is of great significance, can be applied to accurate analysis meter
Billet operating condition is calculated, the real-time tracking for further applying numerical simulation calculation and production scene is shown.Hot-fluid has been determined
Along the distribution equation of crystallizer short transverse, the heat transfer boundary condition in the hot face of copper plate of crystallizer is also defined.
Summary of the invention
The present invention exactly for the technical problems in the prior art, provides and a kind of establishes continuous cast mold heat flux distribution
The method of model, the curvilinear equation are alternatively referred to as curve model, and the curve of the model equation is that a kind of continuous and derivable curve counts
It can continuously lead on, be mainly made of four sections such as zero section, rapid increase section, rapid decrease section, slow descending branch, it is bent
The amplitude of line is adjusted according to mean heat flux value.
To achieve the goals above, technical scheme is as follows, a kind of to establish continuous cast mold heat flux distribution model
Method, the method is as follows: step 1: under conticaster normal operating conditions, acquisition is along crystallizer beginning suitable for reading along throwing height
Spend the heat flow density value of multiple positions in direction.Specific position can be adjusted according to the bolt arrangement etc. of crystallizer, but
It is the acute variation region of heat flow density in 50~150mm height section, sampled point spacing should be no more than 20mm；In 40mm or more
Region, heat flow density is approximately 0, it is not necessary to acquire data；In the region below 200mm, heat flow density variation tends towards stability, and adopts
Sampling point spacing is set as 50~100mm.It is shown in Table 1:
The data point that table 1 measures
Step 2: it is carried out in entire data area primary " cubic spline interpolation ", 1 Test Point Data of table is supplemented,
Obtain the elementary contour of heat flux distribution curve；
Step 3: referring to Fig. 1, the function of judgment curves is exponential distribution function, uses form for y=aef(x)Function pair
Initial data is fitted, and in order to approach fitting more, further sets logarithmic form, i.e. y for the independent variable in f (x)
=aef(lnx).Wherein because having constant term in f (x), therefore coefficient a is negligible.Then target fitting function is set to:
Y=ef(lnx) (1)
Further conversion can obtain lny=f (lnx), and wherein function f (x) is the polynomial function about lnx.If f (x) is
4 order polynomials of lnx, i.e.,
Lny=a (lnx)4+b(lnx)3+c(lnx)2+d(lnx)+h (2)
The parameter such as table 2 obtained is fitted by equation (2),
2 fitting parameter table of table
| a | b | c | d | h |
| -0.2401 | 6.0190 | -55.7934 | 225.8687 | -328.8825 |
The heat flux distribution equation being fitted are as follows:
Lny=-0.2401 (lnx)4+6.019(lnx)3-55.7934(lnx)2+225.8687(lnx)-328.8825 (3)
Equation (3) can be expressed further are as follows:
Step 4: drawing by the equation (4) that fitting obtains, obtain regeneration curve.The curve is characterized in total data model
Enclose interior continuous and derivable (mathematics can continuously be led), and the curve constructed by nearly zero section 1., rapid increase section 2., rapid decrease
Section 3., the slow descending branch four parts composition such as 4..
Step 5: heat flow curve being integrated, checks mean heat flux value.
Equation (4) is integrated, then divided by siding-to-siding block length to get the putting down along entire crystallizer height to heat flow density
Mean value is similar to 1000kw/m just2, this heat flux distribution curve can be considered as basic prototype less than 3 ‰ by error；
Step 6: the amplitude of heat flux distribution curve is adjusted according to the mean heat flux value of actual condition.
The curve of equation (4) is considered as to the mode standard of heat flux distribution, amplitude is adjusted on this basis, can be obtained difference
The heat flux distribution curve of mean value.By equation (4) multiplied by a coefficient, amplitude adjusting can be carried out to entire curve, it is final to obtain
Meet the heat flux distribution curve of actual condition, i.e. equation (5).
When target mean heat flux is 1200kw/m2, then before prototype curvilinear equation multiplied by 1.2 coefficient, obtain
Target heat flow density curvilinear equation is are as follows:
To, again divided by siding-to-siding block length, obtaining mean heat flux is 1197kw/m after target profile integral2, with mesh
Mark 1200kw/m2Error it is very small (less than 3 ‰).
Compared with the existing technology, the invention has the advantages that, to the target profile integral after it is long divided by section again
Degree, the error for obtaining mean heat flux and target is very small (less than 3 ‰), greatly improves simulation calculation and production is existing
The tracking display of field, improves work efficiency.
Detailed description of the invention
The curved profile that Fig. 1 interpolation obtains；
The curve of Fig. 2 fitting；
The heat flux distribution curve that Fig. 3 is regenerated；
The standard profile curve prototype of Fig. 4 fitting；
Fig. 5 standard prototype distribution curve and actual distribution curve；
The heat flux distribution curve of tri- kinds of average values of Fig. 6.
Specific embodiment:
In order to deepen the understanding of the present invention, the present embodiment is described in detail with reference to the accompanying drawing.
Embodiment 1: referring to Fig. 1-Fig. 5, a method of continuous cast mold heat flux distribution model being established, the method is such as
Under: step 1: under conticaster normal operating conditions, acquisition is along crystallizer beginning suitable for reading along multiple positions of throwing short transverse
Heat flow density value.Specific position can be adjusted according to the bolt arrangement etc. of crystallizer, but in 50~150mm height area
Between be heat flow density acute variation region, sampled point spacing should be no more than 20mm；In the region of 40mm or more, heat flow density is close
It is seemingly 0, it is not necessary to acquire data；In the region below 200mm, heat flow density variation tends towards stability, and sampled point spacing is set as 50
~100mm.It is shown in Table 1.
The data point that table 1 measures
Step 2: it is carried out in entire data area primary " cubic spline interpolation ", 1 Test Point Data of table is supplemented,
Obtain the elementary contour of heat flux distribution curve.The result is shown in Figure 1 of acquisition.
Step 3: observation Fig. 1, the function of judgment curves are exponential distribution function.Use form for y=aef(x)Function pair
Initial data is fitted.In order to approach fitting more, logarithmic form, i.e. y further are set by the independent variable in f (x)
=aef(lnx).Wherein because having constant term in f (x), therefore coefficient a is negligible.Then target fitting function is set to:
Y=ef(lnx) (1)
Further conversion can obtain lny=f (lnx), and wherein function f (x) is the polynomial function about lnx.If f (x) is
4 order polynomials of lnx, i.e.,
Lny=a (lnx)4+b(lnx)3+c(lnx)2+d(lnx)+h (2)
By the parameter such as table 2 that equation (2) fitting obtains, figure such as Fig. 2.
2 fitting parameter table of table
| a | b | c | d | h |
| -0.2401 | 6.0190 | -55.7934 | 225.8687 | -328.8825 |
The heat flux distribution equation being fitted are as follows:
Lny=-0.2401 (lnx)4+6.019(lnx)3-55.7934(lnx)2+225.8687(lnx)-328.8825 (3)
Equation (3) can be expressed further are as follows:
Step 4: drawing by the equation (4) that fitting obtains, obtain the regeneration curve of Fig. 3.The curve is characterized in whole
Continuous and derivable (mathematics can continuously be led) in data area, and the curve constructed by nearly zero section 1., rapid increase section 2., fastly
Fast descending branch 3., the slow descending branch four parts composition such as 4..
By Fig. 2,3 as it can be seen that the curve graph 1 that the curvilinear figure constructed is drawn with raw measurement data and interpolation is kissed very much
It closes.There is any discrepancy for position of the peak point of curve in height distance, and there is no big harm, because of actual liquid level fluctuation and liquid level setting
Position is also in lasting small range variation.
Step 5: heat flow curve being integrated, checks mean heat flux value.
Equation (4) is integrated, then divided by siding-to-siding block length to get the putting down along entire crystallizer height to heat flow density
Mean value is similar to 1000kw/m just2, this heat flux distribution curve can be considered as basic prototype less than 3 ‰ by error,
Such as Fig. 4.
Step 6: the amplitude of heat flux distribution curve is adjusted according to the mean heat flux value of actual condition.
The curve of equation (4) is considered as to the mode standard of heat flux distribution, amplitude is adjusted on this basis, can be obtained difference
The heat flux distribution curve of mean value.By equation (4) multiplied by a coefficient, amplitude adjusting can be carried out to entire curve, it is final to obtain
Meet the heat flux distribution curve of actual condition, i.e. equation (5).
When target mean heat flux is 1200kw/m2, then before prototype curvilinear equation multiplied by 1.2 coefficient, obtain
Target heat flow density curvilinear equation is are as follows:
Standard prototype distribution curve compared with actual distribution curve as shown in Figure 5.Distribution curve such as Fig. 5 of equation (6)
Shown in red line, to, again divided by siding-to-siding block length, obtaining mean heat flux is 1197kw/m after target profile integral2, with
Target 1200kw/m2Error it is very small (less than 3 ‰).
Application Example:
Crystallizer heat transfer flux calculation formula are as follows: Q=ρ Vc △ T/A (W/m2Or J/s.m2)；
In formula: ρ is the density of water；V is the volume of water；C is the specific heat capacity of water；△ T is disengaging water temperature difference；A be copper sheet by
Heat area.
The copper sheet heating surface area of scene setting are as follows: 0.8m × 0.21m；
When pulling rate 1.0m/min, the leptoprosopy water 550L/min of practical conticaster, 5.6 DEG C of water temperature difference, production control is calculated
Machine monitoring screen shows that heat transfer flux is 1.3mW/m2.The density 1000kg/m of water3, 4200J/kg. DEG C of specific heat capacity, calculate average
Heat flux (or heat flow density) is 1280kW/m2, it is approximately 1300kW/m2。
If calculated by leptoprosopy entire area 0.85m × 0.215m, heat transfer flux 1180kW/m2, can be approximately 1200kW/
m2。
According to above-mentioned calculating, it is at least also required to 1300kW/m2The distribution curve of heat flux.Its distribution equation are as follows:
The distribution curve of three kinds of average heat flux is as shown in Figure 6.
It should be noted that above-described embodiment, is not intended to limit the scope of protection of the present invention, in above-mentioned technical proposal
On the basis of made equivalents or substitution each fall within the range that the claims in the present invention are protected.
Claims (5)
1. a kind of method for establishing continuous cast mold heat flux distribution model, which is characterized in that the method is as follows:
Step 1: under conticaster normal operating conditions, acquisition is along crystallizer beginning suitable for reading along multiple positions of throwing short transverse
Heat flow density value；
Step 2: it is carried out in entire data area primary " cubic spline interpolation ",
Step 3: the function of judgment curves is exponential distribution function, uses form for y=aef(x) function carries out initial data
Fitting；Step 4: drawing by the equation (4) that fitting obtains, obtain regeneration curve；
Step 5: heat flow curve being integrated, checks mean heat flux value.
Equation (4) is integrated, then divided by siding-to-siding block length to get being averaged along entire crystallizer height to heat flow density
Value,
Step 6: the amplitude of heat flux distribution curve is adjusted according to the mean heat flux value of actual condition.
2. the method according to claim 1 for establishing continuous cast mold heat flux distribution model, which is characterized in that the step
1 is specific as follows, and specific position is adjusted according to the bolt arrangement of crystallizer, is that hot-fluid is close in 50~150mm height section
The acute variation region of degree, sampled point spacing should be no more than 20mm；In the region of 40mm or more, heat flow density is approximately 0, it is not necessary to
Acquire data；In the region below 200mm, heat flow density variation tends towards stability, and sampled point spacing is set as 50~100mm, sees
Table 1.
The data point that table 1 measures
3. the method according to claim 2 for establishing continuous cast mold heat flux distribution model, which is characterized in that the step
3 is specific as follows, sets logarithmic form, i.e. y=ae for the independent variable in f (x)f(lnx)；Because having constant term in f (x), therefore
Coefficient a is negligible, then target fitting function is set to:
Y=ef(lnx) (1)
Further conversion can obtain lny=f (lnx), and wherein function f (x) is the polynomial function about lnx.If f (x) is lnx's
4 order polynomials, i.e.,
Lny=a (lnx)4+b(lnx)3+c(lnx)2+d(lnx)+e (2)；
The parameter such as table 2 obtained is fitted by equation (2),
2 fitting parameter table of table
The heat flux distribution equation being fitted are as follows:
Lny=-0.2401 (lnx)4+6.019(lnx)3-55.7934(lnx)2+225.8687(lnx)-328.88 (3)
Equation (3) can be expressed further are as follows:
4. the method according to claim 3 for establishing continuous cast mold heat flux distribution model, which is characterized in that the step
4 is specific as follows, and curve continuous and derivable, that is, mathematics within the scope of total data can continuously be led, and the curve constructed is by nearly zero section
1., rapid increase section 2., rapid decrease section 3., the slow descending branch four parts composition such as 4..
5. the method according to claim 4 for establishing continuous cast mold heat flux distribution model, which is characterized in that the step
6 is specific as follows, and the curve of equation (4) is considered as to the mode standard of heat flux distribution, amplitude is adjusted on this basis, can be obtained not
With the heat flux distribution curve of mean value amplitude adjusting can be carried out to entire curve, finally obtained by equation (4) multiplied by a coefficient
The heat flux distribution curve of actual condition, i.e. equation (5) must be met；
When target mean heat flux is 1200kw/m2, then before prototype curvilinear equation multiplied by 1.2 coefficient, obtain target heat
Current density curvilinear equation is are as follows:
To, again divided by siding-to-siding block length, obtaining mean heat flux is 1197kw/m after target profile integral2, with target
1200kw/m2Error it is very small (less than 3 ‰).
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111475962A (en) * | 2020-04-21 | 2020-07-31 | 中冶南方连铸技术工程有限责任公司 | Instantaneous heat flow distribution construction method and calculation method for crystallizer |
| CN111998892A (en) * | 2020-07-23 | 2020-11-27 | 麦特勒智能科技(张家港)有限公司 | Mixed steel model system based on flow field and concentration field numerical simulation calculation |
| CN116628983A (en) * | 2023-05-23 | 2023-08-22 | 中国重型机械研究院股份公司 | Numerical calculation model method for funnel-shaped crystallizer funnel-shaped area curved surface of thin-blank continuous casting machine |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111475962A (en) * | 2020-04-21 | 2020-07-31 | 中冶南方连铸技术工程有限责任公司 | Instantaneous heat flow distribution construction method and calculation method for crystallizer |
| CN111475962B (en) * | 2020-04-21 | 2023-04-07 | 中冶南方连铸技术工程有限责任公司 | Instantaneous heat flow distribution construction method and calculation method for crystallizer |
| CN111998892A (en) * | 2020-07-23 | 2020-11-27 | 麦特勒智能科技(张家港)有限公司 | Mixed steel model system based on flow field and concentration field numerical simulation calculation |
| CN116628983A (en) * | 2023-05-23 | 2023-08-22 | 中国重型机械研究院股份公司 | Numerical calculation model method for funnel-shaped crystallizer funnel-shaped area curved surface of thin-blank continuous casting machine |
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