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热能设计外文文献及翻译用于分析在直燃式步进式加热炉本科毕业论文

热能设计外文文献及翻译用于分析在直燃式步进式加热炉本科毕业论文
热能设计外文文献及翻译用于分析在直燃式步进式加热炉本科毕业论文

用于分析在直燃式步进式加热炉

板坯瞬态加热的传热模型

摘要

一个可以预测板坯表面温度分布和热流情况的数学传热模型已开发出来了,主要是通过充分考虑在炉膛内的板坯的热辐射和瞬态热传导方程来实现的。该炉型是参照散热介质在空间中的变恒温过程和恒定的吸收系数来设计的。钢坯由步进梁从一个固定梁移动到下一个固定梁上,是以通过加热炉预热段.加热段和均热段为钢坯热传导方程的边界条件的加热炉模型。辐射热通量的计算是通过采用有限体积法,在炉子的内部,以炉墙.炉顶.炉底构成的充满烟气的环境里,作为板坯的瞬态传导方程的边界条件来进行计算的。板坯的传热特性和温度特性是通过调查可以改变板坯吸收系数和发射率的参数来确定的。比较多次的实践工作表明,目前用于预测板坯在加热炉中的传热过程和热流量的状况示范工程得到了很好的效果。

关键词:加热炉;钢坯加热;辐射传热;瞬态热传导;有限体积法

1 导言

在过去数十年以来,炉子进入降低能源消耗和污染物排放量的阶段,而分析钢坯瞬态热特性,在加热炉工程应用上已吸引了相当多注意。此外,限定板坯在炉子内有均匀的温度分布才能出炉的重要性大大增加了,只有准确、快速的预测炉内板坯的温度,才能为以后的轧制过程提供比较好的原料,因为这决定了钢铁产品质量的高低。在本质上,在炉膛内的整个燃烧过程和由此产生的热气流同时影响传热.对流和热辐射过程。然而,复杂的炉子内部的三维结构包括固定梁和步行梁打滑问题使的难以在经济上做出准确的分析。因此,模型和方法对于预测炉子内部燃烧特性和传热过程中存在着很高的要求。尤其是,准确预测热辐射量是最重要的,因为热辐射传热超过流过板坯表面总热流的90%。

现在没有一个单一的辐射模型就能够解决所有在工程应用中遇到的情况,所以应选择一个合适的途径为自己的侧重点。为了预测通过板坯表面上的辐射热通量,从而准确计算出炉子内板坯的温度分布,其解决方法是板坯必须是做连续运动,无灰的燃烧烟气作为该炉辐射气体,以及复杂的炉壁几何结构包括弯曲的板坯和防滑管道堵塞的影响,还有就是一定量的计算。许多可以预测在加热炉内板坯传热特性的模型和方法已经开发出来了,并且成功的应用到各种不同的炉型中,这些方法可以归类为下面几类:第一个是要解决好控制热气体流动和燃烧过程的节能方程,把热辐射作为辐射热流的能源来源,金大中等人完成了这些三维传热特性的分析,主要是考虑到烟气在步进梁上钢坯的湍流.平流和辐射传热作用,并用简洁的FLUENT代码表示出来。同时可以预测炉子内部的钢坯的温度分布和钢坯上下表面流过的热流量。金正日等人进行了类似的分析,并且做了预测钢坯顺态传热性能的热传导方程。虽然这些都是流体力学计算分析,但是可以用于准确地预测传热和燃烧的特点。在炉子内部钢坯的加热存在着这样的困难,因为处理那么多的方程和复杂的窑炉结构,以及不确定的模式,因而要求进行长期的监测计算和由此产生的费用。第二种方法是把加热炉分成几段炉气成分和性质相同的部分,再用由查仆曼等人提出的一维气体能量平衡进行分析。他们想通

过实验参数的观察,找出影响加热炉内钢坯及耐火墙辐射和燃烧空间高度,以及传热性能的因素。虽然没有什么结果,但是,进行了有关钢坯温度分布的预测,并且进行了一些需要处理极其复杂的步进式加热炉的集合特性修改审议工作。最后比较前面一种方法,这种办法很简单,可以合理的模拟出钢坯的热量分布状况,且把重点放在分析关于气体辐射传热和钢坯内部瞬态传导上,资料五的作者研究的稳态传热模型,在用这个模型时,炉子内的热辐射计算用分区计算的方法,而钢坯的热反应可以通过解析瞬态二维热传导方程来获得。以笔者的了解,用分区计算法计算工程的成本,以及处理复杂的加热炉结构因素还是有一定难度的。而资料6的作者也开发了类似的预测炉子内部的传热模型,炉气充满炉内空腔,在炉墙和防滑管道上,以板坯在炉子内前进的方向为基准的横向二维稳态传热为研究重点。而比起前一种方法,这种方法更加的简单,减少了我们计算所需要的时间。对于更普通的和计算效率更加高的模型,就提出了更高的要求,为快速而准确的预测钢坯内部的温度分布,如果考虑到有用联合模式,及监测和控制炉子内情况,就像是控制燃烧器和板坯停留在炉子内的时间的实时操作。

最近,巴西和杜塔[ 7 ]介绍了一种在直燃型推钢式加热炉,采用有限体积法计算传热辐射的模型。在这项工作中,预测炉内的流过板坯表面热通量和钢坯内温度分布的数学传热模型已经研制成功,在板坯在步进式加热炉中,通过分别考虑在炉膛内热辐射和瞬态传导方程来实现。该炉是仿照关于辐射介质在空间中线性变温和恒定吸收系数来设计的。板坯是由步进梁传送的,由步进梁定期运送通过预热段.加热段和均热段。辐射热通量计算采用有限体积法以辐射热交换与炉膛辐射效果,炉墙,炉顶,和燃烧气体适用瞬态热传导方程的边界条件计算的。在以下几节描述后,这里预测炉过程与加热炉所采用的方法是,查找钢坯传热性能和热通量,通过改变板坯的吸收系数和发射率等参数,而还介绍了与实践数据的比较。最后,作出有一些结论性意见的适当的解释。

2 制定

2.1 炉子说明

?,为加热钢坯所消耗的能加热炉的任务是为随后的轧制过程将钢坯加热到将近1200C

源,由顶部和底部的煤气烧嘴提供的。通常情况下,将加热炉分成5个区域,排烟区,换热区,预热段,加热段和均热段,如图表1显示。这是浦项制铁公司的简化炉模型。钢坯由步进梁从一个固定梁移动到下一个固定梁上,步进梁大约一分钟移动一次,看板坯在炉子内部停留时间来决定的。总的炉子长度规定为39.2米,而炉膛高度是变化的,每一个区用倾斜屋顶连接。每个钢板是长1.16米,厚度是0.23米,钢坯之间的间距是0.2米。因此,在

?时被送入炉内。板坯停留时间,目前炉存在着共计28钢坯。该钢坯被假定为温度21.2C

即从预热段入口到均热段的出口为止,经过180分钟的加热,在炉膛出口板坯获得平均温度约1200C?,因此,钢坯每4.6分钟就移动一次。

2.2 方程

如图2显示了发生在炉膛内部传热过程,在这项研究中,假定向板坯表面热传递模式只有热辐射传热。钢板内部传热可以用瞬态二维热传导方程计算出来,及公式一。其中ρ,C 和K分别为密度,比热,该钢板的导电性。

)()(y T k y x T k x t T C

????+????=??ρ (1)

Ω?=?=Ωd n s s r I q w w R slab ))(,(4π (2) ?=ΩΩ'?→?Φ+-+-=ππ

ωωβ4000)(),(4)()1(),(),(1d s s s r I r I s r I ds s r d b (3) Ω'?-+=??d n s s r I r I s r I w n s w w w bw w w w ),(1)(),(πεε (4)

通过该板坯表面辐射热通量,

R slab q 在图三中已经显示出来了,是用来作为上述方程( 1 )的边界条件,其中(,)w I r s 是钢坯表面w r 和s 方向的辐射强度。w n 是在板坯表面正常的单位向量,Ω是立体角。r 是活性辐射介质辐射在任何方向的强度,沿着路径s 通过介质的吸收,发射和散射可以确定以下方程(3), 0a s k βσ=+是吸收光系数, 00s w σβ=

是散射反照率,

'()s s φ→是从传入方向's 向方向s 散射的散射系数,这个等式,如果平均温度和边界条件强度给出,提供了一个辐射强度分布情况等。一个漫反射与温度w T ,这是方程边界条件。那么方程( 3 )可表示为发射量和反射量的总和,如方程(4), 其中

w ε是

炉墙的发射率,而4/bw I T σπ=是黑体强度的墙上。 2.3 有限体积的解决方法

瞬态热传导方程是由帕坦卡[ 8 ]所建议的使用有限体积法的离散型程序。一个中心差分法用于在X 和Y 方向扩散的条件。由此产生的离散系统,然后反复使用TDMA 的算法来解决,直到温度场的板坯满足下列收敛准则可使用德国马克瓦特的定向量来预测如下: 为获板坯每个时间的温度, 计算从热辐射开始,在加热炉商会给予的对每个板坯表面辐射热通量, 然后,板坯的热传导是顺序模拟从第一到最后第二十八板坯。这一计算回路重复,直到板坯由一个步进梁移动到下一固定梁,上述计算程序是显示在该地点最初的板坯温度进行计算的。这些计算程序终止时,它成为该板坯在加热炉内停留的时间。

一个控制角度给定,但允许它的方向能够变化,可以得到下列等式:

m p m S m S m N m N m w m w m E m E m p m I b I a I a I a I a I a ++++= (6)

)0,max(m i i m l D A a ?-= (7) m

p m i s n w e i i m p V D A a ?Ω?+?=∑=,0,,,)0,max(

β (8)

m p m R m p V S b ?Ω?=)( (9) ?=Ω'-''?ΩΦ+=ππσ44m m m m s b a m R I I k S (10)

m i m l d n s D m Ω?=??Ω)( (11) 其中i A ?和i n 分别是表面单元的外法线量。下流节点强度等于上游节点强度这是已采纳的步骤。离散化过程和有关量很容易找到在Baek 等人的文献中。如在炉内板坯和在底部炉壁块的这些区域存在溶液,比如图4a 的点B ,Chai 等人建议关闭程序。公式10可以被采纳。在这种解决办法中,虽然计算在整个域完成,在活跃的地区这种唯一的解决办法是有意义的。为了解释闭式的解决办法,一个额外的项被带入公式6,如下式12。

m P A P A C A I S S S += (12)

对于在非活跃区域的单元,变为

0=A C S 和LN S A P =(这里LN 是一个非常大的数,比如2010,然而在活跃区域A C S 和A P S 都设定为相同的零值。对于直接接触的的活跃单元,例

如图4a 的W 点,受到下列条件的限制:

)1(1m m W M m m W W bW W m m W W A C

D I I V D A S ?Ω-+?Ω??-=∑=πεε (13)

0=A P S (14) 最终,公式8和9的系数被改变如下:

m A P p m i s

n w e i i m P V S D A a ?Ω?-+?=

∑=)()0,max(,0,,,β (15)

m p A c m R m

P V S S b ?Ω?+=)( (16) 当下面值收敛时,迭代求解过程终止。

6

,10)/max(-≤-m P old m P m P I I I (17)

这里old m P I ,是m P I 以前的迭代值。

一旦获得强度场,在公式2中的板坯表面热辐射流量可以被测得通过使用方向权重如下式:

m w

M m m w w w R

slab

D I d n s s r I q ∑?==Ω=Ω=14),)(,( π (18)

在每个时间段若想要获得每个板坯的温度,计算就要从炉腔体的热腐蚀开始。然后板坯内部的热传导从模拟的第一块到最后的第28块进行。这种计算循环往复,直到板坯通过一个步进梁移动到下一个固定的光束上,上述的计算过程通过之前计算过的一位置点的初始板坯温度进行。当值变为板坯在炉内的停留时间时这些计算程序被终止。 3 结果与讨论

3.1 热行为炉进程

加热炉传热与热辐射模型,上述应用于调查钢坯在炉膛内瞬态热传导和通过钢坯上下表面的热流量,特别是着眼于每一个板坯表面温度分布和对板坯表面辐射热流上。在模型五中的加热炉类似于浦项制铁公司的加热炉。该炉墙和气体温度模拟概况分别作列于表1 ,板

坯的热性能在表2中给出了。 基本的辐射特性,如辐射气体的吸收系数10.15a k m -= ,该

炉墙的辐射系数分别设置为0.75和0.5 ,虽然是假设没有散射,即

0s σ= ,因此,00ω= 。空间网格系统使用在这项研究是()(19829)

x y N N +=?和角系统对()(412)N N θφ+=??。所有计算是在运行频率1.7兆赫的个人电脑进行的,并要求计算时间大约是1260秒。图5说明共计28砖的温度分布和五区的炉温见表1 。第一块板坯以21.2C ?移动到预热段,受到周边热炉气体和炉墙的强烈的热辐射,因为着两者之间有着较高的温度差。然后在右上角地区的板坯被加热至最高温度346.1C ?。正如所料,钢坯通过预热段的预热后,移动到加热段,在加热段内被加热到1150C ? 。不过板坯的温度,在移动到均热段后稍微的有所下降。图5b 显示了炉子内部的热辐射分布情况,即辐射热通量(矢量)和辐射(轮廓)。请注意,在前面的两个区的板坯辐射热流向量都集中在位于炉膛高度中心的位置上,这意味着大量的热气题集中在炉子的高度中心空间附近。通过相邻预热和加热区,钢坯得到了充分的加热,温度峰值出现在加热区。在另一方面,在最后的均热段,因为炉温是稍微下跌了约90C ? ,比前面的加热段,板坯是在高温下几乎到了高炉煤气的温度,一些辐射热通量是从热轧板释放出来的,在以前的情况来说这是相反的情况。因此,钢坯的温度是略有降低,板坯内部温度梯度变小。

上文提到的炉膛内部传热的详细状况可以在图表6中得到了解,每一部分钢坯的热流通量和温度等温线都有说明。 在这里,辐射热通量矢量方向的确定,以查看是否有净热流进入或流出板坯表面。在图6中第一块钢坯,是在加热炉的入口处,因此,左方热通量向量没有。随着热量传递到钢坯的右边,由于钢坯被炉子内部的热气体包围着,更多的热量传递到了钢坯的上下表面。同时我们也应该注意到,在右边的角落,热通量是来自水平和垂直两个方向的,因而正如预期的那样, 最高气温346.1C ?形成在钢坯的右角的地方,而最低气温是发现在板坯的左边中心位置上。在另一方面,虽然第三块板坯在图6中是同样是在 预热段,更多的对板坯表面的热量通量影响是来自炉膛及炉墙,因为比起第一块钢坯来说,更加的深入到预热段的内部,接近加热段。因此,板坯的温度身高的比较快,最高的温度达到547.1C ? ,而最低气温也增加至245.8C ? 。不过,迄今为止,板坯温度分布显示为夏普梯度。在图表6c 中的第七块钢坯已经进入到加热段了,由于板坯从预热段移动过来,那里的板坯温度介于583.9C ?和925.5C ?。但是,由于地砖充分加热,从而板坯和周边炉气和炉墙温差变小,热流量降低的饿幅度在图表6d 中很明显的看出来。同样的原因,在加热段内第17板坯热流跌幅更大,如图6E 中所示,因此,板坯温升减弱,温度分布更均匀。图表6f 说明第26块板坯在均热段内,那里的温度,相比加热段降低的幅度更加大。因此,我们可以看到,从加热段到均热段,炉墙和周围热烟气对钢坯的影响或多或少都在减弱。

此外,如图表7所示,预测板坯在炉膛内沿纵向温度概况,su T ,sc T 和sd T 粉笔指上表面平均温度的,板坯中心线温度,和板坯表面降低的温度幅度。我们可以看到中心线温度呈线性变化的规律,开始是21.2C ?,通过第一个区域后,从60.4C ?升

高到1040.0C ? 。在最后的均热段,气温略有降低,仍几乎恒定在约1010C ?左右。至于上游较低的表面温度,虽然上层温度稍低于预热段,因为较低的炉墙温度,而后加热段的温度发生逆转和上层温度较高,因为存在着两个低温区。与此相反,在均热段,由于上述回热流下表面温度远低于中线温度。

3.2 吸收系数及平板辐射效果

在高温加热炉内,辐射传热是烟气和炉墙主导传热模式。在这里寻找影响辐射特性效应的一些参数进行研究。图8显示介质吸收系数对该板坯纵向温度剖面中心线温度效果影响,板坯中心线温度加吸收系数从0.1增加到10 。这是因为周围介质吸收系数的增加热辐射也增强了。接着,在图9对板坯发射率与温度剖面介绍,板坯发射率是各不相同的,从0.3到1.0 ,而吸收系数和炉壁辐射率均保持在0.15和0.75 之间。正如人们预料的,温度越高,板坯的发射率就越大,因为在板坯表面上由于变成黑色而得到更多的热量。 不过应该指出,目前虽然在一些炉子上的到很好的体现,我想最后的出口温度,是在相对狭窄的范围内。

3.3 对比实验数据

最后,浦项制铁在预测板坯温度上利用现有的模型和实验数据进行比较,如图表10所示。在这些数据中, 在原位测量降低炉区平均温度,这就得到了5个设在板坯上方和下方的热电偶选定的位置的数据,还介绍了与板坯中心线温度实验数据。为了预测板坯的温度,在图10原位测量温度显示,是介质温度和炉墙和楼板辐射系数维持在0.75 和0.5。此外,在吸收系数中,在他的模型[ 13 ]的基础上,通过实验获得的2CO 和2H O 的摩尔分数。值得注意的是,尽管各种测量结果的不确定性也存在着一个合理的预测结果与实测概况。尤其是,在均热段,即出口附近,温度预测已经有了很好的效果,这意味着目前的传热模型,可被成功地应用到预报步进式加热炉内板坯温度上。

4 结论

传热模型和应用已变为传热状况的预测,在五年中,浦项钢铁公司也研发了相似的加热炉模型。在原来的基础上,给出了纵向炉气体和壁面温度,该模型可以预测板坯在加热过程中的辐射热流量和板坯表面温度分布,由耦合的RTE和瞬态热传导方程求解。虽然数值结果在为具体的例子审议中,同样的方法,可用于任何类似的加热炉模型。进一步发展本模型的目标将包括适当为分析防滑标准的形成,燃气及墙温度分布。最后,发展为三维传热模型。

鸣谢

作者表示感谢财政支持由浦项制铁和韩国全北国立大学。此外,作者想感谢,浦项制铁技术

研发中心李先生的建设性评论和实物帮助。

附录C 外文原文

Abstract

A mathematical heat transfer model for the prediction of heat flux on the slab surface and

temperature distribution in the slab has been develcped bv considering the thermal radiation in the

furnace chamber and transient heat conduction governing equations in the slab, respectively.

The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient.The steel slabs are moved on the next fixed beam by the walking beam after being heated up through the non-firing,charging,preheating.heating,and soaking zones in the furnace.Radiative heat flux calculated from the radiative heat exchange within the furnace modeled using the FVM by considering the effect of furnace wall ,slab and combustion gases is introduced as the boundary condition of the transient conduction equation of the slab.Heat transfer characteristics and temperature behavior of the slab is investigated by changing such parameters as absorption coefficient and emissivity of the https://www.doczj.com/doc/926872398.html,parison with the experimental work show that the present heat transfer model works well for the prediction of thermal behavior of the slab in the reheating furnace.

1 Introduction

The analysis of transient heating characteristics of the steel slabs in a reheating furnace has attracted considerable attention during the past few decades since the furnace process should have Jower energy consumption and pollutant emissions.In addition,requirement of the uniform temperature distributions inside the furnace exit greatly increases the importance of accurate and fast prediction of furnace process for the subsequent rolling process because this determines the quality of the steel product.Intrinsically,the combustion process and resulting hot gas flow within the furnace chamber influence the heat transfer process through conduction,convection,and thermal radiation simultaneously.However,complex three dimensional structure of the furnace including stationary and walking skids makes the problem difficult to analyze accurately and economically.Therefore,models and methods fir predicting the furnace combusting behavior and heat transfer processes are in high demand.Especially,accurate prediction of thermal radiation behavior is quite important because the heat transfer by thermal radiation is over 90% of the total heat flux impinging on the slab surface.

Now that no single radiation model can solve all situations encountered in engineering applications,one should select an appropriate approach for his own specific concern.In order to predict the radiative heat flux on the slab surface,thereby,calculate the temperature distribution inside a slab accurately,its solution method must account for the sequential slab movement,nongray behavior of the furnace radiating gases,and complex geometry including

curved furnace wall and blockage effect of slab of slab and skid pipes,as well as moderate computational cost.Numerous practical engineering models and methods for the prediction of thermal heating characteristics of the slab in a reheating furnace have been developed and successfully applied to various different furnace geometries,and these can be classified as below several categories.

The first one is to solve the full Navier-Stokes and energy conservation equations governing the hot gas flow and combustion process in the furnace,where thermal radiation acts as an energy source term via divergence of radiative heat flux.Kim et al. Performed these three dimensional CFD analysis by considering the turbulent reactive flow and radiative heat transfer in the walking beam type slab reheating furnace by using the commercial FLUENT code,and predicted temperature distribution in the furnace and heat fluxes through the upper and Huh conducted similar analysis and predicted the thermal behavior of the slab by considering the transient conduction equation equation in the slab.Although these full CFD analyses can be used for accurate prediction of the thermal and combusting fluid characteristics in the furnace with slab heating,there exist such difficulties as treatment of so many governing equations and complexity of the furnace structure as well as uncertain of the models,therefore,it necessitates long computational time and resulting costs.The second method models the furnace process as several well-stirred gas zones with one dimensional gas energy balance as suggested by Chapman et al .They performed the parametric investigations to find the effects of slab and refractory wall emissivities and height of the combustion space on the thermal performance of the continuous reheating furnace.They did not,however,predict the temperature distribution inside the slab,and some modifications are needed to deal with the complex furnace geometry and walking beam type reheating furnace geometry and walking beam type reheating furnace considered in this work.The final approach,which is simple but can reasonably simulysis of radiative heat transfer of furnace gas and transient transient heat conduction within the slab[5-7].Liet al.[5]developed the mathematical model for predicting steady state heat transfer within the reheating furnace,where thermal radiation in a furnace gas is calculated by using the zone method,while the thermal response of the slab is obtained by solving the transient two dimensional conduction equation.To the author's knowledge,however, the computing cost of the zone method is expensive and extension to general body-fitted coordinates to deal with the complex furnace structure is

somewhat difficult.Yang et al.[6] also developed the similar heat transfer model and predicted the similar heat transfer transverse to the marching direction of the slab in the reheating furnace.Although it is more simple and less computational with the approach of Li et al.[5],more general and computationally efficient model is highly demanded for the fast and accurate temperature prediction of the slab,if considering the useful on-line model which monitors and controls the furnace situations like control of the burner and residence time of the slab within the furnace for real time operation.

Recently,Harish and Dutta [7]presented a computational model for the heat transfer in a direct-fired pusher type reheat furnace by using the FYM for gas radiative heat transfer and WSGGM for nongray behavior of the combustion gases within the furnace.In this work,a mathematical heat transfer model to predict the radiative heat flux impinging on the slab surface and temperature distribution inside the slab has been developed by considering the thermal radiation governing equations in the furnace chamber and transient conduction governing equations in the slab in the walking beam type reheating furnace,respectively.The furnace is modeled as radiating medium with spatially varying temperature and constant absorption coefficient.The slab is moved on the next fixed bean by the walking beam periodically passing through the non-firing,charging,preheating,heating,and soaking zones in the furnace.Radiative heat flux calculated from the radiative heat exchange within the furnace chamber modeled using the finite volume meth od for radiation by considering the effect of furnace wall,slab,and combustion gases is applied as the boundary condition of the transient heat conduction equation of the slab.In the following sections after describing the methodology adopted here for the prediction of furnace process within the reheating furnace ,heat transfer characteristics and thermal behavior of the slab are investigated by changing such parameters as absorption coefficient and emissivity of the slab,while comparison with the experimental data is also presented.Finally,some concluding remarks are given.

2 Formulation

2.1 Furnace description

The role of the reheating furnace is to heat steel slabs nearly up to 1200C uniformly for the subsequent rolling process,and the energy for slab heating is supplied by roof and bottom

tangential https://www.doczj.com/doc/926872398.html,ually,this reheating furnace is composed of five zones,i.e,non-firing,charging,preheating,and soaking zones as shown in Fig,1,which is the simplified furnace model similar to the POSCO unit,Steel slabs charged into the non-firing zone are moved on the next fixed beam by a walking beam about every some minutes depending on the residence time of the slab within the furnace.Overall longitudinal furnace dimension is each zone with inclined connecting roof and blockshaped bottom hill.Each Steel slab has 1.16 m in width and 0.23 m in height with 0.2m interval between the slabs,so that slabs are assumed to be isothermal of 21.2C ? when charging into the furnace to exit from the furnace,is typpically 180 min to obtain the mean slab temperature of about 1200C ? at the furnace exit,therefore,slabs move to the next location every 4.6 min.

2.2 Goering equations

Fig.2 shows the heat transfer path occurred within the furnace chamber,in this study,it is assumed that the heat transfer mode to the slab surface is only thermal radiation while only conduction occurs within the slab.Heat transfer within the steel slab can be calculated from the transient two dimensional heat conduction equation as following;

)()(y T k y x T k x t T C

????+????=??ρ (1) Where ρ,C,and l are density,specific heat,and conductivity of the steel

slab,respectively.The radiative heat flux on the slab surface,

R slab q as shown in Fig.3,is used for the boundary condition of the above Eq.(1),i.e,

Ω?=?=Ωd n s s r I q w w R slab ))(,(4π (2)

Where ),(s r I w is the radiation intensity at slab surface w r and direction w n s , is the unit normal vector at the slab surface ,and Ω is the solid angle.For a radiatively active medium the radiation intensity at any position F,along a path s through an absorbing,emitting and scattering medium can be given by the following RTE:

?=ΩΩ'?→?Φ+-+-=ππ

ωωβ40

00)(),(4)()1(),(),(1d s s s r I r I s r I ds s r d b (3) Where s a k σβ+=0 is the extinction coefficient,00/βσωs = is the scattering albedo and )(s s →Φ is the scattering phase function of radiative transfer from the incoming direction s to the scattering direction s .this equation,if the temperature of the medium )(r I b and boundary conditions for intensity are given,provides a distribution of the radiation intensity in medium.For a diffusely condition of Eq.(3) can be expressed as the summation of emitted and reflected ones like:

Ω'?-+=??d n s s r I r I s r I w n s w w w bw w w w ),(1)(),(πεε (4) Where w ε is the wall emissivity,and

πσ/4w bw T I = is the blackbody of the wall. 2.3 Finite volume sohation methods

The transient heat conduction equation is diseretized by using the finite volume method following the procedure suggested by Patankar [8].A central differencing scheme is used for the diffusion terms is terms in the x and y directions,while the unsteady term is treated implicitly by using the TDMA algorithm until the temperature field in the slab satisfies the following convergence criterion:

610)/max(-≤-ij old ij ij T T T (5) Where old ij T is the previous iteration value of

ij T in the same time level. In order to compute the radiative heat flux on the slab surface expressed in Eq.(2),which is the boundary condition of Eq.(1),the RTE,Eq.(3)must be analyzed.In this work,the finite volume method for radiation suggested by Chui and Raithby[9],and developed by Chai et al.[10]and Baek et al.[11]is adopted to discretization equation,after integrating the RTE over a control volume V ? and control angle m ?Ω as shown in Fig.4a and b, respectively,with the assumption that the magnitude of intensity is constant within a control volume

and a control angle given,but allowing its direction to vary,the following equation can be obtained:

m p m S m S m N m N m w m w m E m E m p m I b I a I a I a I a I a ++++= (6)

Where

)0,max(m i i m l D A a ?-= (7)

m p m i s n w e i i m

p V D A a ?Ω?+?=

∑=,0,,,)0,max(β (8) m

p m R m p V S b ?Ω?=)( (9) ?=Ω'-''?ΩΦ+=ππσ44m m m m s b a m R I I k S (10)

m i m l d n s D m Ω?=??Ω)( (11) Where i A ? and i n are the surface and outward unit normal vector at the surface i,respectively.Also,subscript I represents E,W,N and S,while i does e,w,n and s,respectively.Here is adopted a step scheme in which a downstream face intensity is set to equal to the upstream nodal value,The discretization procedure and related quantities are easily found in Baek et al.[11].

平面设计中英文对照外文翻译文献

(文档含英文原文和中文翻译) 中英文翻译 平面设计 任何时期平面设计可以参照一些艺术和专业学科侧重于视觉传达和介绍。采用多种方式相结合,创造和符号,图像和语句创建一个代表性的想法和信息。平面设计师可以使用印刷,视觉艺术和排版技术产生的最终结果。平面设计常常提到的进程,其中沟通是创造和产品设计。 共同使用的平面设计包括杂志,广告,产品包装和网页设计。例如,可能包括产品包装的标志或其他艺术作品,举办文字和纯粹的设计元素,如形状和颜色统一件。组成的一个最重要的特点,尤其是平面设计在使用前现有材料或不同的元素。 平面设计涵盖了人类历史上诸多领域,在此漫长的历史和在相对最近爆炸视觉传达中的第20和21世纪,人们有时是模糊的区别和重叠的广告艺术,平面设计和美术。毕竟,他们有着许多相同的内容,理论,原则,做法和语言,有时同样的客人或客户。广告艺术的最终目标是出售的商品和服务。在平面

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毕业设计外文翻译资料

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