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1、<p><b> 附錄</b></p><p> Technological Investigation on the Continuous Casting of Mid-Width Thin Slabs</p><p> GAN Yong, ZHANG Bai Ting, ZHANG Hui, NI Man Sen and .JI Xiu Qiu&l
2、t;/p><p> ABSTRACT Continuous casting of thin slabs is a key state project for 7th and 8th five—year plans. On the basis of foundamental works, CISRI conducted the tests of 102 heats in Lanzhou Steel Works in
3、the period of January 1991—June 1992. Three slab assortments of 50×900mm, 70×900mm, 70×500mm were examined. In June of 1992, 412 t steel of 46 heats were cast with the efficiency of 91. 3%. This-result mee
4、ts the requirement of the state in this period. The mould, heft transfer, casting technology and</p><p> KEY WORDS: mould, continuous casting of thin slab, technological properties</p><h5>
5、1. Introduction</h2><p> It is a very important new technique which has been researched and developed recently in the world to cast thin slab continuously and transfer the slab directly to rolling mill. Thi
6、s technique has changed the traditional technology route of strip production with obvious advantages in terms of energy saving, lowering capital investment, productive cost ,metal lose and so on, thus it is suggested tha
7、t it represents the trend of development of strip production. In comparison with the tradition alon</p><p> The key technique of thin slab casting—direct rolling route is the thin slab casting with</p>
8、;<p> three core techniques: mould, submerged nozzle and mould powder. A breakthrough in these core techniques has been made during pilot testing. In this paper, the technological performance of thin slab caster
9、and the study on mould shape, heat transfer, casting technology, the factors effecting slab quality, in particular, surface quality is described.</p><h5> Pilot Caster and Casting 'Technology</h2>
10、<p> The caster at Lanzhou Steel Works is of vertical—curved type with a radius of 2m, metallurgical length of 4390mm. There are two types of moulds: mould of variable section for slabs of 70×900 (mm), 50
11、15; 900 (mm), mould of constant section for slab of 70×500 (mm). The vibration amplitude is ±3mm with a frequency of 0—300cycle/min. The liquid steel for testing was delivered from an arc furnace of 5, in nomin
12、al capacity with a heat weight of about 10t. The tundish capacity is 4t. The main equipments </p><p> The core parts of thin slab caster, which are characteristic for the caster, arc mould and submerged noz
13、zle. The schematic view of the funnel type mould and nozzle is shown in figure 1 and 2.</p><p> From figure 1, it can be seen, that the lower part of the mould is straight and which cross section determines
14、 the slab size. The opening of upper part is widening gradually to allow nozzle to be submerged. The design of such kind of mould is based on solidification of liquid steel and deformation of shell under the external for
15、ce, and the construction of the</p><p> nozzle must be matched with the mould (Figure 2). The nozzle cross section is elliptical, somewhat stretched in direction of major axis, so are the lateral outlets, w
16、hich are made at on incline of a=±250. The nozzles with different incline angle are used for different immersion depth.</p><h5> Study and Manufacture of Mould</h2><p> The design work of
17、 a mould includes: determination of the shape and size, selection of the material to be made of, estimation of cooling intensity. All above mentioned points are essential for a rational design. "The mould shape and
18、size is determined by casting technology.</p><p> 1 Determination of maximum opening</p><p> The maximum opening of the mould must meet with following three requirements: (1)Enough space for s
19、ubmerged nozzle;</p><p> The shell solidification shrinkage of 0. 8%—1.0%to be considered;</p><p> The incline angle of the openingβ≤10°for some mould length and slab thickness (Figure1).
20、The calculated results for different slab width are shown in figure 3. For this test, mould of 900mm in width, 50—70 mm in thickness was used, the reasonable maximum opening was 140—160mm.</p><p> 3. 2 Desi
21、gn of mould curved surface</p><p> According to the shape of cross—line of inner curved surface with straight part, the moulds of thin slab caster can be divided into three groups: trapezoidal, rectangular
22、and elliptical (Figure 4).</p><p> For curved surface design, first of all, the strain of shell must be less than 0. 2%—0.3%, that means</p><p> D / 2R < 0. 2%(1)</p><p> whe
23、reD—shell thickness;</p><p> R—curvature.</p><p> Second factor, which should be considered, is that the curvature in horizontal direction must be always the same, and the curvature is increa
24、sed from top to bottom. The formula of curved surface of elliptical mould is:</p><p> X2 / 3502+ y2 /1752 =1(2)</p><p> wherex—axis in direction of mould thickness;</p><p> y —
25、axis in direction of mould width.</p><h5> Study on Flow Pattern in Mould</h2><p> Mathematical model</p><p> During casting, there are two processes in the mould: solidification
26、 of a shell at the water cooling wall and movement of remained liquid steel caused by teeming stream. The mathematical expression of these processes in terms of three—dimensional steady unpressed transfer is given as:<
27、;/p><p> Continuity equation</p><p><b> ?u j</b></p><p><b> ?xi ??0</b></p><p><b> (3)</b></p><p><b> where<
28、;/b></p><p> i, j —index,</p><p> i, j =1, 2, 3;</p><p> u —speed of liquid steel.</p><p> Momentum equation</p><p><b> ?u ?u</b></p
29、><p><b> 1 ?p</b></p><p> ???? ???u</p><p><b> ?u ?2?</b></p><p><b> ij ???</b></p><p><b> x?</b>
30、</p><p> x ???x ?vl ? x ?</p><p> x ????3 K?ij ?</p><p><b> ?4?</b></p><p><b> ???j???j</b></p><p><b> ? j ??&l
31、t;/b></p><p><b> ? ??j</b></p><p><b> ??i ???</b></p><p><b> where</b></p><p> ?ij —Kronecker mark,</p><p><
32、;b> 1</b></p><p><b> ?ij =</b></p><p><b> 0</b></p><p><b> when when</b></p><p><b> i??j i??j</b></p>
33、;<p> p —pressure;</p><p> ??—density;</p><p> v??— effective viscosity coefficient,</p><p> v?????v ??vt ;</p><p> v —physical viscosity coefficient;</p
34、><p> vt —viscosity coefficient of turbulent flow,</p><p> vt =0. 09exp ?2.5 ?1 ??RT</p><p> 50??K 2 ??,</p><p> Rt ??K??v ;</p><p> K—turbulent energ
35、y;</p><p> ??—emission rate of turbulent energy.</p><p> Turbulent energy equation</p><p><b> ??? ?</b></p><p><b> 2</b></p><p&
36、gt; ??u ???</p><p><b> ?K ?</b></p><p> ? ?? vt</p><p> ??v ???K ????v</p><p> ?ui ? ?ui ?</p><p> j ??? 2v???</p><p&g
37、t;<b> k ? ???</b></p><p><b> (5)</b></p><p> ?t?x ???</p><p><b> ? ?x</b></p><p><b> t ?x</b></p><p&
38、gt;<b> ? ?x</b></p><p><b> ?x ?</b></p><p><b> ???x ?</b></p><p> j ???K</p><p><b> ?j ??</b></p>&
39、lt;p><b> j ?j</b></p><p> i ??j ?</p><p> Emission rate equation of turbulent energy</p><p><b> D??</b></p><p><b> ?? vt&
40、lt;/b></p><p><b> ??????</b></p><p><b> ? ????</b></p><p><b> ??v ???</b></p><p> Dtx j ??? ??B</p><p><
41、b> ???xj ??</b></p><p><b> c ??v</b></p><p> ?ui ? ?ui ?</p><p><b> ?u ?</b></p><p><b> j ?</b></p><p&
42、gt;<b> ??2?</b></p><p><b> c??2v v?</b></p><p><b> 2</b></p><p><b> ?2u ?</b></p><p><b> ?6?</b><
43、/p><p> 1 K t ?x</p><p><b> ? ?x</b></p><p> ?x ?2 K</p><p> t ???x ?x ?</p><p> j ?ji ?</p><p><b> ?ji ?&
44、lt;/b></p><p><b> Where</b></p><p><b> c1 ,</b></p><p><b> c2 ,</b></p><p><b> B ,</b></p><p> K —c
45、onstants;</p><p><b> t —time.</b></p><p><b> ??K =1.3;</b></p><p> c1 ??1.44 ;</p><p> c2 ??1.92?1 ??0.3exp???Rt ???</p><p> E
46、nergy equation</p><p><b> ?T</b></p><p><b> ??cpui</b></p><p><b> X</b></p><p><b> ????</b></p><p> ??
47、?x ?? k?</p><p><b> ?t ?</b></p><p><b> x ??</b></p><p><b> ?7?</b></p><p> ???I??i ?</p><p><b> ??i ?&
48、lt;/b></p><p><b> where</b></p><p> cp —isobaric heat capacity; T—temperature;</p><p> ke —effective heat teanfer coefficient, k—physical heat teansfer coefficient
49、;</p><p> ke = k ??c</p><p> p?t prt ;</p><p><b> prt — pr</b></p><p> number of turbulent flow,</p><p><b> prt =0.9;</b>
50、;</p><p> ?t ??ve ??.</p><p> All the equations mentioned above can be given in this combination form</p><p><b> ??? ?</b></p><p><b> ????<
51、;/b></p><p><b> ?8?</b></p><p><b> ui?</b></p><p><b> ?xj</b></p><p><b> ?</b></p><p><b> ??
52、???S?</b></p><p><b> ?i ?</b></p><p> The calculation for a mould with a complex geometry is quite complicate, this problem in this case was solved by boundary fit coordinat
53、e system. After arithmetic operation the equation (8) is changed to</p><p><b> ??Ju???</b></p><p><b> ?</b></p><p><b> ??JV???</b></p>
54、<p><b> ?</b></p><p><b> ??JW???</b></p><p><b> =</b></p><p><b> ????J?</b></p><p><b> ???2 ???</b&g
55、t;</p><p> 2 ????2 ??</p><p><b> ????</b></p><p> ?????xyz</p><p><b> + ????J?</b></p><p><b> ??</b></p&g
56、t;<p><b> ???2 ??</b></p><p> 2 ???2 ?????</p><p><b> ??</b></p><p><b> ??J?</b></p><p><b> ???2 ???</b><
57、/p><p><b> 2 ???</b></p><p><b> 2 ????S</b></p><p><b> ?9?</b></p><p> The arithmetic operation is described in literature [2].<
58、/p><p> Boundary conditions and method of calculation</p><p> For calculation of heat transfer in mould, it is necessary to estimate flow field first, then the heat field is calculated. In calcul
59、ation, it was assumed that the field is symmetric, thus the calculation was done for 1 /4 part. The boundary conditions were:</p><p> At the nozzle outlets</p><p> At the nozzle outlets, the s
60、peed distribution was given in accordance with the results of water modelling; the temperature was assumed as 1560℃and nozzle outer wall was assumed as isothermic.</p><p> At bottom side and symmetrical sur
61、face</p><p> At the cross section of down stream, all the differentials ofphysical quantities (T, ui k ,</p><p> ??,p) in direction z were assumed zero; at the symmetrical surface, normal sp
62、eed, normal differential of tangential speed and k , ??, Twere zero too.</p><p> Top surface</p><p> It was treated as symmetrical.</p><p> Mould wall</p><p> It
63、 was assumed that at the wall there is a cohesion condition: u=V = ??=0, K= Ke ,</p><p><b> ?????e</b></p><p> For calculation K=10-4. ??=10-5.</p><p> The heat trans
64、fer rate at the mould wall is determined only by casting speed and distance to top surface.</p><p> The flow field and temperature was calculated by SIMPLE method[3], developed by Patark.</p><p&g
65、t; The calculation net is shown in figure 5.</p><p> 3 Quality of thin slab</p><p> Calculated results for flow and temperature field</p><p> The speed and temperature distribut
66、ion for the points at symmetrical surface for y (J=1) is shown in figure 6.</p><p> From this figure 6(a), it can be seen that the flow field can he divided into three zones: efflux region near nozzle outle
67、ts, upper vortex region above nozzle outlets, bottom vortex beneath nozzle outlets. The jet speed in the efflux region is decayed very quickly in direction to narrow face of mould of x. The efflux then is divided in two
68、streams after it is stopped by the narrow face, one goes up forming the upper vortex another goes down forming the bottom vortex. In bottom vortex region, the</p><p> The isotherms in figure 6(b) show clear
69、ly how is the heat of steel transferred to the mould wall in movement. The steel in efflux region is cooled due to strong turbulence, diffusing heat radially. As mentioned before the efflux is divided in upper and bottom
70、 stream after it is stopped by narrow face of the mould, the bottom stream is cooled down continuously, moving along mould face, thus the steel n the bottom vortex is cooler.</p><p> From the calculated res
71、ults, it is clear the steel in the region of higher flow speed is hotter. As a result of striking of high speed stream on the shell, the shell thickness is relatively small.</p><p> So, the shell near the n
72、ozzle and at narrow face in the region of bottom vortex is relative weak and attention should be paid to these regions in operation to prevent vertical cracking and break-out.</p><p> Observed flow field<
73、;/p><p> It was observed in water modeling and hot test, that flow field pattern and efflux has great influence elusion on the content vertical cracking and nonmetallic in due to small opening and short distan
74、ce from nozzle to mould walls. In the beginning of Got test, when larger outlets were used, high vertical cracking index was observed (the cracking was observed in the both regions 100—150mm from central line of slab reg
75、ularly). This defect was reduced a lot when nozzle outlets became smaller and in</p><p> When larger nozzle outlets are used [ Figure 7(a)], the kinetic energy of efflux is smaller and is dissolved quickly,
76、 striking directly on the wide face of the mould, washing the shell at this place making shell growth rate small. On the other hand, the temperature distribution in the mould is abnormal causing high growth speed of shel
77、l near narrow face due to not reaching of efflux to the narrow face, and better cooling conditions. After the slab has left mould, the vertical cracking is observe</p><p> and rapid cooling in second coolin
78、g zone. When smaller nozzle outlets are used [ Figure7 (b)], the efflux guided by outlet periphery is quite stable and strikes directly on the narrow face, thus the high temperature zone and eddy current zone is moved to
79、 narrow face , avoiding meeting with stress concentration region in</p><p> the shell.</p><p> The nonmetallic inclusion content of slab is mainly influenced by nozzle shape and</p>
80、;<p> immersion depth. When the immersion depth is small, the incline angle of outlets is not rational, the efflux strikes on the mould powder directly, making powder layer unstable and entraped or involved into
81、the metal[ Figure 8(b)].This circumstance is observed also in following other two cases: the upper stream formed from efflux is strong enough[A in figure 8 (a)];a negative pressure region is formed due to nonuniform fiel
82、d[R in figure 8(b)]</p><p> From water modeling and hot test it is coneluded that when????±250°, the immersion</p><p> depth is 200—300 mm, the mould powder layer is stable, the nonm
83、etallic inclusion content of steel is reduced obviously.</p><h5> Starting and Casting</h2><p> The starting is a key problem for thin slab casting because of speciality of the mould and nozzl
84、e construction. For funnel type mould, to meet the requirements of shell deformation, the shell thickness at the bottom of deformation zone in the mould must be less than 1/2 of slab thickness, that means, the mould must
85、 be filled with steel within 60 s. From start of teeming, the casting speed must reach the minimum speed of 1 m/min within 80 s, a normal casting speed must be reached within 150 s. Th</p><p> For rectangul
86、ar mould, because of short distance from nozzle to the wall (on1y 12 mm), the nozzle must be preheated to 900—1100℃ before use. In the beginning of casting, a special low melt point exothermic mould powder is added aroun
87、d the nozzle to avoid bridging</p><p> between nozzle and shell, and at starting, the steel should fill the mould and casting is to be</p><p> started within 30 s, the casting speed must reach
88、 1.2 m/min or more within 60 s, a normal casting speed must be reached within 120 s. The process is shown in figure 10.</p><p> For this caster, restricted by metallurgical length and other factors, for sla
89、b 50 mm in thickness, normal casting speed is 3m/min: for slab 70mm in thickness, normal casting speed is 2 m/min. At the end of the casting, speed is reduced at first, after the end is solidified, the strand is dragged
90、rapidly.</p><h5> Conclusions</h2><p> The mould length changes with technology, in general, the length is 950—1110 mm due to higher casting speed in comparison with traditional continuous cas
91、ting.</p><p> Based on technology used and solidification shrinkage, the opening of mould is in some relation with the minimum slab width. The opening is 140—160 mm for slab 900 mm in width.</p><
92、p> The slab quality depends on the curved surface design. Hot test showed the moulds used in test are rational.</p><p> In the region of higher circulating speed of liquid steel, the temperature of the
93、steel is higher and striking of hot metal on the shell gives a negative influence on shell growth.</p><p> The weak points of shell formation in thin slab casting are in the region of efflux and</p>
94、<p> the main stream in bottom vortex.</p><p> The hot test had proved that the starting and casting technology used is rational. REFERENCES</p><p> [1] Chang Xi《.</p><p>
95、Principles of Transfer in Metallurgy》. Seconded. Beijing; Publishing House of</p><p> Metallurgy, 1991, 267—279 din Chinese)</p><p> [2] Wang Laihua. Study on Fluid Field and Heat Transfer in
96、the Mould of Thin Slab Caster.</p><p> Dissertation, CISRI, 1990 (in Chinese)</p><p> [3] Nakato Hetal. Steelmaking Conference Proceedings, 1987, 70, 427—431</p><h2> 中等厚度薄板連鑄技術(shù)研
97、究</h2><p> 闞勇 張百亭 張輝 倪滿森 紀(jì)秀秋</p><p> 摘要 薄板連鑄是七五計(jì)劃和八五計(jì)劃的一項(xiàng)主要工程,在金屬基金協(xié)會支持下,CISIRI 公司于 1991年1 月至 1992 年 6 月期間在蘭州鋼鐵公司對 50×900mm,70×900mm,70</p><p> ×500mm 三種薄板采用 102 種
98、加熱方法進(jìn)行測試。1992 年 6 月采用 46 種加熱方法以 91.3% 的澆注率成功澆注了 412 噸鋼。該結(jié)果滿足了當(dāng)時(shí)的需要。同時(shí)對連鑄機(jī)機(jī)型,重量, 和板帶質(zhì)量影響因素也進(jìn)行了研究。</p><p> 關(guān)鍵詞:結(jié)晶器薄帶連鑄技術(shù)產(chǎn)權(quán)</p><p><b> 1.介紹</b></p><p> 連鑄技術(shù)是最近世界上對薄板的研
99、究和開發(fā)以及直接將板帶變成軋制鋼板的一項(xiàng) 非常重要的新技術(shù)。該技術(shù)以節(jié)能、基建投資少、生產(chǎn)費(fèi)用底、金屬流失少等的明顯優(yōu) 勢改變了傳統(tǒng)的板帶生產(chǎn)技術(shù)。所以它代表了板帶生產(chǎn)的發(fā)展趨勢。與傳統(tǒng)板帶生產(chǎn)技 術(shù)相比薄板帶連鑄技術(shù)生產(chǎn)線的生產(chǎn)費(fèi)用和基建投資分別減少了 10%-20%和 15%-20%。 這項(xiàng)技術(shù)不適合現(xiàn)有的窄帶生產(chǎn)線,但是對新鋼鐵公司,中、小企業(yè)生產(chǎn)板材、帶材非 常有用。據(jù)有關(guān)資料表明該項(xiàng)技術(shù)每生產(chǎn)一噸薄帶連鑄鋼所消耗的能量比傳統(tǒng)生
100、產(chǎn)方式 少 62.8KJ。如果帶材采用熱裝熱軋所節(jié)省的能量會更多。對薄帶材本身而言,薄帶材 連鑄的優(yōu)勢并不能體現(xiàn)出來,因?yàn)樗穸刃〔⑶颐娣e大,除非帶材采用熱裝熱軋。</p><p> 薄帶鑄件直接軋制生產(chǎn)線的關(guān)鍵技術(shù)是薄帶鑄件的三個核心技術(shù):結(jié)晶器,冷卻管, 結(jié)晶器振動裝置。在試驗(yàn)測試期間這些核心技術(shù)都已取得了突破性的成果。本文主要闡 述了有關(guān)薄帶鑄件的產(chǎn)生以及結(jié)晶器形狀的研究,熱交換,澆注技術(shù),帶材質(zhì)量特別是
101、 表面質(zhì)量影響因素。</p><p> 2.試驗(yàn)鑄件和澆注技術(shù)</p><p> 蘭州鋼鐵公司的連鑄機(jī)是垂直彎曲型連鑄機(jī),圓弧半徑是 2 m,冶金長度為 4390 mm, 結(jié)晶器類型有兩種:截面面積為 70×900 mm,50×900 mm 的可變截面帶材結(jié)晶器,和 截面面積為 70×500mm 的固定截面結(jié)晶器。振幅高為±3mm,頻率為 0—3
102、00r/min。測試 的鋼水由電弧爐中運(yùn)來,該爐理論上的容量大約為 10t,鋼包的容量為 4t,該實(shí)驗(yàn)中主 要的設(shè)備有盛鋼桶、鋼包回轉(zhuǎn)臺、鋼包運(yùn)送小車、長水口、結(jié)晶器、振動裝置、二次冷</p><p> 卻區(qū)、夾送輥、翻鋼機(jī)、矯直機(jī)、剪切機(jī),輸送輥道、操作系統(tǒng)、電機(jī)驅(qū)動系統(tǒng)、和控 制系統(tǒng)。最大的拉坯速度為 4m/min。生產(chǎn)的鋼種有 20MnSi,16Mn 和不銹鋼。</p><p>
103、 薄帶連鑄典型的核心部分是結(jié)晶器,長水口。錐型結(jié)晶器和長水口如圖 1 和圖 2 所 示。</p><p> 圖 1 結(jié)晶器示意圖</p><p> 圖 2 浸入示長水口示意圖</p><p> 從圖 1 我們可以看到結(jié)晶器下邊是直的,它的橫截面積決定了帶材的大小。結(jié)晶器 的上部逐漸變寬以使長水口能夠浸入。這種結(jié)晶器的設(shè)計(jì)是根據(jù)鋼水凝固原理以及在外 力作用下凝
104、固殼變形的原理制成的,長水口的結(jié)構(gòu)必須與結(jié)晶器相匹配(圖 2)。長水 口的橫截面積無論在哪個坐標(biāo)面內(nèi)都是橢圓形的,極限偏差為±250mm,出水口也是如 此。長水口分為不同的傾斜角度是為了滿足不同的浸沒深度。</p><p> 3.結(jié)晶器的研究與制造</p><p> 結(jié)晶器的設(shè)計(jì)包括:材料的形狀與大小,材料的選擇,冷卻狀態(tài)下的強(qiáng)度。以上幾 點(diǎn)都是根據(jù)傳統(tǒng)設(shè)計(jì)估算的,結(jié)晶器的形
105、狀和大小要根據(jù)澆注技術(shù)來決定。</p><p> 3.1 最大開口度的決定 結(jié)晶器最大開口度應(yīng)符合以下三點(diǎn): (1)足夠的空間使長水口浸入; (2)考慮外壁具有 0.8%—1.0%的收縮;</p><p> (3)對一定長度的結(jié)晶器和一定厚度的帶材要求開口面傾斜角β≤10°(圖 1)。不</p><p> 同帶寬的計(jì)算結(jié)果如圖 3 所示。該實(shí)驗(yàn)中結(jié)晶
106、器寬為 900mm,厚度為 50—70mm,最大的 合理開口為 140—160mm。</p><p> 3.2 結(jié)晶器曲面的設(shè)計(jì) 對曲面的設(shè)計(jì)而言,根據(jù)橫截面的形狀——垂直部分線性內(nèi)表面,薄帶連鑄機(jī)可以</p><p> 分成三類:扇形,長方形,橢圓形(圖 4)。</p><p> 首先,外殼的應(yīng)力必須小于 0.2%—0.3%,即 D/2R<0.2%(1)
107、式中 D—壁厚;</p><p> R—曲度。 其次考慮的是水平方向上的曲度必須相同,曲度從頂部到底部逐漸增加。橢圓形結(jié)</p><p><b> 晶器曲面公式為</b></p><p> X2 / 3502+ y2 /1752 =1(2)</p><p> 式中 x—結(jié)晶器厚度方向上的坐標(biāo); y—結(jié)晶器寬度方
108、向上的坐標(biāo)。</p><p> 圖 3 不同最大開口度時(shí)帶寬與收縮率的關(guān)系圖 4 三種結(jié)晶器示意圖 結(jié)晶器寬 1100mm,帶厚 50mm(a)扇形(b)長方形(c)橢圓形</p><p> 4 結(jié)晶器中流動方式的研究</p><p> 4.1 數(shù)學(xué)模型 澆注過程中,結(jié)晶器中有兩個變化過程:在水冷過程中凝固殼的固化和鋼水的流動。</p>
109、<p> 整個過程可以用數(shù)學(xué)表達(dá)式表示為: 連續(xù)方程:</p><p><b> ?u j</b></p><p><b> ?xi ??0</b></p><p><b> (3)</b></p><p> 式中i, j —自然數(shù), i, j =1,
110、2,3;</p><p> u—鋼水流動速度。 動量方程:</p><p><b> ?u ?u</b></p><p><b> 1 ?p</b></p><p> ???? ???u</p><p><b> ?u ?2?</b>
111、</p><p><b> ij </b></p><p><b> ? i </b></p><p><b> j ? </b></p><p><b> ????</b></p><p><b&
112、gt; x?x</b></p><p> x ?vl ? x ?</p><p> x ????3 K?ij ?</p><p><b> (4)</b></p><p><b> ???j</b></p><p> 式中?ij —常數(shù)
113、,</p><p><b> ?ij =?</b></p><p><b> ???j?</b></p><p><b> j ??</b></p><p><b> ? ??j</b></p><p><b&g
114、t; ??i ???</b></p><p><b> 1i??j</b></p><p><b> 0i??j</b></p><p><b> p —壓力</b></p><p><b> ??—密度</b></p&
115、gt;<p> v??—理論黏度系數(shù)</p><p> v?????v ??vt</p><p><b> v —實(shí)際黏度系數(shù)</b></p><p> vt —運(yùn)動黏度系數(shù), vt =0. 09exp?2.5 ?1 ??RT</p><p> 50??K 2 ??,</p><
116、;p> Rt ??K??v ;</p><p><b> K—動能</b></p><p> ??—動能變化率; 動能方程:</p><p><b> 2</b></p><p><b> ??? ?</b></p><p>
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