<p>Tundish is the transitional reactor between the ladle and the mold. It is well known that RTD curve can describe the flow characteristic of a tundish, and there are many criterions about characteristic volume fraction to optimize the flow control device in a tundish. But there are still many issues about the relation between the characteristic volume fraction and inclusion removal and the relation between the characteristic time and inclusion removal. Thus, numerical method is applied to obtain the RTD curve and the inclusion collision-coalescence and removal in three tundishes, and Pearson correlation coefficient is introduced to investigate the relation between the characteristic time and the characteristic volume fraction. Numerical results showed that, the plug volume <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{p}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>p</mtext> </msub> </math></EquationSource> </InlineEquation> and the well-mixed volume <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{m}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>m</mtext> </msub> </math></EquationSource> </InlineEquation> can be represented by the peak concentration time <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation>, and the dead volume <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{d}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> can be represented by the mean residence time <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq5.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{t}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>. The inclusion removal rate is neither the monotonic function of characteristic times (minimum residence time <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{\min }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mo movablelimits="true">min</mo> </msub> </math></EquationSource> </InlineEquation>, peak concentration time <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation> and mean residence time <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq5.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{t}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>) nor the monotonic function of characteristic volume fractions (plug volume <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{p}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>p</mtext> </msub> </math></EquationSource> </InlineEquation>, dead volume <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{d}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> and well-mixed volume <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{m}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>m</mtext> </msub> </math></EquationSource> </InlineEquation>). The maximum inclusion removal rate can be determined by tracking the peak concentration time <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation>, mean residence time <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq5.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{t}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>, plug volume <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{p}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>p</mtext> </msub> </math></EquationSource> </InlineEquation> or dead volume <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11663_2025_3699_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$V_{{\text{d}}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>V</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation>.</p>

Relation Between RTD Curve and Inclusion Removal in the Tundish

期刊论文
发表日期：

2025年8月6日

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Han Zhang,
Hong Lei,
Changyou Ding,
Yan Zhao,
Denghui Li,
Tianyu Zhang

摘要

Tundish is the transitional reactor between the ladle and the mold. It is well known that RTD curve can describe the flow characteristic of a tundish, and there are many criterions about characteristic volume fraction to optimize the flow control device in a tundish. But there are still many issues about the relation between the characteristic volume fraction and inclusion removal and the relation between the characteristic time and inclusion removal. Thus, numerical method is applied to obtain the RTD curve and the inclusion collision-coalescence and removal in three tundishes, and Pearson correlation coefficient is introduced to investigate the relation between the characteristic time and the characteristic volume fraction. Numerical results showed that, the plug volume $V_{{\text{p}}}$ $V_{p}$ and the well-mixed volume $V_{{\text{m}}}$ $V_{m}$ can be represented by the peak concentration time $t_{\max }$ $t_{max}$ , and the dead volume $V_{{\text{d}}}$ $V_{d}$ can be represented by the mean residence time $\overline{t}$ $\bar{t}$ . The inclusion removal rate is neither the monotonic function of characteristic times (minimum residence time $t_{\min }$ $t_{min}$ , peak concentration time $t_{\max }$ $t_{max}$ and mean residence time $\overline{t}$ $\bar{t}$ ) nor the monotonic function of characteristic volume fractions (plug volume $V_{{\text{p}}}$ $V_{p}$ , dead volume $V_{{\text{d}}}$ $V_{d}$ and well-mixed volume $V_{{\text{m}}}$ $V_{m}$ ). The maximum inclusion removal rate can be determined by tracking the peak concentration time $t_{\max }$ $t_{max}$ , mean residence time $\overline{t}$ $\bar{t}$ , plug volume $V_{{\text{p}}}$ $V_{p}$ or dead volume $V_{{\text{d}}}$ $V_{d}$ .