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Power-law scaling of mixing in recirculation zones: non-reacting versus reacting flows.

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Title: Power-law scaling of mixing in recirculation zones: non-reacting versus reacting flows.
Authors: Zhang, Jian1 (AUTHOR) zhang-jian@tsinghua.edu.cn, Liu, Xiuyuan1 (AUTHOR), Ren, Zhuyin1 (AUTHOR)
Source: Journal of Fluid Mechanics. 2/10/2026, Vol. 1028, p1-20. 20p.
Subjects: Combustion, Reactive flow, Turbulent mixing, Flame stability, Stagnation point, Mixing machinery, Scaling laws (Statistical physics)
Abstract: The recirculation zone is critical for flame stabilization in combustion processes, yet a quantitative, mechanistic understanding of its inherently complex mixing state remains a challenge. To address this gap, we introduce a novel characteristic parameter, the characteristic mixture fraction ( $Z_u$), defined from the observation of localized mixture uniformity within the zone. Using validated large-eddy simulation combined with the flamelet/progress-variable approach, we systematically examine the relationship between $Z_u$ and the momentum flux ratio ( $J$). The results reveal that a dual-power-law scaling relationship between $Z_u$ and $J$ is a fundamental characteristic of bluff-body stabilized flows, persisting with and without chemical reactions. This scaling, however, is profoundly modified by combustion. Compared with non-reacting flows, reacting flows exhibit a shift in the transition point between power-law regimes to a higher $J$ and a shallower scaling exponent (e.g. approximately −0.15 for reacting versus −0.5 for non-reacting flows in the jet-envelopment regime). These quantitative distinctions are decisively attributed to thermophysical effects induced by heat release, interpreted through two synergistic mechanisms: at the macroscale, thermal expansion reduces density, weakening the recirculation zone's momentum resistance; at the microscale, increased viscosity suppresses turbulent mixing efficiency. Thus, a predictive mechanistic framework centred on the parameter $Z_u$ is established, providing not only a robust metric for quantifying complex mixing states but also fundamental insights into how heat release acts on turbulent mixing. Consequently, it offers new perspectives for combustor optimization and understanding of complex mixing–combustion coupling. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 191814610
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Power-law scaling of mixing in recirculation zones: non-reacting versus reacting flows.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Jian%22">Zhang, Jian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhang-jian@tsinghua.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Xiuyuan%22">Liu, Xiuyuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ren%2C+Zhuyin%22">Ren, Zhuyin</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 2/10/2026, Vol. 1028, p1-20. 20p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Combustion%22">Combustion</searchLink><br /><searchLink fieldCode="DE" term="%22Reactive+flow%22">Reactive flow</searchLink><br /><searchLink fieldCode="DE" term="%22Turbulent+mixing%22">Turbulent mixing</searchLink><br /><searchLink fieldCode="DE" term="%22Flame+stability%22">Flame stability</searchLink><br /><searchLink fieldCode="DE" term="%22Stagnation+point%22">Stagnation point</searchLink><br /><searchLink fieldCode="DE" term="%22Mixing+machinery%22">Mixing machinery</searchLink><br /><searchLink fieldCode="DE" term="%22Scaling+laws+%28Statistical+physics%29%22">Scaling laws (Statistical physics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The recirculation zone is critical for flame stabilization in combustion processes, yet a quantitative, mechanistic understanding of its inherently complex mixing state remains a challenge. To address this gap, we introduce a novel characteristic parameter, the characteristic mixture fraction ( $Z_u$), defined from the observation of localized mixture uniformity within the zone. Using validated large-eddy simulation combined with the flamelet/progress-variable approach, we systematically examine the relationship between $Z_u$ and the momentum flux ratio ( $J$). The results reveal that a dual-power-law scaling relationship between $Z_u$ and $J$ is a fundamental characteristic of bluff-body stabilized flows, persisting with and without chemical reactions. This scaling, however, is profoundly modified by combustion. Compared with non-reacting flows, reacting flows exhibit a shift in the transition point between power-law regimes to a higher $J$ and a shallower scaling exponent (e.g. approximately −0.15 for reacting versus −0.5 for non-reacting flows in the jet-envelopment regime). These quantitative distinctions are decisively attributed to thermophysical effects induced by heat release, interpreted through two synergistic mechanisms: at the macroscale, thermal expansion reduces density, weakening the recirculation zone's momentum resistance; at the microscale, increased viscosity suppresses turbulent mixing efficiency. Thus, a predictive mechanistic framework centred on the parameter $Z_u$ is established, providing not only a robust metric for quantifying complex mixing states but also fundamental insights into how heat release acts on turbulent mixing. Consequently, it offers new perspectives for combustor optimization and understanding of complex mixing–combustion coupling. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2025.11105
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 1
    Subjects:
      – SubjectFull: Combustion
        Type: general
      – SubjectFull: Reactive flow
        Type: general
      – SubjectFull: Turbulent mixing
        Type: general
      – SubjectFull: Flame stability
        Type: general
      – SubjectFull: Stagnation point
        Type: general
      – SubjectFull: Mixing machinery
        Type: general
      – SubjectFull: Scaling laws (Statistical physics)
        Type: general
    Titles:
      – TitleFull: Power-law scaling of mixing in recirculation zones: non-reacting versus reacting flows.
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            NameFull: Zhang, Jian
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          Name:
            NameFull: Liu, Xiuyuan
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          Name:
            NameFull: Ren, Zhuyin
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            – D: 10
              M: 02
              Text: 2/10/2026
              Type: published
              Y: 2026
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              Value: 1028
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