Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe
Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes...
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MDPI AG
2025-01-01
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| author | Shijun Chu Elena Marensi Ashley P. Willis |
| author_facet | Shijun Chu Elena Marensi Ashley P. Willis |
| author_sort | Shijun Chu |
| collection | DOAJ |
| description | Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><mn>5</mn><mi>D</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><mn>25</mn><mi>D</mi></mrow></semantics></math></inline-formula>. Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence. |
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| publishDate | 2025-01-01 |
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| spelling | doaj-art-74b339b267b7497dab85a6f3207289542025-01-24T13:40:05ZengMDPI AGMathematics2227-73902025-01-0113229310.3390/math13020293Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated PipeShijun Chu0Elena Marensi1Ashley P. Willis2Applied Mathematics, School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S3 7RH, UKSchool of Mechanical, Aerospace and Civil Engineering, University of Sheffield, Sheffield S1 3JD, UKApplied Mathematics, School of Mathematical and Physical Sciences, University of Sheffield, Sheffield S3 7RH, UKHeated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><mn>5</mn><mi>D</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mo>=</mo><mn>25</mn><mi>D</mi></mrow></semantics></math></inline-formula>. Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence.https://www.mdpi.com/2227-7390/13/2/293mixed convectionpipe flowdirect numerical simulation |
| spellingShingle | Shijun Chu Elena Marensi Ashley P. Willis Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe Mathematics mixed convection pipe flow direct numerical simulation |
| title | Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe |
| title_full | Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe |
| title_fullStr | Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe |
| title_full_unstemmed | Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe |
| title_short | Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe |
| title_sort | modelling the transition from shear driven turbulence to convective turbulence in a vertical heated pipe |
| topic | mixed convection pipe flow direct numerical simulation |
| url | https://www.mdpi.com/2227-7390/13/2/293 |
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