Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99</m...
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| Autores principales: | , , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/c5b10d0a48c34e5a9acccc1cc53686fa |
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| Sumario: | In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99</mn><mo>%</mo></mrow></semantics></math></inline-formula> of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is presented. The numerical results showed that in the creeping flow limit (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>. For low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>; for high values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>. This work also considers the influence of the elasticity number. |
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