Renormalization Group Approach as a Symmetry Transformation for an Analysis of Non-Newtonian Elastic Turbulence
- Symmetry transformation methods are widely used in fluid flow problems. One such method is renormalization group analysis. Renormalization group methods are used to develop a macroscopic turbulence model for non-Newtonian fluids (Oldroyd-B type). This model accounts for the large-distance and large-time behavior of velocity correlations generated by the momentum equation for a randomly stirred, incompressible flow and does not account for empirical constants. The aim of this mathematical study was to develop a k -ε RNG turbulence model for non-Newtonian fluids (Oldroyd-B type). For the first time, using the renormalization procedure, the transport equations for the large-scale modes and expressions for effective transport coefficients are obtained. Expressions for the renormalized turbulent viscosity are also derived. This model explains the phenomenon of the abrupt growth of the irregularity of velocity at low values of the Reynolds number.
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| Author: | Andriy A. Avramenko, Igor V. ShevchukORCiD, Nataliia P. DmitrenkoORCiD, Alina V. Konyk |
|---|---|
| URN: | urn:nbn:de:hbz:832-epub4-29626 |
| DOI: | https://doi.org/10.3390/fluids10040079 |
| ISSN: | 2311-5521 |
| Parent Title (English): | Fluids |
| Publisher: | MDPI |
| Editor: | Mehrdad Massoudi, Chengcheng Tao |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2025/05/23 |
| GND-Keyword: | Nichtnewtonsche Flüssigkeit; Reynolds-Zahl; Turbulenzmodell |
| Tag: | Non-Newtonian Fluid; Renormalization Group Method; Reynolds Number; Turbulence Model; Turbulent Viscosity |
| Volume: | 10 |
| Issue: | 4 |
| Page Number: | 14 |
| Institutes: | Informatik und Ingenieurwissenschaften (F10) / Fakultät 10 / Institut Allgemeiner Maschinenbau |
| Dewey Decimal Classification: | 600 Technik, Medizin, angewandte Wissenschaften |
| Open Access: | Open Access |
| DeepGreen: | DeepGreen |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |