Spatiotemporal Signatures of Elastoinertial Turbulence
The addition of small amounts of polymers to a Newtonian solvent makes the fluid viscoelastic, and can lead to significant drag reduction in high-speed flows. The interaction of viscoelasticity and inertia in a dilute polymer solution results in the emergence of unique inertioelastic instabilities....
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| Format: | Thesis |
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Massachusetts Institute of Technology
2025
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| Online Access: | https://hdl.handle.net/1721.1/158324 |
| _version_ | 1826193234092621824 |
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| author | Yamani, Sami |
| author2 | Bischofberger, Irmgard |
| author_facet | Bischofberger, Irmgard Yamani, Sami |
| author_sort | Yamani, Sami |
| collection | MIT |
| description | The addition of small amounts of polymers to a Newtonian solvent makes the fluid viscoelastic, and can lead to significant drag reduction in high-speed flows. The interaction of viscoelasticity and inertia in a dilute polymer solution results in the emergence of unique inertioelastic instabilities. The nonlinear evolution of these instabilities engenders a state of turbulence with significantly different spatiotemporal features compared to Newtonian turbulence, commonly termed elastoinertial turbulence (EIT). We explore EIT by studying the dynamics of low-speed submerged jets of dilute aqueous polymer solutions injected through a nozzle into a tank of quiescent water or polymer solution. In a free shear layer, fluid elasticity has a dichotomous effect on jet stability depending on its relative magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. For small levels of elasticity an inertioelastic shear-layer instability emerges, in agreement with existing linear stability analysis of viscoelastic jets, which is independent of bulk undulations in the column of fluid forming the jet. The growth of this instability near the edge of the jet destabilizes the flow, advancing the transition to turbulence to lower Reynolds numbers and closer to the nozzle compared to a Newtonian jet. Increasing the fluid elasticity merges this shear-layer instability into a bulk instability of the fluid column. In this regime, elastic tensile stresses in the sheared polymer solution act like an “elastic membrane” that stabilizes the flow, delaying the transition to turbulence to higher levels of inertia and greater distances downstream of the nozzle. In a wall-bounded shear layer, a separate investigation shows that fluid elasticity generates a self-sustained inertioelastic travelling wave within the wall boundary layer under flow conditions at which a Newtonian wall jet remains completely laminar. The phase velocity of this travelling wave decreases as fluid elasticity increases, resulting in the stabilization of the jet. In the fully-developed turbulent state far from the nozzle, viscoelastic jets exhibit unique spatiotemporal features associated with EIT. The time-averaged angle of jet spreading and the center-line velocity of the jet are self-similar with distance from the nozzle, and the similarity scaling coefficients vary with fluid elasticity. The cascade of turbulent eddies has a universal frequency spectrum independent of fluid elasticity. This spectrum is characterized by a power law with an exponent of −3 that is different from the well-known Kolmogorov law with exponent −5/3 for Newtonian turbulence. EIT also modifies the Lagrangian coherent structures that develop in the turbulent flow. Increasing elasticity generates coherent structures that are larger and more elongated in the streamwise direction, consistent with the suppression of streamwise vortices by EIT. On a larger scale, the elongated coherent structures create a stochastic cycle in EIT that consists of active and hibernating turbulent states with alternating strong and weak turbulent fluctuations. Looking ahead, this new fundamental understanding of EIT can be leveraged to explore the potential of biopolymers as cheap and environmentally-friendly drag reducing agents replacing synthetic polymers made from petroleum oil. Biopolymers are typically semiflexible polyelectrolytes with rheological properties that can be adjusted over a wide range by varying conditions such as the solvent quality and/or the ionic strength. We study aqueous solutions of a typical long chain biomacromolecule (Xanthan gum) in canonical shear and extensional flows and quantify how the rheological properties can be tuned by changing the ionic strength of the solvent. In steady shear flow, increasing the biopolymer concentration dramatically increases both the zero shear viscosity and the extent of shear-thinning, while increasing the ionic strength of the solvent, decreases both the zero shear viscosity and the level of shear-thinning. In transient extensional flow, increasing biopolymer concentration increases the extensional relaxation time of the solution, while increasing the ionic strength of the solvent decreases this relaxation time. Based on our insights from this rheological characterization, we demonstrate that injecting a high inertia jet of aqueous biopolymer solution into quiescent environments at different levels of ionic strength can significantly modify the spectral characteristics of the inertioelastic instabilities that develop and lead to a change in the spatiotemporal signatures of elastoinertial turbulence. Our findings lay out a pathway for identifying the most promising biopolymers to serve as biodegradable drag reducing agents for marine vehicles operating in high salinity environments enabling savings in the cost of transport and future reduction in our carbon footprint. |
| first_indexed | 2025-03-10T07:59:44Z |
| format | Thesis |
| id | mit-1721.1/158324 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2025-03-10T07:59:44Z |
| publishDate | 2025 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1583242025-03-05T15:27:50Z Spatiotemporal Signatures of Elastoinertial Turbulence Yamani, Sami Bischofberger, Irmgard McKinley, Gareth H. Massachusetts Institute of Technology. Department of Mechanical Engineering The addition of small amounts of polymers to a Newtonian solvent makes the fluid viscoelastic, and can lead to significant drag reduction in high-speed flows. The interaction of viscoelasticity and inertia in a dilute polymer solution results in the emergence of unique inertioelastic instabilities. The nonlinear evolution of these instabilities engenders a state of turbulence with significantly different spatiotemporal features compared to Newtonian turbulence, commonly termed elastoinertial turbulence (EIT). We explore EIT by studying the dynamics of low-speed submerged jets of dilute aqueous polymer solutions injected through a nozzle into a tank of quiescent water or polymer solution. In a free shear layer, fluid elasticity has a dichotomous effect on jet stability depending on its relative magnitude, creating two distinct regimes in which elastic effects can either destabilize or stabilize the jet. For small levels of elasticity an inertioelastic shear-layer instability emerges, in agreement with existing linear stability analysis of viscoelastic jets, which is independent of bulk undulations in the column of fluid forming the jet. The growth of this instability near the edge of the jet destabilizes the flow, advancing the transition to turbulence to lower Reynolds numbers and closer to the nozzle compared to a Newtonian jet. Increasing the fluid elasticity merges this shear-layer instability into a bulk instability of the fluid column. In this regime, elastic tensile stresses in the sheared polymer solution act like an “elastic membrane” that stabilizes the flow, delaying the transition to turbulence to higher levels of inertia and greater distances downstream of the nozzle. In a wall-bounded shear layer, a separate investigation shows that fluid elasticity generates a self-sustained inertioelastic travelling wave within the wall boundary layer under flow conditions at which a Newtonian wall jet remains completely laminar. The phase velocity of this travelling wave decreases as fluid elasticity increases, resulting in the stabilization of the jet. In the fully-developed turbulent state far from the nozzle, viscoelastic jets exhibit unique spatiotemporal features associated with EIT. The time-averaged angle of jet spreading and the center-line velocity of the jet are self-similar with distance from the nozzle, and the similarity scaling coefficients vary with fluid elasticity. The cascade of turbulent eddies has a universal frequency spectrum independent of fluid elasticity. This spectrum is characterized by a power law with an exponent of −3 that is different from the well-known Kolmogorov law with exponent −5/3 for Newtonian turbulence. EIT also modifies the Lagrangian coherent structures that develop in the turbulent flow. Increasing elasticity generates coherent structures that are larger and more elongated in the streamwise direction, consistent with the suppression of streamwise vortices by EIT. On a larger scale, the elongated coherent structures create a stochastic cycle in EIT that consists of active and hibernating turbulent states with alternating strong and weak turbulent fluctuations. Looking ahead, this new fundamental understanding of EIT can be leveraged to explore the potential of biopolymers as cheap and environmentally-friendly drag reducing agents replacing synthetic polymers made from petroleum oil. Biopolymers are typically semiflexible polyelectrolytes with rheological properties that can be adjusted over a wide range by varying conditions such as the solvent quality and/or the ionic strength. We study aqueous solutions of a typical long chain biomacromolecule (Xanthan gum) in canonical shear and extensional flows and quantify how the rheological properties can be tuned by changing the ionic strength of the solvent. In steady shear flow, increasing the biopolymer concentration dramatically increases both the zero shear viscosity and the extent of shear-thinning, while increasing the ionic strength of the solvent, decreases both the zero shear viscosity and the level of shear-thinning. In transient extensional flow, increasing biopolymer concentration increases the extensional relaxation time of the solution, while increasing the ionic strength of the solvent decreases this relaxation time. Based on our insights from this rheological characterization, we demonstrate that injecting a high inertia jet of aqueous biopolymer solution into quiescent environments at different levels of ionic strength can significantly modify the spectral characteristics of the inertioelastic instabilities that develop and lead to a change in the spatiotemporal signatures of elastoinertial turbulence. Our findings lay out a pathway for identifying the most promising biopolymers to serve as biodegradable drag reducing agents for marine vehicles operating in high salinity environments enabling savings in the cost of transport and future reduction in our carbon footprint. Ph.D. 2025-03-05T15:27:45Z 2025-03-05T15:27:45Z 2024-09 2025-03-03T16:18:33.957Z Thesis https://hdl.handle.net/1721.1/158324 Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Copyright retained by author(s) https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Yamani, Sami Spatiotemporal Signatures of Elastoinertial Turbulence |
| title | Spatiotemporal Signatures of Elastoinertial Turbulence |
| title_full | Spatiotemporal Signatures of Elastoinertial Turbulence |
| title_fullStr | Spatiotemporal Signatures of Elastoinertial Turbulence |
| title_full_unstemmed | Spatiotemporal Signatures of Elastoinertial Turbulence |
| title_short | Spatiotemporal Signatures of Elastoinertial Turbulence |
| title_sort | spatiotemporal signatures of elastoinertial turbulence |
| url | https://hdl.handle.net/1721.1/158324 |
| work_keys_str_mv | AT yamanisami spatiotemporalsignaturesofelastoinertialturbulence |