insight - Fluid mechanics - # Grade-two fluid model in a contracting duct

Computational Analysis of a Contraction Rheometer for the Grade-Two Fluid Model

Q: How would the identifiability of the grade-two parameters change if the geometry of the contraction rheometer was modified, such as using a different contraction profile or adding additional features like a sudden expansion

Modifying the geometry of the contraction rheometer, such as changing the contraction profile or adding features like a sudden expansion, could have a significant impact on the identifiability of the grade-two parameters. Contraction Profile: Altering the shape of the contraction could affect the flow patterns and stress distribution within the rheometer. A more complex contraction profile may introduce additional complexities in the flow behavior, making it harder to isolate the effects of individual parameters. On the other hand, a simpler contraction profile might lead to more straightforward relationships between the parameters and the measured quantities, potentially enhancing identifiability. Sudden Expansion: Adding a sudden expansion downstream of the contraction could introduce flow instabilities and vortices, impacting the stress-strain relationship. This could complicate the interpretation of the experimental data and make it challenging to uniquely determine the grade-two parameters. However, the sudden expansion could also provide additional information about the fluid behavior, potentially offering new insights into parameter identifiability. Overall Impact: In general, modifying the geometry of the contraction rheometer would require a reevaluation of the computational models and experimental setup. The changes could either improve or hinder the identifiability of the grade-two parameters, depending on how they influence the flow characteristics and the relationship between the parameters and the measured quantities.

Q: What other experimental measurements, beyond the force integral, could be used in conjunction with the contraction rheometer to better identify the grade-two parameters

In addition to the force integral, several other experimental measurements could be used in conjunction with the contraction rheometer to better identify the grade-two parameters: Pressure Distribution: Measuring the pressure distribution within the rheometer could provide valuable information about the stress-strain relationship and help constrain the grade-two parameters. Velocity Profiles: Analyzing the velocity profiles at different points in the rheometer could offer insights into the flow behavior and the impact of the grade-two parameters on the fluid dynamics. Shear Rate Measurements: Measuring the shear rate at various locations in the rheometer could help characterize the non-Newtonian behavior of the fluid and improve parameter identifiability. Rheological Tests: Conducting additional rheological tests, such as oscillatory shear tests or creep tests, could provide complementary data to validate the grade-two model and refine the parameter estimates. By combining multiple experimental measurements with the force integral, researchers can obtain a more comprehensive understanding of the fluid behavior and enhance the accuracy of parameter identification.

Q: The authors focus on the grade-two fluid model, but how might the insights gained here apply to the identification of parameters in other non-Newtonian fluid models using a contraction rheometer

The insights gained from studying the identifiability of grade-two parameters using a contraction rheometer can be applied to the identification of parameters in other non-Newtonian fluid models. Model-Specific Features: Different non-Newtonian fluid models have unique characteristics and governing equations. By adapting the computational analysis and experimental setup to specific model requirements, researchers can apply similar methodologies to identify parameters in various non-Newtonian models. Experimental Design: The experimental design considerations, such as varying flow rates, measuring different quantities, and analyzing the data structure, can be generalized to other fluid models. Researchers can tailor the experimental approach to suit the specific features of the model under investigation. Parameter Identifiability: The challenges and strategies for parameter identifiability discussed in the context of the grade-two fluid model can serve as a foundation for similar studies in other non-Newtonian models. Understanding the limitations and opportunities in parameter estimation can guide researchers in optimizing experimental protocols and computational analyses for different fluid models.

Core Concepts

The authors explore the possibility of simulating the grade-two fluid model in a geometry related to a contraction rheometer, and provide details on several key aspects of the computation. They show how the results can be used to determine the viscosity ν from experimental data, and explore the identifiability of the grade-two parameters α1 and α2 from experimental data.

Abstract

The authors begin by summarizing the main results from a previous paper [16], which introduced a new algorithm for solving the grade-two fluid model equations. They then describe the contracting duct domain over which they will perform force integral computations, and the main characteristics of the flow in this duct.
The core of the paper is Section 3, where the authors define the force integral and provide a detailed study of the structure of the computed data with respect to the model parameters in order to determine a regime in which the contraction rheometer may be used to identify the grade-two parameters.
The authors find that the force integral F(U)/U is approximately linear in the flow rate U, but has a nonlinear dependence on the angle θ between the grade-two parameters α1 and α2. They observe that the trajectories of F(U)/U as a function of θ cross at certain values of θ, suggesting that the individual parameters α1 and α2 may not be identifiable in those regimes. However, they identify a range of θ values, roughly θ ∈ (-5π/16, 3π/16], where the parameters may be identifiable.
The paper also includes details on the computational mesh and local refinement strategies used to accurately compute the force integral near the reentrant corners of the contracting duct.

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Key Insights Distilled From

Computational analysis of a contraction rheometer for the grade-two fluid model

by Sara Pollock... at arxiv.org 04-05-2024

https://arxiv.org/pdf/2404.03450.pdf

Computational analysis of a contraction rheometer for the grade-two fluid model

Deeper Inquiries

How would the identifiability of the grade-two parameters change if the geometry of the contraction rheometer was modified, such as using a different contraction profile or adding additional features like a sudden expansion

Modifying the geometry of the contraction rheometer, such as changing the contraction profile or adding features like a sudden expansion, could have a significant impact on the identifiability of the grade-two parameters.

Contraction Profile: Altering the shape of the contraction could affect the flow patterns and stress distribution within the rheometer. A more complex contraction profile may introduce additional complexities in the flow behavior, making it harder to isolate the effects of individual parameters. On the other hand, a simpler contraction profile might lead to more straightforward relationships between the parameters and the measured quantities, potentially enhancing identifiability.

Sudden Expansion: Adding a sudden expansion downstream of the contraction could introduce flow instabilities and vortices, impacting the stress-strain relationship. This could complicate the interpretation of the experimental data and make it challenging to uniquely determine the grade-two parameters. However, the sudden expansion could also provide additional information about the fluid behavior, potentially offering new insights into parameter identifiability.

Overall Impact: In general, modifying the geometry of the contraction rheometer would require a reevaluation of the computational models and experimental setup. The changes could either improve or hinder the identifiability of the grade-two parameters, depending on how they influence the flow characteristics and the relationship between the parameters and the measured quantities.

What other experimental measurements, beyond the force integral, could be used in conjunction with the contraction rheometer to better identify the grade-two parameters

In addition to the force integral, several other experimental measurements could be used in conjunction with the contraction rheometer to better identify the grade-two parameters:

Pressure Distribution: Measuring the pressure distribution within the rheometer could provide valuable information about the stress-strain relationship and help constrain the grade-two parameters.

Velocity Profiles: Analyzing the velocity profiles at different points in the rheometer could offer insights into the flow behavior and the impact of the grade-two parameters on the fluid dynamics.

Shear Rate Measurements: Measuring the shear rate at various locations in the rheometer could help characterize the non-Newtonian behavior of the fluid and improve parameter identifiability.

Rheological Tests: Conducting additional rheological tests, such as oscillatory shear tests or creep tests, could provide complementary data to validate the grade-two model and refine the parameter estimates.

By combining multiple experimental measurements with the force integral, researchers can obtain a more comprehensive understanding of the fluid behavior and enhance the accuracy of parameter identification.

The authors focus on the grade-two fluid model, but how might the insights gained here apply to the identification of parameters in other non-Newtonian fluid models using a contraction rheometer

The insights gained from studying the identifiability of grade-two parameters using a contraction rheometer can be applied to the identification of parameters in other non-Newtonian fluid models.

Model-Specific Features: Different non-Newtonian fluid models have unique characteristics and governing equations. By adapting the computational analysis and experimental setup to specific model requirements, researchers can apply similar methodologies to identify parameters in various non-Newtonian models.

Experimental Design: The experimental design considerations, such as varying flow rates, measuring different quantities, and analyzing the data structure, can be generalized to other fluid models. Researchers can tailor the experimental approach to suit the specific features of the model under investigation.

Parameter Identifiability: The challenges and strategies for parameter identifiability discussed in the context of the grade-two fluid model can serve as a foundation for similar studies in other non-Newtonian models. Understanding the limitations and opportunities in parameter estimation can guide researchers in optimizing experimental protocols and computational analyses for different fluid models.

Computational Analysis of a Contraction Rheometer for the Grade-Two Fluid Model