insight - Scientific Computing - # Turbulence Modeling

Achieving Rapid Convergence of Turbulence Statistics in Pressure-Driven Channel Flow Using Synthetic Turbulence

Q: How might this method be adapted for use in simulating more complex flow geometries, such as those found in engineering applications?

Adapting the synthetic turbulence generation method to more complex geometries, while promising, presents several challenges: Loss of Homogeneity: The current method heavily relies on the streamwise homogeneity of the channel flow. This allows for the interchangeable treatment of time and the streamwise coordinate using Taylor's hypothesis. In complex geometries, this assumption breaks down, necessitating new approaches to introduce temporal correlations. Boundary Condition Implementation: Accurately representing turbulent fluctuations near complex boundaries (curved walls, sharp corners) becomes significantly more difficult. The STFG would need modifications to ensure realistic turbulence generation near these boundaries, potentially requiring local refinement of the synthetic field or coupling with wall-modeled approaches. Computational Cost: While the STFG is computationally cheap for a channel flow, its extension to complex geometries might increase the computational burden. Efficient algorithms and potentially domain decomposition strategies would be crucial to maintain reasonable computational costs. Possible Adaptation Strategies: Domain Decomposition: Divide the complex domain into simpler subdomains where local homogeneity can be assumed. Generate synthetic turbulence within each subdomain and employ appropriate interface conditions to ensure a smooth transition of turbulent structures. Generalized Coordinates: Formulate the STFG in a generalized coordinate system to handle complex geometries. This would require transforming the governing equations and adapting the digital filter method accordingly. Hybrid Methods: Combine the STFG with other turbulence generation techniques, such as synthetic eddy methods (SEM) or body force methods, to handle specific flow features. For instance, use STFG in regions with relatively simple geometry and SEM near complex boundaries.

Q: Could the reliance on pre-defined turbulence statistics in the synthetic generation method limit its applicability to flows with evolving or unknown turbulence characteristics?

Yes, the reliance on pre-defined turbulence statistics (mean velocity profiles and Reynolds stress tensors) does pose a limitation for flows with evolving or unknown turbulence characteristics. Evolving Turbulence: In flows with evolving turbulence, such as those undergoing transition, separation, or reattachment, the pre-defined statistics might not accurately represent the flow physics. Using incorrect statistics could lead to inaccurate initial conditions and delayed convergence. Unknown Turbulence: When the turbulence characteristics are unknown a priori, which is often the case in practical engineering applications, it becomes challenging to define appropriate input statistics for the STFG. This limits the method's applicability in such scenarios. Possible Solutions: Iterative Approach: An iterative approach could be employed where initial simulations are performed with estimated turbulence statistics. The obtained flow field is then used to extract updated statistics, which are fed back into the STFG for generating improved initial conditions. This process can be repeated until satisfactory convergence is achieved. Data-Driven Methods: Leverage experimental data or high-fidelity simulations to obtain realistic turbulence statistics. Machine learning techniques could be employed to develop models that predict turbulence statistics based on flow parameters or limited experimental measurements. Adaptive STFG: Develop an adaptive STFG that can adjust the generated turbulence statistics based on the evolving flow field. This would require real-time monitoring of flow characteristics and incorporating feedback mechanisms within the STFG algorithm.

Q: If computational resources were not a limiting factor, would there still be benefits to using synthetic turbulence over letting the simulation organically develop turbulence from a simplified initial condition?

Even with unlimited computational resources, using synthetic turbulence offers several advantages over organically developing turbulence from a simplified initial condition: Faster Statistical Convergence: The primary benefit remains the significant reduction in spin-up time. This allows for quicker convergence of statistical quantities, enabling researchers to focus on analyzing the statistically stationary regime and extracting meaningful insights. Controlled Turbulence Development: Synthetic turbulence provides greater control over the initial turbulent flow field. This is particularly useful for studying specific flow phenomena or validating turbulence models where a well-defined initial turbulent state is desired. Reduced Transient Effects: Organically developing turbulence from simplified initial conditions often leads to long transient phases that can contaminate statistical data. Synthetic turbulence minimizes these transient effects, leading to more accurate and reliable results. Improved Repeatability: Simulations initialized with synthetic turbulence exhibit better repeatability compared to those with organically developing turbulence. This is because the initial turbulent field is explicitly defined, reducing the influence of random perturbations and numerical noise. Conclusion: While computational cost is a significant driver for using synthetic turbulence, the benefits extend beyond just efficiency. The ability to control, accelerate, and improve the accuracy of turbulence development makes it a valuable tool even when computational resources are abundant.

Core Concepts

Synthetically generated turbulent initial conditions offer a computationally efficient method for achieving statistically stationary flow conditions in pressure-driven channel flow simulations, significantly reducing spin-up time and computational cost compared to traditional analytical initialization methods.

Abstract

This research paper investigates the effectiveness of different initial condition methods for achieving statistically stationary flow conditions in pressure-driven channel flow simulations. The authors compare three approaches:

Linear profile superposed with random noise and counter-rotating vortices
Linear-log-law profile superposed with random noise and counter-rotating vortices
Synthetically generated three-dimensional turbulence

Research Objective:

The study aims to identify the most computationally efficient method for achieving statistically stationary flow conditions in pressure-driven channel flow simulations, focusing on minimizing the simulation spin-up time.

Methodology:

The authors conduct simulations using an open-source massively parallel CaNS solver to numerically integrate the non-dimensional incompressible Navier-Stokes momentum equations. They compare the convergence of shear stress, mean velocity profiles, rms velocity profiles, Reynolds stress profiles, integral length scales, energy spectra, and turbulent kinetic energy budgets for each initialization method at two different Reynolds numbers (Reτ = 350 and Reτ = 500).

Key Findings:

The synthetic turbulence method achieves statistically stationary flow conditions within 3 eddy turnover times, significantly faster than the linear and log-law profile methods, which require more than 10 eddy turnovers.
The synthetic turbulence method accurately reproduces the expected mean velocity, rms velocity, Reynolds stress, integral length scale, energy spectrum, and turbulent kinetic energy budget profiles, demonstrating its ability to generate realistic turbulent flow fields.
The one-time computational cost of generating the synthetic turbulent initial condition is less than 1 CPU hour, making it a computationally efficient alternative to traditional methods.

Main Conclusions:

Synthetically generated three-dimensional turbulence provides a computationally efficient and effective method for reducing simulation spin-up time and achieving statistically stationary flow conditions in pressure-driven channel flow simulations, particularly when precursor turbulent initial conditions are unavailable.

Significance:

This research offers a valuable contribution to the field of computational fluid dynamics by providing a practical and efficient approach for initializing turbulence simulations, potentially leading to faster and more cost-effective investigations of complex flow phenomena.

Limitations and Future Research:

The study focuses on pressure-driven channel flow simulations, and further research is needed to assess the effectiveness of the synthetic turbulence method in other flow configurations. Additionally, exploring more sophisticated synthetic turbulence generation methods, such as the ensemble synthetic method, could potentially further reduce the spin-up time.

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Stats

The synthetic turbulence method achieves statistically stationary flow conditions within 3 eddy turnover times.
The linear and log-law profile methods require more than 10 eddy turnovers to reach statistically stationary flow conditions.
The one-time computational cost of generating the synthetic turbulent initial condition is less than 1 CPU hour.
Simulations were conducted at Reτ = 350 and Reτ = 500.

Quotes

Key Insights Distilled From

Fake it till you make it: using artificial turbulence to achieve swift converged turbulence statistics in a pressure-driven channel flow

by Aksh... at arxiv.org 11-19-2024

https://arxiv.org/pdf/2411.11416.pdf

Fake it till you make it: using artificial turbulence to achieve swift converged turbulence statistics in a pressure-driven channel flow

Deeper Inquiries

How might this method be adapted for use in simulating more complex flow geometries, such as those found in engineering applications?

Adapting the synthetic turbulence generation method to more complex geometries, while promising, presents several challenges:

Loss of Homogeneity: The current method heavily relies on the streamwise homogeneity of the channel flow. This allows for the interchangeable treatment of time and the streamwise coordinate using Taylor's hypothesis. In complex geometries, this assumption breaks down, necessitating new approaches to introduce temporal correlations.
Boundary Condition Implementation:  Accurately representing turbulent fluctuations near complex boundaries (curved walls, sharp corners) becomes significantly more difficult. The STFG would need modifications to ensure realistic turbulence generation near these boundaries, potentially requiring local refinement of the synthetic field or coupling with wall-modeled approaches.
Computational Cost: While the STFG is computationally cheap for a channel flow, its extension to complex geometries might increase the computational burden. Efficient algorithms and potentially domain decomposition strategies would be crucial to maintain reasonable computational costs.
Possible Adaptation Strategies:

Domain Decomposition: Divide the complex domain into simpler subdomains where local homogeneity can be assumed. Generate synthetic turbulence within each subdomain and employ appropriate interface conditions to ensure a smooth transition of turbulent structures.
Generalized Coordinates:  Formulate the STFG in a generalized coordinate system to handle complex geometries. This would require transforming the governing equations and adapting the digital filter method accordingly.
Hybrid Methods: Combine the STFG with other turbulence generation techniques, such as synthetic eddy methods (SEM) or body force methods, to handle specific flow features. For instance, use STFG in regions with relatively simple geometry and SEM near complex boundaries.

Could the reliance on pre-defined turbulence statistics in the synthetic generation method limit its applicability to flows with evolving or unknown turbulence characteristics?

Yes, the reliance on pre-defined turbulence statistics (mean velocity profiles and Reynolds stress tensors) does pose a limitation for flows with evolving or unknown turbulence characteristics.

Evolving Turbulence: In flows with evolving turbulence, such as those undergoing transition, separation, or reattachment, the pre-defined statistics might not accurately represent the flow physics. Using incorrect statistics could lead to inaccurate initial conditions and delayed convergence.
Unknown Turbulence: When the turbulence characteristics are unknown a priori, which is often the case in practical engineering applications, it becomes challenging to define appropriate input statistics for the STFG. This limits the method's applicability in such scenarios.
Possible Solutions:

Iterative Approach: An iterative approach could be employed where initial simulations are performed with estimated turbulence statistics. The obtained flow field is then used to extract updated statistics, which are fed back into the STFG for generating improved initial conditions. This process can be repeated until satisfactory convergence is achieved.
Data-Driven Methods: Leverage experimental data or high-fidelity simulations to obtain realistic turbulence statistics. Machine learning techniques could be employed to develop models that predict turbulence statistics based on flow parameters or limited experimental measurements.
Adaptive STFG: Develop an adaptive STFG that can adjust the generated turbulence statistics based on the evolving flow field. This would require real-time monitoring of flow characteristics and incorporating feedback mechanisms within the STFG algorithm.

If computational resources were not a limiting factor, would there still be benefits to using synthetic turbulence over letting the simulation organically develop turbulence from a simplified initial condition?

Even with unlimited computational resources, using synthetic turbulence offers several advantages over organically developing turbulence from a simplified initial condition:

Faster Statistical Convergence:  The primary benefit remains the significant reduction in spin-up time. This allows for quicker convergence of statistical quantities, enabling researchers to focus on analyzing the statistically stationary regime and extracting meaningful insights.
Controlled Turbulence Development:  Synthetic turbulence provides greater control over the initial turbulent flow field. This is particularly useful for studying specific flow phenomena or validating turbulence models where a well-defined initial turbulent state is desired.
Reduced Transient Effects:  Organically developing turbulence from simplified initial conditions often leads to long transient phases that can contaminate statistical data. Synthetic turbulence minimizes these transient effects, leading to more accurate and reliable results.
Improved Repeatability:  Simulations initialized with synthetic turbulence exhibit better repeatability compared to those with organically developing turbulence. This is because the initial turbulent field is explicitly defined, reducing the influence of random perturbations and numerical noise.
Conclusion:
While computational cost is a significant driver for using synthetic turbulence, the benefits extend beyond just efficiency. The ability to control, accelerate, and improve the accuracy of turbulence development makes it a valuable tool even when computational resources are abundant.