Dimensionless turbulent diffusion constant versus dimensionless distance from the channel wall (0.01≤𝑥2/𝐻≤1) according to DNS at 𝑅𝑒𝜏=104 and the anisotropic model.
Changes in the way we model turbulence are setting the stage for a clearer understanding and prediction of fluid behavior in complex situations. Prof Emeritus Bert Brouwers has developed a new turbulence model that relies on statistical principles rather than traditional empirical methods. This innovative approach, recently published in the journal Inventions, offers significant improvements in how scientists predict and simulate turbulent flows.
Unlike older turbulence models that depend on trial-and-error adjustments, Dr. Brouwers’ anisotropic turbulence model is built on foundational principles of physics. “By using universal rules instead of guesswork, this model makes it easier to understand how turbulence behaves in different situations,” explained Dr. Brouwers. The model simplifies complex aspects of turbulent flow, such as how momentum and energy, the movement and power carried by fluid particles, spread through fluids, offering a more accurate and straightforward representation.
Scientists tested the model against highly detailed simulations of fluid flow, called direct numerical simulations of the Navier Stokes equations (DNS), a method that captures every detail of fluid movement, and found its predictions closely matched the simulation results. This was not the case with commonly used models, which often fail in specific scenarios. By linking turbulent behavior directly to factors like velocity and flow gradients, which describe how quickly the speed and direction of fluid change, the new model allows smoother integration into computer programs used for fluid dynamics studies.
One of the most important advances is replacing custom-calibrated parameters, such as diffusion rates, the rate at which particles spread out in a fluid, with universally applicable formulas derived from well-established physical constants. Dr. Brouwers emphasized, “This approach avoids guesswork and ensures consistent results across different situations, making it a more reliable tool for engineers and researchers.”
Key highlights of the research include better predictions of how energy is distributed in turbulent flows and insights into how uneven conditions in a flow system impact turbulence. The model also has practical uses in understanding heat and substance transfer, which describe how warmth and materials like chemicals or pollutants move through fluids, in engineering systems. This can benefit industries like aerospace, energy, and environmental management.
Experts evaluated the model using examples of fluid flowing between parallel surfaces. Predictions for factors like fluctuating velocities, changes in speed and direction due to turbulence, energy distribution, and stress levels closely matched observations from advanced simulations. What sets this model apart is its clear mathematical structure, which reduces computational effort without losing precision.
Applications for this upgraded turbulence model extend beyond engineering systems. Dr. Brouwers noted that the universal principles behind it mean it can address challenges in areas such as climate modeling, where turbulence plays a key role in weather patterns and ocean currents. “This model’s adaptability makes it a valuable resource for solving a wide range of problems in science and industry,” he said.
The broader scientific community now has access to a model that not only offers better accuracy but also removes the need for complex and often inconsistent calibrations. The work lays a strong foundation for further developments in turbulence research and opens the door to new possibilities in environmental and technological innovation.
Journal Reference
Brouwers, J.J.H., “Anisotropic k-ϵ Model Based on General Principles of Statistical Turbulence.” Inventions, 2024. DOI: https://doi.org/10.3390/inventions9050095
About the Author
Bert Brouwers was born in 1949 in Heer/Maastricht, The Netherlands. He obtained his MSc in Mechanical Engineering at Eindhoven University of Technology in 1972 (cum laude). A PhD was received at Twente University in 1976. Advisors: prof.dr.ir.L.van Wijngaarden and prof.dr.J.Los (University of Amsterdam).In 1972 he started as Research Engineer at the Ultra Centrifuge Laboratory of UCN/Urenco in Amsterdam. In 1974 he became Head Isotopes Separations Research. In 1979 he joined Royal/Dutch Shell. First he was Group Leader in Offshore Research at the Exploration and Production Laboratory in Rijswijk. In 1983 he moved to London to become Staff Member Economics.Brouwers switched from industry to academia in 1986 when he was appointed as full professor and head of the laboratory of Thermal Engineering at Twente University.In 1998 he came to Eindhoven University of Technology to become full professor and head of the Section of Process Technology of the Mechanical Engineering Department. He retired from university in 2014 to continue his research in topics of classical mechanics and to advance his ideas in new technology. Brouwers has made innovative contributions to science and technology.He is single author of 25+ peer reviewed articles published in scientific and engineering journals: Physics Review E, Physica D Non-Linear Phenomena, Theoretical and Mathematical Physics, Flow Turbulence and Combustion, Journal of Engineering Mathematics, Reliability Engineering, Ocean Engineering, Nuclear Technology, Physics of Fluids, MDPI Journals Fluids, Separations, Mathematics, Inventions. Brouwers is the inventor of patented methods and devices for separating particles and gases employing the principles of centrifugation, fluid flow and diffusion. Know-how and IP rights are vested in companies founded by him. In cooperation with licensing companies practical versions of the inventions are developed and implemented worldwide. In 1999 Brouwers was awarded the Dow Chemical Energy Price. He held short term advisor ships to companies and institutions. He supervised 200+ engineering degrees and advanced engineering degrees and 40+ PhD-degrees awarded at Twente University and Eindhoven University of Technology.
