Large Eddy Simulation of High Reynolds Number Wall-bounded Flows

Name: Peng Wu

Prof. dr. Johan Meyers

This PhD study aims to develop an efficient and accurate large-eddy simulation (LES) method for compressible high-Reynolds-number wall-bounded flows. This work started from an in-house research code FLOWAVE, a second-order code with the capability of LES. However, this code suffered from several major drawbacks preventing it becoming a well suited tool to deal with high-Reynoldsnumber
wall bounded flows. This study seeks to address these problems and provide a pragmatic and robust LES methodology for high-Reynolds-number wall bounded flows.

Within the contextof LES of high-Reynolds-number wall-bounded flows, the first challenge is the undesired odd-even decoupling which contaminates the flow field. In this study, to suppress the odd-even decoupling, conservative boundary filters are constructed without changing flow structures and flow properties such as mass flow rate and momentum. The filters are used in combination with conventional high-order selective filters at the inner points to provide an effective means to solve the odd-even decoupling. The importance of conservative filtering is also proved to be important for the sub-grid stress (SGS) models, in which explicit filters are involved.The conservative filters are
tested over a couple of channel flow test cases and a 2D cavity case to study the influence the filtering on noise prediction, yielding superior results compared with conventional non-conservative filters.

The next challenge is the excessive computational cost due to the resolved LES of high-Reynolds-number wall-bounded flows. In wall-bounded turbulent flows, the length scale of the viscous sub-layer will decrease as Reynolds number increases. As a result, forresolved large eddy simulation, the number of grid points which are needed to resolve the wall layer will increase exponentially. Nevertheless,large Reynolds number wall-bounded flow tends to be the rule in most engineering flows. Therefore for those cases wall-resolved LES would lead to prohibitive computational cost and become impractical. Therefore, hybrid methods, for instance, wall-stress models (WSM) are usually employedfor attached wall flows to prescribe the shear stress at wall, so that the first grid point can be put far away from the wall to reduce the computational cost.

However, conventional hybrid methods, including the WSM when used in combination with a standard Smagorinsky model, are prone to the so-called‘log-layer mismatch’ problem, resulting in poor predictions of the mean velocity and its gradient. Many attempts have beenmade to address this problem; however, they are limited by either theirinability to suppress the log-layer mismatch to an accepted level, or their complexity and uncertainty in real practice.

In view of this, in this work, a theoretical framework was developed in which the relationship between the mean velocity gradient and the turbulent kinetic energy budgets in the log-layer is expressed. In this framework, different factors which may influence the mean shear can be quantified and analyzed. The analysis is then extended to the wall-modeled LES. It is shown that over-dissipation does not necessarily lead over-prediction of the mean shear. Based on this framework, a self-adaptive Smagorinsky model was proposed in which the Smagorinsky coefficient is dynamically adjusted sothat the problem of log-layer mismatch is effectively suppressed. The model has been validated for a channel flow with rough walls at high Reynolds number, yielding desired velocity profile. The model is extended toinclude the viscous effect and applied to a couple of smooth channel flow cases. The log profiles of the mean velocity are more accurately captured compared with the conventional Smagorinsky model.

Finally, the wall-model LES methodology is applied to a square duct using the boththe conventional Smagorinsky model and the new self-adaptive Smagorinsky model. A modified log-law is proposed to give a better fit with the experimental results compared with classic log law. The self-adaptive Smagorinsky model captures the acceleration near the corner, while the Smagorinsky model fails to
capture such phenomenon. In addition, the errors on the friction velocity of the self-adaptive Smagorinsky model are lower than those of the Smagorinsky model, and the modified log law yieldsmore accurate skin frictions compared with the classic log law.

https://lirias.kuleuven.be/handle/123456789/363527

•   Prof. dr. Johan Meyers (promotor)
•   Prof. dr. ir. Paula Moldenaers (voorzitter/chairman)
•   Prof. dr. ir. Wim Desmet (secretaris/secretary)
•   Prof. dr. ir. Martine Baelmans
•   Prof. dr. Herman Deconinck , von Karman Instituut
•   Prof. dr. Bart Merci , Universiteit Gent
•   Prof. dr. Pierre Sagaut , Université Pierre et Marie Curie