Non-equilibrium wall-bounded turbulence

Turbulent flows are ubiquitous, and consist of a wide range of length and velocity scales; resolving the smallest scale in a DNS is difficult. In practical design and analysis, the constraints of time and computational recourses require the use of turbulence models to approximate the effects of the small scales. However, model errors are inevitable, since the models are calibrated in simpler scenarios (e.g., homogenous, equilibrium state with simple wall geometries) than those in reality. DNS of a realistic flow is a useful tool to quantify this error, and aid model improvement.

Turbulent boundary layers in reality are characterized with local strong pressure gradients; examples include flows around airfoils or atmospheric boundary layers above complex terrains. In cases of strong favorable pressure gradients, for instance, the boundary layer undergoes a “relaminarization” process, opposite to the model prediction that an increase of mean-flow kinetic energy leads to higher turbulent kinetic energy (an assumption used in common engineering turbulence models). High-resolution simulations help identify the underlying physics, and where the models go wrong.

Roughness effects on turbulence

Roughness is another widespread phenomenon in real-world boundary layers, such as airplane wing icing, turbine blade erosion, and in a larger scale, plant or ocean canopies. Different roughness geometry affect turbulence in different ways, but this dependence is not included in common turbulence models. This sometimes leads to one-order-of-magnitude difference in friction prediction, seriously affecting the energy efficiency estimate of engineering design, or mispredicts important flow phenomena such as transition and separation.

Here, complex roughness surfaces are either captured or synthesized. Its boundary condition is imposed in the flow using immersed boundary methods. Numerical experiments based on LES and DNS are used to calibrate the turbulence model for a specific roughness geometry a priori.; or better, a database of surface dependence can be established to develop novel friction-prediction techniques for arbitrary surfaces.

Novel closures for non-equilibrium, rough-wall turbulence

We are interested in physics-based or empirical models that enables predictions of complex or non-equilibrium flows. Current work includes the following.

Wall-roughness eddy viscosity model

We proposed a novel eddy-viscosity closure for turbulence in the vicinity of roughness, from a rational analysis of and physical insights into data from DNS. In theory, it is capable of isolating the effects of roughness texture and roughness height for a fully rough flow. This enables added flexibility for the closure to be tuned for non-equilibrium turbulence. The model is tested for boundary layers with favorable or adverse pressure gradients.

Advanced closures for rough-walled non-equilibrium turbulence

A long-standing problem in turbulence modeling is that the Reynolds stress tensor alone is not necessarily sufficient to characterize the transient and equilibrium states of turbulence under arbitrary mean deformation or frame rotation. More complete flow characterizations include additional, single-point structure tensors (e.g. Kassinos, Reynolds and Rogers, JFM 2001), such as the dimensionality, circulicity and inhomogeneity tensors. We explore the role of these tensors in smooth- and rough-wall turbulence, to improve understanding and modeling of these complex flows.

To this end, we developed an immersed boundaries implementation in stream-vector solver. Results show that turbulence characteristics (Reynolds stress, dimensionality, circulicity) are generally more isotropic on a rough wall than a smooth one, encouraging for modeling. However, for near-wall inhomogeneous turbulence, the quantitative connection between the one-point tensors and properties of the actual coherent structure is not yet clear. Currently, we are developing ideas to implement wall roughness in a structure-based modeling framework.

Turbulence across sediment-water interface and hyporheic exchange

Of the total river and stream length in US, 36% percent is in poor biological condition due to excessive levels of phosphorus and nitrogen and 23% contains enterococci levels unsafe for human health. It is critical to develop fundamental understanding and reliable prediction of transport with the hyporheic zone, which is the primary location that controls the metabolism and transport of relevant solutes. Existing predictive methods of mass and momentum transport face an enduring challenge in upscaling from bed-form to watersheds due to the multiscale variation associated with natural exchange processes. A major difficulty is the lack of knowledge in the grain scale, where important processes take place such as turbulence penetration and disturbances due to bed-form roughness.

We use direct numerical simulations (DNS) turbulent flows over grain-resolved sediments, to analyze the link between macroscopic flow-exchange parameters and detailed flow physics. We aim to identify the fundamental transport mechanics in the grain scale for realistic, heterogeneous sediment.