Session M26: Turbulent Boundary Layers V

Reduced-order model for near-wall dynamics with implications to wall-models

The near-wall resolution requirements of wall-resolved large eddy simulations (LES) are almost as high as those of direct numerical simulations (DNS). This restriction severely limits the applicability of LES in high-Reynolds-number flows and complex geometries that are typical of engineering configurations. An alternative to the wall-resolved LES is the wall-modeled simulation, where the resolution requirement is relaxed by prescribing wall-stresses in the vicinity of walls. One such way of providing accurate values of wall-stresses is based on optimal flow-control techniques. In this study we propose models to extend the terminology of predictive control-based wall-models to complex geometries, by defining transfer functions relating the mean velocity to the second moments at an optimal planar location. As a result the added calculation in the near-wall region (for example RANS) will be omitted and replaced by boundary conditions described by pre-existing transfer functions. The relevant transfer functions are extracted using a data-driven as well as model-based approach. The predicted transfer functions are then compared to their system-identified equivalent for verification.   

A nested-LES wall-modeling approach for computation of high Reynolds number equilibrium and non-equilibrium wall-bounded turbulent flows

A nested-LES wall-modeling approach for high Reynolds number, wall-bounded turbulence is presented. In this approach, a coarse-grained LES is performed in the full-domain, along with a nested, fine-resolution LES in a minimal flow unit. The coupling between the two domains is achieved by renormalizing the instantaneous LES velocity fields to match the profiles of kinetic energies of components of the mean velocity and velocity fluctuations in both domains to those of the minimal flow unit in the near-wall region, and to those of the full-domain in the outer region. The method is of fixed computational cost, independent of $Re_\tau$, in homogenous flows, and is $O(Re_\tau)$ in strongly non-homogenous flows. The method has been applied to equilibrium turbulent channel flows at $1000\leq{Re_\tau}\leq10000$ and to non-equilibrium, shear-driven, 3D turbulent channel flow at $Re_\tau\approx2000$. In equilibrium channel flow, the friction coefficient and the one-point turbulence statistics are predicted in agreement with Dean's correlation and available DNS and experimental data. In shear-driven, 3D channel flow, the evolution of turbulence statistics is predicted in agreement with experimental data of Driver \& Hebbar (1991) in shear-driven, 3D boundary layer flow.   

Investigation of a Wall Shear-Stress Inner-Outer Interaction Model for Large-Eddy Simulations

The very small turbulent motions in the thin layer of fluid immediately adjacent to a solid surface in a turbulent boundary layer make it difficult to effectively scrutinise the near-wall dynamics with physical and numerical experiments. These near-wall turbulent motions, and the no-slip condition, directly affect the tangential stress at the surface--the wall shear-stress. This study investigates a new wall-model for large-eddy simulations capable of predicting the fluctuating wall shear-stress from a large-scale velocity input, without the need to fully resolve the smallest structures in the flow. The model is based on the spectral structure of the turbulent boundary layer and the interaction between large-scale events in the logarithmic layer and small-scale events near the wall. Various methods have previously been used to predict the mean wall shear-stress with sufficient accuracy. There are, however, very few models available to predict the fluctuating component. Results from the new wall-model show that it has only a small effect on mean quantities, such as the skin-friction coefficient, but is able to resolve more of the wall shear-stress variance than a ``standard'' wall-model.   

Inference of the turbulent dissipation rates in wall-bounded turbulent flows

Accurate prediction of the dissipation rate of the turbulent kinetic energy ($\epsilon$) in turbulent flows is fundamental for modeling of such flows. However, measuring the dissipation rate of the turbulent kinetic energy has always been a challenge in laboratory experiments, especially near the wall. The focus of this study is to investigate and predict the dissipation rate of the turbulent kinetic energy ($\epsilon$) in fully developed wall-bounded turbulent flows. To this end, new parameterizations for the mixing length ($L_{mix}=(-\overline{u'v'})^{1/2}/S$) in fully developed wall-bounded turbulent flows are proposed and their relationship with the dissipation rate of the turbulent kinetic energy is investigated. Comparisons with different datasets of direct numerical simulation of canonical wall-bounded turbulent flows show remarkable agreement. These findings could be useful for the prediction of $\epsilon$ in wall-bounded turbulent flows, especially in the highly anisotropic near-wall region.   

Validation of Reynolds Stress Transport Models with Velocity/Pressure-Gradient Models in Wall- Bounded Flows

In the traditional formulation of Reynolds Stress Transport (RST) turbulence models, velocity/pressure-gradient correlations are decomposed into pressure-strain correlations and pressure diffusion terms that are modeled separately. In our study, a potential of a different modeling approach for improving simulation results in the near-wall area is investigated. No decomposition of velocity/pressure-gradient correlations is attempted. New linear models for such correlations have been recently developed and successfully validated against DNS data in two-dimensional incompressible turbulent flows such as a zero-pressure gradient boundary layer over a flat plate and a fully-developed channel flow. The models correctly reproduce DNS profiles of velocity/pressure-gradient correlations up to the wall with the same model coefficients in different geometries and at different Reynolds numbers. These models are currently implemented in transport equations for Reynolds stresses. The compatibility of models for such correlations with existing models for the dissipation tensor and turbulent diffusion is investigated. Simulations are conducted with open-source software OpenFOAM and in-house code in two-dimensional wall-bounded flows.   

Space-time characteristics of wall-pressure fluctuation in wall-modeled large-eddy simulation

Assessment of wall-modeled large-eddy simulation (WMLES) has always been based on the prediction quality of the mean velocity and Reynolds stresses. Secondary quantities from WMLES, such as wall pressure/stress fluctuations and their spectra received little attention, and they are usually not reported. Since they are directly related to the structural vibration and noise generation from the immersed bodies, identifying to what extent the near-wall pressure/stress field from WMLES can be utilized for the modeling purpose is of great importance. Here the r.m.s. and space-time characteristics of wall pressure/stress fluctuation obtained from WMLES are reported and analyzed for the first time. WMLES of a high Reynolds number turbulent channel flow at $Re_\tau$ = 2000 by Park and Moin [Phys. Fluids $\textbf{26}$, 015108, (2014)] is considered for this purpose. The r.m.s wall-pressure fluctuation in WMLES is generally under-predicted owing to the very coarse near-wall resolution, but improves with the mesh refinement. The convection velocity and wavenumber/frequency spectra of wall-pressure fluctuation show qualitative agreement with low Reynolds number data in the literature. Quantitative comparison to the $Re_\tau$ = 2000 DNS data will hopefully be presented in the meeting.   

Liquid Jet Impingement Thermal Transport on a Superhydrophobic Surface

Thermal transport for an axisymmetric liquid jet impinging on a horizontal constant temperature superhydrophobic surface with an imposed isotropic hydrodynamic slip length and temperature jump length has been explored analytically. The flow is partitioned into three regions: 1) a region where the hydrodynamic and thermal boundary layers are developing, 2) a region where the hydrodynamic boundary layer is developed and the thermal boundary layer is still developing, and 3) a region where both boundary layers are developed throughout the thin film. An integral analysis has been performed, where third-order velocity and temperature profiles have been assumed. A system of differential equations are solved numerically to obtain boundary layer thicknesses, local shear stress and heat flux, thin film height, and free surface temperature as functions of radial position. The solution for the no-slip scenario shows excellent agreement with previous differential analysis of the same problem. The influence of the magnitude of the slip length and temperature jump length on the thermal transport is presented for a realizable range of slip lengths and typical jet Reynolds numbers.   

Drag Reduction with Super-Hydrophobic Surfaces in Turbulent Channel Flow

Drag reduction (DR) with super-hydrophobic (SH) surfaces is investigated using DNS in turbulent channel flow with SH walls. Both channel walls were covered with longitudinal arrays of SH micro-grooves of width $g$ separated by distances of $w$. The liquid/gas interfaces on these walls were modeled as idealized, flat, shear-free boundaries. DRs of $5-83\%$ were obtained with $4 \le g^{+0} \le 128$ and $g/w=1$, 7 \& 15 at $Re_{bulk} = 3600$. By analysis of the Navier-Stokes equations, it is shown that the magnitude of DR is given by $DR = U_{slip}/U_{bulk} + O(\varepsilon)$, where $U_{slip}/U_{bulk}$ represents the contribution of surface slip to DR, and the $O(\varepsilon)$ term represents DR arising from other sources, such as modifications to turbulence dynamics. Comparison with DNS results shows surface slip to be the `dominant' mechanism of DR even in turbulent flows, and responsible for over 80\% of the DR in both the high and low DR regimes. The effect of the SH surface on the dynamics of turbulence is found to be small and confined to additional production of turbulence kinetic energy within a thin surface layer of size on the order of the width of the surface micro-grooves. Beyond this effect, the normalized dynamics of turbulence proceeds as with no-slip walls.   

Bio-inspired Gecko Micro-surface for Drag Reduction in Turbulent Flows

Direct Numerical Simulations of a turbulent channel flow with a porous wall inspired from the Gecko lizard were performed at Reynolds number of $Re_{\tau} = 450$. Two superposed fluids were considered. As initial condition, one fluid fills the microfibrillar surface, the interface with the overlying fluid being flat and corresponding to the crests plane. The code is based on a finite difference scheme with a Runge Kutta and fractional step. The porous wall is modeled with the immersed boundary method, while the dynamic of the interface between the two fluids is solved with a level set method. A parametric study has been performed varying the viscosity ratio between the two fluids. Two cases have been considered, with and without surface tension. Without surface tension the microfibrillar wall acts as a rough wall increasing the drag. However, when the surface tension is large enough to maintain the interface stable, the external fluid cannot enter into the porous wall and an effective slip is produced. When the fluid in the porous wall has a viscosity 100 times smaller than that of the overlying fluid, a drag reduction of about $60\%$ can be observed. In this case, the near wall coherent structures become significantly weaker.   

Turbulent Taylor-Couette flow over liquid infused surfaces

We experimentally study the flow of turbulent water over a textured surface that is impregnated with a second immiscible liquid. Two configurations are studied: (i) a configuration in which the impregnating fluid is contained within the texture, so that the turbulent flow sees a composite liquid/solid surface and (ii) a configuration in which the impregnating fluid overlies the texture. Experiments are performed in turbulent Taylor-Couette flow at a friction Reynolds number around 150. We characterize the impact the liquid infused surfaces have on the skin friction as well as the critical Reynolds number for transition to turbulence. Particular attention is focused on the influence of the texture geometry and length scale as well as the impregnating fluid properties.