In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

This paper presents results of an experimental investigation of a single drop impact onto a dry, partially wettable substrate and its numerical simulation. Particularly, the drop spreading diameter and the dynamic contact angle are measured at different time instants after impact. Two surfaces, wax (low wettability) and glass (high wettability), are used to study the effect of surface wettability (static contact angle) on the impact dynamics. It is shown that existing empirical models for the dynamic contact angle (e.g., Hoffman–Voinov–Tanner law) do not predict well the change of the dynamic contact angle, especially at high capillary numbers. In addition to the experimental investigations, the drop impact was studied numerically, focusing primarily on the contact angle treatment. The singularity in the neighborhood of the moving contact line is removed from the computational domain and replaced by a local force with some dependence on the instantaneous advancing/receding contact-line velocity. The predicted time dependence of the drop spreading diameter and of the dynamic contact angle agrees well with the experimental data for both the advancing and receding phases of the impact process.

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor ε_ij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part ε^h of the energy dissipation rate. The algebraic expression for the components of ε_ij was then reformulated in terms of ε^h, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of ε_ij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than ε_ij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (u_iu_i) All Overbar, using ε^h instead of ε, agree well with the direct numerical simulations.

The effects of several surface parameters on equivalent sand roughness (k_s) in fully rough regime are investigated by means of direct numerical simulation (DNS) of flow in channels with different wall geometries at $Reτ≅500$. The roughness geometry is generated by randomly distributing roughness elements of random size and prescribed shape on a flat surface. The roughness generation approach allows systematic variation of moments of surface height probability density function (PDF), size distribution of roughness peaks, and surface slope. A total number of 38 cases are solved. It is understood that a correlation based on surface height skewness and effective slope (ES) can satisfactorily predict k_s normalized with maximum peak-to-valley roughness height within a major part of the studied parameter space. Such a correlation is developed based on the present data points and a number of complementary data points from the literature. It is also shown that the peak size distribution can independently influence the skin friction; at fixed values of rms surface height, skewness, kurtosis, and ES, a surface with uniform size peaks causes higher skin friction compared to one with nonuniform peak sizes. Additionally, it is understood that a roughness generated by regular arrangement of roughness elements may lead to a significantly different skin friction compared to a random arrangement. A staggered and an aligned regular arrangement are examined in this paper and it is observed that the former produces significantly closer results to the corresponding random arrangement.