Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

In this study, the stability dependence of turbulent Prandtl number ($$Pr_t$$ P r t ) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $$Pr_t$$ P r t and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.

Designing Multi-Shape Dual-Gas Initial Conditions for the Study of Hydrodynamic Instabilities

The flow resulting from the rotation of a series of thin plates that initially separate two gases of different densities is analysed using Direct Numerical Simulations. The ninety degrees plates' rotation forms a vorticity shear layer and a density interface in between the tips of two neighbouring plates. Results of this study show that the shape of these layers strongly depends on the plate tip-based Reynolds number that can be varied thanks to a parametrisation of the plates' opening law. Different regimes are identified corresponding to single- or multi-mode initial interfaces, with or without the occurrence of starting vortices during the formation of the shear layer. The density interfaces resulting from this procedure are particularly well-suited to serve as initial conditions for the study of the Richtmyer-Meshkov instability-induced mixing. Results of this study also provide a description of vortex formation in stratified flows.

Layering, Instabilities, and Mixing in Turbulent Stratified Flows

Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars such as salt and pollutants in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. This review discusses recent research activity directed at improving community understanding, modeling, and parameterization of the subtle interplay between energy conversion pathways, instabilities, turbulence, external forcing, and irreversible mixing in density-stratified fluids. The conceptual significance of various length scales is highlighted, and in particular, the importance is stressed of overturning or scouring in the formation and maintenance of layered stratifications, i.e., robust density distributions with relatively deep and well-mixed regions separated by relatively thin interfaces of substantially enhanced density gradient.

Study on the Law of Diesel Oil Carrying Water in Lanzhou–Chengdu–Chongqing Product Oil Pipeline Based on Large Eddy Simulation

Water accumulation at the bottom of the product oil pipeline will lead to corrosion damage to the pipeline. The study on water carrying laws of refined oil could provide a reference for the safe operation of the pipeline. In this paper, the actual size of Lanzhou–Jiangyou section of Lanzhou–Chengdu–Chongqing pipeline was taken as the pipeline size. The volume of fluid (VOF) model of oil-water two-phase flow based on large eddy simulation (LES) was established. The numerical simulation of the water-carrying behavior of the product oil in the inclined pipeline was carried out. The LES-based two-phase flow model can capture the characteristics of stratified flow, wavy stratified flow, and dispersed flow under various operating conditions. The model was applied to simulate the water carrying process under various oil inlet velocities and the inclined pipe angles. The results show that as the pipeline inclined angle is 10~20° and the oil inlet velocity is 0.66 m/s, the flow patterns in the pipeline mainly include stratified flow and wavy stratified flow. As the oil inlet velocity is 0.88~1.55 m/s, the flow patterns in the pipe are mainly stratified flow, wavy stratified flow, and dispersed flow. As the inclined angle of the pipeline is 30~40°, the flow patterns in the pipeline mainly include stratified flows, wavy stratified flows, and dispersed flows. Finally, with the increase of flow time, water can be carried completely from the pipeline through the oil. With the increase of oil inlet velocity, the water carrying capacity of oil gradually increases. With the increase of pipeline inclination, the water carrying capacity of oil firstly increases and then decreases.