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A Nonlinear Stability Framework for Interfacial Wave Dynamics

Final Report Summary - PSE2PHASE (A nonlinear stability framework for interfacial wave dynamics)

Project description and objectives

The primary objective of this project is to develop a nonlinear stability method for simulating two-phase shear flows. The approach combines the nonlinear parabolised stability equations (PSE) with a powerful interface tracking scheme, and is validated against high-fidelity direct calculations. Using this approach, we produce an insightful and computationally efficient framework to provide better physical models of interfacial dynamics. This project will study large amplitude instability waves and the evolution of large-scale structures in two-fluid shear flows. The results and methods from these studies can be applied to a variety of industrial problems including oil/gas pipeline behaviour, wind-generated ocean waves, and liquid jet atomisation.

Project work completed

During project months 1-12, this framework for two-fluid flows has been formulated and implemented. As mentioned in the midterm report, this framework development has included two interface tracking schemes: a coordinate transform scheme, and an interface capturing scheme for complex interfacial deformation. The initial phase of the project also studied nonlinear effects and mode competition in spatially developing mixing layers.

Project months 13-24 have focused on the validation of the interface capturing PSE (IC-PSE) method, and its application to various two-fluid problems. In validating the IC-PSE method, several calculations of two-fluid mixing layers were compared against equivalent direct Navier-Stokes (N-S) simulations. The comparisons showed that the IC-PSE method was able to capture the creation of large two-fluid structures in the flow in a computationally efficient manner, but with comparable accuracy to N-S simulations.

In addition, the IC-PSE method has been applied to the study of two-fluid jets and boundary layers. Both confined and unconfined two-fluid jets have been studied, and the development of large scale structures in these flows have also been observed. This method has also been used to investigate transient spatial growth of vortical disturbances.

Major project results

Several major results have emerged during the validation and application of the IC-PSE framework. Comparisons between the IC-PSE and N-S simulations show that large-scale two-fluid structures, such as vortex rolls and ligament formation, can be accurately captured using the nonlinear stability approach. Quantitative statistics compare favourably between the two methods, even though the IC-PSE required an order of magnitude less computational cost.

Three-dimensional simulations were also computed using this approach. These simulations showed the formation of fluid ligaments, and demonstrated the ability of this approach to capture complex interfacial deformations.

Similar to the mixing layer, simulations of two-fluid jets have shown how small interfacial disturbances can develop into large, two-fluid structures. Investigations of confined and unconfined, varicose and sinuous jets show the spread of the liquid jet in response to the growth of interfacial disturbances.

Potential use and impact of results

Because the behaviour of interfacial waves is critical to many different applications, the results of this research work are likely to have a large impact on industrial technology and society at large. For instance, in the design of nuclear power plants, knowing the position of the air-liquid interface is critical to the operation of heat exchangers inside the nuclear reactor. Similarly, the creation of liquid droplets is an important design consideration for spray combustors of gas turbine engines. The broad applicability of this research work can lead to substantial benefits for a variety of European industries, including companies such as BP and BFNL. Gas turbine manufacturers such as Rolls-Royce will also benefit from more efficient simulations of liquid jets.

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