Improved descriptions of turbulent flow
Most fluid flow, including that of both liquids and gases, is turbulent. It continuously undergoes changes in speed and direction rather than moving in smooth paths or layers as in laminar flow. Despite its universality and relevance to numerous fields, complete and accurate description of the evolution from laminar to turbulent flow (hierarchical bifurcations) remains one of the main open topics in science today. EU-funded scientists working on the project T2T-VDG (Transition to turbulence in ventilated double glazing) developed novel numerical techniques to identify with high accuracy the transitions to turbulence. Conventional methods have relied on statistical approaches (Navier-Stokes equations) involving time-averaged properties of fluid flow. Recently, a method based on non-linear differential equations delivered coherent solutions that are universally applicable. The sequence-of-bifurcations, or deterministic approach, requires no a priori assumptions or empirical knowledge (i.e. it is based on first principles). Scientists combined this approach with stability analysis based on essentially conducting dynamic balances via traditional Navier-Stokes equations on moving frames of fluid flow. The subsequent stability analysis is unique to the T2T-VDG computational software. By unifying a variety of mathematical methods, the novel methods capture the transition to turbulence of shear flow and facilitate definition of state-of-the-art control of such transitions. The basis of the sequence-of-bifurcations approach is an analysis of transition to turbulence following hierarchical bifurcations. It determines bifurcations through their symmetry-breaking properties, with the first bifurcation occurring due to instability of the homogeneous primary state. Within the scope of the project, researchers applied the methods to identification of possible bifurcation points for tertiary flow and the stability of that tertiary flow in order to identify quaternary and higher bifurcation points. The toolbox employs alternate simplified numerical methods for higher order bifurcations to save computational time without compromising accuracy. Overall, the research team created a software tool for identifying the bifurcation tree of transition from laminar to turbulent flow associated with complex geometries. The universally applicable solution will be invaluable to European industry and to scientific development worldwide.
Keywords
Turbulent flow, computational toolbox, laminar flow, bifurcations, turbulence, double glazing
