Developing new components for variable flow distribution system modelling in TRNSYS

This study attempts to fill the existing gap in the simulation of variable flow distribution systems through developing new pressure governing components. These components are able to capture the actual ever-changing system performance curve in variable flow distribution systems together with the prediction of controversial issues such as starving, over-flow and the lack of controllability on the flow rate of different branches in a hydronic system. The performance of the proposed components is verified using a case study under design and off-design circumstances. Full integration of the new components within the TRNSYS simulation package is another advantage of this study, which makes it more applicable for designers in both the design and commissioning of hydronic systems.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.