Benchmark solution for the stability of plane Couette flow with net throughflow

This paper investigates the stability of an incompressible viscous fluid flow between relatively moving horizontal parallel plates in the presence of a uniform vertical throughflow. A linear stability analysis has been performed by employing the method of normal modes and the resulting stability equation is solved numerically using the Chebyshev collocation method. Contrary to the stability of plane Couette flow (PCF) to small disturbances for all values of the Reynolds number in the absence of vertical throughflow, it is found that PCF becomes unstable owing to the change in the sign of growth rate depending on the magnitude of throughflow. The critical Reynolds number triggering the instability is computed for different values of throughflow dependent Reynolds number and it is shown that throughflow instills both stabilizing and destabilizing effect on the base flow. It is seen that the direction of throughflow has no influence on the stability of fluid flow. A comparative study between plane Poiseuille flow and PCF has also been carried out and the similarities and differences are highlighted.

Transactive Energy for Flexible Prosumers Using Algorithmic Game Theory

<div>In modern smart grids, the focus is increasingly shifted towards distributed energy resources and flexible electricity assets owned by prosumers. A system with high penetration of flexible prosumers, has a very large number of variables and constraints, while a lot of the information is local and non-observable. Decomposition methods and local problem solving is considered a promising approach for such settings, particularly when the implementation of a decomposition method features a market-based analogy, i.e. it can be implemented in a Transactive Energy fashion.</div><div>In this paper we present an auction-theoretic scheme for a setting with non-convex prosumer models and resource constraints. The scheme is evaluated on a particular case study and its scalability and efficiency properties are tested and compared to an optimal benchmark solution. A game-theoretic analysis is made with respect to how an intelligent agent, that bids on behalf of a prosumer can try to strategize within the auction, in order to make itself better-off. Our simulations show that there is an alignment of incentives, i.e., when the prosumers try to strategize, they actually improve the auction's efficiency. </div>

Transactive Energy for Flexible Prosumers Using Algorithmic Game Theory

<div>In modern smart grids, the focus is increasingly shifted towards distributed energy resources and flexible electricity assets owned by prosumers. A system with high penetration of flexible prosumers, has a very large number of variables and constraints, while a lot of the information is local and non-observable. Decomposition methods and local problem solving is considered a promising approach for such settings, particularly when the implementation of a decomposition method features a market-based analogy, i.e. it can be implemented in a Transactive Energy fashion.</div><div>In this paper we present an auction-theoretic scheme for a setting with non-convex prosumer models and resource constraints. The scheme is evaluated on a particular case study and its scalability and efficiency properties are tested and compared to an optimal benchmark solution. A game-theoretic analysis is made with respect to how an intelligent agent, that bids on behalf of a prosumer can try to strategize within the auction, in order to make itself better-off. Our simulations show that there is an alignment of incentives, i.e., when the prosumers try to strategize, they actually improve the auction's efficiency. </div>

Analytical Buckling Loads of Columns Weakened Simultaneously with Transverse Cracks and Partial Delamination

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution.