A numerical study is made of the development with time of the two-dimensional flow of a viscous, incompressible fluid around a circular cylinder which suddenly starts rotating about its axis with constant angular velocity and translating at right angles to this axis with constant speed. The governing partial differential equations in two space variables and time are reduced to sets of time-dependent equations in one space variable by means of Fourier analysis. By truncating the Fourier series to a finite number of terms, a finite set of differential equations is solved to give an approximation to the theoretical flow. The solutions are obtained by numerical methods. Results are given for the initial development with time of the asymmetrical wake at the rear of the cylinder at Reynolds numbers R [ges ] 200, based on the diameter of cylinder, and at small rotation rates. The detailed results show the formation of a Kármán vortex street. The time development of this separated flow is compared in detail at R = 200 with recent experimental results. The details of the formation and movement of the vortices behind the cylinder and the velocity profiles in several locations are virtually identical in the experimental and theoretical studies. The variations with time of the lift, drag and moment exerted by the fluid on the cylinder are determined both by calculations and by means of approximate analytical expressions. The agreement between these results at small times is excellent.

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

SUMMARYFossil fuels provide a significant fraction of the global energy resources, and this is likely to remain so for several decades. Carbon dioxide (CO 2 ) emissions have been correlated with climate change, and carbon capture is essential to enable the continuing use of fossil fuels while reducing the emissions of CO 2 into the atmosphere thereby mitigating global climate changes. Among the proposed methods of CO 2 capture, oxyfuel combustion technology provides a promising option, which is applicable to power generation systems. This technology is based on combustion with pure oxygen (O 2 ) instead of air, resulting in flue gas that consists mainly of CO 2 and water (H 2 O), that latter can be separated easily via condensation, while removing other contaminants leaving pure CO 2 for storage. However, fuel combustion in pure O 2 results in intolerably high combustion temperatures. In order to provide the dilution effect of the absent nitrogen (N 2 ) and to moderate the furnace/combustor temperatures, part of the flue gas is recycled back into the combustion chamber. An efficient source of O 2 is required to make oxycombustion a competitive CO 2 capture technology. Conventional O 2 production utilizing the cryogenic distillation process is energetically expensive. Ceramic membranes made from mixed ion-electronic conducting oxides have received increasing attention because of their potential to mitigate the cost of O 2 production, thus helping to promote these clean energy technologies. Some effort has also been expended in using these membranes to improve the performance of the O 2 separation processes by combining air separation and high-temperature oxidation into a single chamber. This paper provides a review of the performance of combustors utilizing oxy-fuel combustion process, materials utilized in ion-transport membranes and the integration of such reactors in power cycles. The review is focused on carbon capture potential, developments of oxyfuel applications and O 2 separation and combustion in membrane reactors. The recent developments in oxyfuel power cycles are discussed focusing on the main concepts of manipulating exergy flows within each cycle and the reported thermal efficiencies.

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