32 research outputs found
The Fanno model for turbulent compressible flow
The paper considers the derivation and properties of the Fanno model for nearly unidirectional turbulent flow of gas in a tube. The model is relevant to many industrial processes. Approximate solutions are derived and numerically validated for evolving flows of initially small amplitude, and these solutions reveal the prevalence of localized large-time behaviour, which is in contrast to inviscid acoustic theory. The properties of large-amplitude travelling waves are summarized, which are also surprising when compared to those of inviscid theory
Oxford Study Groups with Industry (1968-1988) - 6 reports
Reports for:
1) 1968-1971
2) 1974-1977
3) 1978-1980
4) 1980-1983
5) 1984-1986
6) 1987-198
Thin-layer solutions of the Helmholtz equation
This paper gives a brief overview of some configurations in which highfrequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics
Dynamic behaviour of jets and spouts in fluidized beds
The dynamics of a spouted fluidized bed are investigated. The formation of bubbles due to nipping was also studied
Mobile radio propagation prediction using ray tracing methods
The basic problem is to solve the two-dimensional scalar Helmholtz equation for a point source (the antenna) situated in the vicinity of an array of scatterers (such as the houses and any other relevant objects in 1 square km of urban environment). The wavelength is a few centimeters and the houses a few metres across, so there are three disparate length scales in the problem.
The question posed by BT concerned ray counting on the assumptions that:
(i) rays were subject to a reflection coefficient of about 0.5 when bouncing off a house wall and
(ii) that diffraction at corners reduced their energy by 90%. The quantity of particular interest was the number of rays that need to be accounted for at any particular point in order for those neglected to only contribute 10% of the field at that point; a secondary question concerned the use of rays to predict regions where the field was less than 1% of that in the region directly illuminated by the antenna.
The progress made in answering these two questions is described in the next two sections and possibly useful representations of the solution of the Helmholtz equations in terms other than rays are given in the final section
Electric arc problem
This problem was concerned with the behaviour of an electric arc as the current supplied to the arc passed through zero. We sought to establish a model that predicts the conditions under which the arc was extinguished. During the study group we attempted to show how an equation of state could be derived by proposing that the arc should be in thermal equilibrium with the surrounding gas. The behaviour of the system as the current goes to zero was examined but no firm conclusions could be draw