ALBERT

Description: Local wall shear rates in steady flow in the entry region of a curved tube have been measured by the electrochemical limiting current method. A semi-circular rigid tube of circular cross-section with radius ratio 1/7 has been employed for a range of Dean number between 139 and 2868. The circumferential and axial distributions of the wall shear rates have been measured at 20° circumferential increments at five different sections of the entry region. The experimental wall shear distributions show a valley in the circumferential wall shear profile and a region of non-monotonic variation of the average wall shear rates with downstream distance, both of which are prominent features of the entry flow in a curved tube. The existence of the valley suggests a vortex structure with several pairs of vortices in a developing curved tube flow in contrast with one pair in a fully developed flow. The circumferential distribution of wall shear also suggest that a potential vortex flow is formed in the upstream core. The wall shear is lowest at the innermost part of the bend and reaches a maximum in the mid-circumference region. The wall shear is significantly enhanced by secondary flows, as much as eight times greater in the curved tube entry flow than in fully developed Poiseuille flow in the range of Dean number between 139 and 2868. The cross-over in shear maximum from the inner part of the bend to the outer part occurs at about 1·9 cross-section radii from the inlet and seems to decrease with Dean number. © 1979, Cambridge University Press

Description: Natural convection produced by a non-uniform internal heat source is studied numerically. Our investigation is limited to a two-dimensional enclosure with an aspect ratio equal to two. The energy source is Joule dissipation produced by an electric potential applied through two electrodes corresponding to a fraction of the vertical walls. The system of conservative equations of mass, momentum, energy and electric potential is solved assuming the Boussinesq approximation with a discontinuous Galerkin finite element method integrated over time. Three parameters are involved in the problem: the Rayleigh number Ra, the Prandtl number Pr and the electrode length Le normalized by the enclosure height. The numerical method has been validated in a case where electrodes have the same length as the vertical walls, leading to a uniform source term. The threshold of convection is established above a critical Rayleigh number, Racr = 1702. Due to asymmetric boundary conditions on thermal field, the onset of convection is characterized by a transcritical bifurcation. Reduction of the size of the electrodes (from bottom up) leads to disappearance of the convection threshold. As soon as the electrode length is smaller than the cavity height, convection occurs even for small Rayleigh numbers below the critical value determined previously. At moderate Rayleigh number, the flow structure is mainly composed of a left clockwise rotation cell and a right anticlockwise rotation cell symmetrically spreading around the vertical middle axis of the enclosure. Numerical simulations have been performed for a specific Le = 2/3 with Ra ϵ [1; 105] and Pr ϵ [1; 103]. Four kinds of flow solutions are established, characterized by a two-cell symmetric steady-state structure with down-flow in the middle of the cavity for the first one. A first instability occurs for which a critical Rayleigh number depends strongly on the Prandtl number when Pr 〈 3. The flow structure becomes asymmetric with only one steady-state cell. A second instability occurs above a second critical Rayleigh number that is quasiconstant when Pr 〉10. The flow above the second critical Rayleigh number becomes periodic in time, showing that the onset of unsteadiness is similar to the Hopf bifurcation. When Pr 〈3, a fourth steady-state solution is established when the Rayleigh number is larger than the second critical value, characterized by a steady-state structure with up-flow in the middle of the cavity. © 2018 Cambridge University Press.

Description: In this paper we formulate answers to three important questions related to Givetian carbonate records and their use for reconstructing million-year-scale past palaeoenvironmental changes. First, we provide detailed illustrations of the fascinating diversity that shaped a significant shallow reefal platform during early to late Givetian time in the Rhenohercynian Ocean; secondly we improve the sedimentological model of the extensive Givetian carbonate platform in the Dinant Basin; and thirdly we evaluate the application of magnetic susceptibility as a tool for long-term trend correlations and palaeoenvironmental reconstructions. These goals are reached by making a sedimentological, geophysical and geochemical study of the La Thure section. Through the early–late Givetian interval we discerned 18 microfacies ranging from a homoclinal ramp to a discontinuously rimmed shelf and then a drowning shelf. The comparison of these sedimentological results with those published for the south of the Dinant Syncline allowed us to provide an up to date model of the vertical and lateral environmental development of one of the largest Givetian carbonate platforms in Europe. This comparison also increased the knowledge on the distribution of facies belts in the Dinant Basin and allowed us to highlight the Taghanic Event. Palaeoredox proxies reveal a substantial change in the oxygenation level, from oxygen-depleted to more oxic conditions, between middle and late Givetian time. We demonstrated the relationship between variation in magnetic susceptibility values and proxies for siliciclastic input (such as Si, Al). The La Thure section is considered a key section for the understanding of internal shelf settings bordering Laurussia's southeastern margin.