Joan Herrero

Influence of the geometry on the structure of the flow between a pair of corotating disks

Constant-property laminar flow in the space between two coaxial disks corotating in a fixed cylindrical enclosure is investigated numerically over the Reynolds number range 0⩽Re⩽82 380 for interdisk spacing to disk radius aspect ratios in the range 0.05⩽S⩽0.20. Most of the 3D calculations correspond to regions in the (Re, S) map slightly above the 2D–3D transition, where the 2D (axisymmetric) steady flow can bifurcate into two different families of unsteady 3D flow; (a) at sufficiently large values of S or Re, into a flow that is asymmetric with respect to the interdisk midplane; (b) at intermediate values of S and Re, into a flow that displays shift-and-reflect symmetry with respect to the interdisk midplane. Qualitative and quantitative comparisons with previous experimental and numerical results are established. The structure of the 3D flow is analyzed as well as the jumps in wave frequency when it experiences a change in its circumferential wave length. It is shown that each family of 3D flows is char...

Stability analysis of the flow in a cubical cavity heated from below

A numerical study of bifurcations and stability of the steady convective flow of air in a cubical enclosure heated from below was carried out using a Galerkin spectral method. The set of basis functions was chosen so that all boundary conditions and the continuity equation were implicitly satisfied. A parameter continuation method was applied to determine the steady solutions and bifurcations of the nonlinear governing equations as a function of Rayleigh number (Ra) for values of Ra up to 1.5×105. The eigenvalue problem associated with the stability analysis of the steady solutions along the different branches of solutions was solved using the Arnoldi method. The convergence of the method was consistent with the number of modes used and the results were also verified by a numerical solution of the unsteady equations of motion using a finite-difference solver. Present results show that different stable convective flow patterns can coexist for different ranges of the Rayleigh number.

Natural convection from narrow horizontal plates at moderate Rayleigh numbers

Abstract The present work deals with the natural convection flow and heat transfer from a horizontal plate cooled from above. Experiments are carried out for rectangular plates having aspect ratios between φ=0.036 and 0.43 and Rayleigh numbers in the range 290⩽Raw⩽3.3×105. These values of Raw and φ have been selected below those commonly considered in previous research in view of a future application to the design of printed circuit boards. The plates are made of two different metals, copper and steel. The choice of a metal is relevant to the present problem because the plates are heated by means of an electric current. Important variations of the surface temperature are observed along the transverse direction for the steel plates. The surface of the copper plates is almost isothermal because of the high thermal conductivity of the metal. Calculations for a semi-infinite plate are carried out to predict the transverse profiles of the surface temperature and heat flux and to visualize the structure of the flow. Three-dimensional calculations are also used at a qualitative level to observe the changes in the flow structure due to the finite length of the plate. Present results are compared with both previous experimental work and analyses that are based on boundary layer theory. It is shown that analyses for an infinite boundary layer are not completely applicable to the present problem because of its different physics. The most relevant feature of the natural convection flow, which is not predicted by boundary layer analyses, is a thermal plume rising near the center of the plate. Present heat transfer results differ from previous experimental work because of the lower Rayleigh numbers and aspect ratios investigated here. The Nusselt number is found to depend on Rawn, with the exponent n=0.17 being lower than most of the values reported in the literature. This comparatively low value is related to the transverse conduction of heat through the air, which becomes increasingly significant as Raw approaches zero. It is shown that such a low-Raw effect can be accounted for in a physically consistent manner by adding a constant term to the heat transfer correlation. On the other hand, it is found that the Nusselt number does not significantly depend on the aspect ratio in the range of φ investigated contrary to what has been previously reported for wider plates.

A near wall k-ε formulation for high Prandtl number heat transfer

Abstract An improved form of the so-called ‘near-wall’ k—e turbulence model is proposed. The damping functions accounting for viscous effects at low Reynolds numbers are modified to yield a turbulent viscosity that properly predicts heat transfer rates over a wide range of Prandtl numbers, using a constant turbulent Prandtl number Prt = 0.9. These modifications aimed at improving the prediction of wall fluxes, also yield a better description of mean velocity and temperature profiles as well as of mean turbulent properties.

Bifurcation analysis of steady Rayleigh-Bénard convection in a cubical cavity with conducting sidewalls

Natural convection in a cubical cavity heated from below with perfectly conducting sidewalls is investigated numerically. A parameter continuation procedure based on a Galerkin spectral method was applied to obtain the bifurcation diagrams for steady flow solutions over the region of Rayleigh numbers Ra ≥ 1.5 x 10 5 at Prandtl numbers pr =0.71 and 130. In both cases, the bifurcation diagrams were more complex than those previously reported for adiabatic sidewalls. Four and nine different convective solutions (without taking into account the solutions obtained by symmetry) that were stable over certain ranges of Ra were respectively identified at Pr=0.71 and 130. The dependence of the bifurcation diagrams and of the topology of the flow patterns on the Prandtl number were also stronger in the case of conducting sidewalls. Most of the flow patterns investigated evolved to double toroid-like topologies with increasing Rayleigh number. This is especially noticeable at Pr = 130, where all flow patterns adopted double-toroid shapes that were superimposed on the characteristic flow patterns observed at values of Ra slightly above the respective bifurcation points where they originated. At sufficiently high Ra the double-toroid pattern configuration prevailed. This phenomenon, which has not been previously observed in the case of adiabatic lateral walls, is related to the thermal activity of the sidewalls, which locally extract/supply relatively large amounts of heat from/to the fluid. These predictions are consistent with experimental flow transitions and topologies reported in the literature. In addition, a complete bifurcation study in the two-dimensional (Ra, Pr)-plane was carried out for the flow pattern with an initial configuration of four connected half-rolls which was stable at both Pr = 0.71 and 130. Since the surface of Nu over the (Ra, Pr)-plane presented several folds and cusps, different regions were identified as a function of the number of particular realizations of this flow pattern, varying between zero and five. Three different regions of stability were identified for this particular flow pattern in the (Ra, Pr)-plane within the range of parameters investigated, i.e. Ra≤1.5 x 10 5 and 0.71≤Pr≤ 130.

Effect of Radial Clearance on the Flow Between Corotating Disks in Fixed Cylindrical Enclosures

Numerical results are obtained for the isothermal laminar flow of air between a pair of disks attached to and rotating with a hub in a fixed cylindrical enclosure. The presence of radial clearances or gaps between the rims of the disks and the curved enclosure wall, and the finite thickness of the disks, are considered in the calculations. The gaps allow time- and circumferentially-dependent axially-directed air flow exchanges between the contiguous inter-disk spaces. As a consequence, axisymmetric calculations of the flow, whether using boundary conditions in the gaps or extended to include the entire flow domain, fail to faithfully reproduce the experimentally measured radial variations of the mean and rms circumferential velocity components in the inter-disk space. Likewise, three-dimensional calculations using the symmetry-plane boundary condition in the gaps also fail to reproduce these variations. In contrast, computationally intensive three-dimensional calculations of the entire flow domain, including the gaps, yield results in very good agreement with the measured mean and rms velocities

Non-isothermal laminar flow and heat transfer between disks corotating in a fixed enclosure

Abstract This is a numerical investigation of the coupled laminar flow and heat transfer in the space between a pair of disks attached to a hub rotating about a vertical axis in a fixed cylindrical enclosure. A temperature variation is imposed in the fluid by setting the disks at different uniform temperatures, the temperature of the bottom disk being higher than that of the top disk. The Boussinesq approximation is used to characterize buoyancy forces in the momentum conservation equations. The different types of interdisk flow that arise as a function of angular velocity are described. At low Reynolds numbers the flow is primarily driven by gravity-induced buoyancy. As the Reynolds number increases, free convection yields to centrifugally-induced buoyancy. At sufficiently high Reynolds numbers, convection patterns induced by the strong shear at the enclosure wall dominate the interdisk flow and heat transfer but centrifugal buoyancy continues to influence the 3-D flow structure with respect to the isothermal case. One of the effects of buoyancy is the appearance of a new transition in the bifurcation diagram previously investigated by the authors for the isothermal flow case. Here, centrifugal buoyancy favors the generation of a 3-D flow which features a strong breaking of its symmetry properties with respect to the interdisk midplane, as in the isothermal case. Heat transfer rates are calculated for a range of Reynolds numbers and interdisk spacings. Special attention is paid to the high Reynolds number forced convection regime which is of practical interest. It is shown that the scales derived from heat and mass transfer analyses of the freely rotating disk apply to the present problem. In many of the present cases, 2-D (axisymmetric) and 3-D calculations yield very similar values for the overall heat transfer rates. This is especially the case for those flows with a wavy 3-D structure, meaning flows which, on average, are symmetrical with respect to the interdisk midplane. However, examples are also provided where the flow is strongly 3-D, requiring computationally intensive calculations to obtain accurate predictions of the corresponding heat transfer rates.

Linear stability analysis and numerical calculations of the lid-driven flow in a toroidally shaped cavity

The lid-driven incompressible flow in a toroidally shaped cavity of square cross-section (d×d) and radius of curvature rc is studied. For discrete values of the curvature ratio (δ=d/rc), the Reynolds number at which the flow becomes three-dimensional (Rec) is determined by means of linear stability analysis. Present results show that both Rec and the wavelength of the critical mode (λc) depend strongly on curvature. For small curvatures (δ=0.125) steady modes of short wavelength (λc≈0.4) render the flow three-dimensional. For δ=0.25 the dominant modes are unsteady and of longer wavelength (λc≈0.8). For larger curvatures (δ⩾0.5), the first active modes are stationary and of even longer wavelength (λc>2.0). Numerical solutions of the Navier–Stokes equations for slightly to moderately supercritical conditions show a good agreement with the structure of the critical mode predicted by linear analyses. The flow is unstable for all curvatures studied due to instability of centrifugal type. The slightly supercrit...

Development of coaching competencies in students through a project-based cooperative learning approach

First-year chemical engineering students carry out a horizontally integrated design project working in teams. The teams are each led by two fourth-year students, one taking on the role of team leader and the other of knowledge manager so that the project is also vertically integrated. Team leaders facilitate project and team management while knowledge managers facilitate the learning process of first-year students in such a way that both are essentially coaches. Fourth-year students experience alternatively both roles during the two semesters (15 weeks) of the academic year. These new roles require a new set of technical and social skills: Team management, facilitative leadership, and project management skills, which are formally introduced in the fourth-year Project Management course and put into practice in the Project Management in Practice course. The real challenge of the whole approach is ensuring that fourth-year students resist the temptation of reproducing the supervisory role of professors in the classical classroom environment, despite the pressure of achieving project objectives, the inexperience of first-year students who are not used to this approach, and the cultural inertia of the professors involved.

Shear-Driven Flow in a Toroid of Square Cross Section

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature R c reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length