Radial Aspect Ratio Research Articles

Validation of 1D model for methane/air/Pt combustion in stagnation flow

A 2D model is built on the package of FLUENT to study the effects of radial aspect ratio (R/W), length-to-width ratio (L/W), strain rate (S R), and buoyancy (Ri=Gr/Re 2) on the validation of the simplified 1D model. In the present 2D model, the methane/air homogeneous reaction mechanism of Peters and the methane/air/platinum heterogeneous reaction mechanism of Deutschmann are applied. By comparison between the 1D and 2D numerical results, it is found that the validation of 1D model is highly related with the catalytic stagnation reactor configuration. For length-to-width ratio L/W = 1 configuration, 1D laminar model is applicable when the radial aspect ratio R/W > 0.4. For R/W = 0.6, the reactor exhibited 1D characteristics when L/W < 1. Compared with the temperature and species profiles, the velocity distribution along the axis is more sensitive to the change of radial aspect ratio and length-to-width ratio. With increasing of the strain rate, the flame front goes closer to the catalytic wall surface and the difference between the 1D and 2D results decreases. For a valid 1D simulation, it is recommended that the strain rate should be greater than 20 s-1. The effects of natural convection can be neglected when Ri < 5.

Three-dimensional natural convection in spherical annuli

Natural convective fluid motions in the gap between two concentric non-rotating spheres are numerically studied. The case of homogeneously heated inner sphere and cooled outer sphere is considered for the radial aspect ratio π = 0.714 and Prandtl number Pr = 0.7. The natural convection problem is characterized by the Rayleigh number associated with the heat transfer within the fluid. For small values of the Rayleigh number an axisymmetric single vortex of crescent shape is formed as the basic flow. By increasing the Rayleigh number, flow patterns with banana-type cells, oriented in north-south direction and aligned in the azimuthal direction, are formed. Various characteristics of these flows as well as their transient evolution are investigated.

Pattern formation in binary mixture convection in cylindrical three-dimensional cells

We present numerical results of pattern selection near the onset of convection for a water-ethanol mixture in a cylindrical container heated from below. Parameter values and boundary conditions relevant to experiments are used. The separation ratio of the mixture we consider is S = −0.09 and the radial aspect ratio of the cell is Γ = 11. The onset of convection occurs via a subcritical Hopf bifurcation. Slightly above the onset, in the linear regime, a m = 1 azimuthal mode consisting of radially travelling waves grows in amplitude. As convection evolves, the pattern focuses into one or several diameters of the cell. We do not observe a direct transition to a stable nonlinear state. Instead, collapses in the convection amplitude followed by subsequent growths take place. This behaviour resembles some experimental observations. The numerical results are obtained with an efficient time-evolution spectral code that solves the full convection equations in cylindrical coordinates.

High heat flux removal using water subcooled flow boiling in a single-side heated circular channel

High heat flux removal from plasma-facing components and electronic heat sinks involves conjugate heat transfer analysis of the applicable substrate and flowing fluid. For the present case of subcooled flow boiling inside a single-side heated circular channel, the dimensional results show the significant radial, circumferential and axial variations in all thermal quantities for the present radial aspect ratio ( R o=outside radius to inside radius) of 3.0. A unified, dimensionless representation of the two-dimensional inside wall heat flux, and the dimensional inside wall heat flux ( q i( φ, z)) and temperature ( T i( φ, z)) data was found and used to collapse the data for all circumferential locations. Finally, 2-D boiling curves are presented and are among the first full set of 2-D boiling data presented for a single-side heated circular configuration.

Axisymmetric numerical simulations of turbulent flow in rotor stator enclosures

We present axisymmetric numerical simulations of transitional and chaotic flow regimes in rotor–stator cavities of radial aspect ratio approximately 8. These simulations are carried out using a second order time and space accurate algorithm which integrates the axisymmetric unsteady Navier–Stokes equations in stream function-azimuthal vorticity-azimuthal velocity form. Detailed flow analysis has been carried out for selected values of the rotational Reynolds number ( Re θ ) up to 10 6. At the largest value considered, computations have been performed using 4096 mesh points in the radial direction, which has required using a multi-domain decomposition algorithm implemented on a parallel machine. The limitations and consequences of the axisymmetry assumption are first discussed and checked against available experimental results. The evolutions of the instantaneous flow structure and of its first and second order statistic moments as the Reynolds number increases are discussed. It is shown that the dynamics of the flow mainly consists of travelling waves propagating in the stator and rotor boundary layers and of inertial waves in the core region, and that for moderate Reynolds numbers ( Re θ ≃3×10 5), the rotor boundary layer is almost completely steady while large amplitude fluctuations are found in the stator boundary layer. The evolution of second order moments confirms the fundamentally asymmetrical role of the boundary layers along the rotor and along the stator. A turbulent kinetic energy budget is shown which exhibits some specific features attributed to the rotation effects and to a lesser extent to the axisymmetry assumption.

Numerical investigation of the first bifurcation for the flow in a rotor–stator cavity of radial aspect ratio 10

The nature of transition to unsteadiness of rotor–stator disk flows of large radial aspect ratio is investigated by means of several numerical tools which consist in computing the base flow even when unstable, performing linearized or non-linear time integrations starting from initial conditions of different amplitudes and computing the spectrum of the Jacobian using the ARPACK library. From these numerical experiments we conclude that, in a cavity of radial aspect ratio 10, the transition to unsteadiness occurs through a subcritical Hopf bifurcation. In addition these calculations show the existence of a large amplitude chaotic branch for values of the Reynolds number far below the linear stability threshold, and onto which the solutions are attracted for large subcritical values due to the strong non-normality of the Jacobian of the evolution operator.

Different convection dynamics in mixtures with the same separation ratio.

We report on convection near threshold in circular samples of radial aspect ratio {Gamma}=11.5 using ethanol-water mixtures with two concentrations {ital x}, but with the same separation ratio {Psi}{approx_equal}{minus}0.08. For {ital x}=0.250, convection begins with transients that lead to a time-independent cell-filling state, typically in a day. For {ital x}=0.011, there is a range of temperature differences where repeated transients and aperiodically fluctuating localized regions of disordered convection persist for many days. In rare cases these lead to an apparently stable {open_quote}{open_quote}wall{close_quote}{close_quote} state of traveling waves surrounding pure conduction. {copyright} {ital 1996 The American Physical Society.}

Transient localized states in 2D binary liquid convection.

We report an experimental study of the onset of convection in ethanol/water mixtures confined in a circular cell of radial aspect ratio of 11.6. The initial bifurcation was to radial traveling waves; however, the linear state typically gave way to a nonlinear one in which convection alternately focused along one cell diameter and then another roughly perpendicular to the first. After a number of cycles, this state frequently contracted radially to a localized pulse of traveling-wave convection very similar to those observed in 1D geometries. The pulses we observed either decayed back to pure conduction or grew to fill or nearly fill the cell.