An investigation of plate-type windborne debris flight using coupled CFD–RBD models. Part I: Model development and validation

AbstractThe development of a coupled computational fluid-dynamics rigid body (CFD–RBD) model is presented. The RBD model deploys rotational quaternions, which are free from the gimbal lock that is associated with Euler rotational matrix. The quaternion model means that the complex 3D spinning flight modes associated with the flight of plate-type windborne debris can be modelled robustly. This paper attempts to determine the accuracy of the CFD–RBD model by comparing the predicted trajectories from a large number of debris simulations with experimentally derived equations of best fit. Agreement is found to be good and, based on the findings, an alternative form for the dimensionless flight distance is presented, which extends the range of the experimental study to longer flight times.The predictions from the CFD–RBD model are then compared against two quasi-steady analytical debris flight models. The second model is based on modified force and moment coefficients, which are informed by the findings from the CFD–RBD model. For plates that have attained a stable, autorotational flight mode, the CFD–RBD and analytical models are in good agreement. Their predictions differ during the initial stages of flight, where the complex non-linear interactions between the plate and its wake are not captured by the analytical models

The computational fluid dynamics modelling of the autorotation of square, flat plates

This paper examines the use of a coupled Computational Fluid Dynamics (CFD) – Rigid Body Dynamics (RBD) model to study the fixed-axis autorotation of a square flat plate. The calibration of the model against existing wind tunnel data is described. During the calibration, the CFD models were able to identify complex period autoration rates, which were attributable to a mass eccentricity in the experimental plate. The predicted flow fields around the autorotating plates are found to be consistent with existing observations. In addition, the pressure coefficients from the wind tunnel and computational work were found to be in good agreement. By comparing these pressure distributions and the vortex shedding patterns at various stages through an autorotation cycle, it was possible to gain important insights into the flow structures that evolve around the plate. The CFD model is also compared against existing correlation functions that relate the mean tip speed ratio of the plate to the aspect ratio, thickness ratio and mass moment of inertia of the plate. Agreement is found to be good for aspect ratios of 1, but poor away from this value. However, other aspects of the numerical modelling are consistent with the correlations

Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects

Motivated by evaluating coating oil films within bearing chambers in an aero-engine application, an analysis is presented for the fluid dynamics relevant in their dual capacity as both coolant and lubricant in highly sheared flows that may approach microscale thickness. An extended model is developed for isothermal rimming flow driven by substantial surface shear within a stationary cylinder. In particular, a partial slip condition replaces the no-slip condition at the wall whilst retaining inertial effects relevant to an intrinsic high speed operation. A depth-averaged formulation is presented that includes appropriate inertial effects at leading-order within a thin film approximation that encompass a more general model of assessing the impact of surface slip. Non-dimensional mass and momentum equations are integrated across the film depth yielding a one dimensional problem with the a priori assumption of local velocity profiles. The film flow solutions for rimming flow with wall slip are modelled to a higher order than classical lubrication theory. We investigate the impact of wall slip on the transition from pooling to uniform films. Numerical solutions of film profiles are provided for progressively increased Reynolds number, within a moderate inertia regime, offering evaluation into the effect of film slippage on the dynamics of rimming flow. We find that slip allows non-unique solution regions and existence of multiple possible steady state solutions evaluated in transforming from smooth to pooling film solutions. Additionally, boundary slip is shown to enhance the development of recirculation regions within the film which are detrimental to bearing chamber flows