The depth-averaged numerical simulation of laminar thin-film flows with capillary waves

Thin-film flows encountered in engineering systems such as aero-engine bearing chambers often exhibit capillary waves and occur within a moderate to high Weber number range. Although the depth-averaged simulation of these thin-film flows is computationally efficient relative to traditional volume-of-fluid (VOF) methods, numerical challenges remain particularly for solutions involving capillary waves and in the higher Weber number, low surface tension range. A depth-averaged approximation of the Navier–Stokes equations has been used to explore the effect of surface tension, grid resolution, and inertia on thin-film rimming solution accuracy and numerical stability. In shock and pooling solutions where capillary ripples are present, solution stability, and accuracy are shown to be highly sensitive to surface tension. The common practice in analytical studies of enforcing unphysical low Weber number stability constraints is shown to stabilize the solution by artificially damping capillary oscillations. This approach, however, although providing stable solutions is shown to adversely affect solution accuracy. An alternative grid resolution-based stability criterion is demonstrated and used to obtain numerically stable shock and pooling solutions without recourse to unphysical surface tension values. This allows for the accurate simulation of thin-film flows with capillary waves within the constrained parameter space corresponding to physical material and flow properties. Results obtained using the proposed formulation and solution strategy show good agreement with available experimental data from literature for low Re coating flows and moderate to high Re falling wavy film flows

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

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 numerical simulation of plate-type windborne debris flight

Wind borne debris is one of the principal causes of building envelope failure during severe storms. It is often of interest in windstorm risk modelling to estimate the potential flight trajectories and impact energy of a piece of debris. This thesis presents research work aimed at the development and validation of a numerical model for the simulation of plate-type windborne debris. While a number of quasi-steady analytical models are available at present, these models are unable to account for the fluid-plate interaction in highly unstable flows. The analytical models are also limited to simple launch flow conditions and require extensive a-priori knowledge of the debris aerodynamic characteristics. In addition, the use of Euler angle parametrisations of orientation in the analytical models results in mathematical singularities when considering 3D six degree-of-freedom motion. To address these limitations, a 3D Computational Fluid Dynamics (CFD) model is sequentially coupled with a quaternion based singularity-free six degree of freedom Rigid Body Dynamics (RBD) model in order to successfully simulate the flight of plate-type windborne debris. The CFD-RBD model is applied to the numerical investigation of the flow around static, forced rotating, autorotating and free-flying plates as well as the treatment of complex launch conditions. Key insights into the phenomena of plate autorotation are highlighted including the genesis of the aerodynamic damping and acceleration torques that make autorotation possible. The CFD-RBD model is then validated against measurements of rotational speed and surface pressure obtained from recent autorotation experiments. Subsequently a general 3D spinning mode of autorotation is demonstrated and the CFD-RBD model is extended to include plate translation in order to simulate windborne debris flight. Using the CFD-RBD flight model, a parametric study of windborne debris flight is carried out and four distinct flight modes have been identified and are discussed. The flight results are contrasted against available free-flight experiments as well as predictions from existing quasi-steady analytical models and an improved quasi-steady force model based on forced rotation results is proposed. The resulting CFD-RBD model presents the most complete numerical approach to the simulation of plate-type windborne debris, directly simulating debris aerodynamics, and incorporates complex launch flow fields in the initial conditions

The numerical simulation of plate-type windborne debris flight

Wind borne debris is one of the principal causes of building envelope failure during severe storms. It is often of interest in windstorm risk modelling to estimate the potential flight trajectories and impact energy of a piece of debris. This thesis presents research work aimed at the development and validation of a numerical model for the simulation of plate-type windborne debris. While a number of quasi-steady analytical models are available at present, these models are unable to account for the fluid-plate interaction in highly unstable flows. The analytical models are also limited to simple launch flow conditions and require extensive a-priori knowledge of the debris aerodynamic characteristics. In addition, the use of Euler angle parametrisations of orientation in the analytical models results in mathematical singularities when considering 3D six degree-of-freedom motion. To address these limitations, a 3D Computational Fluid Dynamics (CFD) model is sequentially coupled with a quaternion based singularity-free six degree of freedom Rigid Body Dynamics (RBD) model in order to successfully simulate the flight of plate-type windborne debris. The CFD-RBD model is applied to the numerical investigation of the flow around static, forced rotating, autorotating and free-flying plates as well as the treatment of complex launch conditions. Key insights into the phenomena of plate autorotation are highlighted including the genesis of the aerodynamic damping and acceleration torques that make autorotation possible. The CFD-RBD model is then validated against measurements of rotational speed and surface pressure obtained from recent autorotation experiments. Subsequently a general 3D spinning mode of autorotation is demonstrated and the CFD-RBD model is extended to include plate translation in order to simulate windborne debris flight. Using the CFD-RBD flight model, a parametric study of windborne debris flight is carried out and four distinct flight modes have been identified and are discussed. The flight results are contrasted against available free-flight experiments as well as predictions from existing quasi-steady analytical models and an improved quasi-steady force model based on forced rotation results is proposed. The resulting CFD-RBD model presents the most complete numerical approach to the simulation of plate-type windborne debris, directly simulating debris aerodynamics, and incorporates complex launch flow fields in the initial conditions

Continuous photo-oxidation in a vortex reactor: efficient operations using air drawn from the laboratory

We report the construction and use of a vortex reactor which uses a rapidly rotating cylinder to generate Taylor vortices for continuous flow thermal and photochemical reactions. The reactor is designed to operate under conditions required for vortex generation. The flow pattern of the vortices has been represented using computational fluid dynamics, and the presence of the vortices can be easily visualized by observing streams of bubbles within the reactor. This approach presents certain advantages for reactions with added gases. For reactions with oxygen, the reactor offers an alternative to traditional setups as it efficiently draws in air from the lab without the need specifically to pressurize with oxygen. The rapid mixing generated by the vortices enables rapid mass transfer between the gas and the liquid phases allowing for a high efficiency dissolution of gases. The reactor has been applied to several photochemical reactions involving singlet oxygen (1O2) including the photo-oxidations of α-terpinene and furfuryl alcohol and the photodeborylation of phenyl boronic acid. The rotation speed of the cylinder proved to be key for reaction efficiency, and in the operation we found that the uptake of air was highest at 4000 rpm. The reactor has also been successfully applied to the synthesis of artemisinin, a potent antimalarial compound; and this three-step synthesis involving a Schenk-ene reaction with 1O2, Hock cleavage with H+, and an oxidative cyclization cascade with triplet oxygen (3O2), from dihydroartemisinic acid was carried out as a single process in the vortex reactor

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

The numerical simulation of plate-type windborne debris flight

Wind borne debris is one of the principal causes of building envelope failure during severe storms. It is often of interest in windstorm risk modelling to estimate the potential flight trajectories and impact energy of a piece of debris. This thesis presents research work aimed at the development and validation of a numerical model for the simulation of plate-type windborne debris. While a number of quasi-steady analytical models are available at present, these models are unable to account for the fluid-plate interaction in highly unstable flows. The analytical models are also limited to simple launch flow conditions and require extensive a-priori knowledge of the debris aerodynamic characteristics. In addition, the use of Euler angle parametrisations of orientation in the analytical models results in mathematical singularities when considering 3D six degree-of-freedom motion. To address these limitations, a 3D Computational Fluid Dynamics (CFD) model is sequentially coupled with a quaternion based singularity-free six degree of freedom Rigid Body Dynamics (RBD) model in order to successfully simulate the flight of plate-type windborne debris. The CFD-RBD model is applied to the numerical investigation of the flow around static, forced rotating, autorotating and free-flying plates as well as the treatment of complex launch conditions. Key insights into the phenomena of plate autorotation are highlighted including the genesis of the aerodynamic damping and acceleration torques that make autorotation possible. The CFD-RBD model is then validated against measurements of rotational speed and surface pressure obtained from recent autorotation experiments. Subsequently a general 3D spinning mode of autorotation is demonstrated and the CFD-RBD model is extended to include plate translation in order to simulate windborne debris flight. Using the CFD-RBD flight model, a parametric study of windborne debris flight is carried out and four distinct flight modes have been identified and are discussed. The flight results are contrasted against available free-flight experiments as well as predictions from existing quasi-steady analytical models and an improved quasi-steady force model based on forced rotation results is proposed. The resulting CFD-RBD model presents the most complete numerical approach to the simulation of plate-type windborne debris, directly simulating debris aerodynamics, and incorporates complex launch flow fields in the initial conditions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Analysis of a Nonlinear Hyperbolic Equation by Energy Method (Discretization Methods and Numerical Algorithms for Differential Equations)

A robust 1D film hydrodynamic model has been sequentially coupled with a 1D core gas model and used to predict the instantaneous mean core gas speed, film interface shear stress and liquid film distribution within an idealised bearing chamber. This novel approach to aero-engine bearing chamber simulation provides a predictive tool that can be used for the fast and reliable exploration of a set of bearing chamber design and operating conditions characterised by the: chamber dimensions, air/oil fluid properties, shaft speed, sealing air flows, oil feed rates and sump scavenge ratios. A preliminary validation of the model against available bearing chamber flow measurements from literature shows good agreement. The model represents a significant step change in predictive capabilities for aero-engine oil system flows compared to previous semi-empirical models. The bearing chamber is idealised as a one-dimensional (2D) domain with a predominantly azimuthal flow in both the rotational oil film and core gas such that axial components may be ignored. A 1D system of depth-averaged film hydrodynamics equations is used to predict oil film thickness and mean speed distributions in the azimuthal direction under the influence of interface shear, gravity, pressure gradient and surface tension forces. The driving shear stress in the film model is obtained from the 1D core-gas model based on an azimuthal gas momentum conservation equation which is coupled to the film model through the interface shear stress and film interface velocity

A coupled 1D film hydrodynamics and core gas flow model for air-oil flows in aero-engine bearing chambers

A robust 1D film hydrodynamic model has been sequentially coupled with a 1D core gas model and used to predict the instantaneous mean core gas speed, film interface shear stress and liquid film distribution within an idealised bearing chamber. This novel approach to aero-engine bearing chamber simulation provides a predictive tool that can be used for the fast and reliable exploration of a set of bearing chamber design and operating conditions characterised by the: chamber dimensions, air/oil fluid properties, shaft speed, sealing air flows, oil feed rates and sump scavenge ratios. A preliminary validation of the model against available bearing chamber flow measurements from literature shows good agreement. The model represents a significant step change in predictive capabilities for aero-engine oil system flows compared to previous semi-empirical models. The bearing chamber is idealised as a one-dimensional (2D) domain with a predominantly azimuthal flow in both the rotational oil film and core gas such that axial components may be ignored. A 1D system of depth-averaged film hydrodynamics equations is used to predict oil film thickness and mean speed distributions in the azimuthal direction under the influence of interface shear, gravity, pressure gradient and surface tension forces. The driving shear stress in the film model is obtained from the 1D core-gas model based on an azimuthal gas momentum conservation equation which is coupled to the film model through the interface shear stress and film interface velocity