No abstract

Tilting pad bearings (TPB) are commonly used in high-speed and high-power turbomachines, due to its contributions in avoiding rotor instabilities. Studies related to the estimation of dynamic coefficients have been carried out considering a uniform value of the geometric parameters (clearance, pre-load) for all bearing pads. These assumptions give a reasonable agreement on the direct coefficients prediction while, recently, some discrepancies have been found on the cross-coupled coefficients. In this work, a numerical study is devised to analyze the influence of the pre-load and clearance variations from pad to pad, due to manufacturing tolerances, on the dynamic coefficients prediction. The numerical code for the estimation of the dynamic coefficients uses the finite element method to integrate the Reynolds’s equation through a perturbation approach. Variations on the pre-load and clearance for each bearing’s pad were performed, producing plots quantifying the sensitivity of the tilting pad bearing cross coupled coefficients to manufacturing tolerances.

Tilting Pad Journal Bearings (TPJB) are commonly used in high-speed and high-power turbomachines, due to their contributions in avoiding rotor instabilities. Studies related to the estimation of dynamic coefficients have been carried out considering nominal values of the geometric parameters (clearance and preload) for all bearing pads. However, the unavoidable uncertainties on these geometric parameters and, therefore their possible influence on the TPJB rotordynamic coefficients do not seem to have been discussed enough. In a previous work, a numerical study was conducted to examine the influence of preload and bearing clearance variations on a five-pad TPJB rotordynamic coefficient. The current work is an extension of that paper, considering at this time the Design of Experiments framework. By means of a 2k factorial design and ANOVA random effect model, uncertainties on bearing clearance and pad preload values are introduced in a standard numerical model (i.e. finite element model) used to estimate the direct and cross-coupled dynamic stiffnesses of the five pad TPJB. The influence on these dynamic coefficients, due to the variance of the aforementioned geometric parameters, is discussed and presented in graphical form in order to illustrate the sensitivity of the TPJB dynamic coefficients. Results derived from this study show that variations on loaded pads affect the direct dynamic coefficients, and unloaded pads variations influence the cross-coupled dynamic coefficients. This work contributes to the understanding of the sensitivity of TPJB dynamic coefficients to manufacturing tolerances.

Flow constituted by drops appears in a wide range of natural, biological and engineering situations. For example, liquid-liquid two phase flow inside capillaries constitutes a model commonly used to represent fluid flow in a petroleum reservoir. The typical modeling approach considers inertial forces negligible in comparison to viscous forces, allowing the use of Stokes equation to study flow dynamics. Very few numerical simulations have been made considering inertial effects. In this project, the flow of a periodic train of drops in a viscous suspending fluid, due to the influence of a fixed pressure gradient, was studied by numerical simulation considering the full Navier-Stokes equations. A numerical approach based on a Volume of Fluid (VOF) formulation was employed using JADIM software, developed by the Institut de Mécanique des Fluides de Toulouse, France. JADIM solves Navier-Stokes equations using a VOF finite volume method, second order in space and time using structured mesh. This two-fluid approach without reconstruction of the interface allows simulating two-phase flows with complex interface shapes. Densities of the drops equal to those of the suspending fluid and a constant interface tension were assumed. The effect of drop size, viscosity ratio, interfacial forces and system pressure gradient on the flow dynamics was studied. Parameters values were chosen to be representative for some particular viscous oil. The result validation shows an excellent agreement between both numerical results. However, there are relative differences between them due to the increase in flow velocity when drop relative size increase and validity of Stokes approach is questionable. Results show non-symmetric eddies in the continuum phase, in a referential frame fixed to the drop. The shape of eddies is strongly influenced by viscosity radio. Drop mobility decreases with increasing size. Additionally, drop mobility also decreases when the viscosity ratio increases. Extra pressure gradient of the system due to the presence of the drop shows a strong dependency on the size ratio between the drop and the pore. For size ratio lower than 0.5, the extra pressure gradient required to move the continuum phase is small. However, when drop to micro-channel ratio exceeds 0.5, the extra pressure gradient significantly increases when the drop size increases. Also, viscosity ratio affects on the system pressure loss, especially in cases where the viscosity ratio is high. The analysis of the capillary number effect on the dynamics of the two-phase system shows that it does not influence drop mobility for the drop sizes considered.

Flows in rivers, floodplains and coastal zones are very complex due to uneven bottom topography and irregular boundaries of the flow domain. In particular, when the flow shows strong gradients in water depth and velocity it is very difficult to predict, with accuracy, flow characteristics such as water profiles in all points of the domain.