Antonio Pascau

Knee model of hydrodynamic lubrication during the gait cycle and the influence of prosthetic joint conformity

BackgroundThe influence of the total joint components’ elastic deformation on lubrication is generally accepted, but little is known about the influence of joint conformity under hydrodynamic lubrication based on fluid film interposition. The aim of this study was to evaluate induced pressure and stresses in the knee under fluid film lubrication during the stance phase of walking under various joint conformity conditions.MethodsA theoretical two-dimensional (2D) geometric model of knee prosthesis contact, with Dirichlet boundary conditions at both edges, and with a conformity index (CI) of 0, 0.3, 0.5, 0.6, 0.7, 0.8, 0.9, 0.92, 0.94, 0.96, 0.98, 0.99, 0.995, and 1.0, was used to calculate the spatiotemporal lubricant flow on a synovial fluid rheological model. With the instantaneous load as a source term, the Reynolds lubrication equation was subsequently solved following a finite volume approach in two dimensions and three dimensions.ResultsConformity strongly influenced the peak pressure, from 47 MPa with CI = 0 to 1.4 MPa with CI = 1, with a definite behavior change from CI = 0.96. The role of hydrodynamic lubrication was restricted to early steps of the stance phase. With CI < 0.96, there was a smooth maximum pressure decrease with increasing CI. In contrast, the maximum pressure fell abruptly with conformity > 0.96.ConclusionThe present model suggested the limited modifying effect of hydrodynamic lubrication in total knee replacement systems. However, its role during the early stance phase, coupled with high conformity, helps significantly to decrease compressive stresses on the polyethylene, fostering the beneficial effect of high conformity in a mixed lubrication regime. This beneficial effect may also be of great interest in total knee replacement systems based on materials with less deformation.

A comparison of segregated and coupled methods for the solution of the incompressible Navier‐Stokes equations

Three different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;- and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.

Numerical Simulation of a Synthetic Jet Actuator Using a Simplified Periodic Boundary Condition

When using a collocated grid for the discretization of the unsteady Navier-Stokes equations special care has to be taken in the evaluation of the cell face velocity as if it is not properly calculated the resulting flow field may be dependent on the time step. This dependency increases as the time step is reduced so this problem can be of paramount importance in rapidly varying flows. As an illustration of the problem in a flow of industrial interest a synthetic jet has been chosen. Although the primary goal of the paper is not to compare computational and experimental results, the assessment with experimental data will highlight the discrepancies in the computational results with different time steps. For comparison purposes a well documented case was chosen: the first test case of the synthetic jet workshop organized by NASA in 2004, but with the new 2006 data. This flow is produced by a moving diaphragm at one of the sides of a cavity connected to an otherwise stagnant air through a slot. Near the slot exit the flow is almost bidimensional so in order to reduce computational time it has been modelled in a 2D domain with a transpiration velocity at the bottom boundary of a simplified cavity. This velocity tries to reproduce the waveform of the measurements at the slot exit with an appropriate combination of Fourier modes.Copyright