Numerical Investigations for Leakage and Windage Heating in Straight-Through Labyrinth Seals

The ability to quantify leakage flow and windage heating for labyrinth seals with honeycomb lands is critical in understanding gas turbine engine system performance and predicting its component life. Variety of labyrinth seal configurations (number of teeth, stepped or straight, honeycomb cell size) are in use in gas turbines, and for each configuration, there are many geometric factors that can impact a seal's leakage and windage characteristics. This paper describes the development of a numerical methodology aimed at studying the effect of honeycomb lands on leakage and windage heating. Specifically, a three-dimensional computational fluid dynamics (CFD) model is developed utilizing commercial finite volume-based software incorporating the renormalization group (RNG) k-epsilon turbulence model with modified Schmidt number. The modified turbulence model is benchmarked and fine-tuned based on several experiments. Using this model, a broad parametric study is conducted by varying honeycomb cell size, pressure ratio (PR), and radial clearance for a four-tooth straight-through labyrinth seal. The results show good agreement with available experimental data. They further indicate that larger honeycomb cells predict higher seal leakage and windage heating at tighter clearances compared to smaller honeycomb cells and smooth lands. However, at open seal clearances larger honeycomb cells have lower leakage compared to smaller honeycomb cells.

Numerical prediction of nozzle flow separation: Issue of turbulence modeling

Numerical simulation of separated flows in rocket nozzles is challenging because existing turbulence models are unable to predict it correctly. This paper addresses this issue with the Spalart-Allmaras and Shear Stress Transport (SST) eddy-viscosity models, which predict flow separation with moderate success. Their performances have been compared against experimental data for a conical and two contoured subscale nozzles. It is found that they fail to predict the separation location correctly, exhibiting sensitivity to the nozzle pressure ratio (NPR) and nozzle type. A careful assessment indicated how the model had to be tuned for better, consistent prediction. It is learnt that SST model's failure is caused by limiting of the shear stress inside boundary layer according to Bradshaw's assumption, and by over prediction of jet spreading rate. Accordingly, SST's coefficients were empirically modified to match the experimental wall pressure data. Results confirm that accurate RANS prediction of separation depends on the correct capture of the jet spreading rate, and that it is feasible over a wide range of NPRs by modified values of the diffusion coefficients in the turbulence model. (C) 2015 Elsevier Masson SAS. All rights reserved.

Benchmark analytical solutions from beams with shared eigenpair

Structures with governing equations having identical inertial terms but somewhat differing stiffness terms can be termed flexurally analogous. An example of such a structure includes an axially loaded non-uniform beam and an unloaded uniform beam, for which an exact solution exists. We find that there exist shared eigenpairs (frequency and mode shapes) for a particular mode between such structures. Non-uniform beams with uniform axial loads, gravity loaded beams and rotating beams are considered and shared eigenpairs with uniform beams are found. In general, the derived flexural stiffness functions (FSF's) for the non-uniform beams required for the existence of shared eigenpair have internal singularities, but some of the singularities can be removed by an appropriate selection of integration constants using the theory of limits. The derived functions yield an insight into the relationship between the axial load and flexural stiffness of axially loaded beam structures. The derived functions can serve as benchmark solutions for numerical methods. (C) 2016 Elsevier Ltd. All rights reserved.

Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

In this work, we present a numerical study of flow of shear thinning viscoelastic fluids in rectangular lid driven cavities for a wide range of aspect ratios (depth to width ratio) varying from 1/16 to 4. In particular, the effect of elasticity, inertia, model parameters and polymer concentration on flow features in rectangular driven cavity has been studied for two shear thinning viscoelastic fluids, namely, Giesekus and linear PTT. We perform numerical simulations using the symmetric square root representation of the conformation tensor to stabilize the numerical scheme against the high Weissenberg number problem. The variation in flow structures associated with merging and splitting of elongated vortices in shallow cavities and coalescence of corner eddies to yield a second primary vortex in deep cavities with respect to the variation in flow parameters is discussed. We discuss the effect of the dominant eigenvalues and the corresponding eigenvectors on the location of the primary eddy in the cavity. We also demonstrate, by performing numerical simulations for shallow and deep cavities, that where the Deborah number (based on convective time scale) characterizes the elastic behaviour of the fluid in deep cavities, Weissenberg number (based on shear rate) should be used for shallow cavities. (C) 2016 Elsevier B.V. All rights reserved.

Numerical Analysis of a Dual Polarization Mode-Locked Laser with a Quarter Wave Plate

Dynamical behaviors and frequency characteristics of an active mode-locked laser with a quarter wave plate (QWP) are numerically studied by using a set pf vectorial laser equation. Like a polarization self-modulated laser, a frequency shift of half the cavity mode spacing exists between the eigen-modes in the two neutral axes of QWP. Within the active medium, the symmetric gain and cavity structure maintain the pulse's circular polarization with left-hand and right-hand in turn for each round trip. Once the left-hand or right-hand circularly polarized pulse passes through QWP, its polarization is linear and the polarized direction is in one of the directions of i45o with respect to the neutral axes of QWP. The output components in the directions of i45" from the mirror close to QWP are all linearly polarized with a period of twice the round-trip time.

Numerical Investigation of Richtmyer-Meshkov Instability Driven by Cylindrical Shocks

In this paper, a numerical method with high order accuracy and high resolution was developed to simulate the Richtmyer-Meshkov(RM) instability driven by cylindrical shock waves. Compressible Euler equations in cylindrical coordinate were adopted for the cylindrical geometry and a third order accurate group control scheme was adopted to discretize the equations. Moreover, an adaptive grid technique was developed to refine the grid near the moving interface to improve the resolution of numerical solutions. The results of simulation exhibited the evolution process of RM instability, and the effect of Atwood number was studied. The larger the absolute value of Atwood number, the larger the perturbation amplitude. The nonlinear effect manifests more evidently in cylindrical geometry. The shock reflected from the pole center accelerates the interface for the second time, considerably complicating the interface evolution process, and such phenomena of reshock and secondary shock were studied.

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma=6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at free-stream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibilty effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely to occur.

Structural Failure Analysis and Numerical Simulation of Micro-Accelerometers under Impulsive Loading

Micromachined accelerometer is a kind of inertial MEMS devices, which usually operate under intensive impact loading. The reliability of micromachined accelerometers is one of the most important performance indices for their design, manufacture and commer

Numerical Analysis of Rainfall Infiltration in the Slope with a Fracture

With the finite volume method, a 2D numerical model for seepage in unsaturated soil has been established to study the rainfall infiltration in the fractured slope.The result shows that more rain may infiltrate into the slope due to existing fracture and then the pore pressure rises correspondingly. Very probably, it is one of the crucial factors accounting for slope failure. Furthermore a preliminary study has been conducted to investigate the influence of various fracture and rainfall factors such as the depth, width and location of a crack, surface condition, rainfall intensity and duration. Pore pressure and water volumetric content during the transient seepage are carefully examined to reveal the intrinsic mechanism.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme

A new finite difference method for the discretization of the incompressible Navier-Stokes equations is presented. The scheme is constructed on a staggered-mesh grid system. The convection terms are discretized with a fifth-order-accurate upwind compact difference approximation, the viscous terms are discretized with a sixth-order symmetrical compact difference approximation, the continuity equation and the pressure gradient in the momentum equations are discretized with a fourth-order difference approximation on a cell-centered mesh. Time advancement uses a three-stage Runge-Kutta method. The Poisson equation for computing the pressure is solved with preconditioning. Accuracy analysis shows that the new method has high resolving efficiency. Validation of the method by computation of Taylor's vortex array is presented.

Intensity Distribution Design for Laser-Induced Thermal Loading Based on Numerical Simulation

To accomplish laser-induced thermal loading simulation tests for pistons,the Gaussian beam was modulated into multi-circular beam with specific intensity distribution.A reverse method was proposed to design the intensity distribution for the laser-induced thermal loading based on finite element(FE) analysis.Firstly,the FE model is improved by alternating parameters of boundary conditions and thermal-physical properties of piston material in a reasonable range,therefore it can simulate the experimental resul...

Numerical Analysis of Theoretical Model of the Rf MEMs Switches

An improved electromechanical model of the RF MEMS (radio frequency microelectromechanical systems) switches is introduced, in which the effects of intrinsic residual stress from fabrication processes, axial stress due to stretching of beam, and fringing field are taken into account. Four dimensionless numbers are derived from the governing equation of the developed model. A semi-analytical method is developed to calculate the behavior of the RF MEMS switches. Subsequently the influence of the material and geometry parameters on the behavior of the structure is analyzed and compared, and the corresponding analysis with the dimensionless numbers is conducted too. The quantitative relationship between the presented parameters and the critical pull-in voltage is obtained, and the relative importance of those parameters is given.