Conservative properties of finite difference schemes for incompressible flow

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm

Simple Bulk Readout of Digital Nucleic Acid Quantification Assays

Digital assays are powerful methods that enable detection of rare cells and counting of individual nucleic acid molecules. However, digital assays are still not routinely applied, due to the cost and specific equipment associated with commercially available methods. Here we present a simplified method for readout of digital droplet assays using a conventional real-time PCR instrument to measure bulk fluorescence of droplet-based digital assays. We characterize the performance of the bulk readout assay using synthetic droplet mixtures and a droplet digital multiple displacement amplification (MDA) assay. Quantitative MDA particularly benefits from a digital reaction format, but our new method applies to any digital assay. For established digital assay protocols such as digital PCR, this method serves to speed up and simplify assay readout. Our bulk readout methodology brings the advantages of partitioned assays without the need for specialized readout instrumentation. The principal limitations of the bulk readout methodology are reduced dynamic range compared with droplet-counting platforms and the need for a standard sample, although the requirements for this standard are less demanding than for a conventional real-time experiment. Quantitative whole genome amplification (WGA) is used to test for contaminants in WGA reactions and is the most sensitive way to detect the presence of DNA fragments with unknown sequences, giving the method great promise in diverse application areas including pharmaceutical quality control and astrobiology.Burroughs Wellcome Fund (Career Award at the Scientific Interface

Numerical investigations of mechanical stress caused in dendrite by melt convection and gravity

In order to investigate the effects of stress around dendrite neck cased by the convection and gravity on the dendrite fragmentation, the novel numerical model, where phase-field method, Navier-Stokes equations and finite element method are continuously and independently employed, has been developed. By applying the model to the dendritic solidification of Al-Si alloy, the maximum stress variations by melt convection and gravity with dendrite growth were evaluated

Numerical Simulation on the Opening Delay of a Discharge Reed Valve in Compressors

The opening delay of a discharge reed valve for compressors caused by the stiction force of the oil film between the reed and the valve seat is investigated. The coupling simulation algorithm including models of cavitation in the oil film is developed. In order to check the validity, the numerical simulation is performed under several conditions of a model experiment. The coupling model consists of the reed deformation, the gas flow, and the oil film flow with cavitation. The two-dimensional reed deformation is expressed by expanding natural modes that are obtained by the finite element method using shell elements. The gas flow is expressed by the thermodynamic model under the assumption of the internal reversible process. The two-dimensional oil film pressure distribution is obtained by solving numerically the Reynolds’ equation through the finite volume method. On the model of cavitation in the oil film, in addition to the case in which cavitation is not taken into account, two cavitation models are tested; the static cavitation model (Reynolds’ condition) in which the minimum oil pressure is set to absolute zero, and the dynamic cavitation model in which the oil film pressure can fall to the absolute negative (tensile in the liquid) due to the direct simulation of the bubble expansion. Comparisons on the opening delay time between simulation results and the experimental result show that the static cavitation model gives the earlier delay time than that in the experiment, and the dynamic cavitation model which simulates the absolute negative pressure in the oil film reproduces accurately the experimental delay time. The simulation through the dynamic cavitation model also reproduces well behaviors of cavitation and blow-by flow (oil film rupture) in the oil film captured by the high-speed camera in the experiment. The relation among the pressure, the thickness, and the cavitation area of the oil film that are obtained in the simulation shows the mechanism of the oil film rupture (valve opening), i.e., the cavitation bubbles promote the increase of the oil film thickness during the stiction and the increased oil film thickness causes the recovery of the oil film pressure, and the subsequent blow-by flow (oil film rupture)

A Streamwise Constant Model of Turbulence in Plane Couette Flow

Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behavior of fully turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes equations. This results in a two-dimensional, three velocity component ($2D/3C$) model. We first use a steady state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the $2D/3C$ model under small amplitude Gaussian forcing of the cross-stream components are compared to DNS data. The results indicate that a streamwise constant projection of the Navier Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A system theoretic approach is used to demonstrate the presence of large input-output amplification through the forced $2D/3C$ model. It is this amplification coupled with the appropriate nonlinearity that enables the $2D/3C$ model to generate turbulent behaviour under the small amplitude forcing employed in this study.Comment: Journal of Fluid Mechanics 2010, in pres

Staggered grids discretization in three-dimensional Darcy convection

We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated using special schemes. Two problems with different boundary conditions are considered to study scenarios of instability of the state of rest. Branching off of a continuous family of steady states was detected for the problem with zero heat fluxes on two opposite lateral planes.Comment: 20 pages, 9 figure

FLUID-STRUCTURE INTERACTIVE SIMULATION USING A VIRTUAL FLUX METHOD

ABSTRACT This paper describes the resent development of a virtual flux method for simulating fluid-structure interaction problems. The virtual flux method is one of the sharp interface Cartesian grid methods. The numerical flux across the interface is replaced with the virtual flux so that proper interface conditions must be satisfied there. In this study, the virtual flux method is applied to numerical flow simulations about reciprocating engines. The compressible Navier-Stokes equations are coupled with the equation of motion of the piston, connecting rod, and crank system. Intake and exhaust valves are lifted up and down according with the crank angle in the intake and exhaust strokes. Instead of modeling the complex fuel combustion process, a proper amount of energy is added to the Navier-Stokes equation at the beginning of each expansion stroke, to retain the four stroke engine cycle at a constant revolution rate. Initially the engine is started by starter motor force, which is added for a few seconds. The engine comes to work at the revolution rate intended after some initial transition cycles. With designing the intake and exhaust valve lift properly, intake mass and revolution rate are improved by several percent. It is confirmed that the virtual flux method is easily applicable to the simulation of fluid-structure interaction problems. INTRODUCTION Numerical simulation of fluid-structure interaction problems is one of the a current topics in the computational fluid dynamics. Using the arbitrary Lagrangian Eulerian (ALE) method[1,2] is a straightforward strategy for simulating the fluid-structure interaction problems. The ALE method may be accurate, since the fluid-structure interface i

Relating statistics to dynamics in axisymmetric homogeneous turbulence

The structure and the dynamics of homogeneous turbulence are modified by the presence of body forces such that the Coriolis or the buoyancy forces, which may render a wide range of turbulence scales anisotropic. The corresponding statistical characterization of such effects is done in physical space using structure functions, as well as in spectral space with spectra of two-point correlations, providing two complementary viewpoints. In this framework, second-order and third-order structure functions are put in parallel with spectra of two-point second- and third-order velocity correlation functions, using passage relations. Such relations apply in the isotropic case, or for isotropically averaged statistics, which, however, do not reflect the actual more complex structure of anisotropic turbulence submitted to rotation or stratification. This complexity is demonstrated in this paper by orientation-dependent energy and energy transfer spectra produced in both cases by means of a two-point statistical model for axisymmetric turbulence. We show that, to date, the anisotropic formalism used in the spectral transfer statistics is especially well-suited to analyze the refined dynamics of anisotropic homogeneous turbulence, and that it can help in the analysis of isotropically computed third-order structure function statistics often used to characterize anisotropic contexts.Comment: Physica

Large eddy simulation of a turbulent non-premixed propane-air reacting flame in a cylindrical combustor

Large Eddy Simulation (LES) is applied to investigate the turbulent non-premixed combustion flow, including species concentrations and temperature, in a cylindrical combustor. Gaseous propane (C3H8) is injected through a circular nozzle which is attached at the centre of the combustor inlet. Preheated air with a temperature of 773 K is supplied through the annulus surrounding of this fuel nozzle. In LES a spatial filtering is applied to the governing equations to separate the flow field into large-scale and small-scale eddies. The large-scale eddies which carry most of the turbulent energy are resolved explicitly, while the unresolved small-scale eddies are modelled using the Smagorinsky model with Cs = 0.1 as well as dynamically calibrated Cs. The filtered values of the species mass fraction, temperature and density, which are the functions of the mixture fraction (conserved scalar), are determined by integration over a beta probability density function (β-PDF). The computational results are compared with those of the experimental investigation conducted by Nishida and Mukohara. According to this experiment, the overall equivalence ratio of 0.6, which is calculated from the ratio of the air flow rate supplied to the combustion chamber to that of the stoichiometric reaction, is kept constant so that the turbulent combustion at the fuel nozzle exit starts under the fuel-rich conditions

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiologicalpulsatileflow in a 3D model of arterialstenosis is investigated by using largeeddysimulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatileflow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatileflow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3