Boundary and internal conditions for adjoint fluid-flow problems

The ever-increasing robustness and reliability of flow-simulation methods have consolidated CFD as a major tool in virtually all branches of fluid mechanics. Traditionally, those methods have played a crucial role in the analysis of flow physics. In more recent years, though, the subject has broadened considerably, with the development of optimization and inverse design applications. Since then, the search for efficient ways to evaluate flow-sensitivity gradients has received the attention of numerous researchers. In this scenario, the adjoint method has emerged as, quite possibly, the most powerful tool for the job, which heightens the need for a clear understanding of its conceptual basis. Yet, some of its underlying aspects are still subject to debate in the literature, despite all the research that has been carried out on the method. Such is the case with the adjoint boundary and internal conditions, in particular. The present work aims to shed more light on that topic, with emphasis on the need for an internal shock condition. By following the path of previous authors, the quasi-1D Euler problem is used as a vehicle to explore those concepts. The results clearly indicate that the behavior of the adjoint solution through a shock wave ultimately depends upon the nature of the objective functional.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.

NMR imaging of fluid pathways during drainage of softwood in a pressure membrane chamber

An experiment was implemented to study fluid flow in a pressure media. This procedure successfully combines nuclear magnetic resonance imaging with a pressure membrane chamber in order to visualize the non-wetting and wetting fluid flows with controlled boundary conditions. A specially designed pressure membrane chamber, made of non-magnetic materials and able to withstand 4 MPa, was designed and built for this purpose. These two techniques were applied to the drainage of Douglas fir sapwood. In the study of the longitudinal flow, narrow drainage fingers are formed in the latewood zones. They follow the longitudinal direction of wood and spread throughout the sample length. These fingers then enlarge in the cross-section plane and coalesce until drainage reaches the whole latewood part. At the end of the experiments, when the drainage of liquid water in latewood is completed, just a few sites of percolation appear in earlywood zones. This difference is a result of the wood anatomical structure, where pits, the apertures that allow the sap to flow between wood cells, are more easily aspirated in earlywood than in latewood. (C) 2007 Elsevier Ltd. All rights reserved.

Numerical simulation of the liquid phase in SnO(2) thin film deposition by sol-gel-dip-coating

The fluid flow of the liquid phase in the sol-gel-dip-coating process for SnO(2) thin film deposition is numerically simulated. This calculation yields useful information on the velocity distribution close to the substrate, where the film is deposited. The fluid modeling is done by assuming Newtonian behavior, since the linear relation between shear stress and velocity gradient is observed. Besides, very low viscosities are used. The fluid governing equations are the Navier-Stokes in the two dimensional form, discretized by the finite difference technique. Results of optical transmittance and X-ray diffraction on films obtained from colloidal suspensions with regular viscosity, confirm the substrate base as the thickest part of the film, as inferred from the numerical simulation. In addition, as the viscosity increases, the fluid acquires more uniform velocity distribution close to the substrate, leading to more homogenous and uniform films.

Absorption of planar waves in a draining bathtub

We present an analysis of the absorption of acoustic waves by a black hole analogue in (2 + 1) dimensions generated by a fluid flow in a draining bathtub. We show that the low-frequency absorption length is equal to the acoustic hole circumference and that the high-frequency absorption length is 4 times the ergoregion radius. For intermediate values of the wave frequency, we compute the absorption length numerically and show that our results are in excellent agreement with the low-and high-frequency limits. We analyze the occurrence of superradiance, manifested as negative partial absorption lengths for corotating modes at low frequencies.

Is Nitric Oxide a Mediator of the Effects of Low-Intensity Electrical Stimulation on Bone in Ovariectomized Rats?

Low-intensity electrical stimulation (LIES) may counteract the effects of ovariectomy (OVX) on nitric oxide synthase (NOS) expression, osteocyte viability, bone structure, and microarchitecture in rats (Lirani-Galvo et al., Calcif Tissue Int 84:502-509, 2009). The aim of the present study was to investigate if these effects of LIES could be mediated by NO. We analyzed the effects of NO blockage (by l-NAME) in the response to LIES on osteocyte viability, bone structure, and microarchitecture in OVX rats. Sixty rats (200-220 g) were divided into six groups: sham, sham-l-NAME (6 mg/kg/day), OVX, OVX-l-NAME, OVX-LIES, and OVX-LIES-l-NAME. After 12 weeks, rats were killed and tibiae collected for histomorphometric analysis and immunohistochemical detection of endothelial NOS (eNOS), inducible NOS (iNOS), and osteocyte apoptosis (caspase-3 and TUNEL). In the presence of l-NAME, LIES did not counteract the OVX-induced effects on bone volume and trabecular number (as on OVX-LIES). l-NAME blocked the stimulatory effects of LIES on iNOS and eNOS expression of OVX rats. Both l-NAME and LIES decreased osteocyte apoptosis. Our results showed that in OVX rats l-NAME partially blocks the effects of LIES on bone structure, turnover, and expression of iNOS and eNOS, suggesting that NO may be a mediator of some positive effects of LIES on bone.

Sphericity of apatite particles determined by gas permeability through packed beds

Because shape is an assessment of the three-dimensional form of a particle, it may be described in terms of sphericity (Psi), which is a measure of how closely a particle approaches a spherical configuration. In this study, Darcy`s law and the Kozeny-Carman model for fluid flow through porous media were applied to packed beds to determine the sphericity (Psi) of apatite particles. The beds were composed of glass spheres or particles of apatite (igneous from Brazil and sedimentary from the United States) of three classes of size (Class 1: -297 +210 mu m; Class 2: -210 +149 mu m; Class 3: -149 +105 mu m). Glass spheres were used to validate the model because of its known sphericity (Psi = 1.00). Apatite particles, either igneous or sedimentary, showed very close values for particle sphericity (Psi approximate to 0.6). Observations on particle images conducted by scanning electron microscopy illustrated that igneous (Psi = 0.623) and sedimentary (Psi = 0.644) particles of apatite of Class 2 predominantly exhibit elongated shape. The close value of particle sphericity (Psi approximate to 0.6) showed by either igneous or sedimentary apatite may be justified by the similarity in particle shape.

Design and Characterization of a Biomimetic Piezoelectric Pump Inspired on Group Fish Swimming Effect

Flow pumps are important tools in several engineering areas, such as in the fields of bioengineering and thermal management solutions for electronic devices. Nowadays, many of the new flow pump principles are based on the use of piezoelectric actuators, which present some advantages such as miniaturization potential and lower noise generation. In previous work, authors presented a study of a novel pump configuration based on placing an oscillating bimorph piezoelectric actuator in water to generate flow. It was concluded that this oscillatory behavior (such as fish swimming) yields vortex interaction, generating flow rate due to the action and reaction principle. Thus, following this idea the objective of this work is to explore this oscillatory principle by studying the interaction among generated vortex from two bimorph piezoelectric actuators oscillating inside the same pump channel, which is similar to the interaction of vortex generated by frontal fish and posterior ones when they swim together in a group formation. It is shown that parallel-series configurations of bimorph piezoelectric actuators inside the same pump channel provide higher flow rates and pressure for liquid pumping than simple parallel-series arrangements of corresponding single piezoelectric pumps, respectively. The scope of this work includes structural simulations of bimorph piezoelectric actuators, fluid flow simulations, and prototype construction for result validation.

Osteocyte Density in the Peri-Implant Bone of Immediately Loaded and Submerged Dental Implants

Background: The role of osteocytes in bone structure and function remains partially unresolved. Their participation in mechanotransduction, i.e., the conversion of a physical stimulus into a cellular response, has been hypothesized. The present study was an evaluation of the osteocyte density in the peri-implant bone of immediately loaded and submerged dental implants. Methods: Fourteen male patients were included in the study; all of them were partially edentulous and needed a posterior mandibular restoration. Implants were inserted in these areas; half of the sample was loaded immediately (included in a fixed provisional prosthesis on the same day as implant surgery), whereas the other half was left to heal submerged. Fourteen implants (seven immediately loaded and seven unloaded) were retrieved with a trephine after a healing period of 8 weeks. The specimens were treated to obtain thin ground sections, and histomorphometry was used to evaluate the osteocyte index in the peri-implant bone. Results: A higher and statistically significant number of osteocytes was found in the peri-implant bone around immediately loaded implants (P=0.0081). A correlation between the percentage of bone-implant contact and osteocyte density was found for immediately loaded implants (P=0.0480) but not for submerged implants (P=0.2667). Conclusion: The higher number of osteocytes in the peri-implant bone around immediately loaded implants could be related to the functional adaptation required by the loading stimulus, which also explains the hypothesized involvement of the osteocytes in the maintenance of the bone matrix. J Periodontol 2009;80:499-504.

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

On the accuracy of two-fluid model predictions for a particular gas-solid riser flow

Literature presents a huge number of different simulations of gas-solid flows in risers applying two-fluid modeling. In spite of that, the related quantitative accuracy issue remains mostly untouched. This state of affairs seems to be mainly a consequence of modeling shortcomings, notably regarding the lack of realistic closures. In this article predictions from a two-fluid model are compared to other published two-fluid model predictions applying the same Closures, and to experimental data. A particular matter of concern is whether the predictions are generated or not inside the statistical steady state regime that characterizes the riser flows. The present simulation was performed inside the statistical steady state regime. Time-averaged results are presented for different time-averaging intervals of 5, 10, 15 and 20 s inside the statistical steady state regime. The independence of the averaged results regarding the time-averaging interval is addressed and the results averaged over the intervals of 10 and 20 s are compared to both experiment and other two-fluid predictions. It is concluded that the two-fluid model used is still very crude, and cannot provide quantitative accurate results, at least for the particular case that was considered. (C) 2009 Elsevier Inc. All rights reserved.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

Stability analysis of core-annular flow and neutral stability wave number

A general transition criterion is proposed in order to locate the core-annular flow pattern in horizontal and vertical oil-water flows. It is based on a rigorous one-dimensional two-fluid model of liquid-liquid two-phase flow and considers the existence of critical interfacial wave numbers related to a non-negligible interfacial tension term to which the linear stability theory still applies. The viscous laminar-laminar flow problem is fully resolved and turbulence effects on the stability are analyzed through experimentally obtained shape factors. The proposed general transition criterion includes in its formulation the inviscid Kelvin-Helmholtz`s discriminator. If a theoretical maximum wavelength is considered as a necessary condition for stability, a stability criterion in terms of the Eotvos number is achieved. Effects of interfacial tension, viscosity ratio, density difference, and shape factors on the stability of core-annular flow are analyzed in detail. The more complete modeling allowed for the analysis of the neutral-stability wave number and the results strongly suggest that the interfacial tension term plays an indispensable role in the correct prediction of the stable region of core-annular flow pattern. The incorporation of a theoretical minimum wavelength into the transition model produced significantly better results. The criterion predictions were compared with recent data from the literature and the agreement is encouraging. (C) 2007 American Institute of Chemical Engineers.