Control Volume Approaches Research Articles

Predicting Coral Reef Carbonate Chemistry Through Statistical Modeling: Constraining Nearshore Residence Time Around Guam

To accurately predict the impacts of ocean acidification on shallow-water ecosystems, we must account for the biogeochemical impact of local benthic communities, as well as the connectivity between offshore and onshore water masses. Estimation of residence time can help quantify this connectivity and determine the degree to which the benthos can influence the chemistry of the overlying water column. We present estimates of nearshore residence time for Guam and utilize these estimates to model the effects of benthic ecosystem metabolism on the coral reef carbonate system. Control volume and particle tracking approaches were used to estimate nearshore residence time. These estimates were paired with observed patterns in the reef carbonate system around Guam using water samples collected by NOAA’s National Coral Reef Monitoring Program. Model performance results suggest that when considering the effects of benthic metabolism on the carbonate system, it is paramount to represent the contact time of the water volume with the benthos. Even coarse estimates of residence time significantly increase model skill. We observed the highest predictive skill in models including control volume derived estimates of residence time, but only when those estimates were included as an interaction with benthic composition. This work shows that not only is residence time critically important to better predict biogeochemical variability in coral reef environments, but that even coarse hydrodynamic models can provide useful residence time estimates at management relevant, whole-ecosystem scales.

Lagrangian interpolation algorithm for PIV data

A new Lagrangian based interpolation scheme is proposed for recovering velocity field data from within masked regions in particle image velocimetry (PIV) experiments. As a first step, the mean field within the masked region is filled through an iterative convolution operation using an optimized kernel. Next, the Lagrangian interpolation scheme estimates velocity field data within the masked region using a weighted average of past and future snapshot data along a mean field streamline from outside of the masked region. The Lagrangian interpolation scheme is compared directly with a traditional bilinear interpolation approach for two datasets: the flow development over a circular cylinder within the laminar vortex shedding regime (ReD=150) and turbulent vortex shedding regime (ReD=3000). The results show that for both Reynolds numbers investigated, the Lagrangian approach provides up to a 5× improvement in average velocity reconstruction error. Application of the proposed interpolation scheme to the estimation of body forces was assessed. For both the momentum and impulse control volume approaches to estimate instantaneous forces, the Lagrangian interpolation scheme provides up to 10× improvement in the estimation of volume integral contributions to instantaneous drag and lift.

On preservation of symmetry in r–z staggered Lagrangian schemes

In the focus of this work are symmetry preservation, conservation of energy and volume, and other important properties of staggered Lagrangian hydrodynamic schemes in cylindrical (r–z) geometry. It is well known that on quadrilateral cells in r–z, preservation of spherical symmetry, perfect satisfaction of the Geometrical Conservation Law (GCL), and total energy conservation are incompatible even on conforming grids. This paper suggests a novel staggered grid approach that preserves symmetry, conserves total energy by construction and tries to do its best by diminishing the GCL error to the order of entropy error. In particular, the forces from an existing volume consistent scheme are corrected so that spherical symmetry is preserved. The incorporation of subcell pressure mechanism to reduce spurious grid deformations is described and the relation of the new scheme to popular area-weighted and control volume approaches studied.

Generalized Darcy's Law by Control Volume Analysis Including Capillary and Orifice Effects

Abstract The equation of motion for single-phase fluid flow through porous media is derived by rigorous analysis of forces acting upon fluid based on a control volume momentum balance approach. Resistive forces associated with pore surface and pore throat are characterized by the capillary-orifice model of porous media. This analysis reveals deficiencies of previous efforts in deriving the generalized momentum equation. The present approach provides resolution to several issues, including porous media averaging of the pressure and shear-stress terms, effect of porous media heterogeneity and anisotropy, and threshold pressure gradient that must be overcome for fluid to flow through porous media. Introduction Derivation of generalized equation of momentum for fluids flowing through porous media has occupied many researchers and is not by any means a trivial task. Since its inception, the fundamental law of flow through porous media given by Darcy(1) has been scrutinized greatly and been the subject for many modifications to take into account the effect of other factors which are not considered by this law. In spite of an exhausting amount of effort, and prolonged occupation and obsession with derivation of an improved formulation, a satisfactory generalized equation of fluid motion in porous media still does not exist. In an effort to shed some light into the adequate treatment of the control volume balance approach, this paper attempts to revisit, modify and improve the generalized formulation presented by Das(2). Many researchers attempted to improve Darcy's law by various approaches to take into account other conditions of practical importance. The outstanding approaches have been developed primarily on the bases of dimensional analysis(3), control volume balance(1, 2) and porous media averaging(4–12). There are some discrepancies, however, between the results presented by various researchers. As pointed out by Civan(13), porous media averaging does not only require extremely complicated and intricate algebraic manipulation procedures, but also has been implemented inadequately in many studies. Consequently, debate about proper handling of various issues dealing with porous media averaging is still continuing, judging by the high number of papers being published. The results presented by various studies do not agree whether the porous media averaged pressure gradient term should include the porosity. The same concern can be raised about shear-stress. Liu and Masliyah(12) emphasize that averaging of pressure and viscosity terms in the microscopic equation of motion should be treated differently than the other terms. Also, the mathematical definition of partial derivatives assumes a limit as control volume approaches zero, i.e., collapses to a point of zero volume. By and large, discussion of differences introduced by the application of such a condition in deriving porous media equations of mass, momentum and energy conservation have been omitted, whereas, representative elementary bulk volume is a finite quantity in definition of volume averaged quantities used for deriving the porous media (macroscopic) equation of motion.

A sensitivity analysis of powder forging processes

The purpose of this paper is to analyze the sensitivity problems in metal forming of rigid-visco-poroplastic materials. A repressing powder forging process is analyzed. Parameter sensitivity, material derivative, and control volume approaches to shape sensitivity analysis are presented, analyzed, and compared. Discretization of the continuum expressions is presented. The numerical solutions for parameter sensitivity in forging problems have been described. Numerical examples concerning simple compression test of cylindrical porous specimen are presented.

Aerodynamic load characterisation of a low speed aerofoil using particle image velocimetry

AbstractParticle image velocimetry (PIV) measurements of the flow around a wing section are employed as a basis for non-intrusive aerodynamic mean loads characterisation, providing sectional lift, drag and pitching moment. The technique relies upon the application of control-volume approaches in combination with the deduction of the pressure from the PIV experimental data through application of the momentum equation. The treatment can also be applied when the flow is unsteady; in that case time-mean loads are obtained from velocity statistics, through the use of Reynolds-averaged formulation of the governing equations. The procedure was applied in the experimental investigation of a NACA 642A015 aerofoil, in which the PIV approach is validated against standard pressure-based methods (surface pressure distribution and wake rake). The chord Reynolds number considered in the investigation ranges between 1 – 7 × 105. In addition, the consistency and potential performance of the method was assessed by means of synthetic velocity field data obtained from a numerical flow simulation.

Heat transfer in porous media

In this work, the effects of electrical double layer (EDL) near the solid/ liquid interface, on three dimensional heat transfer characteristic and pressure drop of water flow through a rectangular microchannel numerically are investigated. An additional body force originating from the existence of EDL is considered to modify the conventional Navier-stokes and energy equations. These modified equations are solved numerically for steady laminar flow on the basis of control volume approaches. Fluid velocity distribution and temperature with presence and absence of EDL effects are presented for various geometric cases and different boundary conditions. The results illustrate that, the liquid flow in rectangular microchannels is influenced significantly by the EDL, particularly in the high electric potentials, and hence deviates from flow characteristics described by classical fluid mechanics.

Evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows

The approach to determine pressure fields and integral loads from planar velocimetry data is discussed, in relation to the implementation for incompressible and compressible flows around two-dimensional objects. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure field from the experimental data, by making use of the flow constitutive equations. In this paper the implementation for two specific application areas is addressed. The first is time-mean pressure field and force evaluation from velocity ensemble statistics, as obtained from time-uncorrelated PIV acquisition, for incompressible flow. Two test cases are considered for this flow regime: the unsteady vortical flow around a square section cylinder at incidence, as well as the force characterization of a low-speed airfoil. The second topic considers the extension of the method to steady compressible flow, with the supersonic flow around a bi-convex airfoil as experimental test case. As in this flow regime the density appears as an extra unknown in the momentum equation, additional flow equations need to be invoked. A convenient approach for this was found, using the gas law and the adiabatic flow condition, with which the pressure-integration procedure becomes essentially the same as for the incompressible case.

Non-intrusive load characterization of an airfoil using PIV

An assessment is made of the feasibility of using PIV velocity data for the non-intrusive aerodynamic force characterization (lift, drag and pitching moment) of an airfoil. The method relies upon the application of control-volume approaches in combination with the deduction of the pressure from the PIV experimental data, by making use of the momentum equation. First, the consistency of the method is verified by means of synthetic data obtained from CFD. Subsequently, the procedure was applied in an experimental investigation, in which the PIV approach is validated against standard pressure-based methods (surface pressure distribution and wake rake).

CAPILLARY PRESSURE: SOME STATIC AND DYNAMIC VIEWS IN SEMI-ORDERED MEDIA AND THEIR APPLICABILITY TO WOOD DRYING

ABSTRACT In most situations where vapor-liquid motion is simulated within porous media, one often sees the conflicting notions of ‘continuous water column’ used alongside the concept of ‘well-mixed liquid-gas system’ within a control-volume. This assumption clearly breaks down when the computational control volume approaches the structural cell dimensions. The ‘grainyness’ of the cell structure and the fluid flow patterns cannot be neglected any longer, if accurate descriptions of water (or any other fluid) content are to be generated. This would be useful especially in predicting the onset of hygroscopicity in regions where the liquid saturation begins to vanish during drying. Using arguments based on a simple mechanical potential energy formulation, the multiplicity of equilibrium states for a fluid/gas system in a semi-ordered structure (where capillary forces dominate, e.g. softwoods) will be explored. By these methods, it is hoped that insight into capillary motion on a mesoscopic scale can be gained.

Material derivative and control volume approaches to shape sensitivity analysis of nonlinear transient thermal problems

The problem of the shape design sensitivity of nonlinear transient thermal systems is considered. The nonlinear shape design sensitivity is formulated by using a weighted residual method employing the continuum description. Both material derivative and control volume approaches for structural shape design sensitivity analysis are presented, analysed and compared. It is shown that the final design sensitivity expressions for the two approaches are theoretically equivalent.

A hydraulics-based/optimization methodology for gating design

Advantages and disadvantages of the differential momentum balance and macroscopic control volume approaches to the analysis of flow during mold filling and the computer-aided design of gating systems are discussed. A gating design methodology based on a control volume hydraulics-based flow model and nonlinear optimization is described. Mathematical formulation of the model yields a system of equations that ensures mass continuity at nodes and conservation of energy along paths. In addition to computational efficiency, the hydraulics approach to flow analysis utilizes a pipe-node-path representation of gating systems that facilitates the analysis of complex three-dimensional configurations. Example simulations of flow distribution in water modeling systems and of flow distribution and mold filling in molten metal experiments are presented. It is concluded that good agreement between model-predicted and experimental results is obtainable if pertinent loss coefficient data are available. However, application of the hydraulics-based methodology to accurate analysis of flow in gating systems requires knowledge of loss coefficients that specifically relate to the flow conditions and types of runner/ingate geometric configurations encountered in industrial castings. An example formulation illustrating the application of nonlinear optimization to gating design is presented.

Structural shape sensitivity analysis - Relationship between material derivative and control volume approaches

The material derivative and control volume approaches for structural shape design sensitivity analysis are presented, analyzed, and compared. Starting with a continuum formulation and a general response functional needing sensitivity analysis, the two approaches are derived. It is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other. Thus, the two approaches are theoretically equivalent. Discretizations of the continuum expressions are presented, and it is shown that the two approaches can lead to different implementations for numerical calculations. A unified interpretation is developed in which the explicit design variations (partial derivatives with respect to the design variables) of the internal and external forces are the major calculations needed to implement the design sensitivity analysis. The discretized forms of the continuum sensitivity expressions are also compared with the ones obtained by starting with the discretized model ab initio. This comparison shows that these two approaches lead to similar expressions for numerical calculations. Therefore, the exact same procedures can be used for computer implementations for both of the approaches. The presented analyses give insights for implementation of the design sensitivity analysis theory with the finite element analysis programs.