Control Volume Scheme Research Articles

Nanofluid effect on dual-flow parabolic trough collector performance accompanies with passive technique using experimental data

Purpose Using passive techniques like twisted tapes and corrugated surface is an efficient method of heat transfer improvement, since the referred manners break the boundary layer and improve the heat exchange. This paper aims to present an improved dual-flow parabolic trough collector (PTC). For this purpose, the effect of an absorber roof, a type of turbulator and a grooved absorber tube in the presence of nanofluid is investigated separately and simultaneously. Design/methodology/approach The FLUENT was used for solution of governing equation using control volume scheme. The control volume scheme has been used for solving the governing equations using the finite volume method. The standard k–e turbulence model has been chosen. Findings Fluid flow and heat transfer features, as friction factor, performance evaluation criteria (PEC) and Nusselt number have been calculated and analyzed. It is showed that absorber roof intensifies the heat transfer ratio in PTCs. Also, the combination of inserting the turbulator, outer corrugated and inner grooved absorber tube surface can enhance the PEC of PTCs considerably. Originality/value Results of the current study show that the PTC with two heat transfer fluids, outer and inner surface corrugated absorber tube, inserting the twisted tape and absorber roof have the maximum Nusselt number ratio equal to 5, and PEC higher than 2.5 between all proposed arrangements for investigated Reynolds numbers (from 10,000 to 20,000) and nanoparticles [Boehmite alumina (“λ-AlOOH)”] volume fractions (from 0.005 to 0.03). Maximum Nusselt number and PEC correspond to nanoparticle volume fraction and Reynolds number equal to 0.03 and 20,000, respectively. Besides, it was found that the performance evaluation criteria index values continuously grow by an intensification of nanoparticle volume concentrations.

A new probabilistic control volume scheme to interpret specimen size effect on fatigue life of additively manufactured titanium alloys

The effect of specimen size on the fatigue performance of additively manufactured (AMed) Ti-6Al-4V is investigated in this paper. The fatigue tests of Ti-6Al-4V specimens made by laser powder bed fusion were conducted via ultrasonic axial cycling up to very-high-cycle regime with stress ratio R = –1. The S-N data of five group specimens show an evident size effect, that is, with the increase of specimen size, the fatigue life or fatigue strength decreasing gradually. A new probabilistic control volume scheme is developed to evaluate the fatigue life of large sized specimens by the tested data of small sized specimens. The applicability of the proposed model is validated by the present data and those of our previous investigation. Moreover, a general form of probabilistic control volume model is derived to show the original and present models are the special cases for conventional cast and AMed alloys.

Numerical Investigation of a Phase Change Material Building Integrating Solar Thermal Collector PCM-BST

Abstract Sensible thermal energy storage (TES) systems can reduce energy environmental fluctuation dependency with the nocturnal energy needs usage in maintaining the building's comfort levels. In the present paper, phase change material (PCM) is introduced to improve the thermal energy storage capacity of a solar collector integrating a novel composite PCM/concrete wall. A mathematical model based upon the conservation and heat transfer equations has been developed using the enthalpy method. The equations that govern the problem were discretized with the control volume scheme and solved iteratively using the tridiagonal matrix algorithm (TDMA). The numerical investigation has been implemented into a personal fortran code. Many series of simulation runs were executed. The position of the PCM layer within the wall and the PCM melting temperature are varied in the range 0 cm ≤ xm ≤ 7.5 cm and 15 °C ≤ Tm ≤ 35 °C, respectively. The objective is to let inner temperature Tin swing close to a comfort threshold. The position of PCM close to the absorber improves the efficiency of the room heating with good nocturnal use of latent heat stored during the day. PCM melting temperature affects deeply the composite PCM/concrete wall/solar collector behavior. Lastly, PCM gained the system an important benefit which is the solar collector high-temperature isolation as to not reach the room and disturb the inside comfort zone by melting and solidifying. Those parameters can be considered as the primary pointers for PCM/wall integrated solar collector design. Also, a daily heating potential, Qh, and thermal load leveling, TLL, are introduced to evaluate the system performance.

Thermodynamically consistent physics-informed neural networks for hyperbolic systems

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers that easily assimilate data. When applied to problems in shock physics however, these approaches face challenges related to the collocation-based PDE discretization underpinning them. By instead adopting a least squares space-time control volume scheme, we obtain a scheme which more naturally handles: regularity requirements, imposition of boundary conditions, entropy compatibility, and conservation, substantially reducing requisite hyperparameters in the process. Additionally, connections to classical finite volume methods allows application of inductive biases toward entropy solutions and total variation diminishing properties. For inverse problems in shock hydrodynamics, we propose inductive biases for discovering thermodynamically consistent equations of state that guarantee hyperbolicity. This framework therefore provides a means of discovering continuum shock models from molecular simulations of rarefied gases and metals. The output of the learning process provides a data-driven equation of state which may be incorporated into traditional shock hydrodynamics codes.

Heat transfer analysis of forced convective flow within an enclosure

The paper is to study about the movement of heat analysis with respect to forced convective flow within sideways four-sided enclosure. The mathematical statements of the flow variables are represented using a discrete quantity by virtue of upwind control volume scheme. Non-dimensional parameters are suitably preferred so as to determine Nu. This Nu for the sake of different fluids are calculated by using a suitable empirical correlation and thereby the transfer of heat between the top wall and forced convective flow of these fluids is examined. It is ascertained that, a substantial rise in Nu and hence the transfer of heat within the four-sided enclosure by way of forced convective flow of any fluid substantially increases within the sideways four-sided enclosure. The average Nusselt numbers for fluids such as air and water at different Rayleigh numbers of 1, 10, 100, 1000, 1700 in the range of Ra ≤ 1708 are calculated and observed to increase linearly.

FEM of Gas-Assisted Injection Molding Based on 3D Model

The gas-assisted injection molding (GAIM) process is so complicated that increasing reliance has been placed on CAE (Computer Aided Engineering) as a tool for both mold designers and process engineers. In this paper, a 3D theoretical model and numerical scheme is presented to simulate the GAIM process, in which an equal-order velocity-pressure formulation method is employed to eliminate the pressure oscillation. In addition, the whole flow field including the gas and melt regions is calculated using a uniform momentum equation with the viscosity of gas raised to a certain order of magnitude, and a 3D control volume scheme is employed to track the flow front of the melt and gas. Finally, the validity of the model has been tested through case studies and experimental verification.

FSIS: a novel fluid–solid interaction solver for fracturing and fragmenting solids

Transient dynamics of fracturing media has received significant attention in recent years, and a number of simulation approaches have been developed. One of these is the combined finite-discrete element method (FDEM). FDEM produces complex fracture and fragmentation patterns in processes such as blast loads, blasting, impact, mining, and oil exploration. To address a wide range of multi-physics problems, numerous approaches have been undertaken to introduce fluid into the FDEM transient dynamics, ranging from application-specific gas models to more advanced hydraulic fracture processes and biomedical applications. None of these have been satisfactory in terms of robustness, accuracy or computational efficiency. In this work, a completely new explicit fluid solver has been tailor-made and fully integrated (as opposed to coupled) into the combined finite-discrete element method. The solver addresses transient pressure wave propagation in fluid, fluid viscosity, equation of state for the fluid, energy transport, momentum transport, and interaction with the fracturing solid domains, which is done through a novel immersed boundary approach. The solver is based on the governing equations being resolved using different control volume schemes, with discretization errors of either third, second, or first order. The solver is fully explicit and conditionally stable with a time step that is synchronized with the FDEM’s time step.

Oscillating Flows in Circular Pipes

Pulsation flows in pipes heated externally produces oscillating temperature field. This type of unsteady flow happens in heat exchangers. Simulating this type of flows is complex in engineering. In this present study the field variables like velocity and temperature are calculated by numerical control volume scheme. Velocity pulsation is applied at inlet of pipe to produce oscillations. Simulation variables like lengths, diameter and thickness of the pipe are considered as parameters for this study. Also additionsl structural constraints has been added to see how it influences effective thermal stresses.

Fast upwind and Eulerian-Lagrangian control volume schemes for time-dependent directional space-fractional advection-dispersion equations

We develop control volume methods for two-dimensional time-dependent advection-dominated directional space-fractional advection-dispersion equations with the directional space-fractional derivative weighted in all the directions by a probability measure in the unit circle, which are used to model the anisotropic superdiffusive transport of solutes in groundwater moving through subsurface heterogeneous porous media.We develop a fast upwind control volume method for the governing equation to eliminate the spurious numerical oscillations that often occur in space-centered numerical discretizations of advection term, which are relatively straightforward to implement. We also develop a Eulerian-Lagrangian control-volume method for the governing equation, which symmetrizes the governing equation by combining the time-derivative term and the advection term into a material derivative term along characteristic curves. Both methods are locally mass-conservative, which are essential in these applications.Due to the nonlocal nature of the directional space-fractional differential operators, corresponding numerical discretizations usually generate full stiffness matrices. Conventional direct solvers tend to require O(N2) memory requirement and have O(N3) computational complexity per time step, where N is the number of spatial unknowns, which is computationally significantly more expensive than the numerical approximations of integer-order advection-diffusion equations. Based on the analysis of the structure of stiffness matrix, we propose a fast Krylov subspace iterative solver to accelerate the numerical approximations of both the upwind and Eulerian-Lagrangian control volume methods, which reduce computational complexity from O(N3) by a direct solver to O(Nlog⁡N) per Krylov subspace iteration per time step and a memory requirement from O(N2) to O(N). Numerical results are presented to show the utility of the methods.

A control volume scheme using compact integrated radial basis function stencils for solving the Richards equation

A new control volume approach is developed based on compact integrated radial basis function (CIRBF) stencils for solution of the highly nonlinear Richards equation describing transient water flow in variably saturated soils. Unlike the conventional control volume method, which is regarded as second-order accurate, the proposed approach has high-order accuracy owing to the use of a compact integrated radial basis function approximation that enables improved flux predictions. The method is used to solve the Richards equation for transient flow in 1D homogeneous and heterogeneous soil profiles. Numerical results for different boundary conditions, initial conditions and soil types are shown to be in good agreement with Warrick’s semi-analytical solution and simulations using the HYDRUS-1D software package. Results obtained with the proposed method were far less dependent upon the grid spacing than the HYDRUS-1D finite element solutions.

A mixed isogeometric analysis and control volume approach for heat transfer analysis of nonuniformly heated plates

A framework for conducting heat transfer analysis of nonuniformly heated plates using isogeometric analysis (IGA) is proposed. The modeling approach represents a method that is capable of capturing the full 3D thermal states of plate structures subjected to nonuniform heating. The formulation can be deemed a mixed IGA and control-volume scheme that describes the governing equations using a set of 2D lumped temperature layers. The non-matching grids between the fire domain and the solid domain are weakly coupled. Numerical results demonstrate that the approach is a suitable first step towards coupled CFD-IGA-based fire-structure simulation.

A study of a conductive laminar jet flow in an applied magnetic field

This study investigates steady two-dimensional laminar confined jet flow in the presence of an applied magnetic field. The magnetohydrodynamic equations with the format of the stream function and vorticity formulation of the fluid flow are solved numerically. A numerical method was developed by using a first-order upwind scheme at the boundaries and a second-order finite control volume scheme in the flow field. The results show that the expansion region of the jet is moving downstream while the channel width and the Reynolds number are increasing. The vortex and the recirculation zone are stretched with increased Hartmann number, and the jet expansion region is moving upstream while the vortex and the recirculation zone are reduced. The channel width and the Reynolds number for the jet development are positive efforts and the Hartmann number has a suppressed effect in the present confined jet flow field.

Time-dependent conductive heat transfer in rarefied polyatomic gases confined between parallel plates

The transient conductive heat transfer through a rarefied gas confined between two infinite parallel plates due to a sudden jump in the temperature of one of the plates is investigated in the whole range of the Knudsen number via kinetic theory. More specifically, the time-dependent heat transfer flow is modelled by the Holway kinetic model subject to diffuse boundary conditions. The governing integro-differential equation is numerically solved using the discrete velocity method in the molecular velocity space and typical finite control volume schemes in time and physical spaces. The time evolution of the density and temperature distributions as well as of the translational and rotational heat fluxes in terms of the two parameters characterizing the heat flow, namely the Knudsen number and the imposed temperature ratio between the plates is provided. The investigation is focused on the effect of the rotational degrees of freedom and a comparison between monatomic and polyatomic gases is performed. It is found that the time needed to reach the steady-state conditions varies between monatomic and polyatomic gases. In all cases the total time to recover the stationary solution in terms of the rarefaction parameter exhibits a minimum close to the well-known Knudsen minimum.

Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian (ALE) method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.

Compressibility Effects in 2d Wall Heating Microchannel flow

In this article we present a numerical solution of the Navier-Stokes equations and energy equation in parallel plate microchannels with the first order slip boundary conditions on the walls, adopting control volume scheme of CFD technique. Wall heating condition was considered on the walls. Noslip boundary conditions for compressible and incompressible flows were also solved to compare the effect of slip conditions. Compressibility effects were also investigated for compressible slip and compressible noslip flow conditions. A series of simulations were performed for different heights and lengths of channels and pressure ratios. Results are presented in graphs and tables and are compared with the available analytical and experimental results. It was found that the friction constants are the highest for noslip compressible flow and lowest for the slip flow against pressure ratio and mach numbers. Friction constant decreases continuously for compressible slip flow but it approaches to an asymptotic value of 96 for compressible noslip flow for the decrease of aspect ratio.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 57-71

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.

Improvement on Spherical Symmetry in Two-Dimensional Cylindrical Coordinates for a Class of Control Volume Lagrangian Schemes

AbstractIn, Maire developed a class of cell-centered Lagrangian schemes for solving Euler equations of compressible gas dynamics in cylindrical coordinates. These schemes use a node-based discretization of the numerical fluxes. The control volume version has several distinguished properties, including the conservation of mass, momentum and total energy and compatibility with the geometric conservation law (GCL). However it also has a limitation in that it cannot preserve spherical symmetry for one-dimensional spherical flow. An alternative is also given to use the first order area-weighted approach which can ensure spherical symmetry, at the price of sacrificing conservation of momentum. In this paper, we apply the methodology proposed in our recent work to the first order control volume scheme of Maire in to obtain the spherical symmetry property. The modified scheme can preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid, and meanwhile it maintains its original good properties such as conservation and GCL. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of symmetry, non-oscillation and robustness properties.

Pressure driven rarefied gas flow through a slit and an orifice

The flow of a monatomic gas through a slit and an orifice due to an arbitrarily large pressure difference is examined on the basis of the nonlinear Bhatnagar–Gross–Krook (BGK) model equation, subject to Maxwell diffuse boundary conditions. The governing kinetic equation is discretized by a second-order control volume scheme in the physical space and the discrete velocity method in the molecular velocity space. The nonlinear fully deterministic algorithm is optimized to reduce the computational effort by introducing memory usage optimization, grid refinement and parallelization in the molecular velocity space. Results for the flow rates and the macroscopic distributions of the flow field are presented in a wide range of the Knudsen number for several pressure ratios. The effect of the various geometric and physical parameters on the flow field is examined. Comparison with previously reported corresponding Direct Simulation Monte Carlo (DSMC) results indicates a very good agreement, which clearly demonstrates the accuracy of the kinetic algorithm and furthermore the reliability of the BGK model for simulating pressure driven flows.

An Eulerian‐Lagrangian control volume scheme for two‐dimensional unsteady advection‐diffusion problems

AbstractWe develop a mass conservative Eulerian‐Lagrangian control volume scheme (ELCVS) for the solution of the transient advection‐diffusion equations in two space dimensions. This method uses finite volume test functions over the space‐time domain defined by the characteristics within the framework of the class of Eulerian‐Lagrangian localized adjoint characteristic methods (ELLAM). It, therefore, maintains the advantages of characteristic methods in general, and of this class in particular, which include global mass conservation as well as a natural treatment of all types of boundary conditions. However, it differs from other methods in that class in the treatment of the mass storage integrals at the previous time step defined on deformed Lagrangian regions. This treatment is especially attractive for orthogonal rectangular Eulerian grids composed of block elements. In the algorithm, each deformed region is approximated by an eight‐node region with sides drawn parallel to the Eulerian grid, which significantly simplifies the integration compared with the approach used in finite volume ELLAM methods, based on backward tracking, while retaining local mass conservation at no additional expenses in terms of accuracy or CPU consumption. This is verified by numerical tests which show that ELCVS performs as well as standard finite volume ELLAM methods, which have previously been shown to outperform many other well‐received classes of numerical methods for the equations considered. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012

Numerical simulation of heat transfer in pressurized solidification of Magnesium alloy AM50

Based on finite difference and control-volume scheme, a model was developed to simulate fluid flow in forced convection and heat transfer in pressurized solidification of a cylindrical squeeze casting of magnesium alloy AM50. Pressure-dependent heat transfer coefficients (HTC) and non-equilibrium solidification temperatures were determined by experimental measurements. With the measured HTC and temperatures under the different pressures, the temperature distributions and the cooling behaviors of squeeze cast were simulated.