Date (1996) introduced a pressure-correction equation containing mass-conserving and smoothing pressure correction terms to solve the Navier-Stokes equations. The benefit of the smoothing terms is satisfying the stoke...
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Date (1996) introduced a pressure-correction equation containing mass-conserving and smoothing pressure correction terms to solve the Navier-Stokes equations. The benefit of the smoothing terms is satisfying the stokes's relation which is often overlooked as well as overcoming the decoupling problem of the pressure-velocity fields, which renders it applicable to collocated (non-staggered) grids. His derivation relied on assumptions relevant to the simple algorithm (Caretto et al., 1972). Such assumptions are, unfortunately, not directly applicable to simpleC procedures (van Doormaal and Raithby, 1984). The main purpose of this paper is to extend the pressure-correction equation proposed by Date (1996) to simpleC algorithms.
Quasi-steady gas-phase combustion of Jatropha bio-diesel in a mixed convective air environment is studied both experimentally and numerically. Porous sphere experiments have been conducted to measure the mass burning ...
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Quasi-steady gas-phase combustion of Jatropha bio-diesel in a mixed convective air environment is studied both experimentally and numerically. Porous sphere experiments have been conducted to measure the mass burning rates and observe the flame shapes of spherical particles fed with bio-diesel. A numerical model has been developed to simulate the experiments. The Jatropha bio-diesel has been considered as a single component fuel (C18H34O2). Transient governing equations in the gas-phase alone are solved through the finite volume approach employing non-orthogonal control volumes in a semi-collocated mesh. Thermo-physical properties are evaluated based on the local temperature and the species concentrations. A single step global reaction with five species (C18H34O2, O-2, N-2, CO2 and H2O) is employed to model the finite rate kinetics. Results have been obtained for a range of mixed convective flow conditions. Comparisons of the results with those of diesel combustion have been made in few cases. It is observed that the burning rate of bio-diesel is less by about 11% than those for diesel for the same air velocity and sphere size. (C) 2008 Elsevier Ltd. All rights reserved.
In this paper, we present a simple based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formu...
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In this paper, we present a simple based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formulae (BDF) of varying order from 1 to 4. We show that the original equation for the pressure correction can be modified by using an equivalent operator stemming from the symmetric interior penalty (SIP) method leading to a reduced stencil *** assess the accuracy as well as the stability and the performance of the scheme, three different test cases are carried out: the Taylor vortex flow, the Orr-Sommerfeld stability problem for plane Poiseuille flow and the flow past a square cylinder. (1) Simulating the Taylor vortex flow, we verify the temporal accuracy for the different BDF schemes. Using the mixed-order formulation, a spatial convergence study yields convergence rates of k + 1 and k in the L-2-norm for velocity and pressure, respectively. For the equal-order formulation, we obtain approximately the same convergence rates, while the absolute error is smaller. (2) The stability of our method is examined by simulating the Orr-Sommerfeld stability problem. Using the mixed-order formulation and adjusting the penalty parameter of the symmetric interior penalty method for the discretization of the viscous part, we can demonstrate the long-term stability of the algorithm. Using pressure stabilization the equal-order formulation is stable without changing the penalty parameter. (3) Finally, the results for the flow past a square cylinder show excellent agreement with numerical reference solutions as well as experiments. Copyright (c) 2015 John Wiley & Sons, Ltd.
A numerical investigation has been made of natural convection heat transfer in a trapezoidal enclosure (representing attic spaces) with offset baffles. Two thermal boundary conditions representing summerlike condition...
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A numerical investigation has been made of natural convection heat transfer in a trapezoidal enclosure (representing attic spaces) with offset baffles. Two thermal boundary conditions representing summerlike conditions (upper surface heated) and winterlike conditions (upper surface cooled) and two baffle heights are studied. For each boundary condition and baffle height, two baffle positions are considered. In position I, the upper baffle is offset toward the heated vertical wall and the lower baffle is offset toward the symmetry plane of the enclosure, whereas in position II, the upper baffle is offset toward the symmetry plane and the lower baffle is offset toward the heated wall. Rayleigh number values range from 10(3) to 5 x 10(7) for summerlike conditions and from 10(3) to 10(6) for winterlike conditions. Predictions reveal a decrease in heat transfer in the presence of baffles. In winterlike conditions, convection starts to dominate at a Rayleigh number much lower than that in summerlike conditions. The maximum reduction in heat transfer is achieved with long baffles placed in position II for summerlike conditions and in position I for winterlike conditions. Average Nusselt number correlation for both boundary conditions are presented.
In this work, Free Element method (FECM) is extended to solve incompressible Navier-Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoint...
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In this work, Free Element method (FECM) is extended to solve incompressible Navier-Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoints are interpolated by improved Momentum Interpolation Method to avoid oscillation caused by decoupling of velocity and pressure. At last, the pressure correction equation is solved to make sure the results satisfying continuity equation. The interpolation of midpoint's velocity is proved to be independent of the under-relaxation factor and time step size. The deferred correction is employed for utilization of higher-order discretization of convective terms. Taylor-Green vortex, flow over a cylinder, lid-driven flow, cooling tunnel, and flow over airfoil are simulated. The results computed by the proposed method are compared with exact solutions and benchmark solutions, which indicates that the new method has the second order accuracy in space. What is more, the proposed method works well on random node distributions as well, which means that the method is much robust.
In this paper, numerical simulation of motion and dispersion of pollutant emissions into the atmosphere under real atmospheric conditions were considered. To solve this problem, a system of Reynolds-averaged Navier-St...
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In this paper, numerical simulation of motion and dispersion of pollutant emissions into the atmosphere under real atmospheric conditions were considered. To solve this problem, a system of Reynolds-averaged Navier-Stokes equations was used, and the standard k-epsilon and SST k-omega turbulence models were used to close this system of equations. Moreover, the test problem was solved numerically to verify the mathematical model and numerical algorithm. The obtained numerical results were compared with the experimental data and modeling results of well-known authors. A proven mathematical model and numerical algorithm was used to describe the process of pollutant emissions from Ekibastuz SDPP (Ekibastuz State District power plant) chimneys and the spread of CO2 in the air flow field under real atmospheric conditions. For this problem, four different speed regimes (the first-0.5 m/s and 1 m/s, the second-1 m/s and 1.5 m/s, the third-2 m/s and 4 m/s, and the fourth-4 m/s and 5 m/s), as well as three different temperature regimes (constant temperature, decrease temperature, and temperature inversion) were considered.
Finite volume methods with co-located variables for incompressible flow suffer from spurious pressure oscillations unless a stabilization method is applied. Variations of the pressure-weighed interpolation (PWI) metho...
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Finite volume methods with co-located variables for incompressible flow suffer from spurious pressure oscillations unless a stabilization method is applied. Variations of the pressure-weighed interpolation (PWI) method are typically used for this purpose. But the PWI method does not only prevent spurious oscillations. Counter-intuitively, it also simplifies the approximation of the Schur complement (pressure matrix) which appears in iterative solution methods such as simple. (C) 2015 Elsevier Inc. All rights reserved.
A computational code has been developed based on finite-volume method (FVM) to investigate fluid flow-through roughwalled rock fractures during shear processes, considering evolutions of aperture and contact area with...
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A computational code has been developed based on finite-volume method (FVM) to investigate fluid flow-through roughwalled rock fractures during shear processes, considering evolutions of aperture and contact area with shear displacement. In the code, the full 3-D Navier-Stokes equation is solved in a cell-centered collocated variable arrangement and the pressure-velocity coupling is performed using the simple algorithm. A series of coupled shear-flow tests under constant normal stress of 3 MPa with different shear displacements of 1-10 mm were conducted and their results were compared with numerical simulations results. The comparison shows good agreement between the simulated and measured results. Aperture distribution during shear was evaluated by superimposing the upper and lower fracture surfaces according to the initial aperture and dilation at different shear displacements. The results show that contact area evolution dominates the variations of flow rate as well as flow pattern in a rough fracture. In addition, there is a linear relationship between aperture coefficient of variation and contact area ratio during shear. The simulation results also demonstrate the deviation of velocity profiles from the ideal parabolic form in some regions due to the formation of eddy flows. This behavior may have been caused by the inertial effects, which can be characterized by the Navier-Stokes equation, while some simplified equations such as Reynolds equation or Stokes equation cannot capture these effects.
作者:
DEMUREN, AONASA
LEWIS RES CTR INST COMPUTAT MECH PROP CLEVELAND OH 44135 USA
Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations ar...
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Calculation methods for turbulent duct flows are generalized for ducts with arbitrary cross sections. The irregular physical geometry is transformed into a regular one in computational space, and the flow equations are solved with a finite-volume numerical procedure. The turbulent stresses are calculated with an algebraic stress model derived by simplifying model transport equations for the individual Reynolds stresses. Two variants of such a model are considered in the present study. These procedures enable the prediction of both the turbulence-driven secondary flow and the anisotropy of the Reynolds stresses, in contrast to some of the earlier calculation methods. The importance of the secondary Reynolds shear stress is stressed, but there are no reliable experimental data for this component. Model predictions are compared to experimental data for developed flow in a triangular duct and a rod-bundle geometry. The correct trends are predicted, and the quantitative agreement is mostly fair. The simpler variant of the algebraic stress model procured better agreement with measured data.
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