The Validity of Approximate Boundary Conditions for Natural Convection With Thermal Radiation in Open Cavities

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Om Singh ◽  
Shireesh B. Kedare ◽  
Suneet Singh
Keyword(s):  
Natural Convection ◽  
Boundary Conditions ◽  
Significant Loss ◽  
Computational Effort ◽  
Computational Domain ◽  
Maximum Difference ◽  
Open Cavities ◽  
Shallow Cavities ◽  
Approximate Boundary Conditions ◽  
The Difference

Abstract The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than  106 and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

scholarly journals Effects of Different Boundary Conditions at the Surfaces of the Extended Computational Domain in Computing the Natural Convection Flow in an Open Cavity

2016 ◽  
Vol 64 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Roushanara Begum ◽  
MZI Bangalee
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Open Cavity ◽  
Stream Line ◽  
Convection Flow ◽  
Computational Domain ◽  
Physical Domain ◽  
Natural Convection Flow ◽  
Different Boundary Conditions

Effects of different boundary conditions at the surfaces of the extended computational domain on buoyancy driven natural convection flow in a three dimensional open cavity are studied numerically. This study is carried out for turbulent flow where Rayleigh number is greater than 108. Air is used as working fluid having properties at 25°C temperature and 1atm pressure. To capture the turbulent nature of the flow k - ? model is used. ANSYS CFX software is used to solve the governing equations subject to the corresponding boundary conditions. The methodology is verified through a satisfactory comparison with some published results. Average mass flow, temperature, stream line, contour velocity and velocity profile are studied at different height. An extended computational domain around the physical domain of the cavity at different surrounding conditions is considered to investigate the effect of its existence on the computation. Effects of different surrounding boundary conditions on the physical domain of the cavity are studied and reported.A relation among non-dimensional parameters such as Nusselt number, Rayleigh number, Prandlt number and Reynolds number is also reported.Dhaka Univ. J. Sci. 64(1): 31-37, 2016 (January)

CFD Determination of Pre-Chamber Flow Pertubation Inlet Boundary Conditions for Seal Rotordynamics Models

2003 ◽  
Author(s):  
Ganesh Venkatesan ◽  
David L. Rhode
Keyword(s):  
Boundary Conditions ◽  
Operating Conditions ◽  
Test Cases ◽  
Computational Domain ◽  
New Approach ◽  
Flow Perturbation ◽  
Cfd Models ◽  
Approximate Boundary Conditions ◽  
Gas Seals

A new approach has been developed and utilized to determine the flow field perturbations (i.e. disturbances due to rotor whirl) upstream of a non-contacting seal. The results are proposed for use with bulk-flow perturbation and CFD-perturbation seal rotordynamic models, as well as with fully 3-D CFD models, to specify the approximate inlet boundary flow disturbance values at the computational domain inlet. The radially bulk-averaged disturbance quantities were evaluated in the upstream chamber from nearly 40 cases of geometry/operating conditions. The proposed upstream chamber boundary conditions are applicable for liquid as well as gas seals. For each of the measurement test cases considered, improved agreement with measurements was obtained when using the new boundary conditions, even though there was generally little room for improvement when not using the new boundary conditions. Based on the findings in this study it is recommended that the first-order correlations developed here be used to specify approximate boundary conditions at the domain inlet to be located in the upstream chamber.

Effect of Thermal Radiation on Accuracy of Restricted Domain Approach in a Square Open Cavity

2016 ◽  
Author(s):  
Om Singh ◽  
Suneet Singh ◽  
Shireesh B. Kedare
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Radiative Heat ◽  
Computational Time ◽  
Restricted Domain ◽  
Nusselt Numbers ◽  
Open Cavities ◽  
Cavity Opening ◽  
Approximate Boundary Conditions

To reduce computational time for simulation of natural convection in open cavities, it is quite common to use a domain restricted to the cavity with approximate boundary conditions at the cavity opening. It had been shown that such approach leads to quite accurate solutions for high Rayleigh number (Ra) flows. Such approach has been extended to flows involving radiative heat transfer as well. However, it is important to note that the effect of radiation on the accuracy of restricted domain approach has not been evaluated. In the present work, a comparison of Nusselt numbers is obtained by restricted domain approach with those obtained by using extended domain approach. The convective as well as radiative Nusselt numbers are considered for comparison for various values of Ra and radiation conduction parameter (Nr). It is observed that the accuracy of the restricted domain approach varies with the radiation conduction parameter as well and the approach is found to be quite accurate for high values of Nr.

Finite-Wellbore-Radius Solution for Gas Wells by Green's Functions

SPE Journal ◽  
2015 ◽  
Vol 20 (04) ◽  
pp. 842-855 ◽  
Author(s):  
Emilio P. Sousa ◽  
Abelardo B. Barreto ◽  
Alvaro M. Peres
Keyword(s):  
Line Source ◽  
Significant Loss ◽  
Computational Effort ◽  
Test Problems ◽  
Well Test ◽  
Gas Reservoirs ◽  
Gas Well ◽  
The Difference ◽  
Diffusivity Equation ◽  
Reservoir Simulator

Summary Even when written in terms of a pseudopressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, nonlinear because the viscosity/compressibility product is pseudopressure-dependent. However, several techniques and analysis procedures neglect such nonlinearity. A new methodology for constructing solutions for gas reservoirs through the Green's-function (GF) technique was recently proposed in the literature. Such methodology handles the viscosity/compressibility product variation rigorously, and it was successfully applied to solve several gas-well-test problems. In those problems, the wellbore is always represented by a line source. This work extends the theory a little further by considering a finite-wellbore-radius (FWR) boundary condition for a single vertical well producing at constant rate from an isotropic homogeneous and infinite gas reservoir. The proposed solution does not consider non-Darcy-flow effects, wellbore storage, and skin. Results from our FWR solution are compared with a commercial finite-difference reservoir simulator that shows a very close agreement. We also compared the FWR solution to the correspondent line-source solution to study the difference between the two solutions. As expected, the pseudopressure solutions by use of line-source and FWR boundary conditions do not match at early times, but they do agree at long times, which is exactly how FWR and line-source well solutions for slightly compressible fluids behave. It seems that, even for gas-well problems, the wellbore can be satisfactorily represented by a line source without significant loss of generality. The line-source assumption greatly simplifies the mathematics and the computational effort. This aspect is especially attractive for complex nonlinear gas-well problems that remain to be solved by the GF approach.

A Numerical Analysis of the Hemodynamic Functionality of Human Coronary Stenosis Under Different Physiologic Conditions and Boundary Condition Formulations

2019 ◽  
Author(s):  
Iyad Fayssal ◽  
Fadl Moukalled
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Functional Significance ◽  
Diffusion Flux ◽  
Computational Effort ◽  
Patient Specific ◽  
Computational Domain ◽  
Artery Disease ◽  
Outflow Boundary

Abstract Coronary artery disease (CAD) is among the foremost causes for human death worldwide. This study aims at investigating the performance of different boundary condition model types to characterize CAD functional significance. In addition, alternate models to estimate FFR using any different combination of boundary conditions at inlet and outlet were analyzed. In the first type of boundary condition, an outflow resistance model is used combined with a fixed pressure at inlet. In the second model of boundary conditions, constant pressure values are imposed at the domain inlet and outlet/s sections. In the third model, a zero diffusion flux is applied at outlet with a pre-specified flow rate at inlet. Numerical simulations performed on healthy and stenosed idealized and physiological arterial models revealed the superiority of the first type of boundary condition to directly capture the level of ischemia in diseased arteries. However, in this model, special numerical treatment at the outflow boundary is needed to dampen pseudo numerical reflections entering the computational domain. Alternative simple methods are developed to tackle the problem incurred in the second and third types of boundary condition types. The alternate models are effective for carrying extensive parametric studies with minimal computational effort. The new developed methods allow results generated via generic simulations under any specified boundary condition type to correctly estimate CAD functional significance. The obtained surrogate models account for the effects of the patient-specific physiologic parameters and can be easily incorporated without modifying existing CFD codes. Moreover, where it is unfeasible to experimentally incorporate the downstream effects of a given diseased arterial segment, an important aspect the alternative models provide is that they can be easily adopted by experimentalists through building in-vitro arterial models to assess the functional significance of the obstruction caused by the disease and its relation to any given patient specific physiologic parameter.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

Study of pumping effect in flow-through electrolysers

1983 ◽  
Vol 48 (8) ◽  
pp. 2232-2248 ◽  
Author(s):  
Ivo Roušar ◽  
Michal Provazník ◽  
Pavel Stuhl
Keyword(s):  
Natural Convection ◽  
Balance Equation ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Pumping Effect ◽  
Flow Through ◽  
The Mean ◽  
The Difference

In electrolysers with recirculation, where a gas is evolved, the pumping of electrolyte from a lower to a higher level can be effected by natural convection due to the difference between the densities of the inlet electrolyte and the gaseous emulsion at the outlet. An accurate balance equation for calculation of the rate of flow of the pumped liquid is derived. An equation for the calculation of the mean volume fraction of bubbles in the space between the electrodes is proposed and verified experimentally on a pilot electrolyser. Two examples of industrial applications are presented.

scholarly journals Mode Shape-Based Damage Detection Method (MSDI): Experimental Validation

2021 ◽  
Vol 11 (10) ◽  
pp. 4589
Author(s):  
Ivan Duvnjak ◽  
Domagoj Damjanović ◽  
Marko Bartolac ◽  
Ana Skender
Keyword(s):  
Boundary Conditions ◽  
Damage Detection ◽  
Mode Shape ◽  
Experimental Validation ◽  
Detection Method ◽  
Dynamic Properties ◽  
Damage Index ◽  
Main Principle ◽  
The Difference ◽  
Different Levels

The main principle of vibration-based damage detection in structures is to interpret the changes in dynamic properties of the structure as indicators of damage. In this study, the mode shape damage index (MSDI) method was used to identify discrete damages in plate-like structures. This damage index is based on the difference between modified modal displacements in the undamaged and damaged state of the structure. In order to assess the advantages and limitations of the proposed algorithm, we performed experimental modal analysis on a reinforced concrete (RC) plate under 10 different damage cases. The MSDI values were calculated through considering single and/or multiple damage locations, different levels of damage, and boundary conditions. The experimental results confirmed that the MSDI method can be used to detect the existence of damage, identify single and/or multiple damage locations, and estimate damage severity in the case of single discrete damage.

On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems

2003 ◽  
Vol 10 (3) ◽  
pp. 401-410
Author(s):  
M. S. Agranovich ◽  
B. A. Amosov
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Fourier Coefficients ◽  
Elliptic Boundary ◽  
A Priori ◽  
Adjoint Problem ◽  
Elliptic Boundary Value ◽  
Right Hand ◽  
The Difference ◽  
The Right

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.

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