Inverse shape design for heat conduction problems via the ball spine algorithm

Mayeli, Peyman; Nili-Ahmadabadi, Mahdi; Besharati-Foumani, Hossein

doi:10.1080/10407790.2015.1096690

Cited by 19 publications

(6 citation statements)

References 39 publications

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“…Based on equation ( 5) and according to the considered range of , the corresponding Froude number range is 0 ≤ ≤ 0.6/ . The governing equations are solved using a control-volume finite element solver [11][12][13][14][15][16][17][18] with a second-order temporal accuracy. A mesh resolution study is performed and it is found that a mesh size of × = 121 2 makes the problem independent of mesh size for both approximations in considered range of the and .…”

Section: Resultsmentioning

confidence: 99%

Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach

Mayeli¹,

Tsai²,

Sheard³

2020

Australasian Fluid Mechanics Conference (AFMC)

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In this study, a benchmark natural convection problem is studied under a Gay-Lussac type approximation incorporating centrifugal effects in the context of a new vorticity-streamfunction approach. This approximation differs from the classic Boussinesq approximation in that density variations are considered in the advection term as well as the gravity term in the momentum equations. Such a treatment invokes Froude number as a non-Boussinesq parameter deviating results from the classic Boussinesq approximation. Numerical simulations of the natural convection in square cavity are performed up to = 10 6 and = 0.3 at = 0.71 via proposed formulation and results are compared against the conventional Boussinesq approximation in terms of the average and local Nusselt number and entropy generation. Comparing results indicate that, up to = 10 5 , mentioned approaches are showing almost identical performance, but as the Rayleigh number exceeds 10 5 , formed thermal boundary layer under Gay-Lussac type approximation is slightly thicker compared to the Boussinesq approximation accompanied by a stronger velocity gradient.

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Section: Resultsmentioning

confidence: 99%

Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach

Mayeli¹,

Tsai²,

Sheard³

2020

Australasian Fluid Mechanics Conference (AFMC)

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“…The solver has been validated in several previous studies. [30][31][32][33][34] A mesh resolution study was conducted on the present problem; it was determined that a mesh having 181 azimuthal and 91 radial elements provided six significant figures of accuracy for pertinent measured quantities.…”

Section: The Annulus Enclosure and Numerical Considerationsmentioning

confidence: 99%

An efficient and simplified Gay‐Lussac approach in secondary variables form for the non‐Boussinesq simulation of free convection problems

Mayeli

Sheard

2021

Numerical Methods in Fluids

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The Gay-Lussac (GL) approach is an incompressible-based strategy for non-Boussinesq treatment of the governing equations for free convection problems that is established based on extending the density variations beyond the gravity term. Such a strategy leads to emerging the GL parameter as a non-Boussinesq prefactor of different terms in the governing equations. In this article, the GL approach is expressed/discussed in terms of the secondary variables, that is, vorticity and stream-function, for the first time and a simplified version of this approach is proposed by removing density variations from the continuity equation. The difference of results under the simplified and traditional GL approach ranges within a maximum of 1% for different parameters. The lower computational cost of numerical solution of governing equations in the secondary variables formula and the corresponding convergence rate is scrutinized for the simplified GL approach showing around 25% lower computational cost. The performance of this approach is evaluated at high relative temperature differences against the low Mach number scheme and the Boussinesq approximations. In this respect, natural convection in an annulus cavity is numerically simulated using a CVFEM solver under the aforementioned approximations up to Rayleigh number Ra = 10 5 at Prandtl number Pr = 1 and high relative temperature differences ( = 0.15 and 0.3).The largest deviations found for either the simplified GL or Boussinesq methods from the low Mach number scheme solution are less than 20% for velocity magnitude, 14% for stream function, 6% for vorticity, and 5% for temperature. Results under the three approximations are also analyzed in terms of the skin friction and local and average Nusselt number, indicating that the Gay-Lussac approach requires some revisions to act more accurately than the classical Boussinesq approximation at high relative temperature differences in natural convection problems, especially within the convection dominated regime.

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“…Convergence criteria is considered as the maximum variation of the velocity and temperature fields over all nodes during two successive iterations less than 10 −7 . Accurate performance of the developed solver has already been validated in References 39‐46, but here it is evaluated by comparing the radial temperature profiles at three different angles including δ = 0 o , 90 o , and 180° vs dimensionless radius (

\overset{true˜}{r} = r - r_{i} / r_{o} - r_{i}

) at Ra = 5 × 10 4 for air with Pr = 0.706. Computed profiles are plotted in Figure 2 and are compared with the results of Kuhen and Goldstein 8 .…”

Section: Description Of the Problemmentioning

confidence: 99%

A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem

Mayeli

Sheard

2020

Numerical Methods in Fluids

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Summary Traditionally, the Boussinesq approximation is adopted for numerical simulation of natural convection phenomena where density variations are supposed negligible except through the gravity term of the momentum equation. In this study, a recently developed formulation based on a Boussinesq approximation is presented in which the density variations are also considered in the advection terms. Extending density‐variations to the advection terms captures centrifugal effects arising from both bulk enclosure rotation and within individual vortices, and thus more accurate results are expected. In this respect, the results of the proposed formulation are compared against the conventional Boussinesq simulations and weakly compressible approximation in the concentric horizontal annulus cavity. A new relation is established which maps the magnitude of the non‐Boussinesq parameter of incompressible flow to the corresponding relative temperature difference of a compressible flow simulation which is in agreement with the maximum allowed Gay‐Lussac number to avoid unphysical density values. For comparison purposes, variations of different thermo‐fluid parameters including average and local Nusselt number, entropy generation, and skin friction up to Ra = 105 are computed. Results obtained under the proposed approximation agree with the classical Boussinesq approximation up to Ra = 103 for large non‐Boussinesq parameter corresponding to the large relative temperature difference, but at Ra = 105, computed thermo‐fluid parameters via the two approaches are not identical which justifies the inclusion of large Gay‐Lussac number for convection dominated regime in natural convection problems.

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Inverse shape design for heat conduction problems via the ball spine algorithm

Cited by 19 publications

References 39 publications

Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach

Studying the natural convection problem in a square cavity by a new vorticity-stream-function approach

An efficient and simplified Gay‐Lussac approach in secondary variables form for the non‐Boussinesq simulation of free convection problems

A centrifugal buoyancy formulation for Boussinesq‐type natural convection flows applied to the annulus cavity problem

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