Numerical Simulation of Natural Turbulent Convection with Vorticity Vector Formulation

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dc.contributor.authorOtulo, Onyango Filentinus
dc.contributor.authorAwuor, Kennedy Otieno
dc.date.accessioned2023-09-05T13:46:30Z
dc.date.available2023-09-05T13:46:30Z
dc.date.issued2023
dc.descriptionarticleen_US
dc.description.abstractBackground: Turbulent natural convection in an enclosure plays a big part in heat transmission and the building environment. Sophisticated buildings around the world are outfitted with costly heaters and coolers to maintain comfortable temperatures for human existence, manufacturing, and sophisticated farming methods, a scenario that many people cannot afford. Over a time, researchers have consistently developed a number of numerical study models to simulate the natural turbulent flow in these rectangular enclosures to solve complex problems associated with turbulent flows. In spite of several experimental studies and model simulations on the structure of natural turbulence convection, the fundamental mechanism in turbulent phenomena is still incomplete. Significant variations in experimental data and model simulation data in previous studies have been noted. This is because the unknown turbulent correlation coefficients resulting from the nonlinear terms of the turbulent flow control equations make it difficult to accurately determine fluid flow variables such as mean velocity distribution, temperature distribution and kinetic energy in a model simulation. Thus, an accurate numerical prediction of natural turbulence convection is crucial to solving the nonlinear equations for subsequent practical applications. Methodology: The performance of a numerical turbulence model k-ε in estimating the amount of heat transfer that occurs as a result of the naturally occurring turbulent convection that takes place within an air-filled rectangular enclosure is investigated in this work using vorticity vector formulation. The workflow of simulating the heat transfer which results from the action of natural convection within an enclosed rectangular cavity takes into account the effect of turbulence for the Rayleigh numbers Ra = 1.552 × 1010, Ra = 9.934 × 1011, Ra = 1.552 × 1013 and Ra = 2.425 × 1014. The Low-Reynolds-number turbulence. k-ε model was employed in this numerical study to model the non-linear relations 𝛻⋅𝜌𝑢′𝑢′̅̅̅̅̅̅̅̅̅̅̅and 𝜕𝐶𝑝𝑇′𝑢′𝜕𝑥𝑖 in the averaged Navier Stokes equation and energy equation respectively to complete the governing equations. Apart from the hot and cold walls, which are maintained at 308K and 288K, respectively, all of the walls of the enclosure are adiabatic. The vorticity vector formulation allowed the pressure term to be removed from the momentum equation. Finite difference approximations were used in the FLUENT program to solve the vorticity, energy, vector potential, and two resultant equations for each model together with their boundary conditions. Results and Conclusion: The outcomes of the study for the distribution of the velocity and temperature components are presented, demonstrating that the number of contours and vortices increases proportionally with the Rayleigh Number. In addition, a higher Rayleigh number indicates more turbulence, which in turn implies a higher absolute value of the velocity hence increased Kinetic energy.en_US
dc.identifier.citationFilentinus, O. O., & Otieno, A. K. Numerical Simulation of Natural Turbulent Convection with Vorticity Vector Formulation.en_US
dc.identifier.issn2278-5728
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/26892
dc.language.isoenen_US
dc.publisherIOSR-JMen_US
dc.subjectVorticity vector formulationen_US
dc.subjectVorticityen_US
dc.subjectStream functionen_US
dc.subjectVector potentialen_US
dc.subjectReynold stressen_US
dc.titleNumerical Simulation of Natural Turbulent Convection with Vorticity Vector Formulationen_US
dc.typeArticleen_US
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