Lattice Boltzmann Modelling of Natural Convection Problems in a Cavity with a Different Wall Temperature

Year 2025, Volume: 29 Issue: 2, 151 - 159, 30.04.2025

Erman Aslan , Özlem Yalçın

https://doi.org/10.16984/saufenbilder.1615457

Abstract

In this study, the cyclic natural convection problem in a square enclosure is modeled using the Lattice Boltzmann Method (LBM) under laminar flow conditions. Four different combinations of boundary conditions are employed to create cases. These cases are denoted as HHHC (Horizontal Hot Horizontal Cold), HHVC (Horizontal Hot Vertical Cold), VHHC (Vertical Hot Horizontal Cold), and VHVC (Vertical Hot Vertical Cold). Four Rayleigh numbers have been utilized to represent laminar flow conditions, namely Ra=104, 105, 106, and 107. For validation purposes, the well-validated finite volume method-based commercial code Ansys-Fluent is employed. In the VHVC model and at the highest Rayleigh number, the results obtained with LBM were compared to and validated against the results obtained with the finite volume method. Nusselt numbers are compared for the four cases based on Rayleigh numbers, and the case with highest heat transfer identified. Cases of HHHC and VHVC have produced the lowest and highest Nusselt number, respectively.

Keywords

Lattice Boltzmann Method, Natural convection, Computational fluid dynamics, Laminar flow, Nusselt number

Farklı Duvar Sıcaklıklarına Sahip Bir Oyukta Doğal Taşınım Problemlerinin Lattice Boltzmann Modelleme Yöntemiyle İncelenme

Abstract

Bu çalışmada, bir kare kapalı alanda döngüsel doğal taşınım problemi, laminar akış koşulları altında Lattice Boltzmann metodu (LBM) kullanılarak modellenmiştir. Farklı durumları oluşturmak için dört farklı sınır koşulu kombinasyonu kullanılmıştır. Bu durumlar HHHC (Yatay Sıcak Yatay Soğuk), HHVC (Yatay Sıcak Dikey Soğuk), VHHC (Dikey Sıcak Yatay Soğuk) ve VHVC (Dikey Sıcak Dikey Soğuk) olarak adlandırılmıştır. Laminar akış koşullarını temsil etmek için dört farklı Rayleigh sayısı kullanılmıştır: Ra=10⁴, 10⁵, 10⁶ ve 10⁷. Doğrulama amacıyla, iyi doğrulanmış sonlu hacim metodu tabanlı ticari Ansys-Fluent kodu kullanılmıştır. VHVC modelinde ve en yüksek Rayleigh sayısında, LBM ile elde edilen sonuçlar, sonlu hacim metodu ile elde edilen sonuçlarla karşılaştırılmış ve doğrulanmıştır. Nusselt sayıları, Rayleigh sayıları bazında dört durum için karşılaştırılmış ve en yüksek ısı transferini sağlayan durum belirlenmiştir. HHHC ve VHVC durumları sırasıyla en düşük ve en yüksek Nusselt sayısını üretmiştir.

Keywords

Doğal Taşınım, Hesaplamalı Akışkanlar Dinamiği, Laminer Akış, Nusselt Sayısı, Lattice Boltzmann Metodu

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