LATTICE BOLTZMANN YÖNTEMİ İLE EŞLENİK ISI TRANSFERİ HESABI

Grafik İşlem Birimi üzerinde eşlenik ısı transferi problemlerini çözebilen bir lattice Boltzmann Metodu çözücüsü geliştirdik. Geliştirilen çözücü, D2Q9 tipi hücrelerden meydana gelen Kartezyen bir ağ kullanmakta ve zamana bağlı ısı denklemlerini akış alanına ait makroskobik büyüklükler elde edildikten sonra hem akışkan hem de katı üzerinde aynı anda çözmektedir. Geliştirilen ısıl çözücü daha önceden geliştirilmiş ve test edilmiş akış çözücüsü üzerine inşa edilmiştir. Her iki çözücü de NVIDIA'nın paralel hesaplama platform ve programlama modeli olan CUDA ile programlanmıştır. Isıl çözücü ilk olarak katıdaki ısıl iletim problemleri için test edilmiş, ardından eşlenik ısı transferi problemleri, akışkan ve katı bölgelerde aynı anda çalışacak şekilde tasarlanmış ısıl çözücü ve akış çözücüsü kullanılarak çözülmüştür. Elde edilen sonuçların literatürdeki analitik ve hesaplamalı sonuçlarla karşılaştırılması geliştirilen çözücünün eşlenik ısı transferi problemlerini gerçekçi bir şekilde modelleyebildiğini göstermiştir. Geliştirilen çözücünün doğrulanmasının ardından, bir eşlenik ısı transferi değerlendirme problemi olan aniden genişleyen sonlu kalınlıklı duvara sahip bir kanal boyunca ısı ve kütle akışı problemi tekrar ele alınmıştır. Prandtl ve Reynolds sayısı gibi parametrelerin farklı değerleri için katı-sıvı ara yüzeyindeki sıcaklığı dağılımları elde edilmiştir. Elde edilen sonuçların literatürdeki mevcut sonuçlar arasındaki tutarsızlığı açıklamaya katkıda bulunacağı düşünülmektedir. Geliştirilen çözücünün en önemli sorunu rakiplerine kıyasla belirgin bir şekilde daha yoğun bir ağa ihtiyaç duymasından kaynaklanan daha uzun olan hesaplama zamanıdır. Bu çalışmada, söz konusu dezavantaj geliştirilen çözücünün Grafik İşlem Birimi üzerinde koşacak şekilde tasarlanması ile aşılmıştır.

CONJUGATE HEAT TRANSFER COMPUTATIONS VIA LATTICE BOLTZMANN METHOD

We developed a lattice Boltzmann Method code that is able to solve conjugate heat transfer problems on graphical processing unit. The solver uses Cartesian meshes of DQ lattices and solves transient heat equation on both fluid and solid regions at once after obtaining the macroscopic quantities from the flow field. The newly developed thermal solver was constructed on the previously developed and verified flow solver. Both solvers were coded using parallel computing platform and programing model of NVIDIA, Compute Unified Device Architecture (CUDA). The thermal solver was tested first for the problems of conduction in solid, then conjugate heat transfer problems were solved using the fluid and thermal solvers in conjunction. The thermal solver was designed to run on both solid and fluid regions. Comparison of the obtained results with the analytical and the computational results available in the literature show that the developed solver is able to model conjugate heat transfer problem realistically. After verification of the solver, a conjugate heat transfer benchmark problem, heat and mass transfer through a suddenly expanded channel with finite thickness of wall was revisited. Solid-fluid interface temperature distributions were obtained for different values of parameters such as Prandtl and Reynolds numbers. These results hopefully contribute to clarify the mismatch between the results available in the literature. The main drawback of the LBM solver is its relatively longer computational time compared to its rivals because of its considerably dense mesh needs. In this study, this drawback is resolved by designing the solver to be able to run on GPU.

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