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Buoyancy force is the defined as the force exerted on the body or an object when inserted in a fluid. Buoyancy force is based on the basic principle of pressure variation with depth, since pressure increases with depth. Hence buoyancy force arises as pressure on the bottom surface of the immersed object is greater than that at the top. Flow problems in buildings were studied since 700 B.C. Recent advancements in CFD and CAE have led to comprehensive calculation of buoyancy flows and flows in buildings. ==Calculation of buoyant flows and flow inside buildings== Since there is natural driven ventilation resulting from the difference in temperature inside the buildings hence flows inside buildings fall under buoyancy force category. The momentum equation in the direction of gravity should be modeled for buoyant forces resulting from buoyancy.〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics. Chapter:10. Retrieved 11 November 2013.〕 Hence the momentum equation is given by ∂ρv/∂t + V.∇(ρv)= -g((ρ-ρ°) - ∇P+μ∇2v + Sv In the above equation -g((ρ-ρ°) is the buoyancy term, where ρ° is the reference density. On discretizing the above equation several instabilities are be obtained during the solution process. Hence we use a transient approach as several relaxations are often required in obtaining a steady state solution. When applied to turbulent flows some additional modifications are to be applied to the calculation of buoyant flows. Hence an additional term is added, as recommended by Rodi(1978) in the k equation of the k- ε model is used below in modelling turbulent buoyant flows. Therefore, the k-equations takes the form〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics. Chapter:3. Retrieved 11 November 2013.〕 ∂ρk/∂t + ∇(ρku)= -g((ρ-ρ°) - ∇(τ∇×k) + G + B - ρε Where G= Usual Production or generation term〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics. Chapter:3.5.2. Retrieved 11 November 2013.〕 = 2µE.E B = Generation term related to buoyancy Also B = βgi (μ/σ) ∂T/∂xi Where, T = Temperature gi = Gravitational acceleration in x-direction β = Volumetric expansion coefficient = -(1/ρ) ∂ρ/∂T Hence for turbulent kinetic energy the modeled transport equation〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics. Page:218. Retrieved 11 November 2013.〕 is given as ∂ρε/∂t + ∇(ρεu) = ∇(τ∇×k) + C1ε (ε/k)(G+B)(1+C3 Rf ) - C2 ε ρ(ε2/k) Where, Rf = Flux Richardson number. C3 = Additional model constant. Flux Richardson number as defined by Hossain and Rodi (1976)〔H.K Versteeg & W. Malalasekera (1995). An introduction to Computational Fluid Dynamics.page:219. Retrieved 11 November 2013.〕 is Rf = -B/G. As C3 is close to unity in vertical buoyant shear layers and close zero in horizontal shear layers hence a single value of C3 cannot be used as Rf. Rf = - Gl/2(G+B) Where, Gl = Buoyancy production in lateral energy component. If we consider the horizontal shear layer where the lateral flow velocity component is in the direction of gravity, the production of buoyancy is given as Gl = 2B If we consider the vertical shear layer then the direction of gravity and the lateral component are normal to each other. Hence Gl = 0. Therefore, we obtain Rf = - B/(B+G) ------------ For horizontal layers Rf = 0 ------------- For vertical layers Finally in a given flow if vertical shear stresses are dominant then we can set Rf equal to zero and take C3 = 0.8. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Calculation of buoyancy flows and flows inside buildings」の詳細全文を読む スポンサード リンク
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