Development of an explicit algebraic turbulence model for buoyant flows – Part 2: Model development and validation

• Development of an explicit algebraic Reynolds stress model for buoyant flows.
• Development of an explicit algebraic turbulent heat flux model for buoyant flows.
• Use of elliptic blending model for wall regions.
• Validation on differentially heated turbulent vertical channel flow for forced, mixed and natural convection regime.

A new model for buoyancy driven flows is proposed. It couples an Explicit Algebraic Reynolds Stress Model (EARSM) and an Explicit Algebraic Heat Flux Model (EAHFM) aiming to reproduce the coupled effects of flow dynamics and heat transfer via the buoyancy terms. The new model is based upon the Wallin and Johansson (2000) model for the EARSM and upon the Wikström, Wallin and Johansson (2000) model for the EAHFM. The two models are extended to account for buoyancy. Wall treatments based on the elliptic blending technique for both EARSM and EAHFM   are implemented. A k-ω-kθ-rk-ω-kθ-r model supplies the turbulent scales, solving transport equations for the turbulent kinetic energy, the specific dissipation and half the thermal variance together with an algebraic equation for the turbulent time-scale ratio. The coupling is performed by an iterative process. This model allows to consider the buoyancy and wall blocking effects whatever the flow configuration. Applications of the new model on the differentially heated vertical plane channel flow lead to encouraging results whatever the convection regime.