Turbulence modelling for supercritical pressure heat transfer in upward tube flow

• Major assumptions of the turbulent models which may result in limitation of application in supercritical pressure heat transfer are discussed.
• Performance of three turbulence models in supercritical pressure heat transfer in upward flow is investigated by comparing with the DNS data.
• Comparing with the others, the EB-AFM appears promising as a candidate for further optimization.

Performance of turbulence modelling for supercritical pressure heat transfer in a upward tube flow is investigated by modelling the case simulated by (Bae et al., 2005) with the direct numerical simulation (DNS). Three major assumptions, i.e. (∂p¯/∂xi)≅ρ¯gi, ρ′=−βρ¯t′ and ρu″ih″¯≅Cpρu″it″¯ are pointed out as the major limitation of existing turbulent models for their application in supercritical pressure heat transfer in an upward flow. For the sake of model evaluation three representative model combinations are selected, i.e. (i) the General Gradient Diffusion Hypothesis (GGDH) model (buoyancy production of turbulent kinetic energy) and the Simple Gradient Diffusion Hypothesis (SGDH) model (heat flux), (ii) the Algebraic Flux Model (AFM) (both buoyancy production of turbulent kinetic energy and heat flux), (iii) the Elliptic Blending-Algebraic Flux Model (EB-AFM) (both buoyancy production of turbulent kinetic energy and heat flux). In general, prediction of turbulent kinetic energy by the EB-AFM model agrees with the DNS data better than the other two. And the agreement is especially good in the near-wall region. Similar to the turbulence kinetic energy, prediction of the radial turbulent heat flux by the EB-AFM model is good in the near-wall region. Good performance of the EB-AFM model in the near-wall region implies that the model holds the correct asymptotic feature towards the wall. In the bulk performance of the EB-AFM model is unsatisfactory because of strong variation of fluid properties. The GGDH + SGDH and AFM model fail to predict the streamwise turbulent heat flux, while the EB-AFM model can qualitatively predict it. The direct simulation by Bae et al. showed that the heat transfer recovery in the downstream is due to negative ∂(ρu″xh″)/∂x∂(ρu″xh″)/∂x. The investigated models do not predict such a phenomenon. Recovery of heat transfer is predicted by the EB-AFM model mainly due to more efficient heat transfer in the radial direction in the downstream. Contrary to the other models, the EB-AFM appears promising aspects as a candidate for further optimization.