Characteristics of turbulent heat transfer in an annulus at supercritical pressure

Abstract

Heat transfer to fluids at supercritical pressure is different from heat transfer at lower pressures due to strong variations of the thermophysical properties with the temperature. We present and analyze results of direct numerical simulations of heat transfer to turbulent CO 2 at 8 MPa in an annulus. Periodic streamwise conditions are imposed so that mean streamwise acceleration due to variations in the density does not occur. The inner wall of the annulus is kept at a temperature of 323 K, while the outer wall is kept at a temperature of 303 K. The pseudocritical temperature T pc = 307.7 K, which is the temperature where the thermophysical properties vary the most, can be found close to the inner wall. This work is a continuation of an earlier study, in which turbulence attenuation due to the variable thermophysical properties of a fluid at supercritical pressure was studied. In the current work, the direct effects of variations in the specific heat capacity, thermal diffusivity, density, and the molecular Prandtl number on heat transfer are investigated using different techniques. Variations in the specific heat capacity cause significant differences between the mean nondimensionalized temperature and enthalpy profiles. Compared to the enthalpy fluctuations, temperature fluctuations are enhanced in regions with low specific heat capacity and diminished in regions with a large specific heat capacity. The thermal diffusivity causes local changes to the mean enthalpy gradient, which in turn affects molecular conduction of thermal energy. The turbulent heat flux is directly affected by the density, but it is also affected by the mean molecular Prandtl number and attenuated or enhanced turbulent motions. In general, enthalpy fluctuations are enhanced in regions with a large mean molecular Prandtl number, which enhances the turbulent heat flux. While analyzing the Nusselt numbers under different conditions it is found that heat transfer deterioration or enhancement can occur without streamwise acceleration or mixed convection conditions. Finally, through a combination of a relation between the Nusselt number and the radial heat fluxes, a quadrant analysis of the turbulent heat flux, and conditional averaging of the heat flux quadrants, it is shown that heat transfer from a heated surface depends on the density and the molecular Prandtl number of both hot fluid moving away from a heated surface as well as the thermophysical properties of relatively cold fluid moving towards it.

A heat transfer - friction analogy for fluids at supercritical pressure

“…The factors α A h , α Ac , c h and c c suggest that the contribution of the hot part to the Nusselt number is different from the contribution by the cold part. In a previous publication, we found evidence that this is indeed the case [18]. Equation ( 16) depends on P r h ≡ P r(T h ) and P r c ≡ P r(T c ).…”

“…In this paper, we present a new heat transfer model, which is based on our observations of direct numerical simulations of heated turbulent flows at supercritical fluids [18]. This model takes variable thermal conductivity, and specific heat capacity into account.…”

Fully Compressible Low-Mach Number Simulations of Carbon-dioxide at Supercritical Pressures and Trans-critical Temperatures

“…One dimensional rarefraction properties in compression shocks have been investigated recently by [ 12 ] for non-ideal gases close to the vapour-liquid critical point. [ 13 ] also investigates the heat transfer characteristics in fully developed turbulent flows of CO 2 in an annular geometry by simulating the low-Mach number approximation Navier-Stokes equations. In many previous works, such as [ 4 , 7 , 9 ] and [ 13 ], Navier-Stokes equations have been solved using the low-Mach number approximation, which takes into account changes in density due to changes in temperature, but ignores the effect of density changes due to the pressure variations.…”

“…[ 13 ] also investigates the heat transfer characteristics in fully developed turbulent flows of CO 2 in an annular geometry by simulating the low-Mach number approximation Navier-Stokes equations. In many previous works, such as [ 4 , 7 , 9 ] and [ 13 ], Navier-Stokes equations have been solved using the low-Mach number approximation, which takes into account changes in density due to changes in temperature, but ignores the effect of density changes due to the pressure variations. In order to further improve our understanding of the fluid dynamics of supercritical fluids and also to capture the compressibility effects, a fully compressible Navier-Stokes solver has been developed, which can include the effects of density changes due to the variation of both pressure and temperature.…”

Turbulence in a heated pipe at supercritical pressure

“…In a follow-up study (Peeters et al. 2017), the authors further analysed the data on the annular flow, specifically focusing on the behaviours of turbulent heat transfer under the influences of the variations of thermal properties. Based on the analyses of the budget of the turbulent heat transfer and quadrant analyses, the authors concluded that both the fluctuations and the mean gradients of the density and molecular Prandtl number had a significant influence on the turbulent heat flux.…”