arXiv subjects

Da-Sol Joo

Publications and source records attributed to Da-Sol Joo.

2 recordsLinked to original sources

arXiv2025

Analysis and reformulation of the $k$--$\omega$ turbulence model for buoyancy-driven thermal convection

The representation of buoyancy-driven turbulence in Reynolds-averaged Navier--Stokes (RANS) models remains unresolved, with no widely accepted standard formulation. A key difficulty is the lack of analytical guidance for incorporating buoyant effects, particularly under unstable stratification. This study derives an analytical solution of the standard $k$--$\omega$ model for Rayleigh--B\'enard convection in an infinite layer, where turbulent kinetic energy is generated solely by buoyancy. The solution provides explicit scaling relations among the Rayleigh ($Ra$), Prandtl ($Pr$), and Nusselt ($Nu$) numbers that capture the simulation trends: $Nu \sim Ra^{1/3} Pr^{1/3}$ for $Pr \ll 1$ and $Nu \sim Ra^{1/3} Pr^{-0.415}$ for $Pr \gg 1$. This framework quantifies the discrepancies in the conventional buoyancy treatment and clarifies their origin. Informed by this analysis, the buoyancy-related modeling terms are reformulated to recover the measured trends: namely $Nu \sim Pr^{1/8}$ for $Pr \ll 1$ and $Nu \sim Pr^{0}$ for $Pr \gg 1$ at moderate $Ra$. Only two dimensionless algebraic functions are introduced, which vanish in the absence of buoyancy, ensuring full compatibility with the standard closure. The corrected model is validated across a range of buoyancy-driven flows, including two-dimensional Rayleigh--B\'enard convection, internally heated convection in two configurations, unstably stratified Couette flow, and vertically heated natural convection with varying aspect ratios. Across all cases, the corrected model provides significantly improved predictions of mean temperature fields and turbulent heat flux distributions.

physics.flu-dyn↗

arXiv2025

A global similarity correction for the RANS modeling of natural convection in unstably stratified flows

This study proposes a global similarity correction for Reynolds-averaged Navier--Stokes (RANS) modeling of buoyancy effects in unstably stratified flows. Conventional two-equation RANS models (e.g., the $k$-$\varepsilon$ model) lack a clear criterion for incorporating unstable buoyancy effects in their scale-determining equations (e.g., $\varepsilon$-equation). To address this gap, a global correction function is introduced, derived from a generalized algebraic formulation that incorporates available potential energy as an additional parameter. This function reproduces a global similarity law commonly observed in natural convection flows--for instance, the correlation among the Nusselt, Rayleigh, and Prandtl numbers, which can be approximately expressed as a single power law over a wide parameter range. A calibration method is proposed in which an approximate analytical solution for Rayleigh--B\'enard convection is obtained via equilibrium analysis, confirming that the proposed model captures similarity relations not addressed by conventional one-point closures. Numerical results show significantly improved agreement with experimental data, accurately reproducing Nusselt number dependencies over broad ranges of Rayleigh and Prandtl numbers in unstably stratified flows, such as Rayleigh--B\'enard convection and two types of internally heated convection. The method remains fully compatible with standard RANS frameworks and reverts to traditional turbulence treatments in shear-driven flows where buoyant effects are negligible. By introducing only a single, simple, algebraic global function in the conventional $\varepsilon$-equation, this approach significantly enhances the accuracy and robustness of buoyancy-driven turbulence simulations.

physics.flu-dyn↗