A New Approach to Correlate Heat Transfer Data for Turbulent Flow in Smooth Pipes Based on Generalization of Reynolds Number

NUMERICAL INVESTIGATION OF TURBULENT HEAT TRANSFER OVER ROUGH SURFACES AT MEDIUM–HIGH PRANDTL NUMBERS

Wall-resolved Large Eddy Simulations are performed to investigate turbulent heat transfer in a rough pipe over a range of Pr. The roughness is generated using a controlled numerical procedure that allows independent specification of roughness correlation length, amplitude, and skewness; a statistically Gaussian height distribution is considered as a baseline case. Simulations are conducted at a bulk Re of 11,700 for Pr = 0.5, 1, 2, and 5, and are extended to additional Re=2000-15000 to assess the robustness of global trends. Time-averaged velocity and temperature profiles, turbulent heat fluxes, and Re stresses are analyzed to examine the interaction between roughness-induced mixing and Pr dependent thermal diffusion. Relative to a smooth pipe, the rough surface produces a systematic downward shift of the mean temperature profile, indicating enhanced heat transfer across all Pr. A sheltering analysis based solely on surface visibility to the incoming flow distinguishes weakly ventilated regions with suppressed heat transfer from exposed windward faces that host intense thermal events. A complementary zonal analysis based on roughness height shows that local heat-transfer enhancement becomes increasingly sensitive to surface elevation as Pr increases. For the Gaussian-type roughness considered here, however, the overall influence of Pr on global and local heat-transfer statistics remains comparatively modest, suggesting a dominant role of geometric sheltering effects. Re sweeps of global metrics further demonstrate that roughness-induced heat-transfer enhancement increase monotonically with Re, confirming that the identified mechanisms persist across a broader range of operating conditions.

New Apparent Friction Factor Correlations for Developing and Fully Developed Laminar Flows in Rectangular Microchannels Via CFD Modeling

A three-dimensional laminar flow for 37 Reynolds numbers, primarily in low Reynolds number regime with water flow through six rectangular microchannels have been modeled conducting 222 simulations to develop correlations for fully developed friction factor and incremental pressure drop number to determine apparent fRe. Results from the present simulations were validated by comparing the fully developed velocity profile, friction factor, and incremental pressure drop number for Re > 100 in rectangular channels reported in the literature. Three new correlations were created from a vast array of numerical data generated from these simulations. First, a new fRe correlation was developed to include all aspect ratios, with a mean and maximum deviation of 0.14% and 0.26%, respectively, from the numerical results. Next, a correlation for the fully developed incremental pressure drop number, K(∞), was developed as a function of aspect ratio and Reynolds number. This correlation was in good agreement with the numerical data, with a mean deviation of 1.75% and a maximum deviation of 4.99%. The final correlation developed was for the incremental pressure drop number, K(z), in the developing region as a function of the non-dimensional axial distance, the aspect ratio, and the Reynolds number. The correlation was in good agreement with the numerical data, with a mean deviation of 0.80% and a maximum deviation of 5.93%. The local fapp,zRe, can be determined using the three correlations, with a maximum deviation of 8.23%, compared with the numerical results.

HEAT TRANSFER FROM A CIRCULAR

Compressible Temperature Transformation Toward Law of the Wall in Turbulent Channel Flows

For compressible wall-bounded turbulence, the logarithmic law for velocity profiles has been extensively investigated through various successful velocity transformations, yet a robust counterpart for the mean temperature remains absent. To bridge this gap, the present study introduces a novel temperature transformation tailored for compressible turbulent channel flows, based on the integrated momentum and energy balances. This approach explicitly incorporates the effects of the external driving force and its work on the fluid while employing the total-heat-flux-based temperature scale that aligns with the well-established Mach-number-invariant function in the velocity field. Extensive direct numerical simulation (DNS) validations (26 cases) involving a wide range of bulk Mach numbers (ranging from 0.7 to 4.0) and Reynolds numbers (ranging from 3000 to 34,000) demonstrate that the proposed transformation effectively maps the mean temperature profiles to the incompressible reference without case-specific tuning, exhibiting superior performance compared to existing temperature transformations.

Flow and Heat Transfer Characteristics of Forced Convection Past an Isoflux Circular Cylinder in Galinstan for Reynolds Numbers up to 600

A numerical investigation of steady forced convection heat transfer from an isoflux circular cylinder immersed in the liquid metal Galinstan is presented. The governing streamfunction, vorticity, and energy equations are solved using a fourth-order compact finite difference scheme in cylindrical coordinates (FOCS--CC) coupled with a stable pseudo-time iteration (PTI) technique. The influence of the Reynolds number ($1 \leq Re \leq 600$) on the flow and heat transfer characteristics is systematically investigated for Galinstan with a Prandtl number of $Pr=0.025$. The performance and accuracy of the proposed scheme are first established through grid independence studies and validation against previously published numerical results for the average Nusselt number and total drag coefficient over a range of Reynolds numbers. Excellent agreement with the available literature confirms the reliability and robustness of the present formulation. The effects of Reynolds number ($1\leq Re\leq600$) on the flow and thermal fields are examined through streamline patterns, isotherm distributions, and local Nusselt number variations. The results reveal that increasing the Reynolds number promotes flow separation, enlarges the wake region, intensifies downstream thermal transport, and significantly enhances convective heat transfer from the cylinder surface. Furthermore, a new empirical correlation for the average Nusselt number is proposed for Galinstan fluid over the Reynolds number range $1\leq Re\leq600$, exhibiting excellent agreement with the numerical data with a coefficient of determination of $R^2=0.99939$.

Computational analysis of turbulent flow around a NACA0012 airfoil at low Reynolds numbers using a two-fluid model

This paper presents a detailed numerical investigation of the turbulent flow structure around a NACA0012 airfoil at low Reynolds numbers using a two-fluid turbulence model implemented in the COMSOL Multiphysics environment. The study focuses on Reynolds numbers ranging from 10,000 to 30,000 at an angle of attack of α = 0°, and from 10,000 to 25,000 at α = 5°. The primary objective is to assess the capability of the two-fluid model in accurately capturing the flow separation, wake development, and turbulent stress distribution in the low-Reynolds-number regime. The obtained numerical results are systematically compared with those from the widely used Menter’s SST (Shear Stress Transport) model and available experimental data from literature to validate the accuracy and robustness of the proposed approach. The simulations demonstrate that the two-fluid turbulence model provides improved agreement with experimental measurements, particularly in predicting the velocity profiles and Reynolds stress distributions in the near-wake region. The implementation of the model within the COMSOL Multiphysics framework shows high numerical stability, reliable convergence, and computational efficiency across all tested flow regimes. Furthermore, the two-fluid model exhibits enhanced capability in describing complex anisotropic turbulence effects that are often underrepresented in traditional RANS-based models. The outcomes of this study confirm that the two-fluid turbulence model is a promising and accurate alternative for analyzing low-Reynolds-number aerodynamics, offering valuable insights for the design and optimization of small-scale air vehicles, micro air vehicles (MAVs), and other low-speed aerodynamic systems.