Turbulence Model Research Articles

Turbulence Closure Modeling with Machine Learning: A Foundational Physics Perspective

Abstract Turbulence closure modeling using machine learning is at an early crossroads. The extraordinary success of machine learning (ML) in a variety of challenging fields had given rise to an expectation of similar transformative advances in the area of turbulence closure modeling. However, by most accounts, the current rate of progress toward accurate and predictive ML-RANS (Reynolds Averaged Navier-Stokes) closure models has been very slow. Upon retrospection, the absence of rapid transformative progress can be attributed to two factors: the
underestimation of the intricacies of turbulence modeling and the overestimation of ML’s ability to capture all features without employing targeted strategies. To pave the way for more
meaningful ML closures tailored to address the nuances of turbulence, this article seeks to
review the foundational flow physics to assess the challenges in the context of data-driven
approaches. Revisiting analogies with statistical mechanics and stochastic systems, the key
physical complexities and mathematical limitations are explicated. It is noted that the current
ML approaches do not systematically address the inherent limitations of a statistical approach
or the inadequacies of the mathematical forms of closure expressions. The study underscores
the drawbacks of supervised learning-based closures and stresses the importance of a more
discerning ML modeling framework. As ML methods evolve (which is happening at a rapid
pace) and our understanding of the turbulence phenomenon improves, the inferences expressed
here should be suitably modified.

Analysis on cause of erosion of guide vane of high‐head Francis turbine in sandy river

AbstractThe Kizilsu River Basin in China is located in the desert Gobi area with high sediment content and high hardness. After 4798h operation, the maintenance of a high‐head Francis turbine in this basin found that the guide vane was seriously worn, and even most of the top and lower skirts of the front of the guide vane were worn off. In this study, the k‐ε turbulence model, ZGB cavitation model and sediment erosion prediction model were used to simulate the solid‐liquid two‐phase flow and cavitation of guide vane. The research results show that the guide vane of a high‐head Francis turbine in a sandy river has a high sediment velocity and serious surface erosion, with the maximum erosion rate of 1.0 × 10−6 kg/(m2·s), while the area near the skirt of the guide vane is a low‐pressure area lower than the saturated steam pressure, and cavitation is very easy to occur, with the maximum vapor volume fraction of 0.9. Serious cavitation erosion occurs near the skirt of the guide vane, and the combined effect of sand erosion and cavitation erosion on the surface of the skirt of the guide vane aggravates the damage of the skirt structure. The research results provide a technical basis for the antiabrasion design of the guide mechanism of the high‐head Francis turbine and the operation and maintenance of the hydropower station in the sandy river.

Computational Fluid Dynamics Simulation on Blade Geometry of Novel Axial FlowTurbine for Wave Energy Extraction

Wave energy converters (WECs) utilizing the Oscillating Water Column (OWC) principle have gained prominence for harnessing kinetic energy from ocean waves. This study explores an innovative approach by transforming the pivoting Denniss–Auld turbine blades into a fixed configuration, offering a simplified alternative. The fixed-blade design emulates the maximum pivot points during the OWC’s exhalation and inhalation phases. Traditional Denniss–Auld turbines rely on complex hub systems to enable controllable blade rotation for performance optimization. This research examines the turbine’s efficiency without mechanical actuation. The simulations were conducted using ANSYS™ CFX 2023 R2 to solve the three-dimensional, incompressible, steady-state Reynolds-Averaged Navier–Stokes (RANS) equations, employing the k-ω SST turbulence model to close the system of equations. A grid convergence study was performed, and the numerical results were validated against available experimental and numerical data. An in-depth analysis of the intricate flow field around the turbine blades was also conducted. The modified Denniss–Auld turbine demonstrated a broad operating range, avoiding stalling at high flow coefficients and exhibiting performance characteristics like an impulse turbine. However, the peak efficiency was 12%, significantly lower than that of conventional Denniss–Auld and impulse turbines. Future research should focus on expanding the design space through parametric studies to enhance turbine efficiency and power output.

Effects of Angle of Attack on Flow-Induced Vibration of a D-Section Prism

The VIVACE device, which utilizes flow-induced vibration for harvesting ocean current energy, has been a research hotspot in the field of renewable energy. In this study, the flow-induced vibration characteristics and energy conversion efficiency of a D-section prism were investigated using the k-ω SST turbulence model and Newmark-β method. The vibration amplitude, frequency, equilibrium position offset, and energy conversion efficiency of the two-degree-of-freedom cylinder were systematically analyzed at seven angles of attack between 0 and 180 degrees. The Reynolds number ranged from 368 to 14,742, corresponding to equivalent speeds of 2 to 20. The results indicate that the angle of attack has a significant influence on the flow-induced vibration response of the D-section prism. As the angle of attack changes, the vibration amplitude of the cylinder continuously increases, and the cylinder sequentially enters the vortex-induced vibration, vortex-induced vibration-galloping, and fully galloping branches. The change in the angle of attack disrupts the symmetry of the cylinder’s vibration in the streamwise direction, leading to a shift in the equilibrium position of the cylinder’s vibration. When the angle of attack is 0°, the energy conversion efficiency of the column reaches a maximum of 11.75%. Additionally, at high Reynolds numbers, the vibration of the cylinder is not self-limiting, making it more advantageous for energy conversion devices compared to cylinders with circular cross-sections.

URANS Prediction of the Hydrodynamic Interactions of Two Ship-like Floating Structures in Regular Waves

A side-by-side configuration of floating structures is commonly used in ocean exploration practices, such as offshore vessels for loading and offloading, floating cranes, and offshore floating wind turbines. Computational Fluid Dynamics (CFD) method is current practice for the analysis of hydrodynamic interactions of the side-by-side vessels. The purpose of this study is yo carry out a benchmark study of CFD method applied for the above analysis. URANS CFD method was applied utilizing a k-ε turbulence model and a volume of fluid (VOF) method to capture the free surface. Different ratios of wave length to vessel’s length and different gaps between between the vessels were considered in the study. Simulation results show that the wave length to vessel’s length ratio /L affects significantly the wave pattern around the vessels and inside the gap. For the shorter waves, the gap influences the wave pattern both inside and outside the gap. Further, the pressure distribution on the keel surface of the vessels is asymmetric about the vertical center plane along the vessel, which resulted in roll motion eventhough the vessel is in head seas. Roll motion was observed in all gap variations considered. Amplitude modulation was observed in the heave and pitch motions, while generation of side-band frequency components were observed in the roll motion, which indicate a non-linear fluid-structure interaction.

CFD and RSM Assist in Reducing the LPG Consumption of Burners for Agarwood Oil Production in Thailand

ABSTRACT This research aimed to optimize LPG consumption in Thai commercial burners used in agarwood oil production, specifically focusing on the KB-10, S-10, and EB-10 burners. Enhancing burner efficiency is crucial due to rising energy costs and environmental concerns. A dual approach using Response Surface Methodology (RSM) and Computational Fluid Dynamics (CFD) was employed in order to achieve the best burner. Central Composite Design (CCD) within the RSM framework determined the optimal swirl and inclination angles combinations. Modified burners with variant combination angles, as suggested by RSM, were numerically investigated. CFD simulations with Ansys Fluent, utilizing the k-ε turbulence and discrete ordinates (DO) radiation models, provided detailed insights into the combustion and heat transfer processes of those modified burners. The modified burners, SB10–1, SS10–3, and SEB10–7, demonstrated significant improvements. Laboratory and field tests indicated energy savings of 16.15%, 23.74%, and 20.75%, respectively. Statistical analysis confirmed these savings with p-values < .05. The 95% confidence intervals for LPG savings were 31.31 ± 0.8%, 33.42 ± 0.7%, and 31.84 ± 0.6%, corresponding to payback periods of approximately 2.99, 4.21, and 8.95 months. Additionally, CO and NOx emissions were kept below 350 ppm and 100 ppm, respectively. The novelty of this study lies in the combined use of RSM and CFD to optimize burner performance, leading to significant energy savings and emission reductions. These findings highlight the potential of these methods for burner optimization, offering both economic and environmental benefits. This research underscores the importance of integrating advanced modeling techniques to achieve sustainable and cost-effective industrial processes.

On the Generalization Capability of a Data-Driven Turbulence Model by Field Inversion and Machine Learning

This paper discusses the generalizability of a data-augmented turbulence model with a focus on the field inversion and machine learning approach. It is highlighted that the augmented model based on two-dimensional (2D) separated airfoil flows gives poor predictive capability for a different class of separated flows (NASA wall-mounted hump) compared to the baseline model due to extrapolation. We demonstrate a sensor-based approach to localize the data-driven model correction to tackle this generalizability issue. Furthermore, the applicability of the augmented model to a more complex aeronautical three-dimensional case, the NASA Common Research Model configuration, is studied. Observations on the pressure coefficient predictions and the model correction field suggest that the present 2D-based augmentation is to some extent applicable to a three-dimensional aircraft flow.

Evolution of underwater noise emission prediction technology for ship-propulsor combinations in an industry environment

ABSTRACT The prediction of underwater noise emissions by marine vessels has evolved significantly over the last decade as the interest shifted from exclusive military to civil use as a result of environmental concerns. Among different research groups, the best practices for the estimation with high-fidelity simulation methods based on hydrodynamic sound emissions are developed considering the complete vessel and propulsor. Here the current state-of-the-art computational fluid dynamics (CFD) approach, centered around propulsion units, is worked out in steps leading to the application for vessels. This consists of incompressible finite volume method flow simulations with large eddy turbulence modelling and volume-of-fluid phase capturing with a Schnerr-Sauer cavitation model in combination with an added permeable surface Ffowcs-Williams-Hawkings method for far-field acoustics. Many mechanistic arguments support it and the final validation cases lead to acceptable accuracy and enrich simulation data acquisition, however, few technical limitations reveal weaknesses compared to traditional approaches.

Computational Hemodynamics-Based Growth Prediction for Small Abdominal Aortic Aneurysms: Laminar Simulations Versus Large Eddy Simulations.

Prior studies have shown that computational fluid dynamics (CFD) simulations help assess patient-specific hemodynamics in abdominal aortic aneurysms (AAAs); patient-specific hemodynamic stressors are frequently used to predict an AAA's growth. Previous studies have utilized both laminar and turbulent simulation models to simulate hemodynamics. However, the impact of different CFD simulation models on the predictive modeling of AAA growth remains unknown and is thus the knowledge gap that motivates this study. Specifically, CFD simulations were performed for 70 AAA models derived from 70 patients' computed tomography angiography (CTA) data with known growth status (i.e., fast-growing [> 5mm/yr] or slowly growing [< 5mm/yr]). We used laminar and large eddy simulation (LES) models to obtain hemodynamic parameters to predict AAAs' growth status. Predicting the growth status of AAAs was based on morphological, hemodynamic, and patient health parameters in conjunction with three classical machine learning (ML) classifiers, namely, support vector machine (SVM), K-nearest neighbor (KNN), and generalized linear model (GLM). Our preliminary results estimated aneurysmal flow stability and wall shear stress (WSS) were comparable in both laminar and LES flow simulations. Moreover, computed WSS and velocity-related hemodynamic variables obtained from the laminar and LES simulations showed comparable abilities in differentiating the growth status of AAAs. More importantly, the predictive modeling performance of the three ML classifiers mentioned above was similar, with less than a 2% difference observed (p-value>0.05). In closing, our findings suggest that two different flow simulations investigated did not significantly affect outcomes of computational hemodynamics and predictive modeling of AAAs' growth status, given the data investigated.

Pressure Loss Modeling for Multi-Stage Obstacles in Pressurized Ducts

Estimating singular pressure losses for multi-stage obstacles in pressurized hydraulic ducts is a challenging task. An experimental study was conducted in a closed-loop hydrodynamic tunnel to characterize the pressure losses of a system consisting of a porous fibrous foam placed in front of a bar rack. The pressure losses of different foam–rack configurations were measured over a range of inlet velocities in order to highlight the mutual influence of their characteristics on the flow. The interdependence between the two stages has been evidenced by both the experimental results and additional numerical simulations using RANS (Reynolds-Averaged Navier–Stokes Equations) simulations with a k-ω SST turbulent closure model. The pressure losses were first modeled using two approaches based on the assumption of either independence or full dependence between the stages. The respective advantages and limitations of these approaches led to an improved analytical formula that considers the transition of the flow from the porous foam to the bar rack. By taking into account an empirical transition factor, the proposed model improves the head loss prediction for all tested configurations, with an average relative error between the formula and experimental results less than that of the two simpler approaches. This study improves our understanding of global pressure losses in multi-stage systems that include a porous foam or other filtering or clogging media in front of bar racks.

Enhancing Sustainable Development: Assessing a Solar Air Heater (SAH) Test Bench through Computational and Experimental Methods

A solar air heater is a device that gathers solar radiation and converts it into heat. The core principle involves air moving through a solar collector, where sunlight naturally increases the air temperature within the collector. The benefit of this technology lies in its affordability and simplicity. The implementation of a solar air heater (SAH) test bench holds significant promise in addressing both global change and sustainable development objectives. The primary goal of this study is to examine the aerodynamic configuration of a novel solar air heater test bench accessible at the Laboratory of Electro-Mechanic Systems (LASEM). This study was carried out using the standard k-ω turbulence model with the use of the ANSYS Fluent 17.0 software. The results indicate that the velocity at the inlet directly influences the velocity fields, temperature, static pressure, and characteristics of turbulence. Furthermore, the numerical findings confirmed that the temperature and velocity profiles in the second channel are in good concordance with the experimental findings in the case of a fan, placed alongside the insulation, operating in a delivery mode. Based on these results, the computational approach is validated. When comparingforced convection to natural convection under identical conditions, there was a notable increase in the energy efficiency, with forced convection showing a significant improvement of approximately 31.8%. Indeed, the range of temperatures reached with the proposed design, is highly beneficial for both industrial and household applications.

Design and Numerical Analysis of an Annular Combustion Chamber

Designing a combustion chamber for gas turbines is considered both a science and an art. This study presents a comprehensive methodology for designing an annular combustion chamber tailored to the operating conditions of a CFM-56 engine, a widely used high bypass ratio turbofan engine. The design process involved calculating the basic criteria and dimensions for the casing, liner, diffuser, and swirl, followed by an analysis of the cooling sections of the liner. Numerical simulations using NUMECA software and the HEXPRESS meshing tool were conducted to predict the combustion chamber’s behavior and performance, employing the κ-ε turbulence model and the Flamelet combustion model. Methane was used as the fuel, and simulations were performed for three fuel injection angles: axial, 45°, and 60°. Results demonstrate that the combustion chamber is properly dimensioned and achieves complete combustion for all configurations. The pressure ratio is 0.96, exceeding the minimum design criteria. Additionally, the emissions of unburned hydrocarbons are zero, while nitrogen oxides and carbon monoxide levels are below regulatory limits. These findings validate the proposed design methodology, ensuring efficient and environmentally compliant combustion chamber performance.

Influence of Reynolds Number on Aerodynamic and Performance Coefficients of a Novel Parabolic-Bladed Savonius Wind Rotor

Abstract The vertical-axis Savonius wind rotor is known for its design simplicity, better starting qualities, and direction independency despite its inferior efficiency when measured against certain other types of vertical-axis wind rotors. Despite a plethora of research work on Savonius rotors, an in-depth analysis of Reynolds number (Re) on aerodynamic and power coefficients of the Savonius rotors is scarce. This paper aims at understanding the influence of Re on the performance of a novel parabolic blade profile through unsteady two-dimensional (2D) computation. The Reynolds-averaged Navier Stokes (RANS) equations are modelled using the ANSYS-Fluent by adopting shear stress transport (SST) k-ω turbulence model. The computational results of the novel blade profile are then compared and analysed with an established semicircular blade profile to draw some meaningful insights into the aerodynamic performance. In the tested range of Re = 5.3 × 104 − 10.6 × 104, the novel parabolic blade profile outperformed the semicircular blade profile in terms of aerodynamic and performance coefficients.

Effect of momentum flow ratio on entrainment of a confined coaxial jet in a co-flow

Iron ore pellet production processes produce large amounts of CO2 emissions when burning fossil fuels. One example is the grate-kiln process, where normally a coal flame is used to indurate pellets. To mitigate the emissions, coal used in rotary kilns can be replaced with for example hydrogen. However, the fuel is mixed with secondary process air, and replacing a solid fuel with a gaseous one changes the mixing characteristics. This demands different means of injecting the fuel. A coaxial jet can be used to control the mixing of fuel and secondary air, as well as the flow field. The aim is to control the mixing of hydrogen and secondary air to achieve a hydrogen flame that is similar to the reference coal flame. This study numerically investigates different coaxial jet configurations. Steady-state simulations of a simplified model of the real kiln are performed using a Reynolds Stress turbulence model. Results show that decreasing the momentum flow ratio between the outer and inner jet, M jet , to a certain value delays the spread of the hydrogen jet and thus gives a longer jet. Further decreasing this ratio gives an even longer jet, but has the side effect of producing recirculation of hydrogen.

Prediction of waves in tanks excited by ship motion and moving walls with a three-dimensional fully linear finite difference approach

Mitigation of waves in shipboard swimming pools excited by ship motions is a topic of current interest that has not yet been extensively investigated. Various damping mechanisms have been applied to mitigate waves excited in tanks, such as porous baffles or different types of internal baffles. However, most of these devices are installed in LNG tanks to prevent serious sloshing effects. Furthermore, these are passive devices and, hence, unable to control wave-induced excitations. Our focus was on the validation and verification of the three-dimensional (3D) fully linear Finite Difference Method (FDM) based on the previously developed method of Qi et al. (2024) for predicting waves in a transversely placed swimming pool excited by ship motions and piston-type actuators. We validated our FDM approach against comparative Computational Fluid Dynamics (CFD) simulations as well as experimental model test measurements. The CFD tools solved the Reynolds-averaged Navier-Stokes (RANS) equations, relied on an appropriate turbulence model and the Volume of Fluid (VOF) method to capture the free surface of the liquid in the model tank, and employed the overset technique to specify the motions of the active actuators. Our FDM considered ship-induced roll excitations as well as simultaneous roll and sway excitations, albeit only at frequencies outside the range of the pool's resonance frequency. For these periods, our approach accurately predicted not only the mitigated waves in the pool, but also the optimum amplitude of the actuators needed to mitigate such waves. Our FDM can be applied to obtain a preview of excited waves under various conditions, leveraging its principal advantage of extreme computational efficiency.© 2017 Elsevier Inc. All rights reserved.

Optimizing CO2 Purification in a Negative CO2 Emission Power Plant

AbstractIn the pursuit of mitigating CO2 emissions, this study investigates the optimization of CO2 purification within a negative CO2 emission power plant using a spray ejector condenser (SEC) coupled with a separator. The approach involves direct‐contact condensation of vapor, primarily composed of an inert gas (CO2), facilitated by a subcooled liquid spray. A comprehensive analysis is presented, employing a numerical model to simulate a cyclone separator under various SEC outlet conditions. Methodologically, the simulation, conducted in Fluent, encompasses three‐dimensional, transient, and turbulent characteristics using the Reynolds stress model turbulent model and mixture model to replicate the turbulent two‐phase flow within a gas–liquid separator. Structural considerations are delved into, evaluating the efficacy of single‐ and dual‐inlet separators to enhance CO2 purification efficiency. The study reveals significant insights into the optimization process, highlighting a notable enhancement in separation efficiency within the dual‐inlet cyclone, compared to its single inlet counterpart. Specifically, a 90.7 % separation efficiency is observed in the former, characterized by symmetrical flow patterns devoid of wavering CO2 cores, whereas the latter exhibits less desirable velocity vectors. Furthermore, the investigation explores the influence of key parameters, such as liquid volume fraction (LVF) and water droplet diameter, on separation efficiency. It is ascertained that a 10 % LVF with a water droplet diameter of 10 µm yields the highest separation efficiency at 90.7 %, whereas a 20 % LVF with a water droplet diameter of 1 µm results in a reduced efficiency of 50.79 %. Moreover, the impact of structural modifications, such as the addition of vanes, on separation efficiency and pressure drop is explored. Remarkably, the incorporation of vanes leads to a 9.2 % improvement in separation efficiency and a 16.8 % reduction in pressure drop at a 10 % LVF. The findings underscore the significance of structural considerations and parameter optimization in advancing CO2 capture technologies, with implications for sustainable energy production and environmental conservation.

Thermal-hydraulic investigation of liquid metal cross flow different arrangements of tube bundles under pulsating

The topic of this paper is to couple the passive and active approaches to enhance the heat transfer performance in the inline tube bundle heat exchanger. Firstly, the k-kl-ω turbulence model and Kays turbulent Prandtl number model are validated by liquid metal cross flow tube bundle experiments and rectangular groove pulsating flow experimental results. Then the numerical studies were carried out for pulsating velocity amplitude of 0.5, frequency of 10, and Re of 20,000 with transverse and streamwise pitch-to-diameter ratios of 1.5, 1.65, and 1.8. The introduction of pulsating flow effectively improves the turbulence characteristics between the tube bundles, especially at the first three rows, where the velocity fluctuation is enhanced by about 1.5–2 times. The tube heat transfer performances are all improved. The performance evaluation criterion (PEC) variation ranges from 1.04 to 1.32, which signifies that the introduction of pulsating flow can enhance the comprehensive heat transfer performance. The per unit flow rate thermal entropy generation decreased by about 9.7–33.3 %, in addition, a phase difference between the transient thermal entropy production and pulsating velocity was found. The correlation equations about Nu and f factor within the scope of this paper are presented.

Bayesian parameter estimation and evaluation of the K-ω shear stress transport model for plane impinging jets

Numerical simulations with semi-empirical turbulence models are commonly used to model impinging jets, often used for cooling solid surfaces. In this work, the constants in the k-ω shear stress transport model in ANSYS FLUENT are calibrated to experimental velocity and heat transfer data for a plane turbulent impinging air jet to determine if Kennedy-O’Hagan calibration (Kennedy and O’Hagan 2001 J. R. Stat. Soc. B 63 425–64) can improve predictions of near-surface velocities and surface Nusselt numbers for similar flows. Impinging jets have been proposed to cool the target plates of the divertor in future magnetic fusion energy reactors, where simulations are used to estimate divertor performance. The flat-plate divertor (Wang et al 2009 Fusion Sci. Technol. 56 1023–7) uses a plane jet of helium issuing from a B = 0.5 mm slot to cool a surface with radius of curvature of 44B at a distance 4B from the slot. Predictions from the calibrated numerical model are compared with independent experimental data at different flow conditions, as well as surface temperature data for a flat plate divertor test section. The contribution of this work is evaluation of the accuracy of a calibrated turbulence model for modest extrapolations in flow geometry and flow conditions for a plane impinging jet.

Performance enhancement of a fin and tube heat exchanger with the novel arrangement of curved winglets using a multi-objective optimization approach

The present study considers performing multi-objective optimization of a fin and tube heat exchanger to enhance its performance. For this, a group of three curved rectangular winglets, placed on alternate sides of the tube, are considered. Two different geometrical arrangements are analyzed. In the first case – referred to as case A – the distance between the three curved blades is varied in a way that the relative gap between the curved blades is the same. In the second case – referred to as case B – the distance between the three curved blades is held fixed at the entry section, but the relative gap is varied at the exit of the curved blades. The experiments are designed using the Latin hypercube sampling technique, and the responses against each set of design variables are calculated using computational fluid dynamics. The conservation equation for mass, momentum and energy are solved along with transition SST (a three equation) turbulence model considering a steady state formulation. The resulting data is used to train the artificial neural network that serves as a surrogate model for GA to generate the Pareto front points. Conclusive results indicate that the optimized models from both cases largely outperform compared to the previously reported studies. Furthermore, the performance of the case B variant is slightly better than for case A.

Numerical analysis of heat transfer and fluid flow structures of jet impingement on a flat plate with different shapes of roughness elements

Jet impingement is a heat transfer technique utilized in different applications in industry. It is used for cooling the turbine blade and the combustor wall because of its high cooling rate. The heat transfer (HT) and flow structure of a circular air-impinging jet over a flat target plate with a circular row of 48 roughness elements are numerically investigated using renormalization group k–ε turbulence model. Different shapes of roughness elements, namely cylindrical roughness elements (CREs), droplet roughness elements (DREs), and hemispherical roughness elements (HREs), are examined. The effects of Reynolds number changed from 7,000 to 35,000, and the roughness elements location relative to jet diameter ( s / d ) of 1.5, 2, 2.5, and 3 at a constant jet-to-target plate distance ( H / d ) of 2 are studied. Temperature distribution, local Nusselt number ( Nu ), average Nusselt number (Nuavg ), average Nusselt number ratio (Nuavg,r ), velocity distribution, turbulence kinetic energy, streamline contours, and static pressure ( p ) over the roughness elements are evaluated and discussed. The results showed that the existence of roughness elements has a significant effect on the thermal and hydraulic characteristics. The Nuavg,r for the CREs, DREs, and HREs is up to 1.61, 2.02, and 1.2, respectively. All roughness element shapes increase the flow velocity in the narrow area between the elements and increase the wetted area. CREs augment the HT rates by increasing the turbulence intensity, while DREs reduce the drag force effects.