Two-equation Turbulence Model Research Articles

Investigation of the effect of three parameters in the GEKO model on the calculation results for backward facing step flow

Abstract. Computational fluid dynamics (CFD) is a field which is attracting more and more focus today for its ability to simulate comprehensive conditions. Reynolds-Averaged Navier-Stokes (RANS), which needs low cost, is one of the most popular methods used in engineering. However, RANS method has insufficient ability to simulate separated flow, which is a major challenge at present. One reason for this is that the model parameters introduce uncertainty into the simulation. This research investigates the effect of three parameters in the Generalized k- (GEKO) two-equation turbulence model on the calculations in backward facing step flow. It is found that C_sep has the greatest influence on the calculation of pressure coefficient and friction coefficient. C_nw has the greatest influence on the reattachment calculation through eddy-viscosity. The calculation results of the three variables show that there is correlation between them. Besides, a better set of parameters is obtained, which will improve the calculation accuracy for these three variables.

A meso- to micro-scale coupled model under typhoon conditions considering vortex structure and coriolis effect for wind farms

Accurate simulations of typhoon-induced wind speeds on wind farms are crucial for the refined assessment of typhoon risks in wind turbines. Southeastern coastal area in China is rich in wind resources but is also severely threatened by typhoons. As an extremely destructive weather system with complex structures, the refined near-surface wind fields of typhoons are difficult to simulate by meso-scale models for risk assessment. Therefore, a coupled meso- and micro-scale model under typhoon conditions is proposed to simulate typhoon-induced winds on a wind farm. The Coriolis force is considered in the coupled model to reflect the rotating effect of typhoons caused by the vortex structure. A coupling algorithm based on objective analysis is proposed to construct boundary conditions at the coupling interface, to consider the variation of inflow variables in the vertical and cross-wind directions. Model constants of the two-equation turbulence model are calibrated based on typhoon field observations, to more reasonably simulate typhoons. A validation study is conducted, and the results show that the maximum wind speed on the wind farm simulated by the coupled model exhibits an increased accuracy compared with that of the meso-scale model, where the absolute error decreases by 34%.

Numerical investigation of turbulent mass transfer processes in turbulent fluidized bed by computational mass transfer

Turbulent fluidized bed possesses a distinct advantage over bubbling fluidized bed in high solids contact efficiency and thus exerts great potential in applications to many industrial processes. Simulation for fluidization of fluid catalytic cracking (FCC) particles and the catalytic reaction of ozone decomposition in turbulent fluidized bed is conducted using the Eulerian–Eulerian approach, where the recently developed two-equation turbulent (TET) model is introduced to describe the turbulent mass diffusion. The energy minimization multi-scale (EMMS) drag model and the kinetic theory of granular flow (KTGF) are adopted to describe gas–particles interaction and particle–particle interaction respectively. The TET model features the rigorous closure for the turbulent mass transfer equations and thus enables more reliable simulation. With this model, distributions of ozone concentration and gas–particles two-phase velocity as well as volume fraction are obtained and compared against experimental data. The average absolute relative deviation for the simulated ozone concentration is 9.67% which confirms the validity of the proposed model. Moreover, it is found that the transition velocity from bubbling fluidization to turbulent fluidization for FCC particles is about 0.5 m·s–1 which is consistent with experimental observation.

Volume of Fluid simulation of air–water co-current and Counter-current flow with variable density turbulence formulation

Co-current and counter-current air–water flows are studied by Volume of Fluid (VOF) simulation, with emphasis on turbulence modelling near the interface. The relevance of constant density (ρ-con) and variable density (ρ-var) formulations of the turbulence transport equations in two classical two-equation turbulence models, k−ϵ RNG and k−ω SST models, is discussed. The Reynolds Stress Tensor (RST) model approach is also investigated and literature results with the two-fluid model are included for comparison. Our results with VOF show that the widely used constant density formulation underestimates the turbulence dissipation without capturing the turbulence jump across the interface, which also affects the interface liquid height, the velocity profiles of both phases and the pressure drop along the domain. In contrast, the variable density formulation significantly improves the results by increasing the turbulence dissipation at the interface. Although the best solutions have been obtained using the RST model, the ρ-var and k−ϵ RNG gave quite good agreement with experimental data. Despite the narrowness of the domains, three-dimensional simulations have been in better agreement than the two-dimensional ones. Both the VOF results obtained with either the RST and the ρ-var turbulence formulations were found to be superior to those reported with the TF model using damping corrections specifically calibrated for the tests. This study demonstrates that VOF simulation combined with ρ-var two equations turbulence models is a suitable method for modelling large-scale interface segregated flows.

Revisiting RANS turbulence modelling for bubble-induced turbulence: Effects of surfactants

Recent experiments of dispersed bubbly flow (Ma et al., 2023) show that contamination of the carrier phase plays a considerable role in bubble-induced turbulence (BIT): although the bubbles rise slower with adding surfactants, the BIT increases. This trend, however, cannot be reproduced by any current BIT models in the framework of Euler–Euler Reynolds-averaged Navier–Stokes two-equation turbulence model, including the model proposed by Ma et al. (2017). The present work revisits this widely used model (Ma et al., 2017) as a representative, which considers the BIT with an additional source term in the k- and ɛ (or ω) - equation, respectively. We have systematically investigated the reason why such a BIT model is unable to capture the BIT modulation caused by different degrees of contamination and discuss the new possibility for the prefactor in the source term of the ɛ-equation that may improve the results.

Numerical Analysis of Altered Parallel Flow Heat Exchanger with Promoted Geometry at Multifarious Baffle Prolongs

This study investigated the influence of BFFSP on the thermohydraulic performance of a SATHEC(s) using a novel computational approach. The novelty lies in the detailed exploration of the interplay between BFFSP, MFRT, and key performance parameters. Unlike prior studies, which often focus on a limited range of operating conditions, this work employs a comprehensive parametric analysis encompassing two BFFSPs (95 mm and 125 mm) and four MFRTs (0.1, 0.3, 0.5, and 0.7 kg/h). This extensive analysis provides a deeper understanding of the trade-off between the HTRFR enhancement and PDP associated with the BFFSP across a wider range of operating conditions. This investigation leverages the power of computational fluid dynamics (CFD) simulations for high-fidelity analysis. ANSYS Fluent, a widely recognized commercial CFD software package, was used as a computational platform. A three-dimensional steady-state model of HEXR geometry was established. The cold fluid was modeled as water, and the hot fluid was modeled as water. The selection of appropriate turbulence models is crucial for accurate flow simulations within the complex geometry of HEXR. This study incorporates a well-established two-equation turbulence model to effectively capture turbulent flow behavior. The governing equations for mass, momentum, and energy conservation were solved numerically within the CFD framework. Convergence criteria were meticulously established to ensure the accuracy and reliability of the simulation results. BFFs are crucial components in HEXRs as they promote fluid mixing and turbulence on the HTRFR surface, thereby enhancing HTRFR. This study explores the interplay between BFFSP and HTRFR effectiveness. It is hypothesized that a larger BFFSP (125 mm) might lead to a higher HTC owing to the increased fluid mixing. However, the potential drawbacks of the increased PDP due to the flow restriction also need to be considered. The PDP across the HEXR is a critical parameter that affects pumping costs and overall system yield. This study investigates the impact of BFFSP on the PDP. It is expected that a larger BFFSP (125 mm) will result in a higher PDP, owing to the increased resistance to fluid flow. Here, we aim to quantify the trade-off between enhanced HTRFR and increased PDP associated with different BFFSPs. The optimal design of an HEXR seeks a balance between achieving a high HTRFR rate and minimizing pressure losses. HTRPD, a metric combining both HTC and PDP, was employed to evaluate the thermohydraulic performance. We hypothesized that a specific BFFSP might offer a superior HTRPD, indicating an optimal balance between HTRFR effectiveness and PDP for the investigated HEXR geometry and operating conditions. CFD simulations were conducted using ANSYS Fluent to analyze the effects of BFFSP and MFRT on the HTC, PDP, and HTRPD. The simulations employed a commercially available HEXR geometry with water as the cold and hot fluid. The results are presented and discussed to elucidate the relationships between the BFFSP, MFRT, and key performance parameters of the HEXR. This study provides valuable insights into the influence of BFFSP on the thermohydraulic performance of HEXRs. The findings can aid in optimizing the HEXR design by identifying the BFFSP that offers the best compromise between HTRFR enhancement and PDP for specific operating conditions. The results contribute to the knowledge base of HEXR design and optimization, potentially leading to improved yield in various industrial applications. The results indicate that a larger BFFSP (125 mm) leads to higher outlet temperatures but also results in a higher PDP compared to the 95 mm design. Conversely, the 95 mm BFFSP exhibits a lower PDP but achieves a lower HTC. In terms of thermohydraulic performance, as indicated by HTRPD, the 95 mm BFFSP with the lowest MFRT (0.1 kg/h) achieved the highest value, surpassing the 125 mm design by 19.81%. This suggests that a 95 mm BFFSP offers a better trade-off between HTRFR effectiveness and pressure loss, potentially improving the overall HEXR performance.

Numerical Study on Mixing Characteristics of Circular and Non Circular Jets

The study of non-circular jet flows has become important due to their various applications such as aircraft exhaust, combustion chambers and injectors. The goal of present paper is to examine the impact of elliptical, square, and triangular shaped orifices on the mixing characteristics of a free jet with Mach number 0.8. Numerical simulations using an SST K-ω two-equation turbulence model were conducted with a Reynolds number of 3.46×105 for all cases. The mean velocity, decay rate, half-velocity width, spread rate, and turbulence intensity of the jet were analysed. The results showed that the triangular orifice provided the best mixing efficiency, with a shorter jet core length. The decay rate was found to be lowest for the square jet and highest for the triangular jet, which matches with the previous research. The asymmetric jets experienced two axis-switching points, while the square jet experienced a 450 rotation of its axes but no axis-switching. The core region had lower turbulence levels, while the highest turbulence levels were in the shear layer.

Effect of Different Flame Deflectors Plate Geometry on Supersonic Jet Impingement Flow and Heat Characteristics from Rocket Exhaust

The numerical investigation has been carried out on an under-expanded supersonic jet impingement on the perpendicular and inclined deflector plates of various shapes, such as flat, sinusoidal, and wedge types. The numerical study considers flat plates at Mach number of 2.2, and pressure ratio of 1.2, and results of flow and heat transfers are obtained using the Reynolds averaged Naiver Stokes (RANS) two-equation turbulence models. Various two-equation models (especially Standard k-ε, Reynolds Normalization Group k-ε, Realizable k-ε, Shear Stress Transport k-ω, and Baseline k-ω) were employed to predict the deflector’s surface temperature and pressure ratios. The pressure ratios are plotted with various two-equation turbulence models, and it is observed that among all turbulence models, the Shear Stress Transport k-ω shows close agreement with experimental results. Moreover, among the three deflectors, the wedge-shaped deflector shows improved performance in deflecting the rocket exhaust plume away from the surface. However, the maximum temperature on the deflector surface for a wedge-shaped deflector is 8.19% and 26% higher than the flat and sinusoidal-shaped deflectors, respectively.

Improved SST turbulence model for supersonic flows with APG/separation

A goal in modeling the turbulent flows in computational fluid dynamics is to find an empirical yet universal model to address the complex scenarios. Menter's Shear Stress Transfer (SST) [1] is a Reynolds-Averaged Navier-Stokes (RANS) based two-equation turbulence model and has been one of the most widely used turbulence models for numerical simulation of viscous flows. However, in some practical cases on supersonic, the standard SST model shows unsatisfactory prediction of flow separation and the often underestimation of Reynolds stress. The error mainly comes from the inappropriate use of Bradshaw's assumption which is proposed under turbulent kinetic energy (TKE) equilibrium flow conditions. This paper proposes an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. Several supersonic test cases are carried out to verify the new model. The calculation results show that the new model exhibits better performance in capturing the separation zones than the baseline model (BSL) and the standard SST model.

Numerical simulation of altering the raw meal inlet position in a novel swirl precalciner

Conducted a numerical simulation to model a novel swirl precalciner, investigating how altering in the position of the raw meal inlet affects the internal gas flow, temperature field, and component concentration field within the precalciner. Applied the Realizable k-? two-equation turbulent model to the continuous phase. For the particle phase (pulverized coal), employed the Discrete Particle Model and the discrete random walk model. Simulated the combustion of pulverized coal and the decomposition of calcium carbonate by using the Species Transport model combined with the Finite-Rate/Eddy-Dissipation model. Modeled the generation of NOx using a NOx model. The results show that, in comparison to the condition with four raw meal inlets, the six raw meal inlets condition has a better coupling of pulverized coal combustion and raw meal decomposition. The decomposition rate of raw meal has seen a slight improvement, and there is a significant improvement in the occurrence of localized high temperatures within the precalciner, resulting in a reduction of the outlet NOx concentration from 1251 ppm to 225 ppm.

Reduced-scale numerical simulation method and its application to urban-scale buoyancy-driven flows

Urban-scale flows such as urban heat island circulation dominate the dissipation of heat and pollutants in urban areas under calm and stable weather conditions. The study of such buoyancy-driven flows at an urban scale is commonly conducted using water tank modeling and numerical simulations. This paper adopts an approach called "numerical water tank" which utilizes computational fluid dynamics to simulate the water tank model. By adopting this method, the research aims to investigate and analyze urban-scale buoyancy-driven flows. This paper proposes an evaluation criterion to assess eight turbulence models in various aspects. The results show that the SST k-ω model and LES perform well. LES is more accurate than RANS, and compared with LES, SST k-ω model can save 1/3-1/2 of the calculation time. For two-equation turbulence models (k-ε and k-ω), which are known for their easier convergence, it is recommended to maintain a Courant number equal to or below 1 (time step 0.5 s). In the case of LES, which is known for its challenging convergence, it is recommended to maintain a control Courant number below 0.2 (time step 0.1s). On this basis, the numerical water tank method based on large eddy simulation is applied to quantitatively study the effect of canopy heat flux attenuation on urban-scale wind field characteristics in valley cities. This paper combines the strengths of water tank modeling and numerical simulation, resulting in a more efficient approach for studying large-scale flows driven by natural thermal pressure.

Optimization of an axial-flow mine ventilation fan based on effects of design parameters

Underground mining safety relies heavily on ventilation, which is energy and maintenance intensive. An optimization method for an axial-flow Chinook ventilation fan, analyzing parameters like angle of attack, tip clearance, rotation speed, hub-to-tip ratio, and rotor blade count using Design of Experiments (DOE) and regression is proposed. The numerical solutions are confirmed with experimental data. Considering a Mach number of 0.4, compressible flow conditions are analyzed using a two-equation turbulence model. During stall, fan efficiency drops to 47 %. High fatigue probability is observed at the blade-root intersection in stall conditions. The optimization pinpoints several operational configurations that meet the required performance while preserving the fan's structure. A particular off-design optimal point indicates that reducing the blade count and decreasing the tip-clearance lead to an average performance improvement of 9 %, with significant benefits in noise, cost, weight, and energy consumption. The numerical forecasts demonstrate precision with an average discrepancy of less than 5 %.

Sensitive analyses of flow property to turbulence model in swirls simulation within aquaculture tanks

Water swirls in tanks with bottom drain(s), which is observed in aquaculture tanks. Numerical simulation of the swirling field with the general two-equation turbulence models fails to describe the swirling phenomenon and the investigating results are less convincing. This study simulates the swirling flow fields with four categories of turbulence models, they are the laminar model, the turbulent-viscosity model, the Reynolds stress model, and the Large Eddy Simulation model. Results show that the swirling phenomenon is successfully numerically reproduced except for the turbulent-viscosity model. Although the flow properties predicted with the turbulent-viscosity model are different from other turbulence models, the results are meaningful from the perspective of statistical items (mean, standard variation, uniformity, PDF, CFD). For cases with swirls, the flow field can be divided into a forced vortex and a free vortex, and their tangential velocity profiles can be described with a theoretical formula. Considering the numerical cost and the reproduction of experiments, the Reynolds stress turbulence model is preferable in studies of the flow properties of aquaculture tanks.

Fluid Flow and Effect of Turbulence Model on Large-Sized Triple-Offset Butterfly Valve

The performance a valve has been frequently estimated with numerical methods owing to limitations such as cost and place. In this study, for the triple-offset butterfly valves, the different sizes in various disc-opening cases was numerically conducted using different turbulence models of the two-equation turbulence models of k–ε, k-ω, and Reynolds stress model. The numerical calculations were validated against experimentally obtained valve flow test results. The numerical effect with the different turbulence models were analyzed with respect to the disc-opening cases. From the numerical analysis, the Reynolds stress model exhibits the most pronounced turbulence effects among the various turbulence models showing higher value of Reynolds normal stress near the valve disc region. The sensitivity of the turbulence model constants was examined using the 300 mm valve to observe the sensitivity of the turbulence model parameters in the two-equation turbulence models.

Study on Three-dimensional Impinging Jet Flow and Heat Transfer of Dryer for Gravure Printing and Coating Machine

Drying system is the largest energy consumption of equipment parts of solvent-based printing and coating equipment. How to optimize to design the equipment is of the highlights of this research field. According to this demand, a mathematical model of fluid flow of the drying oven is developed. By building a testing platform and using RNG k-epsilon two-equation turbulence model in Fluent Software to analyze three-dimensional impinging jet flow and heat transfer process of hot air drying in conventional drying oven. The results show that the separation of some boundary layers and undesirable swirls, which result in the non-uniform velocity field and temperature field of hot air from nozzles and no promotion to the drying effect, because of unreasonable design of the drying oven.

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier–Stokes (RANS) equations are solved using turbulence modelling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been performed for similar performance with two-equation models of the k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically refined mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the model itself. Additionally, in this paper analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Testing a Generalized Two-Equation Turbulence Model for Computational Aerodynamics of a Mid-Range Aircraft

The generalized k-ω formulation provides a relatively new flexible eddy-viscosity Reynolds-averaged Navier–Stokes modeling approach to turbulent flow simulation, where free coefficients allow for fine-tuning and optimal adjusting of the turbulence closure procedure. The present study addressed the calibration of this versatile model for the aerodynamic design of an innovative mid-range commercial airplane by carrying out a series of simulations for varying model coefficients. Comparing the different solutions with each other, as well as with reference experimental and higher-fidelity numerical data, the performance of the generalized procedure in predicting the aerodynamic loading on the aircraft model was systematically examined. While drawing particular attention to the high-lift regime, the set of model parameters giving the best results was practically determined.

Assessment of Compressibility Corrections on Spalart–Allmaras Turbulence Model for High-Mach-Number Flows

In this paper, various compressibility correction terms of the Spalart–Allmaras turbulence model are evaluated in hypersonic compressible flows. A unified transport equation containing six correction terms is equipped to investigate the separate and combined effects of the correction terms. The numerical results of the hypersonic flat-plate cases and corner cases are, respectively, calculated and compared with direct numerical simulation data and experimental data. By using the coarse-grained uncertainty metrics, errors on the profiles and wall coefficients are measured and analyzed in several cases. The results suggest that compressibility corrections should be applied when the strong cold-wall effect or the compressibility effect exists in the hypersonic flows. Catris and Aupoix’s correction (“Density Corrections for Turbulence Models,” Aerospace Science and Technology, Vol. 4, No. 1, 2000, pp. 1–11) and Séror, Rubin, Peigin, and Epstein’s correction (“Implementation and Validation of the Spalart–Allmaras Turbulence Model in Parallel Environment,” Journal of Aircraft, Vol. 42, No. 1, 2005, pp. 179–188) offer much more accurate predictions than other models in hypersonic corner cases. As the compressibility effect further increases, the conservation correction and Shur, Strelets, Zajkov, Gulyaev, Kozlov, and Sekundov’s compressibility correction (“Comparative Numerical Testing of One-and Two-Equation Turbulence Models for Flows with Separation and Reattachment,” 33rd Aerospace Sciences Meeting and Exhibit, AIAA Paper 1995-0863, 1995) drastically increase the prediction error of the profiles. The present work ends by emphasizing the importance of the individual and combined impacts of the correction terms for compressible flows at high Mach numbers, which may provide an understanding for developing further extensions of Spalart–Allmaras models.

Development of an effective two-equation turbulence modeling approach for simulating aerosol deposition across a range of turbulence levels

Pharmaceutical aerosol systems present a significant challenge to computational fluid dynamics (CFD) modeling based on the need to capture multiple levels of turbulence, frequent transition between laminar and turbulent flows, anisotropic turbulent particle dispersion, and near-wall particle transport phenomena often within geometrically complex systems over multiple time scales. Two-equation turbulence models, such as the k−ω family of approximations, offer a computationally efficient solution approach, but are known to require the use of near-wall (NW) corrections and eddy interaction model (EIM) modifications for accurate predictions of aerosol deposition. The objective of this study was to develop an efficient and effective two-equation turbulence modeling approach that enables accurate predictions of pharmaceutical aerosol deposition across a range of turbulence levels. Key systems considered were the traditional aerosol deposition benchmark cases of a 90-degree bend (Re=6,000) and a vertical straight section of pipe (Re=10,000), as well as a highly complex case of direct-to-infant (D2I) nose-to-lung pharmaceutical aerosol delivery from an air-jet dry powder inhaler (DPI) including a patient interface and infant nasal geometry through mid-trachea (500<Re<7,000). Of the k−ω family of models, the low Reynolds number (LRN) shear stress transport (SST) approach was determined to provide the best agreement with experimental aerosol deposition data in the D2I system, based on an improved simulation of turbulent jet flow that frequently occurs in DPIs. Considering NW corrections, a new correlation was developed to quantitatively predict best regional values of the y+limit, within which anisotropic NW turbulence is approximated. Considering EIM modifications, a previously described drift correction approach was implemented in pharmaceutical aerosol simulations for the first time. Considering all model corrections and modifications applied to the D2I system, regional relative errors in deposition fractions between CFD predictions and new experimental data were improved from 19–207% (no modifications) to 2–15% (all modifications) with a notable decrease in computational time (up to ∼15%). In conclusion, the highly efficient two-equation k−ω models with physically realistic corrections and modifications provided a viable, efficient and accurate approach to simulate the transport and deposition of pharmaceutical aerosols in complex airway systems that include laminar, turbulent and transitional flows.

Effect of the Solid Particle Diameter on Frictional Loss and Heat Exchange in a Turbulent Slurry Flow: Experiments and Predictions in a Vertical Pipe

The study deals with experiments and predictions on turbulent flow and heat exchange in a fully developed slurry flow in a vertical upward pipe. Four slurries were considered: two with glass spheres particles with diameters of 0.125 mm and 0.240 mm, respectively, and two with sand spheres particles with diameters of 0.470 mm and 0.780 mm, respectively. The volume concentration of the particles was changed in the range of 10% to 40%. This study has indirectly demonstrated the existence of turbulence suppression to a degree dependent on the diameter of the solid particles. A mathematical model for heat transfer between slurry and pipe was developed using the two-equation turbulence model and a specially designed wall function, including particle diameter and solid concentration. The model assumed a constant wall temperature and heat flux. The study’s objective was to determine the influence of the diameter of the solid particles on the heat exchange. The Nusselt number was found to change sinusoidal, reaching a maximum for a slurry with d = 0.125 mm, and a minimum for d = 0.470 mm. The higher the solid concentration, the lower the Nusselt number. The novelty and value of this study lies in the deeper characterisation and understanding of the influence of the diameter of solid particles on heat exchange.