Equation Turbulence Model Research Articles

Numerical investigation of turbulent fuel jet diffusion and its influence on the auto-igniting diffusive flame development

Abstract Turbulent auto-igniting diffusion flames are common in combustion systems, where the mixing of the fuel jet with the outer oxidant flow is the fundamental mechanism for the flame ignition and development. The paper presents a critical analysis on the Reynolds-Averaged-Navier-Stokes (RANS) simulation of a methane-air flame, done with a two equations turbulence model, in comparison with detailed experimental data. In the first part, the non-reactive jet is simulated with the standard k − ε model and a modified version, obtained with motivated changes of the Cμ and σk constants. In the second part the reactive jet is simulated, introducing a consistent modification of the Cγ constant, in the eddy dissipation concept (EDC) model. The comparison with experimental data confirms the validity of the proposed model and highlights the effect of the proper turbulent jet development on the mechanisms of the diffusive flame ignition and propagation.

Performance sensitivity analysis and aerodynamic optimization of compressor cascades by a turbulence adjoint method

Sensitivity, which is useful for evaluating the contributions of input variations to output changes, favors designers exploiting the most sensitive design parameters and completing design optimization in aerospace. This study introduces the turbulence adjoint method due to its low computational cost in calculating sensitivities with high accuracy and then solves the adjoint partial differential equations with respect to both the Reynolds-averaged Navier–Stokes and turbulence model equations with the assistance of an automatic differentiation tool. By utilizing the turbulence adjoint method, the sensitivities of aerodynamic performance to the blade profile modifications of two-dimensional and three-dimensional compressor cascades are calculated, allowing for the investigations of the impact of geometric variations on the changes in the flow field. Ultimately, aerodynamic optimization of the compressor cascades is conducted. After optimization, the adiabatic efficiency of the two-dimensional cascade increases by 3.11%, and it increases by 1.15% for the three-dimensional cascade. The variations in flow fields of both the original and optimized cascades are illustrated to discover the origins of performance improvements. The changes in blade profile are almost consistent with those forecasted from sensitivity analysis, demonstrating the potential superiority of the adjoint method for aerodynamic design.

Optimizing Winglet Cant Angle for Enhanced Aircraft Wing Performance Using CFD Simulation and Hybrid ANN‐GA

ABSTRACTWinglets are an extended angled or vertical projected at the wing tips used to reduce the drag encountered during the flight of an aircraft. The main aim of this research was to study the effects of winglets on NACA 4412 airfoil at 15° angle of attack. The simulation was done on the basis of the aerodynamic properties such as lift (CL), drag (CD), and lift/drag (CL/CD) ratio for both with and without the winglets at various cant angles. The designing was carried out in ANSYS Design Modeler for both with and without winglet. Further, the meshing part was again carried out in ANSYS Mesh. K‐Epsilon (two equation) turbulence model is used for the simulation at the inlet speed of 100 m/s, since it is the most common model used to simulate the mean flow characteristics for high turbulent conditions. Further, the cant angle has been optimized to get the maximum coefficient of lift using Nelder Mead, Genetic Algorithm, and Genetic Algorithm with ANN optimization techniques.

The continuous adjoint to the incompressible (D)DES Spalart-Allmaras turbulence models

This article formulates the continuous adjoint method for the gradient-based shape optimization of fluid flows governed by the incompressible Detached Eddy Simulation (DES) and Delayed-DES (DDES) models, based on the Spalart-Allmaras turbulence model. As both flow models are inherently unsteady, challenges arise regarding the availability of flow fields during the backward in time integration of the unsteady adjoint equations. To minimize both the computational cost and the memory demands, the computed flow fields are compressed using the iPGDZ+ lossy compression technique, recently developed by the authors. Its application in the context of turbulence-resolving flows, where the compression of flow fields poses an intricate challenge, is a second original contribution of this article. Everything is implemented as an extension to the publicly available adjointOptimisation library of OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization. Using two shape optimization problems in external aerodynamics, it is demonstrated that including the adjoint to the turbulence model equation is crucial for the computation of accurate sensitivity derivatives. In contrast to sensitivities computed under the “frozen turbulence” assumption, which neglects variations in turbulent viscosity due to changes in the design variables, the proposed adjoint method yields sensitivities that align with those obtained using Finite Differences. This is due to the Think-Discrete Do-Continuous adjoint method which, inspired by hand-differentiated discrete adjoint, gives rise to consistent discretization schemes of the terms involved in the equations derived by continuous adjoint. Furthermore, it is demonstrated that the proposed adjoint method can significantly benefit from the iPGDZ+ algorithm, by reducing memory requirements by more than two orders of magnitude, eliminating the need for flow recomputations, while maintaining the accuracy of the computed derivatives. Ways to handle large integration windows of the objective function with this type of flow models are beyond the scope of this article.

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.

Impact of Fan Position and Speed Adjustments in Glass Greenhouse Environments

In the context of the contemporary development of precision agriculture, glass greenhouses, as an important infrastructure for enhancing crop production efficiency and quality, have become a frontier area of agricultural science and technology innovation for the internal microenvironmental regulation, especially the optimization of airflow dynamics and temperature distribution. In this paper, the study is based on the three-dimensional turbulence model equations of Reynolds number and Darcy-Forkheimer law, and modeled the cases without and with crops, simulated their different wind velocity and temperature, generated the corresponding simulation diagrams and analyzed them, and the results show that changing the Wind velocity to 3m/s or changing the fan position to 1m is a better condition than that with Wind velocity of 2m/s and fan position of 1.3m. In this study, it was found that both variables, Wind velocity and fan position, could affect the growth of crops in glasshouse, excluding most of the factors.

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.

Numerical Study on the Self-Pulsation Characteristics of LOX/GH2 Swirl Coaxial Injector

To investigate the self-pulsation characteristics of a liquid-centered swirl coaxial injector with liquid oxygen (LOX) and gas hydrogen (GH2) as the working mediums under supercritical condition, a numerical simulation was employed. The transient simulation of the flow and injection process of cryogenic propellant was carried out using the RNG k−ε turbulence model, VOF model, and Peng-Robinson equation of state. The frequency spectrum of calculated pressure oscillation agreed with the experimental data. The amplitude-frequency characteristics of recess region, LOX, and GH2 paths when self-pulsation occurs were analyzed. The effects of operating parameters, such as the flow rate of LOX or GH2 and the initial GH2 temperature, on the self-pulsation, were evaluated specifically. Results reveal that the self-pulsation results from the periodic variation of pressure and velocity caused by the periodic blocking of annular gas by the liquid sheet. The dominant frequencies of pressure oscillation in the recess region, upstream of LOX, or GH2 path are diverse. But for the points in each region, the dominant frequency is about the same. When the LOX/GH2 mixing ratio increases, the liquid sheet thickness and the number of liquid filaments increase. The position where filaments are massively broken into droplets moves further downstream. For the same mixing ratio, the flow rate of LOX has a greater impact on the atomization features. The pressures corresponding to low or high frequency increase when the initial GH2 temperature raises. The higher temperature would shift the dominant oscillation between the low and high regimes.

Influence of passive strut on the mixing and combustion performance enhancement

The scramjet engine is one of the possible means of reaching supersonic speed using airbreathing engines. As the inflow of air is at supersonic speed, proper mixing and combustion is a challenge. Researchers have used multi-strut arrangements to address the problem. However, the additional supply of fuel from multiple struts with inefficient mixing and combustion leads to losses in terms of fuel and efficiency. Alternatively, the multi-strut configuration could be used to improve the combustion and mixing efficiency passively. In the present investigation, two strut configurations, a fuel injection strut, and a passive strut, have been used. The computational study was done by solving steady Reynolds averaged Navier-Stokes (RANS) equations along with the Shear Stress Transport (SST) k-ω turbulence model, species, and ideal gas equation. Eddy dissipation model was used to solve reacting flow. The introduction of a passive strut in the wake of the fuel injection strut leads to vortices upstream and downstream of the passive strut. These vortices were observed to be responsible for enhancing the mixing and combustion. It was found that judicious placement of the passive strut in the wake of the combustion zone can enhance both the mixing as well as combustion efficiency with minimal loss in total pressure.

Data-driven discovery of turbulent flow equations using physics-informed neural networks

In the field of fluid mechanics, traditional turbulence models such as those based on Reynolds-averaged Navier–Stokes (RANS) equations play a crucial role in solving numerous problems. However, their accuracy in complex scenarios is often limited due to inherent assumptions and approximations, as well as imprecise coefficients in the turbulence model equations. Addressing these challenges, our research introduces an innovative approach employing physics-informed neural networks (PINNs) to optimize the parameters of the standard k−ω turbulence model. PINNs integrate physical loss functions into the model, enabling the adaptation of all coefficients in the standard k−ω model as trainable parameters. This novel methodology significantly enhances the accuracy and efficiency of turbulent flow simulations, as demonstrated by our application to the flow over periodic hills. The two coefficients that have been modified considerably are σω and α, which correspond to the diffusion and production terms in the specific dissipation rate equation. The results indicate that the RANS simulation with PINNs coefficients (k−ω−PINNs simulation) improves the prediction of separation in the near-wall region and mitigates the overestimation of turbulent kinetic energy compared to the base RANS simulation. This research marks a significant advancement in turbulence modeling, showcasing the potential of PINNs in parameter identification and optimization in fluid mechanics.

Performance Evaluation of UAV Airfoil Under Various Ground Conditions

Investigation of ground effects on Unmanned Aerial Vehicle (UAV) are limited. The UAV's ground effect on the water surface and irregular surfaces has not been studied well. The principal objective of this research is to apply numerical solutions to investigate the flow physics and aerodynamic characteristics of selected NACA4412 airfoil for different h/c and surface roughness conditions in the ground effect scenario. The k-ω turbulence model and compressible RANS equations are solved using the Finite Volume Method (FVM). The simulated data is authenticated with the reference data and compared with the DATCOM data. The results express that the lift coefficient variations for various surface roughness are affected by the h/c proportion. The drag coefficient for various roughness has the same pattern for different ratios and almost has the same difference from high to lower values. The result shows that the DATCOM code cannot predict the aerodynamic characteristics with ground effects.

Simulation analysis of enhanced fluidization leaching process and geothermal synergy in deep ground metal mines

Based on the mining of deep metal mineral resources and the current in-situ leaching mining process of uranium ore, combined with the technological characteristics of ?fluidized mining of metal ore? and ?deep geothermal development?, an innovative concept of strengthening the fluidized leaching process of deep metal ore - geothermal co mining is proposed, A numerical simulation method was used to analyze the turbulent flow and heat transfer characteristics of a new type of heat transfer enhancement element - a swirl plate as a support between tubes. The renormalization two equation turbulence model was used for numerical simulation, and the SIMPLEC algorithm was used for pressure and velocity coupling, and the enhanced wall treatment method was used for wall treatment. The periodic changes in the cross-sectional flow field and turbulence intensity of the unit flow channel were analyzed, as well as the synergistic relationship between the flow field and temperature field on the cross-section. The corresponding variation trends of the average Nusselt number and the average synergy angle of the cross-section were compared. The experimental results show that the 270-4.25 cyclone sheet can more fully utilize the enhanced heat transfer of the spin flow, and the overall average Nusselt number is higher than 180-2.0, which is consistent with the experimental results. That is, ?m is low where high Nub and ?m is high where low Nub is low, indicating that the changing trend of the two is fully consistent with the field synergy principle. This paper systematically analyzes the basic theoretical bottleneck, key technical problems and future development trend in the process of geothermal joint mining of deep metal mine, and aims to provide reference for the strengthening of geothermal joint mining and geothermal joint mining of deep metal ore.

Effects of real gas equations on the fast-filling process of compressed hydrogen storage tank

Hydrogen-fueled, fuel-cell-powered cars offer environmentally friendly alternative for near future. One of the critical part of this technology is to store hydrogen efficiently and securely. Many different methods have been developed to store hydrogen. The most popular storage method for hydrogen storage in vehicles is compressible hydrogen storage tanks due to their lightweight and efficiency. One of the most important factors during filling is the filling time. During rapid filling, the tank temperature rises significantly, which can cause damage to the tank and create a dangerous situation. In this research, CFD simulation has been made for fast filling condition for compressible hydrogen storage tanks. It was decided to use the k-ε turbulence model and different real gas equations for numerical simulation. The effects of four different real gas equations and also ideal gas equation on the temperature, the pressure, and filling times are investigated numerically. As a result of the simulation, it was concluded that the use of different real gas equations does not have a significant effect on the temperature and the pressure of the storage tank. However, the filling duration of storage tank is slightly affected by usage of different real gas equations. Filling durations of hydrogen according to Redlich-Kwong equation of state increased for Soave-Redlich-Kwong equation 1.3 %, for Aungier Redlich-Kwong equation 1.5 %, for Peng-Robinson's equation of state 5.85 %, for ideal gas equation of state 24.2 %.

Heat transfer enhancement of supercritical carbon dioxide in eccentrical helical tubes

A type of eccentrical helical tube (EHT) was proposed for more efficient and compact supercritical carbon dioxide (SCO2) heat exchangers in refrigeration systems. The forced convective heat transfer of SCO2 flowing in three designed eccentrical helical tubes with pitches of 25, 50 mm and eccentricities of 0.9, 1.5 mm was simulated by using the three-dimensional steady Reynolds-averaged Navier-Stokes equations, shear stress transport turbulence model and energy equation in ANSYS CFX 2019 R2 at mass fluxes of 200, 400 kg/m2s, inlet pressures of 8, 9 MPa, outwards wall heat fluxes of 12, 24 kW/m2. The flow and heat transfer models were validated in the plain tube with experimental mean heat transfer coefficient and empirical Darcy friction factor. Influences of pitch, eccentricity and operational conditions on heat transfer enhancement were identified. Flow pattern, heat transfer mechanism and vortex kinematics were clarified. Heat transfer enhancement of SCO2 in the EHT was compared with water and air in the EHT, twisted elliptical tube and conical tube, respectively. A pitch of 25 mm and eccentricity of 1.5 mm at 6 mm tube diameter can achieve a better thermal-hydraulic performance. A higher SCO2 mass flux raises Nusselt number and reduces friction factor, a higher inlet pressure and a larger wall heat flux reduces Nusselt number but increases friction factor. The ratio f/f0 is ranged in 2.52–1.68 and drops off with increasing inlet pressure and nominal Reynolds number, the ratios Nu/Nu0, ψ and η curves show a concave shape near the pseudocritical point ranged in 1.68–1.06 and 1.06–1.55, 1.23–0.83 and 0.83–1.30, 0.67–0.50 and 0.50–0.92 at the pitch of 25 mm and eccentricity of 1.5 mm, inlet pressure of 8 MPa, mass flux of 400 kg/m2s, and wall heat flux of 12 kW/m2. A helical flow pattern with a core flow occurs in the EHT, the local heat transfer coefficient can be correlated to absolute helicity. The high-wall shear stress on the ridge of the EHT is responsible for the heat transfer enhancement. The f/f0 value of the EHT is in between the twisted elliptical tube and the conical tube, but the Nu/Nu0 and ψ values are comparable.

Numerical and experimental study of two-vehicle overtaking process

The overtaking process between two simplified Ahmed body models is studied using a set of static experiments to provide a comparison basis for the numerical study. Both steady-state (static) and transient (dynamic) simulations are performed. There are notable differences of the drag and side force coefficients between the predicted and experimental results in the wake effects on the overtaking model as well as under a situation when two models are parallel for the static tests. These differences are attributed to the SST [Formula: see text] model, which is a two-equation Reynolds-averaged Navier-Stokes equation (RANS) turbulence model with an assumption of isotropic eddy viscosity, employed in the simulation. A more advanced turbulence model that simulates large-eddy organized motion in a turbulent flow and which uses an anisotropic eddy viscosity formulation in the near-wall flow subregion would increase the prediction accuracy for the overtaking simulation. A comparison of the results for the steady-state and the transient simulations at various relative velocity ratios ([Formula: see text]) shows that the quasi-steady approach is suited to simulate the dynamic two-vehicle overtaking process when the condition [Formula: see text] is met.

Evaluation of upper airway characteristics in patients with and without sleep apnea using cone-beam computed tomography and computational fluid dynamics.

To determine if upper airway characteristics and airway pressure change significantly between low risk, healthy non-OSA subjects, and OSA subjects during respiration using cone-beam computed tomography (CBCT) imaging and steady-state k-ω model computational fluid dynamics (CFD) fluid flow simulations, respectively. CBCT scans were collected at both end-inhalation and end-exhalation for 16 low-risk non-OSA subjects and compared to existing CBCT data from 7 OSA subjects. The CBCT images were imported into Dolphin Imaging and the upper airway was segmented into stereolithography (STL) files for area and volumetric measurements. Subject models that met pre-processing criteria underwent CFD simulations using ANSYS Fluent Meshing (Canonsburg, PA) in which unstructured mesh models were generated to solve the standard dual equation turbulence model (k-ω). Objective and supplemental descriptive measures were obtained and statistical analyses were performed with both parametric and non-parametric tests to evaluate statistical significance at P < .05. Regarding area and volumetric assessments, there were statistically significant mean differences in Total Volume and Minimum CSA between non-OSA and OSA groups at inhalation and exhalation (P = .002, .003, .004, and .007), respectively. There were also statistically significant mean differences in volume and min CSA between the inhalation and exhalation for the non-OSA group (P < .001 and .002), respectively. While analysis of the CFD simulation was limited by the collected data available, a finding consistent with published literature was that the OSA subject group simulation models depicted the point of lowest pressure coinciding with the area of maximum constriction.

Numerical analysis of thermohydraulic and exergetic performance in corrugated spiral tubes with diverse arc corrugation configurations

This study numerically analyzes the thermohydraulic performance and exergy destruction in a corrugated spiral tube, considering inward, outward, and combined inward-outward configurations versus smooth spiral tubes. It explores how key corrugation geometries like width, height, and pitch as well as flow parameter such as Dean number influence friction factor, Nusselt number, exergy efficiency, and thermal performance factor. The turbulence and thermal aspects of the flow physics are modeled by incorporating the pertinent governing equations, utilizing the SST k-ω turbulence model and Reynolds-Averaged Navier-Stokes (RANS) equations. The results demonstrated that introducing corrugated walls in various configurations enhances the Nusselt number within the spiral tube compared to its smooth counterpart. Nevertheless, this enhancement is accompanied by an increase in both friction factor and exergy destruction. Employing inward corrugations leads to a remarkable 53% surge in the Nusselt number when compared to the smooth tube. Elevating the corrugation height amplifies heat transfer and Nusselt numbers for all configurations, with the inward corrugation (IC) exhibiting the most substantial escalation. Additionally, a corrugation width of (w/Dh=0.1) engenders maximum thermal performance factor values across scenarios. Augmenting the corrugation pitch increases the Nusselt number due to greater heat transfer area, with the inward topology (IC) conferring maximal values. Although the Nusselt number rises with escalating Dean number, the thermal performance factor declines for all tubes owing to a disproportionately larger pressure drop increase. The outward corrugation tube (OC) sustains the highest performance factor across Dean numbers, while the inward-outward configuration (IOC) possesses the lowest.

Effect of a curved turning vane on the heat transfer and fluid flow of four-pass internal cooling channels of gas turbine blades

This numerical study examined the effects of a curved turning vane on the heat transfer and pressure loss of a four-pass internal cooling channel. Three-dimensional omega-based Reynolds stress (RSM-ω) turbulence model equations were used in the computation process. Three different curved turning vane configurations were studied using a simple, without a turning vane under stationary and rotating conditions for Reynolds numbers between 20,000 and 60,000 and a rotation number of 0.042. The numerical results showed good agreement with previous experimental data. Under both stationary and rotating conditions, the curved turning vane in a hub turn reduced the pressure drop significantly compared to the conventional turning vanes. Although a curved turning vane attenuated overall heat transfer, the local heat transfer increased it in particular regions, such as the hub turn and the fourth turn of cooling passages, particularly in cases with smaller radii. Coolant flow through the hub turn of the serpentine channel can reduce recirculation, separation, and flow impingement, which are unfavorable factors of pressure loss, owing to the semi-circular configuration of the curved turning vane. Regarding the rotating conditions, four-pass channels with a smaller radius of a curved turning vane provide better overall cooling performance.

Numerical Simulation of Underexpanded Sonic Jet

Underexpanded sonic jet is numerically simulated using commercial CFD software. Three dimensional Navier Stokes equations alongwith two equation turbulence models are solved. Computed centerline distribution and profiles of various flow variables at various axial stations agree quantitatively with experimental results. The comparison of the flow variables computed with four different two equation models reveals that k - e and RNG k - e models perform very well in predicting both pressure and temperature throughout the flow filed; whereas SST and k - w models fail to predict the flow behavior beyond the first Mach disc.

Swirling jet impingements for thermal management of high concentrator solar cells using nanofluids

Large intensity of irradiance in high concentrator solar cells leads to extremely high temperatures causing an adverse effect on the performance of solar cells. Efficient cooling systems are crucial for the optimal performance of high concentrator cells, which are typically required to operate within a prescribed temperature range (⁓ 110 °C). The implementation of effective cooling strategies poses a significant challenge for High Concentrator Photovoltaic Thermal (HCPV/T) hybrid systems to ensure sustained performance and longevity of the modules. This study proposes a novel method for the thermal management of High Concentrator Solar Cells (HCSC) using swirling nanofluid jets impinging on a heat sink. The study applies RANS (Reynolds-Averaged Navier-Stokes) method with the SST k-ω turbulence model and energy equation to resolve a conjugate heat transfer analysis for three different flow ratios: Qr = 0, Qr = 0.5 and Qr = 1 and two water-based nanofluids: Al2O3-Water and CuO-Water. The numerical results demonstrate a significant decrease in cell temperatures, reaching as low as 71 °C. At a mass flow rate of 50 g/min, the use of Al2O3-Water nanofluid increases the overall electrical efficiency by a maximum of 39.43%. In contrast, a minimum electrical efficiency of 39% for CuO-Water nanofluid is obtained for a lower mass flow rate (25 g/min). Al2O3-Water nanofluid yielded a maximum PEC (Performance Evaluation Criteria) of 116%, while CuO-Water nanofluid yielded about 113%. In addition, an increase of the mass flow rate results in an improvement of temperature uniformity, as demonstrated by a reduction of temperature variation from 6.8 to 5.2. These results suggest that the use of nanofluids is promising. The proposed swirling jet impinging on a heat sink in combination with nanofluid provides an effective cooling technique for HCSC, thereby potentially contributing to the improvement of the cell's performance and longevity.