Two-equation Turbulence Model Research Articles

CFD analysis of Al2O3-syltherm oil Nanofluid on parabolic trough solar collector with a new flange-shaped turbulator model

In this paper, in order to improve the performance of a linear parabolic collector, the thermal effects of using Al2O3-syltherm oil nanofluid with different concentrations and new flange-shaped turbulators are investigated. The simulation was performed by ANSYS-FLUENT-18.2 commercial software using Realizable k-ε two-equation turbulence model. In accordance with the results, it was realized that increasing the volume fraction of nanoparticles (to 5%) and number of turbulators causes the heat transfer coefficient (h) of the fluid to elevate and ultimately the uniform temperature is created in the absorber. For instance, at a flow rate of 4.5kg/s and an inlet temperature of 350 K, the value of h increases by about 8.5 % by changing the number of turbulators from 10 to 15 sets. On the other hand, the results indicate that by changing the arrangement of the turbulators, the heat transfer efficiency of the collector can be increased by 5 % for 350 K, 3.5 % for 450 K and 1% for 550 K inlet temperature.

Application of Linear and Nonlinear Two-Equation Turbulence Models in Hypersonic Flows

A nonlinear two-equation model has been implemented in the OpenFOAM framework and has been assessed for the computation of hypersonic flows with shock-wave boundary-layer interactions (SWBLIs), together with two other linear, low-Reynolds number models, namely the Launder–Sharma model and the shear stress transport model. Supersonic and hypersonic flow computations resulting from the use of these three models have been compared with experimental benchmark cases over a range of conditions. The three original models tested do generally return reasonable predictions of wall pressure in most cases, with the nonlinear model resulting in the best capability among the three in predicting flow separation. The wall heat flux in the interaction region, however, is overpredicted, in most cases by all three models (sometimes showing quite a dramatic overprediction). While the overall wall heat flux predictions of the nonlinear model are closer to the measured values, it is nevertheless evident that there is a need for further improvement. To address this need, the inclusion of a new source term in the dissipation rate equation is proposed, which aims to restrict the turbulent length scales in the shock-wave boundary-layer interaction region. This is inactive in incompressible flows and exerts only a minor influence in supersonic SWBLI cases. Computations of a range of supersonic and hypersonic flows with SWBLI show that this inclusion of the proposed source term in the dissipation rate equation, of both the nonlinear and the linear models, has significant effects only in hypersonic flows. These effects are mainly confined to the thermal predictions of these models. In the nonlinear model predictions, the overestimation of the wall heat flux in the SWBLI region is largely eliminated, while, in the corresponding predictions of the linear model, the overestimation is substantially reduced. The cubic nonlinear model tested, with the proposed new source term to the dissipation rate equation, is thus shown to be a very reliable and cost-effective tool for the Reynolds-averaged Navier–Stokes modeling of supersonic and hypersonic flows.

Comparing the performance of RANS turbulence models between different cavity flow benchmarks

To evaluate the performance of RANS turbulence models, this study compares four different cavity flow benchmarks using the prevailing two-equation turbulence models for indoor airflows, namely the standard and RNG k-ε and the standard and SST k-ω models. A cavity flow consists of one air inlet and one outlet slot. The inlet slot is positioned on the upper left corner of the cavity, whereas the outlet slot is located in the lower right. This cavity flow is representative of mixing ventilation. These four cavity benchmarks differ by their geometry (i.e., the aspect ratio of the room), flow regime and whether the flow is isothermal or not. Measurements of the air velocity and temperature in these benchmarks are used to evaluate the accuracy of the RANS turbulence models. Many existing studies have investigated the airflow and heat transfer over these benchmarks. However, the numerical methods and other relevant CFD parameters are not always described in detail, reducing the transparency and reproducibility of these works. To compare the influence of the RANS turbulence model on the four cavity flows, a same CFD setup is adopted here for all benchmarks. This setup is based on the best practice in RANS, namely a steady second-order spatial discretization on a wall-resolved structured mesh and with a grid convergence analysis. The results show that k-ε models, particularly the standard k-ε model, are best suited in a fully turbulent flow regime without strong pressure gradients. On the opposite, the SST k-ω model performs best in the transitional regime while the k-ε models only give moderate to poor results.

BLOOD FLOW IN ARTERIAL BIFURCATION CALCULATED BY TURBULENT FINITE ELEMENT MODEL

In this paper, turbulent fluid flow is analyzed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results shows that a cardiologist can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries.

Numerical Studies on Particle Dynamics in a Spouted Bed

A coupled computational fluid dynamics (CFD)-discrete element method (DEM) technique has been adopted to examine the dynamic behavior of particles in a rectangular spouted bed. Eulerian method has been used to solve the Navier–Stokes equation for the gas phase (for the CFD) and Lagrangian method (for the DEM) for the particle phase, where the k–ϵ two-equation turbulence model has been used to capture the effect of gas-phase turbulence. In the present work, we sought to predict the minimum spouting velocity (Ums) numerically for a fixed bed height and particular particle properties. The effects of the inelastic collision and the friction on translational and rotational dynamics of the particles in spout, annulus, and fountain zones have been brought out with the intensive parametric study. The results reported here would be a way forward for a better understanding of the spouted bed processing where translational and rotational dynamics of particles play a key role.

Study on Influencing Factors of Helicopter Brownout Evolution Based on CFD-DEM

The gas-solid two-phase flow model is constructed based on the Euler-Lagrangian framework. The SST k−ω two-equation turbulence model and the soft ball model are coupled by computational fluid dynamics (CFD) and a discrete element model (DEM). Brownout is then simulated by the above method with sliding mesh. As the calculation examples show, the simulations and experiments of the Lynx rotor and the Caradonna–Tung rotor are compared. The coupling method is verified through calculation of the rotor lift coefficient, blade section pressure coefficient and tip vortex shedding position. The results show that when the helicopter is hovering at a height of 0.52R from the ground, it will cause brownout and the pilot’s vision will be obscured by sand. When the hovering height is 1R, the phenomenon of brownout is not serious. The movement speed of most sand dust is about 12 m/s, and the height of the sand dust from the ground will gradually increase over time. Large particles of sand are more difficult to be entrained into the air than the small particles, and the particles with a radius of 50 um are basically accumulated on the ground. Moreover, the slotted-Tip rotor has an effect on restraining brownout.

A multi-phase SPH simulation of hydraulic jump oscillations and local scouring processes downstream of bed sills

In the present study, we numerically focus on the vorticity generation mechanism in a scour hole developed downstream of a grade control structure in sand-bed channels. The liquid-granular flow has been simulated through a symplectic Weakly Compressible SPH scheme with a two-equation turbulence model, where the two phases are treated as continua with different rheological properties. The equilibrium configuration of flow field and bed topography is reached after a transient period in which the system oscillates between two flow patterns: (i) the scour hole shows a relatively steep hump downstream of it, increasing the free surface elevation and generating a B-jump type with a counterclockwise rotating macro-vortex structure which pushes the main flow towards the bed, where strong erosive action is observed; (ii) the scour shows a relatively modest inclination of the scour cavity, leading to the formation of a wave jump dominated by a clockwise rotating macro-vortex structure.

Machine learning accelerated turbulence modeling of transient flashing jets

Modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ−Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ−Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier–Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit.

Numerical investigation of aerospike semi-cone angle and a small bump on the spike stem in reducing the aerodynamic drag and heating of spiked blunt-body: New correlations for drag and surface temperature

Aerodynamic drag and heat reduction effectivity of the aerospike attached to the blunt-body at various aerospike semi-cone angles (θS), lateral injection from the aerospike stem, and a small bump on the aerospike stem, at different Mach number is numerically investigated. An open-source computational fluid dynamics code, i.e., rhoCentralFoam, a density-based solver in OpenFOAM is employed to solve the governing equations of supersonic turbulent flow. Menter's two-equation turbulence model, i.e., k−ω shear stress transport model is employed for turbulence modeling. A significant reduction in the total drag force (TDf) on the blunt-body is observed with the increase in aerospike θS at a fixed spike length (L)/blunt-body diameter (D) ratio for Mach 2 and 5. With the increase in θS>15° for L/D = 1 and θS>10° for L/D = 2, a significant decrease in the magnitude of coefficient of pressure is observed for Mach 5. Results show a maximum percentage reduction of 23.611% and 61.414% in TDf at L/D = 2 and θS=45° for Mach 2 and 5, respectively. Correlations are developed for the estimation of total drag force on the blunt-body and average surface temperature of the nose at Mach 2 and 5. Lateral injection substantially improves the aerodynamic heat reduction capability of the aerospike owing to the rapid expansion of the injectant in the main flow. An alternate passive technique (a small bump on the spike stem) capable of producing higher aerodynamic drag reduction compared to the active technique (i.e., lateral injection) is proposed. The small bump on the spike facilitates an early initiation of boundary layer separation and leads to the formation of a large recirculation zone ahead of the nose. Results indicate a higher reduction in aerodynamic drag with the increase in bump height (HB) compared to lateral and no injection at Mach 2 and 5. Present results have been validated with the experimental results available in the literature.

EVALUATION OF THE RANS TURBULENCE MODEL PREDICTIVE CAPABILITY OF FLAT PLATE FILM COOLING

The two-equation turbulence models used for the present study are the commonly used standard k-ॉ model and k-ω model. In order to achieve this target, numerical simulation was initiated in Ansys Fluent to simulate a flow over a flat test surface with a diameter of 4mm straight, circular film cooling hole at angled injections of 25°, 30°, 35°and 40°. The comparison between the numerical calculations and the theoretical results showed the standard k-ω turbulence model gave better predictions against those with the standard k-ω turbulence models. The ability of k-ω model in closely predicting the cooling behavior is due to the precise modeling of the lateral spreading of the film. The isotropic two-equation turbulence models exhibited a huge dissent. The results also indicated that increasing the mass flow rates in the mainstream channels reduces the temperature distribution along the stream-wise direction.

Improved convergence characteristics of two-equation turbulence models on unstructured grids

Second order upwind scheme discretization of Reynolds-averaged Navier–Stokes turbulence models may lack robustness, especially when using unstructured grids. Among several factors that can be traced as the reasons, preserving a monotonic solution plays a key role. A possible remedy is to smooth the variation of the turbulence model dependent variables. To that end, a square root transformation is applied to the dependent variables of a k-ω turbulence model. The new additional source diffusion terms that emerge as a result of the transformation are fully retained. Therefore, the transformed model reproduces the baseline k-ω model performance. Moreover, the transformed model greatly enhances the robustness and reliability of turbulent flow simulations on unstructured grids.

Adjoint Complement to the Universal Momentum Law of the Wall

The paper is devoted to an adjoint complement to the universal Law of the Wall (LoW) for fluid dynamic momentum boundary layers. The latter typically follows from a strongly simplified, unidirectional shear flow under a constant stress assumption. We first derive the adjoint companion of the simplified momentum equation, while distinguishing between two strategies. Using mixing-length arguments, we demonstrate that the frozen turbulence strategy and a LoW-consistent (differentiated) approach provide virtually the same adjoint momentum equations, that differ only in a single scalar coefficient controlling the inclination in the logarithmic region. Moreover, it is seen that an adjoint LoW can be derived which resembles its primal counterpart in many aspects. The strategy is also compatible with wall-function assumptions for prominent RANS-type two-equation turbulence models, which ground on the mixing-length hypothesis. As a direct consequence of the frequently employed assumption that all primal flow properties algebraically scale with the friction velocity, it is demonstrated that a simple algebraic expression provides a consistent closure of the adjoint momentum equation in the logarithmic layer. This algebraic adjoint closure might also serve as an approximation for more general adjoint flow optimization studies using standard one- or two-equation Boussinesq-viscosity models for the primal flow. Results obtained from the suggested algebraic closure are verified against the primal/adjoint LoW formulations for both, low- and high-Re settings. Applications included in this paper refer to two- and three-dimensional shape optimizations of internal and external engineering flows. Related results indicate that the proposed adjoint algebraic turbulence closure accelerates the optimization process and provides improved optima at no computational surplus in comparison to the frozen turbulence approach.

Level set-based topology optimization for two dimensional turbulent flow using an immersed boundary method

This paper presents a topology optimization method for two dimensional turbulent flow based on the Reynolds-averaged Navier-Stokes (RANS) equations using a level set boundary expression and the immersed boundary method (IBM). In this study, two-equation turbulence models, the k-ϵ and the k-ω, are considered. In our proposed method, the level set method is used for capturing the exact fluid-solid interfaces. Additionally, the no-slip boundary condition along the fluid-solid interfaces is imposed explicitly using the IBM during the optimization process. Based on the information of the exact boundary position, the interpolated velocity and pressure values within the viscous sublayer are estimated using the standard wall function. From the above formulations, we construct a topology optimization method for the total pressure drop minimization problems considering two dimensional turbulent flows, under the frozen turbulence assumption. We provide numerical examples to confirm the validity and utility of the proposed method.

Turbulent finite element model applied for blood flow calculation in arterial bifurcation

Background and objectiveDue to the relatively low fluid velocities in major arteries and veins, blood flow is by default laminar, however, turbulence can occur as a result of stenosis or other obstacles. Hemodynamic parameters like Wall Shear Stress or Oscillatory Shear Index can be used for plaque formation prediction, and these parameters are depended on the nature of the flow. Implementation of the k-ω turbulent flow in the Finite Element solver aims to improve numerical analysis of cardio-vascular condition development and progression. Calculation of turbulent fluid flow in this paper is performed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. MethodsImplicit integration of the equations is used for determining the fluid velocity, turbulent kinetic energy and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model with the customized generation of finite element meshes is used for calculating complex blood flow problems. ResultsTurbulent model is verified on an example of fluid flow in the backward-facing step channel and analysis results correspond well with the experimental ones from the literature. Further, a turbulent model is applied for the simulation of blood flow through artery bifurcation. Verification of numerical examples obtained using different commercial software packages (Ansys, COMSOL Multiphysics) ensuring usage and accuracy of PAK in-house solver. ConclusionsAnalysis results show that turbulence cannot be neglected in the modelling of cardio-vascular conditions and that cardiologists can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries. Appropriate agreement between experimental results, and results obtained using commercial solutions and the k-ω turbulent flow in the Finite Element solver PAK, validate methodology presented in this paper. However, small deviations between the results underline the importance of the proper boundary condition prescription and mesh size and node distribution, which is also discussed in this paper. Due to the implicit integration implemented in PAK solver, time step size has an insignificant influence on the analysis results, assuming the initial time increments are sufficiently small to ensure proper discretization of velocity and pressure pulsatile functions.

Analysis of flow field and turbulence predictions in a lung model applying RANS and implications for particle deposition

Airflow and aerosol deposition in the human airways are important aspects for applications such as pulmonary drug delivery and human exposure to aerosol pollutants. Numerical simulations are widely used nowadays to shed light in airflow features and particle deposition patterns inside the airways. For that purpose, the Euler/Lagrange approach is adopted for predicting flow field and particle deposition through point-particle tracking. Steady-state RANS (Reynolds-averaged Navier-Stokes) computations of flow evolution in an extended lung model applying different turbulence models were conducted and compared to measurements as well as high resolution LES (large-eddy simulations) for several flow rates. In addition, various inlet boundary conditions were considered and their influence on the predicted flow field was analysed. The results showed that the mean velocity field was simulated reasonably well, however, turbulence intensity was completely under-predicted by two-equation turbulence models. Only a Reynolds-stress model (RSM) was able predicting a turbulence level comparable to the measurements and the high resolution LES. Remarkable reductions in wall deposition were observed when wall effects were accounted for in the drag and lift force expressions. Naturally, turbulence is an essential contribution to particle deposition and it is well known that two-equation turbulence models considerably over-predict deposition due to the spurious drift effect. A full correction of this error is only possible in connection with a Reynolds-stress turbulence model whereby the predicted deposition in dependence of particle diameter yielded better agreement to the LES predictions. Specifically, with the RSM larger deposition is predicted for smaller particles and lower deposition fraction for larger particles compared to LES. The local deposition fraction along the lung model was numerically predicted with the same trend as found from the measurements, however the values in the middle region of the lung model were found to be somewhat larger.

Heat transfer enhancement and application of multiple stepped jet cooling in a vertical alloying furnace

Jet impingement cooling of vertical moving plate is widely employed in the energy and metallurgical industries. To improve heat transfer and the cooling of these plates in a vertical channel, an innovative stepwise jet cooling design model was proposed in the present study. To investigate the heat transfer enhancement mechanism of this multiple jet cooling, mixed convection in a three-dimensional model of a soaking zone and a jet impingement cooling tower was simulated using the commercial program ANSYS CFX. Navier–Stokes equations, which were solved using the SIMPLEC algorithm, enclosed by an RNG k-ε two-equation turbulence model were employed to calculate the fluid flow and heat transfer. Based on observations of the airflow velocity vector and temperature distribution, the critical equilibrium state for buoyancy and the inertia force was found to occur at a combined Reynolds number of 1.40 × 107. Based on this double-enhancement effect and the effect of different nozzle heights, a multiple stepped jet impingement cooling design that jet velocity decreased with its height increasing was applied to a vertical alloying furnace. The Nusselt number for stepwise jet cooling in the vertical alloying furnace was 111–118% higher than that for constant jet cooling. Therefore, the stepped jet cooling model offers greater energy conservation than does constant velocity when the total jet flow mass is held constant.

Anisotropic SST turbulence model for shock-boundary layer interaction

Menter SST k-ω is a Reynolds-averaged Navier–Stokes based two-equation turbulence model routinely used in industry for predicting aerodynamic flows. It shows excellent performance for low-speed flows, but gives inconsistent predictions for high-speed shock-induced separated flows. The model assumption of using a constant value of 0.31 for the structure parameter contradicts experimental observations. The model is also unable to predict Reynolds stress anisotropy generated by shock waves. In this work, we augment the SST model with quadratic eddy viscosity formulation of an explicit algebraic Reynolds stress model. A new relation for the structure parameter is proposed, making it a function of the local strain-rates and is no longer a constant in the regions of shock/turbulent boundary layer interaction (SBLI). Additional shock-physics is introduced using (Sinha et al., 2003) shock-unsteadiness model and an upper limit to the value of structure parameter is set in regions of shock waves. The new model, termed as SUQ-SST, is validated using a number of SBLI test cases ranging from supersonic to hypersonic speeds and near-incipient to fully-separated flows. Results show that the modifications do not alter the boundary layer prediction capability of the SST model. On the other hand, the new model gives significant improvement in predicting Reynolds stress anisotropy, flow separation, and surface properties in a wide range of SBLI flows.

Ventilation effectiveness of uniform and non-uniform perforated duct diffusers at office room

Half of the energy usages in buildings is due to HVAC systems, and the efficiency of the subsections plays an essential role in the evaluation of the total energy consumption. Previous works on ventilation systems using perforated duct diffusers (PDDs) were mainly concentrated on the calculation of the thermal comfort indices, while their energy consumption and ventilation effectiveness were omitted. In this paper, a mixed experimental-numerical method has been developed to evaluate the real efficiency of PDDs with different perforation patterns. So, an office room facility is used for the full-scale experiments and the validation of the numerical simulations. Incidentally, five RANS models have been benchmarked to highlight the most accurate numerical model for this specific application. As a result, a k-ε Realizable turbulence model with 4.3 million mesh elements has been preferred over the tested two-equation turbulence models to determine the diffuser parameters like age of air, terminal velocities, air-change effectiveness, and air exchange efficiency. Within this model, the required outdoor airflow for four types of PDDs has been calculated following the ASHRAE standard procedure. The discrepancy of the real efficiency and the calculated value for the nearest application in the standards shows that the performance of PDDs is underestimated, and they require lower airflow in reality. Later, it is shown that for the systems using PDDs, the required airflow and energy consumption decrease by up to 18.4%, and a more uniform air distribution is achieved using a non-uniform perforation pattern.

Analysis of Flow Characteristics and Effects of Turbulence Models for the Butterfly Valve

In the present study, the flow characteristics of butterfly valves with different sizes DN 80 (nominal diameter: 76.2 mm), DN 262 (nominal diameter: 254 mm), DN 400 (nominal diameter: 406 mm) were numerically investigated under different valve opening percentages. Representative two-equation turbulence models of two-equation k-epsilon model of Launder and Sharma, two-equation k-omega model of Wilcox, and two-equation k-omega SST model of Menter were selected. Flow characteristics of butterfly valves were examined to determine turbulence model effects. It was determined that increasing turbulence effect could cause many discrepancies between turbulence models, especially in areas with large pressure drop and velocity increase. In addition, sensitivity analysis of flow properties was conducted to determine the effect of constants used in each turbulence model. It was observed that the most sensitive flow properties were turbulence dissipation rate (Epsilon) for the k-epsilon turbulence model and turbulence specific dissipation rate (Omega) for the k-omega turbulence model.

Eddy viscosity modeling around curved boundaries through bifurcation approach and theory of rotating turbulence

A novel approach to curvature effects based on the bifurcation theory and rotation turbulence energy spectrum is implemented to improve the sensitivity of the k−ϵ two-equation turbulence model (Jones–Launder form) to curved surfaces. This is done by accounting for the vorticity tensor, which becomes more significant in curved flows, something that the standard k−ϵ model does not originally consider. This new eddy viscosity model is based on the energy spectrum for a turbulent flow undergoing rotation and is then modeled on the bifurcation diagram in ϵ/Sk−η2/η1 phase space. The approach is demonstrated on three different test cases, 30° two-dimensional curved channel, 90° three-dimensional bend duct, and flow past cylinder, to test for the effects of convex and concave curvatures on turbulence. The results from these test cases are then contrasted against other existing eddy viscosity models as well as experimental data. The proposed approach provides better turbulence predictions along convex or concave surfaces, better memory effects, and are closer to the experimental results. For flow past cylinder, the new eddy viscosity model predicts drag coefficient that is closer to experiments with 8% difference, against 30% difference predicted by standard k−ϵ and Pettersson models.