Turbulence Model Research Articles

Numerical Investigation of Performance and Flow Characteristics of Francis Turbine in Part Load Condition

Abstract Due to the complexity of the flow phenomena inside Francis turbines, it is very time-consuming and expensive to determine their performance and flow characteristics under different operating conditions through model tests and field measurements. The use of computational fluid dynamics (CFD) to improve turbine design and performance is a more cost-effective alternative to traditional methods of forecasting flow characteristics in different flow domains across the whole turbine channel. The performance and flow characteristics of the turbine under various part load working circumstances are studied by numerical simulations employing the shear stress transfer SST (k − ω) turbulence model. Four different operating conditions from 50%,70%,80% and 100% of the maximum and minimum power were analyzed, and the flow characteristics across the entire turbine channel were investigated in detail. The study results shows the calculated efficiencies of four operating condition have good agreement with measured ones, and the efficiency differences between numerical simulation and measurement are below 0.44%. Visualization of velocity and pressure in the whole Francis turbine shows that output torque, output power, and performance are in good agreement with experiment results. This study’s findings can be utilized to improve the design, efficiency, and hydraulic stability of Francis turbines.

Flow mixing and heat transfer deterioration investigation of supercritical carbon dioxide in wire-wrapped bundles

As one selection of the fourth-generation reactors, the gas cooled reactor has received enormous attention such as high power conversion efficiency and simple cycle layout. In this paper, the flow mixing and heat transfer characteristics of supercritical carbon dioxide within a seven-pin wire-wrapped bundle were investigated. Due to the lack of more experiments data of velocity field, two experiments were selected to validate the uncertainty of different turbulence models from the view of temperature field. The analysis of mass exchange between different subchannels revealed that coolant flows consistently in a certain direction in edge and corner subchannels, whereas in center subchannels, the cross flow changes direction periodically. The mixing coefficients at three types of subchannel interfaces were fitted by a sine function with the R2 values are all greater than 0.96. For different mass flux and pressures, the root mean square error between correlations and simulations was less than 1 × 10-3, except when Re equals 15000. Additionally, the heat transfer deterioration of SCO2 was observed. While wire spacers can mitigate the extent of heat transfer deterioration, they cannot completely eliminate it. The Performance Evaluation Criterion (PEC) was introduced to assess the effectiveness of wire spacers in enhancing heat transfer. The results indicate that the PEC exceed unity, meaning that the enhanced heat transfer capability outweighs the additional resistance loss caused by wire spacers. With increasing pressure, the PEC decreases but remains greater than unity. The mixing of coolant between different subchannel induced by wire spacers can reduce the wall temperature of rods at the edge of the bundle. However, the seven-pin wire-wrapped bundle was investigated in this work, and the results may not accurately reflect the flow and heat transfer inside a real reactor rod bundle. In the future, a larger scale rod bundle should be conducted to obtain more universally applicable and realistic flow and heat transfer phenomenon for reactor assembly design.

Numerical study on the influence of the bucket offset angle on the flow field of Pelton turbines with six-nozzles

Abstract Pelton turbines are emerging as a primary means for exploiting ultra-high water head resources. The hydraulic performance of a Pelton turbine is determined by the design of its runner/bucket. Among the critical parameters that affect the hydraulic performance of multi-nozzle Pelton turbines is the bucket offset angle (α). To investigate the influence of bucket offset angle on the flow field of Pelton turbines with six nozzles, this study conducted unsteady numerical simulations of gas-liquid two-phase flow for various bucket offset angles, employing the VOF multiphase model combined with the SST k-ω turbulence model. The results reveal that as the bucket offset angle increases, the axial width of the water sheet formed by the current jet progressively widens, with a tendency to catch up with the water film formed by the previous jet during the torque rising stage. Moreover, the increased bucket offset angle causes the water sheet to distribute more closely to the bucket cutout, raising the risk of leakage from the cutout. Notably, at α= 10°, some of the water sheet has already flowed out of the cutout and collided with the subsequent jet.

A numerical study on transport of dust particles accompanied by air gouging process and energy consumption in a circulating ventilation workshop

A modified circulating layered ventilation system is proposed to address the issue of particulate pollutants in the casting cleaning workshop, taking into account the characteristics of end treatment and production processes. By combining Reynolds Average Navier-Stokes (RANS) turbulence model and Discrete Phase Model (DPM), the particle transport law in the coupled flow process of thermal plumes generated by purified circulating airflow and heat source was explored, and ventilation energy consumption was evaluated from the perspective of particle removal energy efficiency ratio. Comparing three ventilation modes: mixed ventilation (MV), wall-based attachment ventilation (WAV), and wall-based attachment ventilation with deflector (WAV-D), it was found that the large vortex region formed by the change in airflow direction during WAV played a key role in particle transport. Placing deflector helped to reduce the impact of vortex recirculation zones generated by the intersection of airflow and plumes on particles. A higher fresh air rate will weaken the diffusion effect of particles in the horizontal air lake region. Continuously increasing the air supply volume to a certain level has little effect on the transportation of low-inertia particles, yet it still manages to effectively enhance the removal efficiency of medium-inertia particles. However, for high-inertia particles, an increase in air supply can easily lead to excessive particle concentration in local areas. When the particle removal efficiency reaches a certain level, higher supply air volume and fresh air rate may lead to a significant decrease in energy efficiency ratio.

An innovative modification to the Menter shear-stress transport turbulence model employing the symbolic regression approach

Drawing from the non-equilibrium link between the production Pk and dissipation ε of turbulent kinetic energy (TKE), we advocate for the introduction of a limiter to modulate the TKE production term within the Menter shear-stress transport (SST) model. The original SST model is made more sensitive to the adverse pressure gradient (APG) by Bradshaw's assumption. Bradshaw's assumption introduces the equilibrium condition Pk/ε = 1 in most regions of the turbulent boundary layer. In the APG flows with Pk≫ε, the equilibrium condition suppresses the magnitude of TKE (k) within the boundary layer, resulting in an early separation problem. To address this issue, we employ the symbolic regression (SR) to scrutinize the physical correlation between Pk/ε and local turbulence parameters, obtaining an approximate function FSR that encapsulates the relationship between Pk/ε, Sk/ε, and y+ in the APG flow. Following its incorporation into the original SST model in the form of a limiter, the FSR evolves into the SST-Symbolic Regression Evolution model. The SST-SRE is then applied to four cases with APGs. The modification leads to an increase in the skin-friction coefficient Cf in the APGs region and causes a downstream shift in the separation location, improving the consistency with high-accuracy data and experimental results. It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.

Numerical study of particle dispersion in the wake of a static and rotating cylinder at Re = 140 000

In this study, the particle-laden flow in the wake of a static and a rotating cylinder at Reynolds number of 140 000 was investigated using the Reynolds Averaged Navier–Stokes numerical approach. Three turbulence models such as k–ω shear stress transport, Reynolds stress model, and local-correlation transition model (LCTM) were selected to predict the flow topology. Lagrangian approach with one-way coupling was used to track solid spherical particles of different sizes (0.01, 0.1, 2.5, 10, and 50 μm). The study reveals that LCTM is the most accurate to predict the flow topology in both cases. Cylinder's rotation generates different effects on flow structure. It breaks the wake's symmetry and reduces its width, and increases the frequency of vortex shedding and the size of the recirculation zone. Particle transport analysis has revealed that particles' response to the flow depends on their Stokes number and wake flow topology. Particles of 0.01, 0.1, and 2.5 μm distribute in and around vortex cores, while particles of 10 and 50 μm do not penetrate vortex cores. Instead, 10 μm particles accumulate mainly around the periphery of vortices, while 50 μm particles skip the vortex street to the thin shear flow region between vortices to be transported by the mainstream flow. Finally, cylinder rotation reduces the particle spread in the vertical direction and shifts all particle distributions in the cylinder's rotation direction. Analysis of particle dispersion functions showed that cylinder's rotation reduces differences in dispersion extent depending on particle size.

Sensitivity of the endwall flow in a linear vane cascade to blade fillet geometry

Based on the blade chord and inlet velocity, the current computational study uses a linear vane cascade with a large filleted blade-endwall junction with a 2.01 x 105 Reynolds number. Three fillets with related profiles are explored. To evaluate the upshots of geometric differences in a fillet attached to the endwall flow-field, the height and endwall-width of the fillets are changed. The RANS k-ω turbulent model is used in the computations, and the results are compared to experimental results from a similar cascade without the fillet. The computed results of the secondary flow-field in the endwall region along the cascade are compared for baseline (no fillet) and filleted passages. As a result of diminished leading-edge and passage vortices, the fillets lower pitchwise pressure gradients, flow separation, axial vorticity, and overall pressure losses when compared to the baseline. The pros of fillets on endwall secondary flows are however unaffected by fillet's geometric changes.

Design and optimization of injector-type air-curtain equipment for tunnels during construction

During tunnel construction, a lot of dust is produced at the heading face, posing a threat to the health of construction personnel. Dust removal and air curtain (AC) systems are typically used to reduce and isolate dust, respectively. A mechanical mechanism based on jet technology is designed to form an AC. The incompressible N-S equations and the realizable k-ε turbulence model are used to simulate the jet AC and the air flow in the tunnel space, the calculation methods and settings used are verified to be reliable. The effects of the air supply duct (ASD) and its relative position on the AC equipment, air outlet baffle (AOB), and jet air volume on the AC were studied. The AOB can increase the inclination angle of the AC and velocity of the outer edge of the AC, and reduce the air leakage in the tunnel. The jet air volume has limited influence on the AC, and the installation of the ASD can improve the convergence of the AC, particularly when the ASD is located on a different side. The data and conclusions obtained from the simulation analysis can provide reference for the design and manufacture of jet AC.

Parameterized Internal Wave Mixing in Three Ocean General Circulation Models

AbstractThe non‐local model of mixing based on internal wave breaking, IDEMIX, is implemented as an enhancement of a turbulent kinetic energy closure model in three non‐eddy resolving general circulation ocean models that differ in the discretization and choice of computational grids. In IDEMIX internal wave energy is generated by an energy flux resulting from near‐inertial waves induced by wind forcing at the surface, and at the bottom, by an energy flux that parameterizes the transfer of energy between baroclinic and barotropic tides. In all model simulations with IDEMIX, the mixing work is increased compared to the reference solutions without IDEMIX, reaching values in better agreement with finestructure observations. Furthermore, the horizontal structure of the mixing work is more realistic as a consequence of the heterogeneous forcing functions. All models with IDEMIX simulate deeper thermocline depths related to stronger shallow overturning cells in the Indo‐Pacific. In the North Atlantic, deeper mixed layers in simulations with IDEMIX are associated with an increased Atlantic overturning circulation and an increase of northward heat transports toward more realistic values. The response of the deep Indo‐Pacific overturning circulation and the weak bottom cell of the Atlantic to the inclusion of IDEMIX is incoherent between the models, suggesting that additional unidentified processes and numerical mixing may confound the analysis. Applying different tidal forcing functions leads to simulation differences that are small compared to differences between the different models or between simulations with IDEMIX and without IDEMIX.

Impact of low-frequency fluctuations on loads of a fixed-bottom offshore reference wind turbine

Marine atmospheric turbulence is predominantly characterized by large-scale structures associated with low-frequency wind turbulence. However, conventional turbulence models for assessing wind turbine loads often fall short of adequately integrating these low-frequency wind fluctuations. In this study, we used a model for low-frequency wind fluctuations to generate wind fields representative of offshore wind conditions in the North Sea. The IEA 15 MW reference wind turbine was subjected to three distinct incoming wind fields: high-frequency (3D) turbulence, low-frequency (2D) turbulence combined with high-frequency (3D) turbulence, and 3D turbulence scaled by target or measured standard deviation of wind components. We found that increased damage equivalent loads by incorporating the low-frequency wind fields are only significant for the tower base fore-aft and blade root fore-aft moments. The impact of low-frequency wind turbulence on the damage equivalent loads was more pronounced for below-rated wind speeds. The scaled 3D turbulence yielded the highest lifetime damage equivalent loads, i.e., in the range of 8-18% more than the unscaled 3D turbulence and combined 2D +3D turbulence. This method leads to an overestimation of loads and, hence, more expensive turbines. Incorporating 2D+3D turbulence in wind fields resulted in a 3.8% increase in lifetime damage equivalent loads for the tower base fore-aft and blade root flapwise moments compared to unscaled 3D turbulence. These findings underscore the importance of considering low-frequency wind fluctuations in the turbine design process, especially for a more accurate estimation of loads.

Numerical study of separation flows in a U-duct using DDES method

Separation flow in a curved duct is a common phenomenon in engineering applications, and it highly contributes to the performance of fluid machinery. Accurate prediction of curved duct flows using the computational fluid dynamics method remains a challenge due to the limitations of turbulence modeling. Hence, the high-fidelity method of the delayed detached eddy simulation (DDES) approach is employed to simulate the U-duct flow with a Reynolds number of 105. The DDES results are compared with experimental data from the study by Monson et al. (1990) and analyzed in detail. The Q-criterion is defined to analyze the vortex structures and study the mechanism in the flow separation region. Discussions are made on turbulence characteristics, including turbulence energy spectra, helicity density, and turbulence anisotropy in the U-duct flow. Results indicate that the regions near the wall and within flow separation are highly anisotropic. The turbulence near the wall region is in a two-dimensional state, and the turbulence within the flow separation region is in a “rod-like” state.

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Evolution mechanism and interaction of the muzzle combustion-gas jets field of underwater dual-barrel synchronized launch

Despite a certain amount of research that has been done on the muzzle combustion–gas jet field of underwater launching in recent years, there are still few reports on the evolution mechanism and interaction of underwater dual-barrel synchronised launch flow fields. To fill this gap, this study aimed to numerically analyse the effects of different barrel intervals on the transient jet field evolution characteristics of the dual-barrel launch. The three-dimensional unsteady multi-phase mathematical model was created and compared with an underwater sealed emission experiment of data for verification. The volume of fluid multi-phase flow model is used to describe the gas–liquid two-phase flow process, and the k–ε turbulence model simulates the turbulent mixing phenomenon in the jet field. On this basis, the user-defined function coupling internal ballistics process was used to determine the transient jet field of a double-barrelled, 30 mm (d = 30) underwater artillery numerically at the barrel intervals of 3d, 4d and 5d. The calculation results indicate that the closer the interval is, the more chaotic the pressure field is, and the Mach disc structure forms later. When the barrel interval is 3d, the Mach disc formation time is ∼ 0.2 ms, while it forms at ∼ 0.15 ms when the barrel interval is 5d. The movement law of projectiles in water is consistent with the change of Mach disc displacement with time, and both satisfy the exponential growth law. The velocity field core is elliptical, and the vortices on both sides of the muzzle continue to grow within 0.4 ms when the launch interval is 3d. As the barrel interval increases, the core of the velocity field is bottle-shaped, the vortex on both sides of the muzzle increases first and then decreases within 0.4 ms, and the maximum temperature of the flow field increases by 15 %.

Numerical Simulation of Unsteady Cavitation at the Tongue of a Centrifugal Pump

Abstract The flow separation at the tongue of the centrifugal pump will cause a sharp reduction of local pressure, thus inducing the cavitation phenomenon, which hurts the stable operation of the pump. This article focuses on the centrifugal pump as the research object. The Delayed Detached Eddy Simulation (DDES) method based on the SST turbulence model was employed to numerically simulate the cavitation at the tongue of the centrifugal pump. The typical characteristics and unsteady changes of cavitation were observed and studied, and the pressure at the tongue position was monitored for flow rates of 1.36 Q 0 and 1.54 Q 0. The results show that, in the cloud cavitation stage, the area of the cavitation bubble presents periodic changes, the main frequency of the cavitation area pulsation is twice the axial frequency, the periodic shedding of the cavitation bubble is caused by the attached vortex (re-entrant jet) and the pressure gradient, and the wall attached vortex will periodically shed and break. The high intensity vortices generated by flow separation at the tongue will change periodically with the rotation of the blade. With the increase of inlet flow, the pressure pulsation at the tongue increases, and the shedding and collapse of the cavitation bubble will enhance the pressure pulsation.

Observations of Nonthermal Velocities and Comparisons with an Alfvén Wave Turbulence Model in Solar Active Regions

We present a study of spectral line width measurements from the Extreme-ultraviolet Imaging Spectrometer on Hinode. We used spectral line profiles of Fe xvi 262.984 Å, Fe xiv 264.787 Å, Fe xiv 270.519 Å, Fe xiv 274.203 Å, and Fe xv 284.160 Å, and studied 11 active regions. Previous studies of spectral line widths have shown that in hot loops in the cores of active regions, the observed nonthermal velocities are smaller than predicted from models of reconnection jets in the corona or shock heating associated with Alfvén waves. The observed line widths are also inconsistent with models of chromospheric evaporation due to coronal nanoflares. We show that recent advances in higher resolution Alfvén wave turbulence modeling enables us to obtain nonthermal velocities similar to those measured in active regions. The observed nonthermal velocities for the 11 active regions in our study are in the range of 17–30 km s−1, consistent with the spectral line nonthermal widths predicted from our model of 16 interacting flux tubes, which are in the range of 15–37 km s−1.

Study of the Effect of Incoming Flow with Fluctuating Gas Void Fraction on Transient Characteristics of a Three-stage Multiphase Pump

Abstract For the oil field with high gas content, the oil well produced has obvious gas content fluctuation characteristics. The unsteady flow of multiphase pump will be caused by the fluctuation flow into the pump. In this paper, the unsteady numerical simulation of the flow field in a three-stage multiphase pump is carried out by using Euler-Euler two-fluid model and SST turbulence model. The results show that the pressurization and torque of each impeller change with the fluctuation of the inlet gas content. The second stage impeller has the highest fluctuation due to the change of flow pattern. The inlet gas rate pulsation frequency and static and static interference have significant effects on the pressure pulsation in the impeller, and the dominant frequency is gas rate pulsation frequency or 11 times rotation frequency. The dominant frequency of the diffuser is the blade passing frequency and its double frequency, and the pulsation frequency of the gas content is the secondary frequency and the amplitude is relatively stable. The axial force increases with the increase of gas content, while the radial force changes in reverse.

Investigation of resistance performance of anti-icing wave-plate separators for marine gas turbines intake system

Abstract Due to their high power and efficiency, gas turbines are commonly used propulsion systems in hovercraft propulsion systems. In polar and cold marine environments, when a hovercraft rises, a significant number of droplets are generated on the water surface and are drawn into the gas turbine’s air intake with the cold air. This paper takes the structure of the original wave-plate separator as a reference and designs two structures: the rhombic anti-icing wave-plate separator (RAWS) and the streamlined anti-icing wave-plate separator (SAWS). Experimental and numerical simulation methods are employed to calculate the air intake resistance of the two structures at speeds ranging from 1 to 10 m/s. The results show that the K-ε standard enhanced wall function turbulent model is the closest to experimental measurements, with all calculated results having an error below 5%, demonstrating reliability. Compared to RAWS, the calculated total pressure loss for the SAWS structure decreases by 200 Pa under a designed air intake velocity of 7 m/s, representing a relative reduction of 40.8%. This provides a valuable reference for the design and resistance optimization of ship air intake anti-icing devices.

A field inversion and symbolic regression enhanced Spalart–Allmaras model for airfoil stall prediction

A data-driven turbulence modeling method based on symbolic regression (SR) is proposed in this paper to enhance the prediction accuracy of the Spalart–Allmaras (SA) model for airfoil stall. Unlike traditional methods that rely on neural networks and lack physical interpretability, this paper utilizes SR to establish an analytic expression mapping local flow field variables to the SA model correction factor β. The training data are obtained through field inversion with the discrete adjoint method in the flow field of the S809 airfoil. Additionally, a relearning approach proposed in this paper is applied to the SR process to address the issue arising from the multi-solution nature of field inversion. The SA model embedded with β, referred to as the SA-SR model, can be integrated into computational fluid dynamics solvers with negligible computational cost. The generalization performance of the SA-SR model is tested under various conditions and airfoil types. The results indicate that the new model improves the predictive capability for airfoil stall without compromising the performance of the baseline SA model for attached flows.

An ALMA Search for Substructure and Fragmentation in Starless Cores in Orion B North

We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3 observations of 73 starless and protostellar cores in the Orion B North molecular cloud. We detect a total of 34 continuum sources at 106 GHz, and after comparisons with other data, four of these sources appear to be starless. Three of the four sources are located near groupings of protostellar sources, while one source is an isolated detection. We use synthetic observations of a simulation modeling a collapsing turbulent, magnetized core to compute the expected number of starless cores that should be detectable with our ALMA observations and find at least two (1.52) starless cores should be detectable (at 5σ), consistent with our data. We run a simple virial analysis of the cores to put the Orion B North observations into context with similar previous ALMA surveys of cores in Chamaeleon I and Ophiuchus. We conclude that the Chamaeleon I starless core population is characteristically less bounded than the other two populations, along with external pressure contributions dominating the binding energy of the cores. These differences may explain why the Chamaeleon I cores do not follow turbulent model predictions, while the Ophiuchus and Orion B North cores are consistent with the model.

Comparison of Non-Overlap and Overlap Savonius Wind Turbines in the Physics Aspect Using Computational Fluid Dynamics Method

Abstract Wind energy has good potential as a renewable energy source. Savonius-type wind turbines can provide power generation at a low cost with minimal environmental impact. Due to its low efficiency, researchers were focused on increasing it through many methods, such as applying twisted-bladed, optimizing the blade shape, and applying overlap. Most researchers have studied the effects of overlap on Savonius blades only in terms of performance improvements. This study evaluates the effect of overlap on the Savonius blade from a physics perspective using the Computational Fluid Dynamics method to get a new approach based on the improvement. The models are 2-bladed Savonius with non-overlap and 0.2 overlap. The main software used is Ansys Student 2023 R2. The turbulent model chosen is a realizable k- enhanced wall treatment. Then, pressure and velocity coupling were done using SIMPLE: 2nd order upwind, 1st order implicit. As a result, the overlap model has a higher reverse flow but lower pressure for all Tip Speed Ratio. Another finding shows that turbulent kinetic energy decreases with overlap. For the non-overlap model, the amount of turbulence is greater downstream, which causes vortices to form and lowers turbine performance. So, the effects of the overlap blade result in higher average Torque Coefficient than non-overlap.