Reynolds-averaged Navier-Stokes Equations Research Articles

Quantifying a common inconsistency in RANS-VoF modeling of water and oil core annular flow

Current trends in modeling CAF of oil and water combine the interface capturing methodology of VoF with the computational savings of a RANS approach. As demonstrated mathematically, this results in an inconsistency in the overall RANS-VoF treatment and incurs a number of omissions in the solution of oil fraction advection and momentum. To quantify these inconsistencies, five CAF cases with increasing Rew are considered and solved via DNS. Symptoms of the inconsistencies include qualitative errors in the prediction of the flow behavior in the entrance and fully-developed regions, as well as in the transition between these two regions. From a momentum perspective, the more troubling issue is the absence of unclosed terms resulting from fluctuating viscous and surface tension forces in the RANS equations. For momentum advection, terms associated with fluctuating density can be safely ignored due to the similar magnitude between oil and water density.

Design Improvement for Interventional Blood Pumps Based on Flow Analysis

Abstract Interventional blood pumps serve as a crucial component for temporary mechanical circulatory support in the treatment of heart failure, specifically designed to improve blood circulation recovery and survival rate in patients undergoing treatment for acute cardiovascular diseases. This study aims to design a novel interventional blood pump with a focus on achieving exceptional hydraulic performance and superior blood compatibility based on numerical simulation, which considers the interactions between the blood pump and the upstream (drainage cannula) and downstream (aorta) flow fields, establishing a full-scale flow field analysis. For the numerical method, the Reynolds-Averaged Navier-Stokes (RANS) equations coupling with the k-ɛ turbulence model are solved. The result indicates that high shear stress exists around the leading and trailing edges of impeller blades and there is a jet at the outlet of impeller, and the blade leading and trailing edge, and the outlet of the impeller are the dominant regions for higher hemolysis occurrence. It is also noted that the presence of an interventional blood pump generates significant vortex structures within the aorta. To effectively reduce the hemolysis index, back-sweep concept is applied to this study also optimize the impeller’s leading edge. The analysis result confirms that the back swept leading edge of impeller blade helps improve the blood compatibility for interventional blood pumps.

Three-dimensional finite element analysis of turbulent crude oil flow and solid particle deposition patterns in circular curved pipelines

This study presents a numerical investigation of turbulent crude oil flows in circular curved pipelines, with a focus on the deposition patterns of solid particles within the fluid. Simulations were conducted using the Reynolds–Averaged Navier–Stokes equations coupled with the k–ε turbulence model to examine the influence of structural characteristics, such as bend curvature angle and bend curvature radius, on flow dynamics and particle deposition. The results reveal that the complex flow patterns generated by these geometric features significantly affect pressure gradients and particle trajectories. Specifically, the study shows that turbulent flows within bends exhibit intricate behaviors, with deposition patterns being strongly influenced by the pipeline’s geometric parameters. Sand particles, commonly present in petroleum flows, are found to be more effectively transported in pipes with larger curvature angles, while they exhibit a higher propensity to settle at smaller curvature angles and larger bend curvature radii. Furthermore, the simulations indicate that the majority of deposited particles accumulate on the inner wall immediately downstream of the elbow entrance.

Numerical investigation of dynamic gas–liquid separator by population balance model

Dynamic gas–liquid separator (DGLS) can efficiently separate gas and liquid phases and are widely used in aerospace, chemical, and petroleum engineering. The energy loss and separation efficiency within the DGLS are studied through the combination of numerical simulations and experiments. Three-dimensional transient Reynolds-Averaged Navier–Stokes equations were solved to analyze the fluid dynamics within the DGLS. The bubble aggregation and breakup in oil were simulated by using the population balance model. Experimental data were meticulously compared with numerical results to validate the accuracy and reliability of the numerical methods. The findings revealed a direct correlation between the inlet flow rate and various performance metrics of the DGLS. Specifically, as the inlet flow rate increased, the energy loss within the DGLS escalated, resulting in higher power consumption. The degassing rate of the DGLS exhibited a decreasing trend with increasing inlet flow rate, while the de-oiling rate showed an inverse relationship. The optimal performance of the separator was observed at an inlet flow rate of 140 m3·d−1, with ηg* and ηl* reaching 0.94 and 0.99, respectively. The relationship between the Qo and the η* and Po was fitted by a second-order polynomial. Moreover, the rotational speed of the DGLS demonstrated a positive correlation with energy consumption, accompanied by an increase in power output. However, the separation efficiency of the DGLS exhibited a non-linear relationship with rotational speed, peaking at a specific value before marginally declining. The optimization of degassing and dewatering rates occurred at a rotational speed of 2500 r·min−1. These findings underscore the importance of carefully adjusting operational parameters to achieve optimal performance and energy efficiency within DGLS.

Numerical study of vehicle motion during water exit under combined lifting force and wave action

During the retrieval process of the deep-sea mining vehicle (DSMV), the stability of the retrieval system is strongly influenced by the interaction between the vehicle body and the surrounding seawater due to the vehicle's complex shape and wave motion. Naturally, the negative side effects of significant changes in the vehicle's attitude and the water exit position can only increase retrieval's challenge. To investigate the characteristic of the flow field of the DSMV, this study employs the computational fluid dynamics method based on the Reynolds-averaged Navier–Stokes equations integrating the volume-of-fluid multiphase flow model with a fifth-order Stokes-wave model to explore the attitude and displacement changes of the vehicle during the water exit process in the ocean wave environment. The results indicate that the wave phase and lifting force are the major effect factors in the DSMV's water exit process. An appropriate lifting force under a specific wave phase can effectively reduce attitude changes and positional drift of the DSMV during water exit, thereby enhancing recovery efficiency and stability.

MODELING THE ENTRY OF AIR CONTAMINANTS INTO A ROOM

A mathematical model of air contaminant (products of human activity) inflow into the isolated air space has been developed. On the basis of the formula modified by us the simulation of human respiration with carbon dioxide, water vapor and heat emission is implemented. The model also takes into account the heat input from the human body through clothing. Applying numerical modelling ANSYS CFD (Computational Fluid Dynamics) on the basis of continuity equations and Reynolds-Averaged Navier-Stokes equations "RANS" (Reynolds-Averaged Navier-Stokes) the following results on air medium state change in the isolated space were obtained: - the human respiratory cycle is modelled at simultaneous heat transfer from the body surface through clothes into the studied air space; - the exponential equation of the trend line of concentration to observation time was obtained; - monitoring and rendering (visualization) of changes in concentration, temperature and relative humidity in the space under study by time along the room height was performed. These results and regularities served as initial data for solving a number of model non-stationary problems on aerodynamics and heat and mass transfer in the room. The inverse problem of general exchange ventilation was to be solved. Changes in the state of the air environment initially contaminated with carbon dioxide, heat and water vapors were studied when people were in the studied space and the supply and exhaust ventilation was operating. Of the four air change schemes planned for the study, the results for one schemes are presented in this publication. The dynamics of assimilation of excess heat, humidity and carbon dioxide made it possible to assess the efficiency of ventilation systems and to predict improvements in their energy efficiency when air parameters are brought up to standard values.

Oscillatory airflow through the hypopharyngeal and supraglottic airway

Exercise-induced laryngeal obstruction (EILO) is a known cause of exertional dyspnoea, characterised by paradoxical inward collapse of laryngeal tissues. The pathophysiological mechanisms of EILO remain to be fully established, but insufficient mechanical resistance of laryngeal tissues to air-induced loads is hypothesised. It is understood that airflow and anatomic configurations of the airway play a key role in the wall pressure distribution of the larynx. While breathing is a cyclic process with directional changes of airflow, the literature is confined to steady, unidirectional airflow. It is necessary to assess the role of oscillatory airflow on the loads on the laryngeal airway. This study investigates the effect of oscillatory airflow on the laryngeal flow fields and air-induced loads. A computational fluid dynamics model of the upper respiratory tract (URT) is developed using the Reynolds-averaged Navier-Stokes equations. Five oscillatory airflow cases through a single geometry are considered, utilising sinusoidal breathing cycles with different breathing frequencies (24, 32 and 40 breaths per minute) and peak inspiratory flow rates (96, 168 and 240 L/min). Results include the airflow velocity distribution in the URT, and the air-induced pressure and forces. It is demonstrated that inspiratory velocity distribution varies with breathing frequency and intensity. The force acting on the URT walls are in-phase with the airflow rate and therefore exhibit quasi-steady behaviour. These findings are also reflected in the force vectors acting on the aryepiglottic folds and indicate that air-induced closure of the supraglottis in EILO is influenced by the breathing intensity rather than the breathing frequency.

Application of operating scenarios and analysis of unstable flow characteristics at various angles of inlet guide vane.

In this study, we analyzed the performance characteristics of an axial flow pump with different angles of internally installed inlet guide vanes (IGVs). We predicted the pump's performance based on changes in the IGV angle and analyzed the impact of these angle variations on pump operation in the low-flow region. Additionally, we used real operational data from two sewage treatment plants to propose efficient operational scenarios. For turbulence flow analysis, the Reynolds-averaged Navier-Stokes equations were discretized based on the finite volume method. The grid formation was evaluated using the grid convergence index to select the optimal grid. Then, the internal flow was analyzed in detail through transient-state analysis. Through fast Fourier transform analysis, we confirmed that adjusting the IGV angle during pump operation in the low-flow region in response to load changes results in more stable operation compared with the existing method (valve control). Overall, our findings verified that energy reduction and efficient operation can be achieved through IGV angle adjustment compared with valve control.

Study on energy harvest performance of a flapping hydrofoil with swept leading edges by numerical methods

Inspired by the superior hydrodynamic performance of fish tails with swept shapes, whether a flapping hydrofoil with swept leading edges has higher energy harvesting efficiency attracts our great attention. By solving Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras model, a numerical study on flapping swept hydrofoils was conducted. Results show that, compared to a flapping rectangular hydrofoil, a flapping swept hydrofoil has higher efficiency under almost all operating conditions. When the aspect ratio is 4.0, using a hydrofoil with a sweep angle of 10° increases the efficiency by nearly 9%. As the sweep angle increases, the efficiency increases first and then decreases, so there exists an optimal value. As the aspect ratio increases, the optimal sweep angle decreases. When the taper ratio is around 0.6, the efficiency is or is close to the maximum value. Compared with a single horseshoe vortex around flapping rectangular hydrofoils, the double horseshoe vortices around flapping swept hydrofoils and the advance of their formation time are the reasons for the efficiency improvement. The study confirms that a flapping swept hydrofoil turbine has higher efficiency than a flapping rectangular hydrofoil especially when the aspect ratio is from 2.0 to 5.0 and clarifies the reasons for the efficiency improvement.

Annular two-phase flow in a small diameter tube: OpenFOAM simulations with turbulence damping vs optical measurements

In this work, numerical simulations are performed to predict two-phase annular flow of refrigerant R245fa inside a 3.4 mm diameter vertical channel. The VOF (Volume of Fluid) method implemented in an OpenFOAM solver is used to accurately track the vapor-liquid interface. A 2D axisymmetric domain is considered and the Adaptive Mesh Refinement (AMR) method is applied to the cells near the liquid/vapor interface. The Reynolds-Averaged Navier Stokes (RANS) equations are solved and the k-ω SST model is adopted for turbulence modelling in both the liquid and vapor phase. Simulations are used to calculate instantaneous and mean values of the liquid film thickness at mass flux G = 100 kg m-2 s-1 and vapor quality ranging between 0.2 and 0.85. Numerical results are compared against measurements of the liquid film thickness taken during vertical annular downflow. Previous works from the literature and the deviations observed between present numerical and experimental results suggest the need for turbulence damping at the vapor-liquid interface by adding a source term in the ω equation. The simulations show that a low value of the turbulence damping parameter (e.g. 1) causes the average liquid film thickness to increase by 25 %–52 % compared to the non-damped scenario. The interface presents large amplitude disturbance waves in the non-damped case, whereas small ripple waves are predicted when turbulence damping is introduced. Furthermore, the difference between the application of a symmetric and asymmetric treatment for the source term is analysed. From the comparison between experimental data and numerical simulations, it emerges that the value of the correct damping source term to be applied is strictly dependent on the vapor quality.

Nusselt and Reynolds numbers correlation for oscillatory flow of thermoacoustics over heated tube banks

The back-and-forth motion characteristic of the oscillatory flow brings complexity in predicting the heat transfer nature for thermoacoustic wave conditions. Investigating this is crucial as the flow forms the backbone for the thermodynamic cycles of its operation. Often, the steady approximation in calculating heat transfer leads to ambiguity in designing the system. This concern is addressed in this paper via an in-depth analysis of the fluid dynamic behavior and heat transfer characteristics of oscillatory flow within a thermoacoustic framework, spanning experimental works for Reynolds numbers ranging from 300 to 24,000. The investigation focused on a tube bank heat exchanger composed of nine tubes arranged in inline and staggered configurations. Experiments were conducted at constant tube surface temperatures treated at 40 °C and 80 °C, respectively. The distinguishing difference in heat transfer behaviors for oscillatory flow is visualized by the Computational Fluid Dynamics (CFD) models, employing the Reynolds-Averaged Navier Stokes equation with the k-omega turbulence shear stress transport model. The flow never leaves the system, and it cyclically crosses the tubes back and forth with a travel distance that depends on the drive ratio of the flow. The unique nature of the flow forms the foundation for the experimental findings that show a linear relationship between the Nusselt and Reynolds numbers regardless of the configuration of tube banks and tube bank temperature. The Pearson ruler regression analysis was conducted using Matlab R2022b and a Nusselt correlation, Nu = 0.000853RePr⅓, is proposed with a confidence level of 95 %. Notably, the correlation aligns with the constant value known as the Colburn-j factor, with a value of 0.00083. The small Colburn-j value is shown to be the influence of the log-mean temperature difference characteristic of oscillatory flow. It shows a consistent heat transfer process between the heated tubes and surrounding fluid, which is important to sustain the thermoacoustic effect in the system. For future thermoacoustic design, the use of steady heat transfer correlation should be avoided or at least used with caution as the comparative analysis with published works concluded that the Nusselt and Reynolds correlation for steady flow tends to overpredict the heat transfer by two to threefold.

Flow induced form: Shape optimization of bridge piers using CFD analyses and adjoint method

This study investigates the optimization of cylindrical bridge pier geometry using a relatively new technique involving Computational Fluid Dynamics (CFD) and adjoint shape optimization methods. Initially, Reynolds Averaged Navier-Stokes (RANS) equations were used in CFD models, integrated with an adjoint algorithm to reshape the pier and reduce bed shear stress. This approach is hereinafter called the “Flow induced Form”, FiF, aiming to minimize shear stress on the bed while maintaining the pier's cross-sectional and projected areas in the flow direction. Subsequently, Large Eddy Simulation (LES) transient analyses assessed the performance of the optimized geometry. Results show a reduction of approximately 5% in the time average of maximum shear stresses on the bed and a reduction of around 50% in instantaneous maximum values compared to the original pier design. These improvements were achieved with minimal changes to the cross-sectional area and projected area of the original geometry (∼2%), considering that the load-bearing capacity of the bridge pier.

Numerical investigation of the effect of winglet configurations with multiple cant angles on the aerodynamic performance of wind turbine blade

ABSTRACT A numerical investigation of the effects of winglets with multiple cant angles on the power output of the blade of a horizontal axis wind turbine (HAWT) is conducted. Several winglet configurations with single and multiple cant angles are designed and their performance is evaluated. Numerical solutions obtained by RANS equations and moving reference frame method were compared with the experiments and demonstrated that they concur well with the experimental data. In the torque and thrust comparison, the ones with multiple cant angles present better power output enhancement than those with a single cant angle at a relatively high wind speed. The configurations of multiple cant angles are effective in reducing the influence of wing tip vortices, resulting in a higher torque while maintaining the same winglet length and height.

Aerodynamic characteristics of axisymmetric boattail models with different number of longitudinal groove cavities

Reducing aerodynamic drag and increasing flying object performance is an important task in aerospace engineering. The high drag occurs for blunt base models, which are not only for missiles, and projectiles but also for building, bridges. This study presents numerical results regarding subsonic flow characteristics over axisymmetric boattail models equipped with longitudinal grooves, with the number of grooves ranging from 2 to 12. The standard model has a fixed boattail length of 0.7D and an angle 22°. The investigation employs numerical simulation methods utilizing the Reynolds-averaged Navier-Stokes (RANS) equations with the k-ω SST turbulent model. The boundary layer was captured well by the current simulation. The numerical results are initially validated against both simulated and experimental data from previous studies, ensuring accuracy and reliability. The findings indicate that an increase in the number of grooves from 0 to 4 results in a slight increment in drag. However, as the number of grooves is further increased from 6 to 12, a significant reduction in the model's drag is observed. Additionally, the flow patterns around the boattail model are visually depicted and analyzed to explain the drag trend of the model with different groove configurations

Effect of pre-swirl stator angles on broadband noise considering hydrodynamic performance of pump-jet propeller

A pump-jet propeller is composed of a rotor, stator, and duct. A pre-swirl stator is employed to optimize flow into the rotor. The hydrodynamic and noise performances of pump-jet propellers vary with the stator angles. In this study, the hydrodynamic performance of a full-scale submarine and pump-jet propeller is assessed by conducting computational fluid dynamics simulations based on the Reynolds-averaged Navier–Stokes equation. Additionally, broadband noise, blade-passing frequency noise, and a significant factor, that is, underwater radiated noise are predicted using Lighthill’s equation, Green’s function, and wall pressure spectrum. Unsteady forces were extracted from the flow field to obtain the blade-passing frequency noise. Broadband noise could not be calculated directly from the flow field owing to the absence of small eddies, and wall pressure spectrum was used to obtain high-frequency broadband noise. The overall noise, including broadband noise and blade-passing frequency noise, was evaluated. The optimal stator angle for the rotor at the self-propulsion point was determined considering the propulsion efficiency and noise level of the pump-jet propeller.

Impact of Blowing Location on the Aerodynamic Characteristics Over the Delta Wing

The performance of an aircraft can be enhanced by altering the flow field favourably by adopting flow control techniques. The present study deals with the application of the active flow control methods on a sharp-edged delta wing with a wing sweep of 65°. The concept of blowing was employed as an active flow control technique. The blowing technique is applied on the suction surface of the delta wing by varying its location. The various identified locations of the blowing holes are 1.62 %, 3.24 % and 4.86 % of root chord from the leading edge to the centre of the blowing holes. The computation is performed using the commercial software ANSYS Fluent. An unsteady, incompressible Reynolds-averaged Navier–Stokes equation and the shear-stress transport k-ω turbulence model are employed. The angles of attack varied in the range of 0°<α<35° and Reynolds number is 2.64×106 and the jet momentum coefficient is fixed at 0.05. The blowing of air from the injection region enhances the strength of the leading-edge vortices, resulting in a delay in the vortex breakdown. The performance of the delta wing is greatly improved while using the blowing method specifically for the blowing holes located at 3.24 % of root chord from the leading edge compared to without the blowing method.

Characteristics of Deterministic and Stochastic Unsteadiness of Trailing Edge Cutback Film Cooling Flows

Abstract Trailing edge cutback film cooling flows are ubiquitous in small and medium gas turbines, but they are difficult to predict accurately due to the inherent deterministic and stochastic unsteadiness that controls the effectiveness of the cooling system. To help develop accurate closure models for such flows, the characteristics of both types of unsteadiness and their effects on the mean flows are analyzed in this research. Zonal detached eddy simulation (ZDES) is performed on a trailing edge cutback flow model, and the numerical results are validated against the measured data. Then, by using spectral proper orthogonal decomposition (SPOD) reconstruction, the original dataset is segregated into deterministic and stochastic unsteadiness. The characteristics of the stress tensor and the heat flux of each type of unsteadiness are analyzed in detail, and notable differences between the two unsteadiness are identified in terms of the stress tensor anisotropy and distribution of unsteady kinetic energy and heat flux. By propagating the unsteadiness through the Reynolds-averaged Navier–Stokes (RANS) equations, the effect of different unsteadiness on the mean flow prediction is quantified. An accurate prediction of the total stress tensor reduces the prediction error in the velocity field by 79% and cooling effectiveness by 55%. An accurate prediction of the total heat flux vector reduces the prediction error in cooling effectiveness further by 37%. These findings provide valuable knowledge for the physical understanding, turbulence modeling, and aerothermal design of cutback trailing edge flows.

Improving near-stall performance of axial flow compressors using variable rotor tandem stage. A steady analysis

This paper investigates the idea of substituting the first stage of a conventional axial-flow compressor and its inlet guide vane (IGV) row with a variable rotor tandem (VRT) stage to reduce the size and weight of axial-flow compressors. It is expected that a tandem stage gains higher pressure ratio than a conventional stage, and simultaneously, its variable stagger rotor provides more flexibility in handling unsteady phenomena at low mass flow rates. A three-dimensional numerical model based on Reynolds-Averaged Navier–Stokes equations is developed to conduct this investigation. To validate the numerical model, experimental tests are conducted on a tandem single-stage axial-flow compressor test bench in the Dana laboratory of Amirkabir University of Technology, to compare the performance map with numerical results. The validated numerical model is then employed to simulate the performance of both front and aft variable rotor blades. The proposed tandem stage effectively performs the IGV duty, suppresses instabilities at low mass flow rates, and eventually extends the compressor's stable operational range. This proves that a VRT stage is an efficient active surge-control system tool. The detailed survey of the three-dimensional flow field reveals that the aft tandem rotor blade stagger angle is more effective in increasing the stall margin and decreasing the minimum operational mass flow rate than the front row of blades. It is observed that when the aft blades rotate in the direction of decreasing the tandem blades' gap area, the flow momentum increases and causes the compressor stability at lower mass flow rates.

A comprehensive comparison of film cooling characteristics of shaped holes on the leading edge of rotating blade

This study numerically investigates the cooling characteristics and flow features of various hole geometries on the rotating blade leading edge. A comprehensive comparison of cooling effectiveness, heat transfer coefficients, net heat flux reduction, and discharge coefficients is conducted among laidback fan-shaped, fan-shaped, laidback, cone holes, and cylindrical holes with two different diameters. Detailed flow and thermal field analysis reveals the impact of geometry on cooling performance. The blade rotational speed is 600 rpm, with a Reynolds number of 12.4 × 104, blowing ratios from 0.5 to 2.0, and fixed injection and spanwise angles at 90° and 30°. Shaped holes share a uniform hole exit-to-inlet area ratio, and cylindrical holes match their inlet or exit areas. The RANS equations were closed using the SST k-ω turbulence model coupled with the Gamma Theta transition model, and an unstructured grid of 13.0 million cells was employed to attain relatively accurate predictive results. Results show that the lateral expansion on the leading edge significantly enhances cooling performance, with fan-shaped holes outperforming others, especially at high blowing ratios. Additionally, cooling effectiveness and discharge coefficient on the leading edge correlate strongly with hole geometric parameters. Shaped holes with equal area ratios show similar discharge coefficients. Cooling effectiveness at high blowing ratios is proportional to the effective exit width, provided that the coolant flows smoothly without severe lift-off.

Effect of Ramp Geometry on Single Expansion Ramp Nozzle Performance Characteristics

In high-speed flight regimes, the drag plays a significant role in determining the overall performance of the aerospace vehicle. One proposed solution is to integrate a single expansion ramp nozzle (SERN) at the aft of the vehicle to mitigate the drag effects. This work investigates the effects of nozzle geometry on flow and performance characteristics of SERN with a thrust-optimized parabolic and minimum-length nozzle ramp contours, which have not been explored with regard to these aspects. A computational study is carried out on these two ramp contours using compressible Reynolds Averaged Navier–Stokes equations over a range of nozzle pressure ratio (NPR). In the tested range of NPR, the restricted shock separation is found to be the chief mode of flow separation in SERN, along with the change in the size of recirculation zone and separation bubble. At NPR 3, the thrust-optimized parabolic ramp contour shows an increment of thrust coefficient by 29.2% over the minimum-length nozzle; whereas at NPR 3.5, the minimum-length nozzle demonstrates an increment of thrust coefficient by 56.3% over the thrust-optimized parabolic at 0-deg M cowl angle. Further, in the tested range of NPR, the minimum-length nozzle shows an improved lift coefficient at 5 deg cowl angle.