Reynolds-averaged Navier-Stokes Method Research Articles

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

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

Application of convolutional neural network for efficient turbulence modeling in urban wind field simulation

Accurate flow field estimation is crucial for the improvement of outdoor environmental quality, but computational fluid dynamics (CFD) based on the widely used Reynolds-averaged Navier–Stokes method has limitations in this regard. This study developed a turbulence modeling framework based on a convolutional neural network (CNN) to model turbulence in urban wind fields. The CNN model was trained by learning the Reynolds stress patterns and spatial correlations with the use of high-fidelity datasets. Next, the model was integrated into the CFD solver to generate accurate and continuous flow fields. The generalization capability of the proposed framework was initially demonstrated on the simplified benchmark configurations. The validated framework was then applied to case studies of urban wind environments to further assess its performance, and it was shown to be capable of delivering accurate predictions of the velocity field around an isolated building. For more complex geometries, the proposed framework performed well in regions where the flow properties were covered by the training dataset. Moreover, the present framework provided a continuous and smooth velocity field distribution in highly complicated applications, underscoring the robustness of the proposed turbulence modeling framework.

Numerical simulation of the effects of pulsed injection on combustion and flow processes in a supersonic combustor

This paper describes two-dimensional numerical simulations of pulsed injection to a hydrogen-fueled air-breathing ramjet using the Reynolds-averaged Navier–Stokes method. We analyze the effects of sinusoidal pulsed injection on the start-up ignition time, start-up ignition range, combustion efficiency, and flow field evolution of the ramjet and compare the performance with that of steady injection. The results show that pulsed injection shortens the ignition time and optimizes the ignition equivalence ratio of hydrogen. Pulsed injection also improves the combustion efficiency of hydrogen, increasing the thrust of the engine by 7.79% compared with steady injection under the same equivalence ratio. We find that pulsed injection can cause oscillations in the ramjet combustion flow field, and show that the oscillation frequency is affected by the pulsed injection frequency.

Research on supersonic film cooling of hypersonic optical window under different nozzle pressure ratios

When optical imaging-guided aircraft flies at hypersonic speeds in the atmosphere, the optical window withstands severe aerodynamic heating. Conducting the thin film resistance thermometer measurements in a hypersonic gun wind tunnel with a Mach number of 7.1 and total temperature of 670 K, the study investigates the effect of nozzle pressure ratio (NPR = film exit static pressure/nearby mainstream static pressure) on supersonic (Mach 2.43) film cooling for the hypersonic optical window. By combining the flow information near the window obtained using the three-dimensional compressible Reynolds-averaged Navier–Stokes method, the study reveals the mechanism of the effect of NPR on film cooling. The results indicate that increasing NPR can enhance the momentum of the unit volume film and improve the film's ability to resist mainstream mixing. Moreover, the film with a large NPR can better maintain its own momentum, leading to an increase in the film effective cooling length and film cooling effectiveness. The film effective cooling length corresponding to the unit mass flow rate of the cooling gas increases with the increase in NPR. It verifies the nonlinear relationship between the film cooling performance and the coolant mass flow rate, indicating the additional benefits of increasing NPR on the film cooling performance. Through research, it is found that increasing NPR can increase the film thickness, thereby enhancing its ability to isolate the mainstream. Moreover, as NPR increases, the cooling film expands, objectively leading to the widening of the film flow channel, allowing the Mach number of the supersonic film to increase continually. This further reduces the static temperature of the film in the flow field, thereby enhancing its cooling capability for the mainstream.

Effects of propeller boss cap fins on hydrodynamics and flow noise of a pump-jet propulsor

As an underwater thruster, the pump-jet propulsor (PJP) exhibits low radiation noise but generates significant line spectral noise in the low-frequency band. In this paper, we equipped the PJP hub with two types of propeller boss cap fins (PBCF): one fixed and the other rotating with the rotor. The hybrid large eddy simulation and Reynolds-averaged Navier–Stokes method, along with the Ffowcs Williams-Hawkings (FW-H) equation, are employed to systematically analyze the hydrodynamics, exciting force, flow noise, and flow field of PJPs. The results indicate that the fixed PBCF improves the hydrodynamic performance and reduces the exiting force, raising the rotor's thrust coefficient by 9.22%–14.99%. The fixed PBCF also modifies the characteristics of line spectrum noise but causes an increase in the flow noise. The rotating PBCF increases the rotor's thrust coefficient by 2.03%–3.15%, decreasing both exciting force and line spectrum noise. For instance, at the advance coefficient of 0.8, its sound pressure level at the rotor frequency drops to 49.6%. Additionally, the rotating PBCF increases the pressure of the hub wake and effectively reduces the hub vortices' strengths. This paper provides a theoretical foundation for designing PJPs that enhance concealment and minimize vibrations and noise.

Investigation of aerodynamic loss mechanism on turbine leading edge with slot film cooling based on entropy analysis

Discrete film holes are a widely used cooling structure, with increasing cooling performance demands making their optimization increasingly complex. The structure of slot cooling is simpler compared to discrete holes, but it results in greater flow losses while improving cooling performance. To elucidate the sources and mechanisms of losses in slot cooling, this study employs numerical simulations based on the Reynolds-averaged Navier-Stokes (RANS) method. The investigation focuses on the leading-edge cooling of high-pressure turbine guide vanes, using entropy analysis to thoroughly examine the effects of blowing ratio (M) and slot spacing on loss location, composition, characteristics, and mechanisms. The results indicate that the losses associated with hole structures are not sensitive to changes in blowing ratio, while the entropy generation in slot structures generally increases with higher blowing ratios. Near the corner region, the traction effect of the horseshoe vortex expands the thermal loss region of the coolant, weakening the heat exchange in hole structures but significantly enhancing it in slot structures. The hole/slot structures have a minimal impact on the location of the passage vortex core, reducing the cross-flow velocity and cross-flow layer thickness. The greater flow losses are primarily due to increased passage vortex intensity. Slot cooling can achieve superior cooling performance at low M compared to hole structures at high M, with both having similar total pressure loss. However, the thermal losses for slot structures increase by approximately 55 % compared to hole structures on the pressure side of the leading edge, with even more significant increases on the suction side, while the maximum increase in viscous losses is only about 10 %.

Influence of thermodynamic conditions on the mixing characteristics of a supercritical nitrogen jet under mode excitation

Fuel injection mixing is one of the critical factors affecting the energy conversion efficiency and emission level of thermal engines. The effect of thermodynamic conditions on mixing characteristics of supercritical cryogenic nitrogen jet under varicose mode excitation is investigated using the unsteady Reynolds-averaged Navier-Stokes method combined with real-gas thermodynamics and transport properties of nitrogen in NIST database. The ambient-to-jet density ratio is defined to represent different thermodynamic conditions and is found to affect the jet mixing enhancement directly. As the density ratio increases from 0.098 to 0.432, the density gradient reduces in the jet shear layer, mitigating flow stratification. Jet mixing is enhanced with a reduction of density potential core length by 24 % and a tripled density spreading angle. Under varicose mode excitation, large vortices are formatted close to the jet orifice, especially for higher density ratio cases. The peak of the jet turbulent kinetic energy is higher and shifts upstream as density ratio increasing. The jet mixing enhancement is further achieved, with the spreading angle increment growing from 1° to 4° and the velocity decay rate increasing from 0.03 to 0.15. As the excitation amplitude rising from 5 % to 15 %, the growth of jet momentum instability in the jet potential core breaks the velocity gradients inhibition on jet mixing. The supercritical jet enters self-similar region earlier, with density potential core length shortened by 51 % and spreading angle increased by 28 % at a middle density ratio of 0.275.

Simulation of Hypersonic Shock-Boundary Layer Interaction Using Shock-Strength Dependent Turbulence Model

Shock-induced flow separation is important in hypersonic intake unstart and for unsteady aero-thermal loads. This work presents a computational study of shock-boundary layer interaction (SBLI) at hypersonic Mach numbers. The objective is to accurately predict the separation bubble size for oblique shock impingement on a turbulent boundary layer and for two-dimensional axisymmetric cone-flare SBLI cases. We use the Reynolds-averaged Navier Stokes method with an advanced shock-strength-dependent turbulence model. A recently developed transport equation-based shock sensor is employed to identify the location and strength of shock waves. The computational results are found to match experimental measurements of surface pressure and skin-friction coefficient for a series of test cases, highlighting the effects of Mach number, shock generator angle, and wall cooling on the size of the separation bubble. Results are also found to conform to the scaling of SBLI separation size found in the literature. This is one of the few such corroborations for hypersonic axisymmetric SBLI.

Interactions of row blades of a marine compressor based on POD analysis

The complex internal flow of the marine low-pressure compressor (LPC) is characterized by a series of unsteady flow structures, presenting extensive temporal and spatial features that pose challenges to direct data analysis. This paper employs the Unsteady Reynolds-averaged Navier Stokes (URANS) method to simulate a marine 1.5-stage LPC with full-channel configuration. Validation of the compressor’s overall characteristics and the unsteady pressure is achieved through comparison with experimental data. Additionally, the Proper Orthogonal Decomposition (POD) method is applied to decompose the velocity and pressure fields in various computational regions. The results demonstrate that the combined use of URANS and POD facilitates detailed insights into blade interactions. The consistency between time-averaged variables and POD modes underscores the practical physical significance of the POD modes. Furthermore, the study reveals that the Rotor-Stator interaction significantly outweighs the Inlet Guide Vane (IGV)-Rotor interaction. The coherent modal pairs generated by different interferences exhibit diverse characteristics within the computational domain, with distinct frequencies observed for the same interference reaction in the upstream and downstream regions. Notably, the POD modes of the rotor pressure field unveil a separation bubble structure.

Aerodynamic interference between road vehicle and train during meeting on a single-level rail-cum-road bridge under crosswind

A single-level rail-cum-road bridge is a relatively new type of bridge structure that accommodates both roadway and railway traffic on the same level. The aerodynamic interactions between road vehicles, trains, and the bridge deck under strong crosswind are significant, potentially posing safety risks to both vehicles and trains. This study aims to elucidate the aerodynamic interference between a road vehicle and a train during meeting on a single-level rail-cum-road bridge under crosswind. To achieve this, a three-dimensional, incompressible, unsteady Reynolds averaged Navier–Stokes method is utilized to simulate the meeting process between a van and a train on a prototype single-level rail-cum-road bridge under crosswind. Using an established computational fluid dynamics numerical model, the flow structure and aerodynamic loads of the van–train–bridge system under crosswind are studied. The results show that the auxiliary facilities on the bridge deck (such as pedestrian guardrails and anti-glare barriers) significantly alter the flow field around the van and train, affecting their aerodynamic characteristics. Additionally, the aerodynamic interference between the van and the train during their meeting under crosswind is substantial. The aerodynamic coefficients of the van and train, in terms of both magnitude and fluctuation, increase significantly with their driving speeds during the meeting process under crosswind. Furthermore, this aerodynamic interference intensifies as the lateral distance between the van and the train decreases during the meeting under crosswind.

Numerical and experimental approach for dust dispersion and deposition behavior for safe decommissioning activities

ABSTRACT The use of high-fidelity modeling is a promising technique for studying the mechanisms of dust dispersion and deposition in safe decommissioning operations. Detailed multiphysics models for poly-dispersed turbulent flow, particle-laden flow, and particle surface interaction were coupled with a Reynolds Averaged Navier Stokes method for numerical simulation of dust dispersion and deposition. A model that considered the critical viscosity was utilized to estimate the interaction between particles and substrate. The deposition behavior of particles was a result of the competition between adhesion and rebound probabilities during the impact process, and only when the critical viscosity exceeded that of the impacting particles could they attach to the surfaces. To validate the accuracy of the simulation results, deposition experiments using zirconia particles were conducted. The experimental setup included a 3.2 m polycarbonate pipe, a fan regulated by an inverter to control the flow, an ultra-low penetration air filter capable of capturing particles with a minimum diameter of 120 nanometers. An air pump connected to a particle tank and a mixing tank was used for homogenizing the injection of particles. Particle concentration was measured during the experiments using a light scattering spectrometer system, WELASⓇ 2000, from the manufacturer PalasⓇ. This optical measurement technique functioned with a white light source and scattered light detection. The scattered light was collected via optical fibers, which led to the control and evaluation point, and results were displayed through special software. The numerical simulation results were compared with the experimental data and used to validate the numerical approach for flow with zirconia particles deposited on various material surfaces, including iron, titanium, stainless steel 304, and stainless steel 316, for airflow rates ranging from 54 L/min to 124 L/min.

Enhancing the SST turbulence model for predicting heat flux in hypersonic flows through symbolic regression

In the context of hypersonic flows, shock-wave/turbulent boundary-layer interactions (SWTBLIs) can lead to substantial aerodynamic heating. The commonly used Reynolds-averaged Navier–Stokes (RANS) method in engineering applications faces challenges in accurately predicting heat transfer in these conditions, as the assumptions made by Morkovin’s assumption in the RANS method are not applicable in hypersonic SWTBLI flows. This article addresses these challenges by introducing a variable turbulent Prandtl number (Prt) model for non-adiabatic walls, established through field inversion and symbolic regression (SR) techniques. The methodology begins with field inversion for an oblique SWTBLI case at Mach 5. The corrected field, denoted as β(x), obtained from this inversion, is integrated with selected local flow characteristics to derive a corrected expression using SR. Following the necessary adjustments, this expression is incorporated into the RANS solver. Various cases with different wall cooling ratios, Mach numbers, and Reynolds numbers are chosen to assess the generalization ability of the variable Prt model. The outcomes demonstrate a substantial improvement in the model’s ability to predict heat transfer in hypersonic SWTBLI flows without compromising the baseline model’s performance in predicting the undisturbed boundary layer. The correction effect remains notably enhanced even in complex three-dimensional cases.

Scale-resolving simulations of turbulent flows with coherent structures: Toward cut-off dependent data-driven closure modeling

Complex turbulent flows with large-scale instabilities and coherent structures pose challenges to both traditional and data-driven Reynolds-averaged Navier–Stokes methods. The difficulty arises due to the strong flow-dependence (the non-universality) of the unsteady coherent structures, which translates to poor generalizability of data-driven models. It is well-accepted that the dynamically active coherent structures reside in the larger scales, while the smaller scales of turbulence exhibit more “universal” (generalizable) characteristics. In such flows, it is prudent to separate the treatment of the flow-dependent aspects from the universal features of the turbulence field. Scale resolving simulations (SRS), such as the partially averaged Navier–Stokes (PANS) method, seek to resolve the flow-dependent coherent scales of motion and model only the universal stochastic features. Such an approach requires the development of scale-sensitive turbulence closures that not only allow for generalizability but also exhibit appropriate dependence on the cut-off length scale. The objectives of this work are to (i) establish the physical characteristics of cut-off dependent closures in stochastic turbulence; (ii) develop a procedure for subfilter stress neural network development at different cut-offs using high-fidelity data; and (iii) examine the optimal approach for the incorporation of the unsteady features in the network for consistent a posteriori use. The scale-dependent closure physics analysis is performed in the context of the PANS approach, but the technique can be extended to other SRS methods. The benchmark “flow past periodic hills” case is considered for proof of concept. The appropriate self-similarity parameters for incorporating unsteady features are identified. The study demonstrates that when the subfilter data are suitably normalized, the machine learning based SRS model is indeed insensitive to the cut-off scale.

Computational Fluid Dynamics Investigation of Hydrodynamic Forces and Moments Acting on Stern Rudder Plane Configurations of a Submarine

This study presents the predicted hydrodynamic characteristics of different rudder plane configurations on the stern of a full-scale submarine in deep water, which are obtained using the Reynolds-Averaged Navier–Stokes method in Ansys Fluent Solver. First, the results obtained for the X-rudder plane configuration are verified according to previous numerical and experimental results in order to assess the accuracy of the simulation procedure. The X-rudder plane, Y-rudder plane, and Cross-rudder plane configurations in deep water with deflection angles ranging from −21 degrees to +21 degrees are then simulated. Next, the hydrodynamic forces and moments of the Cross-plane, X-plane, and Y-plane rudder configurations obtained through simulation are analyzed using Taylor’s expansion to estimate the hydrodynamic coefficients. The obtained results demonstrate that the X-force of the X-plane rudder configuration is larger than the corresponding forces acting on the Cross-plane rudder and Y-plane rudder configurations. Meanwhile, the Y-force and Z-force of the X-plane rudder configuration are significantly greater than the corresponding forces of the left configurations. The same tendency can be seen in the moment of the X-plane rudder about the y- and z-axes. However, the roll moment induced by the Y-plane and Cross-plane rudder configurations is significantly larger than that under the X-plane rudder configuration.

Simulation and validation of instability transient process in multistage high-speed axial compressor based on the body-force model

In this paper, a method for simulating the instability transient process of the axial compression system based on the body-force model is developed, and a corresponding simulation program is developed. Simulations of the transient process of instability were carried out on a high-speed four-stage compressor and compared with experimental data. At 50% of the design rotational speed, the type of instability was rotating stall, and the simulated and experimental stall cell propagation speed were very close to each other. At 70% of the design rotational speed, the type of instability was surge. A “surge loop” was simulated, and the surge period and the percentage of time spent in each phase were consistent with the experiments. The simulation successfully predicted the blockage in the surge re-pressurization phase, proving the reliability of the simulation results. In addition, the computation yields more information about the flow field. By summing the blade forces of all grids on a blade row by volume, the surge loadings are obtained. The analysis of the axial momentum equation shows that the obtained blade force variations are reasonable. The simulation time of the multistage axial compressor is greatly reduced compared to the full annulus three-dimensional unsteady Reynolds-averaged Navier–Stokes method, demonstrating its great advantage in the design phase of the compressor.

Reducing the contaminant dispersion and infection risks in the train cabins by adjusting the inlet turbulence intensity: A study based on turbulence simulation

Existing studies on ventilation in closed spaces mainly considered the average inlet velocity and ignored the influence of inlet turbulent fluctuation. However, the variation in inlet turbulence intensity (TI) is considerable and significantly affects the dispersion of contaminants. This study conducts numerical simulations verified by experiments to investigate the effect of the inlet TI on train contaminants dispersion and analyze infection probability variation. Firstly, the unsteady Reynolds-averaged Navier-Stokes (URANS) method and improved delayed detached eddy simulation (IDDES) method are compared in simulating the internal airflow characteristics based on the on-site measurement. The results indicate that the latter dominates in capturing airflow pulsations more than the former, although the mean airflow results obtained from both methods agree well with experimental results. Furthermore, the IDDES method is employed to investigate the effect of the inlet TI on contaminant dispersion, and the infection risks are also assessed using the improved probability model. The results show that, with the increase of TI from 5 % to 30 %, the contaminant removal grows considerably, with the removal index rising from 0.23 to 1.86. The increased TI leads to the overall and local infection risks of occupants descending significantly, wherein the former decreases from 1.53 % to 0.88 % with a reduction rate of 42 %, and the latter drops from 3.30 % to 2.16 % with a mitigation rate of 35 %. The findings can serve as solid guidelines for numerical method selection in accurately capturing the indoor dynamic airflow distribution and for the ventilation parameters design regarding TI inside trains to mitigate the airborne infection risk.

CFD simulation of pumping ventilation with two asymmetrically arranged openings on the rear wall in a three-story isolated building

Pumping ventilation, driven by periodic vortex shedding, can effectively improve the ventilation rate of single-sided ventilation. Previous studies on pumping ventilation mainly considered symmetric opening conditions, while the asymmetric opening distribution has not been well studied. Therefore, this study investigates the pumping ventilation of an isolated three-story building with asymmetric opening conditions using computational fluid dynamics (CFD) simulations. Unsteady Reynolds-averaged Navier-Stokes (URANS) method with SST k-ω turbulent model is adopted to conduct the CFD simulations. The effects of horizontal translation distances, internal partitions, and inter-floor interference on time-averaged and fluctuating ventilation rates are investigated. The simulation results show that the mean ventilation rate is larger than the fluctuating ventilation rate. The mean ventilation rate increases while the fluctuating ventilation rate decreases with the increase of the horizontal translation distance. In addition, the internal partition decreases the pumping ventilation rate primarily by reducing the fluctuating ventilation rate rather than the mean ventilation rate. Furthermore, the ventilation rates of the 2nd floor are promoted by simultaneous pumping ventilation of the 1st and 3rd floors compared to the situation that only the 2nd floor is ventilated. The ventilation rates of the 1st floor are the largest, and of the 3rd floor are the lowest. The findings of this study benefit the deeper understanding of pumping ventilation and provide theoretical guidance on the opening designs of multi-story buildings for better ventilation efficiency.

Numerical study of film cooling in single-element injector gaseous CH4/O2 rocket engine with coupled wall function

The investigation of film cooling in CH4/O2 rocket engines holds paramount importance in the advancement of rocket propulsion. However, the wall heat flux is always overestimated in numerical simulation processes. Hence, this article proposes a numerical framework that employs the Reynolds averaged Navier–Stokes method to simulate the single-element gaseous CH4/gaseous O2 combustion chamber, which is the basis for rocket engine simulations. The coupled wall function that considers chemical reaction effects is introduced to enhance the accuracy of wall heat flux prediction. The impact of utilizing a coupled wall treatment on the prediction of wall heat flux and its fundamental parameters are examined. In addition, a single-element combustion chamber experiment is performed to validate the simulation. The results demonstrate that the implementation of the coupled wall function hardly influences the main flow characteristics, whereas the wall heat flux calculated with general wall functions shows an overestimation, which can be reduced by the coupled wall function. Finally, the case with a coupled wall function can improve the cooling efficiency with greater accuracy and the cooling systems with optimized design. The proposed numerical framework and the findings of the study provide profound insights that can improve the design and optimization of rocket engines.

Numerical investigations of the effects of spanwise grooves on the suppression of vortex-induced vibration of a flexible cylinder

Numerical investigations of Vortex-induced Vibration (VIV) suppression of a flexible cylinder with spanwise grooves in the uniform flow have been conducted by viv3D-FOAM-SJTU solver, which imports the thick strip model into OpenFOAM. The Reynolds-averaged Navier-Stokes (RANS) method is adopted to calculate hydrodynamic forces at each fluid strip. The vibrations of cylinder are solved through the Euler-Bernoulli bending beam hypothesis and the Finite Element Method (FEM) in two directions. During simulations, four spanwise grooves are arranged equally around the cylinder with an interval of 90° at two configurations. The spanwise groove keeps a constant width of w = 0.2D and a variable groove depth among 0.08D, 0.12D and 0.16D. Specific comparisons on Root Mean Square (RMS) vibration displacements, vibration modal responses, vibration frequency responses and vortex structures are conducted to analyze suppression effects of the spanwise grooves. Numerical studies indicate that the appropriate choose of groove geometry and arrangement can effectively reduce both crossflow and inline VIV responses.

Numerical study of ignition process of ternary hydrogenated catalytic biodiesel/methanol/n-octanol blends under high-temperature and high-pressure conditions

This article presents a numerical simulation study of the spray combustion process of methanol/n-octanol/hydrogenated catalytic biodiesel (HCB) blended fuel in a high-temperature and high-pressure constant volume combustion chamber environment, using the Reynolds-averaged Navier-Stokes (RANS) method. This study focuses on the effects of the fuel properties on two-stage ignition processes. The blended fuel, denoted as M15, is composed of methanol, octanol, and HCB in volume ratios of 15 %:17 %:68 %. The pure HCB (M0) was also calculated under the same operating condition as references. The results indicate that M15 exhibits significant delays in both high-temperature and low-temperature ignition compared to M0. At low ambient temperatures, methanol demonstrates a strong inhibitory effect on spray ignition in part due to its competition with alkanes for OH radicals. Additionally, high-temperature ignition of M0 primarily occurs at the periphery of the spray, whereas the ignition of M15 transitions toward the fuel-rich region near the nozzle exit. This transition is attributed to the ignition delay, which provides better-mixing characteristics in the M15 spray, along with the oxygen content introduced by methanol.