Navier-Stokes Model Research Articles

Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility

Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility

A study of gust wind speed using a novel unsteady Reynolds-Averaged Navier-Stokes model

A study of gust wind speed using a novel unsteady Reynolds-Averaged Navier-Stokes model

Particle resolved DNS and URANS simulations of turbulent heat transfer in packed structures

An accurate prediction of turbulent heat transfer in packed-bed reactors is fundamental for the design and performance of such reactors. Various classes of Reynolds-Averaged Navier-Stokes models are available in the literature for predicting turbulent heat transfer via closing the Reynolds stress and Turbulent Heat Flux terms. In this work, we investigate the accuracy of representative unsteady RANS turbulence models in modeling heat transfer characteristics in packed-bed reactors. For this accuracy assessment, the performance of the examined unsteady RANS models is compared with particle-resolved Direct Numerical Simulations including heat transfer. The simulations are conducted in a three dimensional periodic domain consisting of randomly arranged cylindrical particles for Reynolds number Rep=1000. The extracted mean quantities (e.g. velocity and temperature), turbulent heat flux components and turbulent kinetic energy are used as a reference for the RANS models' accuracy assessment. The SST k−ω and Spalart-Allmaras models performed well in predicting mean fields. However, all models tended to mispredicted the turbulent quantities including the turbulent viscosity and heat flux vector. The thermal field calculations rely on the turbulent viscosity based Simple Gradient Diffusion Hypothesis for modeling turbulent heat flux, which introduce challenges in capturing the coupling between thermal and turbulent fields.

Influence of Dilution and Effusion Flows in Generating Variable Inlet Profiles for a High-Pressure Turbine

Abstract The elevated flow temperatures and pressures exiting gas turbine combustors affect the efficiency and durability of the high-pressure turbine stage. Understanding the effects that result from the upstream dilution and effusion flow interaction in creating the combustor exit profiles is important to advancing gas turbines. Understanding how common combustor features, such as dilution jets and effusion cooling, interact based on computational predictions guided the design of a non-reacting profile simulator capable of producing a wide range of non-uniform temperature profiles representative of those entering high-pressure turbines. The mechanical design of a new simulator device, which will be experimentally tested in the future, is presented in this paper along with computational predictions of flow and thermal fields. The simulator was designed for modular installation into the Steady Thermal Aero Research Turbine (START), which is a continuous-duration, steady-state turbine facility that houses a single-stage test turbine. Features of the simulator included interchangeable liner panels with multiple rows of dilution jets and wall effusion cooling to study various hole diameters and patterns. The dilution jets generate elevated turbulence intensities and tailor the temperature profiles in the radial and circumferential directions. The air mass flow distribution and source flow temperatures are independently controlled. To aid in the simulator design, computational fluid dynamics (CFD) simulations using Reynolds-averaged Navier–Stokes modeling were conducted with a two-level Design of Experiments (DOE) approach to determine a number of engine-representative target profiles with temperature shapes that are mid-radius peaked, outer-diameter peaked, inner-diameter peaked, and uniform. A sensitivity analysis of the CFD DOE results determined which factors significantly affected the profile shape so that the target profiles could be produced. The analysis indicated that the main contributor to the temperature profile shape at near-wall vane radial span locations of 0–15% and 85–100% was the injection temperature of the effusion flow. The main contributor at radial span locations of 15–40% and 60–85% was the injection temperature of the third-row dilution jets, and at the mid-radius location of 40–60% vane radial span, the main contributor was the diameter of the first-row dilution holes.

Mathematical Analysis of a Navier–Stokes Model with a Mittag–Leffler Kernel

In this paper, we establish the existence and uniqueness results of the fractional Navier–Stokes (N-S) evolution equation using the Banach fixed-point theorem, where the fractional order β is in the form of the Atangana–Baleanu–Caputo fractional order. The iterative method combined with the Laplace transform and Sumudu transform is employed to find the exact and approximate solutions of the fractional Navier–Stokes equation of a one-dimensional problem of unsteady flow of a viscous fluid in a tube. In the domains of science and engineering, these methods work well for solving a wide range of linear and nonlinear fractional partial differential equations and provide numerical solutions in terms of power series, with terms that are simple to compute and that quickly converge to the exact solution. After obtaining the solutions using these methods, we use Mathematica software Version 13.0.1.0 to present them graphically. We create two- and three-dimensional plots of the obtained solutions at various values of β and manipulate other variables to visualize and model relationships between the variables. We observe that as the fractional order β becomes closer to the integer order 1, the solutions approach the exact solution. Lastly, we plot a 2D graph of the first-, second-, third-, and fourth-term approximations of the series solution and observe from the graph that as the number of iterations increases, the approximate solutions become close to the series solution of the fourth-term approximation.

Validation of numerical method of unsteady Reynolds-averaged Navier–Stokes coupled with discrete phase model and optimization for the snow-resistance performance of bogies of a high-speed train

This paper presents an investigation aimed at enhancing the snow resistance of bogies in a three-car grouped alpine high-speed train (HST) that operates in a snowy region. The study employs a combination of the unsteady Reynolds-averaged Navier–Stokes model, coupled with the discrete phase model. This modeling approach has been validated through wind tunnel tests, including flow field tests, two-phase flow tests, and snow-ice tests. The study comprehensively compares the characteristics of the wind-snow flow, spatial snow concentration, and the distribution of snow on the train's underbody between two scenarios: the original train's underbody structure and the multifactor collaborative optimization scheme (MCOS). The results indicate that the MCOS case facilitates the escape of snow particles from the bogie cavities by weakening the upward and reverse flows. Furthermore, the MCOS case significantly reduces the concentration of snow particles around the heat-producing elements and decreases the accumulation of snow on both the lower and upper surfaces of the bogies. As a result, it reduces snow accumulation on the bogies by 50.6%, 56.4%, 60.8%, and 62.4% at train speeds of 200, 250, 300, and 350 km/h, respectively. In summary, this research provides valuable insights for improving the snow resistance of HSTs operating in snowy regions, with potential applications in enhancing railway transportation safety and efficiency.

Viscous-Layer Compressibility Correction for Two-Equation Reynolds-Averaged Navier–Stokes Models

The baseline two-equation Reynolds-averaged Navier–Stokes (RANS) models include fluid density but lack calibration for compressible flows, making them inadequate for high Mach numbers. Various compressibility corrections have been proposed to integrate the van Driest transformation or the semilocal transformation, i.e., a given compressible law of the wall, into the RANS formulation. Prior work has focused mainly on the logarithmic layer, but upon evaluating these log-layer compressibility corrections, we find that they do not significantly improve skin friction estimates. To overcome this challenge, we develop viscous-layer compressibility corrections. We do that by altering the dissipation terms. These corrections conform the RANS model to the semilocal scaling, resulting in more accurate predictions of mean velocity and temperature in a posteriori tests. Although not the primary focus of this study, we also find that the baseline one-equation Spalart–Allmaras model, which was proposed before the concept of semilocal scaling, produces results consistent with the semilocal scaling in a posteriori tests without requiring any compressibility correction.

On the thermodynamic invariance of fine‐grain and coarse‐grain fluid models

AbstractThermodynamics is an essential ingredient of fine‐grain and coarse‐grain models of oceanic and atmospheric flows. Thermodynamic functions and conservative variables, for a given set of observable quantities such as pressure, temperature, and composition, may be defined up to a certain degree of arbitrariness, in the sense that the predictions of the fine‐grain model are insensitive to, for example, some reference enthalpies, entropies, or pressures. Since the compressible Navier–Stokes model, regarded as a “mother” fine‐grain model, is invariant with respect to arbitrary changes in reference enthalpies and entropies, restricted only by phase change, any coarse‐grain model obtained from it, even conceptually, must be invariant at least to the same extent. A framework is devised that enables the systematic examination of this invariance. It is found that the dependence of usual conservative variables on a reference pressure propagates to their fluxes and gradients, and to downgradient closures based on them. To resolve this issue, it is shown how to construct invariant “reduced” gradients and fluxes of enthalpy and entropy. Closure relationships between such “reduced” fluxes and gradients are then guaranteed to be invariant. More work is required to address the invariance of more sophisticated closures, especially shallow and deep convective closures.

Development and evaluation of a buoyancy-driven airflow window with multioperation modes

This study introduces a novel, cost-effective window-integrated passive system (WIPS) that enhances indoor air quality and maintains comfortable temperatures throughout both summer and winter. The WIPS utilizes buoyancy-driven air flow through dual air cavities that alternately preheat or cool the incoming air depending on the season. The system’s design was optimized for Seoul, Korea, through computational fluid dynamics (CFD) simulations using Fluent 2021 R2 software, which employed a Reynolds-Averaged Navier-Stokes (RANS) model with RNG κ-ε turbulence modeling. Key design adjustments included the use of glass and unplasticized polyvinyl chloride (UPVC) to minimize unintended airflow, as well as modifications to the geometry and size of the air cavities to maximize efficient air flow and thermal effectiveness. The optimized design demonstrated significant improvements in thermal performance, achieving a preheating effect up to 35 °C in winter and reducing indoor temperatures by 10 °C in summer. These results underline the potential of WIPS to provide a sustainable solution for building ventilation and climate control.

Separation and reattachment fixed Reynolds-stress model for iced airfoil and wing simulations

Differential Reynolds-stress models (RSMs) are the higher level of Reynolds-averaged Navier-Stokes (RANS) modeling and generally considered to have more potential than eddy viscosity models (EVMs) when applied to separated flows. Nevertheless, some peculiarities have been observed in simulating flows over iced wings. The first is the numerical stability problem caused by non-streamlined wall surfaces. To weaken this, a wall-boundary-natural scale λ=ω−1/8 is introduced into SSG/LRR RSM in this paper. The second is to remedy the problem of the unsatisfactory non-equilibrium characteristic in separating shear layer (SSL), a correction determined by anisotropy of Reynolds normal stresses is developed. The last focuses on the unphysical backbending of the streamlines near stagnation/reattachment (SR) points. Since the SSL correction will worsen this defect, a SR correction is carried out to blended with it. Four two-dimensional iced airfoils and a three-dimensional iced wing are simulated and then the above measures are confirmed to be the positive.

A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$ , respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$ , where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

Analysis and numerical simulation of a generalized compressible Cahn–Hilliard–Navier–Stokes model with friction effects

We propose a new generalized compressible diphasic Navier–Stokes Cahn–Hilliard model that we name G-NSCH. This new G-NSCH model takes into account important properties of diphasic compressible fluids such as possible non-matching densities and contrast in mechanical properties (viscosity, friction) between the two phases of the fluid. The model also comprises a term to account for possible exchange of mass between the two phases. Our G-NSCH system is derived rigorously and satisfies basic mechanics of fluids and thermodynamics of particles. Under some simplifying assumptions, we prove the existence of global weak solutions. We also propose a structure preserving numerical scheme based on the scalar auxiliary variable method to simulate our system and present some numerical simulations validating the properties of the numerical scheme and illustrating the solutions of the G-NSCH model.

Entrainment rate predictions of axis-symmetric non-swirling jets using free-jet-theory, Reynolds-averaged Navier-Stokes modelling and large-eddy-simulations resolved up to Kolmogorov scale

Jet entrainment - relevant to mixers, sprays and combustion technologies - has been the subject of this work. We limit our considerations to air jets issued from convergent nozzles of diameter smaller than 25.4 mm, the nozzle exit Reynolds number in the range 30,000 to 100,000 and Mach numbers not exceeding 0.4. The emphasis is on jet self-similarity region (60 < x/d0 < 210) and the key question is with which accuracy can Computational Fluid Dynamics (RANS and LES) and free-jet theory predict jet entrainment. Seven jets have been considered.The realizable k-є model has outperformed the other models and provides the entrainment predictions within ±6 % margin from the measured data. The standard k-є and the Shear-Stress Transport (SST) k-ω models deliver entrainment figures which are larger than the measured data by 22 % – 24 % whilst predictions of either the Reynolds Stress Model (RSM) or Re-Normalization Group (RNG) k-є models can be off (too large) by as much as 34 % and 40 %, respectively. Such a clarity in classification of turbulence models has been obtained after minimization of numerical related errors to a degree which was not achievable in the past. The Panchapakesan&Lumly's jet has been computed using the Large Eddy Simulations with the filter size of the order of Kolmogorov scale throughout the jet e.g. at the inlet, potential core and the far field. Excellent predictions of the jet spread rate, velocity profiles and the entrainment have been obtained at the expense of huge computational resources.The well-known engineering correlation m˙e/m0˙=0.32(x/d0) provides entrainment figures that are by 10 % or less larger than the measured values.

Drag reduction of lift-type Vertical axis wind turbine with slit modified Gurney flap

This study examines aerodynamic performance enhancement of Vertical Axis Wind Turbine (VAWT) blades with Gurney flap (GF) modified by slits. A quasi-3D computational fluid dynamics solution based on Reynolds-averaged Navier-Stokes model is employed to evaluate the effectiveness of slit GF blades, in particular the lift-to-drag ratio. The computational domain includes three pairs of GFs and slits combination along the blade span-wise direction to allow quasi-3D flow development while applying translational periodic boundary condition on the two end-wall boundaries. The inlet velocity is 9 m/s for a VAWT configuration with Tip Speed Ratios (TSRs) of 1.44, 2.64, and 3.3, respectively and each of these TSRs represents low, medium, and high regimes of TSRs. Simulation results have shown a significant 8% drag reduction for blades with slit GFs at medium range of TSRs, albeit with a 2% decrease in lift compared to blades with clean GFs. This improves the lift-to-drag ratio and enhances moment production. The power generation also shows increases of 1.5%, 6.5%, and 11.3% at low, medium, and high TSR regimes, respectively, for the analysed slit GF blades. The drag reduction is primarily attributed to the generation of small-scale vortices by the slit, dissipating large coherent flow structures more rapidly in the near wake-field.

Performance of dual‐chamber oscillating water column device under irregular incident waves using Reynolds averaged Navier–Stokes model

AbstractThe purpose of this study is to analyze the hydrodynamic performance and efficiency of a dual‐chamber oscillating water column (OWC) device. For the Joint North Sea Wave Project (JONSWAP) incident waves spectrum, a two dimensional numerical wave tank is employed with nonlinear Reynolds averaged Navier–Stokes equations model along with the standard turbulence model. The free surface elevation is measured using the volume of fluid method. The numerical simulation demonstrates the streamline and velocity vector profiles throughout an entire pressure fluctuation cycle inside the chambers of the given OWC device. Further, investigation is carried out to analyze the impact of pressure drop and air flow rate through the orifice of the dual‐chamber OWC device on the power generation. Moreover, the power spectral density analysis of the free surface elevation is provided to know the variation of the parameters in the frequency domain. These results demonstrate that the effectiveness of the dual‐chamber OWC device is more near the significant wave height m.

Wong–Zakai approximation for a stochastic 2D Cahn–Hilliard–Navier–Stokes model

AbstractIn this paper, we demonstrate the Wong–Zakai approximation results for two dimensional stochastic Cahn–Hilliard–Navier–Stokes model. The model consists of a Navier–Stokes system coupled with convective Cahn–Hilliard equations. It describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under the influence of multiplicative noise. Our main result describes the support of the distribution of solutions. As in [2], both inclusions are proved by means of a general Wong–Zakai type result of convergence in probability for nonlinear stochastic PDEs driven by a Hilbert‐valued Brownian motion and some adapted finite‐dimensional approximation of this process. Note that the coupling between the Navier–Stokes system and the Cahn–Hilliard equations makes the analysis more involved.

Numerical investigation gaseous ammonia basic jet and mixing characteristics in the constant volume vessel

Ammonia is considered a promising zero-carbon fuel under the dual-carbon targets. Systematically understanding ammonia's basic jet and mixing characteristics can promote its practical application in the engine field. Thus, a three-dimensional computational fluid dynamics (CFD) model of constant volume vessel (CVV) is established in this paper, and the forecasting abilities of the Large Eddy Simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) models for the gaseous ammonia jet process are compared based on the experimental data. Then, the ammonia jet development rule and mixing characteristics under different ambient temperatures, ambient pressures, and fuel temperatures are investigated. The variation laws of key data such as penetration distance, jet area, ammonia mass concentration distribution, equivalence ratio, and turbulent kinetic energy are obtained and analyzed. The results show that during the injection process, the airflow on the left and right sides of the jet rotates in opposite directions. A higher temperature and lower pressure within the CVV lead to a larger flammable range for ammonia jets. Moreover, the distribution of ammonia mass concentration on the radial plane shows a dynamic development law with time, meaning that it first increases to a maximum value, then gradually decreases, and finally remains stable. The farther the radial plane is from the nozzle outlet position, the lower the ammonia mass concentration. In addition, the ammonia jet's turbulent kinetic energy has a large core region and symmetrical distribution along the central axis. At the beginning of the injection, the core length is small, gradually increasing with time and finally stabilizing.

Aerodynamic study of high-speed railway tunnels with variable cross section utilizing equivalent excavation volume

High-speed railway tunnels, being critical components of transportation infrastructure, are subject to various aerodynamic effects that can impact train operations and passenger comfort. To address these challenges, the concept of tunnels with variable cross sections offers a promising solution, allowing for non-uniform adjustments to tunnel geometry along its length. By employing the notion of equivalent excavation volume, this paper aims to provide a comprehensive aerodynamic analysis of variable cross section tunnels, focusing on different rates of cross section variation (CR). The simulation of high-speed trains (HSTs) passing through tunnels is conducted using the compressible, unsteady Reynolds-Averaged Navier–Stokes model, and the accuracy is confirmed through experimental validation. The transient pressure and peak distribution, slipstream characteristics, micro-pressure waves, and aerodynamic loads acting on trains are fully evaluated. The results indicate that variable cross section tunnels can alleviate the negative pressure on train surface, particularly with streamlined heads and tails exhibiting superior effects, whereas its influence on positive pressure is minimal. The mitigation of both positive and negative pressures on the tunnels is promising, with the maximum peak-to-peak pressures exhibiting a quadratic decrease as the CR increases, resulting in a maximum relief of 17.7%. However, variable cross section tunnels have certain adverse effects on slipstreams and transient loads when HSTs passing through front junctions. Therefore, it is necessary to choose an appropriate CR to control these effects during design process. The findings of this research contribute novel insight for optimizing tunnel design and engineering practices to enhance operational efficiency and passenger comfort.

An Engineering Approach to Improve Performance Predictions for Wind Turbine Applications: Comparison with Full Navier-Stokes Model and Experimental Measurements

An Engineering Approach to Improve Performance Predictions for Wind Turbine Applications: Comparison with Full Navier-Stokes Model and Experimental Measurements

Enhancing pier local scour prediction in the presence of floating debris

AbstractLocal scour poses a grave threat to bridge foundations, potentially causing catastrophic collapses. This study uses FLOW-3D with the Reynolds-Averaged Navier-Stokes model to analyze pier scour and dune formation under bridges. It focuses on submerged debris shapes near the water's surface. Results closely match experiments when specific conditions are met. The study introduces an innovative approach to debris impact assessment. Instead of traditional methods, it proposes a novel equation accounting for debris's effective area and elevation. This enhances reliability by over 20%, improving scour depth assessment in debris-laden scenarios. This advances the understanding of debris's role in local scour, benefiting bridge design and management practices.