Averaged Navier-Stokes Equations Research Articles

Decomposition of the mechanical stress tensor: from the compressible Navier–Stokes equation to a turbulent potential flow model

AbstractWe frame the mechanical stress tensor decomposition in a general procedure which involves the Helmholtz–Hodge decomposition. We highlight the impact of the mechanical stress tensor decomposition on the Navier–Stokes equation, with emphasis on the dissipation function. For fluids with low compressibility, we draw some insights on the Reynolds Averaged Navier–Stokes equations, and on the Reynolds stress tensor decomposition. We derive a turbulent potential flow model, and investigate the transition from viscous potential flow to turbulent potential flow. Under low Mach number approximation, we apply the turbulent potential flow model to one-dimensional propagation of large amplitude pressure waves in liquid-filled pipe.

Numerical Tools For Wave Overtopping At Rubble Mound Breakwaters With Submerged Berms

In the era of climate change, the adaptation of existing coastal structures as a response to potential increasing loads, has become a trending topic in coastal engineering. The combination of sea level rise, storm surge, tides and waves is going to dramatically increase the wave overtopping. In this context, this research is focused on the evaluation of wave overtopping for conventional rubble mound breakwaters, modified by the introduction of a submerged berm. Recent studies illustrated how the introduction of emerged berms on the seaward slope reduces the wave overtopping. The goal then becomes to turn the spotlight on the submerged berms, whose effectiveness has yet to be attested, although it has proven useful in reducing wave loads on the armour layer and seabed pressure under the structure. Therefore, the reliability of two different numerical models in detecting overtopping phenomenon have been assessed. IHFOAM and SWASH have been used (see Figure 1). The first one can solve both Reynolds Averaged Navier Stokes and the Volume Averaged Reynolds Averaged Navier–Stokes equations. The second one solves the non-linear shallow water equations with a non-hydrostatic pressure term, representing a simplified form of the Navier-Stokes equations, with associated limited computational cost. The numerical models have been validated based on experimental tests carried out in a wave flume at the University of L’Aquila.

NUMERICAL SIMULATION OF TURBULENT FLOW AROUND DARRIEUS AND SAVONIUS ROTORS

The study of unsteady processes during the flow around the rotors of vertical-axis wind turbines was carried out based on the Navier-Stokes equations. General definition of the coupled problem on vertical-axis wind turbines rotors aerodynamics and dynamics is formulated. The solution to the system of initial equations is obtained using an implicit finite-volume numerical algorithm based on the method of artificial compressibility and multi-block structured grids. A code for the calculation of vertical-axis wind turbines rotors aerodynamic and power characteristics is developed on the base of Reynolds averaged Navier-Stokes equations for incompressible fluids. Two types of Darrieus and Savonius rotors with different geometric parameters and number of blades were calculated. The influence of Reynolds numbers, tip-speed-ratios and solidity on the power characteristics of the rotors has been established.

The turbulent jet in the scale-relativity framework

The turbulent jet plays an important role in fluid mechanics since it is a prototype of free turbulent flow which presents many unsolved problems, among which the absence of closure of the governing equations. Despite the chaotic nature of turbulence, it is characterized by the existence of many universal structures, in particular dimensionless invariants such as its opening angle or the correlation coefficient of velocities. After having given new exact solutions of the Reynolds Averaged Navier–Stokes equations (RANS), we suggest a solution to this puzzle in the scale-relativity framework. In this theory, the time derivative of the Navier–Stokes equations is integrated in terms of a macroscopic Schrödinger equation acting in velocity-space. This equation involves a constant ℏv which can be identified with the energy dissipation rate, while the pressure gradient manifests itself as a quantum harmonic oscillator (QHO) potential. The squared modulus of its solutions yields the probability density function (PDF) of velocities. The Reynolds stresses can then be derived from this PDF, so that the closure problem is solved in this case. This allows us to obtain a theoretical prediction for the turbulent intensity radial profile (and therefore for the pressure) which agrees with the experimental data. The ratio of axial over radial velocity fluctuations is found to be R=1.3–1.4 from QHO properties, in good agreement with its experimental values; we theoretically predict a jet opening angle α=1/2R3 accounting for its universal value ≈1/5; the mean ratio of turbulent intensity amplitudes over jet centerline axial velocity is predicted to be X=19/80, in good agreement with its universally measured value ≈1/4; from these parameters we derive possible values of the radial turbulent intensity amplitude μ=0.19–0.22 consistent with experiments; finally, we find a correlation coefficient of velocities ρ=1/R3=2 α, suggesting an explanation for the universal value ≈0.4 observed for the turbulent jet and for all free shear flows.

Hypersonic boost-glide systems: Flight mechanics and plasma parameters evaluation through aero-thermo-chemical computational fluid dynamics

Currently, the conception, design, and development of hypersonic space-borne systems is a central topic of discussion among researchers and industrial stakeholders. In the design phase of a hypersonic manoeuvrable vehicle, it is essential to characterise the thermal heating and manage the problem of the communication blackout, in addition to other challenges concerning guidance, navigation and control, and propulsion. The interference of electromagnetic waves propagating in plasma affects the datalink and the radar detection of hypersonic targets. This work aims to provide valuable information about the aero-thermo-chemical behaviour of the fluid in the region around a hypersonic glider. Launch and re-entry phases of boost-glide systems have been modelled to perform trajectory predictions and assess range and flight paths under the effect of different manoeuvres, defining their possible performances. The resulting flight conditions are used to study the flow field surrounding a glider geometry similar to the Hypersonic Technology Vehicle-2. The thermodynamic and chemical fields around the body have been determined, and plasma parameters for novel electromagnetic interaction studies have been evaluated. Computational fluid dynamics simulations have been carried out to solve the averaged Navier-Stokes equations with the k−ω model for turbulent flows, coupled with the energy equation. Chemical non-equilibrium phenomena involving electronic energy relaxation as well as ionisation reactions have also been included. A gas mixture potentially composed of 11 species has been considered, namely oxygen and nitrogen derivatives. The electron number density is computed to evaluate the electron plasma and collision frequencies, essential parameters to characterise the electromagnetic interference caused by the plasma sheath. Among other results, high temperatures are reached at the nose region of the body in specific conditions of velocity and altitude, and non-negligible dissociation or ionisation of chemical species occurs. Plasma frequencies up to tens of GHz are reached in a region close to the body surface, while lower interference characterises the extended ionised wake.

Study of local scour around rectangular and square subsea caissons under steady current condition

Numerical simulations were conducted to investigate steady current scour around rectangular and square subsea caissons. The caissons, which are representative of subsea structures, have a submerged height ranging from 0.5 to several times their longest base dimension. The flow model used is based on the Reynolds Averaged Navier-Stokes equations, and the scour model simulates bed load and suspended load transport to predict the evolution of the seabed profile. The aim of this study is to investigate the mechanisms of local scour, specifically the contribution of the horseshoe vortex and the local streamline contraction near the caisson corners to local scour. The model is validated through comparisons with experimental measurements, indicating reasonable agreement. Based on the numerical model results, the mechanisms of local scour around square and rectangular caissons are found to be qualitatively similar. If the flow is directed perpendicular to one of the caisson faces, both the horseshoe vortex and the local streamline contraction contribute to scour. The maximum scour depth is located at the two upstream corners of the caisson due to the combined effects of the horseshoe vortex and streamline contraction. When the flow approaches the caisson with a diagonal attack angle of 45°, the two upstream faces act like a streamlined wedge that splits the incoming flow. The study found that the horseshoe vortex almost disappears and the scour is primarily caused by the local velocity amplification at the two side corners. If the flow attack angle is 45°, the scour does not initiate near the upstream corner without the contribution from the horseshoe vortex. These findings are expected to serve as a valuable theoretical foundation for the design of scour protection.

On the existence of flux as a function of the surface elevation for long wave solution of shallow water equations

The shallow water equations in mechanics of fluids, govern the motion of a shallow layer of water over a fixed impervious bed. In this paper, the bed form is assumed to be rough and horizontal, and the motion of water is assumed to be of the long wave type (Lamb [1], pp. 254-256) such that the free surface has a gradually varying propagating profile. Gravitation permits such motion but is resisted by the turbulence generated by the bed friction. A model of the governing equations based on the Reynolds averaged Navier-Stokes equations has recently been given by Bose [2], which is highly nonlinear. A heuristic approach of numerically solving the equations for the modified long waves is also presented in that article, by assuming that the horizontal flux across a section of flow is some function of the free surface elevation alone. This key assertion is analysed in this article and proved to hold provided some boundedness criteria are satisfied by the flux gradients. The theory is apparently applicable to find appropriate boundedness conditions on the flux of flow for numerically solving long wave equations in the case of other models for long wave propagation as well.

Numerical analysis of turbulent flow and heat transfer enhancement using V-shaped grooves mounted on the rotary kiln’s outer walls

Rotary kilns have been widely employed in various industrial uses, especially the cement production. This article deals with enhancing the thermal performance of a rotary kiln duct with V-shaped grooves mounted on the outer wall. Four V-shaped grooves with different depths h/D ranging from 0.1 to 0.4 were designed. The Reynolds Averaged Navier–Stokes equations (RANS) of two-dimensional steady-state flow are used to model the governing flow equations by using the finite volume approach (FVM) in FLUENT. k-ε standard, k-ε Realizable, k-ω SST and k-ε RNG turbulence models of the RANS approach and the k -ω SST model has been adopted to validate CFD results. In this study, the numerical results have revealed that the increase in groove depth decrease the temperature of the rotary kiln’s outer wall than the smooth walls and gives the largest Nu number, especially for the groove with h/D =0.3 and 0.4 depths.

A Rapid RI-TP Model for Predicting Turbine Wake Interaction Broadband Noise

Future UHBR (Ultra-High Bypass-Ratio) engines might cause serious ‘turbine noise storms’ but, at present, turbine noise prediction capability is lacking. The large turning angle of the turbine blade is the first major factor deserving special attention. The RANS (Reynold Averaged Navier–Stokes equation)-informed (here called RI) method and LINSUB (the bound vorticity 2D model LINearized SUBsonic flow in cascade), developed to predict fan broadband noise, coupled with a two-flat-plates (here called TP) assumption for the turbine blade, is applied here, and one autonomous rapid RI-TP model for predicting turbine wake interaction broadband noise has been developed. Firstly, taking the single axial turbine test rig NPU-Turb as the object, both the experimental data and the DDES/AA (delayed Detached Eddy Simulation/Acoustic Analogy) hybrid model have been used to validate the RI-TP model. High consistency in the medium and high frequencies among the three designed and off-designed rotation speeds indicates that the RI-TP model has the ability to predict turbine broadband noise rapidly. And compared with the original RANS-informed method, with one thin-flat-plate assumption on the blade, the RI-TP model can enhance the PWL (sound power level) in almost the whole spectral range below 10 KHz, which, in turn, is closer to the experimental data and the DDES/AA prediction results. The PWL trend with a ‘dividing point’ position is also studied. The spectrum would move up or down if the location is away from true value. In addition, the extraction location for turbulence as an input for the RI-TP model is negligible. In the future, multi-stage characteristics and the blade thickness effect should be further considered when predicting turbine noise.

Impacts of hydrocarbons impurities on heat transfer deterioration

Hydrocarbon impurities in Liquified Natural Gas can lead to unwanted occurrences like heat transfer deterioration and pseudo-boiling phenomena. It can pose a challenge for cooling channels in rocket engines. This study examines the impacts of hydrocarbon impurities on heat transfer deterioration in cooling channels. The Reynolds averaged Navier Stokes equation is solved numerically for different commercial LNG flows in circular pipes under supercritical conditions. The thermophysical and transport properties are calculated using the 2008-GERG Equation of states and extended corresponding states models. The simulations reveal that hydrocarbon impurities significantly impact heat transfer deterioration. These impacts vary depending on the concentrations of hydrocarbons. A Nusselt number correlation equation is derived numerically, which describes the heat transfer deterioration of multiple LNGs. In addition, the effects of roughness heights to minimize heat transfer deterioration are studied in detail.

Hydrodynamic Performance Analysis of Camber Ratio Variations on B-series Propeller Types

The hydrodynamic performance of the B-series propeller can be determined by calculating the polynomial equation published by MARIN. Furthermore, analysis and evaluation of B-series propeller modifications can be done by varying the camber ratio of the foil. The camber ratio affects the lift force on the propeller foil, directly affecting the propeller thrust and torque. Numerical calculations were carried out using Computational Fluids Dynamics (CFD), based on Reynolds Averaged Navier Stokes Equations (RANSE) and turbulence model in the form of explicit algebraic stress models (EASM). The overall results of this study show an increase in efficiency of 4.182 on the foil with a camber ratio of 2.2% when compared to the foil camber ratio of 0%.

Development of 1D Model of Constant-Volume Combustor and Numerical Analysis of the Exhaust Nozzle

Development of 1D Model of Constant-Volume Combustor and Numerical Analysis of the Exhaust Nozzle

Numerical study of the effect of a thin wire on the thermohydraulic performance in a plate fin-and-tube heat exchanger

A numerical study on the effect of a wire on the thermohydraulic performance in a plate-and-tube heat exchanger is performed with the Reynolds Averaged Navier-Stokes Equations approach. The heat exchanger is represented by a small finned tube bank with the implementation of periodic boundary conditions and symmetry conditions. The simulation models the turbulence with the Shear-Stress Transport model (SST k-ω). A benchmark case (without thin wire) is validated with PIV measurements of the horseshoe vortex and semi-empirical correlations for heat transfer. Then, twenty-four simulations are conducted at different dimensionless distances (1.0, 1.2, and 1.4) and angles (0, 15, 30, and 45°) of a thin wire. Predictions show that vortical structures around the thin wire contribute to an increase in thermohydraulic performance if the recirculation zones caused by thin wire do not affect the airflow patterns generated by finned tubes. However, the thermohydraulic performance decreases if airflow patterns are affected by the thin wire. Therefore, thin wire located at a dimensionless distance of 1.2 and angle of 15° generates a 5–6 % profit on the thermohydraulic performance with a pressure drop up to 73 Pa for Re = 2100.

Perspectives toward Stochastic and Learned-by-Data Turbulence in Numerical Weather Prediction

Abstract The increased social need for more precise and reliable weather forecasts, especially when focusing on extreme weather events, pushes forward research and development in meteorology toward novel numerical weather prediction (NWP) systems that can provide simulations that resolve atmospheric processes on hectometric scales on demand. Such high-resolution NWP systems require a more detailed representation of the nonresolved processes, i.e., usage of scale-aware schemes for convection and three-dimensional turbulence (and radiation), which would additionally increase the computation needs. Therefore, developing and applying comprehensive, reliable, and computationally acceptable parameterizations in NWP systems is of urgent importance. All operationally used NWP systems are based on averaged Navier–Stokes equations, and thus require an approximation for the small-scale turbulent fluxes of momentum, energy, and matter in the system. The availability of high-fidelity data from turbulence experiments and direct numerical simulations has helped scientists in the past to construct and calibrate a range of turbulence closure approximations (from the relatively simple to more complex), some of which have been adopted and are in use in the current operational NWP systems. The significant development of learned-by-data (LBD) algorithms over the past decade (e.g., artificial intelligence) motivates engineers and researchers in fluid dynamics to explore alternatives for modeling turbulence by directly using turbulence data to quantify and reduce model uncertainties systematically. This review elaborates on the LBD approaches and their use in NWP currently, and also searches for novel data-informed turbulence models that can potentially be used and applied in NWP. Based on this literature analysis, the challenges and perspectives to do so are discussed.

Numerical simulation of gas-solid flow in a cyclone separator with additional inlet

In this study, an additional inlet was added to the gas-solid cyclone separator to enhance the separation efficiency. Four different heights were tested, including 0.95D, 1.4D, 1.5D, and 1.95D (D is the diameter of the cylindrical section). The investigation involved two inlet flow conditions: increasing and dividing the inlet flow rate. The finite volume method and Reynolds stress turbulence model were used to solve the averaged Navier–Stokes equations, whereas the Eulerian–Lagrangian approach and discrete phase model (DPM) were applied to track particles with a uniform diameter of 0.5–1.8 microns as the discrete phase. Owing to the low Stokes number and small and low-volume-fraction particles, a one-way coupling method was employed between air and the particles. The addition of an additional inlet reduced the static pressure in the center and downstream areas and increased the reverse flow velocity at the end of the cyclone. The installation of an additional inlet at 0.95D had the most positive effect on the separation efficiency, with an increase of 28.8% in the increasing flow rate case and 19.6% in the dividing flow rate case compared with the cyclone without an additional inlet. Furthermore, the increase in the separation efficiency of the submicron particles was greater than that of the larger particles in both flow distribution cases.

Simulations of scalar transport in oscillatory flow over a wavy wall

A three-dimensional model that couples Reynolds–averaged Navier–Stokes equations with an advection–diffusion solver for flow and concentration fields over a fixed, non-permeable boundary is presented. The model simulates oscillatory flow over a wavy wall with a constant scalar source to assess the effects of a boundary-induced pressure gradient on passive scalar mixing. Results were compared to experimental data collected in an oscillating tray facility. Hydrodynamic quantities are in favourable agreement with observations. The model captured vortex dynamics correctly, and turbulence statistics were modelled reasonably well. Comparisons of time-resolved and bulk scalar quantities for crest and trough sources were in favourable agreement with observations. Results indicate that the model can be utilized to study processes with highly intermittent phenomena, such as the transport of wastes and dissolved nutrients in the coastal bottom.

Investigation of An Inverted Bow on Frigate Hull Resistance

This study discusses the inverted bow design on the combatant hull form. Changes in the shape of the stem angle and flare bow are used as analytical parameters to investigate the ship's performance. Ship resistance and motion will be predicted using the Computational Fluid Dynamics (CFD) approach using the Reynolds Averaged Navier Stokes (RANS) equation and the k-ε turbulence model. The volume of fluid (VOF) method is applied to simulate the change in the free surface between water and air using an overset mesh technique. The ship's movement is limited to sinkage and trim motions, so the movement's accuracy can be predicted. The results revealed that the inverted bow reduced the total resistance by 6.30%, whereas the trim and sinkage showed no significant changes. The breakdown of the reduction ratio showed that friction resistance components were reduced by 10.62%, wave resistance by 44.05%, and viscous-pressure resistance by 45.33%. This highlights the effectiveness of an inverted bow in optimizing wave and viscous pressure, enhancing overall ship performance.

Computational Fluid Dynamics Analysis of the Influence of Diameter at Inlet 2 on Heat Transfer and Fluid Flow in the Mixing Elbow

This study presents the CFD (Computational Fluid Dynamics) analysis of the mixing elbow by determining the influence of the variation in the diameter of the inlet 2 section, Diameter 2 with the use of the ANSYS FLUENT software. The flow of our problem being turbulent, was described by the Reynolds Averaged Navier-Stokes Equations (RANSE), the k-ε closure model and for the temperature field, the averaged energy conservation equation. To solve them numerically, the finite volume method and the SIMPLE scheme for Pressure-velocity coupling were chosen. The larger the Diameter 2, the more effective mixing areas, the more uniform the temperature and velocity at the outlet and the better the mixing. At the outlet, not only do the velocities and temperatures increase but their gradient also increases with an increase in Diameter 2 up to 0.025m, the presence of turbulence and the rate of heat transfer increase. For Diameter 2 equal to 0.030m, the curves are symmetrical, the temperature and velocity values ​​vary slightly over the entire outlet section, we have a better mixture but with a low heat transfer rate.

Numerical Study of the Effect of the Ejection Angle on the Cooling Performance of a High-Pressure Gas Turbine

In modern gas turbines, the purge flow plays an important role in improving the performance of the gas turbine, as it is adapted against the problem of the ingestion of hot gases in the inter-disc cavity of the turbine. The performance of this purge flow is necessarily influenced by some geometrical and physical parameters. This paper presents a 3D numerical study on the influence of the ejection angle on the cooling performance in a high pressure transonic gas turbine with the presence of the cavity. Five inclination cavity angles are compared (𝝓 = 30°, 45°,60°,75°and 90°) by using ANSYS Fluent, a steady flow Reynolds average Navier-Stokes equations are solved, and the turbulence model k-ω SST has been chosen based on comparison of the distribution of velocity and heat transfer convective coefficient with experimental results in a previous work. It was seen that that cooling is limited to the suction side because of the non-uniform pressure distribution of the main flow and the high pressure of the stagnation point. The optimal configuration was determined for an ejection angle of 30°.

The Dimple Effect on Flettner Rotors for the Wind Power Drive System of a Sailing Merchant Ship

Wind-powered ship propulsion is investigated in relation to reducing ship exhaust emissions, such as the application of Flettner rotor systems. How to increase rotor thrust's contribution to ship speed is an intriguing research question. This paper investigates the influence of dimples on the surface of a Flettner rotor on its ability to generate thrust for a ship. The CFD code, which includes the Reynolds average Navier-Stokes equation and the k-ω model for turbulent flow, is utilized to analyse three rotor designs: one with a smooth surface and two with dimple surfaces of varying diameters. Lift and drag are computed by taking into account varying spin ratios and the incoming wind angle. The CFD results are validated by comparing them to experimental data gathered in a wind tunnel and determining that their error is less than 5%. The addition of dimpled surfaces to the rotor increases lift by 69.6% and decreases drag by 14.8% due to the smooth surface. For the case study, the two rotors are mounted on the sailing ship 900 DWT and can generate the most thrust to give the ship a speed of 8.5 knots with a spin ratio of 4 and apparent wind angles of 90o or 270o relative to its speed.