Navier-Stokes Simulations Research Articles

Disturbance growth and its effect on convection in a buoyancy-driven vertical channel with one heated wall

Three-dimensional buoyancy-driven flow in a vertical channel with one heated wall that resembles a solar chimney is studied employing direct numerical simulation in order to capture the instability and disturbance growth in this flow. The aspect ratio of the simulated channel is 20, and the Grashof number is 6.1×1010. Linearly-unstable sinusoidal perturbations are individually applied to the pressure, velocity, and temperature fields at the entrance of the channel. It is shown that the imposed perturbations grow in time and change the characteristics of the flow from a laminar to a transitional character with a range of active scales of flow disturbances. Two dominant vortical structures identified in the transitional flow consist of two-dimensional spanwise and three-dimensional predominantly streamwise vortices, both growing spatially near the heated wall as the flow rises. For the ranges studied, both vortical structures appear to be independent of the amplitude or the type of the introduced perturbations. Budgets of the fluctuation kinetic energy show that buoyancy plays the main role in producing the fluctuating energy, although the role of shear production becomes more important as the flow rises along the channel. The effect of the disturbance growth on bulk convection in the solar chimney is to increase the friction coefficient, lowering the flow rate by 14% compared to a laminar condition. Moreover, the turbulent Prandtl number diverges significantly from unity near the heated wall, suggesting that the assumption of near-unity turbulent Prandtl number that is commonly made in Reynolds-averaged Navier–Stokes simulations of solar chimneys may lead to inaccurate predictions.

Prediction of the wall pressure spectrum over a curved structure excited by a non-homogeneous turbulent boundary layer in water

In the present study, we introduce a volume approach based on the Poisson equation solved using a Green's function and a semi-analytical turbulence model in space domain. This model can be built from either a Reynolds-Averaged Navier-Stokes (RANS) simulation or an estimation of the boundary layer parameters. Predictions for the power spectral density of the wall pressure fluctuations are compared against measured data obtained for various flow conditions inside a cavitation tunnel. Two geometries are considered. First, we use a NACA 0012 hydrofoil of constant chord length to validate predictions for different flow velocities and angles of attack. Then, we consider a NACA 0009 hydrofoil with a spanwise varying chord length to investigate the contribution of three-dimensional effects.

A region-segmentation combinational loss model based on data-driven machine learning for a boundary layer ingestion fan

The boundary layer ingesting (BLI) fan is continuously working under distorted inflows. The rotor blade moves across the distorted and undistorted regions and the resultant off-design condition makes the loss present a notable non-uniform distribution feature. Accurately capturing the loss is very important for evaluations of BLI fan performances in preliminary design stage. However, unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are extremely computational expensive even though they can well predict the loss, and the traditional empirical or physics-based loss models are usually fade when predicting loss variation trends and absolute magnitudes under complex inflow conditions. This paper develops a data-driven machine learning based region-segmentation combinational loss model to realize a fast and accurate prediction of the aerodynamic loss in a BLI fan rotor. According to the distinctions of loss sources in different spanwise fractions, a region segmentation idea is first used to create local loss model in each sub-region, and then a full-span combinational prediction model is constructed through a data-driven based neural network approach. Results show that the data-driven based region-segmentation combinational loss model presented in this work performs better than the traditional empirical or physics-based loss models in terms of predicting both the loss variation trends and absolute magnitudes. Compared with the high-fidelity URANS simulations, the averaged loss prediction errors in a BLI fan rotor are kept within 10 % under different blade load and inflow distortion conditions.

Supersonic Wind Tunnel Flow Characterization Using Planar Laser CO2 Rayleigh Scattering

A complementary experimental and computational study was performed to characterize the test section flowfield of a variable-Mach-number supersonic wind tunnel. A planar laser Rayleigh scattering technique using CO2 nanocrystals was used to capture cross-sectional flow visualizations at various test section streamwise locations. Reynolds-averaged Navier–Stokes simulations of the wind tunnel flow were performed using a k-ω shear stress transport turbulence model to compare against the flow visualizations. Mach 3.20 and 3.55 flow conditions were investigated in the wind tunnel with an empty test section. The Rayleigh signal profile near the wind tunnel walls was compared against boundary-layer thickness data from shadowgraph visualizations, pitot survey measurements, and numerical simulation predictions to guide the interpretation of the scattering results. A brief discussion regarding the nature and potential source of certain unexpected scattering patterns in the images was provided. The most distinguishable flowfield characteristics observed in the Rayleigh scattering visualizations were the asymmetric thickness of the boundary layers along the test section walls and the appearance of two floor lobes near the flow-path corners. The results of the numerical simulations showed favorable agreement with the experimental data and were used to provide insight into the mechanism that caused the boundary-layer features observed. This study demonstrated the usefulness of CO2 Rayleigh scattering to obtain flow visualization data of great value to better understand flow quality in supersonic wind tunnels with two-dimensional nozzles.

Parameterizing the fluid forces on limpet shells in unidirectional flow

Current parameterizations of the hydrodynamic forces on irregular particles consider some shape dependencies, but lack an explicit dependence on the orientation with respect to the flow. In this paper, we propose a new parameterization of the drag and lift forces acting on whole Limpet shells at arbitrary orientations with respect to the direction of flow through the linear regression of fluid forces against the velocity components in an object frame of reference. The fluid forces were estimated using boundary layer-resolving Reynolds-averaged Navier-Stokes (RANS) simulations. We verified the accuracy of the shear stress transport (SST) k-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k-\\omega $$\\end{document} turbulence model on flat plates with varying angles of attack, and we achieved coefficients of determination versus existing data of approximately 0.95 for both the drag and lift coefficients. From the linear regression of our simulated force data, we developed a model as a function of 3-dimensional orientations to predict the hydrodynamic forces acting on a Limpet shell with coefficients of determination of 0.80 for normal forces and 0.51 for longitudinal forces.

Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier–Stokes (NS) equations. The development of surrogate models relies on involved algebra and several assumptions. Here, we present a data-driven workflow where a handful of detailed NS simulation data are leveraged into a reduced-order model for a prototypical vertically falling liquid film. We develop a physics-agnostic model for the film thickness, achieving a far better agreement with the NS solutions than the asymptotic Kuramoto–Sivashinsky (KS) equation. We also develop two variants of physics-infused models providing a form of calibration of a low-fidelity model (i.e. the KS) against a few high-fidelity NS data. Finally, predictive models for missing data are developed, for either the amplitude, or the full-field velocity and even the flow parameter from partial information. This is achieved with the so-called ‘gappy diffusion maps’, which we compare favourably to its linear counterpart, gappy POD.

Unsteady Reynolds-Averaged Navier–Stokes Simulations of a Ducted Wind Turbine

Abstract An unsteady Reynolds-averaged Navier–Stokes model on body-fitted meshes in a commercial package (SimericsMP+) with a mismatched grid interface is used to study fluid dynamics around a ducted wind turbine. The model is validated by studying turbulent flow past a marine propeller. The nondimensional thrust and torque coefficients are compared against experimental data and results from a large eddy simulation model. Both coefficients are found to be within 3% of experimental results. Following this validation, the impact of different tip speed ratios on the ducted wind turbine's fluid dynamics is assessed. The optimal tip speed ratio is found to be the design value of 3.93 with a maximum power coefficient of 0.465 based on the duct exit area. The corresponding thrust coefficient is found to be 1.02 based on the rotor area. Lower tip speed ratios experience larger flow separation on the duct interior. Higher tip speed ratios decrease the size of the low-velocity region behind the hub. The ducted wind turbine's performance at design conditions is compared to an open rotor. The ducted wind turbine increases the power coefficient by 96% over the open rotor. The impact of hub size on the ducted wind turbine is also studied by simulating a smaller hub with 77% diameter. At the design tip speed ratio, the smaller hub has a power coefficient of 0.417. The maximum power coefficient is found to be 0.446 at a higher tip speed ratio of 4.5.

Numerical Simulations of Internal Tide Dynamics in a Steep Submarine Canyon

Abstract This study investigates three-dimensional semidiurnal internal tide (IT) energetics in the vicinity of La Jolla Canyon, a steep shelf submarine canyon off the Southern California coast, with the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) numerical simulator. Numerical simulations show vertical structure and temporal phasing consistent with detailed field observations. ITs induce large (approximately 34 m from peak to peak) isotherm displacements and net onshore IT energy flux up to 200 W m−1. Although the net IT energy flux is onshore, the steep supercritical slope around the canyon results in strong reflection. The model provides the full life span of internal tides around the canyon, including internal tide generation, propagation, and dissipation. ITs propagate into the canyon from the south and are reflected back toward offshore from the canyon’s north side. In the inner part of the canyon, elevated mixing occurs in the middle layer due to an interaction between incident mode-1 ITs and reflected higher-mode ITs. The magnitude of IT flux, generation, and dissipation on the south side of the canyon are higher than those on the north side. An interference pattern in horizontal kinetic energy and available potential energy with a scale of approximately 20–50 km arises due to low-mode wave reflections. Our results provide new insight into IT dynamics associated with a small-scale canyon topography. Significance Statement Internal waves play an important role in ocean circulations and ecosystems. In particular, internal waves with frequencies of tides, known as internal tides, strongly enhance energy, heat, and mass transport in coastal oceans. This study presents internal tide dynamics in La Jolla Canyon, California, using a high-resolution numerical model. Model results show energy convergence in the canyon leading to internal tide energy dissipation and mixing. Some parts of internal tide energy reflect back offshore resulting in standing internal waves off California. This study provides new insights into internal tide dynamics and energy budgets in submarine canyons.

High fidelity simulation of dense vapours with thermodynamic consistent modelling

The paper describes the implementation of thermodynamic modelling within a high-order finite difference scheme. A new method to ensure thermodynamic consistency for Navier–Stokes simulations of real-gas11A real gas being one which does not obey the ideal gas law. flows is outlined. The paper shows that this method is suited to high fidelity simulations of dense-vapour flows with complex equations of state, such as found in Organic Rankine Cycle turbines. The method is illustrated with two examples of siloxane MM flow in a channel and in a turbine vane. The results show that thermodynamic consistency plays a vital role in the accurate prediction of irreversibility and therefore turbine loss.

Prediction of aerodynamic characteristics of high-lift Common Research Model in ground effect

Abstract Reynolds Averaged Navier-Stokes (RANS) simulations are performed to investigate the aerodynamic characteristics of the NASA Common Research Model (CRM) in its high-lift (HL) configuration in close proximity to the ground. The RANS simulations are conducted at a moderate Reynolds number of $Re = 5.49 \times {10^6}$ and $M = 0.2$ with the use of the Spalart-Allmaras (SA) turbulence model. out of ground effect (OGE) simulation results are validated against available wind tunnel data before proceeding to in ground effect (IGE) simulations. The obtained computational results in the immediate vicinity of the ground with asymmetric aircraft attitudes demonstrate significant changes in the longitudinal and lateral-directional aerodynamic characteristics, which should be taken into account in flight dynamics analysis of aircraft during take-off and landing in crosswind conditions.

A Hybrid Large Eddy Simulation Algorithm Based on the Implicit Domain Decomposition

The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, the near-wall domain decomposition (NDD) approach that was originally developed for Reynolds-averaged Navier–Stokes simulations (RANSs) is extended to the hybrid RANS/LES zonal decomposition. The algorithm is implemented in two stages. First, the solution is computed everywhere with LES on a coarse grid using a new non-local slip boundary condition for the instantaneous velocity at the wall. The solution is then recomputed in the near-wall region with RANS. The slip boundary conditions used in the first stage guarantee that the composite solution is smooth at the inner/outer region interface. Another advantage of the model is that the turbulent viscosity in the inner region is computed based on the corresponding RANS velocity. This shows improvement over those hybrid models that have only one velocity field in the whole domain obtained from LES. The model is realized in the open source code OpenFOAM with different approximations of turbulent viscosity and is applied to the planar channel flow at frictional Reynolds numbers of Reτ=950, 2000, and 4200. Mean streamwise velocity and Reynolds stress intensities are predicted reasonably well in comparison to the solutions obtained with unresolved LES and available DNS benchmarks. No additional forcing at the interface is required, while the log–layer mismatch is essentially reduced in all cases.

Attenuation of Detrimental Hub Leakage Effects in an Axial Compressor Rotor by Customized Geometrical Design Features

Abstract The aerodynamic impact of hub gap leakage on the performance characteristics of an axial compressor rotor in conventional design (no blisk) with a high hub-to-tip ratio has been investigated using three-dimensional steady-state Reynolds-averaged Navier–Stokes simulations. The inclusion of circumferential hub gaps in front of the leading edge and after the trailing edge, as well as inter-platform leakage, reduced the total pressure ratio and the polytropic efficiency of the rotor by as much as 3.74% and 3.97%, respectively, compared to a design case with clean endwalls. Potential design recommendations in terms of improved aerodynamic robustness against leakage effects were derived from the separate sealing of each hub gap. Six geometry modifications were assessed, which based on these results. In a throttled operating condition, large edge radii in the front gap on the disk and platform partially recovered the initial losses of both the total pressure ratio (17.7%) and polytropic efficiency (19.6%). A circular lateral platform shape with the opening pointing toward the blade’s pressure side showed superior loss recovery capabilities at a dethrottled operating point. The combination of both features did not reduce the losses further. However, the circular lateral platform shape combined with smaller front gap chamfers proved more beneficial in a throttled state.

Local estimation of the mixing model constant for transported PDF combustion models

This work presents a novel method for the local estimation of the mixing constant in transported, joint-composition, probability density function (TPDF) combustion models. In the literature, the micro-mixing model’s constant, denoted as Cϕ which represents the ratio between the integral and the mixing time-scale, is usually set to a fixed and uniform value. The selection of the appropriate value of the aforementioned constant is mostly done by trial-and-error procedures, which entails a considerable computational cost considering the complexity of TPDF models. In addition, the assumption of a uniform value for this constant may affect the performance of such models, as local effects are neglected. For these reasons, an approach for the local estimation of the mixing constant based on the transport of a passive scalar is developed in this work. The approach is tested by performing Reynolds-Averaged Navier–Stokes simulations on the Adelaide Jet-In-Hot-Coflow (AJHC) flames at different Reynolds numbers (i.e., 5,000 and 10,000) and oxygen concentrations in the coflow (i.e., 3 and 9% in mass basis). The model is validated against experimental data of temperature and species. The local approach can help to overcome the issues related to the tuning of Cϕ, which in many cases may result in time-consuming trial-and-error procedures.

A Quantitative Approach for the Accurate CFD Simulation of Hover in Turbulent Flow

Time-dependent Navier–Stokes simulations have been carried out for a V22 rotor in hover using an improved, lowdissipation, HLLE ++ upwind algorithm in the OVERFLOW code. Emphasis is placed on lessons learned over the past decade regarding the effects of high-order spatial accuracy, grid resolution, and the use of detached eddy simulation in predicting the figure-of-merit, the rotor's chief performance parameter. A general quick-start procedure is described together with a statistical measure of FM convergence that reduces hover computations by fourfold, similar to computational work for forward flight. Cartesian adaptive mesh refinement is used to resolve the tip–vortex to its correct physical size. This adaptive mesh refinement in the rotor wake also revealed a complex turbulent flow with worm-like structures of various scales. These structures were numerically found a decade ago and recently observed in experiment.

Airfoil optimization for rotors operating in the ultra-low Reynolds number regime

Ultra-low Reynolds number aerodynamics has gained significant attention in recent times, primarily due to the proliferation of micro-aerial vehicles and their utilization in low-density environments such as the Martian atmosphere and high altitudes in Earth's atmosphere. The Martian atmosphere presents a unique combination of low Reynolds numbers and high subsonic Mach numbers, necessitating the use of unconventional airfoil designs in this regime. This study focuses on optimizing airfoils for rotors operating in the compressible ultra-low Reynolds number regime. We demonstrate the capability of XFOIL, a panel method code incorporating an integral boundary layer formulation, to accurately predict airfoil loads when the flow remains attached. We determine the optimal camber and maximum camber positions by analyzing the four digits, two percent thickness, National Advisory Committee for Aeronautics XX02 airfoil family using XFOIL. Subsequently, we employ a multi-objective optimization approach, utilizing a Class Shape Transformation airfoil parameterization to maximize lift and minimize drag. We select several points from the resulting Pareto front and evaluate their performance through unsteady compressible Navier–Stokes simulations. Our findings reveal that incorporating sharp leading-edge variations in these airfoil designs enhances the peak efficiency by over 10%, primarily attributable to the development of laminar separation bubbles on the suction side of the airfoils. Importantly, these modified airfoils maintain favorable performance at low angles of attack.

Water flow in a cylindrical nanopore with an object

Understanding the physics of water movement through a nanopore with an object is critical for better control of water flow and object translocation. It should help in the design of nanopores as molecular and viral sensors. We evaluated how the external electric field and ion concentrations, pore wall charge density, disk radius and charge density, and ion mobility influence the water flow in a charged cylindrical nanopore using Poisson–Nernst–Planck–Navier–Stokes simulations. We dissected water flow induced by the external electric field (“external” component) from that generated by the field induced by the fixed and mobile charges (“charge” component). The velocity and direction of the axial flow “external” component were controlled directly by the external electric field. The pore wall charges also influenced them indirectly by altering the density and distribution of mobile charges. Higher external concentrations enhanced the axial water flow by lowering its charge component. The ion mobility and disk charge slightly influenced the axial water flow. The axial body forces near the wall drive the axial water flow near the pore wall. If the disk is large, water also flows axially in the opposite direction near the pore center. Local forces near the disk do not control the radial water flow near the disk. The axial body force and water flow near the pore wall do. If an annulus replaces a disk, the axial forces near the pore wall control the radial flow near the annulus and the axial flow within its hole.

The unsteadiness of tip leakage vortex breakdown and its role in rotating instability

The unsteadiness due to tip leakage vortex (TLV) breakdown was studied using a special experimental test campaign in parallel with numerical simulations. The back flow vortex (BFV), an isolated vortex caused by TLV spiral-type breakdown, was found to play a key role in rotating instability (RI). High-speed pressure transducers were used to measure the unsteady pressure field at the casing end wall of the blade in an isolated subsonic compressor rotor, which identified a low-frequency fluctuation at the near stall condition. A single-passage unsteady Reynolds-averaged Navier–Stokes simulation was used to study the evolution of unsteady flow structures, validated by the experimental measurements. Two distinct kinds of periodically unsteady flow were revealed by the simulations. A high-frequency fluctuation corresponding to 1.0 blade pass frequency (BPF) was caused by the spiral-type breakdown of the TLV. The other low-frequency fluctuation corresponding to 0.5BPF was caused by the feedback interaction between the BFV and the blade loading. The BFV was generated by the TLV breakdown, which was separated from the twisted vortex core of the TLV, and it moved downstream along the pressure side of the adjacent blade. A larger sized BFV reduced the local loading of the adjacent blade. The TLV was weakened as a consequence of the reduced loading, resulting in a smaller sized BFV. The blade tip loading was relatively less affected by the small sized BFV rather than the larger sized BFV. Therefore, the blade loading recovered and the size of the BFV increased, repeating the cycle. This feedback mechanism produced a pressure fluctuation with a frequency equal to 0.5BPF, which was closely related to RI.

Navier–Stokes simulations of vertical sloshing with time-periodic excitation

An in-house Navier–Stokes multiphase VOF (Volume-Of-Fluid) solver is used to study sloshing phenomena in a partially filled rectangular tank subjected to vertical sinusoidal excitation, with the main goal of characterizing the effects of vertical acceleration and excitation frequency on the flow dynamics. The solver is validated through comparison with analytical solutions and with available experiments of vertical sloshing. We find that the computed forces acting on the tank walls are well predicted, both in two- and three-dimensional numerical simulations. The flow dynamics is found to be significantly affected by the forcing parameters, and to exhibit more chaotic and three-dimensional nature in cases with strong acceleration and low forcing frequency. As a consequence, certain properties as the energy dissipation and the mixing efficiency of the system are poorly predicted from two-dimensional simulations in that range of parameters, making more expensive three-dimensional simulations necessary. The time history of the sloshing force and instantaneous flow visualizations are used to analyze the effects of liquid impacting on the walls on energy exchanges between the fluid and the tank. Finally, the evolution of mixing efficiency and its influence on the energy losses are discussed.

Langevin and Navier–Stokes simulation of three-dimensional protoplasmic streaming

Langevin and Navier–Stokes simulation of three-dimensional protoplasmic streaming

Large eddy simulation of film cooling for a forward expansion hole under main flow oscillation

This study conducted a large eddy simulation (LES) to predict the flow structure and effectiveness of film cooling in a gas turbine. The study focused on a forward expansion hole on a flat plate with an inclined injection angle of 35° and spanwise injection angles (orientation angles) of 0° and 30° under main flow oscillation. In gas turbines, the mainstream flow can exhibit unsteadiness owing to stator–rotor interactions or freestream turbulence. Here, sinusoidal functions are used to approximate the flow oscillations, and their effects are evaluated at frequencies of 0, 8, and 32 Hz, corresponding to Strouhal numbers of 0, 0.603, and 2.413, respectively. The study aims to characterize the film cooling at two time-averaged blowing ratios: 0.5 and 1.0. The range of Strouhal numbers considered in this study is relevant to actual transonic gas turbines. The computational results obtained through LES are validated using experimental data and compared with the Reynolds-averaged Navier–Stokes simulation results. The findings demonstrate the efficiency of LES to predict accurately the distribution of spanwise film cooling effectiveness and spanwise-averaged effectiveness for forward expansion holes on turbine blades under flow oscillations. Comprehensive analyses of various aspects such as the instantaneous turbulent structures of the film cooling flow fields, time-averaged temperature, and root-mean-squared values of the coolant temperature and a proper orthogonal decomposition analysis for velocity vectors are performed. The results show that when the oscillation frequency of the main flow varied from 0 Hz to 32 Hz for a time-averaged blowing ratio of 0.5, the film cooling effectiveness for the forward expansion hole reduced significantly. However, when the frequency increased under a time-averaged blowing ratio of 1.0, the film cooling effectiveness for the hole was only slightly affected by the oscillations. Moreover, an orientation angle of 30° enhanced the film-cooling performance even under flow oscillations. Thus, this paper reports the development of highly effective film-cooling strategies that can guide researchers aiming to mitigate the adverse effects of flow oscillations, thereby enhancing the reliability and efficiency of gas turbine engines.