Large-eddy/Reynolds-averaged Navier–Stokes simulation of a supersonic reacting wall jet

This work presents results from large-eddy/Reynolds-averaged Navier–Stokes (LES/RANS) simulations of the well-known Burrows–Kurkov supersonic reacting wall-jet experiment. Generally good agreement with experimental mole fraction, stagnation temperature, and Pitot pressure profiles is obtained for non-reactive mixing of the hydrogen jet with a non-vitiated air stream. A lifted flame, stabilized between 15 and 20 cm downstream of the hydrogen jet, is formed for hydrogen injected into a vitiated air stream. Flame stabilization occurs closer to the hydrogen injection location when a three-dimensional combustor geometry (with boundary layer development resolved on all walls) is considered. Volumetric expansion of the reactive shear layer is accompanied by the formation of large eddies which interact strongly with the reaction zone. Time averaged predictions of the reaction zone structure show an under-prediction of the peak water concentration and stagnation temperature, relative to experimental data, but display generally good agreement with the extent of the reaction zone. Reactive scalar scatter plots indicate that the flame exhibits a transition from a partially-premixed flame structure, characterized by intermittent heat release, to a diffusion-flame structure that could probably be described by a strained laminar flamelet model.     

A high-resolution Navier–Stokes solver for direct numerical simulation of free shear flow

Abstract

A high-resolution, Navier–Stokes solver is developed for direct numerical simulation (DNS) of free shear flow. All terms in Navier–Stokes equations are discretized using higher order methods. Diffusion term is discretized using fourth order central difference scheme while second order Adams–Bashforth is used for time derivative. Advecting velocity is approximated using fourth order Lagrangian interpolation. For the approximation of advected velocity, a blended fifth order-upwind scheme is proposed. Developed high resolution solver is used for DNS of round jet in transitional and turbulent regimes. A novel open outlet boundary condition (OOBC) is proposed which has the ability to dynamically adjust according to prevailing local condition at the outlet thereby minimizing reflections from outlet. Ability of blended fifth order upwind scheme and fifth order WENO is assessed in terms of algorithmic efficiency as well as fidelity of simulations. It is demonstrated that the proposed blended fifth order upwind scheme outperforms the WENO scheme in terms of algorithmic efficiency. Assessment of fidelity of simulations reveals that WENO displays a tendency to over-predict momentum advection in transitional as well as fully turbulent regime of the round jet. In contrast, the proposed advection scheme is not faced with such limitation.     

Large-Eddy/Reynolds-averaged Navier–Stokes simulation of combustion oscillations in a cavity-based supersonic combustor

Combustion oscillations in a supersonic combustor with hydrogen injection upstream of a cavity flameholder are investigated numerically using a hybrid RANS/LES (Reynolds-Averaged Navier–Stokes/Large-Eddy Simulation) method acting as a wall-modeled LES. A turbulent boundary layer with thickness of δ_inf = 2.5 mm is considered and a recycling/rescaling method is adopted to treat the unsteady inflow. The results show that combustion oscillations can mainly be attributed to two mechanisms. One is the unsteady flame spreading from the cavity shear layer to the main stream, which is greatly influenced by the interaction of the jet-with-cavity shear layer. This mechanism leads to relatively low-frequency oscillations that correspond to the cavity-shear layer oscillations. The other is the auto-ignition of the combustible fluid packets formed around the fuel jet accompanied by the generation of the hairpin-like vortices, which leads to relatively high-frequency oscillations that correspond to the jet instabilities.     

A finite volume method to solve the Navier–Stokes equations for incompressible flows on unstructured meshes

A method to solve the Navier–Stokes equations for incompressible viscous flows and the convection and diffusion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed diffusion scheme with interesting theoretical and numerical properties is tested and integrated into the Navier–Stokes solver. Predictions of Poiseuille flows, backward-facing step flows and lid-driven cavity flows are then performed to validate the method. We finally demonstrate the versatility of the method by predicting buoyancy force driven flows of a Boussinesq fluid (natural convection of air in a square cavity with Rayleigh numbers of 10 ³ and 10 ⁶ ).     

Modeling of Navier–Stokes equations for high Knudsen number gas flows

The possibility of modeling the Navier–Stokes equations and together with the conventional second order slip boundary condition at high Knudsen numbers is explored in this paper by incorporating the Knudsen diffusion phenomenon in rarefied gases. An effective mean free path (MFP) model is augmented to the governing equation and the slip boundary condition, as gas transport properties can be related to the MFP. This simple modification is shown to implicitly take care of the complexities associated in the transitional flow regime, without necessitating dependency of the slip coefficients on the Knudsen number. Unique analytical model with fixed values of slip coefficients is proposed and rigorous comparisons with the experimental and simulation data for pressure driven and thermally driven rarefied gas flows support this conjecture. First and second order slip coefficients have been proposed as 1.1466 and 0.9756 for rectangular channels and 1.1466 and 0.14 for the capillaries, from the continuum to the transition flow regime. The current work is significant from the numerical simulation point of view because simulation tools are better developed for Navier–Stokes equations.     

A detailed comparison between Navier–Stokes and DSMC simulations of multicomponent gaseous flow in microchannels

Numerical results of the Navier–Stokes equations and the DSMC method for H₂/N₂ and H₂/N₂/CO₂ mixtures in planar microchannels are compared in order to verify the accuracy of slip/jump boundary conditions in multicomponent flows. For the solution of the Navier–Stokes and energy equations, a finite-volume method is used together with a complete set of slip/jump boundary conditions derived from the kinetic theory of gases. In order to compare the accuracy of these two methods, different wall temperatures as well as inlet mass flow rates are examined. Isothermal flow is also considered for comparison with available analytical solutions for slip flows. The Knudsen number typically ranged between 0.015 < Kn < 0.09 with a Reynolds number of 5 < Re < 15. The two methods are generally in good agreement under the conditions studied especially at low to moderate Knudsen numbers.     

Partially-Averaged Navier–Stokes method with modified k–ε model for cavitating flow around a marine propeller in a non-uniform wake

Unsteady cavitating turbulent flow simulations need to be responsible for both cavitation and turbulence modeling issues. The Partially-Averaged Navier–Stokes (PANS) computational model developed from the RANS method and the k–ε turbulence model are used to model turbulent cavitating flow with a mass transfer cavitation model in the present paper. An objective of this study is to pursue more accurate estimates of unsteady cavitating flows with large-scale fluctuations at a reasonable cost. Firstly, the unsteady cavitating flow simulations over a NACA66-mod hydrofoil are performed using the PANS method with various values of the resolution control parameters (f_k = 1 ～ 0.2, f_ε = 1) to evaluate the numerical methods based on experimental data. The comparison with the experiments show that the numerical analysis with a f_k = 0.2 can predict the cavity evolution and shedding frequency fairly well. Then, cavitating flow around a marine propeller in non-uniform wake was simulated by PANS method. The calculations show that large cavity volume pulsation as the blade passes through the wake region is resolved better by the PANS method with f_k = 0.2 than by the RANS method with the k–ε or k–ω SST turbulence models. This can be contributed to the fact that a smaller f_k give larger cavity volume pulsations leading to increased cavity volume accelerations and larger pressure fluctuations above the propeller, while a larger f_k overestimates the turbulent viscosity along the rear part of the cavity. Finally, it is confirmed from the simulation by the PANS method with f_k = 0.2 that the whole process of cavitating flow evolution around the propeller in non-uniform wake can be very well reproduced including cavitation inception, sheet cavitation and tip vortex cavitation observed experimentally.     

Influence of the particle–turbulence modulation modelling in the simulation of a non-isothermal gas–solid flow

A gas–solid suspension upward flowing in a heated vertical pipe has been simulated numerically using both Eulerian–Eulerian and Eulerian–Lagrangian approaches. Particular attention has been paid to the influence of the modelling of the particle–turbulence interactions. A model based on a source-term formulation derived from a study by Crowe (Int. J. Multiphase Flow 26 (5) (2000) 719) allows predicting turbulence enhancement due to a strong particle influence in the core of the pipe flow. Calculations of suspension Nusselt numbers, characterizing the heat transfer between the pipe wall and the flow, have therefore been performed, with a satisfactory level of accuracy, compared with available experimental data. Some numerical difficulty remains however, especially due to the near-wall layer interactions which seem very difficult to simulate.     

A comparative study of four low-Reynolds-number k-ε turbulence models for periodic fully developed duct flow and heat transfer

ABSTRACT

In this study, streamwise-periodic fully developed turbulent flow and heat transfer in a duct is investigated numerically. The governing equations are solved by using the finite-control-volume method together with nonuniform staggered grids. The velocity and pressure terms of the momentum equations are solved by the SIMPLE algorithm. A cyclic tri-diagonal matrix algorithm (TDMA) is applied in order to increase the convergence rate of the numerical solution. Four versions of the low-Reynolds-number k-ε model are used in the analysis: Launder-Sharma (1974), Lam-Bremhorst (1981), Chien (1982), and Abe-Kondoh-Nagano (1994). The results obtained using the models tested are analyzed comparatively against some experimental results given in the literature. It is discussed that all the models tested failed in the separated region just behind the ribs, where the turbulent stresses are underpredicted. The local Nusselt numbers are overpredicted by all the models considered. However, the Abe-Kondoh-Nagano low-Re k-ε model presents more realistic heat transfer predictions.     

A review of hybrid integral transform solutions in fluid flow problems with heat or mass transfer and under Navier–Stokes equations formulation

Abstract

The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numerical–analytical approach for fluid flow problems, with or without heat and mass transfer, here with emphasis on the literature related to flow problems formulated through the full Navier–Stokes equations. A brief overview of the integral transform methodology is first provided for a general nonlinear convection–diffusion problem. Then, different alternatives of eigenfunction expansion strategies are discussed in the integral transformation of problems for which the fluid flow model is either based on the primitive variables or the streamfunction-only formulations, as applied to both steady and transient states. Representative test cases are selected to illustrate the different eigenfunction expansion approaches, with convergence being analyzed for each situation. In addition, fully converged integral transform results are critically compared to previously reported simulations obtained from traditional purely discrete methods.     

Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part III. aFNS theory validation

ABSTRACT

For arbitrary Reynolds number Re, aFNS theory O(1; δ²; δ³) significance scaled state variable achieves analytical closure of rigorously space filtered thermal, multi-species Navier–Stokes (NS) conservation principle partial differential equation (PDE) system well-posed on bounded domains (Part I). Validation of boundary commutation error (BCE) and nonhomogeneous Dirichlet boundary condition (DBC) resolution strategies results in AD^h-GWS^h-BCE^h-DBC^h algorithm coupling with aFNS theory optimal Galerkin GWS^h?+?θTS CFD algorithm (Part II), including accuracy/convergence assessments. For Reynolds numbers ranging E+02 <Re?<?2E+04, aFNS theory fully coupled k?=?1 basis Galerkin CFD code generated a posteriori data enable theory quantitative validation. For assured laminar Re range, NS no-slip BC reduced and coupled aFNS theory code predicted quasi-steady thermal-velocity transition to periodic unsteady is validated via linear stability predicted critical Re. For Re exceeding assured laminar, theory coupled CFD data quantify spatial filtering annihilation of (laminar) NS predicted large wave number spectral content. For sufficiently large Re, coupled CFD code a posteriori data document first principles prediction of unsteady periodic wall attached velocity profile transitioning-from-laminar, then separation, fully turbulent profile reattachment followed by relaminarization. These large Re CFD data as well enable validation of perturbation theory O(1; δ²; δ³) significance scaled state variable, AD^h-GWS^h-DBC^h algorithm prediction of O(δ²) state variable non-homogeneous Dirichlet BC DOF data and in concert thoroughly quantify theory generated O(δ²; δ³) state variable distributions.     

Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part I. Theory,resolutions

ABSTRACT

Rigorously space filtering the thermal, multispecies Navier–Stokes (NS) conservation principle partial differential equation (PDE) system embeds a priori undefined tensor and vector quadruples. Large eddy simulation (LES) computational fluid dynamics algorithm resolutions replace the tensor quadruple with a single tensor then secures closure through “physics-based” modeling, assuming the velocity field is turbulent, i.e., the Reynolds number (Re) is large. In complete distinction, a totally analytical closure is derived for the rigorously generated tensor/vector quadruples, achieved totally absent any modeling component or Re assumption. For Gaussian filter of uniform measure δ, derived analytical filtered Navier–Stokes (aFNS) theory PDE system state variable is significance scaled O(1; δ²; δ³) through classic fluid mechanics perturbation theory. That uniform measure δ filter penetrates domain boundaries requires O(1) resolved scale PDE system inclusion of boundary commutation error (BCE) integrals, (unfiltered) NS state variable extension in the sense of distributions, and domain enlargement to encompass all surfaces with Dirichlet boundary condition (DBC) specification. Theory-derived O(δ²) resolved–unresolved scale interaction PDE system, also the O(1) system, is rendered bounded domain, well posed through a priori identification of O(1; δ²) state variable nonhomogeneous DBCs. BCE and DBC resolution algorithm derivations use O(δ⁴) approximate deconvolution (AD) differential definition Galerkin weak forms. Theory analytically derived unresolved scale O(δ³) state variable annihilates discretization-induced O(h²) dispersion error at unresolved scale threshold δ, h the mesh measure. Net is an analytical theory closing rigorously space-filtered NS exhibiting potential for first principles prediction of viscous laminar–turbulent transition, separation, and relaminarization.     

Methodology to estimate the output of a dual solar–wind renewable energy system in Japan

The potentially damaging effects of climate change make it imperative to develop zero-carbon energy systems and societies based on renewable energy sources that do not negatively affect the environment. However, these systems are often criticized for their intermittency, and the present paper proposes a method to analyze the true minimum capacity factor that can be expected from such a system based on a historical hourly estimation of the electricity produced by a given solar–wind generating mix. A simulation was carried out to show how much energy could be produced for a sample future group of scenarios encompassing a variety of solar and wind mixes, and the results show that, with a 1:2 mix of solar to wind energy, the system will always operate at least at 10% capacity from 10:00 to 16:00, as calculated using the meteorological conditions of the year 2001. This study also analyzes the land requirements necessary to implement such a solar–wind energy system, highlighting the vast areas that would be necessary to be covered with wind turbines and solar panels if such a system were to supply the majority of the electricity demand in Japan.     

Totally analytical closure of space filtered Navier–Stokes for arbitrary Reynolds number: Part II. Resolution algorithms,validations

ABSTRACT

For uniform measure δ Gaussian filter, Part I derives the totally analytical aFNS theory closing rigorously space filtered Navier–Stokes (NS) partial differential equation (PDE) system absent a Reynolds number (Re) assumption. aFNS theory state variable is scaled O(1; δ²; δ³) via classic fluid mechanics perturbation theory which also identifies the O(δ²) elliptic PDE system. Filter penetration of domain bounding surfaces requires O(1) PDE system inclusion of boundary commutation error (BCE) integrals. For the O(1; δ²), PDE system to be bounded domain well-posed requires derivation of domain encompassing nonhomogeneous Dirichlet boundary conditions (DBC). Resolution of BCE and DBC requirements is theorized via O(δ⁴) approximate deconvolution (AD) Galerkin differential definition weak form algorithms. Amenable to any space-time discretization, detailed is aFNS theory insertion in the optimal Galerkin weak form CFD algorithm, finite element linear tensor product basis implemented. Coupled Galerkin CFD/BCE/DBC code a posteriori data reported herein validate theory resolution algorithms including accuracy/convergence assessments.     

Hydrogen storage for mixed wind–nuclear power plants in the context of a Hydrogen Economy

A novel methodology for the economic evaluation of hydrogen production and storage for a mixed wind–nuclear power plant considering some new aspects such as residual heat and oxygen utilization is applied in this work. This analysis is completed in the context of a Hydrogen Economy and competitive electricity markets. The simulation of the operation of a combined nuclear–wind–hydrogen system is discussed first, where the selling and buying of electricity, the selling of excess hydrogen and oxygen, and the selling of heat are optimized to maximize profit to the energy producer. The simulation is performed in two phases: in a pre-dispatch phase, the system model is optimized to obtain optimal hydrogen charge levels for the given operational horizons. In the second phase, a real-time dispatch is carried out on an hourly basis to optimize the operation of the system as to maximize profits, following the hydrogen storage levels of the pre-dispatch phase. Based on the operation planning and dispatch results, an economic evaluation is performed to determine the feasibility of the proposed scheme for investment purposes; this evaluation is based on calculations of modified internal rates of return and net present values for a realistic scenario. The results of the present studies demonstrate the feasibility of a hydrogen storage and production system with oxygen and heat utilization for existent nuclear and wind power generation facilities.     

Hydrogen iodide decomposition over nickel–ceria catalysts for hydrogen production in the sulfur–iodine cycle

In this work, pure CeO₂ and three nickel–ceria catalysts prepared by different methods have been tested to evaluate their effect on hydrogen iodide (HI) decomposition in the sulfur–iodine (SI or IS) cycle at various temperatures. BET, XRD, HRTEM and TPR were performed for catalysts characterization. Indeed, the pure CeO₂ also strongly enhance the decomposition of HI to H₂ by comparison with blank yield. Nickel–ceria catalysts show better catalytic activity, especially Ni-doping-G sample. It is found that, through the sol-gel method, the Ni²⁺ ions have dissolved into the ceria lattice instead of the Ce⁴⁺ ions during the synthesis process of Ni-doping-G sample. Oxygen vacancies are formed because of the charge imbalance and lattice distortion in CeO₂. The presence of Ni during the CeO₂ synthesis process of Ni-doping-G also causes smaller average particle size, larger surface area, better thermal stability and better Ni dispersion than the Ni-loading samples. These provide nickel–ceria catalyst with a potential to be used in the SI cycle for HI decomposition.     

Transition from natural to mixed convection for steam–gas flow condensing along a vertical plate

An analysis method based on two-phase boundary layer analysis has been developed to study the effects of superimposed forced convection on natural convection steam–gas flow condensing along a vertical plate. The mechanism by which superimposed forced convection enhances heat transfer is evaluated: the bulk flow blows away non-condensable gases accumulating near the interface, resulting in an elevated condensation driving force. Further, this bulk flow blowing capability may be characterized by a conventional mass transfer driving potential. Results of the new model are shown to be consistent with experimental data. Finally, a simple criterion was developed to identify transition to mixed convection from natural convection steam–gas flow.     

Induction for multiple rotating detonation waves in the hydrogen–oxygen mixture with tangential flow

Rotating detonation engines are studied more and more widely because of high thermodynamic efficiency and high specific impulse. Generally one detonation wave exists in the engines but sometimes multiple detonation waves appear, as is complicated and difficult to explain. Increasing the number of rotating detonation waves uniforms the flow field and weakens the combustion instabilities. A controllable way to induce multiple detonation waves is introduced here. Rotating detonation engine runs with a single detonation wave or multiple detonation waves were both conducted. Pressure sensors were used to record the pressure traces of rotating detonation waves and gas flow controllers controlled the flow rates of reactants. Tangential flow of reactants from the predetonator produces shock waves moving upstream, inducing multiple rotating detonation waves when there is axial flow of reactants from the head of the combustor. The maximum number of detonation waves is subject to the flow rates.     

Mass and heat transport impact on the peristaltic flow of a Ree–Eyring liquid through variable properties for hemodynamic flow

Variable properties play a prominent role in analyzing the blood flow in narrow arteries. Specifically, considering the variation of thermal conductivity and viscosity helps in the understanding of the rheological behavior of blood and other biological fluids, such as urine, spermatozoa, and eye drops. Inspired by these applications, the current study incorporates the impact of variable thermal conductivity and viscosity for modeling the peristaltic flow of a Ree–Eyring liquid through a uniform compliant channel. The governing equations are nondimensionalized with the assistance of similarity transformations. The long-wavelength and small Reynolds wide variety approximation are utilized for solving the governing differential equations. Furthermore, the series solution method (perturbation technique) is utilized for solving the nonlinear temperature equation. The obtained results show that the velocity is greater in the case of the Newtonian liquid than that of the non-Newtonian liquid.     

Diesel reforming to hydrogen over the mesoporous Ni–MgO catalyst synthesized in microfluidic platform

Steam reforming (SR) is a process for converting transportation fuels into hydrogen-rich gas, which can be fed to SOFCs for on-board power supplies. Herein, we prepare Mg_xNi_1-xO (0.5<x < 0.8) with an average particle size in the range of 30.6–35.0 nm in a microfluidic system using a co-precipitation method. Ni particle size, Ni loading, and surface basicity synergistically determine the reforming performance. The Ni(40 wt%)-MgO catalyst demonstrates potential for the SR of n-dodecane, 0^# diesel of China national VI standard, methylbenzene, and methylnaphthalene. The deactivation of the catalysts with time-on-stream is mainly attributed to the sintering of Ni nanoparticles; however, it is almost independent of the negligible amount of carbon deposition. Density functional theory calculations verify that for the same active metal particle size, the energy barrier ratio of the forward to reverse reaction of the CH1 decomposition of the catalyst is smaller with more Ni doped in the MgO.