Showing papers in "Flow Turbulence and Combustion in 2010"

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 1: Theory and Model Description

Abstract: The article gives an overview of the Scale-Adaptive Simulation (SAS) method developed by the authors during the last years. The motivation for the formulation of the SAS method is given and a detailed explanation of the underlying ideas is presented. The derivation of the high-Reynolds number form of the equations as well as the calibration of the constants is provided. The concept of SAS is explained using several generic examples and test cases. In a companion article, the model is applied to more complex industrial-type applications.

The Scale-Adaptive Simulation Method for Unsteady Turbulent Flow Predictions. Part 2: Application to Complex Flows

Abstract: The paper summarises the validation activity performed with the Scale-Adaptive Simulation turbulence model (SAS model) using the two commercial CFD solvers, ANSYS-FLUENT and ANSYS-CFX. Both the KSKL-SAS and the SST-SAS model variants have been tested, although most cases have been computed with the second. The turbulence-resolving capability of the SAS method has been validated with a representative set of test cases, covering both underlying generic flows as well as practical engineering applications. In addition to the purely aerodynamic flows with massive separation and heat transfer they include also such physical phenomena as turbulent combustion and aeroacoustics. The illustrating results show the potentials of the SAS approach for industrial flow simulations. Most of the test case simulations were conducted during the recent EU project “DESider”.

Large Eddy Simulations and Experiments of Flow Around Finite-Height Cylinders

Abstract: The paper presents experimental and numerical results for the flow around a surface-mounted circular cylinder at the two height-to-diameter ratios of 2.5 and 5. The Reynolds number based on approach flow velocity and cylinder diameter is 43,000 and 22,000 for these two cases and the boundary layer of the approach flow has a thickness of about 10% of the cylinder height. The experiments comprise both flow visualizations with dye and laser Doppler velocimeter measurements of all mean velocity and fluctuation components. The numerical study is performed by an elaborate large eddy simulation on a staggered Cartesian grid using the immersed boundary method. The instantaneous flow behaviour including the shedding is analysed with information based on animations. For the long cylinder alternating shedding is found to occur over most of the height while for the shorter cylinder the shedding is observed mainly near the ground where it is also mostly alternating but intermittently also symmetrical. The mean-flow behaviour is analysed with the aid of streamlines and contour plots of mean-velocity and fluctuation components in various planes and a detailed comparison of LES and LDV results is provided, showing generally good agreement. The LES with very fine resolution near the free end allow a detailed study of the complex flow in this region with owl-face topology on the end wall previously observed in experiments. Behind the cylinder, the longitudinal recirculation region, the downstream development of tip vortices and the emergence of trailing vortices further downstream are analysed. The sum of the results, together with those from previous studies that were reviewed extensively, provides a comprehensive picture of the very complex flow behaviour.

Statistical properties of turbulent free jets issuing from nine differently-shaped nozzles

Abstract: This paper reports the centerline evolutions of turbulent statistical properties in nine air jets issuing from differently-shaped nozzles into still air surroundings. All nozzles of investigation have nominally identical opening areas or equal equivalent diameters (De) and their aspect ratio (AR) varies from AR = 1 (circle) to AR = 2.5 (isosceles triangle). Present measurements were made at the Reynolds number (based on De) of approximately 15,000. Results show that the loss of jet-axisymmetry at the exit generally causes the mean velocity decaying faster, and the fluctuating intensity growing, in the near field, thus indicating the increased overall entrainment rate. It is also shown that a change of shape of the nozzle exit does not affect the asymptotic decay rate of the centreline velocity in the far field. The near-field structure of the isosceles-triangular jet is deduced to be most three-dimensional, compared with the circular counterpart from smooth contraction being least. These discrepancies, however, weaken as the downstream distance x is increased. Beyond x/De = 20–30, the normalized velocity spectra for all jets of small AR collapse well, indicating similar statistical behaviors over a wide range of scales in the central region. Indeed, sufficiently downstream from the exit, insignificant differences occur in jets’ velocity probability density function (PDF), the related skewness and flatness factors, and also in their Taylor and Kolmogorov microscales. It is demonstrated that all the length scales grow approximately linearly with x at x/De ≥ 20.

Finite Rate Chemistry Effects in Highly Sheared Turbulent Premixed Flames

Abstract: Detailed scalar structure measurements of highly sheared turbulent premixed flames stabilized on the piloted premixed jet burner (PPJB) are reported together with corresponding numerical calculations using a particle based probability density function (PDF) method. The PPJB is capable of stabilizing highly turbulent premixed jet flames through the use of a small stoichiometric pilot that ensures initial ignition of the jet and a large shielding coflow of hot combustion products. Four lean premixed methane-air flames with a constant jet equivalence ratio are studied over a wide range of jet velocities. The scalar structure of the flames are examined through high resolution imaging of temperature and OH mole fraction, whilst the reaction rate structure is examined using simultaneous imaging of temperature and mole fractions of OH and CH2O. Measurements of temperature and mole fractions of CO and OH using the Raman–Rayleigh–LIF-crossed plane OH technique are used to examine the flame thickening and flame reaction rates. It is found that as the shear rates increase, finite-rate chemistry effects manifest through a gradual decrease in reactedness, rather than the abrupt localized extinction observed in non-premixed flames when approaching blow-off. This gradual decrease in reactedness is accompanied by a broadening in the reaction zone which is consistent with the view that turbulence structures become embedded within the instantaneous flame front. Numerical predictions using a particle-based PDF model are shown to be able to predict the measured flames with significant finite-rate chemistry effects, albeit with the use of a modified mixing frequency.

The Batchelor Spectrum for Mixing of Passive Scalars in Isotropic Turbulence : Submitted for the Special Issue Dedicated to S. B. Pope ()

Abstract: We examine the support for the Batchelor spectrum from well-resolved simulations of high-Schmidt-number mixing in isotropic turbulence, and resolve a conundrum with respect to the numerical value of the prefactor, also known as the Batchelor constant. Our conclusion is that the most probable value of the most compressive principal strain rate is more relevant than its mean, at least asymptotically.

Experiments and Simulations of n-Heptane Spray Auto-Ignition in a Closed Combustion Chamber at Diesel Engine Conditions

Abstract: Auto-igniting n-heptane sprays have been studied experimentally in a high pressure, high temperature constant volume combustion chamber with optical access. Ignition delay and the total pressure increase due to combustion are highly repeatable whereas the ignition location shows substantial fluctuations. Simulations have subsequently been performed by means of a first-order fully elliptic Conditional Moment Closure (CMC) code. Overall, the simulations are in good agreement with the experiment in terms of spray evolution, ignition delay and the pressure development. The sensitivity of the predictions with respect to the measured initial conditions, the spray modelling options as well as the chemical mechanism employed have been analysed. Strong sensitivity on the chemical mechanism and to the initial temperature on the predicted ignition delay is reported. The primary atomisation model did not affect strongly the predicted auto-ignition time, but a strong influence was found on the ignition location prediction.

Implementation Issues of the Conditional Moment Closure Model in Large Eddy Simulations

Abstract: Different ways of transferring information regarding the mixture fraction, its sub-grid scale variance and the scalar dissipation rate are examined in terms of a Large Eddy Simulation (LES)/Conditional Moment Closure (CMC) calculation. In such a simulation, information must be transferred from a fine LES grid to a usually coarser CMC grid. Different options of calculating conditional and unconditional quantities in the CMC resolution are assessed by filtering experimental mixture fraction and scalar dissipation rate data at various resolutions. It was found that when a presumed shape for the Filtered Density Function at the CMC resolution is used, special care must be given to the mixture fraction variance. It was also found that the Amplitude Mapping Closure model can be used for the conditional scalar dissipation rate. LES/CMC with detailed chemistry of a bluff-body stabilised burner was performed using two different ways of calculating the turbulent diffusivity. The structure of the flame is realistic, with little difference noticed when using the two diffusivities.

Extended Proper Orthogonal Decomposition for Analysis of Unsteady Flames

Abstract: The aim of this work is to present the use of proper orthogonal decomposition (POD) and extended proper orthogonal decomposition (EPOD) for revealing flame dynamics as a set of statistical quantities referred as modes. The flame fluctuations are used to derive an empirical functions base representing the most important features of the flame. The capabilities of the technique are exemplified in the case of an unsteady laminar flame. The flame is naturally unsteady and can be excited to amplify the fluctuations. The data base consists of synchronous Particle Image Velocimetry (PIV) and OH-Planar Laser Induced Fluorescence (OH-PLIF) measurements. It was found that the POD based upon the PIV vectors only reveals flow features when the excitation is added. On contrary, the OH-PLIF based POD performs well in any case and constitutes a suitable base for the EPOD analysis.

Large Eddy Simulation of Spark Ignition in a Gas Turbine Combustor

Abstract: Ignition in an aircraft gas turbine combustion chamber is simulated using Large Eddy Simulation (LES) in conjunction with the filtered probability density function (pdf) equation approach, which is solved using the Eulerian stochastic field method. The LES-pdf methodology is used for both dispersed (liquid) and gas phases. The liquid phase is described using a Lagrangian formulation whilst an Eulerian approach is employed for the gas phase. The spark energy deposition was mimicked by a distributed energy source term added to the enthalpy equation. Unsuccessful and successful ignition sequences have been simulated and the results suggest that spark ‘size’ is an important parameter in the ignition of kerosene fuelled combustion chambers.

LES of a Multi-burner Annular Gas Turbine Combustor

Abstract: In this study, Large Eddy Simulation (LES) has been used to predict the flow, mixing and combustion in both a single burner laboratory gas turbine combustor and in an 18 burner annular combustor, having identical cross sections. The LES results for the single burner laboratory combustor are compared with experimental data for a laboratory model of this combustor, and with other LES predictions, with good agreement. An explicit finite volume based LES model, using the mixed subgrid model together with a partially stirred reactor model for the turbulence chemistry interactions, is used. For the annular combustor, with the swirlers parameterized by jet inflow boundary conditions, we have investigated the influence of the a-priori unknown combustor exit impedance, the influence of the swirler characteristics and the fuel type. The combustion chemistry of methane–air and n-decane–air combustion is modeled by a two-step reaction mechanism, whereas NOx is separately modeled with a one-step mechanism. No experimental data exists for the annular combustor, but these results are compared with the single burner LES and experimental results available. The combustor exit impedance, the swirler- and fuel characteristics all seem to influence the combusting flow through the acoustics of the annular combustor. To examine this in greater detail time-series and eigenmodes of the combustor flow fields are analyzed and comparisons are made also with results from conventional thermoacoustic eigenmode analysis, with reasonable agreement. The flow and pressure distributions in the annular combustor are described in some detail and the mechanisms by which the burners interact are outlined.

Effect of Particle Clusters on Carrier Flow Turbulence: A Direct Numerical Simulation Study

Abstract: Experiments indicate that particle clusters that form in fluidized–bed risers can enhance gas-phase velocity fluctuations. Direct numerical simulations (DNS) of turbulent flow past uniform and clustered configurations of fixed particle assemblies at the same solid volume fraction are performed to gain insight into particle clustering effects on gas-phase turbulence, and to guide model development. The DNS approach is based on a discrete-time, direct-forcing immersed boundary method (IBM) that imposes no-slip and no-penetration boundary conditions on each particle’s surface. Results are reported for mean flow Reynolds number Rep = 50 and the ratio of the particle diameter dp to Kolmogorov scale is 5.5. The DNS confirm experimental observations that the clustered configurations enhance the level of fluid-phase turbulent kinetic energy (TKE) more than the uniform configurations, and this increase is found to arise from a lower dissipation rate in the clustered particle configuration. The simulations also reveal that the particle-fluid interaction results in significantly anisotropic fluid-phase turbulence, the source of which is traced to the anisotropic nature of the interphase TKE transfer and dissipation tensors. This study indicates that when particles are larger than the Kolmogorov scale (dp > η), modeling the fluid-phase TKE alone may not be adequate to capture the underlying physics in multiphase turbulence because the Reynolds stress is anisotropic. It also shows that multiphase turbulence models should consider the effect of particle clustering in the dissipation model.

Fractal-Generated Turbulence in Opposed Jet Flows

Abstract: The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1 $\upmu$ m silicon oil droplets providing a relaxation time of ≃ 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

Abstract: A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Fevrier et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.

Eulerian Quadrature-Based Moment Models for Dilute Polydisperse Evaporating Sprays

Abstract: Dilute liquid sprays can be modeled at the mesoscale using a kinetic equation, namely the Williams–Boltzmann equation, containing terms for spatial transport, evaporation and fluid drag. The most common method for simulating the Williams–Boltzmann equation uses Lagrangian particle tracking wherein a finite ensemble of numerical “parcels” provides a statistical estimate of the joint surface area, velocity number density function (NDF). An alternative approach is to discretize the NDF into droplet size intervals, called sections, and to neglect velocity fluctuations conditioned on droplet size, resulting in an Eulerian multi-fluid model. In comparison to Lagrangian particle tracking, multi-fluid models contain no statistical error (due to the finite number of parcels) but they cannot reproduce the particle trajectory crossings observed in Lagrangian simulations of non-collisional kinetic equations. Here, in order to overcome this limitation, a quadrature-based moment method is used to describe the velocity moments. When coupled with the sectional description of droplet sizes, the resulting Eulerian multi-fluid, multi-velocity model is shown to capture accurately both particle trajectory crossings and the size-dependent dynamics of evaporation and fluid drag. Model validation is carried out using direct comparisons between the Lagrangian and Eulerian models for an unsteady free-jet configuration with mono- and polydisperse droplets with and without evaporation. Comparisons between the Eulerian and Lagrangian instantaneous number density and gas-phase fuel mass fraction fields show excellent agreement, suggesting that the multi-fluid, multi-velocity model is well suited for describing spray combustion.

A Priori Testing of Flamelet Generated Manifolds for Turbulent Partially Premixed Methane/Air Flames

Abstract: To reduce high computational cost associated with simulations of reacting flows chemistry tabulation methods like the Flamelet Generated Manifold (FGM) method are commonly used. However, H2, CO and OH predictions in RANS and LES simulations using the FGM (or a similar) method usually show a substantial deviation from measurements. The goal of this study is to assess the accuracy of low-dimensional FGM databases for the prediction of these species in turbulent, partially-premixed reacting flows. It will be examined to what extent turbulent, partially-premixed jet flames can be described by FGM databases based on premixed or counterflow diffusion flamelets and to what extent the chosen molecular transport model for the flamelet influences the accuracy of species mass fraction predictions in CFD-simulations. For LES and RANS applications a model that accounts for subgrid fluctuations has to be added introducing additional errors in numerical results. A priori analysis of FGM databases enables the exclusion of numerical errors (scheme accuracy, convergence) that occur in CFD simulations as well as the exclusion of errors originating from subgrid modeling assumptions in LES and RANS. Four different FGM databases are compared for H2O, H2, CO, CO2 and OH predictions in Sandia Flames C to F. Species mass fractions will be compared to measurements directly and conditioned on mixture fraction. Special attention is paid to the representation of experimentally observed differential diffusion effects by FGM databases.

Numerical Simulation of Riblet Controlled Spatial Transition in a Zero-Pressure-Gradient Boundary Layer

Abstract: To analyze the fundamental physical mechanism which determines the damping effect of a riblet surface on three-dimensional transition several numerical simulations of spatial transition in a flat plate zero-pressure-gradient boundary layer above a riblet wall are performed in this study. Two types of forced transition scenarios are investigated. The first type of transition is defined by K-type transition induced by a dominant two-dimensional Tollmien–Schlichting (TS) wave and a weak spanwise disturbance. The second type of transition is purely excited by two oblique waves. By a qualitative analysis of the occurring maximum wall-normal and spanwise velocity components and the Fourier modes of the disturbances the two-dimensional TS waves are found to be amplified by riblets, whereas three-dimensional structures, i.e., Λ-, hairpin, and streamwisely aligned vortices, are damped. At oblique transition the breakdown to turbulence is delayed by the riblets compared to transition on a clean surface. The investigation of the near wall flow structure reveals secondary flows induced by the riblets and reduced wall normal ejections as well as a reduced downwash.

Reliability Issues of LES-Related Approaches in an Industrial Context

Abstract: Large-Eddy Simulation (LES), Detached-Eddy Simulation (DES) and Scale-Adaptive Simulation (SAS) are increasingly being used as engineering tools to predict the behaviour of complex industrial flows. Often the flows studied have not been examined previously and the required grid resolution is unknown. Industrial users studying these flows tend to be using commercial CFD codes and do not usually have access to high-performance computing facilities. Due to the significant computing times required, it is difficult to undertake systematic grid-dependence studies. There is therefore a risk that LES, DES and SAS will be performed using overly coarse grids which may lead to unreliable predictions. The present work surveys a number of practical techniques that provide a means of assessing the quality of the grid resolution in large-eddy simulations and related approaches. To examine the usefulness of these techniques, a gas release in a ventilated room is examined using DES and SAS. The grid resolution measures indicate that overall the grids used are relatively coarse. Both DES and SAS model predictions are found to be in poor agreement with experimental data compared to steady and unsteady Reynolds-averaged Navier–Stokes (RANS) results using the SST model. The SAS model also shows the greatest grid sensitivity of the four models tested. The work highlights the need for grid-dependence studies and the potential problems of using coarse grids.

Direct Numerical Simulation of Subsonic Round Turbulent Jet

Abstract: Direct numerical simulation(DNS) of spatially developing round turbulent jet flow with Reynolds number 4,700 was carried out. Over 20 million grid points were used in this simulation. Fully compressible three-dimensional Navier–Stokes equations were solved. High order explicit spatial difference schemes and Runge–Kutta time integration scheme were used to calculate derivatives and time marching, respectively. Non-reflecting boundary conditions and exit zone techniques were adopted. Some refined computational grids were used in order to capture the smallest turbulent structures near the centerline of the jet. Low level disturbance were imposed on the jet inflow velocity to trigger the developing of turbulence. Turbulent statistics such as mean velocity, Reynolds stresses, third order velocity moments were obtained and compared with experimental data. One-dimensional velocity autospectra was also calculated. The inertial region where the spectra decays according to the k − 5/3 was observed. The quantitative profiles of mean velocity and all of the third order velocity moments which were difficult to measure via experimental techniques were presented here in detail. The jet flow was proven to be close to fully self-similar around 19 jet diameters downstream of jet exit. The statistic data and revealed flow feature obtained in this paper can provide valuable reference for round turbulent jet research.

Large-Eddy Simulation for an Axisymmetric Piston-Cylinder Assembly With and Without Swirl

Abstract: Large-eddy simulation (LES) has been performed for an axisymmetric piston-cylinder assembly with and without swirl. For both cases, the LES mean and rms velocity profiles show better agreement with experimental data than profiles obtained using a Reynolds-averaged Navier–Stokes (RANS) approach with a standard k − e turbulence model. The sum of the resolved and modeled contributions to turbulence kinetic energy (TKE) approaches grid independence for the meshes used in this study. The sensitivity of LES to key numerical and physical model parameters has been investigated. Results are especially sensitive to mesh and to the subfilter-scale (SFS) turbulence models. Satisfactory results can be obtained using simple viscosity-based SFS turbulence models, although there is room for improvement. No single model gives uniformly best agreement between model and measurements at all spatial locations and at all times. The strong sensitivity of computed mean and rms velocity profiles to variations in the SFS turbulence model suggests that better results might be obtained using more sophisticated models.

Inclusion of Preferential Diffusion in Simulations of Premixed Combustion of Hydrogen/Methane Mixtures with Flamelet Generated Manifolds

Abstract: In this paper we study the possibility to account for preferential diffusion effects in lean turbulent premixed flames in numerical predictions with reduced chemistry. We studied the situation when hydrogen is added to methane at levels of 20% and 40% by volume in the fuel, at lean combustion (φ= 0.7) with air. The base case of pure methane was used as a reference. In this case preferential diffusion effects are negligible. First the sensitivity of the mass burning rate to flame stretch was investigated, in one dimensional computations with detailed chemistry, to set reference values. Then the framework of the Flamelet Generated Manifolds (FGM) was used to construct an adequate chemical method to take preferential diffusion into account, without the need for using detailed chemistry. To that end a generalization of the method was presented in which five controlling variables are required. For this system, proper transport equations and effective Lewis numbers where derived. In practice not all five variables are necessary to include and as a first step we limited the amount in the numerical tests in this study to two controlling variables. The method was then tested in configurations in which there was an interaction of coherent vortices and turbulence with flames. It was demonstrated that a minimum of two controlling variables is needed to account for the changed mass burning rate as function of stretch and curvature. It was shown that one-dimensional FGM as well as one-step Arrhenius kinetics can not describe this relation. © 2010 The Author(s).

A Hybrid-Filter Approach to Turbulence Simulation

Abstract: Germano (Theor Comput Fluid Dyn 17:225–331, 2004) proposed a hybrid-filter approach, which additively combines an LES-like filter operator (F) and a RANS-like statistical operator (E) using a blending function k: H = kF + (1 − k)E. Using turbulent channel flow as an example, we first conducted a priori tests in order to gain some insights into this hybrid-filter approach, and then performed full simulations to further assess the approach in actual simulations. For a priori tests, two separate simulations, RANS (E) and LES (F), were performed using the same grid in order to construct a hybrid-filtered field (H). It was shown that the extra terms arising out of the hybrid-filtered Navier–Stokes (HFNS) equations provided additional energy transfer from the RANS region to the LES region, thus alleviating the need for the ad hoc forcing term that has been used by some investigators. The complexity of the governing equations necessitated several modifications in order to render it suitable for a full numerical simulation. Despite some issues associated with the numerical implementation, good results were obtained for the mean velocity and skin friction coefficient. The mean velocity profile did not have an overshoot in the logarithmic region for most blending functions, confirming that proper energy transfer from the RANS to the LES region was a key to successful hybrid models. It is shown that Germano’s hybrid-filter approach is a viable and mathematically more appealing approach to simulate high Reynolds number turbulent flows.

On the Transition from Deflagration to Detonation in Narrow Tubes

Abstract: The paper is an extension of our recent work on the deflagration-to-detonation transition in narrow channels over the transition in narrow circular tubes under more realistic point ignition conditions. The changes from channel to circular tube geometry and from planar to point ignition result in enhancement of the incipient acceleration of the flame and reduction of the predetonation time and distance.

Pressure–Strain Correlation Modeling: Towards Achieving Consistency with Rapid Distortion Theory

Abstract: In turbulence closure modeling, it is widely accepted that the rapid pressure-strain correlation (RPSC) model be consistent with the rapid distortion theory (RDT). It is desirable to achieve this consistency with a closure model that is computationally tractable and satisfies the requisite mathematical constraints of realizability and linearity in the appropriate variables. In this investigation, starting from a detailed modal analysis of two-dimensional mean flows, we identify important flow features to be incorporated into the model. However, the dynamical system analysis shows that the suggested physics cannot be embodied in a model with all desired computational and mathematical attributes. To resolve this conflict, we propose a slight compromise in the physical requirement and ease one of the linearity constraints leading to a "best possible" tractable model. Overall, the present work provides important insight into RPSC closure modeling challenges—arising from the interplay among physical fidelity, computational viability and mathematical constraints—and proposes avenues for future improvement.

The Scalar Gradient Alignment Statistics of Flame Kernels and its Modelling Implications for Turbulent Premixed Combustion

Abstract: The effects of mean flame curvature on reaction progress variable gradient, \( abla c\), alignment with local turbulent strain rate are studied based on three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame kernels with different initial radii under decaying turbulence. A statistically planar flame is also considered in order to compare the results obtained from the kernels with a flame of zero mean curvature. It is found that the dilatation rate effects diminish with decreasing kernel radius due to defocusing of heat in the positively curved regions. This gives rise to a decrease in the extent of reaction progress variable gradient alignment with most extensive principal strain rate with decreasing kernel radius. The modelling implications of the statistics of the alignment of \( abla c\) with local strain rate have been studied in terms of scalar dissipation rate transport. A new modelling methodology for the contribution of the scalar-turbulence interaction term in the transport equation for the mean scalar dissipation is suggested addressing the reduced effects of dilatation rate for flame kernels and the diminished value of turbulent straining at the small length scales at which turbulence interacts with small flame kernels. The performance of the new models is found to be satisfactory while comparing to DNS results. The existing models for the dilatation contribution and the combined chemical reaction and molecular dissipation contributions to the transport of mean scalar dissipation, which were originally proposed for statistically planar flames, are found to satisfactorily predict the corresponding quantities for turbulent flame kernels.

An Experimental Investigation of the Turbulence Effect on the Combustion Propagation in a Rapid Compression Machine

Abstract: The role of different combustion modes that govern the combustion propagation inside a rapid compression machine is discussed. Aiming at the control of the compression generated turbulence, the careful design of the UPMC-RCM is described. A methodology is then proposed to investigate the influence of the residual post-compression turbulence level on the visible combustion propagation process. Through the fuel type, the main parameter varied is the ratio of the ignition delay time to the characteristic decay time for the post-compression turbulence. A high-speed camera images the visible combustion. Particle Image Velocimetry provides two-dimensional velocity fields of the post-compression flow prior to ignition. The residual turbulence level is shown to influence the combustion propagation phenomenology, highlighting the coexistence of both volumetric and frontlike combustion modes for the shorter aforementioned ratios. This conclusion could contribute to an explanation of the experimental discrepancies among the ignition delays measured in different RCMs as the residual turbulence level is highly set-up dependent.

Application of Rheological Models in Prediction of Turbulent Slurry Flow

Abstract: The paper deals with fully developed steady turbulent flow of slurry in a circular straight and smooth pipe. The Kaolin slurry consists of very fine solid particles, so the solid particles concentration, and density, and viscosity are assumed to be constant across the pipe. The mathematical model is based on the time averaged momentum equation. The problem of closure was solved by the Launder and Sharma k-e turbulence model (Launder and Sharma, Lett Heat Mass Transf 1:131–138, 1974) but with a different turbulence damping function. The turbulence damping function, used in the mathematical model in the present paper, is that proposed by Bartosik (1997). The mathematical model uses the apparent viscosity concept and the apparent viscosity was calculated using two- and three-parameter rheological models, namely Bingham and Herschel–Bulkley. The main aim of the paper is to compare measurements and predictions of the frictional head loss and velocity distribution, taking into account two- and three-parameter rheological models, namely Bingham and Herschel–Bulkley, if the Kaolin slurry possesses low, moderate, and high yield stress. Predictions compared with measurements show an observable advantage of the Herschel–Bulkley rheological model over the Bingham model particularly if the bulk velocity decreases.

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

Abstract: The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.

Implementation Methods of Wall Functions in Cell-vertex Numerical Solvers

Abstract: Two different implementation techniques of wall functions for cell-vertex based numerical methods are described and evaluated. The underlying wall model is based on the classical theory of the turbulent boundary layer. The present work focuses on the integration of this wall-model in a cell-vertex solver for large eddy simulations and its implications when applied to complex geometries, in particular domains with sudden expansions (more generally in presence of sharp edges). At corner nodes, the conjugation of law of the wall models using slip velocities on walls and of the cell-vertex approach leads to difficulties. Therefore, an alternative implementation of wall functions is introduced, which uses a no-slip condition at the wall. Both implementation methods are compared in a turbulent periodic channel flow, representing a typical validation case. The case of an injector for aero-engines is presented as an example for an industrial-scale application with a complex geometry.

Testing of Model Equations for the Mean Dissipation using Kolmogorov Flows

Abstract: Direct Numerical Simulations (DNS) of Kolmogorov flows are performed at three different Reynolds numbers Re λ between 110 and 190 by imposing a mean velocity profile in y-direction of the form U(y) = F sin(y) in a periodic box of volume (2π)3. After a few integral times the turbulent flow turns out to be statistically steady. Profiles of mean quantities are then obtained by averaging over planes at constant y. Based on these profiles two different model equations for the mean dissipation e in the context of two-equation RANS (Reynolds Averaged Navier–Stokes) modelling of turbulence are compared to each other. The high Reynolds number version of the k-e-model (Jones and Launder, Int J Heat Mass Transfer 15:301–314, 1972), to be called the standard model and a new model by Menter et al. (2006), to be called the Menter–Egorov model, are tested against the DNS results. Both models are solved numerically and it is found that the standard model does not provide a steady solution for the present case, while the Menter–Egorov model does. In addition a fairly good quantitative agreement of the model solution and the DNS data is found for the averaged profiles of the kinetic energy k and the dissipation e. Furthermore, an analysis based on flow-inherent geometries, called dissipation elements (Wang and Peters, J Fluid Mech 608:113–138, 2008), is used to examine the Menter–Egorov e model equation. An expression for the evolution of e is derived by taking appropriate moments of the equation for the evolution of the probability density function (pdf) of the length of dissipation elements. A term-by-term comparison with the model equation allows a prediction of the constants, which with increasing Reynolds number approach the empirical values.