The Spectral/HP element method has been applied to perform Direct Numerical Simulations (DNS) over a single T106A turbine blade-row using the open source software Nektar++. The main goal of the current study is to perform preliminary investigations at modest Reynolds and Mach numbers, 8000 and 0.1 respectively, for uniform, steady flow past the aerofoil by employing Nektar++'s solver for the 2D Navier-Stokes equations for incompressible flow. The mesh was firstly validated against results obtained using the same software and for a similar set of parameter values. One dimensional, pitch-wise harmonic vibrations were subsequently imposed on the blade by means of a coordinate transformation. A parametric study in terms of the frequency and amplitude of the vibrations was carried out. The effects of the vibrations on entire domain, along the blade surface and in its wake were assessed. The pressure on the blade surface and the wake loss were each decomposed into components arising due to the mean flow and due to the vibrations. In each case the dominant components were then identified for the values of frequency and amplitude considered here.

Three-dimensional Direct Numerical Simulation (DNS) data of statistically planar turbulent spray flames propagating into mono-disperse droplets for different values of droplet diameter ad and droplet equivalence ratio ϕd has been used to analyse the statistical behaviour of the fuel mass fraction dissipation rate $$ \overset{\sim }{\upvarepsilon_Y} $$ and its transport in the context of Reynolds Averaged Navier-Stokes (RANS) simulations. Closures previously derived for high Damköhler number turbulent stratified mixture combustion have been shown not to capture the statistical behaviour of $$ \overset{\sim }{\upvarepsilon_Y} $$ for turbulent spray flames, because the underlying assumptions behind the original modelling are invalid for the cases considered in this analysis. The modelling of the unclosed terms of the fuel mass fraction dissipation rate $$ \overset{\sim }{\upvarepsilon_Y} $$ transport equation (i.e. the turbulent transport term T1, the density variation term T2, the scalar turbulence interaction term T3, the reaction rate term T4, the evaporation contribution terms T5 and T6, and the dissipation rate term −D2) has been analysed in the context of RANS simulations. The models previously proposed in the context of turbulent gaseous stratified flames have been considered here to assess their suitability for turbulent spray flames. Based on a-priori DNS analysis, suitable model expressions have been identified for T1, T2, T31, T32, T33, [T4 − D2 + f(D)] and [T5 + T6], which have been shown to perform generally satisfactorily for all cases considered here.

A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wave nose and isles of stability/instability as reported experimentally for viscous film flow over inclined topography, providing an attractive trade-off between the accuracy of a full N-S computation and the efficiency of an integral method. The range of parameter values for which the WIBL model remains valid is established; in particular, it is shown that its accuracy decreases with the Reynolds number and corrugation amplitude, but increases with the steepness parameter and ratio of wavelength to capillary length.A computational investigation is conducted concerning the stability of free-surface gravity-driven liquid film flow over periodic corrugated substrate. The underpinning mathematical formulation constitutes an extension of the weighted residual integral boundary-layer (WIBL) method proposed by Ruyer-Quil and Manneville [“Improved modeling of flows down inclined planes,” Eur. Phys. J. B 15(2), 357–369 (2000)] and D’Alessio et al. [“Instability in gravity-driven flow over uneven surfaces,” Phys. Fluids 21(6), 062105 (2009)] to include third- and fourth-order terms in the long-wavelength expansion. Steady-state solutions for the free-surface and corresponding curves of neutral disturbances are obtained using Floquet theory and validated against corresponding experimental data and full Navier-Stokes (N-S) solutions. Sinusoidal and smoothed rectangular corrugations with variable steepness are considered. It is shown that the model is capable of predicting characteristic patterns of stability, including short-wa...

The Favre-averaged scalar dissipation rate transport conditional on local flow topologies in premixed turbulent flames has been analysed based on a detailed chemistry Direct Numerical Simulation database of statistically planar turbulent hydrogen-air premixed flames with an equivalence ratio of 0.7 representing the corrugated flamelets, thin reaction zones and broken reaction zones regimes of premixed turbulent combustion. The local flow topologies have been categorised by the values of the three invariants of the velocity gradient tensor and the statistical behaviour of the Favre-averaged scalar dissipation rate conditional on these flow topologies has been analysed in detail for different choices of reaction progress variable. The qualitative behaviour of the scalar-turbulence interaction term in the Favre-averaged scalar dissipation rate transport equation has been found to be affected by the regime of combustion, whereas the chemical reaction rate gradient contribution to the scalar dissipation rate transport has been found to be affected by the choice of the reaction progress variable. The topologies, which exist for all values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in premixed turbulent flames for all regimes of combustion. In addition, the flow topologies, which are obtained only for positive values of dilatation rate, contribute significantly to the Favre-averaged scalar dissipation rate transport in the case representing the corrugated flamelets regime combustion. An unstable nodal flow topology, which is representative of a counter-flow configuration, has been found to be a dominant contributor to the Favre-averaged scalar dissipation rate transport for all regimes of combustion irrespective of the choice of reaction progress variable.

The advancement of high-performance computing has made computational fluid dynamics (CFD) simulations a viable alternative to expensive experimentation. Most industrial flows are innately turbulent, and the modelling of turbulent flow remains a challenging task. This complexity is augmented in turbulent droplet combustion simulations by the complex interaction of heat and mass transfer associated with evaporation, fluid dynamics, combustion and heat release. As a result of this, the fidelity of CFD simulations of turbulent reacting flows remains sensitive to the accuracy of the combustion modelling, which principally focuses on the prediction of mean chemical reaction and heat release rates. The closure of the mean reaction rate in the context of Reynolds-averaged Navier-Stokes (RANS) simulations in the combustion of turbulent droplet-laden mixtures often requires the knowledge of the variances of the fuel mass fraction YF fluctuations (<(Y-F(2)'')over tilde>the mixture fraction xi fluctuations ((xi ''(2)) over tilde) and co-variance ((Y-F ''xi") over tilde) where (q) over bar, (q) over tilde = (PQ) over bar/(q) over bar are q '' = q - (q) over tilde Reynolds average, Favre mean and Favre fluctuation of a general quantity q and. is the gas density. Algebraic and transport equation-based closures of <(Y-F(2)')over tilde>, (xi ''(2)) over tilde and (Y-F ''xi '') over tilde have previously been considered in the context of purely gaseous phase combustion where variations in equivalence ratio exist. Whilst limited effort has been directed to the modelling of the fuel mass fraction varianceg (Y-F ''(2)) over tilde and mixture fraction variance (xi ''(2)) over tilde for turbulent combustion in droplet-laden mixtures, the statistical behaviour of (Y-F ''xi '') over tilde and its transport in turbulent spray flames are yet to be considered in detail. Furthermore, the validity of existing closures for (Y-F ''xi '') over tilde and the unclosed terms of its transport equation, which were originally proposed for purely gaseous phase combustion, are yet to be assessed for turbulent spray flames. These gaps in the existing literature are addressed by analysing the statistical behaviours of (Y-F ''(2)) over tilde, (xi ''(2)) over tilde and (Y-F ''xi '') over tilde as well as the terms of their transport equations using a three-dimensional compressible Direct Numerical Simulation (DNS) database of statistically planar turbulent flames propagating into droplet-laden mixtures where the fuel is supplied in the form of monodisperse droplets ahead of the flame. This chapter focuses on the effects of droplet diameter ad and droplet equivalence ratio.d (i.e. fuel in liquid droplets to air ratio by mass, normalized by fuel-to-air ratio by mass under stoichiometric conditions) on the statistical behaviours of (Y-F ''(2)) over tilde, (xi ''(2)) over tilde and (Y-F ''xi '') over tilde and their transport in detail. Furthermore, the validity of the existing models for the unclosed terms of (Y-F ''(2)) over tilde, (xi ''(2)) over tilde and (Y-F ''xi '') over tilde transport equations, which were originally proposed for gaseous stratified mixture combustion, has been assessed for turbulent combustion in droplet-laden mixtures. Based on this exercise, either the modification of existing models has been suggested or new models are proposed, wherever necessary, based on the physical insights extracted from DNS data.

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Matlab codes used to produce the figures

The distribution of flow topologies within the flame, and their evolution with flame quenching have been analysed using a Direct Numerical Simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by isothermal inert walls for different values of turbulence intensity and global Lewis number. It has been found that dilatation rate plays a key role in determining the flow topology distribution within the flame and this dilatation rate field is significantly affected by the flame quenching in the vicinity of the wall. The influence of the wall on the dilatation rate field in turn affects the statistical behaviour of all three invariants of the velocity gradient tensor and the distribution of flow topologies. The effects of heat release and thermal expansion strengthen with decreasing Lewis number which give rise to an increase in the probability of obtaining topologies which are specific to high positive values of dilatation rate. As the magnitude of positive dilatation rate and the likelihood of obtaining it decrease with flame quenching, the probability of finding the topologies, which are obtained only for positive values of dilatation rate, decreases close to the wall. The interrelation between the flow and flame topologies has been analysed in terms of Gaussian flame curvature and mean of principal flame curvatures. The contributions of individual flow topologies on the mean behaviour of wall heat flux magnitude, and the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively have been analysed in detail and dominant flow topologies which dictate the mean behaviours of these quantities have been identified. Detailed physical explanations have been provided for the observed flow topology distribution and its contribution to the scalar-turbulence and vortex-stretching terms. The nodal flow topologies have been found to be the significant contributors to the wall heat flux magnitude during head-on quenching of turbulent premixed flames irrespective of the value of global Lewis number.

Enstrophy is an intrinsic feature of turbulent flows, and its transport properties are essential for the understanding of premixed flame-turbulence interaction. The interrelation between the enstrophy transport and flow topologies, which can be assigned to eight categories based on the three invariants of the velocity-gradient tensor, has been analysed here. The enstrophy transport conditional on flow topologies in turbulent premixed flames has been analysed using a Direct Numerical Simulation database representing the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) combustion regimes. The flame in the CF regime exhibits considerable flame-generated enstrophy, and the dilatation rate and baroclinic torque contributions to the enstrophy transport act as leading order sink and source terms, respectively. Consequently, flow topologies associated with positive dilatation rate values, contribute significantly to the enstrophy transport in the CF regime. By contrast, enstrophy decreases from the unburned to the burned gas side for the cases representing the TRZ and BRZ regimes, with diminishing influences of dilatation rate and baroclinic torque. The enstrophy transport in the TRZ and BRZ regimes is governed by the vortex-stretching and viscous dissipation contributions, similar to non-reacting flows, and topologies existing for all values of dilatation rate remain significant contributors.

Turbulent combustion of mono-disperse droplet-mist has been analysed based on three-dimensional Direct Numerical Simulations (DNS) in canonical configuration under decaying turbulence for a range of different values of droplet equivalence ratio (ϕd), droplet diameter (a d ) and root-mean-square value of turbulent velocity (u ′). The fuel is supplied in liquid phase and the evaporation of droplets gives rise to gaseous fuel for the flame propagation into the droplet-mist. It has been found that initial droplet diameter, turbulence intensity and droplet equivalence ratio can have significant influences on the volume-integrated burning rate, flame surface area and burning rate per unit area. The droplets are found to evaporate predominantly in the preheat zone, but some droplets penetrate the flame front, reaching the burned gas side where they evaporate and some of the resulting fuel vapour diffuses back towards the flame front. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for ϕd > 1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets and this predominantly fuel-lean mode of combustion exhibits the attributes of low Damköhler number combustion and gives rise to thickening of flame with increasing droplet diameter. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion and the relative contribution of non-premixed combustion to overall heat release increases with increasing droplet size. The statistical behaviours of the flame propagation and mode of combustion have been analysed in detail and detailed physical explanations have been provided for the observed behaviour.

The distributions of flow topologies within the flames representing the corrugated flamelets, thin reaction zones, and broken reaction zone regimes of premixed turbulent combustion are investigated using direct numerical simulation data of statistically planar turbulent H-2-air flames with an equivalence ratio phi = 0.7. It was found that the diminishing influence of dilatation rate with increasing Karlovitz number has significant influences on the statistical behaviors of the first, second, and third invariants (i.e., P, Q, and R) of the velocity gradient tensor. These differences are reflected in the distributions of the flow topologies within the flames considered in this analysis. This has important consequences for those topologies that make dominant contributions to the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively. Detailed physical explanations are provided for the observed regime dependences of the flow topologies and their implications on the scalar dissipation rate and enstrophy transport.

ABSTRACT The statistics of reaction progress variable, , and mixture fraction, , and their gradients (i.e., and ) in flames propagating in droplet mist, where the fuel was supplied in the form of monodisperse droplets, have been analyzed for different values of turbulent velocity fluctuations (), droplet equivalence ratios (, and droplet diameters ( based on three-dimensional direct numerical simulations (DNS) in a canonical configuration under decaying turbulence. The combustion process in the gaseous phase has been found to take place predominantly in fuel-lean mode, even for . The probability of finding fuel-lean mixture increases with increasing initial droplet diameter due to slower evaporation of larger droplets. It has been shown that the joint probability density function (i.e., joint PDF) of and (i.e., ), cannot be approximated in terms of discrete delta functions throughout the flame brush for the cases considered here. Furthermore, the magnitude of cannot be adequately approximated by the product of marginal PDFs of , and variable, (i.e., ). The statistical properties of the Favre probability density functions (Favre-PDFs) of the mixture fraction, , and oxidizer-based reaction progress variable, , have been analyzed at several locations across the flame brush and a -function distribution has been found to capture the Favre-PDFs of and obtained from the DNS data. Furthermore, a log-normal distribution has been shown to capture the qualitative behaviors of the PDFs of the gradient of the mixture fraction and the gradient of the reaction progress variable, and , respectively, but discrepancies between the log-normal distribution and the DNS data were observed at the tails of PDFs. In addition, the interrelation between and was examined in terms of the PDFs of the cosine of the angle between them (i.e., and it was observed that most droplet cases exhibited much greater likelihood of positive values of than negative values. Finally, the joint PDF of and , , has been compared with that of P( (i.e., assuming statistical independence of and ) and a good level of agreement has been obtained. The bivariate log-normal distribution has been considered both assuming correlation between and and assuming no correlation for the purpose of modeling , and the variant with no correlation has been found to be more successful in capturing qualitative behavior of although quantitative discrepancies have been observed due to inaccuracies involved in parameterizing P( and P(by log-normal distributions.

Perturbations to a vortex ring with largest transient energy growth are calculated and applied to drive the vortex ring to evolve. Optimal initial perturbations appear at azimuthal wave numbers β = 0 and β = 9. The former was described as ‘axial flow’ and is not related to the breakdown of the ring, while the latter is critical to the ring breakdown process as observed in previous direct numerical simulation (DNS) with random initial noise input. In the present work, DNS is conducted to study the nonlinear development of the optimal perturbations, and good agreement with past studies is achieved.

Flame structure, flow topology and the relative alignments of principal strain rates with scalar gradients and the vorticity vector in turbulent spray flames arising from mono-disperse droplets have been analysed using three-dimensional Direct Numerical Simulations (DNS) data. An extensive parametric analysis has been performed for a range of values of droplet equivalence ratio (phi(d)), droplet diameter (a(d)) and turbulence intensity (u'). The results have been analysed to analyse the statistical behaviours of the alignments of the gradients of mixture fraction and reaction progress variable and of the vorticity vector ((omega) over right arrow) with the local principal strain rates. The resulting alignments of reactive scalar gradient and vorticity with local principal strain rates in droplet-laden flames have been compared to those observed for a gaseous stoichiometric premixed flame under the same turbulent flow conditions. The differences in behaviour have been identified in terms of the statistical behaviours of scalar gradient and vorticity alignments with local principal strain rates in terms of the eight local flow topologies, classified as either focal (four topologies) or nodal (four topologies), in four zones across the flame: leading edge, preheat zone, burning reactants and trailing edge. This information has in turn been utilised to offer detailed physical explanations for the observed differences in alignment statistics of reactive scalar gradient and vorticity between turbulent premixed and spray flames. The implications of scalar gradient and vorticity alignment on the statistical behaviours of scalar-turbulence interaction and vortex stretching terms have been discussed in detail along with explanations for their dependences on droplet size, droplet equivalence ratio and turbulence intensity. (C) 2016 The Authors. Published by Elsevier Ltd.