Article

Direct Numerical Simulations of the Turbulent Mixing of a Passive Scalar

March 1988
The Physics of Fluids 31(3):506-520

Authors:

Indian Institute of Technology Hyderabad

The evolution of scalar fields, of different initial integral length scales, in statistically stationary, homogeneous, isotropic turbulence is studied. The initial scalar fields conform, approximately, to 'double-delta function' probability density functions (pdf's). The initial scalar-to-velocity integral length-scale ratio is found to influence the rate of the subsequent evolution of the scalar fields, in accord with experimental observations of Warhaft and Lumley (1978). On the other hand, the pdf of the scalar is found to evolve in a similar fashion for all the scalar fields studied; and, as expected, it tends to a Gaussian. The pdf of the logarithm of the scalar-dissipation rate reaches an approximately Gaussian self-similar state. The scalar-dissipation spectrum function also becomes self-similar. The evolution of the conditional scalar-dissipation rate is also studied. The consequences of these results for closure models for the scalar pdf equation are discussed.

Direct Numerical Simulation of turbulent liquid : gas compressible flows with phase change

Thesis

Jun 2022

Leandro Germes Martinez

Multiphase flows with phase change are part of many industrial applications, e. g., spray combustion, heat exchangers, nuclear reactors. Therefore, a better understanding of heat and mass transfer is essential for optimizing the energy consumption of these processes and thus reducing their pollutant emissions. In this context, numerical strategies are presented for the DNS of compressible two phase flows with phase change. The formalism is based on a mass conservative interface capturing method (CLSVOF) coupled with a pressure-based projection method for the temporal resolution of the Navier-Stokes equations. Additionally, the presented formalism is a fully compressible formalism with an implicit formulation of the acoustic term to reduce the time step restrictions. This allows us to capture several subtle phenomena simultaneously, such as gas density changes due to compressibility effects and mixing, non homogeneous evaporation rate and temperature at the interface, etc. In addition, the spatial and temporal variations of pressure permit the consideration of several liquid and gas structures in the domain, each with independent thermodynamic conditions. Furthermore, a study of the evaporation and turbulent mixing processes is conducted using a compressible two-phase HIT configuration. Here, the effects of the evaporation rate, turbulent velocity field, and the liquid and gas structures interactions on the temporal evolution of the vapor mass fraction main statistics are observed.

Numerical simulation of pulsed and stratified combustion

Thesis

Full-text available

Dec 2021

Eray Inanc

This work numerically investigates pulsed jets and stratified combustion by large eddy simulation (LES) and direct numerical simulation (DNS). In the first part, the numerical models are tested and further developed to reproduce two well-known transient jet experiments. The first experiment is a non-reactive pulsed jet, where the mixing dynamics are investigated by comparing the pseudo-DNS with the experimental evidence. The second experiment is an auto-igniting pulsed jet where the chemistry is described first by a multi-dimensional pressure-sensitive tabulated chemistry method and afterwards by a direct chemistry approach with an advanced chemical mechanism for deeper analysis and validation. The cycle-to-cycle variations of a pulsed jet are analysed in terms of ignition dynamics and thermochemical states of minor species over the entire ignition duration. In the second part, the well-known turbulent stratified burner from Cambridge is simulated. Initially, the stratification effects on one-dimensional unsteady flames are investigated. The conventional flame speed definitions for premixed flames are extended for the stratified flame context. It is shown that even the reduced chemical mechanism can show strong stratification effects, which are amplified in strength when realistic diffusion velocity assumption is employed. The highly stratified Cambridge burner was then recomputed using tabulated chemistry with an artificially thickened flame approach to test the turbulent-flame interaction models. In turbulent flames, the lost flame surface due to the thickening of the flame is reintroduced by wrinkling models initially proposed for premixed flames. The applicability of these wrinkling models to stratified flames is tested. Finally, the moderately stratified Cambridge burner is simulated by pseudo-DNS and tabulated chemistry to analyse the turbulence and stratified flame interactions. The pseudo-DNS data-set is extracted into two separate zones consisting of either premixed or stratified modes of combustion. The analysis focuses on comparing the diffusion fluxes, the flame structure, and the displacement speed of the zone with a premixed flame to the zone with a stratified flame. The present work provides answers to many questions regarding the pulsed jets and stratified flames using state of the art numerical methods.

Lagrangian Supersaturation Fluctuations at the Cloud Edge

Article

Full-text available

Dec 2023

Evaporation of cloud droplets accelerates when turbulence mixes dry air into the cloud, affecting droplet-size distributions in atmospheric clouds, combustion sprays, and jets of exhaled droplets. The challenge is to model local correlations between droplet numbers, sizes, and supersaturation, which determine supersaturation fluctuations along droplet paths (Lagrangian fluctuations). We derived a statistical model that accounts for these correlations. Its predictions are in quantitative agreement with results of direct numerical simulations, and explain the key mechanisms at play.

Lagrangian supersaturation fluctuations at the cloud edge

Preprint

Full-text available

Sep 2023

The effect of Prandtl number on decaying stratified turbulence

Article

Full-text available

Feb 2023
J TURBUL

The effects of the variation in the Prandtl number on turbulence in a stably-stratified fluid is investigated by direct numerical simulation. The results of simulations are presented of the homogeneous decay of turbulence for a given initial Froude number and three different initial Reynolds numbers of increasing values. For each of these cases results for two different Prandtl numbers, 1 and 7, are shown. Various statistics are put forward, including kinetic and potential energy decay rates, kinetic and potential energy dissipation rates, buoyancy fluxes, energy spectra, and statistics conditioned on the local value of the vertical density gradient. It is found that the effect of increasing the Prandtl number is to increase the kinetic energy dissipation rate, while decreasing the potential energy dissipation rate. There is a notable transfer of potential to kinetic energy for the higher Prandtl number case. Finally there is evidence, based upon the analysis of vertical planes and statistics conditional on the local density gradient, that most irreversible mixing of both density and momentum occurs in regions of stronger static stability.

Vapor mixing in turbulent vaporizing flows

Article

Full-text available

Apr 2023
INT J MULTIPHAS FLOW

Recent developments in DNS of turbulent combustion

Article

Aug 2022
P COMBUST INST

The simulation of turbulent flames fully resolving the smallest flow scales and the thinnest reaction zones goes along with specific requirements, which are discussed from dimensionless numbers useful to introduce the generic context in which direct numerical simulation (DNS) of turbulent flames is performed. Starting from this basis, the evolution of the DNS landscape over the past five years is reviewed. It is found that the flow geometries, the focus of the studies and the overall motivations for performing DNS have broadened, making DNS a standard tool in numerical turbulent combustion. Along these lines, the emerging DNS of laboratory burners for turbulent flame modeling development is discussed and illustrated from DNS imbedded in Large Eddy Simulation (LES) and flow resolved simulation of bluff-body flames. The literature shows that DNS generated databases constitute a fantastic playground for developing and testing a large spectrum of promising machine learning methods for the control and the optimisation of combustion systems, including novel numerical approaches based on the training of neural networks and which can be evaluated in DNS free from sub-model artefacts. The so-called quasi-DNS is also progressively entering the optimisation loop of combustion systems, with the application of techniques to downsize real combustion devices in order to perform fully resolved simulations of their complex geometries. An example of such study leading to the improvement of an incinerator efficiency is reported. Finally, numbers are given relative to the carbon footprint of the generation of DNS databases, motivating the crucial need for community building around database sharing.

Towards Direct Numerical Simulations of Reactivity-Controlled Compression Ignition Engine Using n-Octanol/Ethanol Fuel Blends

Article

Full-text available

Jul 2024
FLOW TURBUL COMBUST

The results of a two-dimensional direct numerical simulation of a lean n-octanol-ethanol fuel blend under Reactivity Controlled Compression Ignition (RCCI) conditions are presented in this paper. Stratified temperature and high reactivity fuel fields of Gaussian, bi-modal, and log-normal distributions are studied for uncorrelated and correlated scenarios. The pimple loop is made to run twice to achieve compression heating. A chemical mechanism with 171 species and 734 reactions was developed to capture autoignition characteristics and flame propagation reasonably well. Diagnosing techniques published in the literature are used to determine whether the flame fronts are spontaneously propagating or not. As reported previously for other fuel blends under RCCI conditions, both deflagration and spontaneous ignition flame fronts are observed to co-exist. Gaussian, bi-modal, and log-normal fields respectively move towards a spontaneously igniting mode. Correlating temperature and high reactivity fuel fields not only makes combustion more spontaneously igniting but also more premixed. The analysis reveals the sensitivity of the DNS results with respect to the initial conditions which accordingly should be chosen with care.

Implications of Using Scalar Forcing to Sustain Reactant Mixture Stratification in Direct Numerical Simulations of Turbulent Combustion

Article

Full-text available

Jun 2024

A recently proposed scalar forcing scheme that maintains the mixture fraction mean, root-mean-square and probability density function in the unburned gas can lead to a statistically quasi-stationary state in direct numerical simulations of turbulent stratified combustion when combined with velocity forcing. Scalar forcing alongside turbulence forcing leads to greater values of turbulent burning velocity and flame surface area in comparison to unforced simulations for globally fuel-lean mixtures. The sustained unburned gas mixture inhomogeneity changes the percentage shares of back- and front-supported flame elements in comparison to unforced simulations, and this effect is particularly apparent for high turbulence intensities. Scalar forcing does not significantly affect the heat release rates due to different modes of combustion and the micro-mixing rate within the flame characterised by scalar dissipation rate of the reaction progress variable. Thus, scalar forcing has a significant potential for enabling detailed parametric studies as well as providing well-converged time-averaged statistics for stratified-mixture combustion using Direct Numerical Simulations in canonical configurations.

On the Definition of Reaction Progress Variable in Exhaust Gas Recirculation Type Turbulent MILD Combustion of Methane and n-Heptane

Article

Full-text available

Mar 2024
FLOW TURBUL COMBUST

Three-dimensional Direct Numerical Simulations of Exhaust Gas Recirculation (EGR)-type Moderate or Intense Low Oxygen Dilution (MILD) combustion of homogeneous mixtures of methane- and n-heptane–air have been conducted with skeletal chemical mechanisms. The suitability of different choices of reaction progress variable (which is supposed to increase monotonically from zero in the unburned gas to one in fully burned products) based on the mass fractions of different major species and non-dimensional temperature have been analysed in detail. It has been found that reaction progress variable definitions based on oxygen mass fraction, and linear combination of CO, CO2, H2 and H2O mass fractions (i.e. cO2

{c}_{O2}

and cc

{c}_{c}

) capture all the extreme values of the major species in the range between zero and one under MILD conditions. A reaction progress variable based on fuel mass fraction is found to be unsuitable for heavy hydrocarbons, such as n-heptane, since the fuel breaks down to smaller molecules before the major reactants (products) are completely consumed (formed). Moreover, it has been found that the reaction rates of cO2

{c}_{O2}

and cc

{c}_{c}

exhibit approximate linear behaviours with the heat release rate in both methane and n-heptane MILD combustion. The interdependence of different mass fractions in the EGR-type homogeneous mixture combustion is considerably different from the corresponding 1D unstretched premixed flames. The current findings indicate that the tabulated chemistry approach based on premixed laminar flames may need to be modified to account for EGR-type MILD combustion. Furthermore, both the reaction rate and scalar dissipation rate of cO2

{c}_{O2}

and cc

{c}_{c}

are found to be non-linearly related in both methane and n-heptane MILD combustion cases but the qualitative nature of this correlation for n-heptane is different from that in methane. This suggests that the range of validity of SDR-based turbulent combustion models can be different for homogeneous MILD combustion of different fuels.

An Assessment of the Validity of Damköhler’s Hypotheses for Different Choices of Reaction Progress Variable in Homogenous Mixture Moderate or Intense Low-Oxygen Dilution (MILD) Combustion

Article

Full-text available

Dec 2023
FLOW TURBUL COMBUST

The applicability of Damköhler’s hypotheses for homogenous mixture (i.e. constant equivalence ratio) moderate or intense low-oxygen dilution (MILD) combustion processes (with methane as the fuel) has been assessed using three-dimensional direct numerical simulation data with a skeletal mechanism. Two homogeneous MILD combustion cases with different levels of O2

{{\text{O}}}_{2}

concentration (4.8% and 3.5% by volume) and different turbulence intensities have been investigated to analyse the influence of dilution level, turbulence intensity and the choice of the reaction progress variable definition (i.e. different choices of major species for turbulent burning velocity and flame surface area evaluations) on the applicability of Damköhler’s hypotheses in MILD combustion. It has been found that the normalized volume-integrated burning rate remains of the same order of magnitude as that of the normalized flame surface area only for the reaction progress variable definition based on a species mass fraction which has a Lewis number close to unity (e.g. CH4

{{\text{CH}}}_{4}

) but the level of applicability deteriorates when the Lewis number of the species mass fraction, based on which the reaction progress variable is defined, deviates significantly from unity (e.g. CO2

{{\text{CO}}}_{2}

). Moreover, it has been demonstrated that the flame surface area calculation from the OH mole fraction-based information can lead to significant departures from Damköhler’s first hypothesis. It is also found that the relative magnitudes of normalised volume-integrated burning rate and normalised flame surface area are significantly affected by the level of dilution and the choice of the reaction progress variable definition. Damköhler’s second hypothesis, which provides a relation between the normalised turbulent burning velocity and the ratio of turbulent to molecular diffusivities, has been found to hold in an order of magnitude sense in homogeneous mixture MILD combustion only for the reaction progress variable definition based on species that has a Lewis number close to unity (e.g. CH4

{{\text{CH}}}_{4}

) but the level of disagreement increases as the Lewis number of the reaction progress variable deviates significantly from unity (e.g. CO2

{{\text{CO}}}_{2}

Role of magnetic pressure forces in Fluctuation dynamo saturation

Article

Full-text available

Nov 2023
MON NOT R ASTRON SOC

Using magnetohydrodynamic simulations of Fluctuation dynamos in turbulent flows with rms Mach numbers

\mathcal {M}_{\rm rms}= 0.2, 1.1

and 3, we show that magnetic pressure forces play a crucial role in dynamo saturation in supersonic flows. Firstly, as expected when pressure forces oppose compression, an increase in anti-correlation between density and magnetic field strengths obtains even in subsonic flows with the anti-correlation arising from the intense but rarer magnetic structures. In supersonic flows, due to stronger compressive motions density and magnetic field strength continue to maintain a positive correlation. However, the degree of positive correlation decreases as the dynamo saturates. Secondly, we find that the unit vectors of ∇ρ and ∇B2 are preferentially anti-parallel to each other in subsonic flows. This is indicative of magnetic pressure opposing compression. This anti-parallel alignment persists in transonic and supersonic flows at dynamo saturation. However, compressive motions also lead to the emergence of a parallel alignment in these flows. Finally, we consider the work done against the components of the Lorentz force and the different sources of magnetic energy growth and dissipation. We show that while in subsonic flows, suppression of field line stretching is dominant in saturating the dynamo, the picture is different in supersonic flows. Both field line stretching and compression initially amplifies the field. However, growing magnetic pressure opposes further compression of magnetic flux which tends to reduce the compressive motions. Simultaneously, field line stretching also reduces. But, suppression of compressive amplification dominates the saturation of the dynamo.

A Priori Direct Numerical Simulation Assessment of MILD Combustion Modelling in the Context of Reynolds Averaged Navier–Stokes Simulations

Article

Full-text available

May 2023
FLOW TURBUL COMBUST

A priori Direct Numerical Simulation (DNS) assessment of mean reaction rate closures for reaction progress variable in the context of Reynolds Averaged Navier–Stokes (RANS) simulations has been conducted for MILD combustion of homogeneous (i.e., constant equivalence ratio), methane-air mixtures. The reaction rate predictions according to statistical (e.g., presumed probability density function), phenomenological (e.g., eddy-break up (EBU), eddy dissipation concept (EDC) and the scalar dissipation rate (SDR) based approaches), and flame surface description (e.g., Flame Surface Density) based closures are compared. The performance of the various reaction rate closures has been assessed by comparing the models’ predictions to the corresponding quantities extracted from DNS data. It has been found that the usual presumed probability density function (PDF) approach using the beta-function predicts the PDF of the reaction progress variable in homogenous mixture MILD combustion throughout the flame brush for all cases considered here provided that the scalar variance is accurately predicted. The accurate estimation of scalar variance requires the solution of a modelled transport equation, which depends on the closure of Favre-averaged SDR. A linear relaxation based algebraic closure for the Favre-averaged SDR has been found to capture the behaviour of the Favre-averaged SDR in the current homogenous mixture MILD combustion setup. It has been found that the EBU, SDR and FSD-based mean reaction rate closures do not adequately predict the mean reaction rate of the reaction progress variable for the parameter range considered here. However, a variant of the EDC closure, with model coefficients expressed as functions of micro-scale Damköhler and turbulent Reynolds numbers, has been found to be more successful in predicting the mean reaction rate of reaction progress variable compared to other modelling methodologies for the range of turbulence intensities and dilution levels considered here.

Role of magnetic pressure forces in Fluctuation dynamo saturation

Preprint

Full-text available

May 2023

Using magnetohydrodynamic simulations of Fluctuation dynamos in turbulent flows with rms Mach numbers

\mathcal{M} \approx 0.2, 1.1

\nabla\rho

and

\nabla B^{2}

are preferentially anti-parallel to each other in subsonic flows. This is indicative of magnetic pressure opposing compression. This anti-parallel alignment persists in transonic and supersonic flows at dynamo saturation. However, compressive motions also lead to the emergence of a parallel alignment in these flows. Finally, we consider the work done against the components of the Lorentz force and the different sources of magnetic energy growth and dissipation. We show that while in subsonic flows, suppression of field line stretching is dominant in saturating the dynamo, the picture is different in supersonic flows. Both field line stretching and compression amplifies the field initially. But the growing magnetic pressure opposes further compression of magnetic flux which then dominates the saturation of the dynamo.

Investigating the magnitude and temporal localization of inertial particle mixing in turbulent channel flows

Article

Full-text available

Apr 2023
INT J MULTIPHAS FLOW

Implementation of the Filtered Turbulent Flame Model in Non-premixed Combustion Simulation

Article

Full-text available

Apr 2023
FLOW TURBUL COMBUST

The interaction between flame and turbulence leads to challenging flame dynamics and modeling issues. In this work, a newly proposed filtered turbulent flame model is implemented in the framework of large eddy simulations for non-premixed turbulent combustion. The general principles of model realization are developed, including the structure and physics of the filtered flame, tabulation setup, and the numerical algorithm. Because of the involved modeling parameters for tabulation can be directly calculated from either the resolved or subgrid model quantities, the filtered turbulent flame model is in principle favorable to improve the numerical predictability. Tentative numerical tests and comparisons with other models justify this modeling idea.

Flame Self-interaction and Flow Topology in Turbulent Homogeneous Mixture n-Heptane MILD Combustion

Article

Full-text available

Feb 2023
FLOW TURBUL COMBUST

Moderate or Intense Low-oxygen Dilution (MILD) combustion has potential to achieve both high energy efficiency and ultra-low emissions. This analysis adopts the critical point theory to characterise the Flame-Self Interaction (FSI) events and flow topologies in turbulent, homogeneous mixture, n-Heptane MILD combustion using Direct Numerical Simulations (DNS) with reduced chemical mechanism. The local flame geometry has also been categorised using the mean and Gauss curvatures. It was found that the Tunnel Formation (TF) and Tunnel Closure (TC) topologies are the most probable FSI events at all values of the reaction progress variable c, while the Unburned Pocket (UP) and Burned Pocket (BP) topologies were mostly present towards the unburned and burned mixtures of the flame, respectively. Moreover, increasing the turbulence intensity did not result in any significant changes in the distribution of FSI events. Investigation of the flow topology distribution showed that the features associated with non-zero dilatation rate did not exist in the MILD cases considered. This is a consequence of the negligible thermal expansion effect due to the small temperature rise in MILD combustion cases. Increasing the dilution factor caused a reduction in the frequency of FSI events for all c levels. The distributions of flame self-interaction events in homogeneous mixture MILD combustion have been found to be significantly different from previously reported distributions for conventional turbulent premixed combustion.

A Comparison between Statistical Behaviours of Scalar Dissipation Rate between Homogeneous MILD Combustion and Premixed Turbulent Flames

Article

Full-text available

Dec 2022

Three-dimensional Direct Numerical Simulations (DNS) data has been utilised to analyse statistical behaviours of the scalar dissipation rate (SDR) and its transport for homogeneous methane-air mixture turbulent Moderate or Intense Low oxygen Dilution (MILD) combustion for different O2 dilution levels and turbulence intensities for different reaction progress variable definitions. Additional DNS has been conducted for turbulent premixed flames and passive scalar mixing for the purpose of comparison with the SDR statistics of the homogeneous mixture MILD combustion with that in conventional premixed combustion and passive scalar mixing. It has been found that the peak mean value of the scalar dissipation rate decreases with decreasing O2 concentration for MILD combustion cases. Moreover, SDR magnitudes increase with increasing turbulence intensity for both MILD and conventional premixed combustion cases. The profiles and mean values of the scalar dissipation rate conditioned upon the reaction progress variable are found to be sensitive to the choice of the reaction progress variable definition. This behaviour arises due to the differences in the distributions of the species mass fractions within the flame. The strain rate contribution and the molecular dissipation term are found to be the leading order contributors in the scalar dissipation rate transport for MILD combustion; whereas, in conventional premixed flames, the terms rising from density variation and reaction rate gradient also play leading roles in addition to the strain rate and molecular dissipation contributions. By contrast, the terms due to density gradient and reaction rate gradient remain negligible in comparison to the leading order contributors in MILD combustion cases due to small density variation because of moderate temperature rise and small reaction rate gradient magnitudes. Furthermore, the qualitative behaviour of the strain rate contribution to the SDR transport in premixed flames is significantly different to that in the case of MILD combustion and passive scalar mixing. The findings of the current analysis indicate that the scalar dissipation rate statistics in MILD combustion show several qualitative similarities to the passive scalar mixing despite major differences with the SDR transport in conventional turbulent premixed flames. This further suggests that the scalar dissipation rate models, which were originally proposed in the context of passive scalar mixing, have the potential to be applicable for MILD combustion but the models for the premixed turbulent combustion may not be applicable for MILD combustion of homogeneous mixtures.

Spatial characteristics and modelling of mixture fraction variance and scalar dissipation rate in steady turbulent round jets

Article

Dec 2022
INT J HEAT FLUID FL

The spatial characteristics of scalar dissipation rate (SDR) are investigated in a steady-state turbulent round jet using Direct Numerical Simulation (DNS). Radial distribution of mixture fraction is found to agree well with the experimental data. Radial distributions of the turbulent diffusivities and the turbulent Schmidt numbers show different behaviours, based on how these quantities are defined. Point-wise statistics confirm that the log-normal distribution fits the probability distribution functions (PDFs) of the SDR well, except for a small positive skewness attributed to flow anisotropy. Joint PDFs of mixture fraction and SDR are symmetric with respect to mixture fraction. Self-similarity of the mean SDR, as well as its axial, radial and azimuthal components appears after a certain downstream distance. In the self-similar region, centreline SDR scales with downstream distance, x−4. Normalised SDR radial profiles show an increase near the centreline, followed by a steep decrease, after an off-centreline peak. Magnitudes of the axial, radial and azimuthal components of the mean SDR are approximately the same in the self-similar region. The budget analysis of the mean SDR transport equation reveals that the production term by scalar field stretch and the destruction term due to local curvature effects are the two dominant terms. A modification of an existing model for the self-similar mean SDR radial profiles is proposed. This is found to improve the prediction of mean SDR distributions.

A Priori Direct Numerical Simulation Analysis of the Closure of Cross-Scalar Dissipation Rate of Reaction Progress Variable and Mixture Fraction in Turbulent Stratified Flames

Article

Full-text available

Aug 2022
FLOW TURBUL COMBUST

The cross-scalar dissipation rate of reaction progress variable and mixture fraction εcξ~ plays an important role in the modelling of stratified combustion. The evolution and statistical behaviour of εcξ~ have been analysed using a direct numerical simulation (DNS) database of statistically planar turbulent stratified flames with a globally stochiometric mixture. A parametric analysis has been conducted by considering a number of DNS cases with a varying initial root-mean-square velocity fluctuation u′ and initial scalar integral length scale ℓϕ. The explicitly Reynolds averaged DNS data suggests that the linear relaxation model for εcξ~ is inadequate for most cases, but its performance appears to improve with increasing initial ℓϕ and u′ values. An exact transport equation for εcξ~ has been derived from the first principle, and the budget of the unclosed terms of the εcξ~ transport equation has been analysed in detail. It has been found that the terms arising from the density variation, scalar-turbulence interaction, chemical reaction rate and molecular dissipation rate play leading order roles in the εcξ~ transport. These observations have been justified by a scaling analysis, which has been utilised to identify the dominant components of the leading order terms to aid model development for the unclosed terms of the εcξ~ transport equation. The performances of newly proposed models for the unclosed terms have been assessed with respect to the corresponding terms extracted from DNS data, and the newly proposed closures yield satisfactory predictions of the unclosed terms in the εcξ~ transport equation.

Predicting jet ignitability using a PDF transport model

Article

Full-text available

Jun 2022

P.s. Cumber

For the first time the probability of ignition is calculated successfully using a PDF transport model. At present the model is only accurate where jet intermittency effects are small, away from the jet boundary. A conclusion of this investigation is the probability of ignition field is sensitive to the micro-mixing model used. In this article, four micro-mixing models are implemented and the modified Curl model demonstrated to be the most accurate for the jet ignitability experiments simulated.

Numerical improvement and validation of a naval hydrodynamics CFD solver in view of performing fast and accurate simulation of complex ship-wave interaction.

Thesis

Jul 2021

Young Jun Kim

The present thesis aims to study the efficiency and the accuracy of numerical schemes for naval applications, especially for unsteady wavestructure interaction problems. Specific studies are done on subparts of the solver: the interface model, the time integration schemes and the use of SWENSE model. The study on the interface treatment schemes is performed with the Volume of Fluid interface capturing scheme. Two interface convection methods and two interface conditions are tested for 2D wave propagation and impact cases. The Diagonally Implicit Runge-Kutta (DIRK) time integration schemes are applied to two-phase flow solvers. The DIRK method is applied to an incompressible averaged two-phase flow solver (foamStar) and a two-phase flow solver based on the Spectral Wave Explicit Navier-Stoke Equations (foamStarSWENSE). The validity and the order of convergence of the higher-order DIRK methods are confirmed using a 2D Taylor Green Vortex flow. The efficiency of the DIRK method is then studied on the two-phase regular wave propagation in the periodic domain. With two solvers and various DIRK schemes, two types of applications are performed. First, the qualification analysis on the regular and the irregular wave in the numerical wave tank is performed. The efficiency of each DIRK scheme is compared with various resolutions, and theparameters for qualified wave propagation are proposed. Second, the seakeeping analysis of the Wigley III hull and the KCS with a forward speed is then performed, and the efficiency and the accuracy of the DIRK scheme with two solvers are compared.

Comparison of the Reactive Scalar Gradient Evolution between Homogeneous MILD Combustion and Premixed Turbulent Flames

Article

Full-text available

Nov 2021

Moderate or intense low-oxygen dilution (MILD) combustion is a novel combustion technique that can simultaneously improve thermal efficiency and reduce emissions. This paper focuses on the differences in statistical behaviours of the surface density function (SDF = magnitude of the reaction progress variable gradient) between conventional premixed flames and exhaust gas recirculation (EGR) type homogeneous-mixture combustion under MILD conditions using direct numerical simulations (DNS) data. The mean values of the SDF in the MILD combustion cases were found to be significantly smaller than those in the corresponding premixed flame cases. Moreover, the mean behaviour of the SDF in response to the variations of turbulence intensity were compared between MILD and premixed flame cases, and the differences are explained in terms of the strain rates induced by fluid motion and the ones arising from flame displacement speed. It was found that the effects of dilatation rate were much weaker in the MILD combustion cases than in the premixed flame cases, and the reactive scalar gradient in MILD combustion cases preferentially aligns with the most compressive principal strain-rate eigendirection. By contrast, the reactive scalar gradient preferentially aligned with the most extensive principal strain-rate eigendirection within the flame in the premixed flame cases considered here, but the extent of this alignment weakened with increasing turbulence intensity. This gave rise to a predominantly positive mean value of normal strain rate in the premixed flames, whereas the mean normal strain rate remained negative, and its magnitude increased with increasing turbulence intensity in the MILD combustion cases. The mean value of the reaction component of displacement speed assumed non-negligible values in the MILD combustion cases for a broader range of reaction progress variable, compared with the conventional premixed flames. Moreover, the mean displacement speed increased from the unburned gas side to the burned gas side in the conventional premixed flames, whereas the mean displacement speed in MILD combustion cases decreased from the unburned gas side to the middle of the flame before increasing mildly towards the burned gas side. These differences in the mean displacement speed gave rise to significant differences in the mean behaviour of the normal strain rate induced by the flame propagation and effective strain rate, which explains the differences in the SDF evolution and its response to the variation of turbulence intensity between the conventional premixed flames and MILD combustion cases. The tangential fluid-dynamic strain rate assumed positive mean values, but it was overcome by negative mean values of curvature stretch rate to yield negative mean values of stretch rate for both the premixed flames and MILD combustion cases. This behaviour is explained in terms of the curvature dependence of displacement speed. These findings suggest that the curvature dependence of displacement speed and the scalar gradient alignment with local principal strain rate eigendirections need to be addressed for modelling EGR-type homogeneous-mixture MILD combustion.

Effects of spatial distribution of CO2 dilution on localised forced ignition of stoichiometric biogas-air mixtures

Article

Full-text available

Sep 2021

The localized forced ignition and subsequent flame propagation have been analyzed for stoichiometric biogas-air mixtures (CH4/CO2/air blend) with different spatial distributions (uniform, Gaussian and bimodal) and mean levels of CO2 dilution (i.e. mole fraction of CO2) for different flow conditions (e.g. quiescent laminar condition and different turbulence intensities) using three-dimensional Direct Numerical Simulations. A two-step chemical mechanism with sufficient accuracy is used to capture the effects of CO2 dilution on the laminar burning velocity of the biogas−airmixture. A parametric analysis in terms of the mean, standard deviation and integral length scale of the initial Gaussian and bimodal distributions of spatial CO2 dilution in the unburned gas has been conducted. Qualitatively similar behavior has been observed for all three initial spatial distributions of CO2. A departure from uniform conditions was found to increase the range of reaction rate magnitudes of CH4, which impacts the burned gas volume and, in turn, increases the variability of the outcomes of the ignition event (successful thermal runaway and subsequent self-sustained propagation or misfire). Turbulence intensity and the mean level of dilution were found to have significant impacts on the outcome of the localized forced ignition, and an increase of either quantity acts to reduce the burned gas volume irrespective of mixture composition due to the enhancement of heat transfer from the hot gas kernel, and the heat sink effects of CO2, respectively. An increase of the integral length scale lψ for the spatial distribution of CO2 dilution increased the probability of a successful outcome of the ignition event. A uniform initial spatial distribution was found to be optimal, and in the case of a departure from non-uniform conditions, larger variability in the outcome are obtained for a Gaussian initial distribution of CO2 dilution than a bimodal one. The variance of the CO2 dilution distribution has been found to have a negligible impact on the outcomes observed, as it was dominated by the effects arising from turbulence intensity, nature of initial CO2 distribution and integral length scale of CO2 dilution.

An hybrid particle-grid method for the study of differential diffusion

Article

Jun 2021

Quasi-stationarity of scalar turbulent mixing statistics in a non-symmetric case

Article

Full-text available

May 2021

The existence of an asymptotic shape at large times of the probability density function (PDF) of a non-reacting scalar, mixed by a solenoidal turbulent velocity field and molecular diffusive transport, was investigated by Sinai and Yakhot [Y. G. Sinai and V. Yakhot, “Limiting probability distributions of a passive scalar in a random velocity field,” Phys. Rev. Lett. 63, 1962 (1989)]. The quasi-stationarity of the mixing statistics along the time evolution by Valiño et al. [“Quasistationary probability density functions in the turbulent mixing of a scalar field,” Phys. Rev. Lett. 72, 3518 (1994)] was an extension to symmetric scalar pdfs; analytic solutions for the scalar fluctuation dissipation rates, conditional upon the scalar value, and the pdf were obtained. This manuscript examines the generalization of the latter results to asymmetric scalar pdfs, further scrutinizes underlying mechanisms for a quasi-stationary statistics, and shows a Monte Carlo implementation which allows non-Gaussian relaxations to prescribed values of skweness and kurtosis.

Probing the Morphology of Polarized Emission Induced by Fluctuation Dynamo Using Minkowski Functionals

Article

Nov 2024
ASTROPHYS J

The morphology and the characteristic scale of polarized structures provide crucial insights into the mechanisms that drive turbulence and maintain magnetic fields in magneto-ionic plasma. We aim to establish the efficacy of Minkowski functionals as quantitative statistical probes of filamentary morphology of polarized synchrotron emission resulting from fluctuation dynamo action. Using synthetic observations generated from magnetohydrodynamic simulations of fluctuation dynamos with varying driving scales ( ℓ f ) of turbulence in isothermal, incompressible, and subsonic media, we study the relation between different morphological measures and their connection to fractional polarization ( p f ). We find that Faraday depolarization at low frequencies gives rise to small-scale polarized structures that have higher filamentarity as compared to the intrinsic structures that are comparable to ℓ f . Above ∼3 GHz, the number of connected polarized structures per unit area ( N CC,peak ) is related to the mean p f (〈 p f 〉) of the emitting region as 〈 p f 〉 ∝ N CC , peak − 1 / 4 , provided the scale of the detectable emitting region is larger than ℓ f . This implies that N CC,peak represents the number of turbulent cells projected on the plane of the sky and can be directly used to infer ℓ f via the relation ℓ f ∝ N CC , peak − 1 / 2 . An estimate of ℓ f thus directly allows for pinning down the turbulence-driving mechanism in astrophysical systems. While the simulated conditions are mostly prevalent in the intracluster medium of galaxy clusters, the qualitative morphological features are also applicable in the context of interstellar medium in galaxies.

Synthetic Turbulence with Prescribed Probability Density Function and Application to Scalar Quantities Occurring in Reactive Flows

Article

Full-text available

Nov 2024
FLOW TURBUL COMBUST

Markus Klein

Based on a (synthetic) turbulent signal which obeys a Gaussian probability density function (PDF) together with some form of prescribed two-point statistics (i.e. integral length or time scales or turbulent energy spectrum), a simple algorithm is proposed to transform the original signal, such that it follows a new target PDF. It is shown that for many practical applications the transformation does not change the integral length or time scale more than a few per cent. The algorithm can be combined with any turbulence generator. It has applications for prescribing boundary or initial conditions of non-Gaussian signals in scale resolving simulations of turbulent flows, such as passive scalars like temperature, bounded passive scalars occurring in reactive flows or velocity signals close to walls.

Probing the Morphology of Polarized Emission Induced by Fluctuation Dynamo using Minkowski Functionals

Preprint

Full-text available

Aug 2024

The morphology and the characteristic scale of polarized structures provide crucial insights into the mechanisms that drives turbulence and maintains magnetic fields in magneto-ionic plasma. We aim to establish the efficacy of Minkowski functionals as quantitative statistical probes of filamentary morphology of polarized synchrotron emission resulting from fluctuation dynamo action. Using synthetic observations generated from magnetohydrodynamic simulations of fluctuation dynamos with varying driving scales (

\ell_{\rm f}

) of turbulence in isothermal, incompressible, and subsonic media, we study the relation between different morphological measures, and their connection to fractional polarization (

p_{\rm f}

). We find that Faraday depolarization at low frequencies give rise to small-scale polarized structures that have higher filamentarity as compared to the intrinsic structures that are comparable to

\ell_{\rm f}

. Above

\sim3\,{\rm GHz}

, the number of connected polarized structures per unit area (

N_{\rm CC, peak}

) is related to the mean

p_{\rm f}

(

\langle p_{\rm f} \rangle

) of the emitting region as

\langle p_{\rm f} \rangle \propto N_{\rm CC, peak}^{-1/4}

, provided the scale of the detectable emitting region is larger than

\ell_{\rm f}

. This implies that

N_{\rm CC,peak}

represents the number of turbulent cells projected on the plane of the sky and can be directly used to infer

\ell_{\rm f}

via the relation

\ell_{\rm f} \propto N_{\rm CC,peak}^{-1/2}

. An estimate on

\ell_{\rm f}

thus directly allows for pinning down the turbulence driving mechanism in astrophysical systems. While the simulated conditions are mostly prevalent in the intracluster medium of galaxy clusters, the qualitative morphological features are also applicable in the context of interstellar medium in galaxies.

A Comparison Between Conventional and MILD Combustion Processes of Turbulent Stratified Mixtures

Article

Jul 2024

Detonation structure in the presence of mixture stratification using reaction-resolved simulations

Article

Jun 2024
COMBUST FLAME

A priori direct numerical simulation assessment of MILD combustion modelling in the context of large eddy simulation

Article

Apr 2024
FUEL

Flame self-interactions in MILD combustion of homogeneous and inhomogeneous mixtures

Article

Full-text available

Mar 2024

Flame self-interaction (FSI) events in Moderate or Intense Low-Oxygen Dilution (MILD) combustion of homogeneous and inhomogeneous mixtures of methane and oxidiser have been analysed using three-dimensional Direct Numerical Simulations (DNS). The simulations have been conducted at the same global equivalence ratio (⟨ϕ⟩=0.8

\langle \phi \rangle = 0.8

) for different levels of O2

\mathrm {O_2}

concentration (dilution) and initial turbulence intensities. It has been reported that both homogeneous and inhomogeneous mixture MILD combustion cases exhibit significant occurrences of FSI events, with the peak frequency of FSI events occurring towards the burned gas side in all cases. Moreover, the frequency of FSI events increases with increasing dilution level and turbulence intensity, but the presence of mixture inhomogeneity leads to a reduction in total FSI events. In all cases, the cylindrical FSI topologies (i.e. tunnel formation and tunnel closure) were found to have a higher likelihood of occurrence compared to spherical FSI topologies (i.e. unburned and burned gas pockets). The geometries of FSI topologies were also analysed using the mean and Gaussian curvatures. It has been shown that the inward propagating spherical FSI topologies (i.e. unburned gas pockets) are associated with negative mean curvature, while outward propagating spherical FSI topologies (i.e. burned gas pockets) are associated with positive mean curvature. Moreover, tunnel formation (tunnel closure) FSI topologies predominantly exhibit either elliptic geometries with positive (negative) mean curvature or hyperbolic saddle geometries with negative (positive) mean curvature. It has been shown for the first time in MILD combustion that the mean values of kinematic restoration and dissipation terms in the transport equation of the magnitude of the reaction progress variable conditional upon the reaction progress variable tend to cancel each other in the vicinity of the critical points associated with cylindrical topologies. Thus, the singular contributions in these terms, which are obtained from analytical descriptions in the vicinity of tunnel formation and tunnel closure topologies, do not affect the balance equation of the magnitude of the gradient of the reaction progress variable. Consequently, there is no need for a separate model treatment for singularities in modelling approaches based on the magnitude of the gradient of the reaction progress variable. The FSI events in the reaction dominated and propagating flame regions of MILD combustion have also been analysed for the first time. It has been found that more FSI events occur in the reaction dominated region, particularly towards the burned gas side. However, the majority of spherical FSI topologies are found in the propagating flame region. The findings from this study indicate that turbulence intensity, dilution level and mixture inhomogeneity effects need to be considered in any attempt to extend flame surface-based modelling approaches to MILD combustion.

Radio surface fluctuations in radio relics

Article

Full-text available

Feb 2024

Recent observations have revealed detailed structures of radio relics across a wide range of frequencies. In this work, we performed three-dimensional magnetohydrodynamical (3D MHD) simulations of merger shocks propagating through a turbulent magnetized intracluster medium. We then employed on-the-fly Lagrangian particles to explore the physical processes behind the origination of radio substructures and their appearance in high and low-frequency observations. We employed two cosmic-ray (CR) electron acceleration models, with a fresh injection of electrons from the thermal pool and the re-acceleration of mildly relativistic electrons. We used the relative surface brightness fluctuations, nu , to define a ``degree of patchiness.'' First, we found that patchiness is produced if the shock's surface has a distribution of Mach numbers, rather than a single Mach number. Second, radio relics appear patchier if the Mach number distribution consists of a large percentage of low Mach numbers (

M Furthermore, as the frequency increases, the patchiness also becomes larger. Nevertheless, if radio relics are patchy at high frequencies (e.g., 18.6 GHz), they necessarily will also be patchy at low frequencies (e.g., 150 MHz). Then, to produce noticeable differences in the patchiness at low and high frequencies, the shock front should have a Mach number spread of

M Finally, the extent of the patchiness depends on the Mach number distribution as well as the CR acceleration model. We propose nu as a potential tool for extracting merger shock properties and information on particle acceleration processes at shocks in radio observations.

Development of 3-D Computer Code to Study Autoignition in a Turbulent Medium

Article

Aug 2023

S. Sreedhara

In. this paper, the development and validation of 3-dimensional computer code to analyze autoignition in a non-premixed medium under isotropic and homogeneous turbulence is presented. During autoignition the density changes are considerable and hence the constant density assumption cannot be made. To incLude the effects of density, fluctuations caused due to spatial inhomogeneities in temperature and species, a pressure based method is deveLoped herein, which is a spectral impLementation of the sequential steps followed in the predictor-corrector type of algorithms. The velocity and pressure field are solved in spectral space while the scalars are solved in physical space. The combustion is assumed to take pLace through a single-step irreversible reaction. Simulations are first validated for nonreacting turbulence without any scalars. Next, the decay, of scalar variance has been studied which showed a power law decay as observed by the earLier researchers. Then. the program is extended to analyze the reacting flow problems. The code has been parallelized using MPI calls to run it efficiently on IBM-SP machines. The details of the governing equations, solution methodology and comparison of present results with previous data are presented.

Stochastic modeling of turbulent mixing based on a hierarchical swapping of fluid parcels

Article

Nov 2023
Proc Appl Math Mech

Turbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods.

Surface Density Function and Its Evolution in Homogeneous and Inhomogeneous Mixture n -Heptane MILD Combustion

Article

Mar 2023

Moderate or intense low-oxygen dilution (MILD) combustion is a combustion technique with potential to simultaneously improve thermal efficiency and reduce emissions. This paper focuses on the mean behavior of the reactive scalar gradient characterized by the surface density function (SDF = magnitude of the reaction progress variable gradient) and its evolution for exhaust gas recirculation (EGR) type, homogeneous and inhomogeneous mixture n-heptane combustion under MILD conditions using Direct Numerical Simulations (DNS) with reduced chemical mechanism. Two oxygen concentrations have been considered here for the homogeneous mixture case, namely, 3.0% and 4.5% by volume. The characteristics of the SDF and displacement speed were also analyzed in the reaction and propagating-flame-dominated regions of the domain to illustrate the effect of combustion mode on the mean variations of these quantities. The mean values of the SDF in turbulent MILD combustion cases are found to be smaller compared to the corresponding laminar flame cases. Moreover, the effect of mixture inhomogeneity on the SDF variation is found to be marginal for the parameters considered here. It is found that increasing the dilution factor reduces the percentage of flame thickening with respect to the corresponding laminar flame thickness under identical turbulence conditions. The effects of dilatation rate are found to be weak in the studied cases due to the expected low heat release under MILD conditions which leads to weak thermal expansion effects. The effective flame normal and tangential strain rates are found to be dominated by the additional flame normal and tangential strain rates due to flame propagation, respectively. The effective flame normal strain rate has positive values across the flame which promotes flame thickening and could explain the decrease in the SDF values, while the effective flame tangential strain rate is negative throughout the flame and indicates a fractional reduction in flame area that could be attributed to flame surface interactions. The reaction-dominated regions give rise to reduced level of the SDF in the homogeneous mixture cases and increased level of Sd in all cases compared to those calculated in the propagating-flame region.

Numerical simulations of miscible displacement in an inclined channel by lattice Boltzmann method

Article

Feb 2023

The interfacial instability between miscible fluids in a channel is determined by many factors, such as viscosity contrast and the inclination angle. Considering the effect of the gravity field, we investigate the displacement phenomenon between two miscible fluids with different viscosities in an inclined channel. The results show that when the concentration Rayleigh number Ra C {less than or equal to} 10 ⁵ , the inclination angle θ ranges from 0{degree sign} to 90º, and the natural logarithm of the viscosity ratio R>0, there are three fluid-fluid interfacial instability regions, namely viscous fingering, "Kelvin-Helmholtz" (K-H) instability and "Rayleigh-Taylor" (R-T) instability. A scaling analysis is developed to describe the time evolution of the displacement as described by the displacement efficiency at a fixed viscous ratio. Our analysis indicates that in the viscous fingering region, the time evolution of the displacement efficiency gradually increases with t scaling due to fingering formations; in the the K-H and R-T region, the displacement efficiency rapidly increases with t 1+Ra C /10^6 . When considering the effect of the viscosity ratio in the K-H instability region, the displacement efficiency scales as η∼ t 1+Ra C /10^6 R 0.1 . In addition, when the inclination angle is negative or R < 0, the instability phenomenon is not obvious, and the displacement efficiency decreases as the inclination angle or R decreases.

Chemically reacting mixing in coaxial miscible liquid jets under variable viscosities and reaction rates

Article

Dec 2022
CHEM ENG SCI

Development of Multigrid Sequential Data Assimilation Strategies for Complex Unsteady Flows

Thesis

Full-text available

Jul 2022

Gabriel Moldovan

The analysis and control of complex high-Reynolds-number flows of industrial and practical interest is one of the most distinctive open challenges that the scientific community must face for fluid mechanics applications in the coming decades. Modelling bias and uncertainty may strongly affect the predictive capabilities of both numerical simulations and experimental measurements. Under this perspective, data-driven tools from Data Assimilation, and, in particular, sequential tools such as the ensemble Kalman filter (EnKF), have been recently used to obtain a precise estimation of the physical flow state accounting for bias or uncertainty coming from real conditions in the performance of the investigative tool. A newly developed sequential Data Assimilation algorithm, combining multi-grid aspects and the ensemble Kalman Filter, is presented in this PhD-study. The so-called MGEnKF algorithm (Multi-Grid Ensemble Kalman Filter) exploits physical states obtained on multiple grids of different resolution to perform the state estimation and parametric optimization using EnKF procedures. More precisely, an ensemble of low-fidelity simulations of the flow is run on a coarse grid level together with a single higher-resolution simulation on the finest mesh level. The state estimation obtained at the coarse level and the associated ensemble statistics are used to filter the finest mesh solution and optimise a set of parameters describing the model (boundary conditions, model parameters…). This procedure allows to i) reduce the computational costs of the EnKF and ii) ensure the conservativity and the smoothness of the final solution.The assessment of the method is performed via the analysis of one-dimensional, two-dimensional and three-dimensional test cases, using different models of increasing complexity. The results show that the MGEnKF can successfully update the state of a system with the available observations to increase the global accuracy of the model. In addition, the parametric description of the numerical problem (in terms of prescribed boundary conditions, turbulence closures...) can be adequately optimized taking into account the different mesh resolutions employed in the algorithm. The MGEnKF opens interesting perspectives for potential application to in-streaming Data Assimilation techniques.

Development and validation of a combustion large-eddy-simulation solver based on fully compressible formulation and tabulated chemistry

Article

Aug 2022
AEROSP SCI TECHNOL

This study concerns the development and validation of a high-fidelity CFD solver for large-eddy simulations (LES) of combustion and reacting flows. The solver is built upon a high-resolution numerical scheme and leverages a compressible flamelet formulation, so that it can capture both the turbulent combustion and thermoacoustic effects simultaneously. The validation study is first performed by considering a scalar-mixing case in homogeneous turbulence, and then extended to LES of a non-premixed jet flame. The solver accuracy is assessed by comparing the numerical solutions with the available experimental data. It is found that the newly developed solver is able to accurately predict the time-averaged combustion fields as well as the fluctuation quantities. The predictive accuracy is comparable to that of the state-of-the-art low-Mach solvers in literature.

Study of turbulent dispersion of a concentration plume emitting from a line source over a rib‐roughened surface

Article

Oct 2022
INT J HEAT MASS TRAN

Turbulent dispersion of a concentration plume emitting from a horizontal line source over a rib-roughened surface has been studied using direct numerical simulations (DNS). Four test cases have been compared to investigate the effects of the source elevation and location on the plume dispersion in a turbulent boundary layer. The transport process of the concentration is investigated in both physical and spectral spaces which includes analyses of statistical moments of the concentration field, decay rate, plume width, pre-multiplied spectra of the velocity and concentration fields, and the probability density function (PDF) of concentration fluctuations. It is observed that as the mean plume development enters the long-range dispersion stage, the decay rate of the mean concentration field begins to feature a constant slope of −3/2, while the vertical spread of the mean plume exhibits a constant slope of 1/3 in all four line source release cases in a ribbed wall flow. It is also observed that the profiles of both the mean concentration field and the RMS of concentration fluctuations exhibit a self-similarity pattern downstream of the line source in all four test cases. By comparing the characteristic length scales of the spanwise velocity and scalar fields, two distinct stages of the instantaneous plume development are observed, dominated by the turbulent convective and diffusive mechanisms. It is discovered that the transition from the turbulent convective stage to the turbulent diffusive stage occurs more rapidly for line sources placed near the wall and inside the cavities.

Digital-filter and forward-stepwise method-based synthetic inflow turbulence generation: Applications to horizontal axis turbines

Thesis

Sep 2018

Kutalmis Bercin

The main aim of this study is to create an easy-to-reproduce knowledge unit wherein the digital-filter method-based (DFM) and forward-stepwise method-based (FSM) synthetic inflow generator classes are conceptualised, explored, and improved for large eddy simulation applications (LES). To this end, the following novelties were introduced: [ i ] both classes were abstracted and documented into four non-CFD and five CFD model stages, [ ii ] two new DFM variants were derived, [ iii ] with these two, four preexisting DFM-FSM variants were code implemented, [ iv ] a new analytic function that can transform the skewness-kurtosis of synthetic inflow to target values without changing existing statistics was derived and verified, [ v ] two other skewness-kurtosis transformation approaches were derived and proved ineffectual, [ vi ] five easy-to-code computational speedup techniques for DFM-FSM were introduced and quantified, [ vii ] two new methods to enable DFM-FSM to be computed on nonuniformly-discretized arbitrary boundary geometries were developed, [ viii ] a preliminary method to ensure the divergence freeness in DFM-FSM was studied, [ ix ] each DFM-FSM model stage was evaluated by controlled studies of extensive-than-the-literature range of input variables and output statistics within non-CFD and LES environments through decaying homogeneous isotropic turbulence, homogeneous shear turbulence and smooth-wall plane channel flow, [ x ] five LES post-solution verification approaches were reviewed and compared via these building-block flows. In addition, horizontal axis wind and marine turbine flows were explored by various means including DFM-FSM: [ xi ] for these explorations, in-house codes were written and verified for the blade element momentum theory (BEMT), the time-accurate Euler-Bernoulli beam theory, a BEMT-CFD coupling through the actuator disk method, and the actuator line method, [xii] hydrodynamics of a marine turbine under decaying homogeneous isotropic turbulence with four different turbulence intensities were investigated by wall-modelled & actuator-line modelled LES computations, and twelve analytical wake models, [ xiii ] the arbitrary mesh interface technique under turbulent inflows was quantitatively assessed, and lastly, [ xiv ] considerable amount of for-the-first-time observations and remarks were quantified and reported.

Effect of viscous-convective subrange on passive scalar statistics at high Reynolds number

Article

Feb 2022

An assumption common to many approaches to understanding and modeling turbulent mixing is that the statistics of a passive scalar at small length scales will approach the analogous statistics of the velocity field as the scale separation increases between the flow-specific outer scales and the small scales of interest. This assumption follows from the hypotheses of Kolmogorov, Oboukhov, Corrsin, and Batchelor, although it is well recognized that differences in the scalar and velocity dynamics prevent the overall statistics of the two being the same. Considerable research on the effect of Reynolds number and Schmidt number on the scalar statistics has shown that the assumption is not very good at either high Reynolds number or high Schmidt number individually. Because of limitations in laboratory measurements, direct numerical simulations (DNSs), and in situ measurements of the ocean and atmosphere, it is difficult to obtain data in which the Reynolds number is high enough for an unequivocal inertial-convective subrange, and the Schmidt number is simultaneously high enough for a clear viscous-convective subrange. Our hypothesis is that, when both subranges exist, then there is sufficient scale separation in the velocity field for its statistics to be approximately universal, and also sufficient additional scale separation for the scalar to relax so that its small-scale statistics approach those of the velocity. We explore this hypothesis with DNS resolved on up to 14256×14256×14256 grid points, Taylor Reynolds number Reλ=633, and Schmidt number Sc=[0.1,0.7,1.0,7.0], with the aim of studying the validity of this hypothesis for mixing in air and water. When the Schmidt number is not greater than unity at high Reynolds number, a viscous-convective subrange does not exist and we find that small-scale isotropy, the intermittency exponent, and the probability density function of the scalar dissipation rate are all much different from the analogous velocity statistics, as reported widely in literature. However, when the Schmidt number is greater than unity at high Reynolds number, inertial-convective and viscous-convective subranges both exist, and the velocity and scalar statistics are similar. Since this similarity is a consequence of the presence of both inertial convective and viscous convective subranges, it is achieved only at both high Reynolds and Schmidt numbers, and the statistics show a sharp change when the Schmidt number is changed from from 1 to 7. This suggests that at high Reynolds numbers, the modeling assumption of similarity between velocity and scalar statistics is valid for mixing in water, but not in air.

Scalar Forcing Methodology for Direct Numerical Simulations of Turbulent Stratified Mixture Combustion

Article

Full-text available

Apr 2022
FLOW TURBUL COMBUST

Scalar forcing in the context of turbulent stratified flame simulations aims to maintain the fuel-air inhomogeneity in the unburned gas. With scalar forcing, stratified flame simulations have the potential to reach a statistically stationary state with a prescribed mixture fraction distribution and root-mean-square value in the unburned gas, irrespective of the turbulence intensity. The applicability of scalar forcing for Direct Numerical Simulations of stratified mixture combustion is assessed by considering a recently developed scalar forcing scheme, known as the reaction analogy method, applied to both passive scalar mixing and the imperfectly mixed unburned reactants of statistically planar stratified flames under low Mach number conditions. The newly developed method enables statistically symmetric scalar distributions between bell-shaped and bimodal to be maintained without any significant departure from the specified bounds of the scalar. Moreover, the performance of the newly proposed scalar forcing methodology has been assessed for a range of different velocity forcing schemes (Lundgren forcing and modified bandwidth forcing) and also without any velocity forcing. It has been found that the scalar forcing scheme has no adverse impact on flame-turbulence interaction and it only maintains the prescribed root-mean-square value of the scalar fluctuation, and its distribution. The scalar integral length scale evolution is shown to be unaffected by the scalar forcing scheme studied in this paper. Thus, the scalar forcing scheme has a high potential to provide a valuable computational tool to enable analysis of the effects of unburned mixture stratification on turbulent flame dynamics.

Computational Fluid Dynamics and Heat Transfer

Book

Nov 2021

Pradip Majumdar

Numerical experiments on turbulent entrainment and mixing of scalars

Article

Full-text available

Nov 2021

Numerical experiments on the turbulent entrainment and mixing of scalars in a incompressible flow have been performed. These simulations are based on a scale decomposition of the velocity field, thus allowing the establishment from a dynamic point of view of the evolution of scalar fields under the separate action of large-scale coherent motions and small-scale fluctuations. The turbulent spectrum can be split into active and inactive flow structures. The large-scale engulfment phenomena actively prescribe the mixing velocity by amplifying inertial fluxes and by setting the area and the fluctuating geometry of the scalar interface. On the contrary, small-scale isotropic nibbling phenomena are essentially inactive in the mixing process. It is found that the inertial mechanisms initiate the process of entrainment at large scales to be finally processed by scalar diffusion at the molecular level. This last stage does not prescribe the amount of mixing but adapts itself to the conditions imposed by the coherent anisotropic motion at large scales. The present results may have strong repercussions for the theoretical approach to scalar mixing, as anticipated here by simple heuristic arguments which are shown able to reveal the rich dynamics of the process. Interesting repercussions are also envisaged for turbulence closures, in particular for large-eddy simulation approaches where only the large scales of the velocity field are resolved.

Investigation of three-scalar subgrid-scale mixing in turbulent coaxial jets

Article

Full-text available

Oct 2021

Hybrid particle-grid methods for the study of differential diffusion in turbulent flows

Article

Jun 2021
COMPUT FLUIDS

This paper is devoted to the development and application of hybrid methods combining, on the one hand, semi-lagrangian methods for the advection-diffusion of scalars, and, on the other hand, either finite volume or spectral methods, depending on the flow geometry, for the Navier-Stokes equations. A particular focus is made on the accuracy and scalability of the methods. These methods are then used to study differential diffusion of scalars on two canonical cases: Homogeneous Isotropic Turbulence and a jet flow. We first characterize differential diffusion in terms of spectral distribution. We then use the Reynolds decomposition to bring out the different mechanisms involved in the energy budget of the scalar and we analyze their spatial distribution.

Publisher's Note: “Using approximate inertial manifold approach to model turbulent non-premixed combustion” [Phys. Fluids 33 , 035125 (2021)]

Article

Full-text available

May 2021

Temperature Fluctuations and Scales in Grid-Generated Turbulence

Article

Full-text available

Oct 1980
J FLUID MECH

To study the mixing of a passive scalar in nearly isotropic turbulence, experiments have been made in isotropically mixed thermal fields with thermal mesh size M < M, at locations downstream of the turbulence grid. The heating screen was designed to produce negligible statistical change in the velocity field a short distance downstream. In all the heated grid experiments, for a given initial configuration of the thermal field, the intensity of temperature fluctuations T, and the decay rate of

\overline{\theta^2}

were both independent of the temperature of the grid. The principal effect of having M = M case, and a marginal increase in their decay rate; contrary to expectation, the ratio R of temperature to velocity integral scales in the region of approximate homogeneity did not differ from that corresponding to M/M and A exp [x is downstream distance measured from the heating screen, and T0 is a characteristic turbulence decay time scale at x0 = 0. It was also verified that the skewness of the streamwise temperature derivative is approximately zero sufficiently downstream of the heating screen. Where the present study overlaps with previous measurements, an extensive comparison reveals several points of agreement as well as departure.

A Simple Chemical Reaction in Numerically Simulated Homogeneous Tuburlence

Conference Paper

Mar 1987

The Structure of Diffusion Flames

Article

Jul 1976

R.W. Bilger

The theory for the mixing, and chemical reaction of two streams of fluid is developed for unsteady laminar and for turbulent flow. Only one conserved scalar is required to fully describe the mixing, and various reaction models are considered including the Burke-Schumann flame sheet and shifting equilibrium. A new expression is derived for the instantaneous reaction rate of any species w/sub i/ = -- rhoD(..delta.. xi)/sup 2/d/sup 2/Y/sub i//d xi/sup 2/ where xi is a conserved scalar. New insight is obtained into the structure of the instantaneous reaction zone for both laminar and turbulent flames. Diagnostic parameters are presented for determining when various models are applicable and for what properties.

Ratio of Scalar and Velocity Dissipation Time Scales in Shear Flow Turbulence

Article

Mar 1978

Various studies of thermal turbulence in thin shear flows are re-examined in order to evaluate the ratio of the time scale of the scalar-fluctuation field to that of the velocity-fluctuation field. In all cases considered it is found that the ratio is nearly uniform with a value close to 0.5.

Concentration Fluctuations in a Round Turbulent Free Jet

Article

Jan 1971
CHEM ENG SCI

D.B. Spalding

The root-mean-square fluctuating concentration is supposed to obey a parabolic differential equation containing terms for convection, diffusion, generation and dissipation. This equation is solved numerically, together with similar simultaneous equations for the time-mean concentration, the longitudinal time-mean velocity, the kinetic energy of the turbulent motion, and a measure of the fluctuations of vorticity; the initial and boundary conditions are appropriate to the steady injection of fluid from a nozzle of circular cross-section into a reservoir containing stagnant fluid of equal density. The profiles of concentration fluctuations, and of related quantities, are compared with previously published experimental data. Good agreement is demonstrated. Some possible refinements to the model are discussed.

Theoretical Remarks on a Phenomenological Model of Turbulent Mixing

Article

Oct 1986

George Kosály

In the pdf approach to turbulent combustion the molecular diffusion is to be modeled. In recent years, several authors have employed the Curl model (Curl, 1963) for closure. A modified version of the Curl model has been introduced by Pope (1982b). The modified model contains an unspecified function A∥α) [cf. Eq. (la)] which has been defined in the context of Monte-Carlo simulation. The paper Clarifies the physical meaning of this function by relating it to the physics of the initial phase of mixing of an inert scalar in homogeneous turbulence. A relationship is established between the modified Curl model and the linear mean square estimation closure introduced by Dopazo and O'Brien (1976). The asymptotic behavior of the pdf is discussed.

Relaxation of initial probability density functions in turbulent convection of scalar fields

Article

Jan 1979

Cesar Dopazo

The evolution of an initially binary (zero unity) scalar field undergoing turbulent and molecular mixing is studied in terms of conservation equations for the probability density function of the scalar property. Attention is focused on the relaxation of the dynamic system to a state independent of the initial conditions. A few existing methods are discussed and evaluated and a new mechanistic model is proposed. Classical iteration techniques are used to obtain an equation for the single point probability density and the unperturbed Green's function. It is suggested that use of the true Green's function or perturbed propagator of the system might be necessary in order to obtain the correct evolution of the probability density function.

An Improved Turbulent Mixing Model

Article

Jun 1982

S. B. Pope

It is shown that Curl's (1963) model and the modified Curl model lead to standardized asymptotic probability density functions (pdf) with infinite fourth and higher moments. The improved models produce finite moments by changing the age distribution. One model produces a pdf with flatness = 3.12 and superskewness = 16.8, but the model's overall performance is unacceptable. The recommended model, for which the above values are 3.70 and 29.5 respectively, has an asymptotic pdf that is close to Gaussian. The model is presented for the simple case of a single scalar in homogeneous turbulence.

Statistical Treatment of Non-Isothermal Chemical Reactions in Turbulence

Article

Jul 1976
COMBUST SCI TECHNOL

The goal of this investigation was to link as closely as possible a reactive flow study to one of simple mixing of passive scalar fields. Such a link would allow experimental or theoretical information from relatively simple non-reactive turbulent diffusion systems to be translated into useful reactive flow information. Probability density functions were used as the primary dynamical variables. The particular non-isothermal problem of autoignition, with reactant consumption modeled by an explicit temperature dependent reaction rate was treated in detail. Also presented was a formulation of the problem of generation of acoustic and vorticity modes in homogeneous turbulence by chemically generated heat production. (DDA)

A stochastic model of two-particle dispersion and concentration fluctuations in homogeneous turbulence

Article

Sep 1980
J FLUID MECH

Paul Durbin

A new definition of concentration fluctuations in turbulent flows is proposed. The definition implicitly incorporates smearing effects of molecular diffusion and instrumental averaging. A stochastic model of two-particle dispersion, consistent with this definition, is formulated. The stochastic model is an extension of Taylor's (1921) model and is consistent with Richardson's

\frac{4}{3}

law. Its predictions of concentration fluctuations are contrasted with predictions based on a more usual one-particle model.

An Experimental Study of the Decay of Temperature Fluctuations in Grid-Generated Turbulence

Article

Oct 1978
J FLUID MECH

Previous measurements of the decay rate of the fluctuation intensity of passive scalars in grid-generated turbulence show large variation. New results presented here show that the decay rate of passive temperature fluctuations produced by heating the grid is a function of the initial temperature fluctuation intensity. Although a full reason for this is wanting, spectra of the temperature fluctuations show that, by varying the heat applied to the grid, the wavenumber of the maximum in the temperature spectrum changes, indicating that the geometry of the thermal fluctuations is being altered in some way. In these experiments the one-dimensional temperature spectrum shows an anomalous

-\frac{5}{3}

slope. In order to eliminate the dependence of the decay rate of the temperature fluctuations on their intensity, we describe a new way of generating temperature fluctuations by means of placing a heated parallel array of fine wires (a mandoline) downstream from the unheated grid. Results of this experiment show that the decay rate of passive thermal fluctuations is uniquely determined by the wave-number of the initial temperature fluctuations. In this type of flow there appears to be no equilibrium value for the thermal fluctuation decay rate and hence for the mechanical/thermal time-scale ratio since the thermal fluctuation decay rate does not change within the tunnel length, which is the equivalent of nearly one turbulence decay time.

Large-eddy simulation of passive scalar in isotropic turbulence

Article

Mar 1981
J FLUID MECH

M. Antonopoulos-Domis

TEMTY, a code for large-eddy simulation of a passive scalar in isotropic turbulence, is developed and proved by successful simulation of experiment. The role of each term in the scalar equation and the concept of prefiltering the scalar equation is examined. The ratio of the exponents in the decay of velocity and temperature intensities is found to parametrize with the ratio lambda //u/ lambda //0, where lambda //u, lambda //0 are the velocity and temperature Taylor microscales respectively. Refs.

The interference of thermal fields from line sources in grid turbulence

Article

Jul 1984
J FLUID MECH

Z. Warhaft

The interference of passive thermal fields produced by two (and more) line sources in decaying grid turbulence is studied by using the inference method described by Warhaft (1981) to determine the cross-correlation coefficient ρ between the temperature fluctuations produced by the sources. The evolution of ρ as a function of downstream distance, for 0.075 < d/l < 10, where d is the wire spacing and l is the integral lengthscale of the turbulence, is determined for a pair of sources located at various distances from the grid. It is found that ρ may be positive or negative (thereby enhancing or diminishing the total temperature variance) depending on the line-source spacing, their location from the grid and the position of measurement. It is also shown that the effects of a mandoline (Warhaft & Lumley 1978) may be idealized as the interference of thermal fields produced by a number of line sources. Thus new light is shed on the rate of decay of scalar-variance dissipation. The thermal field of a single line source is also examined in detail, and these results are compared with other recent measurements.

Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar

Article

May 1982
J FLUID MECH

Results of direct numerical simulations (DNS) for the decay of an initially Gaussian field of turbulence convecting a passive scalar are compared with equivalent results for the direct-interaction approximation (DIA) and the test-field model (TFM). The Taylor microscale Reynolds number Rλ and the equivalent Péclet number Pλ of the comparison ranged from 20–8 and 10–4, respectively. The Prandtl number Pr equals 0·5. Our results show a satisfactory agreement of both theories and numerical simulations, with the DIA giving better overall agreement, especially at small scales. This improved small-scale agreement - which appears to hold up to Rλ [simeq R: similar, equals] 30 - is related to the relatively long coherence times of the small scales, and to the fact that the TFM, containing as it does a built-in compliance to the fluctuation dissipation theorem, cannot properly cope with this fact. We also give a comparison of results for the velocity skewness with the experiments of Tavoularis, Bennett & Corrsin (1978).

Numerical simulation of turbulence

Chapter

Jan 1970

Numerical simulations of three-dimensional homogeneous, isotropic turbulence at windtunnel Reynolds numbers (R 20–40) are reported. The results of the simulations are compared with the predictions of turbulence theories.

PDF Methods for Turbulent Reacting Flows

Article

Jan 1985
PROG ENERG COMBUST

S.B. Pope

The aim of the methods described is to calculate the properties of turbulent reactive flow fields. At each point in the flow field, a complete statistical description of the state of the fluid is provided by the velocity-composition joint pdf. This is the joint probability density function (pdf) of the three components of velocity and of the composition variables (species mass fractions and enthalpy). The principal method described is to solve a modelled transport equation for the velocity-composition joint pdf. For a variable-density flow with arbitrarily complex and nonlinear reactions, it is remarkable that in this equation the effects of convection, reaction, body forces and the mean pressure gradient appear exactly and so do not have to be modelled. Even though the joint pdf is a function of many independent variables, its transport equation can be solved by a Monte Carlo method for the inhomogeneous flows of practical interest. A second method that is described briefly is to solve a modelled transport equation for the composition joint pdf.The objective of the paper is to provide a comprehensive and understandable of the theoretical foundations of the pdf approach.

The probability approach to the modelling of turbulent reacting flows

Article

Aug 1976
COMBUST FLAME

S.B. Pope

The formulation of a closed set of averaged equations to describe a turbulent reacting flow is hindered by highly nonlinear relations between instantaneous quantities. This problem is overcome by considering the joint probability distribution of the scalars characterising the reaction. The transport equations for the single and joint probability distributions are derived and the unknown terms in the single probability distribution equation are modelled. Solutions of the modelled equation are obtained and the results are compared with previous models. The ability of the modelled equation to account for the influence of both turbulent mixing and finite chemical reaction rates is demonstrated.

Higher-Order Derivative Correlations and the Alignment of Small-Scale Structures in Isotropic Numerical Turbulence

Article

May 1985

Robert M. Kerr

The classical approach to the investigation of small-scale intermittency in turbulence is based on the higher-order derivative correlations such as skewness and flatness factors. In the study of the small scales, numerial simulations can provide more detail than experiments. In the present paper, a variety of velocity- and scalar-derivative correlations are calculated over a range of Reynolds numbers. Particular attention is given to third- and fourth-order correlations, taking into account also some fifth- and sixth-order correlations to allow comparisons with the phenomenological models. The governing equations are the incompresssible Navier-Stokes equation for the velocity and transport equation for a passive scalar. Two numerical codes are used for the simulations presented. Attention is given to details regarding the numerical method used, forcing, simulation parameters, spectra and skewnesses, and graphics.

Spectral Methods In Fluid Dynamics

Article

Feb 1987

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

Analysis of the Decay of Temperature Fluctuations in Isotropic Turbulence

Article

Sep 1982

Paul A. Durbin

The Lagrangian dispersion theory of Durbin (1980) is used to analyze experiments by Warhaft and Lumley (1978) and by Sreenivasan et al. (1980) on temperature fluctuations in grid-generated turbulence. Both theory and experiment show that the decay exponent m depends on the ratio of the initial length scales of velocity and temperature, although when this ratio is greater than 2.5 such dependence is negligible. The theory shows that m is not truly constant, but within the range covered by the experiments it is nearly so. The agreement between theory and experiment lends credence to the idea that the decay of fluctuations is controlled largely by turbulent relative dispersion.

Numerical Simulation of Turbulent Flows

Article

Feb 1984

Computational models of turbulence in incompressible Newtonian fluids governed by the Navier-Stokes equations are reviewed. The governing equations are presented, and both direct and large-eddy-simulations are examined. Resolution requirements and numerical techniques of spatial representation, definition of initial and boundary conditions, and time advancement are considered. Results of simulations of homogeneous turbulence in uniform shear, the evolution of a turbulent mixing layer, and turbulent channel flow are presented graphically and discussed.

Direct Numerical Simulations of the Turbulent Mixing of a Passive Scalar

Abstract

No full-text available

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