Reactive jet impingement is a 3D bioprinting process which forms cell filled hydrogels through reacting droplets of polymer and crosslinker solutions. This study evaluates for the first time the relationship between the droplet volumes of the hydrogels with the viscosity and surface tension of the starting solutions. Calcium chloride, sodium alginate, thrombin, and fibrinogen solutions are characterised together with two blended solutions: collagen-alginate-fibrin and thrombin-calcium chloride, which combine to create a collagen-alginate-fibrin hydrogel. The influence of cells on bio-ink behaviour has been assessed through suspending TC28a chondrocytes within the thrombin-calcium chloride solution. Viscosity was a greater differentiator in defining print volumes than surface tension, and there is a clear relationship between droplet volume and kinematic viscosity measured at high strain rates (1000 s-1). The addition of cells had a minimal effect on the kinematic viscosity of solutions at high strain rates and, therefore, on processing of cell filled hydrogels, meaning that processing high cell densities is possible without significant adjustments to processing parameters. Reactive jet impingement is a reliable and accurate process for creating high cell density hydrogels, and the kinematic viscosity at high strain rates is the key mechanical property in defining the relative print volumes of different inks.

SENGA+ is a high-order finite difference compressible direct numerical simulation (DNS) code for simulating turbulent reacting flows. It incorporates detailed chemical reactions and transport with high order numerical schemes to achieve high-fidelity simulations and excellent parallel scaling. This paper presents efforts to deploy SENGA+ on next-generation high-performance computing systems, using the OPS DSL. Key challenges in the process are presented, underpinned by specialized optimizations to gain near-optimal performance on multi-core/many-core systems. OPS enables automatic generation of multiple parallelizations, highly customized for the target architectures, reducing developer effort and increasing code longevity. Performance evaluation demonstrates up to 22× reduction in runtime on a GPU node with 4 AMD MI250X compared to the original CPU-only code. We present validation simulations using the re-engineered application with near-optimal scaling on up to 2k GPUs. The new code enables simulating production-level combustion problems at high-fidelity within tractable time-frames that were previously prohibitively expensive.

An a priori assessment of first-order Conditional Moment Closure (CMC) for turbulent lean H2-air premixed flames was conducted using Direct Numerical Simulation (DNS) data for statistically planar flames with equivalence ratios of 0.4 and 0.7 under varying turbulence intensities. A presumed beta-Probability Density Function (PDF) has been shown to capture the qualitative behaviour of the Favre-conditioned PDF of the reaction progress variable, although quantitative discrepancies remain. Existing models for conditional mean velocity perform satisfactorily, while conditional scalar dissipation rate models reproduce DNS trends qualitatively but with quantitative discrepancies linked to inaccuracies in Favre-averaged scalar dissipation rate and PDF predictions. First-order CMC predicts conditional mean reaction rates accurately for H2 and H2O but overpredicts O2 reaction rates due to elevated conditional variance. DNS data also reveal counter-gradient conditional scalar fluxes associated with sub-unity Lewis number effects, highlighting the need for improved scalar flux closures.

The evaporation of a thin liquid film representative of power-law rheology flowing along an inclined channel wall under the combined influence of gravity and surface tension is investigated using a semi-analytical modelling framework. The evolution of film thickness, heat transfer characteristics, and dry-out behaviour are examined as functions of the power-law exponent, Weber number, and inlet film thickness. The results show that a decrease in the power-law exponent leads to a slower reduction in film thickness, resulting in a significant increase in the dry-out length for a fixed value of consistency. This behaviour is attributed to the large effective viscosity developing near the free surface for shear-thinning fluids, in contrast to the negligible surface viscosity observed for shear-thickening fluids. The local Nusselt number increases gradually along the flow direction, followed by a sharp terminal rise marking the onset of dry-out. The mean Nusselt number decreases with increasing power-law exponent, which is consistent with the dry-out length variation with the power-law exponent. The dry-out length is found to be largely insensitive to surface tension for a fixed normalised inlet film thickness, while exhibiting an approximately linear dependence on the inlet film thickness that is nearly independent of the power-law index. Overall, the study establishes a hierarchy of controlling parameters for evaporating power-law films in inclined micro-channels, demonstrating that inlet film thickness primarily governs the dry-out location, while rheology and surface tension exert secondary influences within the parameter ranges considered.

The influence of the fuel Lewis number LeF on Reynolds stresses and their transport during flame–wall interaction (FWI) is studied using a direct numerical simulation database of oblique wall-quenching of V-shaped premixed flames in a turbulent channel flow. Simulations are conducted for LeF=0.6,1.0, and 1.4. Results indicate that LeF significantly affects the magnitude and anisotropy of the Reynolds stresses. In these cases, the location of the FWI is affected by LeF, with the flame at LeF=0.6 interacting closest to the flame holder, while the flame with LeF=1.4 interacts farthest from the flame holder. The wall-normal distributions of the Reynolds stress components deviate significantly from those recorded in the non-reacting turbulent channel flows, with deviations strongly influenced by LeF. The production of the streamwise Reynolds stress component by the mean velocity gradient exceeds sink contributions from other terms, especially downstream of the FWI region. The pressure–strain term plays a dominant role in Reynolds stress transport in the spanwise direction, facilitating Reynolds stress redistribution. In particular, local equilibrium between the generation and dissipation of Reynolds stresses is not achieved, particularly as LeF decreases, leading to anisotropy of Reynolds stresses. These findings highlight the impact of LeF on near-wall flow dynamics and the production, redistribution, and dissipation of Reynolds stresses. The study provides valuable information for improving turbulence models for Reynolds-averaged Navier–Stokes simulations of FWIs under varying LeF conditions, advancing the understanding of turbulent boundary layer flows with premixed flames.

A Flame Surface Density (FSD)-based mean reaction rate closure modified for flame-wall interaction (FWI) in the Bray-Moss-Libby (BML) modeling framework is implemented for RANS simulations in two configurations at turbulent friction Reynolds number $R{e_\tau } = 110$Re tau=110. The first configuration is the oblique wall quenching of a V-shaped premixed flame in a turbulent channel flow, and the second configuration is the head-on quenching of a statistically planar flame in a turbulent boundary layer. RANS simulations have been performed based on standard values of the FSD-based mean reaction model parameters and different choices of the correction factor to account for near wall quenching. A comparison is presented between the Favre mean values of the reaction progress variable and the nondimensional temperature obtained from RANS simulations and the corresponding DNS data. The RANS simulations, employing standard FSD model parameters and a correction factor calibrated using DNS results to account for near-wall quenching capture the Favre mean streamwise velocity and temperature reasonably well. However, discrepancies are observed between the predicted Favre mean reaction progress variable and the corresponding DNS results. These discrepancies are primarily attributed to two sources: (1) inaccuracies in the predicted turbulent kinetic energy and dissipation rate and (2) errors arising from estimating the Reynolds-averaged reaction progress variable from its Favre-averaged counterpart. Despite these disagreements, the FSD-based mean reaction rate closure shows promise in predicting Favre mean velocity and temperature in RANS simulations of premixed flame-wall interaction using the near wall modifications considered in this work.

A scalar dissipation rate-based mean reaction rate closure modified for premixed flame-wall interaction, which was previously proposed based on a priori Direct Numerical Simulation (DNS) analysis, is implemented for Reynolds Averaged Navier-Stokes (RANS) simulations in two configurations. The first configuration is the oblique wall quenching of a V-shaped premixed flame in a turbulent channel flow, and the second configuration is the head-on quenching of a statistically planar flame in a turbulent boundary layer. To avoid uncertainties associated with wall functions in reacting flows, a low Reynolds number k - ε model that resolves the viscous sub-layer is used. Comparisons between RANS simulations using the modified closure and DNS data reveal satisfactory agreement for Favre mean streamwise velocity and Favre mean temperature. However, quantitative discrepancies are found in the predictions of the Favre-averaged reaction progress variable due to differences in mean reaction rate profiles between DNS and RANS results. This behaviour arises from differences in turbulence quantities (e.g. turbulent kinetic energy and dissipation rate) between RANS and DNS, leading to discrepancies in RANS predictions of the mean reaction rate and Favre-averaged scalar dissipation rate, despite these closures performing well in a priori analysis. Even with these discrepancies, the scalar dissipation-based mean reaction rate closure shows promise in predicting mean values of Favre-averaged streamwise velocity and non-dimensional temperature in premixed flame-wall interaction configurations.

In this study, Direct Numerical Simulations are utilized to investigate turbulent premixed NH3/air flames assisted by two distinct methods: non-equilibrium nanosecond plasma discharges and preheating, while maintaining equal input energy levels for both methods. The results show that plasma is more effective than preheating in increasing the turbulent burning velocity, namely by up to 31% under lean and by 26% in rich conditions. Furthermore, the flame structure is less affected by turbulence when using plasma. A negative correlation between flame displacement speed and local flame curvature is observed for all cases. Furthermore, negatively curved parts of the flame front are dominated by the reaction mode of combustion. In contrast, the positively curved parts are controlled by flame propagation mode in both preheated and plasma-assisted cases. It is shown that, when plasma is utilized, NO emissions are less sensitive to local heat release rate, and the amount of NO emissions is found to be 19% lower in comparison to the preheated case.

The influence of fuel Lewis number LeF on the wall-normal variations of mean values of streamwise velocity component, temperature, and Reynolds stresses within turbulent boundary layers have been analysed using a Direct Numerical Simulation (DNS) database of oblique wall quenching of V-shaped premixed flames due to their interaction with inert isothermal walls in a turbulent channel flow configuration. The fuel Lewis numbers of LeF = 0.6, 1.0 and 1.4 have been considered for the current analysis. It has been found that the flame starts to interact with the wall further upstream for a smaller value of LeF due to an augmentation of the volume-integrated burning rate with a decrease in fuel Lewis number. The thermal expansion induced by heat release affects the variations of mean values of both streamwise velocity component and temperature in the wall-normal direction and they show significant deviations from the conventional log-law profiles. Recently proposed density-compensated modified wall functions for streamwise velocity and non-dimensional temperature, which were previously validated for head-on quenching configuration for unity Lewis number, are found to capture the corresponding behaviours extracted from DNS data for flame-wall interaction of V-shaped flames with non-unity LeF. The wall-normal distributions of Reynolds stresses also deviate significantly from the corresponding non-reacting fully developed channel flow profiles during flame-wall interaction and LeF affects the extent of this deviation. The anisotropy of Reynolds stresses has been found to increase with the progress of flame-wall interaction. The physical explanations for the observed mean velocity, mean temperature and Reynolds stress statistics have been provided and their implications for modelling of flame-wall interaction have been elaborated.

Direct numerical simulations (DNS) of laboratory-scale turbulent premixed Bunsen flames have been conducted and compared with an experimental dataset encompassing three methane-hydrogen flames with volumetric hydrogen fractions of 0%, 40% and 70%. The Bunsen flames are representative of the strict flamelet regime of combustion with low turbulence intensity, which allows for the analysis of the effects induced by the combined action of Darrieus-Landau instability and non-unity Lewis number effects. The chemical aspect of DNS is treated using irreversible one-step Arrhenius chemistry, where the effective Lewis number has been determined based on a suitable calculation of the fuel mixture Lewis number along with an appropriate blending with the oxidiser Lewis number. A comparison between 2D experimental flame imaging and 3D DNS results reveals good agreement regarding mean flame shape, flame morphology, turbulent flame wrinkling, and turbulent burning velocity. This shows that simple chemistry simulations with appropriately chosen effective Lewis numbers can accurately describe turbulent burning velocity and flame-turbulence interaction for methane-hydrogen fuel blends. Provided emissions and ignition are not within the focus of the study, this might be very useful for conducting large-scale turbulent combustion simulations or large parametric studies of carbon-free or carbon-reduced fuels, which are enablers for the transformation of the energy industry into a climate-neutral circular economy.

In this study, we use direct numerical simulations to investigate turbulent premixed ammonia flames assisted by non-equilibrium nanosecond plasma discharges and hydrogen addition. The results reveal the coupling effects of turbulence, the hydrogen concentration in the fuel blend, and plasma discharges on the microscopic structure of the flame and chemical pathways. It is found that the flame front assisted by plasma is more distributed, whilst 58 % less stretched when compared to the hydrogen-enriched un-assisted flame. Additionally, turbulence has more pronounced effects on the hydrogen-enriched flame, broadening the flame brush. A comparison of the reaction pathways contributing to the heat release indicates that turbulence shifts the key reactions producing heat from HNO+H=NO+H2 and OH+H2=H + H2O to NH2 dissociation reactions. Additionally, NOx emissions are more influenced by thermal effects in the hydrogen-enriched flame, with NO concentration being 35 % higher than in the plasma-assisted flame. The higher NOx emissions in the hydrogen-enriched flame are attributed to the higher concentration of H radicals, which react with HNO and produce NO.

A scaling relation has been derived to link the fractal dimension of a flame surface with the ratio of the normalised 3D flame surface area to its 2D counterpart. This derivation assumes an isotropic distribution of angles between the measurement plane and the flame’s normal vector, as well as a uniform distribution of angles between the principal direction and the flame’s tangent vector. The validity of the newly derived relation was assessed using an existing Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames, encompassing a range of different Karlovitz numbers. The DNS data-based assessment revealed that the newly derived relations are reasonably accurate for the thin reaction zones regime flames, with the precision of predictions based on isotropy improving, as the Karlovitz number increases. Moreover, 2D measurements of the flame surface fractal dimension and the flame wrinkling factor can be effectively used to predict the actual 3D flame wrinkling factor for flames with Karlovitz numbers much greater than unity. Alternatively, the ratio of the 3D wrinkling factor to its 2D counterpart can provide a reasonable estimate of the 3D fractal dimension for flames in the thin reaction zones regime. The newly derived relations provide an estimation for the value of fractal dimension in the limit of high Karlovitz number using an alternative route.

The effects of droplet diameter, overall equivalence ratio (0.8–1.5), and primary evaporation zone length (2–10 mm) on the burning velocity and thermal flame thickness in laminar n-heptane monodisperse spray flames under varying pressures (1.0–2.0 bar) have been analysed using 1D numerical simulations. It is observed that for gaseous premixed flames, both flame speed and thickness decrease with increasing pressure. However, in spray flames, flame thickness increases while burning velocity decreases as pressure rises, primarily due to reduced evaporation rates that limit fuel vapor availability. Larger droplet sizes further diminish evaporation rates, which lowers burning velocity and increases flame thickness, regardless of pressure. The finite evaporation rate also results in local equivalence ratios that are lower than the overall equivalence ratio in the heat release zone within the flame, especially at high pressures and with large droplets. In overall fuel-rich mixtures (e.g., for an overall equivalence ratio of 1.5), this can lead to more reactive gaseous mixtures and higher burning velocities than corresponding gaseous premixed flames, particularly for small droplets. Notably, the burning velocity in some spray flames can exceed the burning velocity of the corresponding premixed flames at the same gaseous-phase equivalence ratio at the heat release rate location. Enhanced burning velocity is also attributed to the generation of reactive species (e.g., H₂, C₂H₂, C₂H₄) from droplet evaporation and pyrolysis behind the flame front, which diffuse back into the reaction zone and accelerate the combustion process. However, the formation of these species diminishes at higher pressures, reducing this enhancement effect.

This study investigates preferential diffusion effects on the volume-integrated burning rate in turbulent premixed lean hydrogen/air flames, using 3D direct numerical simulations (DNS) to analyze flames at two global equivalence ratios and varying turbulence intensities. By examining the statistical distributions of local equivalence ratios, the analysis confirms pronounced preferential diffusion effects across all cases. Intenser turbulence tends to amplify these effects. Probability density functions (PDFs) of the local equivalence ratio further confirm stronger preferential diffusion at lower global equivalence ratios and significant sensitivity to the choice of reaction progress variable definitions, particularly between hydrogen-based and water-based definitions. To predict the impact of preferential diffusion, the volume-integrated burning rate is estimated by multiplying the laminar burning velocity for the local equivalence ratio with the probability density function of the local equivalence ratio distribution. The subsequent estimates are compared to corresponding values directly obtained from DNS data. Results show that, in cases where preferential diffusion effects are more pronounced, i.e. at lower global equivalence ratios and relatively higher turbulence intensities, the DNS-derived burning rates based on water and temperature progress variables are best approximated using burning rates computed from the local equivalence ratio field conditioned on positive mean curvature. In contrast, cases less affected by preferential diffusion yield burning rate per unit area values comparable to those in the unstretched laminar flames when evaluated using water- and temperature-based definitions. The findings suggest that the burning rate per unit flame area could be modeled using the laminar burning velocity corresponding to the local equivalence ratio, and presumed PDFs representing the distributions of the local equivalence ratio. The gamma (or beta) distribution has been found to reasonably approximate the PDF of the local equivalence ratio, which can be utilized for the modeling of the volume-integrated burning rate in premixed turbulent lean hydrogen/air flames.

The statistical behaviors of the two-point spatial correlations of the turbulent velocity fluctuations based on Reynolds decomposition, Favre decomposition, and density-compensated Favre decomposition have been analyzed at different wall-normal distances for different stages of head-on quenching of premixed flames due to wall heat loss within turbulent boundary layers. Using a Direct Numerical Simulation database for friction Reynolds numbers Re-tau of 110 and 180, it has been demonstrated that Favre fluctuation-based correlations differ quantitatively from Reynolds and density-compensated Favre fluctuation correlations, particularly in the early stages of quenching and when the flame is away from the wall. Despite these differences, the overall qualitative trends remain unaffected by the choice of definition of spatial correlations. As quenching progresses, the quantitative differences reduce due to weakening thermal expansion effects and increasing presence of burned gas in the boundary layer. This effect is strongest for wall-normal velocity fluctuations, as flame-normal acceleration due to thermal expansion primarily influences this direction in this configuration. However, momentum redistribution due to this flame normal acceleration also impacts streamwise and spanwise velocity correlations. These effects manifest in the integral length scales derived from two-point spatial correlations, with their variations evolving as quenching progresses. The longitudinal integral length scale in the streamwise direction exhibits the highest peak value among all considered length scales. While qualitative behaviors of correlations and integral length scales remain largely unaffected by the variation in Re-tau considered here, a higher Re-tau results in a broader wavenumber range before viscous roll-off occurs in the one-dimensional velocity spectrum. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

The statistical behaviours of wall heat flux and wall shear stress and their interdependence during unsteady head-on quenching of statistically planar turbulent premixed flames within turbulent boundary layers due to heat loss through the cold wall have been analysed using three-dimensional Direct Numerical Simulation data with friction Reynolds numbers of Re_τ =110 and 180. In both cases, the mean wall shear stress decreases during flame-wall interaction, whereas the mean wall heat flux magnitude increases with time as the flame approaches the wall and eventually assumes a maximum value before decreasing with the progress of flame quenching. The integral length scales of wall heat flux in both streamwise and spanwise directions have been found to grow with time after the maximum mean heat flux magnitude is obtained for the two Re_τ cases considered. However, the integral length scale of wall shear stress in the streamwise direction grows but the integral length scale of wall shear stress in the spanwise direction decreases with time after the maximum mean heat flux magnitude is reached. Moreover, the correlation coefficient between the wall heat flux magnitude and wall shear stress becomes increasingly negative while the mean wall heat flux increases with time, but this negative correlation weakens with the progress of flame quenching. The first few (i.e., most energetic) Proper Orthogonal Decomposition (POD) modes of wall shear stress and the wall heat flux magnitude have been found to capture the qualitative nature of the correlation between these quantities and their spatial variations. It is found that tens of most energetic POD modes are needed to capture the mean and variances of wall heat flux and wall shear stress. The number of most energetic modes, which contribute significantly to the statistics of both wall heat flux and wall shear stress, decreases with decreasing Re_τ and also with the progress of flame quenching due to the weakening of turbulence effects.

This study investigates the influence of differential and preferential diffusion on turbulent burning velocity and flame surface area in premixed NH3/H2/N2-air flames using a three-dimensional Direct Numerical Simulation (DNS) database of statistically planar flames. The analysis covers three fuel blends-pure NH3-air, 60 %NH3/25 %H2/15 %N2-air, and 40 %NH3/45 %H2/15 %N2-air-all at an equivalence ratio of 0.81, falling within the thin reaction zones regime on the Borghi-Peters diagram. Both the normalised flame surface area (by the projected area in the mean propagation direction) and the turbulent-to-laminar burning velocity ratio are generally comparable (but not equal) across the different fuel blends. However, the normalised flame surface area is found to be smaller than the corresponding normalised turbulent burning velocity, especially in cases involving nonunity Lewis numbers. This discrepancy highlights the impact of differential and preferential diffusion. Among the mixtures studied, the NH3-air flame exhibits the highest effective Lewis number and correspondingly the lowest values of normalised flame surface area and turbulent burning velocity ratio. Despite these variations, the similarity between the normalised surface area and burning velocity across cases lends partial support to Damkohler's first hypothesis. Moreover, the second Damkohler hypothesis reasonably estimates the order of magnitude for the normalised turbulent burning velocity. Overall, the findings suggest that conventional turbulent combustion models relying upon Damkohler's hypotheses may remain valid for hydrogen-enriched ammonia-air flames under the studied conditions, despite the presence of differential and preferential diffusion effects.

Direct numerical simulations (DNS) have been utilised to investigate the impact of different thermal wall boundary conditions on premixed V-flames interacting with walls in a turbulent channel flow configuration. Two boundary conditions are considered: isothermal walls, where the wall temperature is set either equal to the unburned mixture temperature or an elevated temperature, and adiabatic walls. An increase in wall temperature has been found to decrease the minimum flame quenching distance and increase the maximum wall heat flux magnitude. The analysis reveals notable differences in mean behaviours of the progress variable and non-dimensional temperature in response to thermal boundary conditions. At the upstream of the flame-wall interaction location, higher mean friction velocity values are observed for the case with elevated wall temperature compared to the other cases. However, during flame-wall interaction, friction velocity values decrease for isothermal walls but initially rise before decreasing for adiabatic walls, persisting at levels surpassing isothermal conditions. For all thermal wall boundary conditions, the mean scalar dissipation rates of the progress variable and non-dimensional temperature exhibit a decreasing trend towards the wall. Notably, in the case of isothermal wall boundary condition, a higher scalar dissipation rate for the non-dimensional temperature is observed in comparison to the scalar dissipation rate for the progress variable. Thermal boundary condition also has a significant impact on Reynolds stress components, turbulent kinetic energy, and dissipation rates, showing the highest magnitudes with isothermal case with elevated wall temperature and the lowest magnitude for the isothermal wall with unburned gas temperature. The findings of the current analysis suggest that thermal boundary conditions can potentially significantly affect trubulence closures in the context of Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction.

The study analyses the segregation of NH3 and H2 in globally lean premixed turbulent flames of NH3/H2 fuel blends using direct numerical simulation (DNS) data of statistically planar turbulent flames. Turbulent premixed flames for two fuel blends, 60%NH3/25%H2/15%N2 and 40%NH3/45%H2/15%N2, with an equivalence ratio of 0.81, were examined in the thin reaction zones regime. Differences in chemical reactivity and differential diffusion between NH3 and H2 lead to local variations in equivalence ratio within the flame, significantly affecting species distribution compared to one-dimensional (1D) laminar premixed flames. The equivalence ratio variation within the flame causes locally either stoichiometric or fuel-rich pockets despite the globally lean condition in the cases considered here. This also enables localised diffusion mode burning, which is stronger for H2 in the 60%NH3/25%H2/15%N2 blend, whereas it is stronger for NH3 in the case of 40%NH3/45%/15%N2 H2 blend. The transition from lean premixed to non-premixed combustion at the rear end of the flame leads to the misalignment of the normal vectors of NH3, H2, and temperature isosurfaces, impacting reaction-diffusion balance. The displacement speeds of H2 isosurfaces exceed those of NH3, leading to differences in effective normal strain rates, which along with local equivalence ratio variation, influence the behaviour of the scalar gradient magnitude. These findings suggest that the modelling of premixed combustion of NH3/H2 blends must account for variable equivalence ratio combustion and non-premixed burning mode, even for globally lean mixtures.

The interrelation between displacement speed and dilatation rate in premixed turbulent flames has been analysed using three-dimensional Direct Numerical Simulation (DNS) data. The study focuses on statistically planar turbulent premixed flames with single-step chemistry at a unity Lewis number, representing stoichiometric methane-air premixed combustion, and detailed chemistry NH3-air premixed flames with an equivalence ratio of 1.2. It has been shown analytically that the dilatation rate based on fluid velocity is proportional to the product of the density-weighted displacement speed and the reaction progress variable gradient for unity Lewis number adiabatic conditions. This is demonstrated using unity Lewis number single-step chemistry DNS data and detailed chemistry DNS results of NH3-air premixed flames with an effective Lewis number close to unity. The study reveals that density-weighted displacement speed positively correlates with dilatation rate based on fluid velocity, though the relationship is non-linear due to the non-linear relationship between density-weighted displacement speed and the reactive scalar gradient magnitude. The density-weighted displacement speed and the dilatation rate based on flame propagation velocity are negatively correlated for the flames belonging to the wrinkled/corrugated flamelets regime, while their joint PDFs in thin reaction zones regime flames show both positive and negative correlation branches. The curvature stretch rate primarily causes these positive and negative correlation branches, a tendency that strengthens with an increase in Karlovitz number. Additionally, the mean dilatation rate in premixed turbulent flames is found to be proportional to the mean reaction rate in Reynolds Averaged Navier-Stokes simulations, suggesting that the mean dilatation rate could be linked to mean reaction rate closure.