Collision statistics of same-size aerodynamically interacting droplets in homogeneous isotropic turbulence is examined via hybrid direct numerical simulations combined with Lagrangian particle tracking under a point-particle assumption and a one-way momentum coupling. The simulations are performed both in the absence and presence of gravity for various droplet Stokes numbers (0.1–2) over a wide range of liquid water contents (LWCs = 1–30 \(\text {g/m}^3\)). Also, the effects of using different representations of the lubrication forces, i.e. a continuum and a non-continuum one, have been investigated. The results have highlighted the importance of considering the aerodynamic interaction, especially in the presence of gravity for the systems that have high LWCs. Likewise, taking the lubrication force into account shows a notable change in statistics, but a non-continuum representation yields results that are close to the continuum one. In addition, the impact of modeling droplets as fluid drops instead of rigid particles has been examined. Obtaining quite close statistics under both cases demonstrates that a rigid particle assumption for water droplets in air is sufficiently accurate owing to the high water-to-air viscosity ratio. Moreover, the collision efficiency is shown to be in the range 60–100% in the absence of gravity, which approaches 100% as the LWC is enlarged. In the presence of gravity, however, the efficiency grows, with both the Stokes number and the LWC, to values as high as 300%. Finally, for settling droplet systems, the enhancement factor due to turbulence is quantified, exhibiting a growth with the LWC and a reduction with the Stokes number.

The drag reduction of high molecular polymer solutions is well known as the Toms effect. The drag reduction can be divided into two types: Type A and B. Type A corresponds to the solutions of synthetic polymers such as polyethylene oxide or polyacrylic amide. In contrast, Type B corresponds to the solutions of biopolymers such as xanthan gum, guar gum, and polysaccharide. Experiments were performed to measure the friction factor and heat transfer coefficient for the aqueous suspensions of graphene oxide thin-plate particles. The results show that the complex fluids exhibit a Type B drag reduction phenomenon in the turbulent flow range. The onset point of the drag reduction was found to be \(Re\sqrt{f}\cong 260\) for Cw = 0.1 wt%. This point increased compared to the experimental results for Cw = 0.5 wt% graphene oxide solutions that have been reported on drag reduction. The velocity profiles of the aqueous suspensions of graphene oxide thin-plate particles and the dried malted rice culture solutions classified as biopolymer were estimated from the experimental data of the friction factor. In general, aqueous suspensions of fine particles are characterized by an increase in the friction factor and the heat transfer coefficient as compared to water. However, the aqueous suspension of the graphene thin-plate particles produces the drag reduction of the friction factor and increases the heat transfer coefficient. Therefore, the experimental results obtained in this study show that graphene oxide shin-plate particle suspensions become a useful carrier for the cooling pipeline system.

A Direct Numerical and Large Eddy Simulation study is conducted to establish the NASA CS0 diffuser as a test case for scale-resolving simulation methods and to evaluate the ability of such simulations to accurately predict flows with adverse pressure gradients and shallow separation from a smooth surface. The results of fine grid studies are in a good agreement with experimental data and substantially supplement them. These data are used as a basis for testing of LES on reduced grids, using different combinations of wall treatments and turbulence model formulations.

The influence of mixture stratification on the development of turbulent flames in a slot-jet configuration has been analysed using Direct Numerical Simulation data. Mixture stratification was imposed at the inlet by varying the equivalence ratio between 0.6 and 1.0 with different alignments to the reaction progress variable gradient: aligned gradients (back-supported), opposed gradients (front-supported) and misaligned gradients. An additional premixed case with a global equivalence ratio of 0.8 was simulated for comparison. The flame is shortest for the front-supported case, followed by the premixed flame, with the back-supported and misaligned gradient flames being the tallest and of comparable size. This behaviour has been explained in terms of the variations of the mean equivalence ratio within the flame and the volume-integrated reaction rate in the streamwise direction. The difference in mixture composition for these cases results in significant variations in the burning rate, flame area, flame wrinkling and flame brush thickness in the streamwise direction. The globally front-supported case has the highest volume-integrated burning rate and flame area, while the back-supported case has the lowest. The misaligned scalar gradient case exhibits qualitatively similar behaviour to that of the globally back-supported case. The burning intensity is unity for a major part of the flame length but assumes values greater than unity towards the flame tip where the effects of flame curvature become strong. All cases predominantly exhibit the premixed mode of combustion within the flamelet regime, so flamelet assumption-based reaction rate closures, originally proposed for premixed combustion, were evaluated using a priori analysis. The terms which require improved closures have been identified and existing closures have been improved where necessary. It was found that the global nature of mixture stratification does not influence the performance of the mean reaction rate closures or the parameterisation of marginal probability density functions of scalars in turbulent stratified mixture combustion.

The preferential concentration of sedimenting particles in decaying homogeneous isotropic turbulence is investigated using radial distribution functions (RDF). Direct numerical simulations of polydisperse distributions of non-sedimenting and sedimenting particles of radii 10–55 μm are performed. We see a power law behaviour for the RDF in decaying turbulence and the power-law relation derived by Chun et al. (J Fluid Mech 536:219–251, 2005) for the RDF of non-sedimenting particles holds for sedimenting particles as well. Empirical formulas are generated for the power-law coefficients which are shown to be functions of the Stokes number and the Taylor Reynolds number for sedimenting particles. An in-depth analysis of the turbulent kinematic collision kernel for both non-sedimenting and sedimenting collision kernels confirms that gravity enhances the collision kernel for unequal sized particles and decreases for same-sized particles. Models are created for both monodisperse and bidisperse RDFs which are combined with existing models for the conditional radial relative velocities of colliding particles to predict kinematic collision kernels for both non-sedimenting and sedimenting particles. The effect on the collision kernel due to turbulence is also explored and enhancement of factors of up to three is observed with respect to the gravitational collision kernel.

A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier–Stokes equations is presented. The classical SD algorithm is shown to be unstable for test cases involving a multi-species gas whose thermodynamic properties depend on temperature and species mass fractions. It is observed that the extrapolation of conservative variables from the solution points to the flux points is the origin of the instability produced by the classic SD algorithm. An alternative scheme, where primitive variables are computed at the solution points and then extrapolated to the flux points, is shown to make the SD method stable for such cases. In addition, a new, more stable methodology for computing the diffusive fluxes at an interface is detailed. To allow the simulation of combustion, characteristic and wall boundary conditions for multi-species flows in the SD framework are introduced, and the thickened flame turbulent combustion model is adapted to the SD context. Validation test cases from one-dimensional and two-dimensional laminar flames to a three-dimensional turbulent flame are performed showing excellent agreement with each of the reference solutions. To the authors’ knowledge, this is the first time that a 3D turbulent flame is simulated using the SD method. The interest of employing a high-order method, such as the SD, in combustion is demonstrated: high values of the polynomial degree improve the quality of the results which advocates for the use of p-refinement when simulating reacting flows.

Clean and efficient combustion of liquid fuels depends on spray fineness that aids fast fuel vaporization and better fuel–air mixing. Swirl-burst (SB) atomizers generate fine droplets at the injector exit rather than typical jet cores as seen in the conventional atomizers. It integrates the primary breakup by bubble bursting of the Flow Blurring (FB) atomization, and secondary atomization by Rayleigh–Taylor instabilities between the swirling atomizing air and liquid phase. Thus, SB atomization has achieved clean lean-premixed flames of fuels with distinct properties involving diesel and straight oils around fifteen times more viscous. This study gains insights into the effect of the varying internal geometry, H/D ratio, on the atomization process and quantitatively investigates these effects on the near-field spray characteristics of SB injectors using high-spatial-resolution Shadowgraph Imaging Technique (SIT) and particle image velocimetry (PIV) for water sprays. Results acquired by SIT show that the Sauter Mean Diameter (SMD) of the droplets decrease with the reducing H/D ratio. The PIV measurements quantitatively reveal that atomization completion length decreases as the H/D ratio is lowered. Weber number analysis signifies that mostly vibrational and occasionally bag breakup dominates the secondary atomization for all the three H/D ratios. Results also reveal the high scalability of SB concept and its doubled atomization efficiency compared to FB injection.Graphical Abstract

Thickened flame models are prolific in the literature and offer an effective method of resolving flame dynamics on coarse LES meshes. The current state of the art relies heavily on the use of efficiency functions to compensate for impaired wrinkling of the thickened flame. However in practice these functions can involve parameters that are difficult to determine, perform poorly outside of certain ranges or require a posteriori analysis to evaluate performance. An alternative based on a generalised thickening is evaluated across a range of canonical configurations. The approach is demonstrated to perform well across a large range of thickening factors in capturing phenomena such as localised quenching and pinch off as well as generation of flame surface. Including good performance even in the case of large flame dynamics under acoustic forcing where the model has a clear advantage over DNS in achieving grid independence. Finally the approach is unified into an Large Eddy Simulation/Adaptive Mesh Refinement framework and applied to a turbulent Bunsen flame. The results show that even if the internal flame structure is poorly resolved on the original mesh, the global system behaviour is well predicted and compares favourably with other approaches.

The influence of flow configuration on flame-wall interaction (FWI) of premixed flames within turbulent boundary layers has been investigated. Direct numerical simulations (DNS) of two different flow configurations for flames interacting with chemically inert isothermal and adiabatic walls in fully developed turbulent boundary layers have been performed. The first configuration is an oblique wall interaction (OWI) of a V-flame in a turbulent channel flow and the second configuration is a head-on interaction (HOI) of a planar flame in a turbulent boundary layer. These simulations are representative of stoichiometric methane-air mixture under atmospheric conditions and the non-reacting turbulence for these simulations corresponds to the friction velocity based Reynolds number of \(Re_{\tau }=110\). It is found that the mean wall shear stress, mean wall friction velocity and the mean velocity statistics are affected during FWI and the behaviour for these quantities varies under the different flow configurations as well as for the different thermal wall boundary conditions. The behaviour of the quenching distance and mean wall heat flux under isothermal wall conditions is found to be significantly different between the two flow configurations. The variation of the non-dimensional temperature in wall units for cases with isothermal walls suggests that the temperature in the log-layer region is significantly altered by the evolving wall heat flux in both flow configurations. Statistics of the mean Reynolds stresses and turbulence dissipation rate show that the flame significantly alters the behaviour of turbulence due to thermal expansion effects and flow configuration plays an important role.

Due to the proprietary nature of modern motorsport and Formula 1, current scientific literature lacks relevant studies and benchmarks that can be used to understand flow physics in this area, as well as to test and validate new simulation methodology. With the release of a new, open-source geometry (the Imperial Front Wing), we present a computational study of a multi-element aerofoil at a ride height of 0.36h/c and a Reynolds number of \({\mathbf{2}}{\mathbf{.2 \times 10}}^{{\mathbf{5}}}\). A 0.16c slice of the Imperial Front Wing has been examined using high-order spectral/hp element methods. Time averaged force data is presented, finding lift and drag coefficients of \(-\)8.33 and 0.17 respectively. Unsteady analysis of the force and surface pressure data has allowed salient feature identification with respect to the transition mechanisms of each element. The mainplane and flap laminar separation are studied and the cross-spectral phase is presented for the lower frequency modes. At \(\varvec{St = 40}\) an in-phase relationship is identified between mainplane and flap laminar separation bubbles, whilst at \(\varvec{St = 60}\) a distinct out-of-phase relationship is observed. Wake results, including wake-momentum deficit and turbulent kinetic energy are presented, which show wake meandering and subsequent breakdown due to a Kelvin–Helmholtz instability. These results, in particular the transition mechanisms, will allow for the construction of a dataset to validate novel methods in this area.

This paper examines the potential of using ammonia (NH\(_3\)) as a primary fuel in heavy-duty engines for decarbonization, with some challenges yet to be addressed. It presents a numerical study of a Reactivity Controlled Compression Ignition engine, where pilot diesel is used to ignite the premixed ammonia/air mixture. The numerical model and combustion mechanism are validated against engine experimental results using methanol and iso-octane fuels and ignition delay times of ammonia/n-heptane mixtures measured in a rapid compression machine. The findings show that the engine can effectively operate with up to 50% of the total energy supplied by premixed ammonia, albeit with slightly elevated NO emissions compared to a diesel-fueled engine. Increasing ammonia further leads to lower combustion efficiency. Hydrogen can be utilized in the ammonia engine to enhance ammonia combustion; however, NO emissions increase further. Ammonia leakage primarily originates from regions near the cold wall, the center of the cylinder, and the crevice. N\(_2\)O mainly forms at the ammonia flame front. Emission of N\(_2\)O is therefore mainly due to flame front quenching near the wall.

We investigate the precursor coherent flow structures and their interactions with spray that are responsible for the stabilization of lifted spray flames of Jet A1 gel fuel on a bluff body–assisted burner of low blockage ratio. Our approach is based on the description of experimental observations of the cold spray and swirling lifted flames on a laboratory burner, followed by the cold flow computations of gas and liquid phase flow fields carried out on the same burner. Anisotropy of the highly swirling and three–dimensional turbulent flow and inherently high pressure strain were resolved using the quadratic pressure strain–Reynolds stress model, followed by computations of droplet trajectories using their Lagrangian discrete phase and one-way coupled description. Same flow was also computed as a large eddy simulation (LES) while retaining the one-way coupling. The flow and droplet dispersion models were validated using experimental data, independent validation test data, and single-grid LES. Our emphasis on resolving large–scale coherent structures during modeling and rigorous validation tests yields accurate predictions of the flow structures, lift–off height, undisturbed spray height, and spray droplet distributions. Gas–phase flow field of a compound jet system comprising annular combustion air and round spray jet was found to be dominated by the flow structures associated with the round jet. A complex system of vortices that controlled the distribution and mixing of the dominant 3–23 μm size fuel droplets with combustion air in the flame stabilization region was also extracted and described. Cold flow field computed by LES provided an accurate prediction of streamline curvature caused by loss of coherence of a three-vortex system influencing the spray jet.

Motivated by the growing concerns for the noise emissions generated by the interaction between the engine jet and the airframe surfaces consequent to the progressive increase of the engine by-pass ratio in commercial aircraft architectures, we study the estimation of the far-field noise radiated by a jet in an installed configuration based on sensor readings in the near field of the jet. We carry out an experimental investigation of the jet-surface interaction phenomena in a simplified set-up where a flat plate is installed parallel to the nozzle axis of a subsonic jet. Real-time estimation is performed using empirical linear transfer functions identified between near-field sensors and far-field observers. The transfer function and the accuracy of the noise estimation performed are characterised as a function of jet flow conditions, type and streamwise position of near-field sensors and radial distance between the jet and the edge. This analysis can guide the positioning of near-field sensors for the implementation of closed-loop control strategies for the jet-surface interaction noise.

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

In this work, three-dimensional computational technique is adopted to predict the behavior of flames stabilized over the heat flux burner. The reactive fluid dynamics simulations were performed with ANSYS Fluent®. The configuration of the burner, with prime focus on effect of porosity, is altered to visualize its effect on the flatness of the flames developed over the heat flux burner. The results indicated that, to stabilize wrinkle-free flat stoichiometric flames over the top of burner plate, the burner with high porosity (0.51) is superior to baseline burner with low porosity (0.46). In addition, increased porosity also makes the burner more sensitive for unburnt gas mixtures passing through them. This was verified through parameters like reaction rates and stand-off distances. Furthermore, with an increase in burner plate porosity (reduced solid area) from 0.46 to 0.51, the flame appears closer to the top surface of burner plate to ensure the heat loss required for its stabilization. Due to this, the decomposition of CH4 and peak of CH3 come closer to the top surface of the burner plate.

This work presents a numerical study of coolant porous injection in hypersonic turbulent boundary layer, with an analysis of blowing ratio and pore diameter effects on the cooling performance. Direct numerical simulations (DNS) are carried out for a Mach 5 flow over a flat plate with induced transition, and with a porous injection model to mimic injection from a bed of equally-spaced circular pores. The cooling performance in turbulent flow is compared to laminar 2D flow cases. Results show downstream development of a turbulent wedge-shaped structure, where a dramatic decay of the near-wall coolant concentration is observed. Blowing ratio and pore size are seen to affect the calmed and transitional regions, however they have a marginal or negligible effect within the turbulent region. A cooling effectiveness deficit/reduction of 15% to 30% for the turbulent cases, with respect to the laminar 2D cases, is observed above the injection region due to the 3D flow effects associated with the porous injection, whereas it reaches values as high as 80% in the developed turbulent region due to the turbulent convective effects. The present results shed light on the effects of turbulence on porous wall cooling and clearly indicate that alternative (ad-hoc) injection strategies and parameter calibration are needed to guarantee appropriate wall cooling in a turbulent flow.

This study aims to validate the lattice Boltzmann method and assess its ability to accurately describe the behavior of gaseous flows in packed beds. To that end, simulations of a model packed bed reactor, corresponding to an experimental bench, are conducted, and the results are directly compared with experimental data obtained by particle image velocimetry measurements. It is found that the lattice Boltzmann solver exhibits very good agreement with experimental measurements. Then, the numerical solver is further used to analyze the effect of the number of packing layers on the flow structure and to determine the minimum bed height above which the changes in flow structure become insignificant. Finally, flow fluctuations in time are discussed. The findings of this study provide valuable insights into the behavior of the gas flow in packed bed reactors, opening the door for further investigations involving additionally chemical reactions, as found in many practical applications.

In a pyrolysis reactor, organic polymers from biomass or plastic waste are thermally decomposed into volatile gases, condensable vapours (tar or bio-oil) and solid residues (char). Since these products may serve as building blocks for downstream chemical refinement or form the basis of bio-derived fuels, pyrolysis is thought to be instrumental in our progress towards a circular economy. A pyrolysis reactor constitutes a multiphase reactive system whose operation is influenced by many chemical and physical phenomena that occur at different scales. Because the interactions and potential reinforcements of these processes are difficult to isolate and elucidate experimentally, the development of a predictive modelling tool, for example, based on the CFD-DEM (discrete element method) methodology, is attracting increasing attention, particularly for pyrolysis reactors operated with biomass as feedstock. By contrast, CFD-DEM descriptions of plastic pyrolysis remain a challenge at present, mainly due to an incomplete understanding of their melting behaviour. In this article, we provide a blueprint for describing a pyrolysis process within the scope of CFD-DEM, review modelling choices made in past investigations and detail the underlying assumptions. Furthermore, the influence of operating conditions and feedstock properties on the key metrics of the process, such as feedstock conversion, product composition and residence time, as determined by past CFD-DEM analyses is surveyed and systematised. Open challenges that we identify pertain to the incorporation of particle non-sphericity and polydispersity, the melting of plastics, particle shrinkage, exothermicity on part of the gas-particle chemistry and catalytic effects.

Three secondary flows, namely the inward radial flow along the cyclone lid, the downward axial flow along the external surface of the vortex finder, and the radial inward flow below the vortex finder (lip flow) have been studied at a wide range of flow rate 0.22–7.54 LPM using the LES simulations. To evaluate these flows the corresponding methods were originally proposed. The highly significant effect of the Reynolds number on these secondary flows has been described by equations. The main finding is that the magnitude of all secondary flows decrease with increasing Reynolds number. The secondary inward radial flow along the cyclone lid is not constant and reaches its maximum value at the central radial position between the vortex finder external wall and the cyclone wall. The secondary downward axial flow along the external surface of the vortex finder significantly increases at the lowest part of the vortex finder and it is much larger than the secondary flow along the cyclone lid. The lip flow is much larger than the secondary inward radial flow along the cyclone lid, which was assumed in cyclone models to be equal to the lip flow, and the ratio of these two secondary flows is practically independent of the Reynolds number.

A modification of the RANS turbulence model SSG/LRR-\(\omega \) for turbulent boundary layers in an adverse pressure gradient is presented. The modification is based on a wall law for the mean velocity, in which the log law is progressively eroded in an adverse pressure gradient and an extended wall law (designated loosely as a half-power law) emerges above the log law. An augmentation term for the half-power law region is derived from the analysis of the boundary-layer equation for the specific rate of dissipation \(\omega \). An extended data structure within the RANS solver provides, for each viscous wall point, the field points on a wall-normal line. This enables the evaluation of characteristic boundary layer parameters for the local activation of the augmentation term. The modification is calibrated using a joint DLR/UniBw turbulent boundary layer experiment. The modified model yields an improved predictive accuracy for flow separation. Finally, the applicability of the modified model to a 3D wing-body configuration is demonstrated.