Two-dimensional Direct Numerical Simulations Research Articles

The Impact of Roughness and Partitions In Thermal Convection to Enhance the Heat Transport

Abstract This investigation delves into the profound influence of adiabatic partitions on heat transport within a square Rayleigh-Benard (RB) convection enclosure characterized by surface roughness on the lower hot and upper cold plates. These surface irregularities manifest as a rectangular base and a triangular apex. Employing two-dimensional (2D) direct numerical simulations across a Rayleigh number (Ra) range of 106 to 108 and a Prandtl number (Pr) of 1, our study focuses on strategically positioned adiabatic partitions between successive roughness elements. Notably, we uncover a significant enhancement in heat transport with the introduction of partition boards between consecutive roughness elements. As the number of partitions increases from one to four, the heat flux experiences a remarkable augmentation, reaching 2.3 times that of the classical square RB configuration. This enhancement arises from the breakdown of large-scale rolls into multiple rolls, a phenomenon intensified by increased partition height. Intriguingly, configurations featuring roughness with partitions exhibit a 2.7-fold increase in heat flux compared to the classical square RB setup. The interplay of surface roughness and partitions contributes to this improvement, with optimized gap distances between the conduction plate and partition heightening local velocity, thinning the thermal boundary layer, and augmenting overall heat flux. This study sheds light on the synergistic effects of adiabatic partitions and surface roughness in RB convection, indicating the potential for tailored design strategies involving partitions and surface modifications to optimize thermal performance across various applications.

Towards the understanding of convective dissolution in confined porous media: thin bead pack experiments, two-dimensional direct numerical simulations and physical models

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

Flow-induced vibration of two tandem square cylinders at low Reynolds number: transitions among vortex-induced vibration, biased oscillation and galloping

The flow-induced vibrations (FIVs) of two identical tandem square cylinders with mass ratio m* = 3.5 at Reynolds number Re = 150 are investigated through two-dimensional direct numerical simulation (DNS) and linear stability analysis over a parameter range of spacing ratio 1.5 ≤ L* ≤ 5 and reduced velocity 3 ≤ Ur ≤ 34. Three kinds of FIV responses, namely vortex-induced vibration (VIV), biased oscillation (BO) and galloping (GA), are identified. The FIVs are then further classified into the branches of initial VIV (IV), resonant VIV (RV and RV′), flutter-induced VIV (FV), desynchronized VIV (DV), VIV developing from GA (GV), transitional state between VIV and GA (TR), BO and GA based on the characteristics of the vibration responses. The transitions among different FIV branches are examined by combining the DNS with linear stability analysis, where the transition boundaries among the VIV, BO and GA branches over the concerned parameters are identified on the branch maps. The transition from IV to RV or RV′ is found to be related to the unstable wake mode, while the FV, transiting from RV or RV′, is induced by the unstable structural factor in the wake-structure mode. The structural instability is considered as the physical origin of GA, whereas the mode competition between unstable wake and structure leads to DV, GV and TR, and thus delays the appearance of GA. The transition from DV to BO with biased equilibrium position, accompanied by the even-order harmonic frequencies, is essentially induced by the symmetry breaking bifurcation.

Influence of slit asymmetry on blow-off and flashback in methane/hydrogen laminar premixed burners

One way to decarbonize the heat production sector is to gradually replace natural gas with hydrogen. The design of laminar premixed burners capable of operating with both methane and hydrogen is however challenging as these fuels have drastically different burning properties, which narrows the operating range. While methane flames face limitations in stabilization due to blow-off at high power, hydrogen flames tend to be susceptible to flashback at low power. This study investigates the effects of slits symmetry breaking on the blow-off of methane flames and flashback of hydrogen flames through two-dimensional direct numerical simulations of canonical asymmetrical slit configurations, revealing uneven interactions between the main openings and smaller auxiliary slits. The equations governing the reactive flow dynamics are coupled to a heat transfer solver in the solid phase to elucidate the thermal and hydrodynamic mechanisms determining the operability limits. Viscous dissipation in the small auxiliary slits together with a substantial preheating of the fresh gases by heat redistribution through the solid phase is found to govern flame stabilization in asymmetrical geometries, improving blow-off resistance of methane-air flames. Then, flashback of hydrogen-air flame is found to be driven by the competition between (i) the mass flow rate distribution between the main and auxiliary slits, (ii) preheating of the gas through the auxiliary slits and (iii) the ability of the main and auxiliary slits to quench the flame. The interplay of these phenomena gives rise to complex behaviors, wherein asymmetrical configurations could exhibit significantly enhanced resistance to flashback compared to symmetrical geometries. This conclusion, verified for different burner thicknesses and slit spacing, may be used to guide the design of fuel-flexible laminar burners.Novelty and significance statement1. Analyzing the effect of slits symmetry breaking on blow-off of methane flames and flashback of hydrogen flames for multi-perforated laminar burners.2. Defining a strategy for wall heat flux redistribution to assess the asymmetrical interaction between the main and auxiliary flames through the flame-holder.3. Demonstrating and explaining the positive impact of symmetry breaking on the blow-off resistance of methane flames.4. Highlighting the substantial and non-monotonous impact of symmetry breaking on hydrogen flame flashback.5. Identifying the interplay of thermal and hydrodynamic mechanisms in asymmetrical slits leading to improvement of flashback resistance for hydrogen-air flames compared to symmetrical configurations.

Multistability of elasto-inertial two-dimensional channel flow

Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. Two possibilities are currently hypothesized to be linked to the dynamical origins of EIT: (i) viscoelastic Tollmien–Schlichting waves and (ii) a centre-mode instability. The nonlinear evolution of the centre mode leads to a travelling wave with an ‘arrowhead’ structure in the polymer conformation, a structure also observed instantaneously in simulations of EIT. In this work we conduct a suite of two-dimensional direct numerical simulations spanning a wide range of polymeric flow parameters to examine the possible dynamical connection between the arrowhead and EIT. Our calculations reveal (up to) four coexistent attractors: the laminar state and a steady arrowhead regime (SAR), along with EIT and a ‘chaotic arrowhead regime’ (CAR). The SAR is stable for all parameters considered here, while the final pair of (chaotic) flow states are visually very similar and can be distinguished only by the presence of a weak polymer arrowhead structure in the CAR regime. Analysis of energy transfers between the flow and the polymer indicates that both chaotic regimes are maintained by an identical near-wall mechanism and that the weak arrowhead does not play a role. Our results suggest that the arrowhead is a benign flow structure that is disconnected from the self-sustaining mechanics of EIT.

Low-Prandtl-number effects on global and local statistics in two-dimensional Rayleigh–Bénard convection

We present global and local statistical properties of turbulent Rayleigh–Bénard (RB) convection at low Prandtl numbers in this work. A series of high resolution two-dimensional (2D) direct numerical simulations are carried out in a square box for the Prandtl number ranges 0.005≤Pr≤0.07 and 0.01≤Pr≤0.15 at Rayleigh numbers Ra=107 and Ra=108, respectively. The global heat and momentum transport expressed as Nusselt number Nu and Reynolds number Re are found to scale as Nu∼Pr0.14 and Re∼Pr−0.82 for Ra=107, and Nu∼Pr0.11Re∼Pr−0.93 for Ra=108. The local velocity fluctuation at the cell center shows larger amplitudes at lowered Pr, indicating a stronger turbulence in the bulk. The magnitudes of kinetic and thermal energy dissipation rates in the bulk also increase with the decreasing of Pr, due to the intensified velocity gradient and larger thermal diffusivity, respectively. In the cell central region, probability density functions (PDFs) of velocity show a bimodal distribution, and it approaches the Gaussian distribution at higher Pr, while the PDFs of temperature display a stretched exponential shape with intermittent behavior. The kinetic energy spectra further reveal that the velocity cascade follows the Bolgiano–Obukhov scaling in the bulk of the convective flow.

Thermal diffusion, exhaust gas recirculation and blending effects on lean premixed hydrogen flames

Thermodiffusively-unstable lean premixed hydrogen flames are investigated using two-dimensional direct numerical simulation employing finite-rate chemical kinetics. Three databases are generated focussing on the inclusion of the Soret effect, the recirculation of exhaust gas, and blending with methane. A simple rescaling of a classic thermal diffusion model is presented and shown to mimic multicomponent diffusion with very low computational cost and little-to-no loss in accuracy. It is also shown that a previously developed model for mean local flame speeds in lean premixed hydrogen flames [1] can still be used provided Soret effects are taken into account in one-dimensional calculations. The addition of exhaust gas to the unburned mixture is found to enhance thermodiffusive instability; the primary mechanism for this was shown to be the highly-efficient third-body nature of water, with the reduction of adiabatic flame temperature a second-order effect. Again, the existing mean local flame speed model proved sufficient. Finally, blending with methane was found to reduce the thermodiffusive response of the flame, more so than the existing model suggests, despite adjustment of the fuel Lewis number; an adapted model is presented to account for this.

Optimizing flow control with deep reinforcement learning: Plasma actuator placement around a square cylinder

This study introduces a deep reinforcement learning-based flow control approach to enhance the efficiency of multiple plasma actuators on a square cylinder. The research seeks to adjust the control inputs of these actuators to diminish both drag and lift forces on the cylinder, ensuring flow stability in the process. The proposed model uses a two-dimensional direct numerical simulation of flow past a square cylinder to represent the environment. The control approach involves adjusting the AC voltage across three specific configurations of the plasma actuators. Initially tested at a Reynolds number (ReD) of 100, this strategy was later applied at ReD of 180. We observed a 97% reduction in the mean drag coefficient at ReD = 100 and a 99% reduction at ReD = 180. Furthermore, the findings suggest that increasing the Reynolds number makes it harder to mitigate vortex shedding using plasma actuators on just the cylinder's rear surface. However, an optimized configuration of these actuators can fully suppress vortex shedding under the proposed control scheme.

Scaling relations in quasi-static magnetoconvection with a strong vertical magnetic field

The scaling law for the horizontal length scale $\ell$ relative to the domain height $L$ , originating from the linear theory of quasi-static magnetoconvection, $\ell /L \sim Q^{-1/6}$ , has been verified through two-dimensional (2-D) direct numerical simulation (DNS), particularly at high values of the Chandrasekhar number ( $Q$ ). This relationship remains valid within a specific flow regime characterized by columnar structures aligned with the magnetic field. Expanding upon the $Q$ -dependence of the horizontal length scale, we have derived scaling laws for the Nusselt number ( $Nu$ ) and the Reynolds number ( $Re$ ) as functions of the driving forces (Rayleigh number ( $Ra$ ) and $Q$ ) in quasi-static magnetoconvection influenced by a strong magnetic field. These scaling relations, $Nu \sim Ra/Q$ and $Re \sim Ra Q^{-5/6}$ , have been successfully validated using 2-D DNS data spanning a wide range of five decades in $Q$ , ranging from $10^5$ to $10^9$ . The successful validation of the relations at large $Q$ values, combined with our theoretical analysis of dissipation rates and the incorporation of the horizontal length scale's influence on scaling behaviour, presents a valid approach for deriving scaling laws under various conditions.

Wave statistics and energy dissipation of shallow-water breaking waves in a tank with a level bottom

The present study focuses on two-dimensional direct numerical simulations of shallow-water breaking waves, specifically those generated by a wave plate at constant water depths. The primary objective is to quantitatively analyse the dynamics, kinematics and energy dissipation associated with wave breaking. The numerical results exhibit good agreement with experimental data in terms of free-surface profiles during wave breaking. A parametric study was conducted to examine the influence of various wave properties and initial conditions on breaking characteristics. According to research on the Bond number ( $Bo$ , the ratio of gravitational to surface tension forces), an increased surface tension leads to the formation of more prominent parasitic capillaries at the forwards face of the wave profile and a thicker plunging jet, which causes a delayed breaking time and is tightly correlated with the main cavity size. A close relationship between wave statistics and the initial conditions of the wave plate is discovered, allowing for the classification of breaker types based on the ratio of wave height to water depth, $H/d$ . Moreover, an analysis based on inertial scaling arguments reveals that the energy dissipation rate due to breaking can be linked to the local geometry of the breaking crest $H_b/d$ , and exhibits a threshold behaviour, where the energy dissipation approaches zero at a critical value of $H_b/d$ . An empirical scaling of the breaking parameter is proposed as $b = a(H_b/d - \chi _0)^n$ , where $\chi _0 = 0.65$ represents the breaking threshold and $n = 1.5$ is a power law determined through the best fit to the numerical results.

Non-Oberbeck–Boussinesq effects on a water-filled differentially heated vertical cavity

In this study, we examined non-Oberbeck–Boussinesq (NOB) effects on a water-filled differentially heated vertical cavity through two-dimensional direct numerical simulations. The simulations encompassed a Rayleigh number (Ra) span of 107–1010, temperature difference (Δθ̃) up to 60 K, and a Prandtl number (Pr) fixed at 4.4. The center temperature (θcen) was found to be independent of Ra and to increase linearly with Δθ̃, as presented by θcen≈1.18×10−3 K−1Δθ̃. The thermal boundary layer (BL) thicknesses near the hot and cold walls (λ¯hθ and λ¯cθ, respectively) are found to scale as λ¯h,cθ∼Raγ λ¯h,c, where the scaling exponent γ λ¯h,c ranges from −0.264 to −0.262. For more detail, the scaling exponent γ λ¯h displays an increasing trend, while γ λ¯c demonstrates a decreasing trend. However, the sum of the hot and cold thermal BL thicknesses was found to be constant at a fixed Ra in the presence of NOB effects. Our detailed investigation of the Nusselt number (Nu) and Reynolds number (Re) revealed that Nu∼Ra0.258 and Re∼Ra0.364, showing insensitivity to NOB effects. These exponents were smaller than those for Rayleigh–Bénard convection. The NOB modifications on Nu and Re were less than 1.2% and 2.5%, respectively, even at Δθ̃=60 K. Our results also revealed that key parameters such as θcen and normalized ratios [(λ¯NOBθ/λ¯OBθ)h,c, NuNOB/NuOB, and ReNOB/ReOB] exhibit universal correlations with Δθ̃. Remarkably, these relationships are consistent across varying Ra values. This observation underscored the influence of NOB effects on these parameters could be confidently forecasted using just the temperature difference (Δθ̃) for Ra∈[107,1010].

On the wall-bounded model of fingering double diffusive convection

The present work aims at clarifying the effects of a solid boundary on the salt fingers in the wall-bounded double diffusive convection turbulence driven by the salinity and temperature differences between the top and bottom plates. The fluid properties are the same as the seawater, and two-dimensional direct numerical simulations are conducted over a wide range of the thermal and salinity Rayleigh numbers which measure the strength of driving salinity difference and stabilising temperature difference. We find that the bulk density ratio $\varLambda _b$ , defined by the mean temperature and salinity gradients at the bulk, controls the flow morphology. As $\varLambda _b$ exceeds unity, the bulk flow shifts from wide convection rolls to slender salt fingers. Two different regimes are further identified for the cases of salt-finger type. One is the confined salt-finger regime where the characteristic height of salt fingers is comparable to the bulk height and the influences of the solid boundary are noticeable. The other is the free salt-finger regime where the salt fingers are much shorter than the bulk height. In this latter regime, the transport properties versus $\varLambda _b$ are in quantitative agreement with those obtained in the fully periodic domain (e.g. Traxler et al., J. Fluid Mech., vol. 677, 2011, pp. 530–553). For a limited range of density ratio at the highest salinity Rayleigh number considered here, multiple states can be obtained from different initial conditions. The large-scale secondary instability and spontaneous formation of staircase from finger layers are not observed in the current study.

Reduced-order modeling with reconstruction-informed projections

Reduced-order models (ROMs) are commonly employed to address the large computational cost of simulations for high-dimensional, dynamical systems such as those found in combustion. Two key components of building these ROMs include an effective dimension reduction or projection of the high-dimensional system onto a low-dimensional manifold, alongside an accurate method for reconstructing quantities of interest (QoIs) over the projection parameters. A QoI-based approach to projection has been recently introduced, combining these aspects of building ROMs into a single training that learns the projection parameters based on nonlinear reconstruction errors of QoIs. A key advantage to this approach is the ability to inform the projection with reconstruction errors of QoIs that are functions of the projection itself, such as projected source terms influencing evolution over the low-dimensional manifold. We expand on the QoI-based projection method and implement Partition of Unity Network (POUnet) models for reconstruction, which are able to reach high levels of accuracy with small memory footprints by combining classification with localized polynomial regression. Furthermore, we find that sign changes in the projected source terms can negatively impact evolution over the low-dimensional manifold. Therefore, we also include a penalty function favoring positivity in projected source terms of the QoI-based projection method. These modeling improvements are demonstrated in one- and two-dimensional direct numerical simulations (DNS) of a non-premixed laminar flame.

Predicting flashback limits in [formula omitted] enriched [formula omitted]/air and [formula omitted]/air laminar flames

The influence of hydrogen blending on the flashback limit of dihedral premixed laminar flames stabilized on a slit burner is investigated via two-dimensional direct numerical simulations with conjugate heat transfer and detailed chemistry. Flashback limits are determined for CH4/H2/Air and C3H8/H2/Air mixtures with hydrogen contents ranging from 0% to 100% and varying fuel-to-air ratios adjusted according to the iso–Tad and the iso–δT hybridization strategies. The analysis reveals the existence of two different flashback regimes and a critical effective Lewis number for the fuel mixture, Lec=0.5, controlling the switch from one regime to the other. Simulations are also used to explore the dynamics of flames during flashback in these two regimes. They show that for mixtures above the critical effective Lewis number, flashback is symmetric whereas for mixtures below the critical value, an asymmetric flame propagation is observed through the burner slit. These results highlight the impact of preferential diffusion on the stabilization mechanism of hydrogen fuel blends.

Data-driven simulation of ammonia combustion using neural ordinary differential equations (NODE)

The direct use of detailed chemical kinetics in combustion simulations is limited by the extremely high computational costs. Recently, Owoyele and Pal (Energy and AI, 2022), proposed the neural ordinary differential equations (NODE) method to accelerate calculations of chemical kinetics and proved its effectiveness in zero-dimensional calculations of hydrogen combustion considering 9 species and 21 reactions. However, its performance for more realistic high-dimensional calculations and more complex kinetic systems remains unexplored. Therefore, this study further applies the method for more complex chemical kinetics of ammonia combustion, especially with optimizations in the data sampling, model training strategies, and model application methods that remedy the problems of versatility and application to more practical simulations. The newly developed NODE models are comprehensively validated in the zero-dimensional calculations of ammonia auto-ignition, one-dimensional calculations of laminar freely-propagating ammonia-premixed flames, and two-dimensional direct numerical simulation (DNS) of ammonia-premixed flames in a temporally evolving jet. Present NODE models focus on seven chemical species, namely NH3, O2, H2, OH, H2O, N2, and NO, and the results show that, compared with the results obtained by using detailed chemical kinetics, this method is able to reduce the computational costs of the zero-dimensional auto-ignition reaction to 1/24 while reproducing the ignition delay time for a wide range of initial temperatures and equivalence ratios with relatively good accuracy. Additionally, the method is able to reduce the computational costs of the one-dimensional freely propagating flame and two-dimensional jet flame to 1/4 and 1/38 respectively, while acceptable reproduction of the laminar flame speed and temporal evolution of the gas temperature and mass fractions of the interested species can be achieved.

Direct numerical simulations of flows around an array of rough cylinders partially coated with porous media at Re = 3900

In recent years, interest has been growing in the stability control of cylindrical structures in a flow field using full/partial coatings of porous media. However, the partial application of porous coatings to arrays of cylinders with rough surfaces has rarely been studied. This paper numerically investigates the passive flow control of an array of rough cylinders partially coated with porous media on their leeward side in the subcritical flow regime (Re = 3900). This is achieved through two-dimensional direct numerical simulations and the Cartesian cut-cell method, which facilitate flow simulations around complex porous media and rough surfaces in an accurate and flexible manner. In contrast to macroscopic models, this study employs a quasi-microscopic model to simplify the porous structure for each cylinder, providing an accurate and intuitive means of describing the inflow details of porous media near the central cylinder. The porosities and pores per inch of the porous media are defined in terms of the alignment angles and radii. Similarly, the surface roughness of a cylinder is simulated by the attachment of small circular appendages. The accuracy and capacity of the presented numerical approach are demonstrated via a numerical case study with a single smooth cylinder. The influence of the porous media on the flows around a single rough cylinder and an array of rough cylinders is thoroughly investigated and discussed.

Direct numerical simulation of NH3/air combustion with H2 addition under HCCI relevant conditions

In the present work, two-dimensional direct numerical simulations (DNS) of NH3/air turbulent combustion with H2 addition under homogeneous-charge compression ignition (HCCI) relevant conditions were performed to explore the ignition and combustion characteristics. Three hydrogen addition levels in the fuel were considered with molar fractions of 0.0 (pure ammonia), 0.1 and 0.8. The corresponding one-dimensional laminar flames were also simulated to provide reference solutions. The general combustion characteristics were first presented. It was found that turbulence and thermal stratification facilitate the ignition process. The ignition occurs earlier with increasing hydrogen addition levels and temperature fluctuations. After ignition, high heat release rate (HRR) occurs simultaneously over the entire domain with low temperature fluctuations while significant HRR occurs in narrow sheets with high temperature fluctuations. HRR is significantly enhanced in positive curvature regions of the cases with high hydrogen addition levels due to the preferential diffusion of H and other radicals. The combustion mode was examined based on the analysis of the displacement speed and species transport equation budget. The mean displacement speed is decreased with increasing temperature fluctuations and the budget analysis suggests that high temperature gradient facilitates deflagration. The reaction fronts are thinner with increasing H2 addition levels, and the combustion mode of deflagration is promoted. The effects of turbulence intensity on the flame structure and combustion mode were evaluated. The ignition occurs earlier and the area of the reaction front increases with increasing turbulence intensity. The magnitude of the temperature gradient also increases with increasing turbulence intensity, which facilitates the occurrence of deflagration. The turbulent flame structures were compared with the corresponding 0D ignition and 1D thermally stratified flame results, and it was found that the mean turbulent flame structure can be well approximated by 1D thermally stratified flames.

Analysis of knock onset based on two-dimensional direct numerical simulation and theory of explosive transition of deflagration

In this study, we analyzed data from a two-dimensional (2D) direct numerical simulation (DNS) that reproduced the knocking experiment in order to elucidate the knocking phenomenon. First, it was confirmed that the reaction front behavior in 2D DNS could be reproduced as a one-dimensional (1D) laminar premixed flame simulation at extreme conditions. Furthermore, a detailed study using a 1D laminar premixed flame revealed a strong relation between the timing of knock onset and the flame propagation limit of the 1D laminar premixed flame at elevated temperature and pressure conditions. To clarify this relation, we introduced the theory of “explosive transition of deflagration.” This theory shows that when the Lewis number is unity, the time evolution of the normalized fuel mass fraction and temperature in a 0D homogeneous ignition is equal to the temporal evolution observed in a 1D laminar premixed flame, if the spatiotemporal transformation is properly applied. Furthermore, the rate at which the normalized fuel mass fraction decreases in the preheat zone was found to depend on the Lewis number, and when the Lewis number is greater than unity, no flame structure exists above a certain threshold temperature. Finally, the mechanism of knock onset was explained by considering the theory of explosive transition of deflagration and explosive transition boundary plotted on a pressure-temporal diagram.

Background oriented schlieren image displacement estimation method based on global optical flow

Background oriented schlieren (BOS) technology is a recent non-contact optical diagnostic technology, which can be used for the visualization of variable density flow and the quantitative measurement of the refractive index field. The accuracy of BOS image displacement estimation directly determines the accuracy of refractive index field reconstruction. For BOS images, the optical path construction method, vibration and uneven illumination, blurring and defocusing effects, and the refocusing effect of volume refraction make it difficult for the BOS image sequence to satisfy the constant brightness assumption. In this study, the optical flow algorithm based on the assumption of a constant gradient in PIV is improved and applied to BOS image displacement estimation. A data item based on the assumption of constant brightness combined with the assumption of constant gradient is proposed. The first-order div-curl regularization constraint is used as the spatial smoothing condition, and the non-convex Charbonnier penalty function is used to determine the displacement field by the variational method to minimize the energy function. The proposed method is tested on the synthetic images obtained by two-dimensional turbulent direct numerical simulation (DNS), the BOS synthetic images with brightness changes, and the actual experimental BOS images of the flow field above a premixed butane/air combustion flame with different equivalence ratios. Compared with the current advanced optical flow algorithm, this method has higher accuracy and robustness. Overall, the proposed method can not only obtain more accurate results when the brightness of the BOS synthetic image and experimental image changes, but also helps in retaining the flow details such as small divergence and vorticity structure of the heat flow field while reducing the outliers.

Suppression of vortex shedding in the wake of a circular cylinder through high-frequency in-line oscillation

This paper presents a new flow control approach to suppress the vortex shedding in the wake of a circular cylinder through high-frequency oscillation. The circular cylinder is forced to oscillate in the streamwise direction at high-frequency and low amplitude, corresponding to a high Stokes number (β = 100–1000) and low Keulegan–Carpenter number (KC = 0.001–4). Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations of an oscillating circular cylinder in steady current have been carried out in the parameter space of KC, Rec, and β. Our numerical results show that when the flow remains in the two-dimensional vortex shedding regime, the cylinder wake sequentially experiences transitions from the vortex shedding regime to the suppression of the vortex shedding regime and finally to the symmetry breaking regime, with increasing KC. Corresponding wake characteristics and variations of hydrodynamic forces over the three wake regimes are explored. Three quantities that represent shear-layer characteristics, including the length of separating shear layers, the circulation of shear layers and wake recirculation length, reach maxima at the onset of suppression. The physical mechanisms for the suppression of vortex shedding and occurrence of symmetry breaking are also explained. Once the flow becomes 3-D, vortex shedding from the cylinder cannot be suppressed, primarily because the outer shear layers induced by the steady approaching flow are enhanced in 3-D flows. The cylinder oscillation over the frequency range investigated in the present study delays wake transition to 3-D. The cylinder oscillation alters the 3-D vortical structure and its spanwise wavelength significantly.