Two-dimensional Direct Numerical Simulations Research Articles

A direct numerical simulation study of the dilution tolerance of propane combustion under spark-ignition engine conditions

Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.

Prediction of the developing detonation regime in a NTC-fuel/air mixture with temperature inhomogeneities under engine conditions

The developing detonation process resulting in superknock development under realistic engine conditions in the presence of low-temperature chemistry (LTC) is investigated using two-dimensional direct numerical simulations (DNS). A new model is proposed to predict the developing detonation regime under engine conditions. The prediction is validated against the DNS results. Dimethyl ether (DME) exhibiting a typical negative temperature coefficient (NTC) behavior is used as a fuel. In the presence of the NTC regime, the mean distance of dissipation elements of the ignition delay field, l¯DE, is considered as the characteristic length scale of hot spots to improve the predictive accuracy of the model. The model also accounts for the multi-dimensional effect resulting from the interaction and collision of multiple ignition kernels that is found to promote the onset of detonation and reduce the runup distance of detonation initiation as compared to that of 1D laminar detonation cases. The trasient mixture state is also incorporated in the model development. The model is demonstrated to accurately capture the developing detonation boundary that is consistent with the knock intensity level obtained from the statistical analysis of DNS dataset.

A simplified two-mixture-fraction-based flamelet modelling and its validation on a non-premixed staged combustion system

A simplified two-mixture-fraction-based flamelet model is proposed in this work for a non-premixed staged combustion mode in which three feeds are introduced into the flow field. As the third stream is injected downstream of the main port, the system can be considered a special case of the two-mixture-fraction-based systems. It is considered that if a well-mixing is achieved in the upper stream prior to the third-stream injection, the simplification of the two-mixture-fraction-based flamelet model is feasible. In this work, a simplified model is proposed which can greatly reduce the library size compared to the complete two-mixture-fraction-based flamelet library providing identical resolutions for the fuel stream mixture fraction and the progress variable, respectively. Analysis associated with the interpolation strategy has been implemented. Extension of the current model for the cases in which the well-mixing state is not attained is also analysed, as well as the consideration of heat loss. To validate the model, two adiabatic cases of two-dimensional (2D) direct numerical simulations (DNS) have been performed in this work. To describe the chemical events, one is using finite-rate chemistry (FRC), while the other one is realised by means of the current flamelet model (FLM). An a priori test case that directly looks up the libraries by using the tracking parameters obtained from the FRC case is also considered. It is observed that the interpolation along the primary oxidiser mixture fraction direction outperforms that along directions for both fuel and primary oxidiser mixture fractions. It is also found that three one-mixture-fraction-based flamelet libraries which form the current model are sufficient for simulation of the non-premixed staged combustion, while the extended one which composes five libraries is expected to gain higher accurateness. In the FLM case, although the distributions of tracking parameters deviate from the FRC case slightly, good agreements can be obtained in terms of temperature and species mass fractions. The a priori test shows that the current model can reproduce the reacting flow accurately when the tracking parameters are identical to the FRC case. It is confirmed that the current model can be used to predict the characteristics of the reacting flow in the non-premixed staged combustion.

The electrohydrodynamic plumes evolution in viscoelastic fluids with energy transfer process

Two-dimensional direct numerical simulation was carried out to investigate the various dynamic characteristics of electrohydrodynamic plumes in viscoelastic fluids in a complex blade-plate configuration. Here, the effects of different elasticities (Weissenberg number, Wi) and the maximum possible extension lengths (L) of polymer are studied. The results show that a new stem expansion process is found for viscoelastic plumes, which is explained by the transport mechanism of free charges. The rise and spread of plumes are promoted with an increase in elasticity and L, which we interpret from both an energy perspective and through the concept of the first principal normal stress difference (Np) for the first time. Our results suggest that when elasticity is weak, the total currents in the system are slightly enhanced due to the denser charge density, and above a certain value of Wi they are considerably inhibited maximum by 11.8% with the increasing of Wi or L mainly because of the variation in Uy.

Near-wall dynamics of premixed methane/air flames

This work focuses on sidewall quenching (SWQ) for premixed methane/air flames that are forced by a periodic oscillatory inflow with excitation frequency f = 100 Hz. The effects of steady-state and transient flame stretch on the near-wall flame dynamics are evaluated using two-dimensional direct numerical simulation (2D-DNS) and the GRI 3.0 reaction mechanism. The velocity fluctuations lead to significant changes in flame speed and flame stretch, as well as the associated Markstein numbers. The phenomenon of SWQ is analyzed using flame quenching distance, wall heat flux and heat release rate. For steady-state conditions, there is a strong correlation between the maximum wall heat flux WHFmax and the flame quenching Peclet Number (Peq), as well as between the flame speed and the flame stretch; for transient conditions, the flame quenching distance (dq) increases continuously from phase angles of 1/4f−1 to 3/4f−1 in one cycle as time progresses, and the fluctuation of the quenching distance (Δdq) decreases gradually with increasing equivalence ratio (∅). The flame stretch changes from negative to positive in the process from 1/4f−1 to 3/4f−1, while the heat release rate and fuel reaction rate near the wall gradually decrease. Furthermore, the FWI region is dominated by negative flame stretch while positive flame stretch is present at the base of the flame. Moreover, the methane/air flame has a nearly twofold increase in the consumption speed during the oscillation from phase angle 3/4f−1 to the next cycle at 1/4f−1 at ∅ = 0.5 and ∅ = 1.0. These results show that flow field perturbations are not negligible in elucidating the effects of flame-wall interactions.

Solution approaches for evaporation-driven density instabilities in a slab of saturated porous media

This work considers the gravitational instability of a saline boundary layer formed by an evaporation-induced flow through a fully saturated porous slab. Evaporation of saline waters can result in the formation of salt lakes as salt accumulates near the top surface. As gravitational instabilities can impede the accumulation of salt, establishing a relation between their occurrence and the value of physical parameters such as evaporation rate is crucial. One step toward determining when gravitational instabilities can arise is to compute the ground-state salinity. In this work, this ground state is analytically derived within the framework of Sturm–Liouville theory. Then, a linear stability analysis in conjunction with the quasi-steady state approach is employed to investigate the occurrence of instabilities. These instabilities can develop and grow over time depending on the Rayleigh number and the dimensionless height of the porous medium. To calculate the critical Rayleigh number, which is used to determine the stability of a particular system, the eigenvalues of the linear perturbation equations have to be computed. Here, a novel fundamental matrix method is proposed to solve this perturbation eigenvalue problem and shown to coincide with an established Chebyshev–Galerkin method in their shared range of applicability. Finally, a two-dimensional direct numerical simulation of the full equation system via the finite volume method is employed to validate the time of onset of convective instabilities predicted by the linear theory. Moreover, the fully nonlinear convection patterns are analyzed.

First instability of the flow past two tandem cylinders with different diameters

Two-dimensional direct stability analysis and numerical simulation are used to identify and characterize the primary instability of the flow around two tandem cylinders with different diameters. The ratio of the diameter d of the upstream cylinder to the diameter D of the downstream cylinder is varied from 1.0 to 0.4, while the distance L from the center of the upstream cylinder to the front stagnation point of the downstream cylinder is varied from 1.0D to 8.0D. Three typical spacings are chosen to describe the different scenarios observed, and the results for each configuration are described in detail. Three different unstable modes are identified, and the structural sensitivity and nonlinear characteristics of each mode are investigated. The results show that when d/D = 0.6 and L/D ≥ 3.5, the migration of the eigenvalues corresponding to the most unstable modes can be observed for a range of Reynolds numbers. This is ultimately shown to be caused by the transition of the unstable mode. At the same time, this mode transition changes the core region of the instability mechanism. Moreover, two different mechanisms that lead to vortex shedding in the gap between the two cylinders and a secondary bifurcation behavior of the flow around the downstream cylinder under a specific configuration are observed. To obtain a more comprehensive view of the first instability, a transient growth analysis of the flow is also performed, and the critical Reynolds number in each case is discussed.

A numerical investigation of methane ignition in supercritical CO2

The supercritical CO2 power cycle (sCO2) is a relatively new technology, which promises to reduce CO2 emissions with potentially higher efficiencies. However, due to challenging conditions posed by supercritical pressures, the ignition phenomena in sCO2 combustion are relatively less understood and studied. The primary objective of the current study is to elucidate ignition processes using homogeneous ignition calculations (HMI) and two-dimensional direct numerical simulations (DNS). To accurately model the supercritical conditions, the employed formulation includes the cubic Peng–Robinson equation of state, mass, and heat flux vectors derived from nonequilibrium thermodynamics and compressible form of governing equations. For selection of a suitable chemical mechanism, HMI calculations are employed to investigate the performance of existing skeletal mechanisms against shock-tube experimental data. The chemical characteristics of ignition are further studied using path flux and sensitivity analysis, with CH3O2 chemistry exhibiting the largest effect on accelerating the ignition process. Different chemical pathways of fuel breakdown are also discussed to aid in interpretation of subsequent DNS case. In the DNS case, autoignition of a two-dimensional mixing layer perturbed with pseudoturbulence is simulated. The ignition is found to be delayed compared to the HMI case, with the ignition kernels forming in a spotty manner. The two phenomena are primarily attributed to variation of scalar dissipation within the mixing layer. The ignition kernels expand and evolve into a tribrachial edge flame propagating along the stoichiometric isosurface. Further investigation on the structure of edge flame revealed an asymmetrical structure, with CH4 molecules being entirely consumed in the triple point region of the flame along the stoichiometric isosurface, and more stable fuels like CO burning in the non-premixed branch of the edge flame. The edge flame propagation speeds are also calculated, with variations found to be correlated with scalar dissipation and upstream progress variable of the reacting mixture.

Less can be more: Insights on the role of electrode microstructure in redox flow batteries from two-dimensional direct numerical simulations

Understanding how to structure a porous electrode to facilitate fluid, mass, and charge transport is key to enhancing the performance of electrochemical devices, such as fuel cells, electrolyzers, and redox flow batteries (RFBs). Using a parallel computational framework, direct numerical simulations are carried out on idealized porous electrode microstructures for RFBs. Strategies to improve an electrode design starting from a regular lattice are explored. By introducing vacancies in the ordered arrangement, it is possible to achieve higher voltage efficiency at a given current density, thanks to improved mixing of reactive species, despite reducing the total reactive surface. Careful engineering of the location of vacancies, resulting in a density gradient, outperforms disordered configurations. Our simulation framework is a new tool to explore transport phenomena in RFBs, and our findings suggest new ways to design performant electrodes.

Cationic structure of premixed near-stoichiometric CH4/O2/Ar flames at atmospheric pressure: New insights from mass spectrometry, quantum chemistry, and kinetic modeling

The spatial distributions of naturally occurring cations in near-stoichiometric (equivalence ratios ϕ = 0.8 and 1.2) burner-stabilized methane/oxygen/argon flames at atmospheric pressure are studied by molecular beam mass spectrometry (MBMS) and kinetic modeling. The disturbing effect of a nickel sampling cone used in the measurements on the flame was comprehensively modeled using a two-dimensional direct numerical simulation of reacting flow near the axially symmetric probe along with a reduced chemical kinetic mechanism. The use of one-dimensional numerical simulation for predicting the flame structure perturbed by the metallic probe was firmly justified. We also proposed and applied a procedure to correct the measured spatial profiles of cations on the contribution of signals from the hydrates formed slightly upstream the reaction zone due to the sampling probe effects. With all these methodological advantages, we validated the ion chemistry mechanisms proposed earlier in the literature against the novel experimental data on the spatial distributions of the following cations: HCO+, CH3+, H3O+, C2H3O+, CH5O+, C3H3+. The kinetic mechanism published recently by Chen et al. [Combust. Flame 202 (2019) 208] for the charged species formed in methane flames was revised in order to improve its predictive ability. To this end, the highly accurate W2-F12 quantum chemical calculations were used to obtain the reliable formation enthalpies of all cations considered in the mechanism. In the case of C2H3O+ and C3H3+ cations, the calculated values turned out to be profoundly lower than those reported before. Apart from this, the theory also predicted another exit channel for H3O+ + acetylene reaction yielding HCO+ + CH4 instead of C2H3O+ + H2 proposed earlier. The corrections significantly improved the predictive ability of the ion chemistry mechanism. We also considered the most important directions for the further refinement of the mechanism.

Penetration height of weak axisymmetric fountain in homogeneous fluid under the combined temperature and salinity effect

Fountains under combined temperature and salinity effect are common in environmental and industrial settings. The behavior of weak axisymmetric fountains under combined temperature and salinity effect is studied with two-dimensional direct numerical simulations over 0.25 ≤ FrT ≤ 2.0 and −0.75 ≤ N ≤ 5.0, where FrT is the Froude number based on temperature only and N is the buoyancy ratio quantifying the ratio of salinity to temperature contributed to density. The results show that for each FrT, both the initial and time-average maximum fountain heights decrease when N increases as the combined negative buoyancy due to both temperature and salinity is strengthened, whereas as FrT increases, they increase as the overall negative buoyancy reduces. If the overall Froude number, Fr, which is based on density due to the combined temperature and salinity contributions, is used instead of FrT, the existing scaling relations for weak axisymmetric fountains with density coming from temperature only are also applicable for the weak axisymmetric fountains under the combined temperature and salinity effect when Fr ≲ 2.0, although there are slight differences in their quantified correlations due to the extra effect from the co-existing salinity. It is further shown that the effect from the co-existing salinity shifts the scaling relation for intermediate fountains with 2.0 ≲ Fr ≲ 4.0 with density from only one contributor to the scaling relation for weak fountains with Fr ≲ 2.0 with density coming from both temperature and salinity, further showing the additional effect of salinity.

Effect of liquid volume fraction and shear rate on rheological properties and microstructure formation in ternary particle/oil/water dispersion systems under shear flow: two-dimensional direct numerical simulation.

We numerically studied the rheological properties and microstructure formation under shear flow in a ternary particle/oil/water dispersion system. Our numerical simulation method was based on a phase-field model for capturing a free interface, the discrete element method for tracking particle motion, the immersed boundary method for calculating fluid-particle interactions, and a wetting model that assigns an order parameter to the solid surface according to the wettability. The effects of the water-phase volume fraction and shear rate on the microstructure and apparent viscosity were investigated. When the water-phase volume fraction was low, a pendular state was formed, and with an increase in the water-phase volume fraction, the state transitioned into a co-continuous state and a Pickering emulsion. This change in the microstructure state is qualitatively consistent with the results of previous experimental studies. In the pendular state, the viscosity increased with an increase in the water-phase volume fraction. This was due to the development of a network structure connected by liquid bridges, and the increase in the coordination number was quantitatively confirmed. In the case of the pendular state, significant shear thinning was observed, but in the case of the Pickering emulsion, no significant shear thinning was observed. It is concluded that this is due to the difference in the manner in which the microstructure changes with the shear rate. This is the first study to numerically demonstrate the microstructure formation of a ternary dispersion under shear flow and its correlation with the apparent viscosity.

Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

Global POD-Galerkin ROMs for Fluid Flows with Moving Solid Structures

Traditional proper orthogonal decomposition (POD)-Galerkin projection for reduced-order models (ROMs) of fluid flows is based on a fixed domain. The current method removes this limitation by considering a single combined domain of fluid and solid, whereas the original solid boundary conditions are reinforced by additional ROM terms. The combined domain requires a new inner product defined in the same combined domain to compute POD modes and the projection of equations. Solid motion is considered first as a continuous motion, then a decomposed motion, represented by a few solid modes to further reduce the computational cost. This new global approach was applied first on a two-dimensional direct numerical simulation (DNS) database of the flow past an oscillatory cylinder, and then on a three-dimensional DNS database of the flow past an oscillatory sphere. Last, the approach was applied on a high-resolution particle image velocimetry database from an experiment at higher Reynolds number of the flow past a pitching-up NACA0012 airfoil. The ROMs derived by the global POD-Galerkin projection approach, for all three moving-boundary cases, have shown adequate accuracy in the reconstruction of flow fields and the prediction of key aerodynamic features while keeping very low computational costs.

Stability of buoyancy-driven flow in a vertical channel with one heated wall

The stability of the buoyancy-driven flow in a channel between an isothermal heated vertical wall and an adiabatic vertical wall is investigated by numerical integration of the derived two-dimensional stability equations for this type of buoyant flow. Stability calculations are carried out for a Prandtl number of 0.707 inside four vertical channels at Grashof numbers of 6.1×1010 and 1.49×1011 and with length-to-width aspect ratios of 8, 10, 40/3, and 20. The flow within the channel is numerically modeled by means of two-dimensional direct numerical simulations (DNSs), and the solved temperature and velocity fields are used as the base flow properties in the derived stability equations. Solutions of the stability equations yield the phase velocity, wave number, and growth rate for upper- and lower-branch neutrally stable disturbances, disturbances with maximum growth rates, and disturbances with phase velocities equal to the maximum velocity of the base flow inside the vertical channels. The predictions of the linear stability theory are compared with the disturbance growth observed in the simulated flow by means of a short-time Fourier transform of the velocity field computed from the DNS. The results show that while a range of disturbance wave numbers may be amplified in the channel, those that sustain the largest linear amplification have phase velocities equal to the peak velocity of the flow near the heated wall. The frequency of the most amplified disturbance increases linearly with the channel aspect ratio.

Systematic comparison between the generalized Lorenz equations and DNS in the two-dimensional Rayleigh-Bénard convection.

The classic Lorenz equations were originally derived from the two-dimensional Rayleigh-Bénard convection system considering an idealized case with the lowest order of harmonics. Although the low-order Lorenz equations have traditionally served as a minimal model for chaotic and intermittent atmospheric motions, even the dynamics of the two-dimensional Rayleigh-Bénard convection system is not fully represented by the Lorenz equations, and such differences have yet to be clearly identified in a systematic manner. In this paper, the convection problem is revisited through an investigation of various dynamical behaviors exhibited by a two-dimensional direct numerical simulation (DNS) and the generalized expansion of the Lorenz equations (GELE) derived by considering additional higher-order harmonics in the spectral expansions of periodic solutions. Notably, GELE allows us to understand how nonlinear interactions among high-order modes alter the dynamical features of the Lorenz equations including fixed points, chaotic attractors, and periodic solutions. It is verified that numerical solutions of the DNS can be recovered from the solutions of GELE when we consider the system with sufficiently high-order harmonics. At the lowest order, the classic Lorenz equations are recovered from GELE. Unlike in the Lorenz equations, we observe limit tori, which are the multi-dimensional analog of limit cycles, in the solutions of the DNS and GELE at high orders. Initial condition dependency in the DNS and Lorenz equations is also discussed.

Subgrid scale modeling considerations for large eddy simulation of supercritical turbulent mixing and combustion

This paper presents a systematic investigation of large eddy simulation (LES) and subgrid scale (SGS) modeling with application to transcritical and supercritical turbulent mixing and combustion. There remains uncertainty about the validity of extending the LES formalism developed for low-pressure, ideal-gas flows to simulations of high-pressure real-fluid flows. To address this concern, we reexamine the LES theoretical framework and the underlying assumptions in the context of real-fluid mixing and combustion. Two-dimensional direct numerical simulations of nonreacting and reacting mixing layers of gaseous methane and liquid oxygen in the thermodynamically transcritical and supercritical fluid regimes are performed. The computed results are used to evaluate the exact terms in the LES governing equations and associated SGS models. Order of magnitude analysis of the exact filtered and subgrid terms in the LES equations and a priori analysis of the simplifications are performed at different filter widths. It is shown that several of these approximations do not hold for supercritical turbulent mixing. Subgrid scale terms, which are neglected in the LES framework for ideal-gas flows, become significant in magnitude compared to the other leading terms in the governing equations. In particular, the subgrid term arising from the filtering of the real-fluid equation of state is shown to be important.

Curvature effects on NO formation in wrinkled laminar ammonia/hydrogen/nitrogen-air premixed flames

The formation of nitrogen oxide (NO) in wrinkled laminar NH3/H2/N2-air premixed flames is investigated utilizing two-dimensional Direct Numerical Simulation (DNS) with detailed chemical kinetics as well as one-dimensional freely propagating flame calculations. The spatial pattern of NO formation is observed to be closely linked to flame curvature and affected by thermo-diffusive effects acting on key chemical species. Preferential diffusion of H2 into convex-shaped portions of the flame front leads to a local increase in equivalence ratio. This change in local equivalence ratio is found to prominently affect the NO formation. If the fuel-oxidant mixture is globally lean, a local increase in equivalence ratio strengthens the NO formation (locally); in a globally rich fuel-oxidant mixture, conversely, the NO concentration will be reduced in correspondence of local increments of the equivalence ratio. A sensitivity analysis with respect to NO formation reveals that decomposition of NH2 is governed by two competing pathways: the decomposition via NH and N to N2 on the one hand and the oxidation via HNO to NO on the other hand. The local radical pool, which is affected by preferential diffusion of H2 and depletion of O2, and the local fuel-oxidant mixture ratio jointly strengthen further local differences between H2-depleted (concave-shaped) portions of the flame front and H2-enriched (convex-shaped) ones. This is confirmed across a wide range of equivalence ratios from lean to rich conditions.

Numerical Investigation of T-Shaped Microfluidic Oscillator with Viscoelastic Fluid.

Oscillatory flow has many applications in micro-scaled devices. The methods of realizing microfluidic oscillators reported so far are typically based on the impinging-jet and Coanda effect, which usually require the flow Reynolds number to be at least at the order of unity. Another approach is to introduce elastomeric membrane into the microfluidic units; however, the manufacturing process is relatively complex, and the membrane will become soft after long-time operation, which leads to deviation from the design condition. From the perspective of the core requirement of a microfluidic circuit, i.e., nonlinearity, the oscillatory microfluidic flow can be realized via the nonlinear characteristics of viscoelastic fluid flow. In this paper, the flow characteristics of viscoelastic fluid (Boger-type) in a T-shaped channel and its modified structures are studied by two-dimensional direct numerical simulation (DNS). The main results obtained from the DNS study are as follows: (1) Both Weissenberg (Wi) number and viscosity ratio need to be within a certain range to achieve a periodic oscillating performance; (2) With the presence of the dynamic evolution of the pair of vortices in the upstream near the intersection, the oscillation intensity increases as the elasticity-dominated area in the junction enlarges; (3) Considering the simplicity of the T-type channel as a potential oscillator, the improved structure should have a groove carved toward the entrance near the upper wall. The maximum oscillation intensity measured by the standard deviation of flow rate at outlet is increased by 129% compared with that of the original standard T-shaped channel under the same condition. To sum up, with Wi number and viscosity ratio within a certain range, the regular periodic oscillation characteristics of Oldroyd-B type viscoelastic fluid flow in standard T-shaped and its modified channels can be obtained. This structure can serve as a passive microfluidic oscillator with great potential value at an extremely low Reynolds number, which has the advantages of simplicity, no moving parts and fan-out of two.

Turbulent convection in subglacial lakes

Abstract