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The purpose of the present study is to highlight the influence of real fuel droplets on the general mixing layer characteristics.
A hybrid method has been developed for the numerical prediction of turbulent mixing in a spatially-developing, free shear layer. Most significantly, the computation incorporates the effects of large-scale structures, Schmidt number and Reynolds number on mixing, which have been overlooked in the past. In flow field prediction, large-eddy simulation was conducted by a modified 2-D vortex method with subgrid-scale modeling. The predicted mean velocities, shear layer growth rates, Reynolds stresses, and the RMS of longitudinal velocity fluctuations were found to be in good agreement with experiments, although the lateral velocity fluctuations were overpredicted. In scalar transport, the Monte Carlo method was extended to the simulation of the time-dependent pdf transport equation. For the first time, the mixing frequency in Curl's coalescence/dispersion model was estimated by using Broadwell and Breidenthal's theory of micromixing, which involves Schmidt number, Reynolds number and the local vorticity. Numerical tests were performed for a gaseous case and an aqueous case. Evidence that pure freestream fluids are entrained into the layer by large-scale motions was found in the predicted pdf. Mean concentration profiles were found to be insensitive to Schmidt number, while the unmixedness was higher for higher Schmidt number. Applications were made to mixing layers with isothermal, fast reactions. The predicted difference in product thickness of the two cases was in reasonable quantitative agreement with experimental measurements.
Diesel engines are an important technology for transportation of both people and goods. However, historically they have suffered a significant downside of high soot and nitrogen oxides (NO x ) emissions. Recently, ducted fuel injection (DFI) has been demonstrated to attenuate soot formation in compression-ignition engines and combustion vessels by 50% to 100%. This allows for diesel engines to be run at low-NO x emissions that would have otherwise produced significantly more soot due to the soot/NO x tradeoff. Currently the root causes of this soot attenuation are not well understood. To be able to better optimize DFI for use across a variety of engines and conditions, it is important to understand clearly how it works. This study expands on the current understanding of DFI by using numerical modeling under nonreacting conditions to provide insights about the roles of entrainment and mixing that would have been much more challenging to obtain experimentally. We report this study found that DFI enhances charge gas entrainment upstream of the duct and blocks entrainment inside of the duct. Mixing is enhanced by the duct, which results in lower peak equivalence ratios at the exit of the duct.
Entrainment-mixing mechanisms significantly affect cloud droplet number concentration, radius, and spectral shape. Quantitative examination of entrainment-mixing effects on cloud droplet spectral width is lacking. Here, we examine the effects of entrainment-mixing processes on cloud microphysics by 12,218 different setups, each simulated 10 times using the Explicit Mixing Parcel Model (EMPM) driven by the observational data from the Third Tibetan Plateau Atmospheric Scientific Experiment (TIPEX-III) campaign. Parameterizations of entrainment-mixing mechanisms are developed by relating homogeneous mixing degree to transition scale number that depends on the dissipation rate and droplet evaporation time scale. The correlation between relative dispersion of cloud droplet size distribution and homogeneous mixing degree changes from negative to positive with the decreasing homogeneous mixing degree. The different relationships are closely related to the competition between complete and partial droplet evaporation and the number concentration of small droplets, which are quantitatively described by two newly introduced dimensionless numbers. The competition is significantly affected by relative humidity and mixing fraction of entrained air as well as turbulence dissipation rate, but not much by cloud droplet number concentration. Especially, when relative humidity and dissipation rate are high, there is only a negative correlation. This study sheds new light on generalizing the homogeneous/inhomogeneous concept by considering relative dispersion, and also provides parameterizations of entrainment-mixing processes and relative dispersion for atmospheric models.
Fluid transport through fractured geological formations is strongly influenced by the redistribution of solutes at fracture intersections. In this study, we perform detailed numerical simulations of flow and scalar transport within the intersection of two smooth, planar fractures. The analysis focuses on the mixing ratio, the proportion of solute flux exiting along the outlet branch aligned with the primary inlet flow direction, relative to the total solute flux at the outlets. We systematically investigate how the mixing ratio varies with four key parameters: Peclet number, Reynolds number, flow rate ratio between outlet branches, and fracture intersection angle. Results show that the mixing ratio decreases with increasing Peclet number and outlet flow rate ratio, consistent with reduced diffusive spreading and enhanced streamline routing. While low Reynolds numbers have minimal impact, inertial effects at higher Reynolds numbers significantly increase the mixing ratio. Additionally, acute and obtuse intersection angles alter flow partitioning and modify the solute distribution at the outlets. These findings provide a quantitative basis for incorporating physically realistic mixing behavior—intermediate between complete mixing and streamline-following assumptions—into network-scale transport models. The results have direct relevance to subsurface energy systems, including geothermal energy production, carbon sequestration, and contaminant remediation.
In this research, lean mixed-mode combustion is numerically investigated using computational fluid dynamics (CFD) in a spark-ignition engine. A new E30 fuel surrogate is developed using a neural network model with matched octane numbers. A skeletal mechanism is also developed by automated mechanism reduction and by incorporating a NO x submechanism. A hybrid approach that couples the G-equation model and the well-stirred reactor model is employed for turbulent combustion modeling. The developed CFD model is shown to well predict pressure and apparent heat release rate (AHRR) traces compared with experiment. Two types of combustion cycles (deflagration-only and mixed-mode cycles) are observed. The mixed-mode cycles feature early flame propagation and subsequent end-gas auto-ignition, leading to two distinctive AHRR peaks. The validated CFD model is then employed to investigate the effects of NO x chemistry. The NO x chemistry is found to promote auto-ignition through the residual gas, while the deflagration phase remains largely unaffected. Sensitivity analysis is finally performed to understand effects of fuel properties, including heat of vaporization (HoV) and laminar flame speed (S L ). An increased HoV tends to suppress auto-ignition through charge cooling, while the impact of HoV on flame propagation is insignificant. In contrast, an increased S L is found to significantly promote both flame propagation and end-gas auto-ignition. The promoting effect of S L on auto-ignition is not a direct chemical effect; it is rather caused by an advancement of the combustion phasing, which increases compression heating of the end-gas.
The Rich-burn/Quick-mix/Lean-burn (RQL) combustor has been identified as a potential gas turbine combustor concept to reduce NO(x) emissions in High Speed Civil Transport (HSCT) aircraft. To demonstrate reduced NO(x) levels, cylindrical flametube versions of RQL combustors are being tested at NASA Lewis Research Center. A critical technology needed for the RQL combustor is a method of quickly mixing by-pass combustion air with rich-burn gases. Jet mixing in a cylindrical quick-mix section was numerically analyzed. The quick-mix configuration was five inches in diameter and employed twelve radial-inflow slots. The numerical analyses were performed with an advanced, validated 3D Computational Fluid Dynamics (CFD) code named REFLEQS. Parametric variation of jet-to-mainstream momentum flux ratio (J) and slot aspect ratio was investigated. Both non-reacting and reacting analyses were performed. Results showed mixing and NO(x) emissions to be highly sensitive to J and slot aspect ratio. Lowest NO(x) emissions occurred when the dilution jet penetrated to approximately mid-radius. The viability of using 3D CFD analyses for optimizing jet mixing was demonstrated.
The Rich-burn/Quick-mix/Lean-burn (RQL) combustor was identified as a potential gas turbine combustor concept to reduce NO(x) emissions in High Speed Civil Transport (HSCT) aircraft. To demonstrate reduced NO(x) levels, cylindrical flametube versions of RQL combustors are being tested at NASA Lewis Research Center. A critical technology needed for the RQL combustor is a method of quickly mixing by-pass combustion air with rich-burn gases. Jet mixing in a cylindrical quick-mix section was numerically analyzed. The quick-mix configuration was five inches in diameter and employed twelve radial-inflow slots. The numerical analyses were performed with an advanced, validated 3-D Computational Fluid Dynamics (CFD) code named REFLEQS. Parametric variation of jet-to-mainstream momentum flux ratio (J) and slot aspect ratio was investigated. Both non-reacting and reacting analyses were performed. Results showed mixing and NO(x) emissions to be highly sensitive to J and slot aspect ratio. Lowest NO(x) emissions occurred when the dilution jet penetrated to approximately mid-radius. The viability of using 3-D CFD analyses for optimizing jet mixing was demonstrated.
A direct numerical simulation of a plane turbulent mixing layer has been performed. The simulation was initialized using two turbulent velocity fields obtained from direct numerical simulation of a turbulent boundary layer at momentum thickness Reynolds number 300 (Spalart, 1988). The mixing layer is allowed to evolve long enough for self-similar linear growth to occur, with the visual thickness Reynolds number reaching 14,000. The simulated flow is examined for evidence of the coherent structures expected in a mixing layer (rollers and rib vortices). Before the onset of self-similar growth, such structures are present with properties similar to the corresponding laminar or transitional structures. In the self-similar growth regime, however, only the rollers are present with no indication of rib vortices and no indication of conventional pairing. This results in a reduction of mixing and layer growth.
Direct numerical simulations (DNS) of temporally developing, three dimensional, CH 4 /CO 2 , CH 4 /O 2 and CO 2 /O 2 mixing layers, are conducted at a supercritical pressure of 300 atm. To effectively model the supercritical regime, the employed formulation includes the compressible form of the governing equations, the cubic Peng-Robinson equation of state and a generalized formulation for heat and mass flux vectors derived from non-equilibrium thermodynamics and fluctuation theory. A linear inviscid stability analysis is also performed for each case, to determine its most unstable wavelength. Flow visualizations reveal the presence of high density gradient magnitude regions for all three mixing layers, with conditional averages indicating increased presence of heavier fluid species within these regions. No significant departures are observed from perfect gas behavior, with compressibility factors very close to unity for all three mixing cases. Applicability of presumed probability density function methods (PDF) is examined for the three supercritical mixing layers. An a priori analysis is also conducted to investigate various simplifying assumptions employed in modeling various subgrid scale (SGS) flux models. Two additional terms are identified in the large eddy simulations (LES) equations, the gradient of SGS contribution of pressure in the momentum equation and the gradient of SGS contribution of heat flux in energy equation, whose magnitudes are similar and comparable with their respective resolved terms. The performance of the scale similarity model to represent these additional terms is investigated. Lastly, the performance of Smagorinsky, gradient and scale similarity models are also investigated.
The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.
An eduction scheme has been developed in an attempt to determine the characteristics of large-scale vortical structures in a turbulent mixing layer. This analysis scheme has been applied to a set of experimental data taken in a new, larger mixing layer facility designed to minimize boundary and resonance effects. A similar scheme has been developed to apply to the results of a direct numerical simulation of a temporally growing mixing layer. A comparison of the two approaches shows important similarities in the coherent structures. The numerical simulations indicate that low levels of coherent forcing can dramatically change the evolution of the mixing layer. In the absence of such forcing, the numerical simulations and experiments show a lack of regularity in the transverse position, spacing, amplitude, shape and spanwise coherence of the large-scale vortical structures.
Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.
Numerical simulation of isothermal multi-component gas flow was conducted to study fluid flow and mixing in a scaled low-pressure, low-temperature test facility for the fission product venting system (FPVS) of a gas cooled fast reactor (GFR). The geometry of FPVS test facility was an open loop including gradual expansion coupling and two 90°pipe elbows. First, the validation of large eddy simulation (LES) wall-adapting local eddy-viscosity (WALE) turbulent model was performed for transitional flow in a circular pipe with gradual expansion. The reactingFOAM solver in OpenFOAM v8 was employed. By introducing appropriate turbulence disturbance at the flow inlet, such as turbulence intensity, the numerical results showed good agreement in (1) the velocity profile downstream of the pipe expansion measured by particle image velocimetry (PIV) in this study, and (2) the reattachment length reported in the literature. Using this validated model, the numerical simulation of flow and component mixing was performed for the FPVS with an inlet flowrate corresponding to a Reynolds number of 2,400 to investigate the flow behavior and component mixing. Standard deviation of the mass fraction of component, referred to as absolute mixing index (AMI), was calculated to quantify the mixing of components, showing that the component mixing length determined by AMI is related to the reattachment length downstream of the expansion. Additionally, this study was able to identify the best location in the FPVS test facility to measure the velocity and concentration profies where multicomponent flow is well mixed.
The vortical evolution of mixing layers subject to various types of forcing is numerically simulated using pseudospectral methods. The effect of harmonic forcing and random noise in the initial conditions is examined with some results compared to experimental data. Spanwise forcing is found to enhance streamwise vorticity in a nonlinear process leading to a slow, secondary growth of the shear layer. The effect of forcing on a chemical reaction is favorably compared with experimental data at low Reynolds numbers. Combining harmonic and subharmonic forcing is shown to both augment and later destroy streamwise vorticity.
The vortical evolution of mixing layers subject to various types of forcing is numerically simulated using pseudospectral methods. The effect of harmonic forcing and random noise in the initial conditions is examined with some results compared to experimental data. Spanwise forcing is found to enhance streamwise vorticity in a nonlinear process leading to a slow, secondary growth of the shear layer. The effect of forcing on a chemical reaction is favorably compared with experimental data at low Reynolds numbers. Combining harmonic and subharmonic forcing is shown to both augment and later destroy streamwise vorticity.
Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Here we present the development of a methodology to rapidly and efficiently numerically simulate mixed fracture-matrix flow systems for evaluation of well design and completion options. An example evaluation based on a small fracture network representative of FORGE Well 16(A and B)-78(32) follows a discussion of the theory and model validation.
Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Here we present the development of a methodology to rapidly and efficiently numerically simulate mixed fracture-matrix flow systems for evaluation of well design and completion options. An example evaluation based on a small fracture network representative of FORGE Well 16(A and B)-78(32) follows a discussion of the theory and model validation.