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Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) have been conducted of a temporal mixing layer laden with evaporating drops, in order to assess the ability of LES to reproduce dynamic and mixing aspects of the DNS which affect combustion, independently of combustion models.
The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings was simulated numerically. Initial conditions for all simulations consisted of a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found both to inhibit the growth of infinitesimal three-dimensional disturbances and to trigger the transition to turbulence in highly three dimensional flows. The mechanisms responsible for the growth of three-dimensionality as well as the initial phases of the transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of span wise vorticity, which undergo a secondary roll up. Transition also produces an increase in the degree of scalar mixing, in agreement with experimental observations of mixing transition. Simulations were also conducted to investigate changes in span wise length scale that may occur in response to the change in stream wise length scale during a pairing. The linear mechanism for this process was found to be very slow, requiring roughly three pairings to complete a doubling of the span wise scale. Stronger three-dimensionality can produce more rapid scale changes but is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one span wise scale to a similar array at a larger span wise scale.
Numerical integrations using a potential enstrophy-conserving scheme are presented for the flow within a mixed layer over hilly terrain using the hydrostatic shallow-water equations with a quadratic drag law. The mesoscale area treated is 150 km on a side; cyclic lateral boundary conditions are used. It is found that for the idealized conditions treated (no surface heating, no entrainment and no pressure adjustments aloft), the topography quickly induces a steady state flow pattern by means of surface friction. Unsteadiness does not occur unless a surface-friction Reynolds number is greater than approximately 100. Effects of varying the Rossby number, Froude number and terrain-height parameter are examined.
Presented are the results of a study of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than 1/2, and the other is slow with speeds less than 1/2. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. It is shown that three dimensional modes have the same general behavior as the two dimensional modes but with higher growth rates over some range of propagation direction. Finally, a group of very low frequency unstable modes was found for sufficiently large Mach numbers. These modes have very low phase speeds but large growth rates.
Presented are the results of a study of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than 1/2, and the other is slow with speeds less than 1/2. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. It is shown that three-dimensional modes have the same general behavior as the two-dimensional modes but with higher growth rates over some range of propagation direction. Finally, a group of very low frequency unstable modes was found for sufficiently large Mach numbers. These modes have very low phase speeds but large growth rates.
Some preliminary results from the Turton and Nicholls mixed layer model using typical FIRE boundary conditions are presented. The model includes entrainment and drizzle parametrizations as well as interactive long and shortwave radiation schemes. A constraint on the integrated turbulent kinetic energy balance ensures that the model remains energetically consistent at all times. The preliminary runs were used to identify the potentially important terms in the heat and moisture budgets of the cloud layer, and to assess the anticipated diurnal variability. These are compared with typical observations from the C130. Sensitivity studies also revealed the remarkable stability of these cloud sheets: a number of negative feedback mechanisms appear to operate to maintain the cloud over an extended time period. These are also discussed. The degree to which such a modelling approach can be used to explain observed features, the specification of boundary conditions and problems of interpretation in non-horizontally uniform conditions is also raised.
A preliminary experimental investigation to establish some of the characteristics and further the understanding of the initial development of a turbulent free mixing layer for hypersonic speeds has been conducted. Mean profile data at about 6 inches downstream of the exit of a hypersonic nozzle have been obtained in nitrogen for a nominal Mach number of 19.5, total temperature of about 1670 K and Reynolds number range from about 50,000 to 110,000 per foot and have been compared with profiles upstream of the nozzle exit. Static pressure varied across the shear layer for the present tests. The outer 80 percent of the high-velocity portion of the free shear layer can be calculated by a rotational method of characteristics. However, turbulent mixing is evidently important in the low-velocity region, and effects of eddy viscosity and eddy conductivity should be included in a theoretical analysis.
Three high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers (TML) for different convective Mach numbers (Mc) ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method (H.C. Yee and B. Sjogreen, Proceedings of ICOSAHOM09, June 22-26, 2009, Trondheim, Norway) is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results of Barone et al. (2006), and published direct numerical simulations (DNS) work of Rogers & Moser (1994) and Pantano & Sarkar (2002), whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.
The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.
The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon sup -1), where (epsilon much less than 1) is the crossflow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.
The dependence of product generation on Peclet and Reynolds numbers in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is related theoretically to the fractal dimension of the passive scalar interfaces. This relation is verified using product generation measurements and dimensions derived from a standard box counting technique. A transition from a low initial dimension to a higher one of approximately 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transitions, either in the spectra of the vorticity field or in the mixing behavior, are found for Reynolds numbers up to 90,000.
Synthetic Aviation Turbine Fuels (SATFs) are promising for reducing soot emissions from the aviation sector and diversifying Jet Fuel (JF) sources. Accurately predicting the combustion and emissions behavior of SATFs (and other JFs) necessitates robust experimental databases to elucidate the chemistry of long-chain iso-paraffins, which can compose up to two-thirds of SATF blends and whose behavior is considered to be well-represented by that of iso-dodecane isomers. Here, this study characterizes two laminar non-premixed Planar Mixing Layer Flames (PMLFs) with mild soot loads fueled by nitrogen-diluted ethylene, pure and doped with 2,2,4,6,6-pentamethyl-heptane, respectively. The two PMLFs have the same stoichiometric mixture fraction and total hydrocarbon mole fraction in the fuel stream (X F,F =X C2H4,F +X C12H26,F = 0.260), resulting in nearly the same maximum temperature (T max ≈1800 K) and simple identification of the effects of doping. Importantly, any horizontal PMLF cross-section has a self-similar structure that can be modeled as an equivalent One-Dimensional Counterflow Flame (1D-CF) with vanishingly small strain rate (a). The cross-section at a Height Above the Burner (HAB) of 50 mm is characterized in terms of C 0 -C 18 gas species using capillary sampling followed by GC-MS analyses. Laser-Induced Emission Spectroscopy (LIES) quantifies the soot volume fraction (ƒ v ) profiles at HAB=25 and 50 mm where Elastic Laser Light Scattering (E-LLS) is performed to determine the a of the equivalent 1D-CFs and the profile of the E-LLS equivalent diameter ( d 6,3 ) of soot. The substitution of 1500 ppm of ethylene with 2,2,4,6,6-pentamethyl-heptane causes an increase of ≈1.5 in the concentrations of several polycyclic aromatic hydrocarbons and fv. Concurrently, the measured d 6,3 doubles in the oxidizer stream, yet remains the same in the fuel stream, at HAB=50 mm. Instead, at HAB= 25 mm, the iso-dodecane doping does not affect the d 6,3 profile in either stream. The experimental results partially validate the chemical reactions and soot formation kinetic model developed at Lawrence Livermore National Laboratory and provide directions to further improve its predictions.
Digital image analysis has been applied to a shadowgraph motion picture of a helium nitrogen mixing layer in order to characterize the coherent vortex structures in the flow. Both the primary spanwise coherent vortices and secondary streamwise vortices are considered. Pattern recognition algorithms were designed to take advantage of the more pronounced features of the vortices and of their temporal coherence to isolate them and to measure their characteristics. The resulting data base permits a deterministic description of the evolution of primary and seconary vortices.
The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.
We consider analytically the evolution of a three-dimensional wave packet generated by an impulsive source in a mixing layer. The base flow is assumed to be spreading due to viscous diffusion. The analysis is restricted to small disturbances (linearized theory). A suitable high-frequency ansatz is used to describe the packet; the key elements of this description are a complex phase and a wave action density. It is found that the product of this density and an infinitesimal material volume convecting at the local group velocity is not conserved: there is a continuous interaction between the base flow and the wave action. This interaction is determined by suitable mode-weighted averages of the second and fourth derivatives of the base-flow velocity profile. Although there is some tendency for the dominant wave number in the packet to shift from the most unstable value toward the neutral value, this shift is quite moderate. In practice, wave packets do not become locally neutral in a diverging base flow (as do instability modes), therefore, they are expected to grow more suddenly than pure instability modes and do not develop critical layers. The group velocity is complex; the full significance of this is realized by analytically continuing the equations for the phase and wave action into a complex domain. The implications of this analytic continuation are discussed vis-a-vis the secondary instabilities of the packet: very small scale perturbations on the phase can grow very rapidly initially, but saturate later because most of the energy in these perturbations is convected away by the group velocity. This remark, as well as the one regarding critical layers, has consequences for the nonlinear theories.
The dependence of product generation on Peclet and Reynolds numbers in a numerically simulated, reacting, two-dimensional, temporally growing mixing layer is related theoretically to the fractal dimension of the passive scalar interfaces. This reaction is verified using product generation measurements and fractal dimensions derived from the box counting technique. A transition from a low initial dimension to a higher one of approximately 5/3 is identified and shown to be associated to the kinematic distortion of the flow field during the first pairing interaction. It is suggested that the structures reponsible for this transition are nondeterministic, nonrandom, inhomogeneous fractals. In the range of Schmidt numbers investigated (0.25-4), only the large scales are involved. No further transitions, either in the spectra of the vorticity field or in the mixing behavior, are found for Reynolds numbers up to 90,000.
An experimental study was conducted to investigate the generation process of random small-scale turbulence in an originally laminar mixing layer. The evolutions of the two types of deterministic structures, the spanwise and streamwise vortices, were first clarified in order to determine their roles in the transition process. A scaling rule for the streamwise distance from the trailing edge of the splitter plate to the vortex merging position was found for various velocity ratios. After this stremwise lengthscale was determined, it became clear that the spanwise wavelength of the streamwise vortices doubled after the merging of the spanwise structures which nominally doubled streamwise wavelengths. The most interesting finding was that the random small-scale eddies were produced by the interactions between the merging spanwise structures and the streamwise vortices.
Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.