Large-Eddy Simulations of Spray a Flames Using Explicit Coupling of the Energy Equation with the FGM Database

This paper provides a numerical study on n-dodecane flames using Large-Eddy Simulations (LES) along with the Flamelet Generated Manifold (FGM) method for combustion modeling. The computational setup follows the Engine Combustion Network Spray A operating condition, which consists of a single-hole spray injection into a constant volume vessel. Herein we propose a novel approach for the coupling of the energy equation with the FGM database for spray combustion simulations. Namely, the energy equation is solved in terms of the sensible enthalpy, while the heat of combustion is calculated from the FGM database. This approach decreases the computational cost of the simulation because it does not require a precise computation of the entire composition of the mixture. The flamelet database is generated by simulating a series of counterflow diffusion flames with two popular chemical kinetics mechanisms for n-dodecane. Further, the secondary breakup of the droplet is taken into account by a recently developed modified version of the Taylor Analogy Breakup model. The numerical results show that the proposed methodology captures accurately the main characteristics of the reacting spray, such as mixture formation, ignition delay time, and flame lift-off. Additionally, it captures the “cool flame" between the flame lift-off and the injection nozzle. Overall, the simulations show differences between the two kinetics mechanisms regarding the ignition characteristics, while similar flame structures are observed once the flame is stabilised at the lift-off distance.

     

The equilibrium limit of a constitutive model for two-phase granular mixtures and its numerical approximation

In this paper we analyze the equilibrium limit of the constitutive model for two-phase granular mixtures introduced in Papalexandris (2004) [13], and develop an algorithm for its numerical approximation. At, equilibrium, the constitutive model reduces to a strongly coupled, overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase. First we carry a perturbation analysis based on standard hydrostatic-type scaling arguments which reduces the complexity of the coupling of the equations. The perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator. Further, based on the Helmholtz decomposition and Ladyzhenskaya’s decomposition theorem, we develop a projection-type, Successive-Over-Relaxation numerical method. This method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro-structure. We also prove that this method is both stable and consistent hence, under standard assumptions, convergent. The paper concludes with the presentation of representative numerical results.     

On the applicability of Stokes’ hypothesis to low-Mach-number flows

Continuum Mechanics and Thermodynamics - Stokes’ hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Although not valid for many fluids, it is common practice...     

Structural characteristics of detonation expansion from a small channel to a larger one

We report on numerical simulations of the evolution of two-dimensional detonation waves that are expanded from a small channel to a larger one. In accordance with experimental data, the simulations predict three different types of evolution, namely, supercritical, critical and subcritical detonations. In a supercritical detonation, the reaction zone remains always attached to the precursor shock, whereas in a critical one it temporarily detaches and then re-attaches to the front. In the subcritical type, the extinction is permanent, i.e., the detonation quenches. The effects of the fuel’s activation energy and the channel-width ratio are studied via a parametric study. It is found that sufficiently large values of these two parameters can result to flows of the critical and even the subcritical type. Finally, three-dimensional simulations have also been performed and are briefly discussed herein.     

Statistical analysis of instantaneous turbulent heat transfer in circular pipe flows

Turbulent heat transfer in circular pipe flow with constant heat flux on the wall is investigated numerically via Large Eddy Simulations for frictional Reynolds number Re _τ  = 180 and for Prandtl numbers in the range 0.1 ≤ Pr ≤ 1.0. In our simulations we employ a second-order finite difference scheme, combined with a projection method for the pressure, on a collocated grid in cylindrical coordinates. The predicted statistical properties of the velocity and temperature fields show good agreement with available data from direct numerical simulations. Further, we study the local thermal flow structures for different Prandtl numbers. As expected, our simulations predict that by reducing the Prandtl number, the range of variations in the local heat transfer and the Nusselt number decrease. Moreover, the thermal flow structures smear in the flow and become larger in size with less sharpness, especially in the vicinity of the wall. In order to characterize the local instantaneous heat transfer, probability density functions (PDFs) for the instantaneous Nusselt number are derived for different Prandtl number. Also, it is shown that these PDFs are actually scaled by the square root of the Prandtl number, so that a single PDF can be employed for all Prandtl numbers. The curve fits of the PDFs are presented in two forms of log-normal and skewed Gaussian distributions.