Session KD: Reacting Flows I*

Flameless Combustion for Gas Turbines

An experimental study of a novel flameless combustor for gas turbine engines is presented. Flameless combustion is characterized by distributed flame and even temperature distribution for high preheat air temperature and large amount of recirculating low oxygen exhaust gases. Extremely low emissions of NOx, CO, and UHC are reported. Measurements of the flame chemiluminescence, CO and NOx emissions, acoustic pressure, temperature and velocity fields as a function of the preheat temperature, inlet air mass flow rate, exhaust nozzle contraction ratio, and combustor chamber diameter are described. The data indicate that larger pressure drop promotes flameless combustion and low NOx emissions at the same flame temperature. High preheated temperature and flow rates also help in forming stable combustion and therefore are favorable for flameless combustion.   

Reacting Flow in the Entrance to a Channel with Surface and Gas-Phase Kinetics

In many catalytic reactors the conversion process is most intense at the very beginning of the channel where the flow is not yet fully developed; hence there will be important interactions between the developing flow field and reaction. To study this problem we have written an object-oriented code for the analysis of reacting flow in the entrance of a channel where both surface reaction and gas-phase reaction are modeled with detailed kinetics. Fluid mechanical momentum and energy equations are modeled by parabolic ``boundary layer''-type equations where streamwise gradient terms are small and the pressure is constant in the transverse direction. Transport properties are modeled with mixture-averaging and the chemical kinetic sources terms are evaluated using Cantera. Numerical integration is done with Matlab using the function pdepe. Calculations were completed using mixtures of methane and air flowing through a channel with platinum walls held at a fixed temperature. GRI-Mech 3.0 was used to describe the gas-phase chemistry and Deutchmann's methane-air-platinum model was used for the surface chemistry. Ignition in the gas phase is predicted for high enough wall temperatures. A hot spot forms away from the walls just before ignition that is fed by radicals produced at the surface.   

Initial-value problem for stability of detonations rehabilitated

Erpenbeck (1962) formulated the hydrodynamic stability of detonations as an initial-value problem. Unfortunately, instead of directly solving the dispersion relation numerically, Erpenbeck used the principle of the argument utilizing both analytical and numerical approaches to establish the existence of the poles in the Laplace variable plane for the case of idealized one-reaction detonations (1964). The numerical implementation was so daunting that it is still believed that the method is ``hard to implement and it does not give a computationally direct way to determine the stability boundaries or the dispersion relation that defines the unstable modes.'' As a result, the normal mode approach was suggested in 1990. In the present work, we revisited the stability problem of idealized one-reaction detonations, and showed that the spectrum of the normal mode approach is equivalent to the discrete spectrum stemming from Erpenbeck' s dispersion relation. The dispersion relation requires solving the homogeneous ODEs for the adjoint system (instead of inhomogeneous equations in the normal mode formulation), and evaluating an integral through the reaction zone. The solution of the initial-value problem also leads to a method of expansion of the perturbation field into modes of discrete and continuous spectra. In addition, it gives a convenient tool for getting the receptivity problem solution. It is necessary to explore the receptivity coefficients together with the conventional eigenvalue analysis in order to understand the flow dynamics.   

Shock and initial disturbance induced initiation of the idealized condensed phase explosives.

Using a model of condensed phase explosive with reaction rate proportional to $p^n$ ($p$ is pressure and $n$ is an adjustable parameter), we investigate detonation induced either by the passage of the shock or by an initial disturbance. A large $n$ asymptotic analysis is performed. It shows that the evolution begins with an induction stage, followed by a sequence of pressure runaways, resulting in a propagating, decelerating weak detonation. Secondary shock and super-detonation (i.e. strong detonation) form once the weak detonation reaches the Chapman-Jouguet speed. We use parametric integration to obtain the path of the weak detonation and predict the time and location of the strong detonation formation. For small amplitude long wave length initial perturbation induced initiation we construct asymptotic solution. The path and the strong detonation formation point, given solely in terms of the initial pressure and velocity perturbations, are in good agreement with numerical solution. Numerical simulations for order $O(1)$ values of $n$ show that idealized condensed phase model can qualitatively describe wide range of experimentally observed behaviors.   

Formation of Reactivity Gradients for Detonation Initiation through Turbulent Flame Quenching

Deflagration-to-detonation transition (DDT) in gaseous reactive systems usually occurs through the Zeldovich's gradient mechanism that involves the propagation of a spontaneous reaction wave through a preconditioned region containing a gradient of reactivity. One of the many possible ways for creating this gradient is the flame quenching in the turbulent flow and subsequent mixing of burned and unburned materials. We study these phenomena using compressible reactive Navier-Stokes numerical simulations. The reactive system considered is a stiochiometric hydrogen-oxygen mixture with a simplified one-step Arrhenius kinetics of energy release. Two-dimensional simulations of a flame interacting with a diffracting shock and with a turbulent flow behind the shock show the local flame quenching. This leads to the mixing of burned and unburned materials and the formation of reactivity gradients. Because such flame-quenching phenomena can create conditions leading to DDT in unconfined systems, they are important for hydrogen safety issues and for Type Ia supernovae.   

Flow Velocity Computation, from Temperature and Number Density Measurements using Spontaneous Raman Scattering, for Supersonic Chemically Reacting Flows.

The closure problem in chemically reacting turbulent flows would be solved when velocity, temperature and number density (transport variables) are known. The transport variables provide input to momentum, heat and mass transport equations leading to analysis of turbulence-chemistry interaction, providing a pathway to improve combustion efficiency. There are no measurement techniques to determine all three transport variables simultaneously. This paper shows the formulation to compute flow velocity from temperature and number density measurements, made from spontaneous Raman scattering, using kinetic theory of dilute gases coupled with Maxwell-Boltzmann velocity distribution. Temperature and number density measurements are made in a mach 1.5 supersonic air flow with subsonic hydrogen co-flow. Maxwell-Boltzmann distribution can be used to compute the average molecular velocity of each species, which in turn is used to compute the mass-averaged velocity or flow velocity. This formulation was validated by Raman measurements in a laminar adiabatic burner where the computed flow velocities were in good agreement with hot-wire velocity measurements.   

A Numerical Method for DNS/LES of Compressible Reacting Flows

A non-dissipative, implicit, all Mach number algorithm for direct numerical and large eddy simulation of compressible reacting flows, is described. The compressible Navier-Stokes equations are rescaled so that the zero Mach number reacting equations are discretely recovered in the limit of zero Mach number. The dependent variables are co--located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non--reacting limit. The species equations are implicit to allow for stiff chemical mechanisms, and are readily applied to complex chemistry. Numerical examples ranging from one--step chemistry to a nine species, nineteen reaction mechanism for H2 and O2 (Mueller et al, {\it Int. J. Chem. Kinet.} 1999) will be shown.   

Compressible fluid response to extremely rapid thermal power deposition.

``Gasdynamics of explosions is{\ldots}best defined as the science dealing with the interrelationship between energy transfer occurring at a high rate in a compressible medium and the concomitant motion set up in the this medium'' (Oppenheim, A.K.and Soloukhin, R.I.,1973, ``Experiments in Gasdynamics'', Ann. Revs. Of Fluid Mechs., \textbf{5}, 31-55,). Asymptotic modeling is used to show that the interaction depends on the ratio of the dimensional time scale for substantial chemical heat release, t$_{H}$', into a local region of length scale l', and local acoustic time t$_{A}$'= l '/a' where a' is the local speed of sound. When t$_{H}$'/t$_{A}$'$<<$1 local heat addition occurs in a nearly constant volume process (local inertial confinement) with a low Mach number fluid response. The temperature rise is accompanied by a concomitant pressure rise, so that for a brief instant a hot, high-pressure spot exists in a relatively low pressure and temperature environment. Subsequent expansion of the spot on the t$_{A}$'-time scale, driven by the large pressure gradient between the spot and the environment is the source (``piston'' effect) of compression waves in the environment. Wave coalescence can lead to shock wave formation.