Krishnan Radhakrishnan

A fully implicit time accurate method for hypersonic combustion: application to shock-induced combustion instability

A new fully implicit, time accurate algorithm suitable for chemically reacting, viscous flows in the transonic-to-hypersonic regime is described. The method is based on a class of Total Variation Diminishing (TVD) schemes and uses successive Gauss-Seidel relaxation sweeps. The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts, but a fully coupled interaction is still maintained. As a result, the matrices that have to be inverted are of the same size as those obtained with the commonly used point implicit methods. In this paper we illustrate applicability of the new algorithm to hypervelocity unsteady combustion applications. We present a series of numerical simulations of the periodic combustion instabilities observed in ballistic-range experiments of blunt projectiles flying at subdetonative speeds through hydrogenair mixtures. The computed frequencies of oscillation are in excellent agreement with experimental data.

Pulsating one-dimensional detonations in hydrogen–air mixtures

The propagation of one-dimensional detonations in hydrogen–air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit time marching algorithm. The hydrogen–air combustion is modelled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies for an equivalence ratio range of 0.4–2.0, initial pressure range of 0.2–0.8 bar and different degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel–air equivalence ratio and pressure. For equivalence ratios less than approximately 1.2 and for all pressures, the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures exhibit a period-doubled bifurcation that depends on the initial pressure. Parametric studies over a degree of overdrive range of 1.0–1.2 for stoichiometric mixtures at 0.42 bar initial pressure indicate that stable detonation wave propagation is obtained at the high end of this range. For degrees of overdrive close to one, the detonation wave exhibits a low-frequency mode characterized by large fluctuations in the detonation wave speed. The McVey–Toong short-period wave-interaction theory is in qualitative agreement with the numerical simulations; however, the frequencies obtained from their theory are much higher, especially for near-stoichiometric mixtures at high pressure. Modification of this theory to account for the finite heat-release time significantly improves agreement with the numerically computed frequency over the entire equivalence ratio and pressure ranges.

Computational study of NOx formation in hydrogen-fuelled pulse detonation engines

The formation of NOx in hydrogen-fuelled pulse detonation engines (PDE) is investigated numerically. The computations are based on the axisymmetric Euler equations and a detailed combustion model consisting of 12 species and 27 reactions. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation front. Computed NO concentrations are in good agreement with experimental measurements obtained at two operating frequencies and two equivalence ratios. Additional computations examine the effects of equivalence ratio and residence time on NOx formation at ambient conditions. The results indicate that NOx formation in PDEs is very high for near stoichiometric mixtures. NOx reduction requires use of lean or rich mixtures and the shortest possible detonation tube. NOx emissions for very lean or very rich mixtures are, however, fairly insensitive to residence time.

A fully implicit time accurate method for hypersonic combustion - Application to shock-induced combustion instability

A new fully implicit, time accurate algorithm suitable for chemically reacting, viscous flows in the transonic-tohypersonic regime is described. The method is based on a class of Total Variation Diminishing (TVD) schemes and uses successive Gauss-Seidel relaxation sweeps. The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts, but still maintaining a fully coupled interaction. As a result, the matrices that have to be inverted are of the same size as those obtained with the commonly used point implicit methods. In this paper we illustrate the applicability of the new algorithm to hypervelocity unsteady combustion applications. We present a series of numerical simulations of the periodic combustion instabilities observed in ballistic-range experiments of blunt projectiles flying at subdetonative speeds through hydrogen-air mixtures. The computed frequencies of oscillation are in excellent agreement with experimental data.

Simulation of Unsteady Hypersonic Combustion Around Projectiles in an Expansion Tube

Abstract. The temporal evolution of combustion flowfields established by the interaction between wedge-shaped bodies and explosive hydrogen-oxygen-nitrogen mixtures accelerated to hypersonic speeds in an expansion tube is investigated. The analysis is carried out using a fully implicit, time-accurate, computational fluid dynamics code that we recently developed to solve the Navier-Stokes equations for a chemically reacting gas mixture. The numerical results are compared with experimental data from the Stanford University expansion tube for two different gas mixtures at Mach numbers of 4.2 and 5.2. The experimental work showed that flow unstart occurred for both the Mach 4.2 cases. These results are reproduced by our numerical simulations and, more significantly, the causes for unstart are explained. For the Mach 5.2 mixtures, the experiments and numerical simulations both produced stable combustion. However, the computations indicate that in one case the experimental data were obtained during the transient phase of the flow; that is, before steady state had been attained.

Structure and stability of one-dimensional detonationsin ethylene-air mixtures

Abstract.The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of

Computational and Experimental Study of NOx Formation in Hydrogen-Fueled Pulse Detonation Engines

0.5 \le \phi \le 3

Structure and Stability of One-dimensional Detonations in Ethylene-Air Mixtures

for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures (

Computational study on use of single- point analysis method for quantitating local cerebral blood flow in mice

\phi > 1.2

A Quantitative Study of Oxygen as a Metabolic Regulator

) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.