The research expertise at CCL lies in the area of numerical simulations of compressible fluid-dynamics and combustion. In general, CCL research interests are in chemically reacting flows and processes where the coupling of fluid mechanics and kinetic scales is important. We are interested in mixing-layers, boundary layers, transitional flows in rocket motors and detonations. Several specific topics that we are currently pursuing or we will in the immediate future are outlined below.

1. Vibrational relaxation effects on hypersonic transitional flows.

This research is concerned with identifying the effect of the vibrational relaxation on shear and boundary layer spatial development. Coupling between the vibrational relaxation and the instability process occurs near the nose of hypersonic vehicles because of the proximity of the point of inception of the boundary layer and the leading edge shocks. It also occurs in the nozzle of hypersonic thrust generators due to sudden flow expansion, which yields an out-flowing gas not in a Boltzmann equilibrium state. Experiments and computations generally agree on the stabilizing effect of the vibrational relaxation. Bertolotti strongly disagrees with this conclusion, and points out that different flow conditions lead to different results. Most of previously published studies on the subject treat the vibrational process in a very simplified way, e.g., with the ideal dissociating gas approximation or with the two temperature model. Recently, we performed a linear stability analysis on post-shock shear layers using a state resolved master equation approach based on quasi-classical quantum transfer modeling.
The large temperature associated with viscous heating at the shear line produces molecular NO, through the Zeldovich mechanism. The energy distribution of the nascent NO strongly affects the instability modes. Classical two temperature models fail to predict the effect of vibrational transfers on the shear layer growth because of the assumption of a Boltzmann (log-linear) vibrational energy distribution. The appearance of NO gas through the Zeldovich mechanism also implies that pure nitrogen experiments are not appropriate test cases.
Stream-wise relaxation effects on the perturbation dynamics have been neglected by the majority of linear analyses, where the mean flow is assumed parallel. For a Mach 7.1 flow [2] the post shock vibrational relaxation time scale is approximately 0.25 µs while the convective time scale is approximately 0.02 µs. Considering that characteristic fluctuation scales are a fraction of the convective time, the perturbation growth and the stream-wise relaxation processes are coupled, already at Mach 7.1. Given the large number of vibrational levels needed in a master equation approach a non-linear analysis is not practical in this instance. We plan to perform a parabolic stability linear analysis, where a weakly non-parallel perturbation expansion is considered. Deviation from a Boltzmann distribution will be quantified on the basis of equivalent vibrational and dissociation temperatures for the diatomic species. The goals of the analysis are to clarify the dynamics of vibrational and dissociation equivalent temperatures in the linearized flows, to identify the spatial growth of the deviation from the log-linear law, and to determine changes in the surface heat transfer perturbations associated with vibrational non-equilibrium. The analysis will identify shortcomings in simplified models, and lead to a more rigorous treatment of relaxation processes in transitional flows.

Further Reading

1. Bertolotti, "The influence of vibrational and rotational relaxation on boundary layer stability", J. Fluid Mech. 372:93-118.
2. Massa, Austin, "Spatial linear stability of a hypersonic shear layer with non-equilibrium thermochemistry," Physics of Fluids, 20(8), 2008.

2. Richtmeyer-Meshkov instability and the initiation of detonation waves.

The role of the Richtmeyer-Meshkov instability (RMI) resulting from flame shock interaction on the formation of hot spots in a premixed mixture was analyzed by Khoklov et al., [1-2]. The phenomenon is of physical importance in the context of detonation initiation and baroclinic mixing. Our main interest is in the role of combustion on instability growth and scaling effects. The Richtmeyer shock problem has no geometrical length scale, so that, in the non-reactive case, the normalized growth rate of an interface disturbance scales linearly with the disturbance wave number. The premixed combustion problem that supports detonation initiation has, in its most simple form, the induction length as associated scale. The relationship between induction and disturbance wave number introduces a scaling parameter. A more detailed discussion on the scaling is described in one of our recent studies [3]. Khokhlov and co-authors note the absence of fine scales interface disturbances in burning computations. The rationale provided in their paper is that the flame consumes the small scales. In previous attempts to model the RMI, a thorough examination of the mixture thermo-chemical properties on the surface deformation rate was not performed, the induction length scale was not considered, and the interaction between chemical (flame thickness) and fluid-mechanics scale (interface wave number) was explicitly neglected. It is widely acknowledged that non-reacting shocks are stable to linear perturbations, while detonations are unstable for realistic values of the heat release. In the non-reactive Richtmeyer-Meshkov problem, the interface deforms at a linear rate, while the shocks relax towards the unperturbed state with an exponential decay. In the reactive case, the resonant interaction between surface deformation and unstable detonation structures may support super-linear growth rates of interface disturbances.
Instability patterns associated with the RMI plays a fundamental role in the mixing rate through the strain driven gradient steepening at the interfaces. The contribution of the initial patterns to the instantaneous mixing rate was measured to be up to 80% of the peak mixing rate, in non-reactive measurements [5]. On the other hand, for reactive mixtures, we expect the scaling effect to alter shock induced mixing, and favor the process at selected wave numbers.
We are in the process of carrying out both a linear stability analysis with detailed kinetics, and a three-dimensional non-linear analysis with reduced kinetics. The reduction of the kinetics mechanism will be based upon linear analysis theory; thermodynamic equilibrium will be used to eliminate fast time scales. This analysis will identify scaling effects in the perturbation growth of linear interface disturbances under combustion conditions (linear analysis), determine thermo-chemical mixture properties that can lead to non-linear growth (linear analysis), and shed light on the contribution of the RMI patterns to the instantaneous mixing rate under combustion conditions (non-linear analysis).

Further Reading

1. Khokhlov, Oran, Chtchelkanova and Wheeler, "Interaction of a shock with a sinusoidally perturbed flame," Combustion and Flame 117:99-116, 1999.
2. Khokhlov, Oran and Thomas, "Numerical simulation of deflagration to detonation transition: The role of Shock-Flame interaction in turbulent flames," Combustion and Flame 117:323-339, 1999.
3. Massa and Lu, "Role of the induction zone on turbulence-detonation interaction," 2008, Physics of Fluids, (under review, preprint available from the authors).
4. Short and Stewart, "Cellular detonation stability. Part 1. A normal mode linear analysis," J. Fluid Mech. 368:229-262, 1998.
5. Tomkins, Kumar, Orlicz and Prestridge, "An experimental investigation of mixing mechanism in shock accelerated flow," J. Fluid Mech., 611:131-150, 2008.

3. Analysis of erosive behavior in rocket chambers

Erosive burning describes burn rate augmentation in solid rocket engines, as a result of cross-flow conditions. There have been many attempts to identify the mechanism responsible for the measured increase in burn rate over the zero-cross flow burn rate. "Flame bending", "heat transfer from core to propellant surface", "increase in heat flux due to turbulence" are classical examples. Most analyses have relied on empirical fits often based on turbulent profiles over a flat plate; none have been based on a rigorous analysis of the equations. Penetration of eddys in the combustion sublayer that supports the solid pyrolization is inhibited by the blowing effect at the boundary, thus the dynamics of the interaction are fundamentally different from a flat plate problem. we have recently submitted a new study that includes a rigorous thermo-chemical analysis of the interaction and compares characteristic solutions of coupled and decoupled eigenproblems . The comparison highlights the marked influence of the burning characteristics on convective penetration inside the combustion layer. Non-linear enthalpy-velocity correlations are decreased by an increase in burning rate and the increase in thermal perturbation fields in the layer scale consistently with the experiments.
Erosive burning is responsible for strong overpressure at the rocket firing stage. A better understanding of the influence of burning characteristics on erosive sensitivity can improve rocket design techniques and propellant choices. we plan to perform parabolic stability and non-linear Navier-Stokes calculations using a reduced chemistry model building on our previous work. The focus of the research will be on validation of linear analysis results, modes saturation, transition to turbulence, and analysis of the effect of corrugation and particle scales on the stability and transition problems. The goals of the research are to validate empirical correlation models based on fluid-mechanical interaction, identify the role of particle scales on the augmentation phenomenon, and analyze propellant responses to spatially evolving perturbations.

Further Reading

1. Massa, "Spatial linear analysis of the flow in a solid rocket motor with burning walls," 2008, Combustion and Flame, (under review, preprint available from the author).

4. Flame stability in supersonic hydrocarbon flameholders

A recent experimental investigation has shown that flame stability and blow-out injection rates in supersonic combustors are strongly dependent on the injection location, the flame holder shape and the fuel characteristics [1]. The flame holder shape was also found to modify the mixing-layer stability, because of acoustic coupling. Hydrocarbon chemistry is acknowledged to affect both flame stability and shear layer spreading rate [2], but the basic mechanism is not well understood. Combustion modifies the density mean profile, with a strong effect on baroclinc torque. In a recent paper we analyzed the effect of thermo-chemistry on the characteristics of hydrocarbon fuel shear layers using a detailed chemistry approach [4]. The linear and non-linear analyses identify the role of pressure-strain rate correlations on the growth of the perturbation kinetic energy. The link between normal velocity gradients and density gradients through the continuity equation points to baroclinic effects as responsible for the reduction in vorticity caused by an increase in heat release.
The success of hypersonic combustors is directly related to the success in increasing the combustion efficiency without affecting the drag. Reaction patterns in flame holders and their dependence on the cavity injection location are the main factors. The shape of the reaction front depends on both the recirculation bubble in the cavity and the shear-layer entrainment region.
In order to understand the effect of chemistry and cavity geometry on the shear-layer spatial growth and the flame stability, we plan to perform a linear (non-parallel) eigenvalue analysis with reduced chemistry and a set of non-linear numerical simulations with detailed carbon chemistry. The goals of the research are to match experimental values of blowout injection rates, determine the role of volume and flamelet reaction patterns on the combustion efficiency, and analyze the effect of baroclinic terms on the shear-layer instability. The research will involve determination (and improvement if necessary) of the best numerical algorithm, large scale parallel computations, and close interaction with the experimental research facilities.

Further Reading

1. Rasmussen, Dhanuka and Driscoll, "Visualization of flameholding mechanism in a supersonic combustor using PLIF," Proc. Comb. Inst., 31:2505-2512, 2007.
2. Pickett and Ghandhi, "Combustion generated instabilities in a hydrocarbon-air planar mixing layer," Combust. Flame, 129:324-341, 2002.
3. Buttsworth, "Interaction of oblique shock waves and planar mixing regions," J. Fluid Mech., 306:43-57, 1996.
4. Massa, Austin, and Jackson. "Triple Point Shear Layers in Gaseous Detonation Waves." J. Fluid Mech., 586:205-248, 2007.

5. Turbulence-Detonation interaction

Detonations possess a set of structural length scales which correspond to natural frequencies for two-dimensionally unstable waves and to pseudo-natural frequencies (pseudo-eigenvalues of the non-normal homogeneous interaction problem) for two-dimensionally stable waves. In both cases, acoustic, vorticity and entropy power spectra of convected disturbances are amplified several times above the non-reactive shock analog. One-dimensional wave parameters (e.g., heat release, overdrive and effective activation energy) substantially change the amplification of advected patterns. Moreover, the correspondence of peak post-shock frequencies with structural analogs introduces a scaling parameter identified by the ratio between the turbulence longitudinal length and the induction distance.
This problem is of interest because of two reasons. First, resonance conditions between the wave and convected vortical structures can lead to intensification or failure of the detonation, depending on the wave and scaling parameters. Second, acoustic amplification behind a detonation can lead to significant thermo-acoustic instability due to reflection of acoustic signals in the chamber.
we plan to improve the linear interaction analysis discussed above to include detailed kinetic time scales, and to analyze the three-dimensional non-linear interaction problem with reduced kinetics. The emphasis will be on changes of the wave induction structure as a result of the disturbance convection, on non-linear effects close to resonance conditions, on disturbance-structure scaling effects, and on comparison between linear and non-linear interaction at pseudo-natural frequencies. The research will improve knowledge on the propagation of detonation waves in disturbed flows, and on the acoustic characteristics of detonation motors.

Further Reading

1. Massa and Lu, "Role of the induction zone on turbulence-detonation interaction," 2008, Physics of Fluids, (under review, preprint available from the authors).