Fluid Mixing at Extreme Conditions Laboratory

FMECL

Research

Hypersonic Droplet Breakup

Hypersonic vehicles encounter atmospheric water droplets with sizes from microns to millimeters. These droplets are processed in the bow shock, breaking up and evaporating, and may then impact the vehicle surface causing damage. The acceleration created by the 3D bow shock is complex leading to an unsteady acceleration history. We aim to extend the current breakup models to account for complex acceleration histories using experiments, simulations, and hydrodynamic stability theory.

Droplet breakup is a long-studied but complex problem involving several concurrent interfacial processes occurring over a wide range of length and time scales. During breakup, hydrodynamic instabilities (HIs), resulting from strong accelerations, shear, and surface tension forces, act on the droplet surface leading to fragmentation and child droplet formation. Shock-driven droplet breakup is a fundamental and challenging problem in hypersonic flight where it plays a central role in external flow problems, such as impact damage, and boundary layer transition. Atmospheric droplets are present in low concentrations (<0.1% by volume) in a wide range of sizes from sub-micron droplets encountered in upper-atmospheric clouds to millimeter-sized rain droplets encountered near sea-level. Droplet impacts pose a significant threat to hypersonic vehicle aerodynamic and thermal protection systems and can limit weapon availability or flight trajectory due to weather conditions. Droplet-induced erosion can increase surface roughness altering the laminar-to-turbulent boundary layer transition, resulting in additional vehicle heating and drag. The impact of droplets on hypersonic vehicles is complicated by their interaction with the vehicle bow shock, which acts to breakup droplets and mitigate their threat. The kinetic energy of small droplets may be significantly reduced by shock acceleration, breakup, and evaporation, while larger droplets may persist, only undergoing deformation or partial breakup. The bow shock structure is complex, and droplets will travel through a system of shock and expansion waves, with an unsteady acceleration history that is beyond the capability of current droplet breakup models. Predicting droplet breakup and evaporation under these conditions is essential to developing resilient hypersonic vehicles.

We have several collaborators for this research. Prof. Dorrin Jarrahbashi of Texas A&M University performs DNS and Partcile-in-Cell simulations of droplet breakup and impact in hypersonic applications.  Prof. Praveen Ramaprabhu of the University of North Carolina in Charlotte performs DNS of droplet breakup and is working with us to develop hydrodynamic instability models for breakup. We also collaborate with scientists at Lawrence Livermore National Laboratory to develop new diagnostic methods and to perform droplet breakup simulations.

Our research in this area has been funded by the Office of Naval research, the National Science Foundation, and Lawrence Livermore National Laboratory.

Mach Number 1.35

Gas Velocity (Vg ~ 180 m/s)

Weber number ( We ~450)

Droplet diameter (170 um)

More to come…

Multiphase Detonations

Detonation waves are complicated by the presence of liquid or solid fuel particles. Under detonation conditions liquid fuel droplets must breakup, vaporize, and react rapidly. We perform experiments and simulations to develop new models for droplet breakup, evaporation, and reaction under these challenging conditions. Experiments allow us to visualize droplet breakup under these conditions, and to study the resulting detonation properties (e.g. velocity and pressure). Simulations, using the particle in cell method, allow us to understand the motion of droplets and the mixing and reaction of fuel vapor.

In detonation-driven combustion of liquid fuels droplets must breakup, evaporate, and react under extreme (high temperature and pressure) and rapidly changing conditions. This problem involves many interacting physical mechanisms occurring over a wide range of length and time scales. It is a fundamental problem in the development of high-speed, high efficiency flight technologies. For decades, aircraft propulsion has been largely limited to the use of Brayton cycles, with only occasional forays into more advanced technologies for high-speed aircraft such as supersonic combustion (sc)ramjet, and pulse (PDE) and rotating detonation engines (RDE).  Detonation engines have the possibility to increase thermal efficiency by 30% over conventional Brayton cycles. These engines can be used for stationary electric power generation and propulsion of aircraft, missiles, and naval vessels including as augmentors, rocket motors, and scramjets. To be practical for propulsion applications, detonation engines must use high-density liquid fuels. Similar challenges are faced in scramjet engines where fuel droplets or particles are processed by shock-expansion wave systems and rapidly reacted . Detonation engines have developed slowly as they require corresponding advances in simulation and experimental capabilities for studying and controlling rapid multiphase mixing and combustion. Advances in gaseous detonation simulation and experimental methods have contributed to the development of gas-fueled RDEs and PDEs, yet liquid-fueled detonations remain challenging to predict and poorly understood. Improving our understanding of droplet breakup and multi-scale mixing in detonations will allow us to overcome the challenges in developing advanced propulsion cycles.

We collaborate on this research with Prof. Praveen Ramaprabhu of the University of North Carolina in Charlotte. Dr. Ramaprabhu’s lab has developed DNS capabilities to resolve droplet breakup and reactions.

Our research in this area has been funded by the Office of Naval Research and the National Science Foundation.

Below is an image of droplets (n-dodecane) undergoing breakup in a detonation (oxygen gas). On the left side are pre-detonation droplet. The shock wave is visible as a vertical distortion in the image. The droplets seem to increase in size as they breakup, but in reality we are seeing a cloud of child droplets stripped from the parent droplet. the droplets then evaporate and react rapidly, causing them to disappear from the image as we travel to the right.

 

 

  1. Tarey, P., Ramaprabhu P., McFarland, J., “Evolution of a shock-impacted reactive liquid fuel droplet with evaporation effects: A numerical study”, J. of Multiphase Flow (2024).
  2. Young, C., Duke-Walker, V., Agee, S., Ramaprabhu, P., McFarland, J., “Droplet Size Effects in Liquid-Fueled Multiphase Detonations”, AIAA SCITECH (2024)
  3. Musick, B., Paudel, M., Ramaprabhu, P., McFarland, J., “Numerical Simulations of Droplet Evaporation and Breakup Effects on Heterogeneous Detonations”, Comb. and Flame (2023).
  4. Musick, B., Manoj P., McFarland, J., “Numerical Study of Fuel Droplet Combustion Under Heterogeneous Detonation
    Conditions” 13th United States National Combustion Meeting (2023).
  5. Young, C., Duke-Walker, V., McFarland, J., “Investigations in Multiphase Detonation Phenomena”, 13th U.S. National
    Combustion Meeting (2023).

Shock-Driven Multiphase Instability

The Shock-Driven Multiphase Instability (SDMI) occurs when a multiphase flow field with strong gradients in particle parameters (e.g. number density or diameter) is accelerated by a shock wave. This acceleration deposits vorticity at the interface which causes the multiphase flow field to mix. It is similar to the Richtmyer-Meshkov instability, but as the particle grow in size, they become slow to react and reduce the overall vorticity deposition and mixing. Understanding this instability may lead to new methods for enhancing or limiting mixing in shock driven applications (fusion power, SCRAMjet engines, detonation engines).

The Shock-Driven Multiphase Instability (SDMI) develops when a multiphase interface is impulsively accelerated by a shock wave, developing in a phenomenologically similar manner to a Richtmyer-Meshkov instability (RMI). The multiphase fluid is composed of a gaseous carrier phase and a dispersed particle phase consisting here of spherical non-deforming and non-evaporating solid particles. During the SDMI’s development, the shock wave instantaneously accelerates the carrier gas, while the acceleration of the particles is delayed, depending on their respective mass and drag. Smaller particles will rapidly accelerate to equilibrium, while larger particles will lag significantly, exchanging momentum with the gas over a finite equilibration time. In the limiting case of infinitesimally small particles momentum coupling is nearly instantaneous, and the SDMI and RMI behave similarly.

The RMI is a fluid instability characterized by the development of vorticity due to a misalignment between pressure and density gradients. This misalignment facilitates the deposition of baroclinic vorticity along the interface of fluids with varying densities as can be seen in the enstrophy equation. The baroclinic source term is what characterized the strength of vorticity deposition, which induces an unstable growth in the fluid interface, generating multiple length scales and fostering the mixing of different species across the interface. This dynamic process ultimately leads to turbulent mixing. In addition, when adding particles, the multiphase source term will determine the momentum transfer through the particle drag force. Particles with relatively large diameters will advect through the gas, affecting its momentum over a larger area, resulting in decreased vorticity deposition.

We have collaborated with Los Alamos National Laboratory and Lawrence Livermore National Laboratory to study this problem with their codes in additional to our own. We have also worked with Air Force Research Laboratory and used their computational resources to simulate this problem as part of the summer faculty fellows program.

Our research in this area has been funded by the National Science Foundation.

The image below shows the development of a cylindrical particle laden interface subjected to a Mach 1.35 shock wave resulting in SDMI. Each interface has the same particle mass (effective density, Atwood number) but different particle sizes. The images are taken at the same time but show different development due to the particle size. The image on the right has very small particles in a heavy gas (same effective density as other interface) and shows development much like an RMI. As particle size increases, the circulation (mixing energy) decreases due to particle lagging behind the gas.

  1. Duke-Walker, V., Agee, S., McFarland, J.A., “Particle Lag Effects in Shock-Driven Multiphase Instability with Solid Particles”, Bulletin of the American Physical Society (2023).
  2. Duke-Walker, V., Maxon, W.C., Almuhna, S., McFarland, J., “Evaporation and Breakup Effects in the Shock-Driven Multiphase Instability”, J. of Fluid Mech. (2021).
  3. Duke-Walker, V., Allen, R., Maxon, W.C., McFarland, J.A., “A method for measuring droplet evaporation in a shock-driven multiphase instability”, Int. J. of Multiphase Flow (2020)
  4. Middlebrooks J., Avgoustopoulos C., Black W., Allen R., McFarland J., “Droplet and Multiphase Effects in a Shock-Driven Hydrodynamic Instability with Reshock“, Exp. in Fluids, (2018).
  5. Paudel M., Dahal J., McFarland J., “Hydrodynamic effects on particle evaporation in a shock driven multiphase instability”, International Journal of Multiphase Flows, (2018).
  6. Black W., Denissen N., McFarland J., “Particle Force Model Effects in a Shock-Driven Multiphase Instability”, Shock Waves, (2018).
  7. Dahal J., McFarland J., “A numerical method for shock driven multiphase flow with evaporating particles”,  Journal of Computational Physics (2017).
  8. Black W., Denissen N., McFarland J., “Evaporation Effects in Shock Driven Multiphase Instabilities”. of Fluids Engineering, (2017).
  9. McFarland J., Black W., Dahal J., Morgan B., “Computational study of the shock driven instability of a multi-phase particle-gas system”. Physics of Fluids (2016).

Ejecta Transport and Breakup

Ejecta are small particles released from an intensely shocked material’s surface defects. The subsequent transportation and breakup, especially during the secondary breakup process, creates an interesting multiphysics problem which involves hydrodynamics, chemical reactions, and multiphase materials. These physics occur under extreme conditions and must be simulated.

Ejecta are small particles within an impulsively driven flow. Of importance to the research at FMECL is the study of ejecta that propagate from a material when the surface is rapidly accelerated, such as during an intense shock. In this case, a shock driven Richtmyer-Meshkov instability causes the initial ejecta release from the material, in which the shock wave interacts with the small imperfections on the surface of the material. Such shocks are often intense enough to cause some sort of melting of the material, creating a difficult multiphysics problem that involves the considerations of multiphase materials, hydrodynamics, heat and mass transfer, and chemical reactions. Studies on ejecta are also found in volcanic explosions, astrophysics, respiratory events, and other high-energy applications.

We collaborate with scientists at Los Alamos National Laboratory to simulate this complex multiphysics problem using their state-of-the-art hydrodynamics codes.

Our research in this area has been funded by Los Alamos National Laboratory and the Joint Center for Resilient National Security (JCRNS) at Texas A&M University.

Velocity and temperature fields for a resolved simulation of solid particle shock acceleration. [1]

  1. R Myers, F Ouellet, N Denissen, J Regele, J McFarland, “Analysis of a Reaction Mechanism for Use in Ejecta Particle Simulations” APS Topical Group on Shock Compression of Condensed Matter (2023) – Presentation (PowerPoint)
  2. R Myers, F Ouellet, T Nielsen, N Denissen, J Regele, J McFarland, “Implementation of Diffusion and Reaction Mechanisms for Reactive Ejecta Simulations” APS Division of Fluid Dynamics (2022)
  3. Maxon, W. C., Nielsen, T., Denissen, N., Regele, J. D., and McFarland, J. (April 9, 2021). “A High Resolution Simulation of a Single Shock-Accelerated Particle.” ASME. J. Fluids Eng. July 2021; 143(7): 071403. https://doi.org/10.1115/1.4050007

Astrophysical Hydrodynamics and Instabilities

Dust being ejected by stars leads to an interesting multi-physics problem. We simulate the transport of this dust and track the hydrodynamic development of the gas and dust over large domains and time periods. The competition of radiation and gravitational accelerations on the particles leads to complex hydrodynamic instabilities, like the Radiation-Driven Rayleigh-Taylor instability. We study these instabilities using simulations and particle models to gain a fundamental understanding of the physics and mixing involved in the formation and ejection of dust from stars.

Stellar luminosity variations and dust hydrodynamics in Asymptotic Giant Branch (AGB) stars, and the consequences for dust survival and mass-loss, remain elusive. We broadly investigate the role of dust and radiation hydrodynamics in the formation of dust and gas structures, heterogeneous clumps, observable in AGB remnants, and planetary nebulae (PNe). Spatial perturbations arise due to luminosity variations from turbulent thermal convection within the star and stellar atmosphere. These variations in the radiation field drive spatial perturbations of the dust and gas field and may be responsible for the formation of larger clumps, such as cometary knots, seen in the PNe phase. We use FLASH for studying this problem at large length and time scales. Simulations are performed in 2D solving the Euler equations with source terms resulting from the particle phase, represented by free Lagrangian points. We implement radiation coupling for the particle phase, modeling radiation heating and acceleration of the particles, and subsequent coupling to the gas phase through non-continuum heat and momentum transfer models.

Research is done in conjunction with Dr. Angela Speck at the University of Texas, San Antonio.

The work was funded by the National Science Foundation.

Development of dusty gas from an AGB star in an Euler-Lagrange simulation (FLASH). Particle velocity is on the color scale and gas velocity is on the gray scale.

  1. Zargarnezhad, H., Myers, R., Speck, A., McFarland, J., “Radiation driven-dust hydrodynamics in late-phase AGB stars”, Astron. Comput. (2023).
  2. H Zargarnezhad, J McFarland, “Analysis of a Multiphase Radiation-Driven Rayleigh-Taylor Instability“, APS Division of Fluid Dynamics (2023) – Presentation (PowerPoint)
  3. H. Zargarnezhad, J. McFarland, A. Speck, F. Stribling “Radiation Driven-Dust Hydrodynamics in late-phase AGB stars“, Bulletin of the AAS (2021)

Past Research Projects and Topics

The lab has performed work and collaborated on various other research topics. These include Richtymer-Meshkov Instability, ejecta formation, magnetohydrodynamic mixing, and nano-particle reactions. We are always looking for new collaborations that leverage our interest and capabilities.

The Richtmyer-Meshkov Instability (RMI) is driven by the impulsive acceleration of a perturbed interface between two fluids of different densities. The shock deposits baroclinic vorticity at the interface, and the perturbations grow through the linear and nonlinear stages, and eventually to a state of decaying turbulence. The baroclinic term of the vorticity equation is proportional to the misalignment between the density and pressure gradients. The strength of the  RMI can be quantified by the Atwood number which describes the interface density gradient, and the incident shock wave Mach number, describing the pressure gradient.

We have collaborated with Los Alamos and Lawrence Livermore National Laboratories and with Prof. Devesh Ranjan and Dr. Mohammad Mohaghar of Georgia Tech on this research topic.

Ejecta can be produced from a Richtmyer-Meshkov instability (RMI) acting on a solid interface. When the shock is sufficiently strong, the material will yield and flow like a fluid. In some cases the interface will melt. As the RMI spikes elongate, they begin to breakup into particles or droplets. These particles are ejected at high velocity away from the original solid interface becoming ejecta.

We have worked with Los Alamos National Laboratory and Prof. Praveen Ramaprabhu on this research area.

The Richtmyer-Meshkov Instability occurs when an interface between fluid of different densities is accelerated by a shock wave. When one or both of these fluids is conducting, it can react to the presence of a magnetic field. The resulting magnetohydrodynamic effects can suppress the mixing normally observed in the Richtmyer-Meshkov Instability.

We have collaborated with Los Alamos and Lawrence Livermore National Laboratories on this research topic.

Nano-sized metal particles show a drastically increased reactivity that can be leveraged in thermites, explosives, and solid fuels. The reason for this increased reactivity is poorly understood. Nano-partilces, such as aluminum, have a passive shell layer (Al2O3 in this case). One explanation for the increased reactivity is that this shell fails from internal stresses due to heating, melting, and possibly vaporization of the aluminum core. This results in an explosive decompression, which sends reactive ejecta particles out into the surrounding oxidizing material, which subsequently react at much higher rates.

we collaborated with Profs. Shubhra Gangopadhyay , Keshab Gangopadhyay, and Matt Maschmann at the University of Missouri.