Donald F. Hawken Ph. D.

Flow Simulation Work

Detonation with finite-rate chemistry• 0.05 meter 1D domain with 1500 cells• 298.15 °K and 1 atmosphere ambient• 0.001 meter driver at 3000° K and 30 atmospheres• Spatially first-order explicit HLLC solver for

fluxes• Sources use implicit 6th order Runge-Kutta

algorithm• Compared to results of CFD++ code

H2-O2 detonation: 6 species, 7 reactions

Nozzle flow of H2-O2 products

H2-Air detonation: 12 species, 27 reactions

FCT solver with solution adaptive mesh • 10 atmosphere 300 °K cylinder of air expands into

one atmosphere air• Domain: 10 meters x 10 meters with 40 x 40 cells• Two levels of cell refinement in response to

pressure gradients• FCT solver modified to handle cell refinement

Pressure contours at 4 milliseconds (Pascal)

Mesh at 4 milliseconds

Level Set Tracking• Location of shock-, detonation-, or contact front is tracked

using scalar value, G, that is zero at front.

• Value of G in a cell is the signed distance from the front

• Shock or detonation front moves at speed determined by Hugoniot relation

• Contact front moves at flow speed

• Two states are maintained in cells containing front or near to front.

• Front states change in response to edge fluxes and front fluxes

• Spatially second-order explicit HLLC solver

Pressure and G profiles for tracked shock (100 cells)

Pressure profiles for captured shock (100 cells)

Pressure: tracked shock (100 cells) and captured shock (400 cells)

Pressure contours for tracked circular shock (40x40 cells)

Pressure contours for captured circular shock (40x40 cells)

Contours of front distance, G, for tracked circular shock

High-pressure gas compresses water (with and without 3 levels of refinement) (tracked contact)

High-pressure gas bubble expands in water (with and without 3 levels of refinement) (tracked contact)

Simulation of explosive blast

(near field to far field) • Domain: 10.9 meters x 5.1 meters with 100 x 140 cells

• Detonation front is tracked with two levels of refinement until solid explosive cylinder is consumed

• Spatially second-order explicit HLLC solver used for explosive products and air

• Trajectory of shock at height of burst matches raw experimental data at mid field and far field

• Simulation produces better estimate of front pressures near burst compared to extrapolated experimental fit to raw experimental data

Close up showing simulation initial conditions (click for movie)

Blast pressure movie (direct shock overtaken by ground shock)

Blast fireball movie

Location of shock front at height of burst

Improved near-field estimate of shock front pressure at height of burst

Detonation of explosive charge mixed with inert metal particles (near field to mid field)

• Expanding sphere of combustion products and particles

• JWL gas equation of state - combustion products

• van der Waals gas equation of state - air

• Dense particle equation of state

• HLLC solver - combustion products and air

• FCT Solver - particles

• Momentum and energy exchange between gas and particle phases

Shock and particle front histories compared to

experiment

Shock front pressure histories compared to experiment

Detonation of liquid explosive mixed with reactive metal particles (near field)

• HOM condensed equation of state - liquid explosive

• HOM gas equation of state - explosive combustion products

• van der Waals gas equation of state - air

• Particle equation of state

• HLLC solver - liquid explosive, combustion products, and air

• FCT solver - particles

• Momentum, mass, and energy exchange between gas and particle phases

Chemical Reactions

• Arrhenius combustion model for nitromethane

• Nitromethane H20 + (CO2-CO)

• Particle-diameter controlled oxidation rate

• Metal+H20 + (CO2-CO)+O2 metal oxides

Pure nitromethane detonation in 25 mm glass tube

Detonation of pure nitromethane cylinder (100x200 cells, 2 refinement levels)

Gas density movie

Nitromethane-particle detonation in 15 mm glass tube

Detonation of nitromethane-particle cylinder (100x200 cells, 2 levels of refinement)

Particle-phase density movie