LBNE

PMT Implosion Study

N. Simos, PhD, PEEnergy Sciences & NSLS II

June 2, 2010

The Problem:

Phase I: Based on the geometry and parameters of the upcoming test (PMT and experimental set-up) make “blind” predictions of the implosion and the subsequent shock pulse

Phase II: Using the navy pressure chamber test results, benchmark the simulation/prediction model (equation of state, constitutive relations of glass including fracture rate, etc., all of them being crucial but also difficult to determine even after decades of study)

Phase III: Utilize the benchmarked multi-physics simulation model to design the optimal configuration of PMTs in the detector

The Approach:

“Blind” Prediction (Phase I):

Implosion is an extremely complicated problem

Use multi-physics formulation

Arbitrary Eulerian-Lagrangian Formulation (ALE) that allows the “communication” between fluid phases and solids

Complex constitutive relations and fracture processes in glass. This is key since it will determine the rate of fracturing and thus the appearance or not of a shock pulse and its intensity level (many attempts in the past have forced a rate of fracture on the system until they match the recorded pulse with no regard on the imploding material and its fracture characteristics)

Implosion Simulation:

PMT geometry and modeling

3-D formulation and modeling of PMT, surrounding fluid

Physics associated with glass adopted for the PMT wall

PMT fracture initiation:

Induced during upcoming test

Imperfection in the thin wall of PMT that leads to micro-crack formation and propagation as a result of the stress field until fracture is initiated at the location. Cracking characteristics of the material PMT wall is made of, controlled by fracture energy and how brittle it is (stress-strain relations) will dictate the rate of collapse, which in turn will dictate the intensity and sharpness of the shock or pressure pulse.

Implosion analysis employs the LS-DYNA code in conjunction with TrueGrid

Highly non-linear processes, impact, fracture, ALE, Equations of State (EOS)Variety of constitutive models for PMT wall entertained to describe the brittle behavior/failure

Johnson-Holmquist Constitutive Model currently implemented

There are five sensors at .5 meter from the tube. Four of those sensors are around the “equator” of the tube. A sixth sensor is at 1 meter distance.

Preliminary PMT Implosion Test Configuration

Pressure Pulse (s) Sources:Glass fracture pressure wave

Collapse of funnel where 1st breach occurs

Finally, compression at PMT center from water collapsing on itself

Jet Formation

On-going Implosion Simulations

2mm & 1mm Elliptical Glass (> 10 atm pressure)

PMT (2mm glass wall) (P > 3 and 10 atm)

Goal is to assess the coupled effect of pressure, thickness, constitutive relations, poking velocity, etc.)

Results of recent BNL studies predicting very high rate processes and using multi-physics, ALE formulations

Projectile-Wall Impact Benchmark Study

According to test results, missile- induced dent on upstream face of wall = 20 mmAnalysis prediction matched the experimental data precisely !

High Velocity Hard & Soft Missile Tests - Benchmarking

What’s next:

Complete these computationally intensive implosion simulations and by adopting them to EXACTLY what the Navy test will be, make predictions PRIOR to the test

In the meantime, attempt to perform side experiments on the fracture characteristics of PMTs (impact and fracture capturing holographically and with very fast camera)

Use ultrasonic system to get a feel as to whether we are departing the pressure pulse domain and enter into shock

Upon completion of the test and processing of the data, compare with predictions and fine-tune the multi-physics simulation model (enhance constitutive relations primarily)

Use the fine-tuned or benchmarked process to guide the configuration and design of the PMT array