Resolving the Velocity Vector in Two Dimensions

Transcription

1 Resolving the Velocity Vector in Two Dimensions Presentation for the 5 th annual PDV Conference and Workshop, Ohio State University, Columbus, Ohio Matthew Briggs, Michael Shinas, Larry Hull Los Alamos National Laboratory Abstract: Velocimetry techniques measure only the component of velocity along the beam. The dynamics of the vector nature of the velocity are of interest in the modeling of the responses of materials to shock loading. We present an example of using 2 crossed PDV beams to resolve the direction of motion in addition to the speed.

2 2 Resolving the Velocity Vector in Two Dimensions Matt Briggs, Los Alamos National Laboratory 2010 PDV Conference and Workshop Ohio State University, Columbus, Ohio v 1 φ a What we really do is PDS = Photon Doppler Speedometry v a v b v c φ b φ c PDViants: Steve Hare, Mike Shinas, Jim Faulkner, Larry Hull. Firing site: Michael Archuleta, Rudy Archuleta, John Echave, Joe Lynch, Pam Scott.

3 Measuring direction elucidates dynamics The dynamics of many tests involve changes in direction in 2 and 3-D. The evolution from v a to v is about to occur at A, A` in the grazing detonation test shown at right. We have been asked to measure this in damage/recovery tests, cylinder tests and expansion tests to help understand the material response. Detonation front M C M θ A, A` A`` Air shock front Product gas boundary Detonation velocity D Direction of motion Original charge position Original metal position θ θ/2 θ/2 v n P P` v v a (Diagram from Zukas & Walters, Explosives Effects and Applications, Springer, P``

4 2 Beams Resolve the Velocity Vector v in 2D PDV probe 1 One convenient choice is to pick beam 1 as a coordinate axis: v 1 = vcos(φ) v 2 = vcos(θ φ) V 2 / V 1 = cos(θ φ)/cos(φ) φ = tan -1 [ (v 2 /v 1 cos(θ))/sin(θ)] v v 1 θ v 2 φ velocity v measured at beam intersection PDV probe 2

5 PDV probe 1 (normal) PDV 3, +30º PDV 2, -30º (θ, φ <0 as drawn) PDV 4 (normal) U N C L A S S I F I E D Copper Plate, Driven Transversely v v v φ n θ v a v n θ v a φ Line-wave Det. Copper Plate, 1 in Detasheet, 8mm Foam, 0.25 in, 5 The effects of shockwave profile shape and shock obliquity on spallation: kinetic and stress-state effects on damage evolution, R.T. Gray et al., Shock Compression of Condensed Matter 2009, CP1195, Ed M.L. Elert, 2009 Note beams cross ~ 1mm in front of surface; only at crossing is interpretation certain. Copper plate after Probes 1,3 Probes 2,4

6 The lower pair show overlap (results from Ta plate) Signal from angled probe detected by normal probe Signal from normal probe detected by angled probe 6

7 Overlap region: 19 µs, 2.4 mm ~ D/tan(θ/2) D ~ 0.6 mm θ = 30 D D/tan(θ/2) 7

8 Cross talk, location of overlap are as expected Cross talk analyzes to ½ v(cosφ + cos (θ φ)) for both probes. Overlap at experiment layout at about 2 mm (integrated data = distance only because motion is ~ along normal probe.) 8

9 One convenient choice is to pick beam 1 as a coordinate axis: v 4 = vcos(φ) v 2 = vcos(θ φ) V 2 / V 4 = cos(θ φ)/cos(φ) φ = tan -1 [ (v 2 /v 4 cos(θ))/sin(θ)] Take the ratio of v 2 to v 4 and use the measured θ find φ, then substitute back to find v. U N C L A S S I F I E D Find φ and v from the measured data PDV 2, -30º (θ, φ <0 as drawn) PDV 4 (normal) v v n Results: lower (black) and upper (red) Velocity vectors for 20 µs after start of motion θ v a φ 9 20 µs 15 µs 10 µs 5 µs Start of Motion

10 Technique works, next need to optimize We can measure the direction of the velocity vector over the 1 to 2 mm overlap region. The resolution was ~ ± 1, ± 2% estimated from noise in the results. Need to test for systematic errors (model, use redundant probes or 1-D tests.) Need to understand optimization: angle resolved better with larger angle between probes, but signal strength falls off with angle from surface normal. 10

11 Details of the HE Assembly 11

12 UNCLASSIFIED As Built Shot 2 12