Special Issue | October 2014 91

BARC NEWSLETTERFounder’s DayGENERATION AND THERMODYNAMIC CHARACTERIZATION OF FGM INDUCED

ISENTROPIC COMPRESSION

Aditi Ray Theoretical Physics Division

Abstract

The feasibility of achieving isentropic compression using functionally graded materials (FGM) has been explored in

both gas gun and explosive driven systems. Qualitative analyses of temporal profiles of pressure pulse generated

with various density distributions within FGM impactors showed that quadratic density variation is most suitable

for this purpose. The signatures of isentropic compression are established from basic thermodynamic aspects like

target temperature rise and deviation of entropy from theoretical isentrope. Optimum density profile within FGM

flyer that leads to minimum entropy change found to follow quadratic variation. Further, it is shown that efficiency

of spherical implosive system can be enhanced by use of FGM flyers with optimum density interval.

Dr. Aditi Ray is the recipient of the DAE Scientific & Technical Excellence Award for the year 2012

Introduction

High energy density (HED) physics deals with behavior

of matter under extreme thermodynamic conditions of

pressure and temperature. Several fields of research

involve high energy density; e.g., astrophysics,

geophysics, inertial confinement fusion (ICF), explosive

and impact loading of materials, Z -pinch devices, etc1.

With the advent of modern laser based technologies,

ICF has driven much of the development of HED

physics at laboratory level, National Ignition Facility

(NIF) of USA being one example of it. Realizing HED

by any approach involves dynamic compression

experiments where energy is deposited in a small

region at extremely fast rate leading to hydrodynamic

motion and propagation of shock waves. Though static

compression techniques like diamond anvil cell can

lead to Mbar pressures, but disadvantage associated

with long time duration makes them unsuitable.

Dynamic compression is realized either in strong

shock loading or isentropic compression experiments

(ICE). Difference between the two is that there is an

abrupt increase of material temperature by shock

(ns timescale), which is in contrast to relatively low

temperature rise for isentropic methods, that occur

over longer (μs) timescales. It is known that, maximum

achievable compression in strong shock is limited

due to irreversible heating and subsequent melting

or vaporization. On contrary, there is no theoretical

limit on maximum attainable compression by the

latter. Thus, isentropic method offers a practical way

for comprehensive determination of material response

in a broad range of phase diagram that cannot be

achieved by strong shock techniques.

Shock pressures are generated by impact of high

velocity flyer plates accelerated in a powder gun, single/

two-stage gas gun or by burning high explosives (HE)2.

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CONTENTS

92 Special Issue | October 2014

BARC NEWSLETTERFounder’s DayThere are several approaches to generate ICE each

with the aim of increasing peak pressure and its rise

time. In laser systems, it is realized by suitably tailoring

the pulse shape3. Other approaches include: multiple

shock, shock reverberation and shaped current pulses

for magnetic compression4.

Recent advances in fabrication of FGM have opened a

new front in generating smooth, continuous isentrope

in gas gun devices6,7. FGMs are composite materials

with composition varying along thickness in such a

way that certain material property is allowed to vary

continuously or step-wise from one side to the other.

The idea of varying density along the thickness is to

generate a smooth variation of shock impedance,

which is the product of density and shock speed.

We have carried out detailed study on generation

and thermodynamic characterization of isentropic

compression wave by FGM7,8. The present article

provides a brief description of our achievements

towards generating ramp pressure waves and brings

out new insight in this area.

Isentropic loading in gas gun system

Simulation of typical hydrodynamic experiments

performed by impact loading of normal and FGM

flyers accelerated by gas gun, as displayed in Fig. 1,

shows longer rise time of pressure pulse obtained

by FGM. Isentropic compression is characterized

from the temporal profiles of pressure pulse applied

at target by different functional forms of density

variation along FGM thickness. Quantitative analysis

supported by physical reasoning enables us to arrive at

the conclusion that quadratic variation is best density

profile for FGM layers for generating ideal ramp

compression7. Simulation results for pressure profile

with 1 km/sec impact of Al, linear (L) and quadratic

(Q) FGM flyers on to Cu target are illustrated in Fig.

2. In case of LFGM, peak pressure as well as its rise

time is more, but the pulse shape does not have

characteristics of ideal isentrope. The pulse shape is

reminiscent of linear ramp wave with QFGM. Profile of

target-window interface velocity, measured through

VISAR techniques, followed similar ramping pulse7.

Fig.1: Schematics of impact loading exp., either in gas gun or HE burn

Fig.2: Time profile of pressure pulse applied to a target by normal, linear and quadratic FGM flyers

Isentropic loading by HE driven FGM plates: Since flyers can be accelerated to higher velocities by

explosive burn, the possibility of generating isentropic

wave in HE driven FGM plate impact has also been

explored. Our study revealed the first observation

that with moderate flying HE driven QFGM produces

smooth ramp pressure pulse leading to an ideal

isentrope, as displayed in Fig. 3. Pressure pulse in

Fig.3: Pressure profile for HE driven normal and graded density flyer impact

Special Issue | October 2014 93

BARC NEWSLETTERFounder’s Daycontact geometry shows up an undesirable initial spike

due to shock jump7. Moreover, peak pressure realized

in HE driven system is much greater than what can be

achieved by gas gun system with identical FGM flyer.

Thermodynamic characterization of FGM induced isentropes: Signatures of isentropic

compression have been identified from basic

thermodynamic aspects of target temperature rise and

entropy increase from an ideal isentrope. Theoretical

evaluation of EOS temperatures along Hugoniot and

FGM induced isentropes show that for significant

compression the temperature rise by shock pressure

is much larger than that generated by any kind of

FGM flyer8. Nevertheless, target heating due to all

types of FGMs are nearly same. Fig. 4 compares target

temperature for Hugoniot pressure and isentropic

pressures of Fig. 3, delivered by HE driven QFGM.

Further, optimum density profile of a 14-layer FGM flyer

that produces minimum entropy at target with pre-

decided peak pressure has been obtained by finding

densities of individual layer through optimization

technique. Interestingly, profile fits very well with

quadratic function as shown in Fig. 6

Fig.4: Temperature rise with pressure along Hugoniot and HE driven FGM flyer impact

Increase in entropy on any arbitrary (P-V) state from

an ideal isentrope is the measure of irreversible energy

loss due to shock heating. Thus lower this entropy

deviation, better it is for ICE. Fig. 5 displays the entropy

increase as a function of pressure along Hugoniot and

isentropes obtained with linear and quadratic FGMs in

gas gun acceleration. It is clear that entropy change by

FGM loading is nearly two orders of magnitude smaller

than that of Hugoniot8. It is also obvious that, QFGM

is most suitable as it leads to least entropy change for

a specific peak pressure.

Fig.5: Entropy production vs pressure for Hugonion and FGM induced isentropes

Fig.6: Optimized density profile of FGM for least entropy prodcution

Effect of FGM flyer in spherical geometry: Due to

converging detonation waves produced by explosive

burn, it is possible to achieve higher velocities and

pressures in spherical geometry than planer case. Our

simulation of spherical implosion system, as depicted in

Fig. 7, shows that use of FGM flyer enhances impact

velocity, W at target to some extent for LFGM and to a

great extent with QFGM, as compared to normal flyer7.

Table-1 compares the maximum attainable impact

velocities for Fe flyer and those found by optimizing

densities of front and rear layers of FGM flyers with

given configuration.

94 Special Issue | October 2014

BARC NEWSLETTERFounder’s Day

Conclusions

Results of detailed hydrodynamics simulations of

dynamic compression experiments for generating

isentropic pressures are presented. The main

conclusions emerging from the studies are: shape of

pressure pulse can be suitably tailored by appropriate

density variation within FGM and quadratic FGM is

best choice for ICE since it produces linear ramp pulse

with least temperature rise and entropy production in

the target.

Acknowledgements

Author is indebted to Dr. Vinod Kumar and Dr. N.

K. Gupta for constant encouragement and technical

support provided during this work.

References

1. R.P. Drake, High-Energy-Density Physics:

Fundamentals, Inertial Fusion, and Experimental

Astrophysics, Springer-Verlag (2006)

2. W. J. Nellis, Rep. Prog. Phys. 69, 1479 (2006).

3. K.T. Lorenz, M.J. Edwards, A.F. Jankowski, S.M.

Pollaine, R.F. Smith, B.A. Remington, High Ener.

Dens. Phys. 2, 113 (2006).

4. D.B. Hayes, C.A. Hall, J.R. Asay, M.D. Knudson, J.

Appl. Phys. 96, 5520 (2004).

5. N. Holmes, Sci. and Tech. Rev. LLNL, Livermore,

(2000).

6. J.H. Nguyen, D. Orlikowski, Frederick H. Streitz,

John A. Moriarty, and Neil C. Holmes, J. Appl.

Phys. 100, 023508 (2006).

7. A. Ray and S.V.G. Menon, J. Appl. Phys, 105,

064501 (2009)

8. A. Ray and S.V.G. Menon, J. Appl. Phys, 110,

024905 (2011)

Fig.7: Typical spherical implosion system

Table 1: Optimized density intervals for LFGM and QFGM correspoinding to maximum impact velocity