Spectroscopic characterization of hypervelocity jetting: Comparison with a standard theory ·...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. El2, PAGES 30,825-30,845, DECEMBER 25, 1999

Spectroscopic characterization of hypervelocity jetting: Comparison with a standard theory

Seiji Sugita •'2 and Peter H. Schultz Department of Geological Sciences, Brown University, Providence, Rhode Island

Abstract. Symmetric collision between two identical plates has yielded successful theoretical models for the jetting process. Consequently, assessment of impact jetting at planetary scales has been largely based on the theories developed for such specific types of collisions. Little experimental work has been done, however, to measure both temperature and target-to-projectile mass ratio of jetting created by spherical projectiles impacting planar targets, which typify planetary impacts. The goal of this study is to examine the validity of applying planar-impact theories to jetting due to impacts of spherical projectiles into planar targets. Using a newly developed spectroscopic approach, we observe jetting created by Copper spheres impacting planar dolomite targets at hypervelocities. In contrast with previous experiments using quartz projectiles, the observed mean temperatures of jets due to copper projectiles does not correlate well with the vertical component of impact velocity. Instead, the observed temperatures of jets show much better correlation with impact velocity than the vertical component of impact velocity and impact angle. The experiments also reveal that the target-to-projectile mass ratio within a jet increases with impact angle (measured from the horizontal). In order to understand the significance of these experimental results, they were then compared with a jetting model for asymmetric collisions based on standard theories. Such a comparison indicates qualitative consistencies, such as complete vaporization of the carbonate target (as opposed to mere degassing of carbon dioxide due to incomplete vaporization of carbonate) and higher target-to-projectile mass ratio in a jet at higher impact angles. Quantitative comparison, however, also reveals significant inconsistencies between theory and experiments, such as an impact-angle effect on jet temperature and a correlation in jet temperatures between projectile and target components. In order to resolve these inconsistencies, new factors such as viscous shear heating and the nonsteady state nature of the jetting processes may need to be considered.

1. Introduction

High-speed ejection of a small mass of highly shocked material has been observed in various configurations of obliquely colliding surfaces, such as a collapsing lined cavity [e.g., Birkhoff et al., 1948; Walsh et al., 1953; Al'tshuler et al., 1962], a sphere impacting a flat target [e.g., Gault et al., 1968], and a cone- shaped projectile impacting a flat target [e.g., Allen et al., 1959; Jean and Rollins, 1970]. This phenomenon is called jetting. Such jets exhibit extremely high ejection velocity, which is several times the velocities of the colliding surfaces. It is worth noting that so-called bazooka cannons take advantage of the penetration power of shaped-charge jets resulting from this extremely high ejection velocity. It is also observed that jetting has a critical angle below which the phenomena do not occur [e.g., Walsh et al., 1953]. The characteristic high ejection velocity of jetting and the existence of a critical angle of colliding surfaces for jetting have been successfully explained by analytical models and verified by both flat-plate experiments [Walsh et al., 1953;

ion leave at NASA Ames Research Center, Moffett Field, California. 2permanently at Department of Earth and Planetary Physics, Faculty

of Science, University of Tokyo, Tokyo, Japan.

Copyright 1999 by the American Geophysical Union.

Paper number 1999JE001061. 0148-0227/99/1999JE001061 $09.00

Al'tshuler et al., 1962] and experiments with cone-shaped projectiles [Allen et al., 1959; Jean and Rollins, 1970].

Another important aspect of jetting is its high degree of shock heating. Kieffer [1977] used the symmetric jetting theory to show that the jetting process can induce shock melting at relatively low impact velocities, i.e., velocities insufficient to produce melting for head-on collisions. Such jet-induced melting/vaporization at relatively low impact velocities has many important implications in planetary science. For example, jetting has been considered as a mechanism for the origins of chondrules [Kieffer, 1975], Pluto [McKinnon, 1989ab], the Moon [Melosh and Sonett, 1986], tektites, and impact glasses [Vickery, 1993].

Calculations for most planetary applications, however, are based on jetting models developed for a symmetric collision between two thin plates [Walsh et al., 1953; Al'tshuler et al., 1962] and a method to estimate shock heating from the pressure at a stagnation point by Kieffer [1977]. These models, however, have several potential problems: (1) Shock waves due to asymmetric blunt-body collision may not be approximated by a steady state solution, which is assumed in the symmetric flat- plate models. (2) The method to approximate a shock pressure by a stagnation pressure overestimates the shock heating. Although the discrepancy is reasonably small in symmetric thin-plate collisions [Kieffer, 1977], it may be much more significant in asymmetric blunt-body collisions. (3) By definition, a symmetric jetting model cannot take into account either impedance contrasts or difference in effective impact velocity with respect to the collision point between impactor and target. Collision between

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30,826 SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING

unequal materials is expected to characterize the surfaces of both planets and small bodies in the solar system, which consist of a variety of materials such as silicates, ices, and metals. As discussed in detail in section 4, blunt-body impacts constantly change the "wedge" angle between the surfaces of target and projectile with respect to the collision point during the penetration stage. Consequently, the effective impact velocities of target and projectile are unequal in general. Thus effects of asymmetry in material properties and impact velocity deserve significant considerations. (4) Effect of viscous shear heating is not taken into account in previous theories. All heating has been ascribed to pure shock heating by Rankine-Hugoniot equations. This assumption is justified for a symmetric collision between two identical plates because there is no velocity shear expected in such a collision. As shown in section 4, however, an asymmetric collision between two surfaces leads to a large velocity shear along the contact surface. Consequently, the effect of viscosity may be significant in jetting during planetary impacts.

One reason why such issues remain understudied may be the absence of observational data. Although jetting velocity has been measured for many different conditions, few observations have focused on the degree of heating of jets, particularly for blunt- body collisions. Kieffer et al. [1976] showed that microscopic textures of shocked Coconino sandstone are consistent with

heating in excess of 3000 K, which is most likely due to shock heating by the local jetting process. Yang et al. [1992] observed radiation from jetting and obtained a blackbody temperature higher than 3000 K, even at relatively low impact velocities (< 2 km/s). In spite of the value of these pioneering works, however, their results may not be readily used for testing theories of jetting created by planetary impacts. For example, the shocked sandstone observation by Kieffer et al. [1976] does not provide precise constraints for the intensity of the shock that caused the jet-induced melting. The jetting experiments by Yang et al. [1992] used flat plates instead of (three-dimensional) blunt bodies, and the impact velocities are low (< 2 km/s). Such low- velocity impacts may not reach the hydromechanical regime of the impact material used in the experiments [see, e.g., Kieffer, 1977]. At much higher impact velocities, however, it may be difficult to use Planck's radiation law. The extremely high shock heating for the jet may vaporize the jetted material. A radiation spectrum from a high-temperature vapor is not generally approximated by the Planck function. In fact, the radiation of higher' velocity impacts at early times often contains strong atomic line emission and molecular band emission [e.g., Gehring and Warnica, 1963; Jean and Rollins, 1970; Schultz, 1996; Schultz et al., 1996; Adams et al., 1997; Sugita et al., 1998], indicating that it is dominated by optically thin gas phases. Consequently, the pyrometer approach based on blackbody radiation is not applicable to jetting created by higher velocity impacts. Recent spectroscopic observations of hypervelocity impacts, however, have shown that the temperature of such vaporized jets can be determined by measuring relative intensities of atomic emission lines [Sugita et al., 1998] and molecular emission bands [Sugita and Schultz, 1998]. The observations by Sugita et al. [1998] revealed that the jet temperature due to impacts by quartz spheres into solid dolomite targets ranges from 4000 to 6000 K and moderately correlates with the vertical component of impact velocity. It is uncertain, however, if these results are unique to quartz impactors, and temperature information on jets derived from the projectile was not obtained.

The goal of this study is to assess the validity of standard jetting theories based on symmetric thin-plate experiments to

jetting created by spherical impacts into planar targets. We use projectiles with material properties very different from quartz in order to determine if the results by Sugita et al. [1998] can be generalized. An appropriate selection of projectiles also allows temperature measurement of jetting derived from a projectile as well as a target. Such simultaneous temperature measurements of both components permit the target-to-projectile mass ratio in a jet to be estimated. Here, both temperature and mass ratio are determined from the measured spectra as a function of time, impact velocity, and angle. The experimental results are then compared to predictions of theoretical models in the literature and a new semi-analytical model based on the standard jetting theories developed by Walsh etal. [1953] and Kieffer [1977]. Finally, we discuss plausible causes for the discrepancy revealed by the comparison.

2. Experiments

A series of hypervelocity impact experiments were conducted at NASA-Ames Vertical Gun Range (AVGR). The two-stage light gas gun at AVGR allowed both high impact velocities (3.9- 5.8 km/s) and variable impact angles (15ø-90 ø, measured from the horizontal). The experimental setup is essentially the same as given by Sugita et al. [ 1998] and illustrated in Figure 1.

Copper projectiles were selected in this study for a number of reasons. First, copper has much higher shock impedance than quartz, thereby leading to a higher peak pressure at a given impact velocity. Second, because copper is a ductile material, the projectile failure pattern is expected to be different from brittle quartz, particularly in oblique impacts [e.g., Schultz and Gault, 1990]. Third, emission lines of copper are widely separated in wavelength [e.g., Reader et al., 1980]. This separation minimizes interference with emission lines from target materials. Transition elements such as iron and chromium have such a large number of emission lines that very high spectral resolution is required to

IC ro

Impact Chamber

• "':-"":•i..•{ Target Figure 1. Schematic diagram of the setup for impact experiments. The spectrometers equipped with intensified charge-coupled devices (ICCD) view the target plane through a window on the top of the impact vacuum chamber.

SUGITA AND SCHULTZ: SPECTROSCOPIC OBSERVATION OF IMPACT JETTING 30,827

resolve each emission line [e.g., Reader et al., 1980]. Although aluminum does not have a large number of atomic emission lines, previous experiments have shown that intense molecular emission from aluminum oxide (A10) molecules can cause strong interference with other emission [Schultz, 1996; Schultz et al., 1996, Adams et al., 1997]. Fourth, the upper states of electronic transitions of dominant emission lines of copper are widely distributed in energy level [e.g., Fu et al., 1995]. The wide energy separation is very beneficial for determining temperatures accurately [Sugita et al. 1998].

The same solid polycrystalline dolomite target blocks were used here as in the previous experiments by Sugita et al. [1998], thereby allowing target temperature measurements from the calcium emission line. Because the spectral distributions of emission lines of copper and calcium are similarly sparse, the same spectroscopic system with the identical setup (i.e., spectral range and resolution) as in the previous experiments can be used. The use of the identical observation system greatly reduces possible systematic measurement errors between the present and the previous experiments.

Only a brief summary of the method to determine temperatures is described here because the theoretical background and detailed procedures are described by Sugita et al. [1998]. First, both the source element and the electronic transition of each emission line are identified from its wavelength and relative intensity. Here, the relative intensity of observed spectra are calibrated with a National Institute of Standards and Technology (NIST) traceable standard tungsten filament lamp. Second, the intensity of the line is measured and then normalized by its Einstein A coefficient, statistical weight, and frequency. When the normalized intensities are plotted against the energy levels of the upper states of the corresponding electronic transitions (i.e., Boltzmann plot), they follow a straight line if the emission source is in thermal equilibrium and its opacity is small. The inverse of the slope of this straight line gives the temperature of the radiation source. Here, it is noted that the temperature determined in an impact experiment is an average temperature of the radiation source, which may be heterogeneous. This average temperature, however, is shifted toward the highest temperature with respect to the mass-averaged temperature. An observed emission line from an impact vapor cloud is the sum of luminescence of each part of the impact vapor cloud with different radiation temperatures. Because radiation intensity is generally a very strong function of temperature, the highest temperature component in a radiation source dominates the observed emission spectrum.

Einstein A coefficients of calcium and copper atoms used for the analysis in this study are given by Sugita et al. [1997] and Table 1, respectively. Relatively old data by Kock and Richter [1968] are used for the analysis in this study. Although a recent comprehensive compilation by Fu et al. [1995] lists more recent data, these newer data do not provide accuracies in temperature determination as good as those by Kock and Richter [ 1968]. The newer data are either drawn from even older experimental measurements or represent new experimental measurements for much fewer Einstein A coefficients. Data by Kock and Richter [1968] are still the newest values derived directly from a single set of experiments that cover all the emission lines necessary for our study. In fact, a relatively new compilation by Reader et al., [1980] adopts the data by Kock and Richter [1968] for emission lines of Cu I in the experimental wavelength region for our study, i.e., 430-650 nm. However, it is important to note that both Kock and Richter [ 1968] and Reader et al. [1980] do not cover some of

Table 1. Einstein A Coefficients of Cu I Emission Lines

Observed in This Study

• (nm) g•, Eu/k (K) Atu Error % g•Atuvt• (108s -1) (1022 s '2)

448.035 2 76042.4 0.030 a 20 0.401 450.735 6 96609.6 0.25 b -50 ½ 9.98 450.937 2 92767.3 0.275 a 18 3.66 452.511 4 97802.8 0.46 b -50 ½ 12.2 453.079 2 76042.4 0.084 a 15 1.11 d 453.970 4 91489.9 0.212 • 15 5.60 d 458.700 6 90574.4 0.320 • 12 12.5 a 464.258 4 93900.8 0.12 • -50 ½ 3.10 465.112 8 89790.3 0.380 • 12 19.6 a 467.472 6 90574.4 0.12 • -50 ½ 4.62 469.749 4 91489.9 0.10 • -50 ½ 2.65 470.459 8 89790.3 0.055 a 15 2.80 a 510.554 4 44293.7 0.020 a 12 0.470 515.324 4 71850.3 0.604 a 12 14.1 d 521.820 6 71860.1 0.750 a 12 25.9 a 522.007 4 71850.2 0.150 a 12 3.45 a 529.252 8 89790.3 0.109 a 15 4.94 a 570.024 4 44293.7 0.0024 a 14 0.0505 578.213 2 43936.3 0.0165 a 12 0.171

Here •, g•, Eat'k, At,,, and vt,, are wavelength in nanometer, the statistical weight of the upper energy state of electron transition, the energy of the upper state divided by Boltzmann constant in Kelvin, Einstein A coefficient in 108 s -1, and frequency in s 'l, respectively. The values for both wavelengths and energy levels are taken from Fu etal. [1995]. The sources of the Einstein A

coefficients are indicated by footnotes c and d.

aKock and Richter [ 1968].

•Corliss [ 1970].

CCorliss [1970] estimates that errors for the Einstein A coefficients are at least 30-66 %.

aValues used in actual spectral analysis.

the moderately strong emission lines in our experimental wavelength range. These lines are covered by Corliss [1970], and the same data are listed by Fu et al. [ 1995]. These particular lines are often located very close to other Cu I emission lines and cannot be resolved with the current configuration of our spectrometers, which are intended to capture a wide range of wavelength with moderate spectral resolution. As a result, the intensity of the omitted lines would be measured as a part of other lines listed by Kockand Richter [1968] and Reader et al. [1980], leading to a significant overestimate of the intensities of some emission lines. To avoid this problem, we removed emission lines that are contaminated by these "hidden" lines. The emission lines used in the actual temperature analysis are indicated in Table 1.

Here it is important to discuss the effect of an ambient atmosphere on the measured jet temperatures. All the experiments in this study were conducted in -0.5 torr of air pressure. Since impact jets collide with an ambient atmosphere at extremely high velocities, reheating of jets by this interaction could be a significant concern in interpreting the experimental results. Experimental data by Gehring and Warnica [1963] and Schultz [1996], however, indicate that the emission intensity of early-time impact-induced light emission is not influenced significantly by ambient air pressure less than - 1 torr. Hydrodynamic calculations using Rankine-Hugoniot equations also indicate that the collision between an expanding high-


pressure jet and a low-pressure ambient atmosphere will not form a shock front within the jet until a significant mass of the atmosphere has been traversed. An extremely intense shock front then forms only in the surrounding atmosphere, thereby leading to intense heating of ambient air. Consequently, the temperature inside the impact jet should not be influenced directly by such a collision with the thin ambient atmosphere for the experimental conditions in this study. If the mass and density of an impact jet is extremely small, the interaction between jetting vapor and ambient air may be described as free-molecular flow, in which collisions between individual atoms and molecules are important. Then atoms/molecules in both an impact jet and ambient air should be heated simultaneously. If either heating mechanisms is significant, emissions from heated air molecules (e.g., N 2 and N2 +) should be observed, as well as emissions from molecules and atoms (e.g., Ca, Mg, Cu, and CaO) in the jet. However, we have not observed any light emission from ambient air species. Consequently, the possible effect of an ambient atmosphere on radiation from impact jetting is not important for the experimental conditions in our study. When the atmospheric pressure is as high as 10-100 torr (a factor of 20-200 greater than this study), the effect of an ambient atmosphere on impact- induced light emission becomes very prominent [e.g., Schultz, 1996; Sugita and Schultz, 1998]. However, detailed discussion of the nature of this phenomenon is beyond the scope of this study and is discussed elsewhere [Sugita, 1999].

When temperature is determined, normalized emission intensities can be extrapolated to the zero energy level. This extrapolated intensity (i.e., intercept on the vertical axis) corresponds to the number of ground-state atoms in the emission source [e.g., Sugita et al., 1998]. When an emission spectrum contains lines from two different elements, the ratio of the

ground-state atoms of the two elements in the emission source can be estimated from the difference in the vertical intercepts of two Boltzmann plots. In the present study, the number ratio of copper and calcium atoms can be used to estimate the target-to- projectile mass ratio in a jet. However, it is noted that the number ratio does not exactly match the mass ratio. Mass refers to atoms not only in the ground state but also in all the excited and ionized states. The degree of excitation and ionization of atoms can be estimated from the intensity of an ion line [e.g., Griem, 1964; Sugita et al., 1998]. However, because no emission line of copper ions was observed in the experiments, such a direct estimate was not possible. The number ratio of ground-state atoms, however, generally approximates the mass ratio well because the contribution of excited states and ionized states are relatively minor at moderate temperatures.

Another source of uncertainty is the fact that the calcium is only one component of the target material of dolomite. As we discuss below, emission of calcium oxide is observed, and a

significant amount of carbon dioxide is inferred to be released during an impact. Consequently, the spectroscopically observed mass of calcium is most likely a small fraction of the total mass of jetting vapor. This possible small fraction of vapor mass, however, has rather well-defined significance. Since the generation of atomic calcium (also magnesium) vapor requires much higher energy than that for molecular vapor (such as CaO and CO O , atomic vapor represents the highest temperature component within impact-induced vapor. Thus the mass ratio of Ca to Cu atoms may be usable as a measure for the target-to- projectile mass ratio within the highest temperature portion of an impact jet.

3. Experimental Results

First we describe qualitative characteristics of emission spectra and their temporal variation. Then the results of temperature measurements and the mass ratio of target to projectile components are presented. Comparison with theoretical expectations is deferred to section 4.

3.1. Impact Flash as a Function of Time

Emission spectra were captured with several different exposure times in order to observe the temporal variation of the radiation. The earliest and shortest exposure time is 0-2 ps after the first contact of impact, which was detected with a photodiode placed near the impact site. This exposure time is the same as in many previous experiments of quartz impacts [Sugita et al., 1998]. This allows a direct comparison of the results between the current and previous experiments. However, it should be noted that the diameter of copper projectiles used in this study (3.18 mm) is half that of quartz projectiles used previously [Sugita et al., 1998].

All the emission spectra with this early exposure time exhibit strong line emissions from both copper and calcium atoms as well as strong band emission of CaO but do not show the strong MgO band observed for quartz impacts [Sugita et al., 1998]. Typical spectrograms are shown in Figure 2. Little interference between calcium and copper lines occurs for the selected spectral resolution and coverage. This ensures accurate temperature measurements of both elements. The level of continuum thermal

background is much lower for copper impactors than for quartz impactors at all the impact angles. In fact, copper projectiles impacting at 15 ø exhibit emission lines large enough to allow quantitative intensity measurements, whereas those by quartz impacts show few significant emission lines but a very strong thermal background [Sugita et al., 1998]. The weak blackbody radiation and strong line emission from copper impactors indicate that the radiation source is dominated by a gas phase with very little liquid/solid phases during this early stage of the collision process.

The small thermal blackbody background also allowed observation of atomic lines at later stages of the impact with high precision. Figures 2a-2c show the emission spectra taken in exposure times of 0-2 •s, 2-5 •s, and 5-15 •s, respectively, after the first contact of impacts with the identical viewing geometry of the spectrometers. The field of view of the spectrometers, which are looking down on the target, is -2 cm in radius and its center is located 2.5 cm downrange from the point of impact. The uprange edge of the field of view is adjacent to the point of impact but does not include it. All the emission spectra were taken with this viewing configuration, unless mentioned otherwise. Great care was taken to maintain this setup of the spectrometers during the three impact experiments presented in Figures 2a-2c. Thus direct comparison of emission intensity among the three experiments is valid despite the arbitrary intensity unit. It is noted that the arbitrary unit used in this study is calibrated in terms of relative intensity within a spectrogram but is not calibrated for an absolute scale of irradiance. The

method of intensity calibration and its uncertainty are described by Sugita et al. [1998].

As shown in Figures 2b and 2c, the emission intensity at later times is much weaker than that in the earliest time (Figure 2a). Note that intensity scales of Figures 2b and 2c are 1/2 and 1/4 of that of Figure 2a, respectively. Unlike in quartz impacts, the


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Figure 2. Emission spectra of jetting due to copper impacts into dolomite blocks. The impact angle, velocity, and exposure time after the first contact of impact are indicated in each part. The field of view of the spectrometers, which are looking down on the target, is -2 cm in radius, and its center is located 2.5 cm downrange from the point of impact. The constant setup of the spectrometers maintained during the experiments (Figures 2a-2c) allows direct comparison among their radiation intensities. Although the viewing geometry was changed between Figures 2d and 2e, the change is very small, and the intensity scale was not altered significantly. However, the intensity scales may be significantly different between the cases at 60 ø of impact angle (i.e., Figures 2a-2c) and those at 30 ø (i.e., Figures 2d and 2e) because of a large change in viewing geometry. The source atoms and molecules of emission lines and bands are indicated.


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Figure 2. (continued)

blackbody radiation does not dominate at later times. This precludes the possibility that the late-time reduction in the intensity of atomic emission lines may be due to absorption by opaque fine-grained debris/droplets, which would exhibit strong blackbody radiation. Thus the amount of self-luminous vapor within the field of view does reduce significantly at later times. Two alternative interpretations are possible: (1) The high- temperature self-luminous vapor observed in the earliest exposure time cooled very rapidly to a temperature too low to be self-luminous and (2) the self-luminous vapor has physically moved beyond the field of view. Two consecutive impact experiments at 30 ø of impact angle were conducted to resolve this issue. Observations were made in both the nominal field of view in the first 2 Us and in a field of view 2.5 cm farther downrange than the nominal cases 2-5 Us after impacts. Although the intensity units in the two experiments are not strictly the same, the change in the absolute intensity scale is expected to be small because the change in viewing geometry of the spectrometers is very small. The experimental results reveal that the intensity of atomic/molecular radiation farther downrange at later times (Figure 2e) is comparable to that in the first 2 Us in the nominal view area (Figure 2d). This clearly demonstrates that the second interpretation is correct; most of the emission-source gas is formed rapidly but travels beyond the nominal field of view within the first 2 gs after impact. The time difference and travel

distance correspond to a velocity -20 km/s. Both the high velocity and rapid generation of the self-luminous gas confirms that the gas is predominantly jetting material. Also note that the relative intensity ratios among different emission lines are significantly different between Figures 2d and 2e. However, this difference results from a change in temperature of a jet not from a compositional change as shown in section 3.3.

3.2. Temperature

Strong emission lines and the low thermal background allowed determination of the temperatures of both copper and calcium for almost all impacts during the first 2 Us. Here copper and calcium represent projectile- and target-derived jets, respectively. A typical example of a Boltzmann plot to obtain temperatures is shown in Figure 3. Measured temperatures are shown as functions of impact velocity, angle, and the vertical component of impact velocity in Figures 4 and 5. Unlike jetting due to quartz projectiles [Sugita et al., 1998], the temperature of jetting due to copper projectiles does not show significant correlation with the vertical component of impact velocity. Although jet temperatures due to copper impacts exhibit slight increases as functions of impact angle, this trend is weak. Instead, calcium and copper temperatures generally show a flat trend with impact angle. However, the temperatures have good correlation


2O

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ß ,•-.•- Cu Emission; T = 6060 K

,,

Ca Emission; T = 5740 K '•', 0 20,000 40,000 60,000 80,000 100,000

E/k: Energy Level (K) _

Figure 3. A Boltzmann plot of atomic line emission. The emission is induced by a copper impact into a dolomite block at 45 ø of impact angle and 5.48 km/s of velocity. The exposure time is 0-2 gs after the first contact of impact. The distributions of intensities of emission lines of copper and calcium indicate 6060+_150 K and 5740_+410 K of temperatures, respectively.

with impact velocity. As impact velocity increases, the temperatures of both projectile- and target-derived jets increase significantly over the experimental range (Figures 4 and 5).

Another result of the temperature measurements is the correlation between temperatures for the two elements. Figure 6 reveals that the two temperatures also correlate well with each other but that the temperature for copper is roughly 1000 K higher than that for calcium. In some cases, the temperature of projectile-derived (Cu) jet is 2000 K higher than that of target- derived (Ca) jet. Estimated temperatures, however, are expected to have considerable errors due to uncertainties in both Einstein A coefficients and measurements of emission intensities. Such errors can be assessed from the scatter in Boltzmann plots. The uncertainty in temperature based on the method by Press et al., [1992] is presented as error bars in Figures 4, 5, and 6. Further discussion about error analysis is given by Sugita et al. [1998]. Because the offset in temperature between calcium and copper is significantly greater than the errors, we conclude that the temperature gap is probably a real signal. Consequently, copper and calcium atoms may not be in the same thermal equilibrium; instead, they may belong to two physically separated vapor jets with different temperatures. Perhaps a jet derived from the projectile overrides a jet derived from the target. Different temperatures even for the same peak shock pressure may be possible because their shock Hugoniot equations of states and rates of adiabatic cooling are different between projectile and target materials.

3.3. Mass Ratio

The method to estimate the mass ratio involves an

extrapolation procedure of emission intensity with an equilibrium temperature; consequently, it is very susceptible to uncertainty in our temperature measurements. Estimation of the mass ratio requires a reliable temperature measurement. Figure 7, however,

clearly shows that the target-to-projectile mass ratio (Ca/Cu) increases steadily with impact angle 0 (measured from the horizontal). Since the scale of the vertical axis of Figure 6 is logarithmic, the mass ratio actually changes dramatically. The

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Figure 4. Temperatures of jets due to copper impacts into dolomite blocks. The temperature of the target component (calcium vapor) is shown as a function of (a) impact velocity, (b) impact angle, and (c) the vertical component of impact velocity. The exposure time is 0-2 }as after the first contact of impact. Note that impact angle is fixed at 45 ø in Figure 4a and impact velocity is limited to be 5.43_+0.33 km/s in Figure 4b.


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Figure 5. Temperatures of jets due to copper impacts into dolomite blocks. The temperature of the projectile component (copper vapor) is shown as a function of (a) impact velocity, (b) impact angle, and (c) the vertical component of impact velocity. The exposure time is 0-2 ps after the first contact of impact. Note that impact angle is fixed at 45 ø in Figure 5a and impact velocity is limited to be 5.43+0.33 krn/s in Figure 5b.

mass ratio of calcium to copper at the vertical impact angle (90 ø ) is -10 times that at 15 ø of impact angle. The data follow a linear trend when cos0 is used for the horizontal scales. When other

variables, such as 0, sin& and tan& are used, the logarithmic mass ratio does not follow a linear trend.

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Figure 6. Correlation of jet temperatures between the projectile and target components. The copper temperatures represent the projectile component; the calcium components represent the target components. The impact angles and exposure times after the first contact of impact are given.

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5000

-2

15030 ø 45 ø 60 ø 75 ø 90 ø

ß Iog(Ca/Cu I 0-2us •t Iog(Ca/Cu 2-5us

V=5.35+0.41km/s

I 0.8 0.6 0.4 0.2 0

cos 0

Figure 7. The mass ratio of the target component to the projectile component in jets due to hypervelocity impacts of copper projectiles into dolomite blocks as a function of impact angle. Calcium and copper represent the target and projectile components, respectively. The values of the mass ratio shown in the diagram include only atoms in the ground state not those in the excited or ionized states. The exposure times after the first contact of impact are shown in the diagram. Results from a limited range of impact velocity (5.35+0.41 krn/s) are shown.


The increases in the target-to-projectile mass ratio with impact angle is not unique to the combination of a copper projectile and a dolomite target. Time-exposed observations of emission spectra created by aluminum projectiles impacting pumice powder also shows that the projectile signature (A10 band emission) is dramatically reduced at the vertical impact angle [Schultz et al., 1996].

The experimental results also constrain temporal variation in the mass ratio in impact jets. With the limited data available at later times, the mass ratio does not change with time even though there is a large change in temperature. This observation demonstrates the reliability of this measurement method and also suggests that recombination processes of free atoms (e.g., Ca + O --> CaO) may not be very rapid in these high-temperature jets.

4. Theoretical Calculations

Impact velocity, angle, and projectile properties all contribute to the temperature of a jet simultaneously. Isolating the effects of these factors is difficult based just on the experimental data. Consequently, theoretical calculations based on asymmetric jetting provide a useful framework for interpretation. Melosh and Sonett [1986] and Vickery [1993] developed theoretical models for jetting due to impacts by spherical projectiles. Their models, however, approximate an asymmetric collision that occurs between surfaces of a spherical projectile and either a spherical or a planar target with symmetric collision between two identical surfaces. This simplification prohibits us from assessing the effects of differences in both shock impedance and impact velocity with respect to the collision point between the projectile and the target. These effects are important because our experiments with quartz and copper projectiles yielded significantly different results. Then we construct a new theoretical model for jetting due to an asymmetric collision by taking into account the effects of differences in both shock impedance and collision velocities with respect to the collision point. Our model is based on an asymmetric jetting theory by Walsh et al. [1953] and a method to assess maximum shock heating of jetting by Kieffer [ 1977]. First, we briefly describe the classical symmetric jetting theory by Walsh etal. [1953] and Kieffer [1977]. Models by Melosh and Sonett [1986] and Vickery [1993] used this combination of theories. Second, an extension of the jetting theory to asymmetric collision done by Walsh et al. [1953] and its validity are discussed. Third, the application of the asymmetric jetting theory to a blunt-body impact is presented. The model described in section 4 assumes both pure shock heating and steady state condition in shock. Such assumptions are used not because they precisely represent the experimental conditions in this study but rather because they have been the standard assumptions usually used in both analytical and numerical methods in the literature. Comparison between such a model based on the standard assumptions and the experimental results will help us understand both validity and limitation of the assumptions.

4.1. Symmetric Jetting Theory

When two identical plates collide at an angle, oblique shock fronts develop at the contact point O of the two plates (Figure 8a). This type of simple flow with oblique shocks is called the "regular regime" [Al'tshuler et al., 1962]. The shock fronts travel at a velocity V• given by

V x - Vø , (1) sin•p

where V o and q0 are impact velocity and deflection angle, respectively [Walsh et al., 1953]. When this system is observed in the collision-centered coordinate, in which the shock front is

stationary (Figure 8b), the plates are colliding into the shock front with the velocity of V•:

V7 = V o cot q0. (2)

Note that the effective impact velocity V• in the collision- centered coordinate system is much larger than impact velocity Vo in the laboratory coordinate system when the deflection angle q0 is small. When the deflection angle q0 exceeds a certain value, the regular-regime flow becomes unstable and transforms into the "irregular regime" with jetting [Walsh et al., 1953; Al'tshuler et al., 1962]. Both laboratory experiments [e.g., Walsh et al., 1953] and numerical calculations [e.g., Harlow and Pracht, 1966] indicate that the velocity of the jetting in the collision-centered coordinate (Figure 8c) is approximately the same as the effective impact velocity V•. Thus the jetting velocity V• in a laboratory coordinate is approximated by

= Vs = +cøSv o, (3) sinq0

which is several times the impact velocity Vo at low deflection angles q0. This is experimentally confirmed by Birkhoffet al. [1948] and Walsh et al. [1953]. Here it is emphasized that majority of the mass of colliding plate is not incorporated into a jet but stays in the less shocked zone downrange, which is often called "slug" (Figure 8c).

In the regular regime, the pressure behind the oblique shock front and the deflection angle q0 of the plates are connected by geometry and the Rankine-Hugoniot relation:

cos2 q> = (1- Ps) (4) 1_ •+2ps '

/,t+l

where St and b• are compression and normalized shock pressure defined by the following:

/,t -- P.•_s_ 1 (5) Po

Ps : Ps (6)

The symbols P•, Po, and Ps are dimensional shock pressure and densities before and after shock compression, respectively. The detail of the derivation of expressions similar to (4) are given by Walsh et al. [1953], Kieffer [1977], and Vickery [1993]. The relation between compression St and shock pressure b,. are given by shock Hugoniot equation of state [e.g., Meyers, 1994];

bs = + (7)

where M• is Mach number of the effective velocity V• and given by

M•= VJco. (8)


Shock Front •

•, .,•:• . ,• •.•..`.•?.`•`•;•.•(`.*•...``.•...•••:•.•::•.•..•`:•<• •:• ......

•i•re 8m A schematic diagram of the flow field around a symmetric oblique impact of two identical plates. Velocities are measured in a laborato• coordinate. The flow is in the regular regime• that is, •etting does not occur. The symbols V•, V•., and • are impact velocity, shock velocity, and deflection angle of the plates, respectively. The thick solid line dividing the regions with different gray colors indicates the shock front.

The constant s is defined in a linear relation between particle velocity V•, speed of sound Co, and shock wave velocity V*:

V*= Co + sV• (9)

This relation is observed for a variety of material over a wide range of impact velocities [e.g., Marsh, 1980]. Substituting (7) into (4) yields the deflection angle q0 as a function of compression # and Mach number M•,

•= • (•, MO. (10)

A graphical approach shows that (10) has a maximum value, above which a regular-regime flow does not exist [Walsh et al., 1953; Kieffer, 1977; Vickery, 1993]. This critical condition is

accordingly given by 0.__•_½ = 0 (11)

Equation (13) is solved iteratively using the shock equation of state (7), yielding both the critical deflection angle (•0cr and the critical shock pressure bcr.

In the irregular regime above this critical angle, the flow field is very complex, and no general analytical solution has been found. The pressure of the stagnation point, however, can be estimated. Assuming that the pressure P•t at the stagnation point is approximately the same as the pressure P• just behind the shock front and that the enthalpy of colliding material before shock compression is much smaller than thereafter, Kieffer [1977] derived an expression relating the effective impact velocity V• and the stagnation pressure P•t from Bernoulli' s law:

1V• 2 = Ps•t •s•t . (14) 2 2Po •st + 1

and equivalently by

(12)

Substituting (4) into (12) gives

(g+1)2-sg2 =(g+l) } (13) Es t= Pst gst M/2 {•(1-s)+ 1} 3 {•-(• + 1)fix ' 2Po •st + l'

Vo

.... •,.....:• ............. :: .............. :. ..................... • -;: ........

From (5), (6), (7), (8), and (14), the pressure P•, and compression #•., at the stagnation point are iteratively obtained as functions of the effective impact velocity V•. The internal energy E•, at the stagnation point is given by the Rankine-Hugoniot relation for energy

Figure 8b. A schematic diagram of the flow field around a symmetric oblique impact of two identical plates. Velocities are measured in the collision-centered coordinate, in which the conversion point of the two plates O is stationary. The symbol V• is the effective impact velocity of the plate with respect to the shock front.

(15)


ShocksFront

Fibre 8c. A schematic diagram of the •ow field around a symmetric oblique impact of two identical plates. The •ow is in the i•eg•lar regime; that is, jetting occurs. The velocities are measured in the collision-centered coordinate. The symbol • is jetting velocity.

The energy given by (15) can be used as a reference for shock heating within the jet. In reality, however, the shock front does not elevate the pressure directly to the stagnation pressure. The matedhal compressed at the shock front is adiabatically compressed until it reaches the stagnation pressure. Thus (15) overestimates the internal energy of a jet. Kieffer [ 1977], in fact, points out that the internal energy at the stagnation point obtained by numerical calculations by Harlow and Pracht [1966] is -80% of that predicted by this method. Moreover, the maximum internal energy of jetted matedhal whose streamline does not pass the stagnation point is less than the internal energy at the stagnation point. Consequently, the energy given by (15) should approximate an upper limit for shock heating of jetting.

For a given impact velocity V o, the effective impact velocity V• decreases with deflection angle 9 (see (2)). Because shock heating during jetting increases with the effective impact velocity V•, a lower deflection angle 9 results in a higher energy (see (2)). However, because there is no jetting below the critical deflection angle 9cr, the maximum heating of jetting occurs at the critical angle.

4.2. Asymmetric Jetting

Unless two colliding plates have symmetric impact velocities as well as identical thickness and material properties, the

collision becomes asymmetric. The flow field in such an asymmetric collision is schematically shown in Figure 8d. Because of the asymmetry, the effective impact velocities V• and V 2 and the deflection angles q0• and q02 of the two surfaces are not equal. The ratio of the two deflection angles q0• and q02 is determined by the boundary condition on the matedhal boundary behind the shock fronts. Walsh et al. [1953] assumes a free-slip boundary condition at the material boundary. This assumption requires that both the velocity component perpendicular to the boundary and the pressure gap across the boundary is zero but allows a jump in the velocity component parallel to the boundary. Such an assumption, however, is not correct in a strict sense because no real fluids are inviscid; hence, no velocity jump is allowed anywhere. Thus it can also be assumed that two velocity components are equal across the boundary [Ang, 1990]. For the latter assumption, however, a pressure jump exists across the boundary. The pressure gradient is in the direction to change the deflection angles to those predicted in the free-slip assumption. In reality, the boundary may not strictly follow either boundary condition but may undergo oscillation as observed in explosive welding experiments [e.g., El-Sobky, 1983], analytical calculations [e.g., Godunov et al., 1970], and numerical simulations [Miller, 1998]. Nevertheless, impact experiments of asymmetric collisions using cone-shaped projectiles and flat

Figure 8d. Schematic diagram of the flow field around an asymmetric oblique impact. The deflection angles q0• and q02, effective impact velocities V• and V 2, and shock front velocities V• and V•2 in the two plates are different, respectively. The wedge angle o• of the two plates is equal to the sum of the two deflection angles q0• and q02.


targets by Allen et al. [1959] show that the critical condition is predicted well by the asymmetric collision model with the free- slip boundary condition assumed by Walsh et al. [1953]. Consequently, we adopt the free-slip boundary condition in this study as a reasonable working assumption and neglect effects of shear around the material boundary. The significance of this simplification is discussed in section 5.

The solution for this boundary condition problem needs an iterative procedure. First, initial values of deflection angles •0• and % (= a- q9•) are assumed. For the assumed deflection angles and given effective impact velocities V• and V2, the shock pressures P,. behind the shock fronts are calculated for both sides of the material boundary using (4) and (7). Second, the deflection angles are adjusted. For example, if the shock pressure in the upper zone is higher than the lower zone, the deflection angle •0• of upper zone is decreased and hence that % of lower zone is increased. Third, the shock pressures are recalculated. This procedure is repeated until both shock pressures coincide.

As the wedge angle a of the plates increases, the shock pressure P,. and the deflection angles q9• and % increase. When the wedge angle a reaches a certain value, one of the deflection angles reaches its critical value. Above this angle, a regular- regime flow cannot exist, and jetting occurs [Walsh et al., 1953]. This critical angle a•.r of asymmetric jetting is calculated in the following way.

For the given effective impact velocities V• and V2, the critical pressures Pcr and the critical deflection angles q)lcr and q)2cr can be calculated for both plates of the collision using the method for symmetric jetting (i.e., (7) and (13)). If the critical shock pressure of the upper plate is lower than that of lower plate, the shock pressure of the lower plate for the deflection angle of oc- q)lcr is calculated, where q)lcr is the critical deflection angle of the upper plate. If the newly calculated shock pressure is lower than the critical pressure of the upper plate, the deflection angles of the upper and lower plates must decrease and increase, respectively, in order to achieve balance in pressure across the boundary. Then the deflection angle of the upper plate becomes smaller than the critical angle. The deflection angle of the lower plate is also a subcritical value because the shock pressure for the critical condition for the lower plate is higher than that of the upper plate here. Thus a regular-regime flow exists in this condition. If the newly calculated shock pressure is higher than the critical pressure of the upper plate, however, jetting occurs. If the two pressures are equal, it is a critical condition.

As in the symmetric jetting case, shock heating in asymmetric jetting maximizes at a critical condition for a given impact velocity. The energy of a jet is calculated with the method by Kieffer [1977], i.e., (7), (14), and (15). Because the effective impact velocities V• and V 2 of the two plates of an asymmetric collision are generally unequal, different degrees of shock heating are obtained for jetting from the upper and lower plates. This method for symmetric jetting assumes that the ejection velocity of jet is aligned to the material boundary behind the shock fronts. Although such alignment is not strictly guaranteed, analytical calculations by Pack and Curtis [1990] indicate that departure from such alignment is small.

4.3. Application to Spherical Impactors

When a spherical projectile impacts a half-space target, the wedge angle oc between the surfaces of projectile and target continuously and rapidly increases as the projectile penetrates into the target (Figure 9). Thus the effective impact velocities for

a

Projectile

b

Figure 9. Geometric configuration of an oblique impact by a spherical projectile into a half-space target. (a) The geometric configuration is shown in a three-dimensional perspective. Impact angle, the vector of impact velocity, and horizontal azimuthal angle from the impact direction are denoted by 0 and ¾im, and •, respectively. The impact velocity is measured in the laboratory coordinate and decomposed to V//and Vt. The central plane is also shown. This plane is defined here as a vertical plane that constrains the projectile center and is parallel to the impact- velocity vector. (b) The cross section along the central plane is shown. Note that the deflection angles of projectile q9• and target q92 and wedge angle a• change with time as projectile penetrates into the target.


a projectile V• and a target V 2 with respect to the shock fronts (see Figure 8d for definition) change with time and are expressed as functions of impact velocity V, .... impact angle 0, and wedge angle

V/- sin•0 V/m (16) sin o•

V2 = sin(a + 0•) V/m. (17) sina

These relations are graphically shown in Figure 10. Note that (16) and (17) are valid only at the leading edge of a projectile. The effective impact velocities depend generally on azimuthal direction from the center of a projectile [see Melosh and Sonett, 1986; Vickery, 1993]. Our spectroscopic observations, however, are focused on the downrange side of the impact point, where

jetting material from the leading side is expected to be observed. Thus calculations with the leading-edge velocities given by (16) and (17) are appropriate for comparison with the experimental data.

Then using the asymmetric jetting theory described above, the critical wedge angle %r for an impact of a sphere can be calculated for a given impact velocity Vim and an impact angle 0. The maximum shock heating of jetting from both projectile and target material is also calculated with the asymmetric theory.

It is noteworthy that the above two-dimensional formulation for shock compression on the vertical plane including the leading edge of a spherical projectile is identical to that for shock compression of impact of a cylinder into a planar target. There is no particle/shock velocity component perpendicular to the two- dimensional plane in either case. There is, however, a subtle but distinctive difference between the two cases. In the following, the

•. , \",,• Impact angle, 0 ', / \',,,• •90 o •. , \",• ......... 75 ø

•, \ ?,,•,, 60ø 45 ø , ", _-'•_-_ • 30 ø

-.-_ -

a _

illllllllllllllllllllllllllllllllllllllll IIIIIIIIIIIIItlilllllllllllllllllllllllllllllll

30 60 90

Wedge Angle, o• (degree)

',, ", , i•,. Impact angle, O :: / '. •, ---90 ø .•

4.- ', • ,•;, ......... 75 ø : : '• • \•, ---60 ø : i • , \x;:. ____45 ø : : 15 ø', •, '•', ..... 30 :

s 3 }- • 3øøx,45x,o•,'•,, -- .... 15 ø •

2 • .,.• x.•• •

1 : "•'•' •' • .......

0 ,, ........ , ......... , ......... , ......... , ......... , ......... , ..... 0 30 60 90

Wedge Angle, a (degree)

Fibre 10. The effective impact velocities for the projectile V] and the target V2 in an impact of a spherical projectile into a half-space target as functions of both impact angle 0 and wedge angle •. (a) The effective impact velocity for the projectile normalized by impact velocity Velcro. (b) The effective impact velocity for the target no•alJzed by impact velocity Vff½•. (c) The ratio of effective impact velocities for the projectile to that for the target 'V•2. (d) The difference between the effective impact velocities of the projectile and the target no•alized by impact velocity (V2-V•)•i•.


Impact angle, 0 90 ø

......... 75 ø 60 ø 45 ø

2 30 ø 15 ø

ß

/

..........

c

0 30 60 90

Wedge Angle, c• (degree)

d ......... 75 ...... 30 ø • -- -- - 60 ø - - 15 ø

0 30 60 90

Wedge Angle, c• (degree)

Figure 10. (continued)

direction perpendicular to the above vertical plane is referred to as • direction, and the vertical plane is referred to as the central plane (see Figure 9a). A spherical impact has divergence due to • direction velocity even on the central plane because • direction velocity in the neighbor of the central plane is not zero, whereas there is no divergence due to • direction velocity anywhere in a cylindrical case.

This finite difference in velocity divergence, however, is not important for the shock calculation in the present study. Since the width of a shock front is practically infinitesimal in general, the divergence of particle velocities perpendicular to a shock front is virtually minus infinity [e.g., Landau and Lifshitz, 1987]. The size of this negative infinity of velocity divergence determines the degree of shock heating. Thus finite difference in velocity convergence does not influence the degree of shock heating. Consequently, the above two-dimensional formulation is applicable to the shock within the central plane of a spherical impactor.

However, it is obvious that shock compression off the central plane is different from the result of the above two-dimensional

approach. It requires further consideration. The vector of impact velocity Vim can be decomposed to the vertical (Vñ --V/m sin0 ) and horizontal (V//= V/m cos0 ) components for impact angle 0 measured from the horizontal, where gi,--IV•ml. When the vector of impact velocity Vim is projected to a vertical cross section that contains the center of the spherical projectile and azimuthal angle • measured from the impact direction (Figure 9a), it has Vñ of vertical component and V//cos• of horizontal component. The component perpendicular to the cross section is V//siny/. It does not contribute to shock compression on the collision between the target and the projectile, however, because this velocity component is perpendicular to the local collisional contact surface. Consequently, the shock compression at the contact surface at • of azimuthal angle away from the leading edge of the projectile can be estimated by the same method described above with an azimuthal correction factor of cos• for the horizontal velocity component. The azimuthal correction factor is equal to 1 for • = 0 ø, 0.99 for • = +8 ø, and 0.9 for • = +_26 ø. Thus the effect of azimuthal angle is relatively minor over a considerable range of angle.


4.4. Calculation Results

The critical angle %r for jetting was calculated for experimental conditions of impact velocity Vim and impact angle 0 and material properties (Figure 11). Since Hugoniot data for dolomite are not available, calcite data are used here. All the

Hugoniot data are taken from Marsh [ 1980] and Meyers [ 1994]. Figure 11 also shows deflection angles (p• and (p: of the projectile and target at critical conditions and reveals the material reaching its critical condition first.

The deflection angle (p• of the projectile is larger than that of the target q•: in the quartz impacts. However, the relation is reversed in copper impacts. This results from the difference in the impedance between the two projectile materials. Because copper has a much higher density than both quartz and carbonates, it is more resistant to deflection owing to shock compression. As a result of the small deflection angle, the range of impact

conditions where the projectile can reach a critical condition prior to the target is much narrower in a copper case than in a quartz case. At low impact angles, however, a projectile will reach a critical condition first, even if the impedance of projectile material is much higher than that of the target material. The reason is the following. The effective impact velocity V• of a projectile is much smaller than that of a target V2 at all wedge angles a when the impact angle t9 is small (Figures 10c and 10d). Both theory and experiments indicate that jetting occurs when an effective impact velocity is lower than a critical velocity for a given deflection angle [e.g., Walsh et al., 1953; Kieffer, 1977]. Consequently, a projectile is more susceptible to jetting at lower impact angles. At higher impact angles 19, however, the effective impact velocity V 2 of the target is similar to or smaller than that V• of the projectile (Figures 10c and 10d). Thus the target becomes more prone to jetting at higher impact angles.

35 •:•- .................................................................... -• Projectile

(• 30

• 25

< 20

• 15

•- 10 o

(• 5

0

Target

a •

o 30

Quartz Projectile i I,, , I,,I,,,,,,, I,,,,,,,,,I,,,,•,

60 90

Impact Angle, 0 (degree)

35

e 30

v

e 25

< 20

• 15

c 10 o

5

0 30

Target

60 90


Figure 11. Critical conditions for impacts by (a) quartz and (b) copper projectiles into calcite targets. The critical wedge angle O•cr and deflection angles of both the projectile (Dlcr and the target (D2cr are shown as functions of impact angle 19. The jet-initiating material is shown at the top of the diagrams. Impact velocity of 6 km/s is used for calculation.

30,840 SUGITA AND SCHULTZ' SPECTROSCOPIC OBSERVATION OF IMPACT JETTING

The critical wedge angle O•cr at different impact velocities Vim is compared in Figure 12. The critical wedge angle act is greater at higher impact velocities Vi, n because the effective impact velocities of both projectile and target V• and V2 increase with impact velocity. It is also noted that a critical wedge angle %r as a function of impact angle 0 has a maximum (Figures 11 and 12). At lower impact angles, the effective impact velocity V• of a projectile increases with impact angle 0 and reaches a critical condition first (Figure 10a). Since a higher impact velocity requires a higher wedge angle cr for jetting [e.g., Walsh et al., 1953; Kieffer, 1977], the critical wedge angle Crc• increases with impact angle 0. At higher impact angles 0, however, the critical wedge angle is controlled by the target because it reaches a critical condition first. For wedge angle cr higher than -25 ø, the effective impact velocity V2 of a target has its maximum at an impact angle 0 of-60 ø (Figure 10b). Thus, for impact angles 0

higher than -60 ø, the critical wedge angle %• decreases with impact angle 0. Consequently, the critical angle%• has a maximum value.

Maximum shock heating of jets derived from both a projectile and a target is calculated with (7), (14), and (15) and shown in Figure 13. The heat of vaporization and shock heating of calcite by plane-normal shock are also shown for comparison. The plane-normal shock cases are calculated with impedance matching method [e.g., Gault and Heitowit, 1963]. The heat of vaporization (11.3 MJ/kg) of calcite is calculated from thermodynamic data [Chase et al., 1985; Woods and Garrels, 1987] assuming that the vapor phase of calcite consists of CO2 and CaO gases and that the vapor temperature is 3000 K. It is worth noting that the heat of incomplete vaporization or degassing of calcite is much smaller; 2.5 MJ/kg [Chase et al., 1985; Woods and Garrels, 1987]. Here the end products of

............................................... • Target __• 6,i km/s Projectile -• 35 .......................................... ->< • 3o

• 25

• 20

ß 15

• 10

o

6 km/s

4 km/s

m

Quartz Projectile

0 30 60 90


Projectile 35 •' ................................ "'"

. b

-o 25

•!/ 20

o 15

g lO

5

Target 6 km/s •, 4 km/s •

6 km/s

4 km/s

Copper Projectile: _

0 30 60 90

Impact Angle, e (degree)

Figure 12. Critical wedge angle %• of (a) quartz impacts and (b) copper impacts as a function of both impact velocity Vim and impact angle 0. Solid calcite targets are assumed for these calculations. The jet-initiating material is shown at the top of the diagrams. Impact velocity is indicated.


35

3O

25

2O

15

10

i i i , , I i l

a. Quartz projectile .......... Projectile jet

Target jet

i i I i i , [ i

6 km/.s,. ß

ß

ß

Heat of vaporization ,," 4 km/,s of calcite . c' ...-'

ß -' 4 km/s -

.

. ß

ß o

ß ß

Plane-normal shock at 6 km/•

Plane-normal shock at 4 kmh

35

3O

25

10

b. Copper projectile ..... Projectile jet 6 km/s '

Target jet • ß ' 6 km/s

,

ß

,

,

ß

,,' ß

ß

o

,

ß

,, ß

ß

,, ß 4 km/s

Heat of vaporization ..,,' '• of calcite .

ß ß .

ß

ß . __

ß-' ß-' Plane-normal shock- .

.,, ... at 6 km/s ß ,

ß

ß o

ß • .

..- . . Plane-normalshock, ß

:::.-' at4 km/s

i I i I i I I I I I I I I I I I 0 0

0 30 60 90 0 30 60 90

Impact Angle (degree) Impact Angle (degree)

Figure 13. Comparison of shock heating of asymmetric jets, heat of vaporization of carbonate, and shock heating of plane-normal impacts. Calculations used (a) quartz and (b) copper projectiles. The maximum shock heating of both projectile and target components in asymmetric jets is shown. The jetting model assumes that a spherical projectile impacts a half-space calcite target. The plane-normal impact model shows shock heating of calcite targets only. Impact velocities are indicated in the diagram. The heat of vaporization of carbonate used here is the enthalpy to vaporize calcite at room temperature to carbon dioxide and calcium oxide gases at 3000 K.

incomplete vaporization are assumed to be CO2 gas and CaO solid at 1000 K. Consequently, much weaker shock heating than jetting may induce significant vaporization of carbonate. Nevertheless, resulting impact vapor due to such weak shock should not contain significant amounts of CaO or Ca gasses.

There is a significant difference between the projectile and target components of jetting. The maximum shock heating of the projectile component at .low impact angles is very small; even smaller than plane-normal shock heating. However, it increases monotonically with impact angle and becomes comparable to or even greater than shock heating of the target component at high impact angles. These are readily explained by the behavior of the effective impact velocity V• of a projectile, which is very small at low impact angles 0 and increases monotonically with impact angle 0 (Figure 10a). However, shock heating of the target component is always much higher than that due to a plane-normal shock and has a maximum value at an intermediate impact angle 0 (Figure 13). This is also consistent with the behavior of the effective impact velocity V2 of a target, which is significantly larger than impact velocity Vim for relevant wedge angles a (<45 ø) and has a maximum at an intermediate impact angle 0 (Figure 10b).

Copper and quartz impacts have different dependencies for the degree of shock heating in the jet as a function of impact angle 0 (Figure 13). This difference results from the behavior of the critical wedge angle %r (Figures 11 and 12). The critical angle O•cr for quartz impactors increases up to an impact angle 0 of -70 ø , where the transition of jet-initiating material occurs. The increase in wedge angle tx lowers the effective impact velocities and hence decreases shock heating. For copper impactors,

however, the critical wedge angle O•cr reaches a plateau (O•cr • 200-25 ø) at relatively low impact angles: 0- 45 ø (Figures 1 lb and 12b). For a constant wedge angle tx, the effective impact velocity V2 of a target increases with impact angle 0 until it reaches its maximum at relatively high impact angles, 0 = 60-75 ø (Figure 10b). Thus shock heating of the target-component jet due to a copper impactor has its maximum at higher impact angles 0 than that for a quartz impactor.

5. Comparison Between Theory and Experiments

In this section, we compare the results of the theoretical calculations with the spectroscopic observation data, showing both consistencies and inconsistencies. Then the causes for the

disagreements between theory and the experiments are discussed.

5.1. Jet Temperature

One of the most important consistencies between jetting theory and the experimental results may be the extremely high degree of heating. The observed high-temperature gas with little liquid/solid phases cannot be attained by plane-normal shock (Figure 13). Shock due to jetting, however, can easily heat carbonate target to its complete vaporization. Another consistency between theory and experiments is the velocity effect on jet temperatures. Theoretical calculations indicate the temperatures of both projectile- and target-derived jets increase with impact velocity. This result applies to both quartz and copper projectiles impacting carbonate targets (Figure 13). This theoretical prediction is very consistent with experimental results.


Spectroscopic observation in this study indicates that the temperatures of both target- and projectile-derived jets increase with impact velocity for the combination of copper projectiles and dolomite targets (Figures 4a and 5a). Results of previous experiments by Sugita et al. [1998] also indicate that the temperature of target-derived jets created by quartz impacts into dolomite targets increases with impact velocity. Here the temperature Of projectile component was not measured because of the lack of strong emission lines/bands from quartz projectiles in the observed wavelengths.

Comparison of the effects of both impact angle and impedance contrast on jet temperatures, however, reveals significant inconsistencies between theory and the experimental results. First, the high temperature in the projectile component for copper impactors at low impact angles observed in the experiments (Figure 5) is not readily explained by the jetting model. Predicted degrees of shock heating at low impact angles shown in Figure 13b are comparable to or less than the enthalpy (6.2 MJ/kg; Chase et al. [1985]) to generate copper vapor at 3000 K. Here it is emphasized that the shock heating calculated in the model is the internal energy at a peak shock pressure, after which the internal energy of jetting vapor decreases rapidly by adiabatic decompression. Our spectroscopic observations capture the temperature of jetting vapor, which has experienced substantial adiabatic decompression. Consequently, the calculated internal energy shown in Figure 13 provides an upper limit for the observed jet temperatures. Second, the theoretical model cannot account for the quantitative dependence of temperature on impact angle and impedance contrast. The theoretical model predicts that the target component of jetting due to quartz impacts should have a lower temperature at the impact angle 0 of 90 ø than at 45 ø (Figure 13a). The experimental data for quartz, however, reveal a trend of increasing temperature as a function of impact angle between 30 ø and 60 ø [Sugita et al., 1998]. Third, the minimal effect of impact angle on the jet temperature for impacts of copper projectiles into dolomite targets (Figures 4b and 5b) is not consistent with a large increase in temperature obtained from the model calculations (Figure 13b). Fourth, the theoretical model predicts that shock heating of the target-component jetting should be significantly higher with a copper projectile than with a quartz projectile at all impact angles for a given velocity because of the higher shock impedance of copper (Figure 13). Experimental data of both the present study (Figures 4 and 5) and Sugita et al. [1998], however, indicate that the range of distribution in the calcium temperature for copper impacts is comparable to that for quartz impacts.

Another important discrepancy in jet temperature between the theory and the experiments is the correlation between the target and projectile components. As mentioned above, the experimental results indicate that the copper temperature (projectile component) correlates well with calcium temperature (target component) and that the projectile component is constantly about 1000 K higher than the target component for a wide range of impact angles (Figure 6). The jetting model, however, does not predict such a correlation between target and projectile components (Figure 13).

5.2. Mass Ratio

The observed target-to-projectile mass ratio in a jet can be compared to theoretical prediction in the literature. Vickery [1993] estimated target-to-projectile mass ratio within the whole jetting phase ejected from all the azimuthal angles around a projectile. Her theoretical model qualitatively reproduces the

experimental results well; specifically, the target-to-projectile mass ratio increases steadily with impact angle. Here it should be noted that the definition of impact angle by Vickery [1993], who measures it from the vertical, is opposite from the usage in this study. The predicted change in target-to-projectile mass ratio in a jet as a function of impact angle [Vickery, 1993], however, is smaller than the experimental results by about a factor of 5.

5.3. Model Reassessment

The above agreements and discrepancies between theories and experimental results indicate that the jetting model based on standard theories accounts for some qualitative characteristics of the jetting phenomena due to oblique impacts by blunt bodies but cannot predict specific features quantitatively. We will discuss three possible causes for the discrepancies on jet temperature and a possible explanation for disagreement on mass ratio in a jet.

5.3.1. Stagnation-point approximation. First, the method to estimate shock heating of jetting material is potentially problematic. The maximum shock heating of a target and a projectile is estimated at a stagnation point independently using (7), (14), and (15). This approach by Kieffer [1977] implicitly assumes that the stagnation pressures of the two components are different. If the flow during jetting is steady state, however, the stagnation points of the two components must coincide and hence have the same pressure. A proof is the following.

The flow in the central plane is considered (see Figure 9). Them is no velocity component across the central plane. If the flow is in a steady state, the material boundary is stationary and has no velocity component' perpendicular to it. When jetting occurs, the velocity component parallel to the boundary line in the jet has the opposite direction of that in the slug part, viewed from the collision-centered coordinate in which the apex of the two colliding surfaces appears stationary (compare Figure 8c). Consequently, there is a point on the boundary line where the velocity component parallel to the material boundary is zero. Because the vertical velocity component is always zero along the boundary, this point has no velocity, i.e., a stagnation point. If both the target and projectile components have jetting flows, then both have a stagnation point on the boundary line. The whole boundary line belongs to a streamline. As a result, pressure along the material boundary on each side has its maximum at the stagnation point according to Bernoulli's law. Because the pressures on the both sides of the boundary are the same, the location and the pressure of the maximum-pressure points of both projectile and target components must coincide. Consequently, the stagnation points of the both sides of the material boundary coincide and have the same pressure. In reality, however, a large differential velocity exists near the boundaries and viscous effects become important. Thus Bernoulli's law may not apply strictly at the boundary. Nevertheless, if viscosity is relatively small, a thin viscous boundary layer forms along the interface around the boundary, in which pressure is approximately constant in the direction perpendicular to the interface boundary [e.g., Landau and Lifshitz, 1987]. Because most of the velocity gradient is concentrated in the viscous boundary layer, the flow field and pressure distribution outside the viscous boundary layer may be approximated well by the inviscid model [e.g., Landau and Lifshitz, 1987]. Thus the above argument on stagnation pressure in an inviscid fluid is approximately applicable to flow with a thin boundary layer.

The coincidence in stagnation pressure, however, does not necessarily account for the observed correlation between the projectile and target jet components. Because the effective impact


velocities V• and V2 of a projectile and a target are different, the ratio of pressure increase by adiabatic compression to that by shock compression must be different between the target and the projectile in order to attain the same stagnation pressure. More specifically, this ratio is higher for the component with a lower effective impact velocity because adiabatic compression raises pressure higher than shock compression for a given collision velocity. Thus the ratio of adiabatic compression is larger for the projectile component than the target component in low-angle impacts, in which the effective impact velocity of a projectile is smaller than that of a target (Figures 10c and 10d). Because adiabatic compression does not contribute to an increase in thermal energy, the contrast in degree of heating in Figure 13 would be increased further when the effect of coincidence of

stagnation pressure is taken into account. Consequently, uncertainty in the method by Kieffer [1977] to estimate shock heating does not account for the discrepancy between the theory and the experiments.

5.3.2. Steady state approximation. A second possible cause for the discrepancy between observed and expected jet temperature may involve the assumption of a steady state flow. A colliding matehal may not stop at the mean material boundary but may overshoot and penetrate through it; that is, the material boundary departs from its average line. Then the overshoot through the mean boundary may lead to backlash; that is, the material boundary moves back beyond the mean boundary. Such oscillatory motion of the material boundary (i.e., Kelvin- Helmholtz instability) is observed in explosive welding experiments with jetting [e.g., EI-Sobky, 1983], analytical calculations [e.g., Godunov et al., 1970], and numerical simulations [Miller, 1998]. Because such oscillatory motion of the material boundary gives rise to motion of shock fronts around the collision point, the effective impact velocity of incoming flow with respect to the shock front will also fluctuate. Thus the resulting shock heating in the jet should have fluctuation. Since our observation using emission spectroscopy is more sensitive to a higher temperature component, the fluctuation in shock heating may bias the measured jet temperature upward. This may reduce the temperature gap between 'theoretical predictions and experimental results.

Another possible consequence of break down of steady state approximation is an inaccurate prediction of the critical condition for jetting. When the flow around an asymmetric collision is not in a steady state, the angle of shock front with respect to a colliding surface may not be controlled simply by the ratio of shock compression as shown in Figure 8d but may be controlled directly by Huygens' law wherein a shock wave front is an envelope of wave circles from preceding collision points. Huygens' law, however, needs to be modified to accommodate the effect of nonlinear superposition of shock waves. Unlike an impact of long thin flat plates, the shock condition of a blunt- body impact changes constantly with time. Consequently, the flow field around the collision may not be approximated properly by a steady state model. Then the critical condition for jetting, which is strongly controlled by the angle of the shock fronts, may not match predictions from a steady state model, thereby contributing to the observed discrepancy.

A series of impact experiments with cone-shaped projectiles described by Allen et al. [1959] may be useful in understanding the effect of angle of the shock fronts with respect to colliding surfaces. Because the thickness of the cone is not small, the

steady state assumption is not strictly applicable in this case. Then the angle of the shock front with respect to the surface of

the cone-shaped projectile may not be controlled by shock compression but by Huygens' law. Their experimental results, however, showed that the critical condition is predicted well by an asymmetric jetting theory based on the steady state assumption by Walsh et al. [1953]. Thus the effect of time- dependent flow may not be very important for a critical condition for impact jetting.

5.3.3. Inviscid approximation. The effects of viscous shear heating may also contribute to the difference between the theoretical and experimental results. The difference in velocity across the material boundary between a projectile and a target is unavoidable in an asymmetric collision. Here, it is emphasized that the differential motion on the material boundary does not occur in a symmetric impact of two identical plates. The differential motion may cause significant shear heating as inferred for later stages of impact vaporization [Schultz, 1996]. This process may greatly change the jet temperature. Because lower angle impacts have larger differential velocity (Figure 10d) at probable critical wedge angles (30 ø < 0 < 40% greater shear heating will occur along the material boundary. This may contribute to greater heating of the projectile component at low impact angles and may fill the gap in temperature between the theory and experiments. The good correlation between the projectile and target components in a jet is also consistent with viscous heating, since the differential velocity (i.e., shear) across the material boundary and resulting viscous heating are shared by both sides of the boundary.

Among the three factors discussed above, the effect of viscous shear heating can account for the discrepancy in jet temperature between theoretical predictions and experimental results most successfully. Nevertheless, the effects of nonsteady state flow and other unknown factors still need to be considered viable and

will be the focus of future studies.

5.3.4. Alternation in material to jet. One possible cause for the large discrepancy is that the mass ratio in a jet as modeled by Vickery [1993] is solely based on the difference in ejection velocities between target- and projectile-derived jets. This model assumed that the thickness of target-derived jet and that of projectile-derived jet are the same. The thickness of the two components of a jet, however, does not necessarily have to be identical. In fact, Ang [1990] argues that a jetting phase may be dominated by material from either projectile or target depending on which component reaches the critical condition for jetting first. Both the effective impact velocity and wedge angle between projectile and target change during penetration. In general, neither projectile nor target meets a critical condition for jetting at the first contact of impact. During penetration, either the projectile or target eventually will reach a critical condition for jetting. If the projectile reaches a jetting condition first, Ang [1990] argues that the resulting jet will be dominated by projectile material. Using an analytical approach, he found that some combination of projectile and target matedhals has impact velocities at which the matedhal (i.e., either projectile or target) reaching a jetting condition alternates. Ang [1990] suggests further that this transition may cause the anomalous luminosity change as a function of impact velocity observed in micro-impact experiments [Eichhorn, 1976].

Although Ang [1990] discusses only velocity effects for vertical impacts, the same argument may hold for oblique impacts. It is noted here that the model by Vickery [1993] was developed for a collision between the same material of projectile and target. Hence, any effects of impedance contrast between the two cannot be assessed. If a jetting phase is dominated by the


material that reaches a jetting condition first, then this may account for the large variation in mass ratio within a jet as a function of impact angle. In fact, the projectile reaches the jetting condition first at lower impact angles, whereas the target reaches this condition at higher angles (Figures 11 and 12). This is consistent with the observation that the target-to-projectile mass ratio increases with impact angle.

Ang [1990] also predicts an abrupt transition in the observed mass ratio as a function of impact angle; however, we do not observe such a jump or an abrupt transition here (Figure 7). There are two factors accounting for this discrepancy. First, when either the target or the projectile meets a jetting condition, the other may be mixed into a jet by a Kelvin-Helmholtz instability [Miller, 1998] and/or a viscous drag force acting along the material boundary between the projectile and target. Such mixing will make the transition in the mass ratio of the jetting material gradual, rather than sudden as expected by Ang [1990]. Second, when the impact angle is the transition angle for alternation in material that reaches a jetting condition first, both projectile and target reach the jetting condition at the same stage of the penetration process. Since local impact conditions, such as effective impact velocities V• and V2 for a given wedge angle a (compare (16) and (17)), do not change abruptly as a function of impact angle, both projectile and target reach jetting conditions at similar stages during penetration when the impact angle is close to the critical angle. When one side (i.e., either projectile or target) reaches a jetting condition, the other side is almost "ready" to form a jet. Then, the second side will be easily dragged out as a jet once the first side forms a jet. As the projectile penetrates farther into the target, the second side reaches a jetting condition soon as well. Consequently, this alternation in jetting material may result in a gradual transition in mass ratio with a jet. The above argument, nevertheless, is qualitative and deserves further study.

6. Conclusions

A new spectroscopic method allows determination of both the temperature and the target-to-projectile mass ratio in hypervelocity jets. Such data are not accessible with conventional observational techniques. Jetting due to blunt-body impacts was the focus for this study because of its relevance in planetary science. The experiments have yielded new insights for the jetting phenomena: (1) The observed high temperature and almost pure gas phases in jets indicate that the degree of heating of the jetting phase is several times higher than heating expected from plane-normal shock. (2) The temperature of a jet is strongly controlled by projectile properties. The jet temperature for copper impactors does not show significant correlation with the vertical component of impact velocity, in contrast with results for quartz impactors. (3) The temperature of the projectile component of jetting correlates well with that of the target component. (4) The mass ratio of the target component to the projectile component in a jet increases steadily with impact angle from 15 ø to 90 ø (vertical angle).

These data are qualitatively consistent with the predictions of the asymmetric-collision model in this study and the model by Vickery [1993] as follows: (1) Shock heating in jets created by impacts of spherical copper projectiles into half-space carbonate targets ranges from values comparable to the vaporization energy of carbonates to twice this value. (2) The impedance contrast between a projectile and a target strongly controls the effect of impact angle on jet temperature. (3) The target-to-projectile mass ratio within a jet increases with impact angle [Vickery, 1993].

However, quantitative comparisons also reveal significant differences between observations and theoretical predictions: (1) The theoretical prediction for the effect of impact angle on jet temperature departs from our observations, particularly for the projectile component at low impact angles. (2) The jetting theory does not account for the correlation in jet temperatures between projectile and target components. (3) The observed change in mass ratio within a jet as a function of impact angle is larger than the prediction of the model due to Vickery [1993] by about a factor of 5.

The difference in the jet temperature between the experiments and theoretical calculations may reflect new factors that conventional jetting theories have not yet addressed, such as viscous shear heating along the projectile/target boundary and perhaps the nonsteady state nature of the flow around the collision points. The larger-than-expected increase in target-to- projectile mass ratio within a jet with impact angle may indicate alternating materials (i.e., either projectile or target) reaching the jetting condition. Further investigation of such factors using both experimental and theoretical approaches will contribute greatly to understanding of jetting phenomena created by planetary impacts.

Acknowledgments. The authors would like to thank Wayne Logsdon and John Vongrey at the NASA Ames Vertical Gun Range for their indispensable and excellent technical support. J. T. Heineck provided critical help and creative insights. This study has benefited greatly from discussions with O. S. Barnouin-Jha, E. M. Parmentier, and M. B. Boslough. This research was supported by NASA Grants NAGW-705 and NAGS-3877 and Jet Propulsion Laboratory Director's Discretionary Fund (JPL-960879) led by M. A. Adams. The support by M. A. Adams and JPL for part of this effort is gratefully acknowledged.

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P. H. Schultz, Department of Geological Sciences, Brown University, Box 1846, Providence, RI 02912. ([email protected])

S. Sugita, Department of Earth and Planetary Physics, Faculty of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 133- 0033, Japan. ([email protected])

(Received April 5, 1999; revised September 28, 1999; accepted October 5, 1999.)

Spectroscopic characterization of hypervelocity jetting: Comparison with a standard theory ·...

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