Nuclear Engineering and Design 238 (2008) 2693–2698

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Nuclear Engineering and Design

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A study on bubble detachment and the impact of heated surface structure insubcooled nucleate boiling flows

Wen Wua,∗, Peipei Chenb,1, Barclay G. Jonesc,2, Ty A. Newelld,3

a General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, United Statesb University of Illinois at Urbana-Champaign, Department of Nuclear, Plasma & Radiological Engineering, 230A Nuclear Engineering Laboratory,103 South Goodwin Avenue, Urbana, IL 61801-2984, United Statesc University of Illinois at Urbana-Champaign, Department of Nuclear, Plasma & Radiological Engineering, 214 Nuclear Engineering Laboratory,103 South Goodwin Avenue, Urbana, IL 61801-2984, United Statesd University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, 2115 Mechanical Engineering Laboratory,1206 West Green Street, Urbana, IL 61801, United States

a r t i c l e i n f o

Article history:Received 18 April 2008Accepted 26 May 2008

a b s t r a c t

This study examines the bubble detachment phenomena under subcooled nucleate boiling conditions,in order to obtain a better understanding of the bubble dynamics on horizontal flat heat exchangers.Refrigerant R134a is chosen as a simulant fluid due to its merits of having smaller surface tension, reducedlatent heat, and lower boiling temperature than water. Experiments are run with varying experimentalparameters, e.g. pressure, inlet subcooled level, flow rate, etc. Digital images are obtained at frame ratesup to 4000 frames/s, showing the characteristics of bubble movements. Bubble departure and bubble lift-off, which are described as bubbles detaching from the original nucleation sites and bubbles detachingfrom the horizontal heated surface respectively, are both considered and measured. Results are comparedagainst the model proposed by Klausner et al. for the prediction of bubble detachment sizes. While goodoverall agreement is shown, it is suggested that finite rather than zero bubble contact area should be

assumed, which improves the model prediction at the pressure range of 300–500 kPa while playing nosignificant role at a lower pressure of 150 kPa where the model was originally benchmarked. The impact

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of heated surface structur

. Introduction

The mechanism of the bubble detachment process has been ofarticular interest for decades due to its significant contribution tohe flow boiling heat transfer. Investigators have sought to under-tand the forces acting on the vapor bubbles generated from theucleation sites on a heated surface, and to calculate the bubbleetachment sizes from a balance of forces. Chang (1963) devel-ped a predictive model for the vapor bubble departure diameter

n flow boiling, by applying a force balance condition at the instant

hen bubble departure occurs. In this model the buoyancy, the sur-ace tension, and the dynamic forces were considered. Levy (1967)eveloped an equation for bubble departure in vertical upward sub-

∗ Corresponding author. Tel.: +1 858 455 3821; fax: +1 858 455 3586.E-mail addresses: wen.wu@gat.com (W. Wu), pchen5@uiuc.edu (P. Chen),

gjones@uiuc.edu (B.G. Jones), tynewell@uiuc.edu (T.A. Newell).1 Tel.: +1 217 333 2831; fax: +1 217 333 2906.2 Tel.: +1 217 333 3535; fax: +1 217 333 2906.3 Tel.: +1 217 333 1655; fax: +1 217 244 6534.

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029-5493/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.nucengdes.2008.05.013

udied whose results provide support to the above assumption.© 2008 Elsevier B.V. All rights reserved.

ooled flow boiling, by considering the buoyancy, the drag, and theurface tension forces. Koumoutsos et al. (1968) also obtained anquation for bubble lift-off diameter by incorporating the buoy-ncy, the drag, and the surface tension forces. Although bubbleliding was observed by Hsu and Graham (1963) and Koumoutsost al. (1968) in their experiments, it was not included in any ofhe above models. Cooper et al. (1983) examined vertical laminarow by using n-hexane and also observed bubble rolling/slidinglong the heated surface. Therefore, they claimed that the point ofeparture was not well defined. Further, they concluded that theorce balances used by Levy (1967) and Koumoutsos et al. (1968)ere insufficient for modeling their experimental data. Addition-

lly, in the above models, the difference between the advancingnd receding bubble contact angles was not considered but com-ensated by inserting a proportionally constant in computing theurface tension. This approach is not fundamentally sound.

Early models of bubble detachment have had limited success,artially because of the complexity of the problem and a lack ofeliable information to model various force components. Recentpproaches, despite of the difference between each other, haveroduced much better agreement with the experimental data.

2694 W. Wu et al. / Nuclear Engineering and

Nomenclature

cpl liquid specific heat, constant pressure (J/kg K)dw bubble contact diameter (mm)hfg latent heat (J/kg)Ja Jacob numberr bubble radius (mm)Re Reynolds numberU flow velocity at bubble center (m/s)

Greek symbols˛ advancing contact angleˇ receding contact angle� kinematic viscosity (m2 s)� density (kg/m3)� surface tension (N/m)

Subscriptsb bubbleB bulk region, or buoyancyd departureg bubble growthl liquidqs quasi-steady drags surface tensionsat saturated conditionsl shear lift forcesub subcooled condition

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2

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bvrm

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4

v

v vaporw wall

Klausner et al. (1993) examined bubble detachment in horizon-al flow boiling and applied an asymmetric growth force whichs caused by the bubble inclination when bubbles grow. Thispproach required knowledge of the inclination angle as well as thedvancing and receding contact angles. Zeng et al. (1993a, 1993b)implified Klausner’s approach by assuming a zero contact area,hich waived the difficulty of determining the dynamic bubble

ontact angles. This simplified model produced fairly good results,specially when applied to solve for the bubble departure andift-off diameters in saturated flow boiling. Kandlikar and Stumm1995) in their experiments obtained bubble departure data inorizontal, subcooled boiling condition and concluded that Zeng’s1993b) model was able to predict bubble departure diameter forubbles larger than 500 �m. The authors also concluded that con-ucting a similar force balance on the entire bubble might not be aalid approach for smaller diameter bubbles. Van der Geld (2000)xamined the bubble growth force and suggested that it was over-stimated in Zeng et al. (1993b). Finally, Thorncroft et al. (2001)e-examined their model and presented a more rigorous methodf deriving the bubble growth force, etc. An arbitrary constant wasliminated. They compared this improved prediction with variousxperimental results, with fairly good agreement shown.

. Current study

In this study the bubble detachment is investigated with theelp of a high speed digital imaging system. Experiments are

un at 300–500 kPa, which corresponds to a typical bubble sizeanging within 10–100 �m, smaller than the application range sug-ested in Zeng’s (1993b) model. Digital images at frame rates up to000 frames/s are collected and analyzed to provide the bubble sizend the bubble center coordinates. Bubble inclination angle and

bf

Design 238 (2008) 2693–2698

ubble advancing and receding contact angles are also measuredia digital image processing. Some assumptions of Zeng’s model aree-examined and verified with experimental observations. Com-entary on the results is given.

. Experimental facility and setup

.1. Test loop configuration

A test loop in the Air Conditioning and Refrigeration CenterACRC) at the University of Illinois at Urbana-Champaign is utilizedor the experiment. The loop was originally designed and built in989 to determine two-phase heat transfer coefficients for alterna-ive refrigerants (Fig. 1). Modification was made by the author andis colleague, Chen, in 2003 to observe and measure the subcooledoiling heat transfer phenomena.

.2. Test section

The test section is installed in the middle of a 1-m long rect-ngular stainless steel flow channel. A test piece with smooth flateated surface polished by #2000 sand paper with the average par-icle size being 10.3 �m is made for the experiments. Eight type-Khermocouples are installed under the heated surface to measurehe local wall temperatures and the heat flux. These thermocouplesre calibrated using an ice bath reference and are considered validrom 5.0 ◦C to 100.0 ◦C with an uncertainty of ±0.1 ◦C. Surface heatux is reduced from the temperature at the different location in theeated surface whose uncertainty is estimated to be ±5.0%.

The height of the flow channel is adjustable, with the initialeight being set at 12.7 mm. Three plastic windows are installed

n the walls for visualization purposes. The test section is heatedy seven cartridge electric heaters which provide a maximum totalf 5050 W power. The electric power level is controlled by an auto-ransformer and measured using a voltmeter and ammeter in theower circuit. Each heater contains one continuous 76.2-mm longeated section. The heater is coated with an INCOLOY sheath tonhance thermal contact with the transition part and to provideigh temperature performance. Fig. 2 shows the assembly of theest section in details.

. Experimental results

In the sections below, results on the bubble growth rate, theubble contact area, and the dynamic bubble contact angles arerst addressed, which are related to the evaluation of the bubblerowth force and the surface tension force. Results on the bubbleeparture and lift-off radii will follow.

.1. Image calibration

Images of an object with its actual size already measured areaken to calibrate the digital camera before the experiments. Theelative errors of the measurement of bubble radius and bubbleoordinates are estimated to be no more than 4.0% for a typicalubble radius of 50 �m, by assuming a constant error of 0.5 pixelsuring the discretization in imaging process.

.2. Review of the bubble force balance model

Zeng et al. (1993b) evaluated the force balance on horizontal andertical directions to obtain the condition for bubble departure and

ubble lift-off, respectively, and then summarized the equations oforce balance as∑

Fx = Fqs + Fg,b + Fg,x + Fs,x ∼ 0∑Fy = FB + Fs,y + Fsl + Fg,y ∼ 0

(1)

W. Wu et al. / Nuclear Engineering and Design 238 (2008) 2693–2698 2695

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F

F

F

F

F

F

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Fig. 1. Schematic diag

n which Fqs, Fg, Fs, FB, and Fsl stand for quasi-steady drag in theow direction, unsteady drag due to bubble growth, surface tension

orce, buoyancy force, and shear lift force, respectively. To betterllustrate, the expression for each force component is provided here

�qs = 6��l�Ur

⎧⎨⎩2

3+[

12Reb

+ 0.75

(1 + 3.315

Re1/2b

)]−1⎫⎬⎭ (2)

g,b = 2��lr2Ur (3)

g,x = −��lr2(1.64r2 + 0.4rr) (4)

s,x = −1.25dw��(˛ − ˇ)

�2 − (˛ − ˇ)2(sin ˛ + sin ˇ) (5)

s,y = −dw��

(˛ − ˇ)(cos ˇ − cos ˛) (6)

B = 43

�r3(�l − �v)g (7)

4

sF

Fig. 2. Assembly of th

f the refrigerant loop.

sl = 12

U2��lr2� 1/2

⎧⎨⎩[

1.146J(ε)

Re1/2b

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+(

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⎫⎬⎭

1/2

(8)

n which

= ∂U

∂y

r

U, J(ε) ≈

{0.6765{1 + tanh[2.5 log10 ε + 0.191]}×{0.667 + tanh[6(ε − 0.32)]} 0.1 ≤ ε ≤ 202.255 ε > 20

nd

=√

2�

Reb

.3. Bubble growth rate

As is shown in Section 4.2, bubble size and its first- andecond-order derivatives are required information in calculatingg. However, an expression for bubble growth in the flow boundary

e test section.

2696 W. Wu et al. / Nuclear Engineering and Design 238 (2008) 2693–2698

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Table 1Measured bubble growth data

Cb (×103) n ul (m/s) Tsat (◦C)

0.362986 0.36714 0.16 4.640.536315 0.42138 0.16 4.640.430507 0.38879 0.20 4.630.409468 0.37143 0.20 4.630.385656 0.43829 0.20 4.630.318787 0.35918 0.25 4.360000

4

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4

btsuperheat Tw is fixed, the radii are functions of only the mean flowvelocity. Fig. 4 shows the measurement of bubble departure andlift-off radii as functions of mean flow velocity. Measurements aremade at the same condition as the experiments described in Section4.3. For comparison, the model predicted departure radii are also

Fig. 3. Bubble growth rate.

ayer accounting for the nonuniform temperature field is currentlyot available. Therefore, Zuber’s diffusion controlled bubble growthodel (Zuber, 1961) is used for estimating the bubble growth

ates, because the model produces results which agree well withost existing experiments. Additionally, it allows adjustment to its

mpirical constant b to account for various conditions and to fitxperimental data.

In this model, the solution is given as

(t) = 2b√�

Ja√

t (9)

here

a = �lcpl Tsat

�vhfg(10)

Bubble growth rate is measured and compared with Zuber’sodel, as is shown in Fig. 3. The data are measured with pres-

ure at 398.0 kPa and inlet subcooling at 14.81 ◦C with varying flowelocity. The controlled wall superheat varies within a range of.36–4.76 ◦C.

Zuber in his study (Zuber, 1961) suggested b = 1.73 for his model.eng et al. (1993b) also found the best fit with b = 1.73 for theiresults. In our experiments however, b ≈ 1.2 agrees the best withhe data, which deviates from the value of 1.73. In comparing theifference in the experimental conditions and the process of modelevelopment, it is believed that higher subcooling is the major

actor that leads to this deviation. Zuber’s model was originallyeveloped under the assumption of uniformly super-heated liq-id, while in the present studies the flow was subcooled. In Zengt al. (1993b), the inlet subcooling was ∼2 ◦C as was confirmedy the authors, which did not significantly deviate from the sat-ration boiling cases. The results shown in Fig. 3, however, areeasured at Tsub = 14.81 ◦C. Therefore, we believe that the effect

f nonuniform subcooled temperature field plays an important rolend results in lower bubble growth rate.

In referring to Zuber’s model, the experimental growth rates cane approximated by a power law curve fit,

n

(t) = Cbt (11)

here Cb and n are empirical constants as reported in Table 1. Fromhe table it is observed that the growth data fit a power law rangingrom about t1/3 to t1/2. The upper bound of t1/2 is expected since its the limit of bubble growth in diffusion-controlled region.

.854398 0.4989 0.25 4.36

.438389 0.43221 0.25 4.36

.343661 0.35208 0.30 4.76

.300365 0.3184 0.30 4.76

.4. Bubble inclination and bubble/surface contact

The bubble inclination angle, the dynamic bubble contactngles, and the bubble/heated surface contact area are importantarameters in evaluating the bubble forces and assessing the valid-

ty of bubble departure and bubble lift-off prediction. However,hese variables are very difficult to measure, in part due to the lackf resolution at the base of the bubble. Additionally, the model pre-iction of the above physical properties is limited. Therefore, thealues reported here are the averages of multiple measurementsith the upper limit of the uncertainty estimated. The inclination

ngle, the advancing, and the receding contact angles are measuredo be 18◦, 35◦, and 45◦, respectively, by taking the averages of morehan 30 data points for the range of the experiments. These are closeo the average results of 20◦, 36◦, and 45◦ in Klausner et al.’s study.he uncertainty of these angle measurements is estimated to beess than ±10%. The bubble/heated surface contact diameter is esti-

ated to be 8–10 �m, corresponding to 2–4 pixels on the collectedigital images.

.5. Bubble departure and bubble lift-off

From the model proposed by Thorncroft et al. (2001), the vaporubble radius upon departure and lift-off can be computed fromhe measured macroscopic experimental conditions. When the wall

Fig. 4. Bubble departure radius with varying liquid velocity at fixed Tsat.

W. Wu et al. / Nuclear Engineering and Design 238 (2008) 2693–2698 2697

dpo

r

w‘bot

5

ttf(p

iepribtttyaosnbd

Fig. 5. Comparison between predicted and measured departure radii.

isplayed. Very good agreement is achieved between the modelrediction and the experimental results. Following the definitionf relative deviation, r.d., which is given as

.d. = 1N

N∑k=1

|rm,k − rp,k|rp,k

× 100 (12)

here N is the total number of data points, and subscripts ‘m’ andp’ refer to the measured and predicted radius, respectively. It cane found that r.d. = 5.4% and 4.0% for measured departure and lift-ff radii, respectively. Figs. 5 and 6 show the comparison betweenhe predicted and measured data.

. Discussion of the bubble force balance model

In calculating the bubble departure and lift-off radii, it is noticed

hat the relative magnitudes of the force components varies withest liquid and experimental conditions. Fig. 7(a) shows the majororce components at bubble departure provided by Klausner et al.1993). As a comparison, (b) and (c) show the typical force com-onents for different bubble radii on the predicted curve shown

5

se

Fig. 7. Force balance at bubble de

Fig. 6. Comparison between predicted and measured lift-off radii.

n Fig. 5. It is observed that due to different fluids and differentxperimental conditions, the relative magnitudes of the force com-onents are different. When the inlet is highly subcooled whichesults in reduced bubble growth rate, the force balance equations reduced into the case of the quasi-steady drag being balancedy the x-component of surface tension force. Therefore, the surfaceension force, which is contributed by finite bubble/surface con-act area, should not be neglected when high pressure exists. Forhe same reason, at bubble lift-off shown in Fig. 7(d) and (e), the-component of the surface tension force is balanced by the buoy-ncy and the shear lift force, which again requires the assumptionf finite bubble contact area. For bubble sizes less than 100 �m, theurface contact area and therefore the surface tension force shouldot be assumed to be zero, in order to avoid underestimating bub-le detachment sizes. Further analysis of the force balance at bubbleeparture is provided in the next section.

.1. Analysis on bubble force balance at bubble departure

It is noticed in (b) and (c) of Fig. 7 that with different bubbleizes the force components remain the same. The calculation andxplanation is provided below.

parture and bubble lift-off.

2698 W. Wu et al. / Nuclear Engineering and

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Wen Wu was born in Guangdong, PR China. He received a Bachelor of Science degree

Fig. 8. SEM image of heated surface structure.

The expression of the three forces, Fs,x, Fqs, Fg,b, are given by

s,x = −dw��(˛ − ˇ)

�2 − (˛ − ˇ)2(sin ˛ + sin ˇ) (13)

�qs = 6��l�Ur

⎧⎨⎩2

3+[

12Reb

+ 0.75

(1 + 3.315

Re1/2b

)]−1⎫⎬⎭ (14)

g,b = 2��lr2Ur (15)

First, due to the facts that the advancing and receding contactngles, ˛ and ˇ, remain nearly unchanged at high pressures and thathe expression of Fs,x is relatively insensitive to the values of ˛ and, the magnitude of Fs,x is approximately proportional to dw. Basedn the observation that dw is approximately a constant that is notignificantly affected by the size of bubbles, Fs,x becomes a constant.econd, Fqs is not sensitive to Reb so it is approximately proportionalo Ur from its expression, in which U is the flow velocity at the centerf the bubble. Third, in Zurber’s model, r is proportional to t1/2,hich means Fg,b is also proportional to Ur. Therefore, the whole

orce balance is reduced to

r = const. (16)

This result is the approximation of the predicted bubble depar-ure radius shown in Fig. 5. At very low mean flow velocity, theredicted bubble departure radius is larger than the predicted bub-le lift-off radius, which is not physically meaningful. In this case,ubbles directly departure/lift-off from the heated surface so theredicted lift-off radius is also the bubble departure radius.

.2. Analysis on the effect of surface structure

It is also observed in the experiments that the bubble contactiameter dw before bubble departure remains nearly a constantegardless of increasing bubble size, with varying bulk flow veloci-ies and inlet subcoolings. A measurement of dw at high precision isxtremely difficult to obtain due to the local surface finishing andhe fidelity of available imaging instruments. In our experiments,w is estimated to be 8–10 �m from the images of the vapor bub-les on the heated surface. This can be partially confirmed from the

esults of SEM surface structure measurement.

Fig. 8 shows the typical SEM heated surface structure image. Ass mentioned in Section 3.2, the average particle size of the #2000and paper used to polish the heated surface is measured to be0.3 �m. Therefore, typical width of the surface grooves on the

iMRrG

Design 238 (2008) 2693–2698

eated surface is expected to be within 10 �m, as can be observedrom the image. Within the grooves, very few finer structures exist.arlier studies (Jones et al., 1999) have confirmed that there are twoypes of nucleation site candidates, which are pit type and grooveype. In considering that bubbles form on top of the nucleation cav-ties with appropriate sizes and shapes, it is reasonable to suggesthat the size of bubble attachment should be in the same order ofhe magnitude of geometric dimension of the cavity mouths. There-ore, the value of 8–10 �m for dw at bubble departure is confirmedo be in the valid range.

. Conclusion

This paper examined the effect of heated surface structure onhe bubble detachment under SNB conditions. Bubble growth rateas measured with varying experimental conditions and compared

gainst the model prediction, with the effect of subcooled tem-erature field identified. Bubble departure and lift-off radii wereeasured and compared with the existing force balance models,hich suggested the assumption of nonzero bubble/surface contact

rea. The analysis of the force balance at bubble departure con-luded that the product of the bubble departure radius and the flowelocity at bubble center was nearly constant. The above assump-ion and analysis have been confirmed by the SEM measurementsn the heated surface structure, making them good complementso the original bubble force balance model.

cknowledgements

The study is performed in the Air Conditioning and RefrigerationACRC) Center at University of Illinois at Urbana-Champaign. Theroject is sponsored by the U.S. Department of Energy contract DOEEFG07-00ID14601.

eferences

hang, Y.P., 1963. Some possible critical conditions in nucleate boiling. J. Heat Trans-fer 85 (2), 89–100.

ooper, M.G., Mori, K., Stone, C.R., 1983. Behavior of vapor bubbles growing at a wallwith forced flow. Int. J. Heat Mass Transfer 26 (10), 1489–1507.

su, Y.Y., Graham, R.W., 1963, A visual study of two-phase flow in vertical tube withheat addition, NASA TND-1564.

andlikar, S.G., Stumm, B.J., 1995. A control volume approach for investigatingforces on a departing bubble under subcooled flow boiling. J. Heat Transfer 117,990–997.

lausner, J.F., Mei, R., Bernhard, M., Zeng, L.Z., 1993. Vapor bubble departure in forcedconvection boiling. Int. J. Heat Mass Transfer 36, 651–662.

oumoutsos, N., Moissis, R., Spyridonos, A., 1968. A study of bubble departure inforced convection boiling. J. Heat Transfer 90, 223–230.

ones, S.F., Evans, G.M., Galvin, K.P., 1999. Bubble nucleation from gas cavities – areview. Adv. Colloid Interface Sci. 80, 27–50.

evy, S., 1967. Forced convection subcooled boiling prediction of vapor volumetricfraction. Int. J. Heat Mass Transfer 10, 951–965.

horncroft, G.E., Klausner, J.F., Mei, R., 2001. Bubble forces and detachment models.Multiphase Sci. Technol. 13 (3–4), 35–76.

an der Geld, C.W.M., 2000. A note on the bubble growth force. In: Proceedings ofthe Boiling 2000 Conference, Anchorage, Alaska.

eng, L.Z., Klausner, J.F., Bernhard, D.M., Mei, R., 1993a. A unified model for the pre-diction of bubble detachment diameters of boiling systems. I. Pool boiling. Int. J.Heat Mass Transfer 36, 2261–2270.

eng, L.Z., Klausner, J.F., Bernhard, D.M., Mei, R., 1993b. A unified model for the pre-diction of bubble detachment diameters of boiling systems. II. Flow boiling. Int.J. Heat Mass Transfer 36, 2271–2279.

uber, N., 1961. The dynamics of vapor bubbles in nonuniform temperature fields.Int. J. Heat Mass Transfer 2, 83–98.

n engineering physics from Tsinghua University in July 2000. Since August 2000,r. Wu has been a graduate student in the Department of Nuclear, Plasma, and

adiological Engineering at the University of Illinois at Urbana-Champaign. Aftereceiving his Ph.D. degree in May 2007, Mr. Wu continues his research career ineneral Atomics, Inc.