- Email: [email protected]
High power target measurements and finite element calculations for ISL targets
Nuclear Instruments and Methods in Physics Research A 397 (1997)209-220
NUCLEAU INSl’RUMSNTS 8 METMooS IN PWStCS RE%!!H
ELSEVIER
High power target measurements and finite element calculations for ISL targets J-A. Maddi”, M.A. Stoyer
b** , L.F.
Archambau~ta, J.J. Ayersa, J.M. Nitschke”*’
a Lawrence Berkelqv National Laboratog: Berkeley, CA 94720. USA h Laulrence Livermore National Laboratoy. P.O. Box 808, Mail Stop L231. Lioermore, CA 94550. USA
Received 8 May 1997 Abstract
Methods for cooling thick spallation targets (emphasis is on targets for an ISL facility) to uniform temperatures are discussed along with methods for testing targets in a manner that does not require an accelerator facility or result in induced radioactivity. Empirical data is supplemented by computer models using a custom finite element analysis package which allows modeling of combined heat and fluid flow.
1. Introduction
Proper cooling and temperature control of thick spallation targets is critical to the operation of radioactive nuclear beam (RNB) facilities such as the proposed IsoSpin Laboratory (ISL) [l]. An ISL target would be bombarded by approximately 1OQuA of protons at 1 GeV resulting in 50 kW of power being deposited unevenly through the target [2]. A cooling system must not only dissipate this power but also bring the target to operating temperature with little variation in temperature throughout. As diffusion times for nuclei increase with a decrease in target temperature, significant reduction in the production rates of shorter lived nuclei could result if a region of the target is colder than the chosen operating temperature. As much of the interest in an ISL facility is founded upon its ability to produce these shortlived nuclei in relative abundance, cold regions must be minimized. However, regions above the operating temperature would produce undue stresses on the welds reducing the useful life of the target and thereby increasing the quantity of radioactive material which must be disposed of annually by an RNB facility. These regions would also increase the vapor pressure of liquid-core targets consequently resulting in unfavorable conditions for in-line strippers which must deal with the core vapor in addition to the produced nuclei.
*Corresponding author. Tel.: + 1510423 3079; fax: + 1510 422 3160; e-mail: [email protected]. ’ Prepared posthumously.
The cooling system and target must also be simple and compact. The major weaknesses of targets occur at the welds [33. By keeping the number of welds to a minimum, the target’s life will, in general, be extended. Furthermore, in an ISL facility, radiation hazards wili require that used targets are remotely replaced. As current robotic technology is clumsy, the fewer the connections between the target and support equipment, the better. The first few targets we tested used a water jacket to cool the surface of the target. It was found that water was too efficient and excessively cooled the regions with which it was in contact. This resulted in non-uniform thermal expansions tearing the target apart at the welds. In this paper, focus will be on a target cooied with gaseous helium flowing through a manifold integrated into the target. We will consider methods for achieving the aforementioned control over the target temperature as well as methods we have used for empirically and computationally testing designs.
2. Helium cooled target
The current design, a thick helium-cooled target, is shown in Fig. 1. The target is a stainless steel approximately 23 cm long and 3 cm in diameter. Two large axial-channels running the length of the target and 72 narrower circumferential-channels comprise a manifold for the helium, distributing it to and from four pipe connections. A tight-fitting sheath over the target
0168-9002/97/$17.00 Copyright !c! 1997 Elsevier Science B.V. All rights reserved PII SO 168-9002(97)00805-x
210
He
J.A. Maddi et al. I Nucl. Insf~ and Meth. in Phw. Res. .4 397 (1997) 2W
in
Sheath
---’
Fig. I. The current target design. The target is heated using electron bombardment by a filament passing through the central bore. Axial and circumferential channels direct the cooling helium.
encloses the channels to contain the gaseous helium. The spacing and number of the circumferential channels allow control over the flow of the helium to various portions of the target and thus control over the temperature profile. The incident proton beam would enter parallel to the axis. Helium was chosen as a coolant for its high specific heat and its chemical stability. Furthermore, when a proton beam is incident on the target, high-energy protons will scatter from the core into the helium causing spallation. For helium, the daughter nuclei will be hydrogen, deuterium. and tritium, all relatively easily dealt with in comparison to the spallation products of heavier elements which constitute other coolants. Helium’s freezing point exceeds the three spallation products by 16 K, a sufficient difference to purify the coolant by freezingout the hydrogen isotopes and evacuating the still gaseous helium. To heat the target without an accelerator facility, a 30 mil tungsten filament, passed through an axial bore running the length of the target, is heated by an adjustable AC supply to produce thermal electron emission. High voltage (up to 5 kV), applied to the filament, accelerates the electrons to the grounded target body, thereby heating the target. Nine tungstenrhodium thermocouples, evenly spaced along the target’s length, measure the temperature of the surface. Since the helium flows in a thin layer near the surface of the target, there has been some concern over the stresses resulting from the interior thermally expanding within the cold sheath. This could weaken the target’s welds and shorten the useful lifetime. The greatest stress would occur as the target is initially heated by the incident proton beam. The sheath has to be heated by conduction, which would cause its temperature to lag behind that of the core. A possibility for reducing this initial
X0
stress is to turn the core to a slightly smaller diameter than the interior diameter of the sheath. This would allow the core to expand a bit without stressing the colder sheath. Initially, helium would leak into sections that were not cut with channels, but as the interior warms, the core would expand to fit into close contact with the sheath, which will always remain somewhat cooler than the core. Another method is to first thermally expand the sheath by passing heated helium through the manifold and then activating the proton beam. As the proton beam heats and expands the interior. the heating of the helium would be removed and the helium would return to being a coolant. The sheath, already expanded, would not be stressed by the expanding interior. We have tested neither method but present them for those interested.
3. Target test stand A schematic of the helium handling system is shown in Fig. 2 and is divided into three major sections. The first consists of the pump and regulation system for the helium coolant. The helium from the target is brought to approximately room temperature by two water-cooled heat exchangers and then brought up to pressure by a compressor. The flow passes through a valve to control the flow rate and then continues on to the target. A pressure regulator controls helium flow, bypassing the target, so as to provide proper helium flow to the helium compressor independent of the flow through the target. A pressure-regulated helium bottle is used as a reservoir to replace helium lost through leaks at the pipe connections. This helps to provide a constant flow through the target without having to manually weak the flow control valves. The second section consists of the target housing, vacuum pumps, and the helium supply lines for the target. The target is mounted in a bell jar kept at a vacuum of about 10dh Torr by a cryopump. The supports for the target consist of thin molybdenum disks fitted on circumferential grooves on the ends of the target’s sheath. Through these disks are passed the supporting bars. Flexible metal hoses with the bell-jar supply the target with cold helium and vent away the hot helium to be cooled by the heat exchangers. The tungsten filament passing through the axial hole in the target is kept under tension by molybdenum washer springs between the filament clamps and the supports. Multistrand copper cables, bolted to the clamps, supply the AC heating current and the electron bombardment voltage. The mounting of the target and filament are symmetric around the midpoint of the target. Lastly, the electrical supply for heating the filament and providing the high-voltage needed for electron bombardment heating of the target is shown in Fig. 3. The AC for heating the filament is provided by a variable
He
RE:GULAIIClN SCALE-
0
3CCN
I
SCALEcT--$i-_26~0
L - -
TEST _---
WAND
CM
--
Fig. 2. The test setup for the helium-cooled target is divided into three sections: helium pumping and regulation, target mounting and vacuum systems. and electrical systems. The helium handling system is shown in this schematic. The electrical system is shown in Fig. 3.
20 V/50 A supply is coupled to the heating filament through an isolation transformer. The variable high-voltage supply is coupled to the output side of the isolation transformer through two balancing resistors to assure that the current supplied by the high-voltage source to replace the electrons emitted from the filament flows equally from both ends of the filament. This assures the symmetry of the system, The maximum power we have provided to a target with this system has been 10 kW; however, this is not necessarily the limit.
There has been a persistent problem with the heating system. Belying the symmetry of the test setup and the target, the axial temperature profile is not symmetric and shows an overall tilt. Using the hot filament to radiatively heat the target without the high-voltage needed for electron bombardment resulted in a reasonably symmetric profile. This eliminates the thermocouples and cooling system from consideration as the source of the asymmetry and points to the electron bombardment. The asymmetric temperature profile has displayed several
LA. h4addi et al. / Nucl. Insrr. and Meth. in Phvs. Res. .4 397 (3997) 209--2,7ll ,-- Filament
From0 _ IOkV
USER INPUT
ANALYSIS
Balancing resistors
EVALUATE
GEOOUT Fig. 3. The electrical system for heating the target consists of a variable AC supply to heat the filament and a 10 kV variable
supply to produce an accelerating potential between the filament and the target.
7
geometry/ results /
I
T
PostScript
curiosities which will not be mentioned here. Two possible causes for the asymmetry based on the hypothesis that it is an artifact of the electron bombardment have been considered: uneven degradation of the filament and impurities affecting the work Function of the filament material. However, the phenomenon is not understood. A different filament design [4] consisting of a helical filament wound on a ceramic rod might provide benefits over the straight filament discussed above. By varying the spacing of the filament windings, the heating profile could be controlled to produce a distribution similar to that of an incident proton beam instead of the uniform heating from a straight filament. This would allow target designs which have shown promise to be tested with the heating profile they would experience under operation without having to deal with safety and disposal problems associated with subjecting a target to a proton beam. A simple version of this type of filament was briefly tested. Sagging and shorting of the coils to the target was a problem and prevented an analysis of the filament’s capabilities.
4. The DBLFLW program program, Our custom finite element analysis DBLFLW, is a set of three routines which model combined heat and fluid flow through two-dimensional regions. The method for solving the governing differential equations is the Galerkin finite element method [5,6] which reduces the differential equations, geometry, and boundary conditions into a set of necessary conditions in
Fig. 4. The structure of the DBLFLW routines. The information for creating the model is entered into a script file. This is read by the ANALYSIS routine which creates the mesh and assigns boundary conditions. The EVALUATE routine creates the matrix describing the problem and solves for the variables. GEOOUT displays results in PostScript.
the form of linear equations. The Galerkin method attempts to find a solution which, for each element of the mesh, results in zero when the differential equation’s residual is integrated over that element. As we shall see in the next section, the results are reasonable and do not seem to contain any egregious violations of the governing differential equations. The relations between the three routines comprising DBLFLW is shown in Fig. 4. The ANALYSIS routine takes the information supplied by the user and forms the mesh and assigns boundary conditions. The regions are subdivided into a mesh of tr~angufar elements by a semiautomated mesh generator. The interpolating and weighting functions used for the Galerkin method are Lagrangian [63 with three of the nodes at the vertices of the triangles and three at the midpoints of the sides. EVALUATE creates the matrix of linear equations which are solved using the banded Lower-Upper (LU) factorization routines of LINPACK [7] obtained from GAMS [S]. The results are displayed in PostScript by the third routine, GEOOLJT. The fuid flows are calculated by the conservation of mass and are very simplistic, producing only laminar,
J.A. Maddi et al. I Nucl. Instr. and Meth. in Phxv. RCS. A 397 11997) 209-220
inviscid flow. The actual caiculation is performed for a scalar function F which has the property that VF is the mass flow rate per unit area where V = (?,/a.+ + (?/Sy)j. Conservation of mass in an equilibrium state becomes V2F = 0.
(1)
For real flows, the flow rate goes to zero at the interface with a solid. However, the interpolating functions only allow one boundary condition to be specified for any particular region. In order to prevent loss of fluid through the boundaries between solid and fluid regions, the condition that the flow-rate perpendicular to boundaries is zero is used. That prevents the specification that the flow parallel to the boundaries also be zero and results in further inaccuracies in the fluid flows. For the heat flow. the governing differential equation is V.(-/VT
+ c7’VF) = Q.
(2)
where k is the conduction constant of the material(s), c is the specific heat of the fluid(s), Q is the heat production per unit voIume, and F is the flow function that has been solved from Eq. ( 1).The scalars k and c are assumed to be only functions of material and not of temperature or pressure. The terms - kVT and cTVF are the heat flows due to conduction and convection, respectively.
5. Analysis of current target To model the helium manifold with DBLFLW, the pattern of axial and circumferential channels on the surface of the target was entered into DBLFLW as a Bat region as shown schematically in Fig. 5. The actual region is shown in Fig. 6(a) which is an isothermal plot of results obtained by DBLFLW. The results will be considered later. As the target is symmetric around two axis, only one-fourth of the target is modeled. The region entered into DBLFLW consists of two materials. The first is stainless steel and forms those regions which do not have helium flowing over them. The second material is a composite of the characteristics of helium and of stainless steel and forms the regions through which helium flows. This composite is needed instead of pure helium so as to account for the conductivity of the stainless steel below the helium channels. The thermal condtlctivity of the composite is the weighted sum of the conductivity of helium and of stainless steel. The weight for the conductivity for these regions is the percentage of the depth each material occupies in a cross section of the unrolled plate (Fig. 5) through a helium channel. The specific heat of the composite is the same as that for helium as it is only the helium that is flowing in the channels. The heating of the target was modeled by specifying heat generation within the plate. This heat generation occurs in both the pure steel sections and the helium/steel sections.
213
The result from DBLFLW with the helium mass flow rate and electron bombardment power ~uniform heating) set to correspond to the full target specifications of 3 g s- 1 and 5 kW. respectively, is shown in Fig. 6(a) as an isothermal plot. Note that the effects of the fluid flows are calculated by clearly visible. The temperatures DBLFLW at the locations of the nine thermocouples along with empirical results for the target running at the same helium flow rate and bombardment power levels are compared in Fig. 7. Since the DBLFLW output only covers half the length of the target, the temperatures for the second half of the target were obtained by mirroring the first. As the two-dimensional region models the full radial thickness of the target. the values obtained from DBLFLW can be considered to be radial averages of the target temperatures. Comparison between the theoretical and empirical data is difficult as the surface temperatures of the target are bound to be cooler than that of the radial average since the helium flows on the surface and the heat production is in the core. The cross-section mode1 of Fig. 6(b) gives an idea of the radial variations of the temperature. Again the thermal conductions for the various sections are the weighted sums of the thermal conductions of stainless steel and helium except that now the weights are the percentage of the length of the target each occupies. As such, the temperatures shown are roughly lengthwise averages. Furthermore, this models a target where the fluid enters along the full length of one side of the target and not at a few distinct inlets as in the real target. The heat is introduced uniformly into the interior section which is 1.9 cm in diameter. Even though in the test target, the heat is introduced through the wall of the hole, the cross-section temperatures should be nearly identical, In order to get a relation between the radial average and the surface temperature, we will assume a linear relation between the two. A calculation of the average radial temperature, from Fig. 6(b) under the position of the thermocouples gives 299 + 2 C. The associated surface temperature is 220 & 3 f. These two values give us the first point for determining the relationship. The second point comes from the extremum case where there is no heating. In that case the whole target will come to the same temperature as the input helium. Setting this temperature to 20’ C gives a surface temperature of Tsu,r = (200~279)(T~” - 20 C) + 20 C where Ts,,,r and ‘r,,~ are the surface and average temperatures, respectively. A similar relation, T,,,, = (340/279) (T,, - 20 C) + 20-C gives the core temperature. Surface and core temperatures given by the linear fits to the modeled target are included in Fig. 7. it is the surface values that are comparable to the empirical data. Both graphs show the same trends. The heiium cools the region near the inlet very well. However, as the helium flows away from the inlet. along the axial manifold, it warms. This causes the ends and center of the target to be
214
Fig, 5. In order to convert the three-dimensional target profile into a two-dimensional one that DBLFLW can model, one quarter of the symmetric target (a) is ‘unrolled’ to form a plate (b). The light gray is the metal core and the dark gray is the helium. The depth of the plate is chosen so that the cross-sectional area is equal to that of the corresponding cross-section shown in (a), The same is true of the depth of the helium channels.
at a much higher temperature than the temperature near the inlet. This is confirmed during the experiment by the presence of a dull red glow at the center and the output axial channel when the flow rate and power level are set to the levels of Fig. 7. A check of the model is easily performed by noting that all of the heat generated within the target must translate into a temperature increase in
the helium as it is the helium that is carrying away the totality of the heat. The following shows that the temperature change in the helium, which has a specific heat of approximately 5.2 J g-r K-l, needs to be AT=
5 kW 523g-‘K-‘x3gs-’
= 321-C.
(3)
Fig. 6. DBLFLW output for the current tat-get at 5 kW power input and 3 gs _ ’ helium Now. Helium enters at 30 ‘C through the bottom port and out through the top. (a) Model of one-quarter of the target’s surface. The center of the target is the right edge. See Fig. 5. (b) Section of target perpendicular to its axis. For lb). only one-half of the symmetric profile is modeled.
hxlal distance
tcml
Fig. 7. Comparison between the measured axial surface tem~ratures for the current target at 5 kW and 3 gs’- ’ (solid, diamond), the values given by DBLFLW (dash-dot. square), adjusted using the cross-section temperature profile to give the surface temperatures (dashed line, X) and core temperatures (dot line. 0). See text for further explanation.
The DBLFLW output shown in Fig. 6. which gives a helium outlet temperature of 312 * IO’, agrees with the calculation. However, Fig. 6 shows much more cooling at the inlets than is observed empirically. This may be due to the absence of viscosity corrections in Eq. (1) which introduces Aow resistance in the
circumferential channels and may reduce the flow of helium in the channels near the inlets. However, the DBLFLW program definitely gives a qualitatively correct result and, at the center and ends of the target. gives quantitative results of within 50°C of measured temperattires.
216
J.A. Maddi et al. J Nucl. Instr. and Meth. in Phys. Rex A 397 (1997) 209-220
6. Elevated power levels
In the operation of a facility such as the ISL, the target would have to dissipate approximately 50 kW (rough calculation from energy absorption from a proton beam given in Ref. [2]) of heat generated by the beam and would operate at higher temperatures than have so far been discussed. For a liquid-core target, temperatures could run as high as 2OOO’C.Furthermore, most metals have higher thermal conductivities than stainless steel which is about 0.2 W cm-’ Km ’ (this is a rough value based upon the various conduction values for different types of stainless steel as given in Ref. [9]). The higher conductions and greater heat production may significantly affect the temperature profile of a target. Setting the conduction of the metal to 0.5 Wcm-‘K-l, full target heat production to 50 kW (only a quarter of this is introduced into the quarter-section model) and full target helium flow rate to 4.81 g s-l (this value was used so as to require that the helium reach 2000 C to remove the full 50 kW), DBLFLW gives the profile in Fig. 8. There are significant axial and circumferential gradients. The gradients are much reduced from calculations of stainless steel targets at this power level. However, they need to be reduced further. The axial gradient can probably be controlled by varying the spacing and number of circumferential channels. But, no matter how one arranges these channels, it remains that the helium temperature must increase by an amount only dependent upon the mass flow rate of the helium and the quantity of heat the helium must remove. Thus, the temperature difference between the inlets and outlets is fixed by these
two quantities no matter the design of the channels or target. A possible way to reduce the axial gradient is to increase the helium flow. The DBLFLW output of the target manifold and cross section for the same 50 kW power level but with a fourfold increase in fluid flow to 19.2 gs- ’ is shown in Fig. 9. The axial gradient and variation across the section have been significantly reduced from Fig. 8, effectively quartering all target temperatures. However, the increased helium flow introduces two problems. One, the helium may remove too much heat, thereby reducing the temperature of the target and, consequently, increasing the diffusion times for the created nuclei. This can be overcome by externally heating the helium flowing into the target. This will raise the base temperature of the target without changing the axial gradient (assuming no radiation of heat). The second problem occurs with the pressures needed to bring about the elevated flow rates. For 3 gs-‘, the target required the inlet gauge pressure to be about 60 psi. The pressure at the outlet is unknown but is probably less than atmosphere due to the pump. Higher pressures would produce extra stress on the welds of the outer sheath and the welds of inlet and outlet tubes, possibly reducing the effective life of the target. In order to reduce the needed pressures, the circumferential channels could be widened or cut deeper. Investigation of this probability requires advanced fluid-analysis package than a more DWBLFLW and has not been analyzed. If a mass flow were reached, the temperature difference rateoflOOgs_’ between the incoming and outgoing helium would be approximately 100°C for 50 kW of generated heat.
a>
Fig. 8. Tantalum target with the helium flow rate elevated See Fig. 6 for (a) and (b) descriptions.
to 4.8 g s-
’ and heat production
elevated
to 50 kW. Helium enters at 20’ C.
.J.A. ~~ddi et ai. / Nucl. Itrstr. and h&h. in Phys. Rex A 397 (1997) 209--220
217
a)
Fig. 9. ~e~iurn-c(~oled target with helium flow rate elevated to 19.2 gs -’ but with the same SOkW of generated heat. The overall temperature gradient has been to reduce from the 4.8 g s- ’ case shown in Fig. 8. Helium enters at 20 C. See Fig. 6 for (a) and (b) descriptions
The design shown in Fig. 10 is one possibility for a target that could possibly handle such high fluid flows. It is divided into three parts. The lower target-housing forms the helium manifold. The spacing of the helium inlets into the lower housing controls the distribution of the helium and with it the cooling. The target, with a sealing gasket made of a soft metal, sits in the lower housing. The upper housing is lowered over the thin frame holding the target and pressure is applied to assure that the metal gasket around the target frame has sealed. The upper housing provides the support against the pressure needed for the high flow rates, Spikes (not shown) project from the lower housing into the helium channels to break laminar flows that would result in a thin layer of helium on the surface of the target from heating to a temperature in excess of the 100°C. As it does not experience the direct proton beam, the casing will not degrade as quickly as the target and will thus need to be replaced as often. This allows one to build the casing sturdy enough to safely handle the high pressures needed for such a flow rate. The target is left as a simple, easily manufactured design. Using a fit to the LAHET calculations on energy absorption presented in Ref. [2], one can enter the heating profile of a proton beam into DBLFLW. Applying this to a high flow rate target like the one described above, DBLFLW gives the results shown in Fig. 11. The proton beam enters from the left and decays away until it exists the right side. The helium is introduced into evenly spaced sections along the target in propor-
tion to the quantity of heat that each section will generate due to the proton beam. The flow rate per unit area is constant along the inlet to each section, but the areas of the inlets vary to control the fluid flow. The manifolds necessary to produce such a profile of fluid flow would be more complicated than described, but this is a good first approximation that can be easily modeled. The axial temperature variation along the centerline of the model is 8O.C; however, the majority of this variation is just at the entrance of the beam. By recessing this end into the helium flows, the variation should reduce. However, the current model indicates that this design should work if the fluid flows could be adjusted properly, a good possibility. This design, however, requires that the helium enter the target at elevated temperatures, posing problems with the transportation, compression, and purification of the helium. If after passing through the target at, for example 15Oo”C, the helium flowing at 100 g s-l is cooled to 500°C to be compressed, it would require approximately half a megawatt to bring it back to 1500°C. Thus, cooling the helium for processing is not viable and the support system for the helium would have to handle the full temperature. Another problem occurs when working with liquidcore targets. If a target were to fail, releasing the core into the housing, the whole assembly would have lo be replaced. Since the housing pieces are bulky, this results in an increase in disposed material. However, the
J.A. Maddi et al. / Nucl. Instr. and Meth. in Phys. Res. A 397 (1997) 209--220
Upper target housing Soft metal seal
Target Assembly
Fig. 10. Preliminary design for a target manifold to handle high flow rates. See text for description.
Fig. 1I. DBLFLW temperature profile for a high helium flow target. The heat generation is similar to that produced by a proton beam which enters from the left. The heat generation is maximum on the left and decays as the proton beam loses intensity. The arrows indicate the direction in which the helium enters. See text for a further description.
J.A. Audi
et al. cluck. Ins@. and A&h. in Fhys. Res. A 397 (39973 209-220
719
Fig. 12. Exploded view of a target and manifold design which uses alternating helium flows in adjacent channels to reduce the cross-sectional variation in temperature.
contamination would be contained in the housing with some contamination in the helium. An alternative to using high flow rates to control the circumferential temperature variations is to introduce a time average effect. For instance, on the cooled design presented in Fig. I, one could periodically alternate the direction of helium flow. If the period is short enough (in relation to the thermal conductivity of the target), the time variations in temperature do to the alternations would be significant only in a thin layer at the surface of the target. The time average of these variations might be more uniform than for the case where the flow is constant in one direction. The interior would effectively see the surface at a temperature equal to the time average and thus be more circumferentially uniform. However, this process would repeatedly thermally shock those areas in contact with the flow as the flow changes temperature due to the cycling. This could lead to stress failures of the welds. A third design, which uses counter propagating flows, is shown in an exploded view in Fig. 12. The two outside pieces form four axial channels distributing helium to the circumferential channels cut into the central cylinder and covered by a sheath in a manner similar to that shown in
Fig. 1 but without the axial channels. In adjacent channels, the direction of helium flow is opposite. This would produce the same averaging of temperature as above without the thermal shocks. However, additional connections, welds, and material are needed to direct the flows.
7. Conclusion We have discussed several designs for temperature regulation of thick targets for use in radioactive nuclear beam facilities and the testing of these designs. The most recently tested design uses helium following in a manifold cut into the surface of a cylindrical target. Tests have shown that this is a feasible design for control over the axial temperature gradient of the target; however, the helium flow rates necessary to suppress the circumferential gradient may be beyond the structural capabilities of this manifold design. An alternate design has been presented which trades the fine axial temperature control for higher flow rates. Using a combined heat and fluid-flow modeling program, this design has been preliminarily shown to be effective.
220
J.A. Maddi et al. / Nucl. Instr. and Meth. in Phys. Res. A 397 (1997) 209-220
Acknowledgements We would iike to thank Albert Ghiorso for his assistance and contributions to the above work and the Environmental Health and Safety Department at LBNL for providing computing resources. Work supported by the Nuclear Science Division at LBNL and the U.S. Department of Energy under contract No. DE-AC0376SFOOO98. The work at LLNL was performed under the
auspices of the U.S. Department tract No. W-7405-ENG-48.
[3] [4] [S] [6]
of Energy under con-
References [l] The IsoSpin Laboratory: Research Opportunities with Radioactive Nuclear Beams, North American Steering Committee for the IsoSpin Laboratory LALP 91-51. [2] R.J. Donahue et al., Radiation problems in the design of a radioactive nuclear beam facility. Proc. Specialists Meet-
17)
[S]
[9]
ing on Shielding Aspects of Accelerators, Targets and Irradiation Facilities, Arlington, TX, 28-29 April 1994, pp. 323-340. H. Ravn, NACRIST ‘94, Vancouver. BC, K-12 August 1994, private communication. A. Ghiorso. private communication, 1994. J.N. Reddy, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, New York, 1993. J.-C. Sabonnaditre, J.-L. Coulomb, Finite Element methods in CAD: Electrical and Magnetic Fields, Springer, New York, 1987. J.J. Dongarra et al., LINPACK: Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, 1979. CAMS: Guide to Available Mathematical Software. Telnet gams.nist.gov and enter gams or xgams at the login prompt to gain access to this extensive list of mathematical software (including graphics routines). GAMS can E-mail copies of requested public domain software. Fred Rosebury, Handbook of Electron Tube and Vacuum Techniques, Addison-Wesley, Reading, MA, 1965.
NUCLEAU INSl’RUMSNTS 8 METMooS IN PWStCS RE%!!H
ELSEVIER
High power target measurements and finite element calculations for ISL targets J-A. Maddi”, M.A. Stoyer
b** , L.F.
Archambau~ta, J.J. Ayersa, J.M. Nitschke”*’
a Lawrence Berkelqv National Laboratog: Berkeley, CA 94720. USA h Laulrence Livermore National Laboratoy. P.O. Box 808, Mail Stop L231. Lioermore, CA 94550. USA
Received 8 May 1997 Abstract
Methods for cooling thick spallation targets (emphasis is on targets for an ISL facility) to uniform temperatures are discussed along with methods for testing targets in a manner that does not require an accelerator facility or result in induced radioactivity. Empirical data is supplemented by computer models using a custom finite element analysis package which allows modeling of combined heat and fluid flow.
1. Introduction
Proper cooling and temperature control of thick spallation targets is critical to the operation of radioactive nuclear beam (RNB) facilities such as the proposed IsoSpin Laboratory (ISL) [l]. An ISL target would be bombarded by approximately 1OQuA of protons at 1 GeV resulting in 50 kW of power being deposited unevenly through the target [2]. A cooling system must not only dissipate this power but also bring the target to operating temperature with little variation in temperature throughout. As diffusion times for nuclei increase with a decrease in target temperature, significant reduction in the production rates of shorter lived nuclei could result if a region of the target is colder than the chosen operating temperature. As much of the interest in an ISL facility is founded upon its ability to produce these shortlived nuclei in relative abundance, cold regions must be minimized. However, regions above the operating temperature would produce undue stresses on the welds reducing the useful life of the target and thereby increasing the quantity of radioactive material which must be disposed of annually by an RNB facility. These regions would also increase the vapor pressure of liquid-core targets consequently resulting in unfavorable conditions for in-line strippers which must deal with the core vapor in addition to the produced nuclei.
*Corresponding author. Tel.: + 1510423 3079; fax: + 1510 422 3160; e-mail: [email protected]. ’ Prepared posthumously.
The cooling system and target must also be simple and compact. The major weaknesses of targets occur at the welds [33. By keeping the number of welds to a minimum, the target’s life will, in general, be extended. Furthermore, in an ISL facility, radiation hazards wili require that used targets are remotely replaced. As current robotic technology is clumsy, the fewer the connections between the target and support equipment, the better. The first few targets we tested used a water jacket to cool the surface of the target. It was found that water was too efficient and excessively cooled the regions with which it was in contact. This resulted in non-uniform thermal expansions tearing the target apart at the welds. In this paper, focus will be on a target cooied with gaseous helium flowing through a manifold integrated into the target. We will consider methods for achieving the aforementioned control over the target temperature as well as methods we have used for empirically and computationally testing designs.
2. Helium cooled target
The current design, a thick helium-cooled target, is shown in Fig. 1. The target is a stainless steel approximately 23 cm long and 3 cm in diameter. Two large axial-channels running the length of the target and 72 narrower circumferential-channels comprise a manifold for the helium, distributing it to and from four pipe connections. A tight-fitting sheath over the target
0168-9002/97/$17.00 Copyright !c! 1997 Elsevier Science B.V. All rights reserved PII SO 168-9002(97)00805-x
210
He
J.A. Maddi et al. I Nucl. Insf~ and Meth. in Phw. Res. .4 397 (1997) 2W
in
Sheath
---’
Fig. I. The current target design. The target is heated using electron bombardment by a filament passing through the central bore. Axial and circumferential channels direct the cooling helium.
encloses the channels to contain the gaseous helium. The spacing and number of the circumferential channels allow control over the flow of the helium to various portions of the target and thus control over the temperature profile. The incident proton beam would enter parallel to the axis. Helium was chosen as a coolant for its high specific heat and its chemical stability. Furthermore, when a proton beam is incident on the target, high-energy protons will scatter from the core into the helium causing spallation. For helium, the daughter nuclei will be hydrogen, deuterium. and tritium, all relatively easily dealt with in comparison to the spallation products of heavier elements which constitute other coolants. Helium’s freezing point exceeds the three spallation products by 16 K, a sufficient difference to purify the coolant by freezingout the hydrogen isotopes and evacuating the still gaseous helium. To heat the target without an accelerator facility, a 30 mil tungsten filament, passed through an axial bore running the length of the target, is heated by an adjustable AC supply to produce thermal electron emission. High voltage (up to 5 kV), applied to the filament, accelerates the electrons to the grounded target body, thereby heating the target. Nine tungstenrhodium thermocouples, evenly spaced along the target’s length, measure the temperature of the surface. Since the helium flows in a thin layer near the surface of the target, there has been some concern over the stresses resulting from the interior thermally expanding within the cold sheath. This could weaken the target’s welds and shorten the useful lifetime. The greatest stress would occur as the target is initially heated by the incident proton beam. The sheath has to be heated by conduction, which would cause its temperature to lag behind that of the core. A possibility for reducing this initial
X0
stress is to turn the core to a slightly smaller diameter than the interior diameter of the sheath. This would allow the core to expand a bit without stressing the colder sheath. Initially, helium would leak into sections that were not cut with channels, but as the interior warms, the core would expand to fit into close contact with the sheath, which will always remain somewhat cooler than the core. Another method is to first thermally expand the sheath by passing heated helium through the manifold and then activating the proton beam. As the proton beam heats and expands the interior. the heating of the helium would be removed and the helium would return to being a coolant. The sheath, already expanded, would not be stressed by the expanding interior. We have tested neither method but present them for those interested.
3. Target test stand A schematic of the helium handling system is shown in Fig. 2 and is divided into three major sections. The first consists of the pump and regulation system for the helium coolant. The helium from the target is brought to approximately room temperature by two water-cooled heat exchangers and then brought up to pressure by a compressor. The flow passes through a valve to control the flow rate and then continues on to the target. A pressure regulator controls helium flow, bypassing the target, so as to provide proper helium flow to the helium compressor independent of the flow through the target. A pressure-regulated helium bottle is used as a reservoir to replace helium lost through leaks at the pipe connections. This helps to provide a constant flow through the target without having to manually weak the flow control valves. The second section consists of the target housing, vacuum pumps, and the helium supply lines for the target. The target is mounted in a bell jar kept at a vacuum of about 10dh Torr by a cryopump. The supports for the target consist of thin molybdenum disks fitted on circumferential grooves on the ends of the target’s sheath. Through these disks are passed the supporting bars. Flexible metal hoses with the bell-jar supply the target with cold helium and vent away the hot helium to be cooled by the heat exchangers. The tungsten filament passing through the axial hole in the target is kept under tension by molybdenum washer springs between the filament clamps and the supports. Multistrand copper cables, bolted to the clamps, supply the AC heating current and the electron bombardment voltage. The mounting of the target and filament are symmetric around the midpoint of the target. Lastly, the electrical supply for heating the filament and providing the high-voltage needed for electron bombardment heating of the target is shown in Fig. 3. The AC for heating the filament is provided by a variable
He
RE:GULAIIClN SCALE-
0
3CCN
I
SCALEcT--$i-_26~0
L - -
TEST _---
WAND
CM
--
Fig. 2. The test setup for the helium-cooled target is divided into three sections: helium pumping and regulation, target mounting and vacuum systems. and electrical systems. The helium handling system is shown in this schematic. The electrical system is shown in Fig. 3.
20 V/50 A supply is coupled to the heating filament through an isolation transformer. The variable high-voltage supply is coupled to the output side of the isolation transformer through two balancing resistors to assure that the current supplied by the high-voltage source to replace the electrons emitted from the filament flows equally from both ends of the filament. This assures the symmetry of the system, The maximum power we have provided to a target with this system has been 10 kW; however, this is not necessarily the limit.
There has been a persistent problem with the heating system. Belying the symmetry of the test setup and the target, the axial temperature profile is not symmetric and shows an overall tilt. Using the hot filament to radiatively heat the target without the high-voltage needed for electron bombardment resulted in a reasonably symmetric profile. This eliminates the thermocouples and cooling system from consideration as the source of the asymmetry and points to the electron bombardment. The asymmetric temperature profile has displayed several
LA. h4addi et al. / Nucl. Insrr. and Meth. in Phvs. Res. .4 397 (3997) 209--2,7ll ,-- Filament
From0 _ IOkV
USER INPUT
ANALYSIS
Balancing resistors
EVALUATE
GEOOUT Fig. 3. The electrical system for heating the target consists of a variable AC supply to heat the filament and a 10 kV variable
supply to produce an accelerating potential between the filament and the target.
7
geometry/ results /
I
T
PostScript
curiosities which will not be mentioned here. Two possible causes for the asymmetry based on the hypothesis that it is an artifact of the electron bombardment have been considered: uneven degradation of the filament and impurities affecting the work Function of the filament material. However, the phenomenon is not understood. A different filament design [4] consisting of a helical filament wound on a ceramic rod might provide benefits over the straight filament discussed above. By varying the spacing of the filament windings, the heating profile could be controlled to produce a distribution similar to that of an incident proton beam instead of the uniform heating from a straight filament. This would allow target designs which have shown promise to be tested with the heating profile they would experience under operation without having to deal with safety and disposal problems associated with subjecting a target to a proton beam. A simple version of this type of filament was briefly tested. Sagging and shorting of the coils to the target was a problem and prevented an analysis of the filament’s capabilities.
4. The DBLFLW program program, Our custom finite element analysis DBLFLW, is a set of three routines which model combined heat and fluid flow through two-dimensional regions. The method for solving the governing differential equations is the Galerkin finite element method [5,6] which reduces the differential equations, geometry, and boundary conditions into a set of necessary conditions in
Fig. 4. The structure of the DBLFLW routines. The information for creating the model is entered into a script file. This is read by the ANALYSIS routine which creates the mesh and assigns boundary conditions. The EVALUATE routine creates the matrix describing the problem and solves for the variables. GEOOUT displays results in PostScript.
the form of linear equations. The Galerkin method attempts to find a solution which, for each element of the mesh, results in zero when the differential equation’s residual is integrated over that element. As we shall see in the next section, the results are reasonable and do not seem to contain any egregious violations of the governing differential equations. The relations between the three routines comprising DBLFLW is shown in Fig. 4. The ANALYSIS routine takes the information supplied by the user and forms the mesh and assigns boundary conditions. The regions are subdivided into a mesh of tr~angufar elements by a semiautomated mesh generator. The interpolating and weighting functions used for the Galerkin method are Lagrangian [63 with three of the nodes at the vertices of the triangles and three at the midpoints of the sides. EVALUATE creates the matrix of linear equations which are solved using the banded Lower-Upper (LU) factorization routines of LINPACK [7] obtained from GAMS [S]. The results are displayed in PostScript by the third routine, GEOOLJT. The fuid flows are calculated by the conservation of mass and are very simplistic, producing only laminar,
J.A. Maddi et al. I Nucl. Instr. and Meth. in Phxv. RCS. A 397 11997) 209-220
inviscid flow. The actual caiculation is performed for a scalar function F which has the property that VF is the mass flow rate per unit area where V = (?,/a.+ + (?/Sy)j. Conservation of mass in an equilibrium state becomes V2F = 0.
(1)
For real flows, the flow rate goes to zero at the interface with a solid. However, the interpolating functions only allow one boundary condition to be specified for any particular region. In order to prevent loss of fluid through the boundaries between solid and fluid regions, the condition that the flow-rate perpendicular to boundaries is zero is used. That prevents the specification that the flow parallel to the boundaries also be zero and results in further inaccuracies in the fluid flows. For the heat flow. the governing differential equation is V.(-/VT
+ c7’VF) = Q.
(2)
where k is the conduction constant of the material(s), c is the specific heat of the fluid(s), Q is the heat production per unit voIume, and F is the flow function that has been solved from Eq. ( 1).The scalars k and c are assumed to be only functions of material and not of temperature or pressure. The terms - kVT and cTVF are the heat flows due to conduction and convection, respectively.
5. Analysis of current target To model the helium manifold with DBLFLW, the pattern of axial and circumferential channels on the surface of the target was entered into DBLFLW as a Bat region as shown schematically in Fig. 5. The actual region is shown in Fig. 6(a) which is an isothermal plot of results obtained by DBLFLW. The results will be considered later. As the target is symmetric around two axis, only one-fourth of the target is modeled. The region entered into DBLFLW consists of two materials. The first is stainless steel and forms those regions which do not have helium flowing over them. The second material is a composite of the characteristics of helium and of stainless steel and forms the regions through which helium flows. This composite is needed instead of pure helium so as to account for the conductivity of the stainless steel below the helium channels. The thermal condtlctivity of the composite is the weighted sum of the conductivity of helium and of stainless steel. The weight for the conductivity for these regions is the percentage of the depth each material occupies in a cross section of the unrolled plate (Fig. 5) through a helium channel. The specific heat of the composite is the same as that for helium as it is only the helium that is flowing in the channels. The heating of the target was modeled by specifying heat generation within the plate. This heat generation occurs in both the pure steel sections and the helium/steel sections.
213
The result from DBLFLW with the helium mass flow rate and electron bombardment power ~uniform heating) set to correspond to the full target specifications of 3 g s- 1 and 5 kW. respectively, is shown in Fig. 6(a) as an isothermal plot. Note that the effects of the fluid flows are calculated by clearly visible. The temperatures DBLFLW at the locations of the nine thermocouples along with empirical results for the target running at the same helium flow rate and bombardment power levels are compared in Fig. 7. Since the DBLFLW output only covers half the length of the target, the temperatures for the second half of the target were obtained by mirroring the first. As the two-dimensional region models the full radial thickness of the target. the values obtained from DBLFLW can be considered to be radial averages of the target temperatures. Comparison between the theoretical and empirical data is difficult as the surface temperatures of the target are bound to be cooler than that of the radial average since the helium flows on the surface and the heat production is in the core. The cross-section mode1 of Fig. 6(b) gives an idea of the radial variations of the temperature. Again the thermal conductions for the various sections are the weighted sums of the thermal conductions of stainless steel and helium except that now the weights are the percentage of the length of the target each occupies. As such, the temperatures shown are roughly lengthwise averages. Furthermore, this models a target where the fluid enters along the full length of one side of the target and not at a few distinct inlets as in the real target. The heat is introduced uniformly into the interior section which is 1.9 cm in diameter. Even though in the test target, the heat is introduced through the wall of the hole, the cross-section temperatures should be nearly identical, In order to get a relation between the radial average and the surface temperature, we will assume a linear relation between the two. A calculation of the average radial temperature, from Fig. 6(b) under the position of the thermocouples gives 299 + 2 C. The associated surface temperature is 220 & 3 f. These two values give us the first point for determining the relationship. The second point comes from the extremum case where there is no heating. In that case the whole target will come to the same temperature as the input helium. Setting this temperature to 20’ C gives a surface temperature of Tsu,r = (200~279)(T~” - 20 C) + 20 C where Ts,,,r and ‘r,,~ are the surface and average temperatures, respectively. A similar relation, T,,,, = (340/279) (T,, - 20 C) + 20-C gives the core temperature. Surface and core temperatures given by the linear fits to the modeled target are included in Fig. 7. it is the surface values that are comparable to the empirical data. Both graphs show the same trends. The heiium cools the region near the inlet very well. However, as the helium flows away from the inlet. along the axial manifold, it warms. This causes the ends and center of the target to be
214
Fig, 5. In order to convert the three-dimensional target profile into a two-dimensional one that DBLFLW can model, one quarter of the symmetric target (a) is ‘unrolled’ to form a plate (b). The light gray is the metal core and the dark gray is the helium. The depth of the plate is chosen so that the cross-sectional area is equal to that of the corresponding cross-section shown in (a), The same is true of the depth of the helium channels.
at a much higher temperature than the temperature near the inlet. This is confirmed during the experiment by the presence of a dull red glow at the center and the output axial channel when the flow rate and power level are set to the levels of Fig. 7. A check of the model is easily performed by noting that all of the heat generated within the target must translate into a temperature increase in
the helium as it is the helium that is carrying away the totality of the heat. The following shows that the temperature change in the helium, which has a specific heat of approximately 5.2 J g-r K-l, needs to be AT=
5 kW 523g-‘K-‘x3gs-’
= 321-C.
(3)
Fig. 6. DBLFLW output for the current tat-get at 5 kW power input and 3 gs _ ’ helium Now. Helium enters at 30 ‘C through the bottom port and out through the top. (a) Model of one-quarter of the target’s surface. The center of the target is the right edge. See Fig. 5. (b) Section of target perpendicular to its axis. For lb). only one-half of the symmetric profile is modeled.
hxlal distance
tcml
Fig. 7. Comparison between the measured axial surface tem~ratures for the current target at 5 kW and 3 gs’- ’ (solid, diamond), the values given by DBLFLW (dash-dot. square), adjusted using the cross-section temperature profile to give the surface temperatures (dashed line, X) and core temperatures (dot line. 0). See text for further explanation.
The DBLFLW output shown in Fig. 6. which gives a helium outlet temperature of 312 * IO’, agrees with the calculation. However, Fig. 6 shows much more cooling at the inlets than is observed empirically. This may be due to the absence of viscosity corrections in Eq. (1) which introduces Aow resistance in the
circumferential channels and may reduce the flow of helium in the channels near the inlets. However, the DBLFLW program definitely gives a qualitatively correct result and, at the center and ends of the target. gives quantitative results of within 50°C of measured temperattires.
216
J.A. Maddi et al. J Nucl. Instr. and Meth. in Phys. Rex A 397 (1997) 209-220
6. Elevated power levels
In the operation of a facility such as the ISL, the target would have to dissipate approximately 50 kW (rough calculation from energy absorption from a proton beam given in Ref. [2]) of heat generated by the beam and would operate at higher temperatures than have so far been discussed. For a liquid-core target, temperatures could run as high as 2OOO’C.Furthermore, most metals have higher thermal conductivities than stainless steel which is about 0.2 W cm-’ Km ’ (this is a rough value based upon the various conduction values for different types of stainless steel as given in Ref. [9]). The higher conductions and greater heat production may significantly affect the temperature profile of a target. Setting the conduction of the metal to 0.5 Wcm-‘K-l, full target heat production to 50 kW (only a quarter of this is introduced into the quarter-section model) and full target helium flow rate to 4.81 g s-l (this value was used so as to require that the helium reach 2000 C to remove the full 50 kW), DBLFLW gives the profile in Fig. 8. There are significant axial and circumferential gradients. The gradients are much reduced from calculations of stainless steel targets at this power level. However, they need to be reduced further. The axial gradient can probably be controlled by varying the spacing and number of circumferential channels. But, no matter how one arranges these channels, it remains that the helium temperature must increase by an amount only dependent upon the mass flow rate of the helium and the quantity of heat the helium must remove. Thus, the temperature difference between the inlets and outlets is fixed by these
two quantities no matter the design of the channels or target. A possible way to reduce the axial gradient is to increase the helium flow. The DBLFLW output of the target manifold and cross section for the same 50 kW power level but with a fourfold increase in fluid flow to 19.2 gs- ’ is shown in Fig. 9. The axial gradient and variation across the section have been significantly reduced from Fig. 8, effectively quartering all target temperatures. However, the increased helium flow introduces two problems. One, the helium may remove too much heat, thereby reducing the temperature of the target and, consequently, increasing the diffusion times for the created nuclei. This can be overcome by externally heating the helium flowing into the target. This will raise the base temperature of the target without changing the axial gradient (assuming no radiation of heat). The second problem occurs with the pressures needed to bring about the elevated flow rates. For 3 gs-‘, the target required the inlet gauge pressure to be about 60 psi. The pressure at the outlet is unknown but is probably less than atmosphere due to the pump. Higher pressures would produce extra stress on the welds of the outer sheath and the welds of inlet and outlet tubes, possibly reducing the effective life of the target. In order to reduce the needed pressures, the circumferential channels could be widened or cut deeper. Investigation of this probability requires advanced fluid-analysis package than a more DWBLFLW and has not been analyzed. If a mass flow were reached, the temperature difference rateoflOOgs_’ between the incoming and outgoing helium would be approximately 100°C for 50 kW of generated heat.
a>
Fig. 8. Tantalum target with the helium flow rate elevated See Fig. 6 for (a) and (b) descriptions.
to 4.8 g s-
’ and heat production
elevated
to 50 kW. Helium enters at 20’ C.
.J.A. ~~ddi et ai. / Nucl. Itrstr. and h&h. in Phys. Rex A 397 (1997) 209--220
217
a)
Fig. 9. ~e~iurn-c(~oled target with helium flow rate elevated to 19.2 gs -’ but with the same SOkW of generated heat. The overall temperature gradient has been to reduce from the 4.8 g s- ’ case shown in Fig. 8. Helium enters at 20 C. See Fig. 6 for (a) and (b) descriptions
The design shown in Fig. 10 is one possibility for a target that could possibly handle such high fluid flows. It is divided into three parts. The lower target-housing forms the helium manifold. The spacing of the helium inlets into the lower housing controls the distribution of the helium and with it the cooling. The target, with a sealing gasket made of a soft metal, sits in the lower housing. The upper housing is lowered over the thin frame holding the target and pressure is applied to assure that the metal gasket around the target frame has sealed. The upper housing provides the support against the pressure needed for the high flow rates, Spikes (not shown) project from the lower housing into the helium channels to break laminar flows that would result in a thin layer of helium on the surface of the target from heating to a temperature in excess of the 100°C. As it does not experience the direct proton beam, the casing will not degrade as quickly as the target and will thus need to be replaced as often. This allows one to build the casing sturdy enough to safely handle the high pressures needed for such a flow rate. The target is left as a simple, easily manufactured design. Using a fit to the LAHET calculations on energy absorption presented in Ref. [2], one can enter the heating profile of a proton beam into DBLFLW. Applying this to a high flow rate target like the one described above, DBLFLW gives the results shown in Fig. 11. The proton beam enters from the left and decays away until it exists the right side. The helium is introduced into evenly spaced sections along the target in propor-
tion to the quantity of heat that each section will generate due to the proton beam. The flow rate per unit area is constant along the inlet to each section, but the areas of the inlets vary to control the fluid flow. The manifolds necessary to produce such a profile of fluid flow would be more complicated than described, but this is a good first approximation that can be easily modeled. The axial temperature variation along the centerline of the model is 8O.C; however, the majority of this variation is just at the entrance of the beam. By recessing this end into the helium flows, the variation should reduce. However, the current model indicates that this design should work if the fluid flows could be adjusted properly, a good possibility. This design, however, requires that the helium enter the target at elevated temperatures, posing problems with the transportation, compression, and purification of the helium. If after passing through the target at, for example 15Oo”C, the helium flowing at 100 g s-l is cooled to 500°C to be compressed, it would require approximately half a megawatt to bring it back to 1500°C. Thus, cooling the helium for processing is not viable and the support system for the helium would have to handle the full temperature. Another problem occurs when working with liquidcore targets. If a target were to fail, releasing the core into the housing, the whole assembly would have lo be replaced. Since the housing pieces are bulky, this results in an increase in disposed material. However, the
J.A. Maddi et al. / Nucl. Instr. and Meth. in Phys. Res. A 397 (1997) 209--220
Upper target housing Soft metal seal
Target Assembly
Fig. 10. Preliminary design for a target manifold to handle high flow rates. See text for description.
Fig. 1I. DBLFLW temperature profile for a high helium flow target. The heat generation is similar to that produced by a proton beam which enters from the left. The heat generation is maximum on the left and decays as the proton beam loses intensity. The arrows indicate the direction in which the helium enters. See text for a further description.
J.A. Audi
et al. cluck. Ins@. and A&h. in Fhys. Res. A 397 (39973 209-220
719
Fig. 12. Exploded view of a target and manifold design which uses alternating helium flows in adjacent channels to reduce the cross-sectional variation in temperature.
contamination would be contained in the housing with some contamination in the helium. An alternative to using high flow rates to control the circumferential temperature variations is to introduce a time average effect. For instance, on the cooled design presented in Fig. I, one could periodically alternate the direction of helium flow. If the period is short enough (in relation to the thermal conductivity of the target), the time variations in temperature do to the alternations would be significant only in a thin layer at the surface of the target. The time average of these variations might be more uniform than for the case where the flow is constant in one direction. The interior would effectively see the surface at a temperature equal to the time average and thus be more circumferentially uniform. However, this process would repeatedly thermally shock those areas in contact with the flow as the flow changes temperature due to the cycling. This could lead to stress failures of the welds. A third design, which uses counter propagating flows, is shown in an exploded view in Fig. 12. The two outside pieces form four axial channels distributing helium to the circumferential channels cut into the central cylinder and covered by a sheath in a manner similar to that shown in
Fig. 1 but without the axial channels. In adjacent channels, the direction of helium flow is opposite. This would produce the same averaging of temperature as above without the thermal shocks. However, additional connections, welds, and material are needed to direct the flows.
7. Conclusion We have discussed several designs for temperature regulation of thick targets for use in radioactive nuclear beam facilities and the testing of these designs. The most recently tested design uses helium following in a manifold cut into the surface of a cylindrical target. Tests have shown that this is a feasible design for control over the axial temperature gradient of the target; however, the helium flow rates necessary to suppress the circumferential gradient may be beyond the structural capabilities of this manifold design. An alternate design has been presented which trades the fine axial temperature control for higher flow rates. Using a combined heat and fluid-flow modeling program, this design has been preliminarily shown to be effective.
220
J.A. Maddi et al. / Nucl. Instr. and Meth. in Phys. Res. A 397 (1997) 209-220
Acknowledgements We would iike to thank Albert Ghiorso for his assistance and contributions to the above work and the Environmental Health and Safety Department at LBNL for providing computing resources. Work supported by the Nuclear Science Division at LBNL and the U.S. Department of Energy under contract No. DE-AC0376SFOOO98. The work at LLNL was performed under the
auspices of the U.S. Department tract No. W-7405-ENG-48.
[3] [4] [S] [6]
of Energy under con-
References [l] The IsoSpin Laboratory: Research Opportunities with Radioactive Nuclear Beams, North American Steering Committee for the IsoSpin Laboratory LALP 91-51. [2] R.J. Donahue et al., Radiation problems in the design of a radioactive nuclear beam facility. Proc. Specialists Meet-
17)
[S]
[9]
ing on Shielding Aspects of Accelerators, Targets and Irradiation Facilities, Arlington, TX, 28-29 April 1994, pp. 323-340. H. Ravn, NACRIST ‘94, Vancouver. BC, K-12 August 1994, private communication. A. Ghiorso. private communication, 1994. J.N. Reddy, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, New York, 1993. J.-C. Sabonnaditre, J.-L. Coulomb, Finite Element methods in CAD: Electrical and Magnetic Fields, Springer, New York, 1987. J.J. Dongarra et al., LINPACK: Users’ Guide, Society for Industrial and Applied Mathematics, Philadelphia, 1979. CAMS: Guide to Available Mathematical Software. Telnet gams.nist.gov and enter gams or xgams at the login prompt to gain access to this extensive list of mathematical software (including graphics routines). GAMS can E-mail copies of requested public domain software. Fred Rosebury, Handbook of Electron Tube and Vacuum Techniques, Addison-Wesley, Reading, MA, 1965.