Design of the NSLS infrared beamline mirror number 1

168

Nuclear Instruments and Methods in Physics Research A246 (1986) 168-172 North-Holland, Amsterdam

DESIGN OF THE NSLS INFRARED BEAMLINE MIRROR NUMBER 1 R. A L F O R Q U E ,

P. T A K A C S ,

M. SHLEIFER

a n d J. C O L B E R T

National Synchrotron Light Source, Brookhaven National Laboratory, Upton, New York 11973, USA J. W I L L I A M S Comarco, Inc., 1201 North China Lake Blvd., Ridgecrest, California 93555, USA

The mechanical design of the infrared beamline mirror # 1 (IRBL M1) at the NSLS facility was done with the aid of finite element modeling. Preliminary heat load calculations indicated that the Gaussian peak power density incident on M1 is - 345.8 W / c m 2. The thermal gradient due to the this concentrated high heat density striking M1 may result in undesirable distortions that can seriously impair its function. In addition, the thermal stress might reach l~vels beyond the yield strength of the mirror thereby compromising its structural integrity. Hence, a finite element model was developed to study the associated thermal and structural problem. The generation of the finite element mesh was done with the PREP7 module of ANSYS [1]. After applying the appropriate parameters and boundary conditions, a thermal analysis was performed and the results were passed into the structural model in order to obtain the displacement/stress solution. A similar finite element model was analyzed using SUPERTAB and SUPERB of SDRC's IDEAS [2]. Since the mirror, obviously, needs an active cooling loop, various cooling design schemes were explored during the numerical analysis. In order to avoid further complications during full power operation, it was decided that the mirror be kept as an independenl free body sandwiched in between two chilled blocks. The heat transport process then becomes a function of the characteristics of the interface between the mirror and the chilled blocks. In a previous report [3], the advantage of using a silicon carbide mirror was described chiefly based on the experience of the lasel community. Therefore, using the finite element model that was developed for M1, we compared the performance of silicon carbide and copper mirrors under identical operating conditions. We will present the results of the analysis as well as the final design of the IRBL mirror # 1.

1. Introduction Fig. 1 shows a portion of the infrared b e a m l i n e currently u n d e r construction at the NSLS at Brookhaven N a t i o n a l Laboratory. M o r e details of this beamline are discussed by Williams [4] in his report elsewhere in these proceedings. M i r r o r M1 is the first reflector in the whole system a n d it is subjected to the most intense and hardest X-ray flux from the source. This high thermal loading poses a significant p r o b l e m with regards to the possible structural response of the mirror. Thus, in order to be able to build a satisfactory reflector, the following guidelines [3] were used as the f u n d a m e n t a l basis in the engineering design process of M1 : (a) It must operate in ultrahigh vacuum ( U H V ) at pressures less than 10 9 Torr and must not be a source of v a c u u m contamination. (b) It must resist structural damage from intense X-ray irradiation a n d must stabilize rapidly upon initial exposure. (c) It must be polishable to a supersmooth, lowscatter surface finish and must m a i n t a i n surface figure within acceptable limits under thermal loading a n d ac0 1 6 8 - 9 0 0 2 / 8 6 / $ 0 3 . 5 0 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division)

tive cooling conditions; degradations during its estim a t e d working life should be within a tolerable level. (d) It must be chemically inert and easily cleaned a n d recoated a n d must be commercially available at a reasonable cost. The a b o v e - m e n t i o n e d requirements and loading considerations have p r o m p t e d a careful and closer view of the engineering design of M1. The physical dimensions of this mirror are shown in fig. 2. Two candidate materials were considered, namely copper and silicon carbide, a n d a detailed numerical study was done. In the end, silicon carbide was chosen over copper since it exhibited better overall performance characteristics. We will present in this p a p e r the finite element analysis that was utilized as the basis for the final mechanical design of mirror M1.

2. Finite element model 2.1. Case 1. Two-dimensional model The design plan for this model is shown in fig. 3. Two water cooled chilled blocks are pressed against the

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surfaces of the mirror parallel to the midplane where the beam strikes. Heat is removed by conduction through the mirror and then transported to the chilled blocks through the interface where the mode of heat transfer is nearly convective and is a function of the contact pressure. Since the problem is obviously symmetric, a two-dimensional thermal model was utilized to study the situation with the use of ANSYS [1], a general purpose

finite element code. The finite element mesh with 2-D isoparametric thermal elements and the corresponding loads and boundary conditions are shown in fig. 4. The width of the elements near the point of thermal load application were made narrow enough in order to achieve a better approximation. The incident X-ray radiation has a very nearly Gaussian shape with a peak power density of approximately 345.8 W / ( c m 2 A). The rectangular approximation of the Gaussian power distribution gives the width of the beam to be ~- 1.31 mm whereas the smallest element in fig. 3 is 0.669 mm wide. The total integrated power over the full vertical width of the beam is 37.922 W / ( c m A), or 328.6 B T U / ( h in. H A). The concentration of this power is about the Gaussian peak, thus without sacrificing accuracy, the nodal heat loads as shown in fig. 4 were calculated by interpolation from the Gaussian power density distribution. Two studies, differing only in the applied boundary conditions, were made using this two-dimensional model. The first one assumed that the temperature of the mirror surface that is pressed against the watercooled copper chilled blocks is 158°F. This presupposes a 90°F temperature differential on the interface, with the chilled blocks maintained at room temperature. This

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Fig. 4. differential is a good first approximation since with a good contact pressure the temperature difference between the surfaces can be decreased. The second study was a little bit more realistic. A convective film coefficient of 1.72 B T U / ( h in. 2 °F) was imposed over the interface. This coefficient corresponds to a contact pressure of approximately 30 psi. In both cases, after the temperature distribution over the whole model was obtained, the mesh was converted into a structural model and a stress/deflection analysis was performed. For each thermal run, two structural studies were made with the following boundary conditions: (1) fixed ends, and (2) free ends. A similar analysis was done using the I D E A S [2] package. The elements in the I D E A S model, however, were not exactly the same as the elements in the ANSYS model but the boundary conditions were. The results of both analysis were very close, thus reinforcing the validity of the technique.

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2.2. Case 2. Three-dimensional model

In this particular case, the chilled blocks are pressed against the mirror surfaces normal to the midplane as shown in fig. 3. As a result of this design plan, the heat transfer problem becomes essentially a three-dimensional one. Therefore, a 3-D finite element mesh was developed with ANSYS. This model is shown in fig. 6. The total load here is equivalent to that of case 1, thus p = 328.6 × ( 2 . 5 / 4 ) = 205.4 B T U / ( h A), since the horizontal length of the beam is approximately 2.5 in. and the model was only a quarter of the whole mirror. This total heat load was equitably applied to 18 nodal points. The constant temperature boundary condition was not used but instead only the convective mode of heat transfer was imposed on the interface between the mirror and the chilled blocks. As in case 1, a convective

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film coefficient, h = 1.72 B T U / ( h in. 2 °F), was applied over this interface. The succeeding steps that follow after generating the mesh are the same as in case 1.

3. R e s u l t s

The results of the steady-state thermal analysis of case 1 are s u m m a r i z e d in table 1. It can be seen that due to its poorer conductive property, the SiC mirror will a t t a i n higher temperatures t h a n the copper mirror. Tmax is the m a x i m u m n o d a l t e m p e r a t u r e for each particular run, a n d obviously it occurs at the node where the highest heat load was applied, i.e. n o d e 1 in fig. 4. T a b l e 2 summarizes the result of a linear static analysis of the

structural model using the t e m p e r a t u r e distribution obtained from the t h e r m a l run. T h e relative displacement as shown in the table is the difference between the m a x i m u m a n d m i n i m u m y-axis deformation, Uy. F o r b o t h fixed a n d free ends, the SiC mirror showed m u c h smaller deformations, hence it is more favorable over copper because it will cause less distortion. Fig. 5 shows a typical c o n t o u r plot of the t e m p e r a t u r e distribution within the model. Since the advantage of the SiC was obvious from the numerical study of case 1, we decided to r u n case 2 only for a silicon carbide mirror. The thermal r u n indicated that the m a x i m u m n o d a l t e m p e r a t u r e will be 240°F. In c o m p a r i s o n to 300°F (table 1) from case 1, the advantage of side cooling is obvious. Furthermore, the

Table 1 Case 1: Top/bottom cooling (thermal analysis) Material

Copper SiC

Material Properties E ( X 106 psi)

a ( X 10 6/°F)

K (BTU/(h in. °F))

16.9 58.9

9.80 1.48

18.667 6.050

Tmax(OF) a)

Tmax(OF) b)

194 269

225 300

a) Boundary condition: T=158°F. b) Boundary condition: h,= 1.72. II(a). INTEGRATED BEAM LINES

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Table 2 Case 1: Top/bottom cooling (structural analysis) Material

Copper SiC

Boundary condition: Boundary condition: T=158°F h =1.72 Rel. Disp. (×10 4 in.) Rel. Disp. ( x l 0 4 in.) Fixed

Free

Fixed

Free

5.72 0.124

1.45 0.68

7.33 1.48

1.45 0.68

a n d the mirror should be at least 30 psi, or preferably higher. Finally, mirror M1 was designed using the aforementioned guidelines. This work was performed under the auspices of the U.S. D e p a r t m e n t of Energy, u n d e r contract DE-AC0276CH00016.

References

relative displacement that could cause distortion is only 0.35 × 10 -4 in.

4. Conclusion Based on the above results, it was r e c o m m e n d e d that I R B L M1 should be made of silicon carbide with side cooling. The contact pressure between the chilled blocks

[1] ANSYS, A general purpose finite element code from Swanson Analysis Systems, Inc., Houston, Pennsylvania. [2] IDEAS, Integrated Design and Engineering Analysis System from Structural Dynamics Research Corporation, Milford, Ohio. [3] P.Z. Takacs et al., Third National Conf. on Synchrotron Radiation Instrumentation, Brookhaven National Laboratory (1983). [4] G.P Williams, P.Z. Takacs, R.W. Klaffky and M. Shleifer, these Proceedings (Synchrotron Radiation Instrumentation, Stanford, 1985) Nucl. Instr. and Meth. A246 (1986) 165.