Extending the allowable exposure time of rotating X-ray anodes via an embedded lithium pulsating heat pipe: A 3D multiphase analysis

Amini, Mohsen; Sarhaddi, Faramarz; Azarkish, Hassan

doi:10.22104/jpst.2026.8247.1291

Extending the allowable exposure time of rotating X-ray anodes via an embedded lithium pulsating heat pipe: A 3D multiphase analysis

Articles in Press

Document Type : Research Article

Authors

Mohsen Amini

Faramarz Sarhaddi

Hassan Azarkish

Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran

10.22104/jpst.2026.8247.1291

Abstract

Thermal management of high-power X-ray rotating anodes is strictly constrained by the intense, localized heat fluxes generated during brief exposure times. This study proposes the integration of a lithium-based rotating pulsating heat pipe (RPHP) into the anode and investigates its transient thermal-hydraulic performance using a volume of fluid (VOF) multiphase model, which is heavily influenced by both extreme centrifugal forces and the intense heat flux applied during the exposure time. The results reveal a fundamental thermodynamic trade-off governing the optimal rotational speed: while higher rotational speeds enhance internal fluid circulation as well as latent and sensible heat transport, they simultaneously generate massive hydrostatic pressures that cause a significant transient delay in the phase-change (boiling) process. Consequently, the maximum allowable exposure time exhibits a non-monotonic dependence on the rotational speed. A case study based on the RAD-14 X-ray tube was investigated with a heat input of 20 kW on a minimum focal spot size (0.3 mm). A critical temperature limit of 2200 K was defined to evaluate and compare the allowable exposure times across different configurations. Compared to a conventional solid anode (which is limited to an exposure time of 0.436 s), the RPHP integration at 8500 rpm achieves optimal thermal performance, extending the allowable exposure time to 0.706 s (a 62 % increment). However, further increasing the speed to 10000 rpm exacerbates the pressure-induced boiling retardation, leading to an exposure time of 0.619 s (a 42 % increment relative to the solid base, but a 12 % reduction compared to the 8500 rpm peak).

Graphical Abstract

Extending the allowable exposure time of rotating X-ray anodes via an embedded lithium pulsating heat pipe: A 3D multiphase analysis

Highlights

Novel application of a pulsating heat pipe for rotating anode X-ray tube cooling.
Extended X-ray exposure times and improved tube rating charts.
Precise VOF modeling of pressure-dependent phase change at extreme speeds.
Predicting nucleation delay from high centrifugal pressure at 10000 rpm.

Keywords

Rotating anode X-ray tube

Rotating pulsating heat pipe (RPHP)

Volume of fluid (VOF)

Thermal management

Subjects

Modelling and Simulation

[1] Lee, S. M. (2015). Thermal Characteristics of Rotating Anode X-Ray Tube with Emissivity in Aging Process for Digital Radiography. Applied Science and Convergence Technology, 24(5), 125-131. https://doi.org/10.5757/ASCT.2015.24.5.125

[2] Bushong, S. C. (2012). Radiologic Science for Technologists: Physics, Biology, and Protection. (10^th ed.). Mosby Elsevier.

[3] Lee, S. M. (2015). Compact Anode Design with the Heat Capacity Performance in Rotating Anode X-Ray Tube for Digital Radiography. Applied Science and Convergence Technology, 24(5), 136-141. http://dx.doi.org/10.5757/ASCT.2015.24.5.136

[4] Li, X., Wang, X., Li, Y., & Liu, Y. (2020). Production and Heat Properties of an X-Ray Reflective Anode Based on a Diamond Heat Buffer Layer. Materials, 13(1), 241. https://doi.org/10.3390/ma13010241

[5] Taubin, M. L., Yaskolko, A. A., & Chesnokov, D. A. (2018). Thermal Analysis of the Focal Spot of Anodes of Powerful X-Ray Tubes. Biomedical Engineering, 51, 328-331. https://doi.org/10.1007/s10527-018-9741-z

[6] Kumar, R., Ratnala, S. R., B, V. K. G., & Gouda, P. S. S. (2018). Thermal Analysis on X-Ray Tube for Exhaust Process. IOP Conference Series: Materials Science and Engineering, 310, 012162. https://doi.org/10.1088/1757-899X/310/1/012162

[7] Pajovic, S., Roques-Carmes, C., Choi, S., Kooi, S. E., Gupta, R., Zalis, M. E., Čelanović, I., & Soljačić, M. (2025). Nanophotonic Thermal Management in X-Ray Tubes. ACS Nano, 19(35), 31363-31370. https://doi.org/10.1021/acsnano.5c05186

[8] Wang, Y., Jiang, S., Shi, S., & Yu, Y. (2025). Optimization Design of Heat Dissipation Structure for Rotating Anode CT Tube Based on Simulation Analysis. Proceedings of the 2025 5^th International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC `25), 165-175. https://doi.org/10.1145/3745533.3745561

[9] Wang, Y., Jiang, S., & Shi, S. (2024). Thermal Analysis on 3.5 MHU Rotating Anode X-Ray. 2024 7^th International Conference on Mechatronics, Computer Technology and Engineering (MCTE), Guangzhou, China, pp. 1334-1338. https://doi.org/10.1109/MCTE62870.2024.11778585

[10] Akachi, H., Structure of a Heat Pipe, US Patent No. 4921041 (issued May 1, 1990).

[11] Zhang, Y., & Faghri, A. (2002). Heat Transfer in a Pulsating Heat Pipe with Open End. International Journal of Heat and Mass Transfer, 45(4), 755-764. https://doi.org/10.1016/S0017-9310(01)00203-4

[12] Khandekar, S., Dollinger, N., & Groll, M. (2003). Understanding Operational Regimes of Closed Loop Pulsating Heat Pipes: An Experimental Study. Applied Thermal Engineering, 23(6), 707-719. https://doi.org/10.1016/S1359-4311(02)00237-5

[13] Khandekar, S., Charoensawan, P., Groll, M., & Terdtoon, P. (2003). Closed Loop Pulsating Heat Pipes Part B: Visualization and Semi-Empirical Modeling. Applied Thermal Engineering, 23(16), 2021-2033. https://doi.org/10.1016/S1359-4311(03)00168-6

[14] Kwon, G. H., & Kim, S. J. (2014). Operational Characteristics of Pulsating Heat Pipes with a Dual-Diameter Tube. International Journal of Heat and Mass Transfer, 75, 184-195. https://doi.org/10.1016/j.ijheatmasstransfer.2014.03.032

[15] Ebrahimi, M., Shafii, M. B., & Bijarchi, M. A. (2015). Experimental Investigation on the Thermal Management of Flat-Plate Closed-Loop Pulsating Heat Pipes with Interconnecting Channels. Applied Thermal Engineering, 90, 838-847. https://doi.org/10.1016/j.applthermaleng.2015.07.040

[16] Kwon, G. H., & Kim, S. J. (2015). Experimental Investigation on the Thermal Performance of a Micro Pulsating Heat Pipe with a Dual-Diameter Channel. International Journal of Heat and Mass Transfer, 89, 817-828. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.091

[17] Wang, J., Ma, H., Zhu, Q., Dong, Y., & Yue, K. (2016). Numerical and experimental investigation of pulsating heat pipes with corrugated configuration. Applied Thermal Engineering, 102, 158-166. https://doi.org/10.1016/j.applthermaleng.2016.03.163

[18] Frey, Y., Dörr, A., & Lorenz, M. (2023). Experimental Investigation of Pulsating Heat Pipes with Different Evaporator Roughness Values. Applied Thermal Engineering, 233, 120999. https://doi.org/10.1016/j.applthermaleng.2023.120999

[19] Yu, R. Li., Wang, X. Y., Jiao, D. S., Qi, R. D., Wang, Z. H., Li, Z. L., Zhu Q. R., & Xia, L. Z. (2025). Effect of Improving the Performance of Pulsating Heat Pipes on Heat Transfer in an Extruder. Experimental and Computational Multiphase Flow, 7, 537-550. https://doi.org/10.1007/s42757-024-0211-4

[20] Hong, Y., Kang, Z., & Fan, J. (2025). Heat Transfer Enhancement of Pulsating Heat Pipes with Novel Structures. Applied Thermal Engineering, 268, 125720. https://doi.org/10.1016/j.applthermaleng.2025.125720

[21] Moayad, N. A., & Sarsam, W. S. (2026). Thermal Performance of a Pulsating Heat Pipe Heat Exchanger for Energy Recovery in Air Conditioning Systems in a High Ambient Temperature Country. Journal of Engineering and Applied Science, 73, 47. https://doi.org/10.1186/s44147-026-00897-9

[22] Aboutalebi, M., Moghaddam, A. M. N., Mohammadi, N., & Shafii, M. B. (2013). Experimental Investigation on Performance of a Rotating Closed Loop Pulsating Heat Pipe. International Communications in Heat and Mass Transfer, 45, 137-145. https://doi.org/10.1016/j.icheatmasstransfer.2013.04.008

[23] Kammuang-lue, N., Phommavongsa, D., On-ai, K., Sakulchangsatjatai, P., & Terdtoon, P. (2016). Thermal Resistance of a Rotating Closed-Loop Pulsating Heat Pipe: Effect of Centrifugal Accelerations. Applied Mechanics and Materials, 851, 292-298. https://doi.org/10.4028/www.scientific.net/AMM.851.292

[24] Qian, N., Fu, Y., Zhang, Y., Chen, J., & Xu, J. (2019). Experimental investigation of thermal performance of the oscillating heat pipe for the grinding wheel. International Journal of Heat and Mass Transfer, 136, 904-915. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.065

[25] Ebrahimi Dehshali, M., Nazari, M. A., & Shafii, M. B. (2018). Thermal Performance of Rotating Closed-Loop Pulsating Heat Pipes: Experimental Investigation and Semi-Empirical Correlation. International Journal of Thermal Sciences, 123, 14-26. https://doi.org/10.1016/j.ijthermalsci.2017.09.009

[26] Gao, Y., Xu, Z., Zhai, E., Liang, K., Zhao, R., Li, H., Wang, L., Liu, S., & Li, X. (2023). Cooling Pitch Cabinets in Wind Turbines Using a Pulsating Heat Pipe: A Case Study. Case Studies in Thermal Engineering, 50, 103461. https://doi.org/10.1016/j.csite.2023.103461

[27] Behling, R., Hulme, C., Tolias, P., & Danielsson, M. (2025). The Impact of Tube Voltage on the Erosion of Rotating X-Ray Anodes. Medical Physics, 52(2), 814825. https://doi.org/10.1002/mp.17528

[28] Siller, M., Gamerdinger, M., Evers, T., Schatte, J., Gerzoskovitz, S., Olschok, S., Reisgen, U., & Mark, M. (2026). Focal Track Wear of Rotating Anodes: Revealing the Interaction of the Microstructure, Surface Degradation, and Resulting Changes in X-Ray Emission. International Journal of Refractory Metals and Hard Materials, 139, 107854. https://doi.org/10.2139/ssrn.5928858

[29] Suresh, J. V., & Bhramara, P. (2018). CFD Analysis of Copper Closed Loop Pulsating Heat Pipe. Materials Today: Proceedings, 5(2), 5487-5495. https://doi.org/10.1016/j.matpr.2017.12.138

[30] Wang, S. F., Lin, Z. R., Lee, Z. Y., & Zhang, L. W. (2012). Numerical Simulation on Flow and Heat Transfer in Oscillating Heat Pipes. Frontiers in Heat Pipes, 3(1), 013002. https://doi.org/10.5098/fhp.v3.1.3002

[31] Wang, J., Wang, Z., & Li, M. (2014). Thermal Performance of Pulsating Heat Pipes with Different Heating Patterns. Applied Thermal Engineering, 64(1-2), 209-212. https://doi.org/10.1016/j.applthermaleng.2013.12.004

[32] Suresh, J. V., & Bhramara, P. (2017). CFD Analysis of Multi Turn Pulsating Heat Pipe. Materials Today: Proceedings, 4(2), 2701-2710. https://doi.org/10.1016/j.matpr.2017.02.146

[33] Pouryoussefi, S. M., & Zhang, Y. (2017). Analysis of Chaotic Flow in a 2D Multi-Turn Closed-Loop Pulsating Heat Pipe. Applied Thermal Engineering, 126, 1069-1076. https://doi.org/10.1016/j.applthermaleng.2017.01.097

[34] Lin, Y. H., Kang, S. W., & Wu, T. Y. (2009). Fabrication of Polydimethylsiloxane (PDMS) Pulsating Heat Pipe. Applied Thermal Engineering, 29(2-3), 573-580. https://doi.org/10.1016/j.applthermaleng.2008.03.028

[35] Varian Medical Systems. RAD-14 X-Ray Tube (Rev. M). https://www.yumpu.com/fr/document/read/4465693/rad-14-rev-m-varian (Access June 2024)

[36] ANSYS Inc. (2024). ANSYS Fluent Theory Guide (Release 2024 R2). ANSYS Inc. http://ansyshelp.ansys.com/public/account/secured? (Access May 2026)

[37] Lee, W. H. (1979). A Pressure Iteration Scheme for Two-Phase Modeling (Technical Report LA-UR-79-975). Los Alamos Scientific Laboratory. https://codethatflows.wordpress.com/wp-content/uploads/2021/08/406441216-lee-model-pdf-1.pdf (Access May 2026)

[38] Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A Continuum Method for Modeling Surface Tension. Journal of Computational Physics, 100(2), 335-354. https://doi.org/10.1016/0021-9991(92)90240-Y

[39] Chen, G., Nie, T., & Yan, X. (2020). An Explicit Expression of the Empirical Factor in a Widely Used Phase Change Model. International Journal of Heat and Mass Transfer, 150, 119279. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119279

[40] Liu, H., Tang, J., Sun, L., Mo, Z. Y., & Xie, G. (2020). An Assessment and Analysis of Phase Change Models for the Simulation of Vapor Bubble Condensation. International Journal of Heat and Mass Transfer, 157, 119924. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119924

[41] Ma, H. (2015). Oscillating Heat Pipes (1^st ed.) Springer New York. https://doi.org/10.1007/978-1-4939-2504-9

[42] Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2006). Fundamentals of Heat and Mass Transfer (6^th ed.). John Wiley & Sons.

[43] Wieland Duro. TZM Technical Data Sheet. https://www.wieland.com/fr/content/download/12678/file/TZM_EX_EN.pdf (Access May 2026)

[44] Park, Y. H., Tanshen, M. R., Nine, M. J., Chung, H. S., & Jeong, H. M. (2012). Characterizing Pressure Fluctuation into Single-Loop Oscillating Heat Pipe. Journal of Central South University, 19, 2578-2583. https://doi.org/10.1007/s11771-012-1313-x