# (204v) Analysis of High-Speed Rotating Flow inside Gas Centrifuge Casing

- Conference: AIChE Annual Meeting
- Year: 2017
- Proceeding: 2017 AIChE Annual Meeting
- Group: Engineering Sciences and Fundamentals
- Session:
- Time:
Monday, October 30, 2017 - 3:15pm-4:45pm

**Title: Analysis of high-speed rotating flow inside gas centrifuge casing**

**Author: Dr. Sahadev Pradhan**

**Affiliation: Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012, India**

**ABSTRACT: **

**The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Î©_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (Ï‡), which is derived from the equations of motion in an axisymmetric (r âˆ’ z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.**

**REFERENCES: **

** 1. Avery, D. G. & Davies, E. 1973 Uranium enrichment by gas centrifuge Mills and Boon Ltd. London.**

** 2. Babarsky, R. J. & Wood, H. G. 1990 Approximate eigensolutions for non-axisymmetric rotating compressible flows. Comp. Meth. Appl. Mech. and Engg. 81, 317.**

** 3. Babarsky, R. J. & Herbst, W. I. & Wood, H. G. 2002 A new variational approach to gas flow in a rotating system. Phys. Fluids. 14(10), 3624.**

**4. Bark, F. H. & Bark, T. H. 1976 On vertical boundary layers in a rapidly rotating gas. J. Fluid Mech. 78, 749.**

**5. Berger, M. H. 1987 Finite element analysis of flow in a gas-filled rotating annulus. International Journal for Numerical Methods in Fluids. 7, 215.**

**6. Bird, G. A. 1963 Approach to translational equilibrium in a rigid sphere gas. Phys. Fluids. 6, 1518.**

**7. Bird, G. A. 1981 Monte-Carlo simulation in an engineering context. In S. S. Fischer, editor, Rarefied Gas Dynamics, proceedings of the 12th international symposium - part-1., 239.**

**8. Bird, G. A. 1987 Direct simulation of high-vorticity gas flows. Phys. Fluids. 30, 364. **

**9. Bourn, R. & Peterson, T. D. & Wood, H. G. 1999 Solution of the pancake model for flow in a gas centrifuge by means of a temperature potential. Comp. Meth. Appl. Mech. and Engg. 178, 183.**

**10. Cercignani, C. 2000 Rarefied gas dynamics. From basic concepts to actual calculations. Cambridge University Press.**

**11. Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 2nd edition. Cambridge, Cambridge University Press.**

**12. Kumaran, V. & Pradhan, S. 2014 The generalized Onsager model for a binary gas mixture. J. Fluid Mech. 753, 307.**

**13. Pradhan, S. & Kumaran, V. 2011 The generalized Onsager model for the secondary flow in a high-speed rotating cylinder. J. Fluid Mech. 686, 109.**

**14. Olander, D. R. 1981 The theory of uranium enrichment by the gas centrifuge. Progress in Nuclear Energy. 8, 1.**

**15. Wood, H. G. & Morton, J. B. 1980 Onsagerâ€™s pancake approximation for the fluid dynamics of a gas centrifuge. J. Fluid Mech. 101, 1.**

**16. Wood, H. G. & Sanders, G. 1983 Rotating compressible flows with internal sources and sinks. J. Fluid Mech. 127, 299.**

**17. Wood, H. G. & Jordan, J. A. & Gunzburger, M. D. 1984 The effect of curvature on the flow field in rapidly rotating gas centrifuges. J. Fluid Mech. 140, 373.**

**18. Wood, H. G. & Babarsky, R. J. 1992 Analysis of a rapidly rotating gas in a pie-shaped cylinder. J. Fluid Mech. 239, 249.**

### Checkout

This paper has an Extended Abstract file available; you must purchase the conference proceedings to access it.

#### Do you already own this?

Log In for instructions on accessing this content.

### Pricing

####
**Individuals**

AIChE Members | $150.00 |

AIChE Graduate Student Members | Free |

AIChE Undergraduate Student Members | Free |

Non-Members | $225.00 |