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VENECIA
SOFTWARE PACKAGE FOR THERMAL HYDRAULIC ANALYSIS
OF
FORCED FLOW COOLED SUPERCONDUCTING EQUIPMENT
AND THEIR PRIMARY CRYOGENIC SUBSYSTEMS
NUMERICAL SOLUTION
For computations, the analysis equations (1)-(3), (8), (9) were re-written in the non-conservative form using pressure P, enthalpy H and velocity V as flow variables. The Gruneisen parameter f and
isentropic speed of sound c were introduced in the equations [1]. Using the basic thermodynamic identity
the equations (1)-(3) are transformed to the form
where
Equations (8) and (9) are re-written as
So, the time derivatives for different helium parameters are separated and assigned in explicit form.
All equations related to channels and conductors are represented via finite differences with respect to the space variable x using the following approximation for the first and second order derivatives in a mesh node "i"
where h is a step of uniform spatial discretization. A special attention is paid to approximation of derivatives in the boundary nodes. In VENECIA, this approximation is significantly improved and allows provide stable calculation for very fast process at the boundaries (explosion of pipe etc.). As a result of such discretization procedure, the initial system of three partial differential equations for the P-H-V channel parameters is transformed into 3N ordinary differential equations for the parameters in the mesh nodes with respect to time.
The number of steps (nodes) on the space variable x is arbitrary and individual for each channel. For the channels coupled by heat and mass transfer in the longitudinal direction the number of nodes should be identical.
where t is the time step for integration.
The numerical method for solving equation (14) is based on a semi-explicit spliting-up method for parabolic partial differential equations [3].
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Germany (headquarters): Alphysica GmbH. Unterreut, 6, D-76135, Karlsruhe, Germany,
Phone: +49 (0)163 904-85-61,
Fax: +49 (0)7219 444-26-55, E-mail: info@alphysica.com
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USA: Alphysica Inc., Harvard Square, One Miffin Place, Cambridge, MA 02138, USA,
Phone/Fax: +1 (617) 715-1978, E-mail:usa@alphysica.com
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China: Alphysica Ltd. 1 Jianguomenwai Avenue
Beijing, 100004, China,
Phone/Fax: +86 10 5737 2626 E-mail:china@alphysica.com
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Russia: Alphysica Ltd. 55, Nevsky pr., 191025, St.Petersburg, Russia,
Phone/Fax: +7 (812) 335-95-04, E-mail: russia@alphysica.com
Copyright © 1994-2011
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