Analytical solution for the multidimensional degradation of a packed bed thermocline
A multidimensional, time-dependent model of the thermocline degradation in a packed bed thermal storage tank is presented. In earlier reports a one-dimensional model, incorporating the effects of heat losses out the ends of the tank, was solved analytically using both separation of variables and transform methods. The multidimensional analysis presented here includes the additional effects of heat losses out of the sides of the tank for the types of boundary conditions of greatest interest, and is thus a more realistic model of the problem. The technique used to solve the coupled pair of partial differential equations describing the degradation of the thermocline is based on a vectorized separation of variables approach. Assuming cylindrical geometry, the analysis leads to separate eigenvalue problems for the radial, angular, and axial spatial dependencies of the fluid and solid temperatures in the bed. The eigenvalues are readily calculated and the corresponding eigenfunctions are shown to form a complete set of spatial basis functions for the solution space. The applicability of the method is illustrated by an example and important conclusions are drawn from the results.
- Research Organization:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 5128218
- Report Number(s):
- SAND77-8512
- Country of Publication:
- United States
- Language:
- English
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Anharmonic analysis of a time-dependent packed bed thermocline
Anharmonic analysis of a time-dependent packed bed thermocline
Related Subjects
25 ENERGY STORAGE
PACKED BED
SENSIBLE HEAT STORAGE
TEMPERATURE GRADIENTS
THERMAL ENERGY STORAGE EQUIPMENT
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
EIGENVALUES
FLUID FLOW
GEOMETRY
HEAT LOSSES
MATHEMATICAL MODELS
TANKS
TIME DEPENDENCE
CONTAINERS
ENERGY LOSSES
ENERGY STORAGE
EQUIPMENT
HEAT STORAGE
MATHEMATICS
STORAGE
CSP
Concentrating Solar Power
142000* - Solar Energy- Heat Storage- (1980-)
250600 - Energy Storage- Thermal