Anharmonic analysis of a time-dependent packed bed thermocline
The problem of thermocline degradation in a packed bed thermal storage tank, important to the proposed central solar receiver power plants, is considered. In an earlier report (SAND77-8032), the mathematical model, which incorporates the effects of heat losses out the ends of the tank, was solved analytically using a transform technique. Although that method is applicable for completely general boundary conditions, the actual application to any particular example is usually tedious and is thus primarily valuable for the illustration of the types of phenomena which are described by the model. In the present work, a much more user-oriented method is used to solve the problem for the types of boundary conditions of greatest interest. In particular, a vectorized separation of variables approach is applied to the coupled pair of parabolic partial differential equations describing the degradation of the thermocline. The time-dependent, one-dimensional model includes the effects of finite tank length, thermal conduction in the direction parallel to the tank walls, and heat transfer between the fluid and solid components of the bed. For certain classes of boundary conditions, the analysis leads to an eigenvalue problem for the spatial dependence of the fluid and solid temperatures in the bed. The eigenvalues and corresponding eigenfunctions are readily calculated, and completeness of the eigenfunctions follows from a transformation to an integral equation by the construction of a Green's tensor function. The method is illustrated by several examples and important conclusions are drawn from the results. In particular, the analysis shows that a thermocline may be maintained for a period of several hundred hours in a well-insulated tank of the size and type currently under consideration.
- Research Organization:
- Sandia Labs., Livermore, Calif. (USA)
- DOE Contract Number:
- EY-76-C-04-0789
- OSTI ID:
- 6867666
- Report Number(s):
- SAND-77-8686; CONF-780608-1
- Resource Relation:
- Conference: 8. U.S. national congress of applied mechanics, Los Angeles, CA, USA, 26 Jun 1978
- Country of Publication:
- United States
- Language:
- English
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Anharmonic analysis of a time-dependent packed bed thermocline
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Related Subjects
25 ENERGY STORAGE
PACKED BED
SENSIBLE HEAT STORAGE
TEMPERATURE GRADIENTS
THERMAL ENERGY STORAGE EQUIPMENT
MATHEMATICAL MODELS
TOWER FOCUS POWER PLANTS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EIGENVALUES
FLUID FLOW
FOURIER ANALYSIS
GREEN FUNCTION
HEAT TRANSFER
ONE-DIMENSIONAL CALCULATIONS
TANKS
VECTORS
CONTAINERS
ENERGY STORAGE
ENERGY TRANSFER
EQUATIONS
EQUIPMENT
FUNCTIONS
HEAT STORAGE
POWER PLANTS
SOLAR POWER PLANTS
SOLAR THERMAL POWER PLANTS
STORAGE
TENSORS
142000* - Solar Energy- Heat Storage- (1980-)
140702 - Solar Thermal Power Systems- Central Receiver
250600 - Energy Storage- Thermal