NESC0599 TOPLYR2

1. NAME OR DESIGNATION OF PROGRAM:  TOPLYR2.

3. DESCRIPTION OF PROBLEM OR FUNCTION

TOPLYR2 applies the first law of thermodynamics to compute the temperature of a water mass flowing in an open channel. The program is designed to accommodate variable depth, velocity, and cross section. The source of energy (location of the discharge) is assumed to be sufficiently distant from the river segment under examination that the momentum associated with the discharge is insignificant. Velocity distribution at both the inlet and outlet of the reach as well as the temperature distribution at the inlet as a function of time and at the outlet initially are specified. Eddy diffusivities, ambient meteorological conditions, and geometry are also supplied to the code. Although the lateral eddy diffusivity is allowed to vary spatially, the effect of density disparity is not treated explicitly by the code. Temporal behavior induced by variations in the ambient meteorological and boundary conditions are computed.

4. METHOD OF SOLUTION

TOPLYR2 divides the water mass into an array of rectangular prisms of non-uniform depth where vertically averaged quantities are employed. The mathematical model employs an energy balance of temporal, convective, diffusional and source terms and a mass balance. The equations are transformed to a second-order finite-difference form and an alternating direction implicit scheme is used to compute the temperature field. The two-dimensional tridiagonal arrays produced by the ADI method are solved by Gaussian elimination. Provisions have been included in the program to accommodate non-uniform diffusivity. The energy source results from weather conditions and Newton's cooling law boundary conditions.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Subscripted variables are dimensioned at compilation time using the UNIVAC1108 procedure definition processor. Code instructions require relatively little storage. A typical river simulation problem with adequate geometric-time mesh involves about 10,000 decimal words of storage (instructions, blank common and data).

6. TYPICAL RUNNING TIME

For a typical 17 x 10 node spatial grid and 200 time-steps, 1 to 3 minutes are required depending upon problem complexity.

7. UNUSUAL FEATURES OF THE PROGRAM

To eliminate the possibility of any non-physically plausible temperature form entering into the analysis a scheme proposed by Hains is employed. The use of the Hains principle assures that the second law of thermodynamics is not violated. A default algorithm assigns a uniform diffusion coefficient to the flow field. Local depth and velocity are available for the user to construct a non-uniform diffusion coefficient matrix. Currently, an algorithm based on one-dimensional frictional flow is provided.

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES

- D. C. Kolesar:
Mathematical Modeling of Thermal Plume Dispersion in a Receiving Water  Body, presented at the Second Annual Thermal Power Conference, Washington State University, Pullman, Washington, October 1971.
- A. J. Policastro, J. V. Tokar:
Heated-Effluent Dispersion in Large Lakes, State-of-the-Art of Analytical Modeling ANL/ES-11 (1972) Part 1, Critique of Model Formulations, 1972.

- D.C. Kolesar and J.C. Sonnichsen, Jr.:
  TOPLYR-II A Two-Dimensional Thermal Energy Transport Code
  HEDL-TME 72-46 (March 1972)
- TOPLYR2 ACC No. 599, HEDL Note, 1973

11. MACHINE REQUIREMENTS:

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   EXEC2 or CSCX.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Two versions of TOPLYR2 are available - one employs a constant diffusivity and the other a local depth and velocity dependent diffusivity. The latter version implements the empirical correlation.

15. NAME AND ESTABLISHMENT OF AUTHORS

                 D. C. Kolesar and J. C. Sonnichsen
                 Hanford Engineering Development Laboratory
                 Westinghouse Hanford Company
                 P. O. Box 1970
                 Richland, Washington  99352

File name	File description	Records
NESC0599_01.001	INFORMATION	1
NESC0599_01.002	SOURCE PROGRAM (F4,EBCDIC)	1838
NESC0599_01.003	SAMPLE PROBLEM INPUT DATA	118
NESC0599_01.004	SAMPLE PROBLEM PRINTED OUTPUT	354