Document: NRC Regulatory Guide
Document ID: f4c5fb1d-efb9-4168-9804-5ad3f6f64d06
Document Type: regulatory_guide
Title: Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in Natural Water Bodies
Source: NRC Regulatory Guide Division 4
Source URL: https://www.nrc.gov/docs/ML0037/ML003739535.pdf
Revision Date: 2023-06
Chapter: 
Section ID: RG-4.4
CFR Part: 
CFR Title: 

Content:
avior of the flow field is handled directly. The most promising stochastic solution technique is the Monte Cado 'method, in which the probabilistic behavior of the 514,._.A. Lotiuk, J. C. Andenon, and T. Belytschko, "H•]nna Analyis by the Finite Element Method," ASCE ,oemat of Hydmulks Dwinoa. VoL 98, No. YI11, November 1972. 4.4-16 fliw field is modeled directfly by the assignment of % ,tochastic properties to dispersing "packets" of particles as they are tracked from the release point. The excess temperature within any given region is proportional to the local particle density. The model associates a temperature contribution, a deterministic velocity, and a dispersion rate with each moving particle. As each particle is tracked over a given tiTe interval, it is assigned a total displacement consisting of the sum of two vectors. The first vector displacement is caused by the known deterministic flow field and is given by [D1,At, U2At]. The second displacement, which represents dispersion, is a random Gaussian function with zero mean and is derived from the relationship of the eddy coefficient Di to the dispersion rate: I d 2 Di =)(B-32) where oi2 is the particle variance in the i-direction. From Eq. (B-32) the random displacement vector is given by 1(2D1At)'/ 2,(2D 2At)1/ 2]. By use of a digital computer, many particles are released from the source, allowing the stochastic behavior of each particle to be simulated until it passes beyond the region of interest. The Monte Carlo method has the advantage of direct dispersion simulation, and also the very appealing features of conceptual and programmatic simplicity. It should be noted, however, that with this technique it is still necessary to specify eddy diffusion coefficients. (3) Phenomenological Models In the sense used here, phenomenological far-field models differ from either deterministic or stochastic models in that they do not derive directly from solution of the basic transport equations, but rather from a