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:
e instantaneous quantities, ui, p, and T, are each written as the sum of an average component (denoted by a bar over the symbol) and an instantaneous fluctuation about the average (denoted by a primed symbol): p -• p' T =T+T' v is the coefficient of kinematic viscosity - 'A P0 and AP = -Po a (T- To) The energy equation reduces to where the average is taken over a suitably chosen time period that is small compared with the time scales of interest. Pritchard 3 discusses certain advantages in performing ensemble rather than time averaging. (B-7) However, the more conventional concept of time averaging is followed here. Comistent with the Bouulnesq approximation, the above equations do not contain a term representin fluctuations in density. 8T + V2 T (B.8) whee x - k is the thermometric conductivity. pocv Note that the viscous energy dissipation function, 4, has been dropped under the Bouinmeq approximation. For an Incompresible flud,, the dissipation function is #v by ;,[aE, a uJ] 2 From Eqs. (B-6) and (B-7), the velocity scale is of the order (aeTJXld)l/ 2 where d isa characteristic length scale and [Xi becomes the acceleration of gravity in any practical problem. Consequently, the scale of 0 is of the order pnaTS/d. From Eq. (B-3), the scale of i relative to that of diffusion is pood/k, which for typical length swales (d-l cm) is much smaller than unity. Hence, dropping the dissipation function has negligible effect on the heat energ equation. Equations (5-S) through (M-8) express the bai conservation laws subject to the Bousunesq approximation. If the above expresions are substituted into Eqs. (5-4), (3-S), and (B.6) and the system is averaged, the following onsevation equations in mean quantities remst: Equa•oem of oiate 7 = p. 11 - a(T- TO)] Commuvaliom i a9 a+ 8 = ( air -X X &U1+ ý U - 2% $in(*u I a + - -- a - x-(j N 5 (W-9) (B-10) (B-11) 3 D. W. Pritchard, "Threedimenional Models," in Estuarine Modelb. An Asmigt, Eurkoumsatal Protection Aency, Water