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:
a df2hr f r dr] =d (N-26) d -[2x f7 V(T -T..)r dr]u dT_ -Q- dT- 2w lim (-r) (&27) k- -2w U2 r dr] d-s =[2w f ag(1 - T_.) r d] 0S 4.4-14 + E [u., - 2w tim (ruIv (B-28) where the subscript s indicates a component in the s-direction, and the upper integration limit, ", for practical purlpses, is the physical edge of the jet. Equation (B-26) represents conservation of mass and states that the rate of change of volume flux Q along the jet trajectory a is equal to the rate of entrainment - 21r lim (rV) = E of fluid at the jet edge. Equation (B-27) states that the rate of change of flux of excess temperature G along the jet trajectory is balanced by the rate of entrainment of fluid of ambient temperature T. and the turbulent flux - 27hr im 7 ) of heat energy at the jet edge. Equation (B-28) represents the conservation of bulk momentum. It states that the rate of change of s-momentum flux M. along the jet path is balanced by (1) the s-component of buoyancy (with temperature replacing density), (2) the entrainment E[u..]s of ambient momentum by the mean radial flow at the jet edge, and (3) the turbulent flux - 21 lim (rV of momentum at the jet edge. Note that in the buoyancy term, the equation of state has been used to express the density in terms of the temperature. Clnmue of the set of conservation equations requires that the radial distributions of jet velocity and temperature (step 2) and the entrainment function (step 3) be specified. Beyond the zone of flow establishment (the reion in which the jet possess a potential core), all radial profiles are assumed to have Gaussian forms, as discussed in Appendix A: a = (u. - [U._,) e-(r/b) 2 + 1U.1J T - T. = (Tm - T,.) e-(i/xb) 2 (13.29) where um and Tm represent centerline values, b is the jet half-width (b - o'4), X is the spreading ratio introduced in Appendix A, and [u. I s is the component of ambient velocity in the s-direction. Substitution of Eq. (B-29) into Eqs. (B-26) through (B-28) results in a set of equations in