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:
-. uTs- +V - Thrv., (B-23) (B-24) 4E. A. Hirt, "Analysi of Round, Turbulent, Buoyant Jets Discharged to Flowing Ambients,' ORNL-4685, Oak Ridge National Laboratory, 1971. •au• vau [• 1, (,•.ll o ,t.S where u a time-averaged axial velocity component v a time-veraged radial velocity component [es0A] g = the axial component of s buoyancy acceleration. Only the axial momentum equation is shown here, since this is sufficient to illustrate the approach used in near-field analysis. This approach consists essentially of three steps designed to reduce the complete set of partial differential equations to a set of ordinary differential equations expressing the centedine velocity components, temperature, and Cartesian position as functions of s. These three steps consist of (1) removal of the r-dependence by integration of the conservation equations over the jet cross section, (2) specification of the radial profiles of temperature and velocity, and (3) introduction of an entrainment function. The radial integration of the first step places the equations in so-lled "integral" form. These are not integral equations in the strict mathematical sense, but rather in the sense that radial distributions of properties have been integrated away. The simpler set of ordinary equations expresses only bulk properties of the flow as functions of jet trajectory. Retrieval of the lost details requires the second step, in which radial distributions of velocity and temperature are secified. These are usually maumed to have a Gaussian form, as discussed in Section 3a of Appendix A. The third step is an attempt to atpreu the radial flux of dilution water into the jet in tern of the axial flow. In accordance with the first step above, integration of Eqs. (B-23) through (&-25) over the area 'Yea 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