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:
reading 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 which the unknowns are un, Tm, and b (not considered here are the three additional equations relating the jet position to the fixed Cartesian coordinates). In the third step, the entrainment function must be expressed in terms of the centerline value of jet velocity, un. The simplest relationship that has been used is of the form, E = aum , (B-30) which states that the entrainment rate is proportional to the centerline jet velocity. The constant of proportionality a is known as the entrainment coefficient. Such a relationship, at. best, satisfies the intuitive expectation that a fast jet will have a higher entrainment rate than a slow jet. However, the correct choice of a for any given problem is open to considerable question. It is also unlikely that a simple proportional relationship such as Eq. (B-30) applies in nature. lConsiderable theoretical and experimental work over the put decade has resulted in increasingly more complex (and hopefully realistic) forms for the entrainment function. HirSt 4 presents the most general expression to date: E = (0.057 + 097 sin2 [blum - [u.I I + 9.0b Vu2ru- [U].I (B-31) where 02 is the elevation angle of the plume above the horizontal and FL is the local densimetric Froude number. This expression is similar to but considerably more sophisticated than that shown in Eq. (B-30). From the Froude number and angular dependence, it is seen that the "entrainment coefficient" is a dynamic quantity that changes with the evolution of the jet. Also, the secnd term in braces gives an enhanced entrainment rate for the case of the jet and ambient flow not being collinear. In keeping with the usual definition of the near-field as being the region where dilution by jet entrainment dominates the dilution due to turbulent diffusion, terms describing