**Experimental modeling and analysis help predict structural stormwater BMP performance**

Many stormwater structural best management practices (BMPs) rely on gravitational particle settling for sediment removal. The University of Minnesota’s St. Anthony Falls Laboratory (SAFL), together with BaySaver Technologies, Inc. (BaySaver), a manufacturer of hydrodynamic BMPs, developed empirical correlations between the dimensionless Peclet Number (*Pe*) and sediment-removal efficiencies in BaySaver’s separators. This article outlines the use of *Pe*-sediment removal relationships and experimental data to develop models for projecting BMP sediment-removal performance.

Rigorous analysis of solid-liquid separators, such as hydrodynamic BMPs, can be a complex task. In many instances, the approximate solution of such fluid flow equations is approached via numerical methods. More recently, with the widespread use of computational fluid dynamics software, characterization of fluid flow patterns in hydrodynamic BMPs also has been achieved. Empirical correlations involving dimensionless numbers, such as the Reynolds Number, Froude Number, and *Pe*, have been used for many years to solve fluid flow problems. This empirical technique does not require a complete analytical formulation of the phenomena per se, but a general understanding of the factors that affect the process being studied. The use of empirical correlations involving dimensionless numbers is used widely in many areas of engineering, such as fluid flow and heat and mass transfer.

The benefit of using empirical correlations involving dimensionless numbers is that once the equations are developed for a particular process, these same correlations can be used to predict the behavior of similar processes having different relative dimensions. Because these empirical correlations are developed based on experimental techniques and statistical data analysis, the solutions obtained are approximate. Empirical techniques, however, often provide useful solutions to real-life problems.

**The BaySaver Separator**

For context, it is useful to understand how Baysaver’s hydrodynamic BMP functions. It is a physical separator, relying on gravity settling, flotation, and other related mechanisms, to remove sediments, floating debris, and free oils from stormwater. The system comprises three main components (see Figure 1): the BaySaver Separator Unit, the Primary Manhole (PM), and the Storage Manhole (SM). Both manholes are of standard concrete construction and function as sediment-accumulation sites.

*Figure 1: Components of the BaySaver Separator*

During a storm event, the Separator Unit acts as a flow control to route the influent flow through the most effective flow path for treatment. For example, under low-flow conditions, the entire influent flow is treated in the PM and SM. Under moderate flows and up to the maximum treatment rate (*MTR*), water is treated through both the PM and SM, with a portion of these flows diverted through T-pipes.

The T-Pipes are structures that enhance the performance of the system during high-intensity storm events that are below the *MTR* of the separator. This flow path allows for full treatment of floatable pollutants, while still treating sediments under moderate flow conditions. During maximum flow conditions or maximum hydraulic rate, most of the influent flow passes over the bypass plate and will not be treated.

**The Peclet Number**

*Pe* can be defined as the ratio of advective mass transport to turbulent mass transport in the vertical direction. Specifically, in studying particle settling phenomena, *Pe* has been defined as:

*Pe* = *Vs* *L _{1}* /

*Diff*(Equation 1)

where *Vs* is the particle settling velocity (feet per second), *L1* a length scale (feet), and *Diff* is the turbulent diffusion coefficient (square feet per second). *Pe* has no dimensions. *Vs* can be calculated using the well-known Stokes Law for particles having a particle Reynolds Number less than 1.

Of the three terms that comprise *Pe*, *Vs* and *L1* are, in most cases, relatively easy to determine. The *Diff* term is much more difficult to establish, both theoretically and experimentally. Based on experimental work and theoretical understanding, SAFL researchers estimated the turbulent diffusion term in the BaySaver separator by:

*Diff Q * / *L _{2}* (Equation 2)

where

*L2*is a scale length (feet), and

*Q*is the flow through the manhole (cubic feet per second). The scale length refers to a particular and functionally relevant dimension of the BMP device being studied. Only similar systems having the same

*Pe*will exhibit similar particle-removal dynamics. Sediment-removal correlations based on Pe for a specific BMP design cannot be used to predict the behavior of a geometrically dissimilar BMP design that might have the same

*Pe*.

The final form of the *Pe* determined by SAFL and used in the analysis of the separator is:

*Pe* = *Vs Dm* / (*Q */ *h*) (Equation 3)

where *Vs* is the settling velocity for the d50 particle in the sediment gradation, *Dm* is the diameter of either the PM or the SM, *Q* is the flow through the separator with *Q* less than or equal to *MTR*, and *h* is a dimensional scale characteristic of every BaySaver separator. Note that each manhole will have its own *Pe*-sediment removal correlation.

How can the *Pe* be used to predict the behavior of a stormwater BMP? An approach used by SAFL and BaySaver Technologies was to develop a family of dimensionless equations for the BaySaver separators as a function of flow (*Q*) through the system, *MTR*, and mass accumulation measurements in both the PM and the SM. Mass accumulation measurements were then used to calculate sediment-removal efficiencies in the BaySaver System. A sediment gradation manufactured by U.S. Silica, F-95, was added to the source water as the source of sediment mass (see Table 1).

Sediment size (μm) | Percent finer |

425 | 100 |

300 | 99 |

212 | 90 |

150 | 60 |

106 | 18 |

75 | 3 |

53 | 0 |

In general terms, sediment-removal efficiency of a BMP is defined in Equation 4, which has been used in other types of BMP efficiency analysis efforts:

Removal Efficiency = Mass of sediment collected / Mass of sediment injected(Equation 4)

Based on the experimental work at SAFL, dimensionless relationships were developed for percent sediment removal (100 x Removal Efficiency) in the SM and PM as a function of *Pe* in each structure (*Pe*PM and *Pe*SM). The empirical equations developed as a result of this ongoing experimental program are presented in Figures 2 and 3. *Pe* correlations can provide a useful approach toward understanding and predicting sediment-removal mechanisms and efficiencies in stormwater BMPs.

For a given BaySaver Separator configuration, the sediment-removal efficiency was evaluated over a range of treatment flows as a function of the *Pe* in both the PM and the SM. The results of this evaluation were then expanded into a family of equations having the following general form:

Percent Sediment Removal for Separatori = A ln( *Q */ *MTR* ) + *B* (Equation 5)

where *A*, *MTR*, and *B* are specific to each separator design; *A* and *B* are numerical constants; and *Q* is the stormwater flow with *Q* __less than or equal to__ *MTR*. These equations then formed the basis for the development of a software model for the optimum design of BaySaver separators based on target percent sediment-removal requirements, precipitation data, and economics.

The percent sediment-removal efficiency in both the PM and SM increase as the *Pe* increases (see Figures 2 and 3). Additionally, the following observations, summarized in Table 2, can be made based on Equation 4:

- As the particle settling velocity increases, the efficiency of the separator increases. The opposite also is true.
- As manhole depth increases, the efficiency of the separator increases. It is believed that an increased distance between the turbulent region in the manholes and the sediment-rich strata toward the bottom of the manhole mitigates particle re-suspension and upward sediment transport, resulting in more effective particle settling.
- As manhole diameter increases, the efficiency of the separator increases. A larger manhole diameter creates a longer horizontal trajectory and a correspondingly greater hydraulic retention time between the inlet and the outlet. Therefore, particles have a greater chance of reaching the quiescent areas of the manhole, increasing settling efficiency.
- As the flow increases, system efficiency decreases. It is believed that this is caused by a decrease in residence time in the system and by increased turbulence that works against particle settling and removal.

*Figure 2: Measured removal efficiency of the Primary Manhole versus Peclet Number and the proposed function to describe the relationship. Source: University of Minnesota, St. Anthony Falls Laboratory*

*Figure 3: Measured removal efficiency and the percent removed in the Storage Manhole versus Peclet number and the proposed functions to describe the relationships. Source: University of Minnesota, St. Anthony Falls Laboratory*

Factor | Increase Vs | Increase h | Increase Dm | Increase Q |

Pe in PM | + | + | + | - |

Pe in SM | + | + | + | - |

Sediment-removal efficiency |
+ | + | + | - |

+ = increases

- = decreases

**Conclusions**

The Peclet Number is a useful tool in characterizing the performance of hydrodynamic separators. It is believed that statistically valid correlations between the Peclet Number and sediment removal in BMP structures can be obtained through the use of robust data collection and analysis procedures.

In a hydrodynamic BMP, particle settling is opposed by turbulence in the BMP structure. The Peclet Number predicts that the higher the particle settling velocities (advection) relative to the turbulence in the BMP, the more effective the separator will be in removing sediments, all other factors being equal. Hence, higher Peclet Numbers lead to higher sediment-removal efficiencies.

It is likely that resultant particle-removal efficiencies in the BaySaver System also are influenced by mechanisms such as particle interactions, particle characteristics, and wall effects. However, the influence of these factors was not quantified during this project.

*John Mosheim, P.E., is director of engineering at BaySaver Technologies, Inc. Throughout his 20-year career, he has designed several water and wastewater treatment facilities, provided engineering services related to pollution prevention, and assisted the private sector with regulatory analysis and compliance issues. He can be contacted at jmosheim@baysaver.com.*

**References**

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