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Effectively managing floods in urban regions requires effectively designed and well-maintained runoff collection system. The absence of such a system and intense rainfall event will have the potential to disrupt the urban life and cause significant economic loss to properties. Grated inlets, which are a key component in urban drainage network, are used to capture the runoff. In this work, a three dimensional CFD model was developed based on open-source CFD tool, OpenFOAM<sup>®</sup>, to model flow over a grated inlet. An incompressible, transient, multiphase flow, Volume of Fluid (VOF) simulation was performed to predict the water flow rate through the grate inlet. The predicted flow rates are compared with the HEC-22 monograph values. The close agreement between the results shows the potential of using CFD modeling approach to test the reliability of existing drainage inlets for different flow scenarios.

A key constituent of urban drainage infrastructure is the surface runoff collection system. Proper design and maintenance of the components in this collection system can minimize the effect of damage and flooding from a storm event. Such a system will collect the surface runoff, carry the flow through the sewer network, and discharge it to water receiving body. The components in the collection system are 1) street gutters 2) stormwater inlets, and 3) storm sewers. The street gutters collect the runoff from the street and convey it to a storm inlet so that there is no disruption to the traffic on the street. Inlets collect the water from the streets and transit the flow to the sewer network, and provide access for maintaining the storm sewer system. Storm sewers transport the water to a receiving water body.

The stormwater inlets, also known as Street inlets, are the connecting elements between the surface and the underground sewer system. Street inlets can be four types. These are 1) grate inlets 2) curb-opening inlets 3) combination inlets and 4) slotted drain inlets (Brown et al. 2009). Some of the grate inlets that are being used include parallel bar grate (P-1-7/8), parallel bar grate with transverse rods at the surface (P-1-7/8-4), parallel bar grate with spacers (P-1-1/8), 45˚ tilt bar grates (45-3-1/4-4, 45-2-1/4-4), 30˚ tilt bar grate (30-3-1/4-4), and curved vane grate (CV-3-1/4-4-1/4).

In this work, our focus is on P-1-7/8 grate. P-1-7/8-4 grate refers to a parallel bar grate with center-to-center spacing of the longitudinal bars of 48 mm (1-7/8 in). For various sump depth values, the discharge values are compared between the monograph values given in HEC-22, and the CFD model predicted data. The CFD model was developed using the popular open-source OpenFOAM^{®} software. Our goal is to show that the CFD model can be reliably used to design, evaluate, and predict the efficiency of grates for different flow scenarios.

The CFD model was developed using Open Field Operation And Manipulation (OpenFOAM^{®}). OpenFOAM^{®} is the leading free, open-source software for CFD, owned by OpenFOAM^{®} Foundation and distributed exclusively under General Public License (GPL). It has a large user base across most areas of engineering and science, from both commercial and academic organizations. OpenFOAM^{®} has an extensive range of features to solve anything from complex fluid flows involving turbulence and multi-phase, chemical reaction to acoustics, solid mechanics, and electromagnetics. Its versatile C++ toolbox for the Linux operating system enables developing customized, efficient numerical solvers and pre-/post-processing utilities for all kinds of CFD applications by solving the Navier-Stokes equations. OpenFOAM^{®} uses a cell-centered Finite Volume Method (FVM) to solve the partial differential equations of continuum mechanics and fluid flow. In this approach, the equations are integrated over each of the control volumes (cells) on the mesh, and volume integrals that contain a divergence term are converted to surface integrals using Gauss’s theorem. The surface integrals can then be evaluated by summing the contributions from each of the

cell faces. This approach to the solution of the equations requires a method to extrapolate the velocity stored at the centroid of the cell to the value of the velocity at the face of the cell. Many methods to perform this extrapolation are available in OpenFOAM, and these are documented in the Users Guide [^{®} provides a variety of turbulence model options from Reynolds-Averaged Navier-Stokes (RANS) to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). The available solvers, options in specifying the boundary conditions, mesh generation tools, flow visualization software, and extensive documentation are making OpenFOAM^{®} popular among the CFD modeling community.

The approach used for analyzing flow in grates in HEC-12 and the subsequent HEC-22 [

Galambos [^{®} software to model the flow through a gully. To arrive at the efficiency of the inlet system, Shepherd et al. [

Depending on the flow depth, the flow over the grate inlet can be either a weir flow or orifice flow. For shallow depths, the inlet operates like a weir, and for greater or submerged depths, the inlet operates like an orifice [

The capacity of grate inlets operating as weirs is given by (Equation 4.26 in HEC-22)

Q w = C w P d 1.5 (1)

where P = perimeter of the grate in ft disregarding bars and the side against the curb, d is the average depth across the grate and C_{w} = Coefficient of weir = 3.0.

The capacity of a grate inlet operating as an orifice is given by (Equation 4.27 in HEC-22)

Q o = C o A ( 2 g d ) 0.5 (2)

where C_{o} = orifice coefficient = 0.67; A = clear opening area of the grate = 0.9*Area of grate, ft^{2}; g = 32.16 ft/s^{2}.

The inlet grate capacity is minimum (Q_{w}, Q_{o}).

CFD simulation was carried out with the opensource software package OpenFOAM^{®} described by Weller et al. [

InterFoam, a Volume of Fluid (VOF) based solver, was used to compute, capture, and track the interface between air and water. The VOF method was first introduced and developed by Noh and Noh and Woodward [

The VOF method is a surface-tracking technique that models two-phase flows with a dimensionless scalar field representing the fluid volume fraction alpha (α). A volume fraction value of zero represents fluid “a,” e.g., air and a value of one represents fluid “b” e.g., water. The scalar volume fraction alpha (α) is advected with the flow via a transport equation. The transport equation is solved simultaneously with the equations of mass and momentum conservation. The full set of governing equations for the fluid flow is:

∇ U = 0 (3)

∂ ρ u ∂ t + ∇ ⋅ ( ρ u u ) − ∇ ⋅ ( ( μ + μ t ) s ) = − ∇ p + ρ g + σ K ∇ α (4)

∂ α ∂ t + ∇ ⋅ ( u α ) = 0 (5)

where u and p are velocity and pressure fields, μ t is the turbulence eddy viscosity, s is the strain rate tensor, σ is surface tension and K is the surface curvature.

Following are the possible conditions for alpha (α):

α = 1 : volume cell occupied 100% by water.

α = 0 : volume cell occupied 100% by air.

0 < α < 1 : volume cell occupied by water and air.

Therefore the phase fraction alpha (α) must be conserved and bounded. Since the phase fraction alpha (α) can have any value between 0 and 1, the interface cannot be resolved sharply. The interface between the phases is not explicitly computed; therefore, the sharpness of the interface depends on mesh resolution around it. A sharp interface cannot be maintained if the advected term ∇ ⋅ ( u α ) gets diffusive and numerical schemes do not reliably overcome the diffusion issue, therefore OpenFOAM^{®} introduces a counter-diffusive term to the alpha (α) transport equation that can be used to compress the interface. The compressive convection term is presented in the third term of the transport equation below:

∂ α ∂ t + ∇ ⋅ ( u α ) + ∇ ⋅ ( u c α ( 1 − α ) ) = 0 (6)

where u c is the compressive velocity.

Physical properties of phases are calculated as weighted averages based on the alpha fraction. The density ρ and dynamic viscosity μ are calculated as follows:

ρ = α ρ w a t e r + ( 1 − α ) ρ a i r

μ = α μ w a t e r + ( 1 − α ) μ a i r

The 10 × 5 × 2 m domain (

The top boundary of the domain was the atmosphere, and the total pressure was set to zero. The sides of the domain were prescribed to the wall with slip conditions on velocity. The ground was segmented into two parts, one inner part around the grate and two, outer part attached to sides of the domain (

The K-Omega SST (Reynolds Averaged Navier-Stokes type) was used as a turbulence model in this study. Gravity acceleration was activated (perpendicular to the ground) to compute the hydrostatic pressure. Wall function was used to model the near-wall conditions, where the viscous layer is not resolved explicitly, approximations are introduced to account for the flow behavior across it. Automatically adjustable time step was used based on Courant number to maintain solver stability. A transient, incompressible, and multiphase (VOF) flow was used to compute the flow fields such as velocity vector, pressure, Alpha water, turbulence properties (K, Omega) and turbulent viscosity.

The current direction in computational hydraulic modeling advances is to resolve sets of interconnected hydraulic features into component models and develop CFD type representations of the various component sub-models, construction a system of CFD submodels. These sub modeling components are, in turn, reusable throughout the global problem domain, enabling a library of sub modeling components to be developed over time. Some civil engineering computational software products provide such reusable component CFD type models. For example, Advanced Engineering Software [

In the current paper, the focus is on the important submodule for drainage inlet hydraulics. Such inlets are of high population and commonly used in the design of drainage systems and in the master planning of City-wide Master Plans of Drainage. The drainage inlet submodule is the first and perhaps a fundamental component in a comprehensive CFD library of civil engineering drainage modeling elements. A library of submodules is under development and will parallel the modeling strategy used in the link-node model, such as seen in the cited Advanced Engineering Software and published in papers and texts. The close agreement of results (

Grated inlets are an important component of urban infrastructure, and numerical models that can predict the flow characteristics over a grate can help in simulating various flow scenarios. In this work, a three dimensional CFD model which solves the full-dimensional Navier Stokes Equations using OpenFOAM software was developed for evaluating the flow characteristics over a grate. The model results, for a range of flow depths, are compared with the HEC-22 published data. In light of the observed results, it can be concluded that the developed CFD model can be reliably used for analyzing and predicting the flow characteristics over inlet grates. Although the focus was running the model on parallel bar grate (P-1-7/8), it can be used across other grate inlets.

The authors declare no conflicts of interest regarding the publication of this paper.

Hromadka II, T.V., Rao, P. and Battoei, M. (2020) CFD Analysis of Flow in a Grated Inlet. Open Journal of Civil Engineering, 10, 32-42. https://doi.org/10.4236/ojce.2020.101004