Validation of CORMIX model in simulation of single port brine discharge into seawater

Abstract
1. Introduction
Over recent decades, utilizing desalination plants with reverse osmose technology has been expanded all around the world whereas discharging their brine has become a serious environmental concern since this phenomenon can have catastrophic environmental consequences. Consequently, numerical models have grown which enable engineers to simulate and predict brine discharge before erecting marine outfalls. CORMIX is a functional and useful model which is able not only predicts discharge effluent behavior but also applies environmental limitation in its simulation. Therefore a plethora of researchers have used the CORMIX to design marine outfall and recognize jet's behavior in waterbodies. However, evaluating the reliability and accuracy of the CORMIX is crucial.

2. Materials and methods
2.1. Methodology
In this study, the CORMIX model was evaluated for the simulation of discharging dense jets via a single port diffuser in a stagnant and dynamic seawater body. Discharge velocity (u0) and diffuser diameter (d) have been chosen as two main variables which play an effective role in jet behavior. Next, the primarily jet characteristics including dilution at the impact point (Si), the horizontal location of the impact point (Xi), the horizontal location of the centerline peak (Xm), and vertical location of the centerline peak (Zm) were calculated, then their governed equations were extracted. Then, quantitative and qualitative analysis of CORMIX model results was performed with experimental data by using standard deviation and RMSE statistical methods.

2.2. The CORMIX model
The CORMIX (Cornell Mixing Zone Expert System) is a computer model for analyzing, forecasting, and designing for the discharge of effluents, toxic water, or conventional contaminants into a variety of aquatic environments. This model is the most popular for modeling wastewater discharge. The modules of this system emphasize designing geometric parameters and dilution in the initial mixing area, to comply with legal restrictions and also to predict the behavior of the discharged effluent. There is a flow classification system within CORMIX. Flow classes are presented based on technical principles and using hydrodynamic models with dimensional analysis relationships from experimental data. Dimensional analysis is the simplest way to formulate reasonable assumptions in complex physical conditions. Variables are considered to have the greatest effect on dilution, and variables are kept constant with the least effect, to reduce the number of independent variables in the problem. The selected independent variables are related to each other by the size of the flux, which represents the main forces controlling the effluent behavior. The main fluxes on which saline effluent behavior is described are mass flux (Q), momentum flux (M), and buoyancy flux (B). After identifying the flow class in the model, a simplified quasi-experimental formula derived from the discharge process based on dimensional analysis is applied to calculate the main characteristics of effluent jet behavior.

2.3. Experimental data for the dense jet in stagnant and dynamic ambient
Based on (Roberts and Toms 1987), in a stagnant ambient for a specific discharge angle, jet dilution and geometric properties are a function of port diameter (d) and densimetric Froude number (Fr). So dimensionless parameters consist of Si/Fr, Xi/(d.Fr ), Xm/(d.Fr), and Zm/(d.Fr) are commonly evaluated to describe jet behavior. For discharge in the dynamic ambient besides port diameter and densimetric Froude number, discharge velocity (u0), ambient velocity (ua), and the horizontal angle of the port for the ambient current are effective. So dimensionless parameter Si/Fr =Ci (ur.Fr )^(1/2) was used to evaluate jet behavior. Where Ci is constant and ur is relative velocity and is defined as ur=ua/u0.

3. Result and discussion
After conducting approximately 180 simulations, the CORMIX outcome for dilution at the impact point (Si), the horizontal location of the impact point (Xi), the horizontal location of the centerline peak (Xm), and the vertical location of the centerline peak (Zm) were normalized in dimensionless form.

3.1. Validation of dense jet discharge into stagnant ambient
As for Si and Xi parameters, the more port diameter and discharge velocity decline, the more dilution rate at the impact point increase until the relation Fr>15 applied on CORMIX Results. After that, the outcome followed the experimental data trend with 0.2 and 0.025 differences for Si and Xi, respectively, meanwhile, they were underestimated which is so vital to be considered when the brine is discharged in a water body with a sensitive ecosystem. In addition, the Si parameter was more sensitive to discharge velocity fluctuation whereas Xi was not so reliant on port diameter and discharge velocity. However, Zm, which is an effective parameter for brine discharge in shallow water, was sensitive to both port diameter and discharge velocity also its results were accurate and reliable only if Fr>30. About Xm, the outcome of CORMIX for Fr>25 with grate turbulence followed experimental data while they were underestimated with 0.14 error.

3.2. Validation of dense jet discharge into dynamic ambient
In dynamic ambient, due to lack of studies in terms of jet geometric features for θ =60° and σ =0, the study limited to dilution at the impact point. For Si, overall, decreasing port diameter and discharge velocity had a positive effect on the dilution rate increase. Although their changes were negligible when ur.Fr <0.2. Also, CORMIX results were overestimated with 0.77 compared to experimental data.

4. Conclusion
According to this study, in a stagnant ambient, port diameter and discharge velocity were capsulated in densimetric Froude number. Therefore, the results of CORMIX will be reliable only if the values of Fr has located in the specified domain (for Si and Xi, Fr>15 and for Xm and Zm, Fr >30). In dynamic ambient, besides port diameter and discharge velocity, the ambient velocity has an effective impact on dilution rate and jet geometric properties. Consequently, the design should be done based on relation ur.Fr >0.2 for Si parameter. Nevertheless, since CORMIX results were underestimated compared to experimental studies, calculated errors must be considered.