# Hydraulic Analysis of a Passive Wedge Wire Water Intake Screen for Ichthyofauna Protection
## 2 Materials and Methods
### Numerical Simulations  
In order to obtain detailed information on velocity distributions and current lines around the screen, as well as visualization, simulations using computational fluid mechanics (CFD) methods were carried out. The discretization and numerical solution of partial differential equations describing the flow allows approximate determination of the distribution of flow parameters such as velocity, temperature, and pressure, among others [40; 41; 42]. The modeling of fluid motion is based on the principles of conservation of mass and momentum, which are expressed as [43; 44]:  
Equation of conservation of mass:  
\[\frac{\partial\rho}{\partial t}+\
abla(\rho v)=0 \tag{5}\]  
where:  
\(\rho\)--density of the fluid,  
\(v\)--velocity vector,  
Equation of conservation of momentum:  
\[\rho\frac{dv}{dt}=\rho f+\
abla P \tag{6}\]  
where:  
\(\rho\)--density of the fluid,  
\(v\)--velocity vector,  
\(f\)--vector of mass forces,  
\(P\)--stress tensor matrix. These equations for the transient flow of a compressible fluid with variable viscosity are difficult to solve. Water can be considered an incompressible fluid and a fluid with constant density. Under the assumption that water is a Newtonian fluid, i.e., exhibiting a linear dependence of stress and strain rate, the coefficient \(\mu\) called viscosity is a constant value, a system of Navier-Stokes equations and continuity equations of the form can be formulated:  
\[\frac{\partial v}{\partial t}+\left(v\
abla^{T}\right)v=-\frac{1}{\rho}\
abla p +v\
abla v+f \tag{7}\]  
\[\
abla v=0 \tag{8}\]  
Because turbulent flow is a transient flow and its accurate simulation requires a lot of computing power, the most common approach is to look for the solution of the time-averaged Navier-Stokes equations, the so-called RANS--Reynolds-Averaged Navier-Stokes equations. The RNG \(k\)-\(\varepsilon\) model was used during the simulation. This model is more accurate and reliable for a wider class of flows than the standard \(k\)-\(\varepsilon\) model because, among other things,it takes into account the analytical formula for turbulent Prandtl numbers. The basis of this model is the equations describing the kinetic energy of turbulence \(k\) in the form:  
\[\frac{\partial v}{\partial t}+\Big{(}v\
abla^{T}\Big{)}v=-\frac{1}{\rho}\
abla p +v\
abla v+f \tag{9}\]  
\[\frac{\partial(\rho\varepsilon)}{\partial t}+\frac{\partial(\rho\varepsilon v _{i})}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\Bigg{(}\alpha_{ \varepsilon}\mu_{eff}\frac{\varepsilon}{\partial x_{j}}\Bigg{)}+C_{1 \varepsilon}\frac{\varepsilon}{k}(G_{k}+C_{3\varepsilon}G_{b})-C_{2\varepsilon }\rho\frac{\varepsilon^{2}}{k}R_{\varepsilon}+S_{\varepsilon} \tag{10}\]  
where:  
\(k\)--kinetic energy,  
\(\rho\)--density of the fluid,  
\(v_{i}\)--component of velocity in the corresponding direction,  
\(\alpha_{k}\)--the inverse of Prandtl number for k,  
\(\alpha_{\varepsilon}\)--the inverse of Prandtl number for \(\varepsilon\),  
\(\mu_{off}\)--coefficient of viscosity,  
\(G_{k}\)--coefficient taking into account turbulence kinetic energy generation due to averaging of velocity gradients,  
\(G_{b}\)--factor accounting for turbulence kinetic energy generation due to displacement,  
\(Y_{M}\)--coefficient representing the contribution of turbulent dilation to the rate of energy dissipation,  
\(S_{k}\), \(S_{\varepsilon}\)--additional coefficients that can be defined by the user,  
\(\varepsilon\)--turbulence kinetic energy dispersion rate. The constants in the above formulas are:  
\(\sigma_{k}=0.7194\)  
\(\sigma_{\varepsilon}=0.7194\)  
\(C_{1\varepsilon}=1.42\)  
\(C_{2\varepsilon}=1.68\)  
\(C_{\mu}=0.0845\). Numerical studies were carried out in ANSYS Fluent 19.1 software. After loading a properly prepared geometric model, generating a mesh, and introducing boundary conditions, simulations of flow in a hydraulic flume were performed, the results of which, juxtaposed with the results of laboratory tests, are presented in Section 3.9.