Inlet Boundary Conditions

Inlet Boundary Conditions for a Velocity Component Perpendicular to the x-Direction

When dealing with inlet boundary conditions where the flow is perpendicular to the x-direction (i.e., the flow enters the domain in the y-direction), here’s how you implement the conditions:

1. Grid Arrangement

  • Location: The grid at the inlet boundary extends outside the physical boundary. The nodes along the line $$ ( i = 1 ) (or ( i = 2 ) for ( u )-velocity)$$ are used to store the inlet values of flow variables such as $$( u_{\text{in}} ), ( v_{\text{in}} ), ( \phi_{\text{in}} ), and ( p_{\text{in}} ).$$

refer figure 9.2 for example.

2. Velocity Component

  • U-Velocity: For an inlet perpendicular to the x-direction, the $( u )$-velocity is\ specified at the inlet.
  • Implementation:
    • Velocity at the Inlet: The inlet value for the $( u )-velocity, ( u_{\text{in}} )$, is stored at the boundary node ( I = 1 ) or ( i = 2 ) (depending on the grid arrangement).
    • Internal Cells: The solution for the first internal cell (shaded in diagrams) begins just downstream of this node.

3. Discretization of Equations

  • U-Velocity and Scalar Variables: The discretized equations for ( u )-velocity and scalar variables remain unaffected at the boundary cells. All links to neighboring nodes remain active.

  • Pressure Correction Equation:

    • Boundary Condition: For the pressure correction equation, the link to the boundary cell (west) is set to zero. Thus, the coefficient $( a_W )$ in the discretized equation is set to zero.
    • Velocity Correction: The velocity at the boundary is directly set as $( u^*_W = u_W )$, meaning no correction is needed at the inlet.

4. Pressure Reference

  • Absolute Pressure: To obtain an absolute pressure field, a reference pressure is often fixed at one inlet node. The pressure correction at this node is set to zero, providing a reference from which absolute pressures can be derived within the domain.

5. Turbulence Parameters

  • Turbulent Kinetic Energy $( k )$ and Dissipation Rate $( \epsilon )$: If measured values are unavailable, approximate formulae based on turbulence intensity (1% to 6%) and a length scale are used to estimate $( k ) and ( \epsilon )$ for the inlet conditions.