No-slip condition is basically applied to the viscous fluid in which the fluid at a solid wall will have zero velocity to the boundary. The no-slip condition states that the velocity of the fluid at a solid boundary (surface) is equal to the velocity of the boundary itself. For a stationary boundary, this means the fluid velocity at the boundary is zero.
This condition implies that there is a thin layer of fluid, known as the boundary layer, where viscous effects are significant.Within this boundary layer, the fluid velocity transitions from zero (at the wall) to the free stream velocity (away from the wall).The no-slip condition is a direct consequence of fluid viscosity.
\fbox{\textbf{\Large Inviscid flow}}Inviscid flow assumes that the fluid has no viscosity. In mathematical terms, it means the viscosity coefficient is zero. In inviscid flow, there are no shear stresses, and the velocity gradients perpendicular to the flow are negligible.The flow is governed by Euler’s equations rather than the Navier-Stokes equations.The concept of a boundary layer does not exist in inviscid flow; the velocity profile is uniform across any section.
\fbox{\textbf{\Large Boundary layer theory}}Real fluids are viscous, so the no-slip condition always applies at solid boundaries. However, in many practical applications, the effects of viscosity are confined to a thin boundary layer near the walls.Outside the boundary layer, the flow can often be approximated as inviscid because the viscous forces are negligible compared to inertial forces.
We can consider two regimes:
Viscous (no-slip): Near the boundary within the boundary layer, where viscous forces dominate, the no-slip condition is crucial.
Inviscid: Away from the boundary layer, in the main flow region, the inviscid assumption simplifies analysis since the flow can be treated as if there were no viscosity.
\fbox{\textbf{\Large Zero gradient BC}}A “zero gradient” boundary condition, also known as a Neumann boundary condition, is a type of boundary condition used in computational fluid dynamics (CFD) and other numerical simulations. It specifies that the gradient (rate of change) of a variable in the direction normal to the boundary is zero. This means that the value of the variable does not change as you move across the boundary. (No change accross boundary, especially for farfield).
\frac{\partial \phi}{\partial n} = 0Physical meaning:
- Outflow Boundary: In fluid dynamics, a zero gradient condition is often used at outflow boundaries. It implies that the flow exits the computational domain smoothly without any artificial reflections or disturbances.
- Velocity: The zero gradient condition for velocity at an outflow boundary means that the velocity profile remains constant in the direction normal to the boundary, implying no acceleration or deceleration as the fluid leaves the domain.
- Pressure: Often, a constant pressure or a specified pressure boundary condition is used instead of zero gradient for pressure at outflow boundaries to ensure physical realism.
- Far-Field Boundary: For large or open domains, a zero gradient condition can approximate the behavior of variables far from any solid boundaries or sources/sinks, where changes in the variable are negligible.
- Symmetry Boundary: A zero gradient condition is appropriate for symmetry planes, where the variable’s rate of change across the plane is zero, maintaining a mirror symmetry.
!! So slip BC is a type of Neumann boundary condition where
- The normal component of the velocity at the boundary is usually set to zero
- The tangential component of the velocity has a zero gradient in the direction normal to the boundary