Boundary Conditions

What is physical and mathematical significance of a boundary condition?

The boundary conditions of any problem is used to define the upper and lower limits of the field variables (albeit in absence of any source or sink). Basically, they are the operating conditions which governs both the micro- and macro behavior of these variables. A suitable choice of boundary conditions is as good as a good test set-up!

There are different (combination) of boundary conditions. For example, in a structural simulation, the number of boundary conditions can be varied to ensure the force- and moment balance of the entire system. This can be achieved by applying boundary condition at just one node or at 6 different nodes! Similarly, in any fluid problem, there must be an entry and an exit for the fluid (as an exception buoyancy-driven flow can be omitted for the time being). This most basic condition is termed as "Inlet" and "Outlet" boundary conditions in CFD parlance, though the choice of "field variables" such as velocity, pressure, temperature, mass flow rate, may vary as per problem set-up.
  1. Inlet: This is the 1st member of the pair of boundary conditions which are must for any CFD calculations. The primary consideration of an inlet B.C. is to select between the Mass Flow , Static Pressure and Total Pressure based on the actual information available about the operating conditions of the system and robustness of the solver, (the matrix inversion) algorithm which keeps running till solution is achieved. While tempting to use velocity inlet B.C. care needs to be taken to account for change in cross-sectional area when an arc is represented by a set of connected lines. Some other considerations during application of Inlet B.C. is "Fully Developed Flow" Vs "Developing Flow". For example, if you are a beginner learning tips and trick of CFD by trying to simulate HTC and correlating it with Dittus-Boelter equation, make sure that the flow regime is fully developed. Sometimes, the inlet of the problem set-up is moved upstream the actual location to get the flow a bit developed. Specification of turbulence parameters (turbulent kinetic energy, TKE and turbulent eddy dissipation, TED) should be based on actual measurement of as far as possible. When there are any source of momentum such as centrifugal fan in the computation domain or sharp edges , the overall result gets affected by the turbulence set at the inlet. Followings are the method to specify turbulence:
    • Specify TKE [m2/s2] and TED [m2/s3] explicitly
    • Turbulent Intensity [%] and Turbulent Viscosity Ratio (TVR) [-]
    • Hydraulic Diameter [m] and Turbulent Intensity [%]
    • Turbulent Intensity [%] and Length Scale [m]
  2. These requirements on turbulent parameters further depends on flow type: external or internal. The length scale 'L' For external flows is typically the length scales along the flow direction.
    • External Flows
      • Length Scale = 0.07 x L
      • Turbulent Intensity: Based on upstream condition
      • Turbulent Viscosity Ratio: 1 < TVR < 10
    • Internal Flows
      • ~ Length Scale = Hydraulic Diam.
      • Turbulent Intensity: 0.16 x Re-1/8
      • Turbulent Viscosity Ratio: 1 < TVR < 10

Wall Boundary - What is physical and mathematical significance?

Walls are required to store a liquid or contain the expansion (mixing) of gases. Since all the fluid flow has to be contained inside walls or at least in a channel, wall B.C. is natural extension into the numerical simulation process. Wall are not only the source of 'turbulence' that gets generated in the flow domain, its surface characteristics becomes important if certain assumptions gets violated. In any CFD software it is not necessary to create 'named' 2D regions for the walls. This is because any faces of a 3D region which do not explicitly have a 2D region assigned to them, are automatically assigned to the default B.C. 'wall' having 'Adiabatic' condition. In case one wishes to create walls such as "Isothermal / Rotating / Heat Flux Wall", it must be created during the pre-processing. Typically, there is no flow across the wall boundary conditions. However, in case of permeable or porous walls, flow does occur across the wall. Similarly, in case of suction or blowing (for example transpiration cooling in Gas Turbine Blades), the mass flow rate specifications are required on the wall boundary conditions. Typical classification of wall B.C. is:
  • No-slip: Velocity of fluid at wall boundary is same as fluid velocity.
  • Free slip: Velocity component parallel to wall has finite value (computed by the solver), but the velocity normal to the wall & shear stress both set to zero. Zero gradients for other field variables are not enforced in slip wall conditions.
  • Wall Roughness: Walls are assumed to be hydraulically smooth so long the "sand roughness height" is inside the Laminar Sub-layer. Roughness is also called "Rugocity". Typically roughness is caused by small protrusions over the mean surface of a manufactured component. Any such "technical roughness" can be converted into a "equivalent sand roughness".
  • ks = Sand Roughness Height, k+ = ks/dv = ks . uτ / n where dv is characteristic height of Wall Layer.
  • ks >> dv: In this case roughness element take up all of the wall layer and hence the viscosity is of no further importance (also call "Fully Rough Regime" where flow is independent of Reynolds Number.
  • ks < 5. dv: Here roughness elements are still completely within the purely viscous sub-layer and the flow can be assumed to be "hydraulically smooth", that is, there is no difference as compared to the ideal smooth surface.

Periodic Boundary Conditions

Strictly speaking, this is not a boundary condition. That is, any numerical simulation can proceed without it. However, this is a great tool to reduce the computational effort and resource if the flow can be envisaged to be symmetrical about a plane or pair of planes. It must be noted that there is a subtle difference between geometrical symmetry and periodicity. Periodic interfaces are treated as if one side of the interface has been translated or rotated to align with the second side of the interface. The periodic type determines the type of transformation (translational or rotational) used to map one side of the interface to the other.
  • They must be in pairs.
  • They have to be physically identical.
  • There is a symmetry. But, unlike a symmetry BC, there is a flow normal to the BC
  • The flow field in at one BC is equal to the flow field out at the other
  • Types of periodic boundaries
    • Transnational Periodic BC: In this case the two sides of the interface must be parallel to each other such that a single translation transformation can be used to map Region List 1 to Region List 2. Flow around a single louver in a whole array in a heat exchanger fin is an example
    • Rotational Periodic BC: In this case the two sides of the periodic interface can be mapped by a single rotational transformation about an axis. Flow domain through an Axial Flow Fan can be reduced using rotational periodic B.C. Rotational Periodic Boundary

Symmetry Boundary Conditions

Strictly speaking, this also is not a boundary condition. That is, any numerical simulation can proceed without it. However, this is a great tool to reduce the computational effort and resource if the flow can be envisaged to be symmetrical about a plane or pair of planes. It must be noted that the geometrical symmetry does not guarantee symmetry of the flow. Similarly, cases where micro-structure of flow eddies are being captured such "Large Eddy Simulation" or "DES – Detached Eddy Simulation", symmetry cannot be used owing to inherent 3D nature of the eddies.
  • By definition, a symmetry BC refers to planar boundary surface. If 2 surfaces which meet at a sharp angle & both are symmetric planes, set each surface to be a separate named boundary condition, rather than combine them into a single one.
  • Velocity component normal to the Symmetry Plane Boundary = 0. Scalar variable gradients normal to the plane is also =0
  • If a particle reaches symmetry plane, it is reflected back.
  • Symmetric geometry doesn't necessarily imply that the flow field is also symmetric. For example, a jet entering at the centre of a symmetrical duct will tend to flow along one side above a certain Reynolds number. This is known as the Coanda effect. If a symmetry plane is this situation, an incorrect flow field will be obtained.

CFX Recommendation on pair - combination of boundary conditions

Solver Behaviour Inlet Outlet
Most Robust Velocity or Mass Flow Rate Static Pressure
Somewhat Robust Total Pressure Velocity or Mass Flow Rate
Sensitive of Guess (Initialization) Total Pressure Static Pressure
Unreliable Static Pressure Static Pressure
Not possible (divergence guaranteed) Any Total Pressure

CFX Recommendation on pair - combination of boundary conditions

Solver Behaviour Inlet Outlet
Most Robust Velocity or Mass Flow Rate Static Pressure
Somewhat Robust Velocity or Mass Flow Rate Outflow or Outlet-vent
Only for incompressible flows Velocity Inlet Outflow
Not available Any Mass Flow Rate
Not for compressible Specified Velocity Any


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