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The Most Common Boundary Condition in a CFD Analysis

Figure 1. A representative internal flow domain for CFD consulting
July 31, 2015 By: Hsin-Hua Tsuei

Mathematically, The Navier-Stokes equation is a boundary value problem.  In a CFD analysis, we need to assign many boundary conditions to “define” how the system operates.  Out of many boundary condition types (inlet, outlet, wall, symmetry, etc.), a wall boundary condition is without a doubt the most commonly used boundary condition in a CFD analysis.  Why, you ask?

For external flow analysis, the wall boundary condition represents the intrusive object’s surface in the middle of the flow domain. For example, analysis of flow over an airplane, a car, etc., may require hundreds, if not thousands of surfaces, to define the complex shape and curvature of the object of interest. Each surface requires a wall boundary condition associated with it. 

Internal flow analysis is often performed on complex flow passages in a system. The flow domain is the volume and gaps among solid objects. The internal flow domain is therefore comprised of many oddly shaped flow regions.  The external boundaries of these regions are walls, which include hundreds of surfaces. As shown in Figure 1, the internal flow domain of interest has 1 inlet, 1 outlet, and 201 external walls.  Compared to inlet or exit boundary condition used (like one inlet and one outlet for internal flow), the wall boundary conditions certainly outnumber the rest by a large margin.

When it is required to assign several hundreds of wall boundary conditions for each CFD analysis, it becomes a time-consuming process and is prone to human error.  Because of this reason, most commercially available CFD solvers, such as ANSYS Fluent and CFX, have made the wall boundary condition the default boundary condition. This means all boundary surfaces are assigned as a wall unless it’s been changed to another condition (inlet, exit, etc.). The default wall boundary condition feature saves the user a lot of time, and has made the CFD model development process more efficient. By the way, the default wall boundary condition really means a viscous no-slip wall, because most real world engineering applications deal with viscous flows. If you are interested in analyzing an inviscid flow (which is more likely used in academia when developing a new numerical algorithm for the non-linear convective terms in the Navier-Stokes equation), make sure to check, or modify the default wall boundary condition to apply a slip wall situation instead of using the default no-slip condition.

If the energy equation is a part of the analysis, then the default wall boundary condition is extended to include a zero heat flux condition for heat transfer. This means the default wall is adiabatic, or fully insulated, which does not allow any form of heat in and out from this location.  If a wall boundary condition other than the default no-slip adiabatic wall is required, a specific boundary condition has to be applied to that particular location.  These may include specified wall temperature, wall heat flux, wall heat transfer coefficient, or coupled-wall to represent a fluid-solid interface in a Conjugate Heat Transfer (CHT) analysis.  If radiation is part of the heat transfer, then the default wall boundary will include variables such as emissivity, which is determined by the wall material.  For example, an aluminum wall has a different emissivity than a concrete wall, leading to a different wall temperature distribution. 

Therefore making sure the default wall boundary condition is properly modeled is essential in a CFD model. Any mistake will be amplified (simply because there are so many of them) to render a potentially misleading result.