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We will assume that the flow is axisymmetric. This means that in cylindrical coordinates (r, θ, z), there is no variation in the circumferential direction (θ). So the geometry in the simulation is a rectangle as shown below. Revolving the rectangle 360 degrees about the axis gives the full 3D pipe geometry. We need to solve a boundary value problem. The governing equations for this problem are conservation of mass, conservation of momentum (in r and z directions), and conservation of energy. The governing equations and boundary conditions are shown below. We will solve this boundary value problem numerically using the ANSYS FLUENT solver.

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