• Fluid mechanics

• Three-dimensional flow in a curved pipe

      A curved pipe of 180 degree with its radius of 0.5 cm and the curvature radius of the pipe is 2.5 cm. The fluid 
                          parameters are: viscosity = 0.04 g / cm · s， density = 1.0 g /cm³ . Initial condition:velocity and gauge 
                          pressure are equal to 0. Boundary condition:inlet velocity  = cm/s，  = . On the tube wall，     
                          , outlet pressure (gauge) is 0. The flow field and the pressure in the pipe are to be solved. This 
                          example shows that a convection-predominated flow problem can be well solved in FEPG by using   
                          operator-splitting technique.
                          The controlling equations include:

      Momentum equation:

      Continuity equation:

      where  is the velocity vector,  and  are the velocity components in the axial and radial directions,  
                          respectively.  is the fluid density,   is the fluid viscosity,  is the body force,  is the pressure.

                          The problem is solved by use of fractional step approach:
                           1.First, solve the Navier-Stokes equation without the convection term;

                           2.Then solve the equation with convection term.

                                      
                          Result:

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