TITLE : 2D LAMINAR BACKWARD FACING STEP FLOW

BY : CHAM Development Team - M R Malin
VKI, Belgium - N P Waterson

FOR : Validation of Convection Discretisation Schemes

PROBLEM CONSIDERED:

• 2d steady, incompressible, laminar, backward-facing-step flow at Reynolds numbers of Re=150 and 450, where Re is based on 2h where h is the flow inlet height.

• This test problem is widely used for assessing the accuracy of numerical methods because of the dependence of the reattachment lengths on Re.

• PHOENICS Library Case N103

EXPERIMENTAL OBSERVATIONS:

• The flow has been studied experimentally by Armaly et al [1983], and numerically by many workers, including Gartling [1990], Gresho et al [1993] and Freitas [1995].

• Two cases are simulated by PHOENICS, namely Re=150 and Re=450.

• At Re=150, a primary recirculation zone develops immediately downstream of the step with reattachment at X1/H=4.2, where H is the step height.

• At Re=450, primary reattachment is at X1/H=9.5 and an additional separation cell forms on the upper wall of the channel, with separation at X2/H=7.6 and reattachment at X3/H=11.3.

• For Re>450, 3d effects become significant, and for Re >6,600 the flow is fully turbulent and 2d.

CALCULATION DETAILS :

• PHOENICS calculations are performed on a 32 by 200 mesh with 3 different discretisation schemes for convection: HYBRID, CUBIC UPWIND and VAN ALBADA.

• No grid refinement studies have been performed.

• The PHOENICS solutions are compared below with the data of Armaly et al [1983] in terms of the reattachment lengths:

  
          Re=150     Data   Hybrid  Cubic-Upwind  Van-Albada
            X1/H      4.2    4.17       4.24        4.25
          Re=450
            X1/H      9.5    8.79       9.13        9.06
            X2/H      7.6    7.66       8.26        8.09
            X3/H     11.3   11.14      11.39       11.52
            DX/H      3.7    3.48       3.13        3.43
  

  1. Laminar Backward Facing Step, Velocity Vectors & Streamlines; cubic upwind scheme
  2. Laminar Backward Facing Step, Velocity Vectors & Streamlines; van Albada scheme