Fig. 1 Geometry of the stationary two-dimensional laminar channel flow.
Keywords
Stationary laminar flow, air, velocity profile
Purposes
• Validation of momentum diffusion and gravitational terms in the momentum equation of GASFLOW.
• Convergence of numerical finite-difference solution with analytical solution of the appropriate partial differential equation.
Descriptions
• Stationary two-dimensional laminar channel flow of incompressible fluid (air) with constant viscosity between two vertical parallel plates. The flow is driven by gravity only.
Fig. 1 Geometry of the stationary two-dimensional laminar channel flow.
Analytical solution
• The analytical solution is obtained from integration of the partial differential equation for the momentum flux by considering only the instationary, the convective, and the gravitational term. Pressure gradients and dissipation are neglected. These assumptions result in
• Initial and boundary conditions are
w= 0 at 0 ≤ y ≤ H, t = 0
w = 0 at y = 0, t > 0 and y = H, t > 0
• The closed solution is
Numerics
• Grid: 2d, Cartesian grid in y-z direction, 1 x 33 x 25 numerical cells, (4 x 8 x 100 cm)
• Boundary condition: zero velocity at the walls.
Results
• The analytical and numerical results are compared in Fig. 2.
Fig. 2 Stationary air flow between two parallel plates with
a) plot of the analytical velocity profile w(y) and
b) comparison of numerical GASFLOW solution with analytical result
Conclusions
• Very good agreement was obtained between the analytical solution and the numerical simulation for the stationary velocity profile in the channel. 33 numerical cells across the channel were sufficient.
• The GASFLOW momentum balance was validated for this particular case with known closed analytical solution.
Reference
W. Breitung, et. al; Innovative Methoden zur Analyse und Kontrolle des Wasserstoffverhaltens bei Kernschmelzunfällen, Report FZKA 7085, Forschungs-zentrum Karlsruhe, Wissenschaftliche Berichte (Febr. 2005), full text available under http://bibliothek.fzk.de/zb/abstracts/7085.htm