Separated Laminar Flow Over a Blunt Plate

In this application, AcuSolve is used to simulate the separation of laminar flow over a blunt plate. AcuSolve results are compared with experimental results as described in J.C. Lane and R.I. Loehrke (1980). The close agreement of AcuSolve results with the experimental results validates the ability of AcuSolve to model cases with external laminar flow including separation.

Problem Description

The problem consists of external, laminar flow over a blunt plate 1.5 m long and 0.09 m thick, as shown in the following image, which is not drawn to scale. The fluid flows with a uniform horizontal velocity (v) of 0.045133 m/s. The fluid material used for the simulation has a density of 1.0 kg/m3 and a dynamic viscosity of 1.7894 X 10-5 kg/m-s. The resulting Reynolds number for the flow, based on the plate thickness, is approximately 227. This indicates that the flow over the plate is laminar. As the fluid flows past the leading edge of the plate, the pressure decreases, resulting in a separation region downstream of the leading edge. At some distance downstream from the leading edge, the pressure gradient decreases, and viscous forces cause the recirculation zone to dissipate, allowing the flow to reattach to the plate.
The simulation was performed as a two dimensional problem by constructing a volume mesh that contains a single layer of elements in the extruded direction, normal to the flow plane, and by imposing symmetry boundary conditions on the extruded planes. In addition, the half symmetry of the geometry was exploited to allow for modeling only the top half of the geometry. These characteristics allow for accurate simulation of the flow while minimizing computational time. The following images show the mesh distribution and a refined mesh zone around the blunt plate.

AcuSolve Results

The AcuSolve solution converged to a steady state and the results reflect the mean flow conditions over the blunt plate. The flow velocity is reduced to zero at the leading face, forming a stagnation point at the center. The flow reaches a maximum velocity as it flows around the leading edges and separates from the plate. Flow separation (shear stress parallel to the wall becomes negative) occurs downstream of the leading edge, leading to a recirculation zone. The flow reattaches 0.37 m downstream of the leading edge. The velocity in the laminar boundary layer increases from zero at the wall to free-stream velocity at the boundary layer edge. Along the plate length, the boundary layer slowly grows in thickness. The following image shows the contours of the flow velocity parallel to the streamwise direction and the recirculation region in the wake of the plate edge.

Downstream of the leading edge, the flow eventually reattaches to the plate at the point where the shear stress parallel to the wall passes from negative through zero to positive. The reattachment point is 0.37 m from the leading edge of the plate and corresponds to the trailing edge of the contours.

The results for the predicted and experimental reattachment length (xreattach) are presented in the table below. T represents the plate thickness.
Table 1.
AcuSolve xreattach AcuSolve xreattach/T Experimental xreattach/T Percent error (%)
0.37 4.11 4.0 2.8

Summary

In this application, a constant flow inlet velocity and symmetric boundary conditions were used to model 2D flow over a blunt plate. The AcuSolve solution compares well with experimental results for the separation of laminar flow over a blunt plate. The non-dimensional reattachment length obtained from the AcuSolve steady state solution compares well with the experimental solution, with an error of less than 3.0 percent. The results of this simulation validate the ability of AcuSolve to accurately predict the reattachment point in cases with external, laminar flow with separation.

Simulation Settings for Separated Laminar Flow over a Blunt Plate

HyperWorks CFD database file: <your working directory>\blunt_plate_laminar\blunt_plate_laminar.hm

Global

• Problem Description
• Analysis type - Steady State
• Turbulence equation - Laminar
• Auto Solution Strategy
• Relaxation Factor - 0.2
• Material Model
• Fluid
• Density - 1.0 kg/m3
• Viscosity - 1.7894e-005 kg/m-sec

Model

• Volumes
• Fluid
• Element Set
• Material model - Fluid
• Surfaces
• Back
• Simple Boundary Condition
• Type - Symmetry
• Freestream
• Simple Boundary Condition
• Type - Slip
• Front
• Simple Boundary Condition
• Type - Symmetry
• Inlet
• Simple Boundary Condition
• Type - Inflow
• Inflow type - Velocity
• Inflow velocity type - Cartesian
• X Velocity - 0.045133 m/s
• Outflow
• Simple Boundary Condition
• Type - Outflow
• Plate
• Simple Boundary Condition
• Type - Wall
• Symmetry
• Simple Boundary Condition
• Type - Symmetry

References

J.C. Lane and R.I. Loehrke. "Leading Edge Separation from a Blunt Plate at Low Reynolds Number". Journal of Fluids Engineering. 102(4):494-496. 1980.