Flows through sudden enlargement(expansion)geometries is an important point of study in the field of Fluid Mechanics because of its application in heat exchanger, Nuclear reactor, pipe lines and Dump combustor. Axis-symmetric sudden enlargement geometry looks simple but internal flow involves complexities such as separation and reattaching flows. Over decades many research have been carried by researchers on investigating steady and unsteady recirculating flows at high Reynolds number in both numerical and experimental methods.
Losses due to sudden expansion
Due to abrupt deviation of the boundary, it is unable to follow the flow emerging from the small pipe. Flow takes diverging pattern as it gradually reaches the expansion point causing turbulent eddies/vortex in the corners as shown in Fig.1 resulting in mechanical energy dissipation into inter-molecular energy.
Fig.1 Flow in sudden expansion pipe (finite enlargement)
Understanding the flow mechanism from Fig.1, the inlet velocity V1 will be higher compared to the outlet velocity V2 as a outcome of continuity. Due to low kinetic energy near the walls, the fluid particles cannot overcome the adverse pressure in the flow path and hence causing the reverse flow under pressure gradient (from p2 to p1). This creates recirculating zones near the walls of a pipe at sudden expansion cross sections resulting in loss of total mechanical energy.
The loss of head in such pipes can be derived by applying Bernoulli's equation for the control volume of horizontal pipe considering flow to be incompressible. The loss of head (hL) obtained is as shown in equation below.
where,
V1 and A1 are upstream velocity and cross-sectional area
V2 and A2 are downstream velocity and cross-sectional area
g is acceleration due to gravity
With these understanding, problem was defined for two-dimensional flow with axis-symmetry. Geometry, Meshing and Analysis were carried using commercial Computational Fluid Dynamics (CFD) software. The meshing of the fluid domain chosen structured quad mesh is as shown in Fig.2.
Fig.2 Quad mesh
The meshed model was set for iteration after applying necessary boundary conditions. The results obtained from the analysis is as shown in Fig.3, it highlights high velocity zones, development of flow at boundary layers and recirculating/vorticity zones.
Fig.3 (a) Velocity contour (b) Velocity vector (c) Stream function and (d) Vorticity magnitude
Also velocity at different locations are studied as shown in Fig.4, it shows the variation in the center-line axial velocity.
Fig.4 Center-line axial velocity
Like wise, other cross-sections (Fig. 5) can also be studied to understand the complex flow phenomena involved due to sudden change in cross sections in flow through pipes.
Fig.5 Simulation- Flow at sudden bends
Conclusion
Sudden expansion or enlargement flow through pipe is a benchmark problem every fluid-thermal engineers should understand in order to investigate and predict complex flow phenomena in any relevant engineering design. Over the decades, every scientist and engineer involved in fluid research studied this problem from fundamentals to advance which led to innovative systems/structures involving complex pipe designs with varying cross-sections. Problem at fundamental levels can be understood through analytical method with some assumptions in the flow but complex flows to be understood through experimentation and numerical techniques for accuracy.
For more understanding on the problem, visit below video links.
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