1. Flow Through a Pipe Elbow (Comsol)
CHEM-E Fluid Flow in Process Units, Project Work
Flow Through a Pipe Elbow (Comsol)
Shahid Sarfraz
James Kabugo
May 15, 2017

2. Contents Introduction Model geometry (in Comsol)
Results and validation
Conclusions

3. Introduction: Pipe elbows
Highlighted part was not included in this study!!
Introduction: Pipe elbows
Commonly applied pipe elbows include:
45° bends, 90° bends and 180°bends
Mainly applied to purposely to change the direction of flow in the pipe (e.g. in pipe connections, cooling coils, e.t.c)
Shortcomings:
Notable pressure losses or head losses in the pipe line
In somes cases pipe elbows are more susceptible to corrosion or erosion than equivalent straight pipes.
In this study, a 90° pipe elbow (circular) based on the given Figure (on the right) was studied.
Ref. Homicz (2004)

4. Introduction: Flow through a 90° Pipe elbow
Dean’ vortices
Flow separation
Pressure losses
Ref. Homicz (2004)
Ref. Jayanti (Thermopedia)

5. Parameters& Assumptions
Single-phase turbulent flow in circular pipe elbow
Incompressible fluid: water at 90° C &absolute pressure of 20 bar
Isothermal conditions
Fully turbulent flow at the pipe inlet (Average velocity of 5 m/s)
Fluid density of kg/m3
Dynamic viscosity, 3.145× 10 −4 Pa.s
Symmetry of the x-y plane

6. Modeling methodology The model was divided into two study parts:
Study 1, a 2D axis symmetry model (2D pipe of 3.55 m length i.e. 100 *D & width of D/2)
Study 2, a 3D elbow geometry
Study 1 results were mapped onto to the inlet of the 3D pipe elbow (initial inlet boundary conditions)
Use of turbulent flow model with wall functions
k-ω model was selected according to the tutorial
Other models: k-𝜀 model, Low Reynolds k-𝜀 model & SST model were tested
Model testing with use of coarser mesh and different COMSOL discretization methods

7. Pipe Elbow Model Geometry &Mesh
Geometry of the 90° pipe elbow. Ref. (Comsol)
Meshed geometry of the 90° pipe elbow.

8. Results: Wall Resolution
Study 1: wall lift-off in viscous units (below units!)
Study 2: wall lift-off in viscous units (below 100 units!)
Study1: Turbulent viscosity along the symmetry axis (constant before the inlet!)

9. Results: Velocity field & pressure at 45° cutplane

10. Results: effect of coarser mesh
Wall lift-off in viscous units is above 100 units!
Flow at the walls not well resolved!

11. Results: effect of changes in the average inlet velocity
Study 1: Wall resolution for 10 m/s (above units!)
Study 1: Wall resolution for 2.5 m/s ( acceptable at units)

12. Results: other turbulence models &Discretization
k-𝜀 model perfomed fairly similar to the k-𝜔 model
Low Reynolds k-𝜀 model did not converge
No results obtained in the case of the Shear stress transport (SST) model
No significant differences between P2+P1 and P3+P2 COMSOL fluid flow discretization methods

13. Validation of numerical results
Ref. Homicz (2004)
Ref. Homicz (2004)

14. Validation of numerical results
Determination of the diametrical pressure coefficient: estimated at 45° of pipe elbow.
𝑐 𝑘 = 𝑝 0 − 𝑝 𝑖 𝜌 𝑈 𝑎𝑣𝑔 2 =1.55
Compared to an empirical correlation below for bends with curvature ratio, 𝑅 𝑐 /𝐷>2. Note here, 𝑅 𝑐 𝐷 =1.41
𝑐 𝑘 = 2𝐷 𝑅 𝑐 = (𝑓𝑜𝑟 𝑅𝑒>5× 10 5 )
Estimation of the friction factor from the pressure drop and comparison with empirical correlations.
𝑓 𝑓 = ∆𝑝 2𝜌 𝑈 𝑎𝑣𝑔 2 𝐷 𝐿 =7.45× 10 −3
𝑓 𝑓 = 𝑅𝑒 𝐷 𝑐 𝐷 =7.26× 10 −3
Note: evaluated at half way through the bend i.e. at 45°!
Correlation for friction factor through a curved pipe (noted accuracy of ±15%!).

15. Conclusions
Higher pressure development on the outer wall of the curvature
Increase in flow velocity and maximum velocity observed along the centerline
Formation of two counteracting vortices (swirling behaviour)
Separation of the flow as it leaves the pipe elbow
Pressure or head losses are experienced in the pipe elbow
With a coarser grid, flow near the walls was poorly modeled