BY : CHAM Consultancy Team: - M.R.Malin

Date : 1997 PHOENICS Version: 3.1

FOR : THE GAS INDUSTRY

- The flow of natural gas through an elbow meter located in a
gas-transmission pipeline.
- Elbow meters are often used in the gas industry as a flow-metering
device when access to the pipeline is difficult, as for example in
a compressor station.
- The elbow meter exploits the basic principle that the mass flow rate through the pipe elbow is proportional to the pressure difference between the inside and outside of the pipe bend.

- The purpose of the present calculation is to compute the pressure
differential across the pipe bend for the specified mass flow rate.
- The resulting pressure differential is then compared with that
given by the flow-rate vs pressure-difference correlation used in
the gas industry.
- The measuring station is located 22.5 degrees into the pipe elbow.

- 3D steady, incompressible, isothermal, turbulent flow
- The inlet Reynolds number is 3.52E7. The pipe diameter is 0.89m, and the pipe bend is a sudden contraction with a diameter of 0.874m and a mean radius of curvature of 1.315m.

- The supply pressure is 44 bar, the fluid density is 35.35 kg/m^3, the volumetric flow rate is 8.57m^3/s, and the bulk velocity in the pipe elbow is 14.29m/s.

- The turbulence is represented through use of the standard k-e
model plus wall functions.
- The calculations use a curvilinear BFC mesh with 20 circumferential,
35 radial and 54 streamwise grid cells.
- The GCV solver option is used with Cartesian-velocity components
selected as dependent variables.
- The MINMOD scheme is employed for the discretisation of the convection
terms.
- The Q1 for this case can be found in the BFC input library.

- The predicted pressure differential at the measuring station is
about 54mbar, which is in excellent agreement with the value
given by the correlation used in the gas industry.
- Flow in a curved bend is characterised by secondary flow in planes
normal to the streamwise flow direction. The secondary flow is
driven by radial pressure gradients which are caused by the
centrifugal forces associated with lateral curvature of the
streamwise flow.
Pictures as follows

Computational Grid

Velocity vectors at the symmetry plane

Pressure contours at 22.5 degrees

Pressure contours at the symmetry plane

Pressure contours at the symmetry plane

Streamwise velocity contours at 22.5 degrees

Velocity vectors at 22.5 degreeswbs