TITLE : 3D TURBULENT GAS FLOW IN AN ELBOW METER

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

Date : 1997 PHOENICS Version: 3.1

FOR : THE GAS INDUSTRY

THE PROBLEM CONSIDERED:

• 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 PROBLEM CONSIDERED (contd):

• 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.

FLOW DETAILS:

• 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.

FLOW DETAILS (contd):

• 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.

COMPUTATIONAL DETAILS :

• 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.

RESULTS:

• 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 degrees

  wbs