Hafiz bin Haji Khozali, Muhammed (1981). Computer aided mathematical modelling of turbulent flow for orifice metering. (Unpublished Doctoral thesis, The City University)

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Abstract
The timeaveraged NavierStokes' partial differential equations have been used in the mathematical modelling of fluid flow for steady, incompressible noncavitating, high Reynolds number turbulence through an orifice plate. The model developed for orifice plates was based on a particular closed form turbulent model: the kε two equation model developed at Imperial College, London and embodied in the TEACHT finite difference computer code. A basic model for axisymmetric flow through an orifice meter was developed by appropriate modification of the TEACHT program to incorporate orifice plate geometry, upstream/downstream distances, Reynolds number, inlet velocity profile and the calculation of output quantities of interest such as discharge and pressure loss coefficients. The model vas tested for convergence and general adequacy on an orifice of diameter ratio β= .7 in a 4 inch pipe line and at a Reynolds number of 105. Quantitative tests were then conducted on thin orifice plates in the range .3 β .7. Results were compared with those from BSI 1042 for discharge coefficients (flange, DD/2 and corner tappings) and published results for pressure loss coefficients.
The results show that the discharge coefficients predictions are within 3% of experiment with very close agreement in the midrange (β = .45). The pressure loss coefficients predictions are within 15" of experiment.
Sensitivity tests were then conducted to see how these coefficients varied with such quantities as inlet velocity I profile, turbulence levels and orifice plate thickness. These results indicated that the orifice is relatively insensitive to velocity profiles (1/12 power law and uniform) and. turbulence levels. Also below a certain orifice plate thickness ratio the discharge coefficient is almost constant.
It is concluded that such modelling can be a most valuable aid in understanding the behaviour of the orifice meter and similar devices. In particular this would aid in the design of novel flow meters based on the differential pressure principle.
Extensive mathematical and computational details including the derivation of the kt model equations from first principles are relegated to appendices. A source listing of the developed model is also provided in appendix G.
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