Fourth International Conference on CFD in the Oil and Gas, Metallurgical & Process Industries SINTEF / NTNU Trondheim, Norway 6–8 June 2005 PREDICTION OF TWO-PHASE PIPE FLOWS USING SIMPLE CLOSURE RELATIONS IN A 2D TWO-FLUID MODEL Svend Tollak Munkejord 1∗ Mona J. Mølnvik 2 Jens A. Melheim 1 Inge R. Gran 2 Robert Olsen 1 1 Norwegian University of Science and Technology (NTNU), Department of Energy and Process Engineering, Kolbjørn Hejes veg 1A, NO-7491 Trondheim, Norway 2 SINTEF Energy Research, Energy Processes, Kolbjørn Hejes veg 1A, NO-7465 Trondheim, Norway ABSTRACT This paper presents a comparison of pressure drop and liquid hold-up as calculated using different modelling strategies; a two-dimensional two-fluid model, a one- dimensional simulator, and engineering correlations. The numerical results are compared with experimental data. In- terestingly, the two-dimensional two-fluid model performed well, using simple constitutive relations being functions of the local flow conditions. In the present work, a two-fluid model has been imple- mented in the framework of a two-dimensional multiphase Computational Fluid Dynamics (CFD) code. The govern- ing equations were spatially discretized using the finite- volume technique, and the time-integrator was an explicit low-storage five-step fourth-order Runge-Kutta scheme. Numerical results from the present program, the OLGAS simulator, the Beggs and Brill correlation, and the Friedel and the Premoli correlations have been compared to 52 data points from the TILDA two-phase pipe flow database at the SINTEF multiphase flow laboratory. The data were taken in a 0.189m inner-diameter pipe. The liquid volumetric flux j ℓ varied between 0.1 and 1.0m/s, the gas volumetric flux j g was in the range from 0.5 to 12m/s, and the pressure p ranged from 20 to 90bar. Inclination angles of 0 and 1° were used, with the majority of the data coming from the horizontal pipe. We find it interesting to note the relatively good corres- pondence between experimental data and the computed res- ults of the CFD program, particularly when considering the simple constitutive relations employed. Keywords: multiphase flow, pipe flow, computational fluid dynamics (CFD), closure relations, pressure drop, li- quid hold-up, explicit scheme NOMENCLATURE Latin letters A Area m 2 A Control surface m 2 B k Displacement factor – C Friction parameter, see equation (14) m −1 C µ , C 1 , C 2 Constants in the k -ε turbulence model – c Speed of sound m/s d Diameter m * Corresponding author. E-mail: stm (a) pvv.ntnu.no E Constant in wall function – F Force per unit volume N/m 3 f Body force field m/s 2 h Channel height m I Unitary tensor – j Volumetric flux (superficial velocity) m/s k Turbulence energy m 2 /s 2 N Number of data points – δn Normal distance from wall m n Unit normal vector m P k Production rate of turbulence energy m 2 /s 3 p Pressure Pa δ p Local pressure variation, see equation (6) Pa Re Reynolds number – t Time s T k,w Wall-function variable, see equation (29) Pa · s/m u Velocity vector m/s V Volume m 3 V Control volume m 3 x Length coordinate m y + Non-dimensional distance from wall in turbulent shear layer – y + 0 Constant in wall function – Greek letters α Volume fraction – α ℓ Liquid hold-up – ε Dissipation rate of turbulence energy m 2 /s 3  Friction factor between phases k and l , see equa- tion (13) – Ŵ Mass source kg/(m 3 s) κ Constant in wall function – µ Molecular viscosity Pa · s µ T Eddy (turbulent) viscosity Pa · s ρ Density kg/m 3 σ Turbulent Prandtl/Schmidt number – τ w Wall shear stress Pa τ Stress tensor Pa ψ General variable – Subscripts d Drag – 1