A Reynolds Average Navier-Stokes Solver for Unsteady Closed Conduit Flows

A new two-dimensional Reynolds Average Navier-Stokes (RANS) solver for transient flow is presented. The model was tested for laminar and turbulent flow conditions. Four two-equation turbulence models for smooth and rough pipes were used to solve for the Reynolds stresses. The new model allows determination of detailed flow properties during unsteady flow.

The turbulent models considered were:

• Standard k-ε
• Standard k-ω
• Low Reynolds Number k-ω (LRN k-ω)
• Low Reynolds Number k-ε. (LRN k-ε)

The model solves the axisymmetric RANS equations using the finite volume method with staggered grid and SIMPLE, SIMPLEC or SIMPLER algorithms for pressure correction. Upwind, power law and hybrid numerical schemes were tested. The model was tested for the following flow conditions:

• Starting laminar flow.
• Pulsatile laminar flow.
• Pulsatile turbulent flow.
• Periodic laminar flow
• Periodic turbulent flow
• Laminar waterhammer flow
• Waterhammer flow in a transitionally rough pipe

The log profile was used for smooth pipes and Van Driest velocity distribution was used for smooth and rough pipes with k-ε models. The model results were compared with analytical and experimental data.

k-ε performed better for steady and pulsatile flow without a strong adverse pressure gradient. k-ε, k-ω and LRN k-ω, were able to simulate turbulent flow with reverse velocities. k-ω and LRN k-ω proved to be more robust for these conditions.

The three numerical schemes (upwind, power law and hybrid) performed very well when compared with the analytical solutions; however, the hybrid scheme performed best.

The RANS model provided good results tracking the pressure damping in a transitionally rough pipe combined with rapid downstream valve closure. SIMPLEC and SIMPLER provided identical results for this case. Similar results were obtained with time-varying and freeze eddy viscosity conditions.

The model will be used to increase understanding of boundary layer development during waterhammer flow events, friction velocity evolution and the relation between turbulent structure, energy dissipation, and wall shear stress. In general, any fluid variable as a function of the primitive variables, such as the velocity components and the pressure field, can be computed.