Optimizing the design of penstock manifold with 3D computational fluid dynamics (CFD) simulation

The geometry of the manifold is typically created in Inventor or Solidworks and is imported to Ansys. A proper mesh methodology is then applied to this geometry, which usually creates about 7 ~ 10 million elements, with the finer elements being in the critical areas for more details. In addition, an inflation mesh technique is used for the fluid volume near the pipe wall, which generates 10+ thin layers of elements within the boundary layer region to better capture the near wall flow performance (see Figure 1).

Model set up

The hydraulic model is based on the standard K-episilon turbulence model to capture the turbulence formations and the associated kinetic energy. This model is the most widely used engineering turbulence model for industrial applications. Various papers and researches have proven that this type of analysis is stable and robust. A scalable wall function is added to this turbulence model to increase model accuracy for the near wall / edge turbulence behaviour. The pipe walls are assigned with a proper roughness as per the liner specification. To account for the different scenarios during the operation (including the cases of partial closure of one or multiple units), the inlet (the pipe section before the manifold) and outlet (the pipe section that connects to the valve) boundary conditions are assigned with the associated flow rate, pressure, turbulence intensity and length scale.

Suspended sediment size and property in the river (if known) is also input in the model to simulate erosion inside the manifold. This sub-model is based on Iain Finnie’s theory on erosive wear for ductile material surfaces. The sub-model first calculates the number of particles, particle velocity, angle of impact and kinetic energy of the particles that will impact the pipe wall, based on the particle size and flow velocity field. It then calculates the amount of the surface material that will be removed during impact. Based on this model, the designer can identify the potential problematic areas for erosion issues and the erosion rate can also be obtained.

Figures 2 to 5 show some examples of model results.

Model validation

To validate model accuracy, aside from manual calculation, a series of sensitivity analyses is performed by changing one input parameter while keeping the rest of the parameters unchanged (see below). The results of the sensitivity cases are compared to the base model for difference.

Grid independent analysis

The mesh quality is important to the accuracy and convergence of the model, therefore, a grid independent analysis is carried out by checking the model with all unchanged parameters, except the meshing methodology and element size, which were varied. The mesh element quality is checked against orthogonality, aspect ratio, expansion rate and other criteria.

Turbulence models

A separate simulation using the Shear Stress Transport (SST) turbulence model is created to compare with the base case (i.e., k-ε turbulence model) for pressure distribution, velocity field, turbulence kinetic energy, etc.

Boundary conditions

Different boundary conditions are assigned to the model one at a time to see how sensitive the flow field will be with regard to a certain boundary condition. These sensitivity cases include varying flow rates at each of the turbines, changes in pipe roughness, changes in the size and amount of suspended sediment, etc.

In conclusion

CFD modeling is an efficient way to analyze the hydraulic performance of the penstock and other hydraulic structures / equipment (e.g., turbines, valves, etc.). It provides reliable and detailed information regarding the flow characteristics for the designer to optimize the geometry and improve hydraulic efficiency. It also predicts the erosion on the structure surfaces due to the suspended sediment in the river, which helps the designer address the long-term maintenance issue during the design stage.

Additionally, this CFD model can be coupled with a mechanical model (i.e., another numerical 3D model to analyze the stress and strain of the structure) of the manifold in Ansys. In that case, both the hydraulic model and mechanical model will share the inputs and results (i.e., the deformed shape of the structure from the mechanical model will be the geometry input for the hydraulic model, and the pressure distribution calculated from the hydraulic model will be input force for the mechanical model). Both models will run in parallel until they reach the convergence at the same time, which will reveal a more realistic structural and hydraulic behaviour of the manifold than if done separately. This fluid-structure interactive (FSI) model will be presented and discussed in another paper.