Multiblock Meshing of Ship Propeller

Figure 1: Structured multi-block grid for a ship propeller.

1319 words / 7 minutes read

Quest for Improvement

Ships are considered to be the most efficient mode of transportation for every unit load carried. And yet, there is a constant drive to increase ship energy efficiency by bringing in newer design modifications. This quest to improve energy efficiency is not just for achieving reduced fuel costs and operational expenses but also for environmental benefits.

Marine Propeller design has a major role in dictating the propulsion efficiency in ship systems. Designed with the objective of converting rotational velocity to useful thrust, propeller blades come in all shapes and sizes depending on the load and performance required.

Ever since their conception, researchers have focused on maximizing the energy efficiency potential of the propellers by introducing newer design modifications. These iterative improvements have led to large variations in designs for a wide range of application cases.

In the initial phases of propeller development, designs were solely based on open-water tests using prototype models. Later, empirical models were introduced which enabled designers to predict the performance of design variants without actual experimental runs. However, though very handy, empirical methods do not generate correct results consistently.

Next, numerical methods based on potential theory became the popular tool to investigate the flow around propellers. However, since the last decade, RANS-based solvers have become the work-horse for propeller performance predictions.

Meshing Ship Propellers

The capabilities of the CFD tools have improved immensely with time. Yet the main ingredient which dictates the success of a CFD simulation is still grid type and quality.

Ship propeller blades with geometric complexity of high rake and pitch, pronounced curvatures at the edges and tip, and pose many challenges to generate good quality structured grids for most multi-block grid generators. As a consequence, many steer away from structured grid-generators and opt for unstructured approaches like hybrid meshing, polyhedral, cartesian, etc. Though well aware of the fact that unstructured grids introduce diffusivity leading to less accurate solution prediction, a larger section of the CFD community relies on them. This is quite understandable as less learning effort, ease of grid generation, and semi-automatic nature of hybrid mesh generation make them more attractive.

But, if the engineers want to make a detailed investigation with a focus on local flow studies, then the structured approach is the penultimate solution. Mesh type has an appreciable effect on simulation results. Difficulties in generating structured grids are easily eclipsed by significant benefits like – better geometric feature capturing with minimal cells, augmentation solver robustness, simplification of numerical calculations, which lead to a noticeable reduction in overall computational time.

Another significant reason why CFD practitioners choose a structured approach is that it is much more conducive to performing systematic grid convergence studies. Once the base topology is created, it is very easy to generate a family of grids that are systematically refined and geometrically identical. Computational error estimates obtained using a series of structured grids are far more accurate than those obtained from unstructured grids.

The pain point of building topologies for complex geometries is considerably reduced by the dynamic boundary conforming concept in GridPro. Users can handcraft the blocks around the geometry and rapidly fill the domain. Finer blocks can be placed with ease at critical locations by tools like Enriching, while tools like Nesting help to rapidly coarsen out as we move away towards the domain boundaries. In a way, the options in GridPro bring home the best in both structured and unstructured approaches.

The following sections present abridged steps to mesh ship propeller blades using GridPro.

**Figure 2:** Surface mesh for a ship propeller blade.

General Steps in Meshing Ship Propellers by Structured Multi-Block Approach

There are different approaches to meshing a propeller blade in GridPro. It can be a bottom-up approach or a top-down approach or a hybrid approach combining both. For simpler blades, the top-down approach could be handy, while for blades with a high twist or skew the bottom-up or the hybrid approach may be more appropriate. We have addressed the two approaches here. 1. The section below presents the bottom-up approach with a series of steps and, 2. A video demonstration of a hybrid approach.

Bottom-Up Approach

Figure 3: 2D profile grid: a. Sheet view. b. Isometric view of 2 sheets w.r.t blade.

2D Profile

Multi-block meshing for the ship propeller blade starts with constructing a 2D topology. Propeller blades pose a challenge to mesh due to the pitch, rake, and skew of the geometry. Since it may be difficult to build 3D blocks directly in some cases, we adopt this approach to – build a 2D profile, preferably near the maximum chord location and extend this profile towards the tip and the root sections. Figure 3 shows a 2D profile at the mid-section of the propeller.

Figure 4: Extension of the 2D profile towards the tip and root of the blade.

Covering the Length of the Blade

Once a 2D sectional profile is created, it can be swept along the length of the blade towards the tip and the root. As we copy the profile and move along, 3d blocks are created. The in-between sections are subjected to local transformation like rotation, translation, scaling, etc. to ensure that the blocks are outside the geometry. Figure 4 shows the extension of the 2D profile in the 3rd direction.

Staggering to attain healthy positioning of blocks for a ship propeller blade — **Figure 5:** Staggering to attain healthy positioning of blocks.

Staggered Blocks

For a blade with a high pitch and rake, the mesh blocks cannot be uniform on either side of the blade. This also makes it difficult to ensure orthogonality of the blocks at the blade wall and at the periodic boundaries with the regular O-H topology. Introducing an appropriate stagger will help to channelize some of the blocks from the inlet/outlet towards the periodic BC, and also ensure maintenance of high block quality with minimal skewness. Figure 5 shows the 2D profile with staggered grid sheets.

**Figure 6:** Wrapping the blocks: a. Block wrapping around blade tip. b. Wrap around hub front.

Wrapping the Blocks Around the Blade

Next, the blocks are closed around the blade tip and the faces around the geometry are wrapped to create an O-grid. This ensures the placement of orthogonal blocks around the ship propeller blade and the hub. Figure 6 shows a cut section of the wrapped blocks.

Enrichment to increase local grid resolution for a ship propeller blade — **Figure 7:** Enrichment to increase local grid resolution.

Local Refinement

High gradient, flow active regions like the leading edge, tip, and trailing edge needs to be resolved with fine mesh. An additional layer of compact enrichment is done around the leading edge for sheet cavitation. This can be done either by introducing an internal tube-like structure along the outer profile or enriching the blocks just adjacent to it. Figure 7 shows the local refinement by the two approaches.

Mesh around the fillet region for a ship propeller blade — **Figure 8:** Mesh around the fillet region.

Fillet Capturing

It is very essential for accurate capturing of the blade-hub junction region. Local refinement in the filleted region ensures high grid density. Figure 8 shows the mesh in the fillet region.

**Figure 9:** Nesting to coarsen out the grid away from the ship propeller blade.

Reverse Nesting

Grid density in the vicinity of the blade is usually high, as the various blade features and flow physics demand placement of finer blocks around the blade. However, this fineness is not needed as we move away from the blade surface. They just add to the computational cost without bringing in significant improvement in flow prediction. In GridPro, we use Nesting which helps to address this issue effectively by bringing a systematic orderly reduction in the grid resolution from blade towards the farfield. Figure 9 shows the block reduction by nesting for a propeller blade case.

Video 1: Shows the steps to mesh a ship propeller blade using a combination of bottom-up and top-down approaches.

Multi-block generation steps outlined in the above sections ensure good quality grid generation for propeller blades. Scripting these steps helps to automate the whole gridding process. Also, it makes the topology versatile to be used more than once with minor modifications for a class of blade profiles typically seen in design optimization cycles.