The Art and Science of Meshing Turbine Blades

Multi-blade staggering for a turbine blades.

2771 words / 13 minutes read

Let’s Step-In

Meshing techniques for turbomachinery flow fields are well established and have evolved and matured over the last couple of decades. Early CFD practitioners made use of various flavors in structured multi-block strategies like the H-type, C-type, O-type, etc, and were satisfied with the CFD results. However, over time, the turbine blade designs started to take on complex forms with larger twists, narrower flow passages, higher pitch, newer geometrical features like cooling holes with internal passages, cut back trailing edges, shroud cavities, snubbers, etc and the industry workhorse(in terms of meshing) i.e, structured blocking strategies were inadequate to handle these newer challenges.

With the emergence of unstructured and cartesian meshing techniques, Engineers took a detour from the structured approaches and started to embrace these newer meshing algorithms. However, many soon realized that, although the newer approaches, facilitated faster discretization and lesser human intervention, the ultimate objective of getting accurate, reliable computational results were in jeopardy. This paved the way to look for an amalgamation of techniques, giving rise to hybrid grids. The emerging thought was, to make use of structured blocks where ever possible especially in critical flow regions, and to switch to unstructured methods, in regions of geometric complexities. With this, the discretization of complex turbomachinery domains has been possible. The hybrid approach, though not an ideal solution, is largely accepted in the CFD community and has kept the ball rolling.

**Figure 1:** Structured multi-block grid for turbine blades with cooling holes.

Interestingly, structured multi-block researchers haven’t given up their quest for faster, reliable, and robust meshing. Time and again, they have come up with newer, smarter techniques to meet the gridding challenges. Innovative blocking strategies like staggering, local enrichment, nesting, and faster meshing through automated blocking, template-based approaches, etc, The approaches exploit the advantages of unstructured meshes and have made structured gridding possible even for geometries that were thought to be un-meshable a decade ago. Structured grids are regaining back their lost prominence and are still the darling of the turbomachinery practitioners.

In a series of articles starting with this, we will be taking the reader into the art and science of meshing turbine blades. We will wade through conventional blocking techniques, grid staggering, single topology automated gridding approaches, ways to handle geometric complexities like cooling holes, cavities, leading-edge probes, snubbers, end-wall contours, scallops, etc. and advanced blocking techniques. With this intro, let’s dive in.

**Figure 2:** *Structured multi-block grid around an airfoil and turbine blades.*

Meshing Turbine Blade Profiles or Airfoils, are they not alike?

Turbine blades outwardly look very similar to aircraft wings and this implants a wrong notion in our minds that meshing turbine blades are similar to meshing wings. Though topologically the same, meshing turbine blades are a lot trickier, even at a 2D profile level.

In external aerodynamic computations, the domains are large and there is a lot more free space around airfoils. This gives you the freedom to easily construct the blocks which can place themselves orthogonally around the body and the outer domain with almost zero skewness. The extra space provides the luxury for grid blocks to relax, adjust and reposition themselves to provide a high-quality grid. On the contrary, due to the close proximity of inlet/outlet and periodic boundaries, attaining orthogonal grids with an acceptable skewness becomes a challenge. Especially when high curvature blades with large periodicity, the flow passage shrinks and contours, which makes meshing them a lot harder. Though block creation may take less time, having them aligned to the domain boundaries and also ensuring periodicity, grid quality, especially at the LE and TE becomes an uphill task.

In 3D, the complexity scales up multiple times with turbine blades having twists in the spanwise direction, and with narrow tip clearance gaps, it becomes a nightmare. As a consequence, the turbine blades need blocking strategies that are fairly different from those needed for a wing.

Interestingly, when seen from an unstructured perspective meshing an airfoil or a turbine blade are very similar. Abundance or lack of space no more becomes an issue, the unstructured grids adjust accordingly to give a healthy grid. If such is the flexibility offered by the unstructured methods, then why do CFD engineers still wish to mesh their blades the structured way?

**Figure 3:** Hybrid unstructured for a turbine blade. Image source reference 1.

Why Still Live in a Hex Mesh World?

Cartesian and unstructured meshing techniques are fast, time-efficient, and are more amenable for automation. But they fall short in providing the quality and solution level accuracy the Engineers are looking for. On the other hand, well-organized flow-aligned hexahedral cells in structured grids provide reliable results with lower truncation and discretization errors. This results in faster solver convergence, more robustness, higher solution feature capturing, and more accurate CFD predictions.

Where unstructured scores are in situations where the time to mesh is a critical factor. Also, structured grids lose the edge when the flow path is unknown or is rapidly changing. Further, unstructured grids can provide flexible resolution control through local clustering. More importantly, unstructured grid generators can handle geometric complexities that most structured grid generators can’t even think of.

However unstructured approach loses the battle in situations where it is required to obtain almost identical grids even when the geometric profile is changing. A classical example can be the turbine blade optimization cycle, where the optimizer throws multiple variants and the CFD engineer wishes to have the same set of grids points to capture the variants. This requirement is very efficiently met in a structured approach even for a highly twisted blade.

Since unstructured is fully automated, the control over the number and the shapes of the elements poses a challenge. They fail for highly twisted blades with narrow flow passages, as grid skewness will exceed acceptable thresholds. In order to preserve the prismatic topology of the unstructured region, the blade-to-blade mesh must be generated on a single section and then cloned to other sections. This will lead to excessive shearing of the prisms for highly staggered 3D blades.

Also, in many cases along with the topology, the grid density needs to be kept as consistent as possible to the baseline grid in order to minimize the errors in computing the flow sensitivities. Unfortunately, this is particularly difficult to control when using unstructured grid generators as the total number of grid points cannot be fixed apriori.

Structured multiblock grid generated using blade centered and passage centered topology for turbine blade — **Figure 4**: Structured multiblock grid generated using blade-centered and passage-centered topology.

Conventional Blocking Strategies

Structured blocking strategies for turbomachinery applications can broadly be classified into passage-centered and blade-centered topologies. Figure 4 shows the two approaches. In passage centered approach, the periodic boundaries cut right across the leading and trailing edges of the blade. Though this approach results in generating good grids with less skewed cells for highly cambered blades with large pitch angles and narrow flow passages, they are more prone to trigger stability issues while running the solver. This is mainly because periodic boundaries in high gradient areas such as the leading edge and trailing edge could influence the flow field and reduce the solution accuracy for certain cases.

On the other hand, in the blade-centered approach, the periodic boundaries are placed away from the blade. This reduces the negative influences of the periodic boundaries on flow physics in the near vicinity of the blade and thereby improves solver stability, robustness, and accuracy of CFD simulation.

Moving further, the next level of classification can be made depending on the block arrangements around the blade. Three popular approaches are in usage namely, the H-type, the C/O- type, and the H-O-H type.

**Figure 5:** H-type topology. Image source reference 1.

The H-Type

Figure 5 shows an H-mesh. This approach is acceptable for blade profiles with sharp leading and trailing edges. With blunt blades, they end up creating singularity points. Singularities capture curvature regions inaccurately, implant high aspect ratio cells in cross-flow direction and in viscous grids, they induce transverse propagation of boundary layer. In a CFD simulation, this will result in thickening of the boundary layer which in turn triggers excessive thickening and separation of the boundary layer downstream.

**Figure 6:** C-type topology. Image source reference 2.

The C/O- Type

The limitations of the H-type are overcome by C/O- type meshes. C/O–grid has good resolution at the leading and trailing edges, captures the curvature regions effectively, and also provides good resolution of the wake. Figure 6 shows an example of a C-type grid. Using this topology, one can expect a good quality grid for low cambers, but for blades with large camber or higher pitch, C/O-pattern end up generating skewed grids in the mid-passage region. Also, they harbor mesh singularities at the junction of the upstream/downstream boundaries and periodic surfaces.

H-O-H topology mesh for turbine blade — **Figure 7:** H-O-H topology.

The H-O-H Type

A marriage of the above two approaches results in what is known as the H-O-H approach. This brings in the positives of both the H-type and the O-type and generates an effective mesh for a large class of blade profiles. O-pattern around the blade provide orthogonal cells in the viscous regions of the blade, while the H-pattern induces orthogonality at the periodic surfaces. It does contain singularities where the H-blocks meet the O-blocks. But since they are physically placed away from the high-gradient regions of leading and trailing edges, they are benign and do not inflict any adverse reaction while running CFD codes.

**Figure 8:** Ideal block flow pattern for the turbine blade.

What Should my Ideal Grid Look Like?

For a large range of camber and pitch, just the H-O-H topology generates good grids. But their limitations are exposed for cases with higher values of camber and pitch. Figure 8 shows the ideal block flow pattern for the specified blade. In Figure 9A we can see that a regular H-O-H topology gives non-orthogonal blocks at the boundaries, far away from our ideal requirements. What we need is a strategy that will control, re-orient and guide the blocks in the direction we want. We need to convert the block flow pattern in A to that in B. And this can be achieved by what is called staggering.

**Figure 9:** Transition from straight periodic-to-periodic topology to staggered topology.

Staggered Approach

Attaining high grid quality and orthogonality becomes a stiff challenge for highly cambered blades with larger periodic angles. Reduction in space starts taking a toll on grid quality. The cell skewness, aspect ratio starts to increase especially around leading and trailing edges. These grid issues arise due to the presence of periodic boundary conditions which demand a one-to-one periodic match-up of grid points. With reduced flow passage, the grid lines have difficulty turning sharply and aligning themselves with the inlet and outlet boundaries.

To overcome these gridding issues, gridding engineers have developed what is called as staggered-grids. Staggering is a blocking approach where the grid blocks do not necessarily start from inlet to outlet or from periodic to periodic. They could start at any given boundary and end on a perpendicular boundary rather than a parallel boundary. These blocking strategies in a given flow path ensure highly orthogonal grids at every boundary ensuring an overall high-quality grid.

The staggering is even possible easily in GridPro because of its automatic periodic surface creating feature. This feature does contoured periodic surface itself between the passages to give the user a perfectly periodic and highly flexing boundary.

The staggering can be in different flavors. Depending on the need, staggering is made from inlet/outlet-to-periodic BCs, or from periodic-to-periodic BCs, or inlet-to-outlets and in certain cases truly 3D with staggering from hub-to-shroud passing through the blade.

H-O-H topology for turbine blades — **Figure 10:** Basic H-O-H topology.

Case 1: Staggering from Inlet/Outlet to Periodic

Here we start with a regular H-O-H topology (shown in figure 10). As seen, the resultant mesh is non-orthogonal in the periodic boundary and stretched especially in the narrow passage between the blade. This is highlighted in figure 11.

Turbine blade mesh: Skewed cells and lose in orthogonality observed near the leading and trailing edge — **Figure 11:** Skewed cells and loss in orthogonality observed near the leading and trailing edge.

The primary reason for this behavior is the delicate balancing needed to have grids orthogonal on the blade and the boundaries, with the additional requirement of the boundary grid points to be periodic to each other. In order to relax the tension between the blocks, the blocks on the left need to be pushed upwards while the blocks on the right need to be moved downwards as shown in figure 12.

Turbine blade mesh: Block transition needed to improve grid quality. — **Figure 12:** Block transition needed to improve grid quality.

To push the blocks and to have the grid points periodic, it becomes necessary to stagger the blocks. This can be achieved by splitting the blocks with the faces as highlighted in figure 13a. The block splitting is done from the inlet to the periodic and from the outlet to the periodic BC.

Turbine blade meshing: Staggering achieved by block splitting. — **Figure 13: a.** Staggering achieved by splitting the blocks along the path shown from inlet/outlet to periodic BC, b. shows the staggered topology.

In Figures 14-15 the resultant grid is obtained which satisfies all the grid quality criteria for a good grid. The skewness, stretching at the LE and TE are completely eliminated and the orthogonality at the blade and periodic boundaries are enforced.

Turbine blades meshing: 3D staggered grid — **Figure 14: a.** Show the 2D section grid, b. shows the 3D staggered grid for the blade.

Mesh for turbine blade: Improved skewness and orthogonality. — **Figure 15:** Grid skewness improved, orthogonality established at the boundaries.

Case 2: Staggering Across Blades (multiple blades)

In the case shown in Figures 16-17, the flow passage is abnormally narrow and there is hardly any space between the blade and the periodic surfaces. Without staggering it could be impossible to mesh.

Turbine blades meshing: Staggering of blocks. — **Figure 16: a.** Shows the block faces which need to be split to achieve staggering. b. shows the 2D staggered topology.

In this case, (as shown in fig 17 b) the staggered block originates at the inlet (violet grid sheet) intersects the blade orthogonally, and ends in the periodic boundary, which then is a starting point for the ( pink grid sheet ) passes through the next blade and ends in the outlet boundary. The grid sheet here may start at the inlet, pass through at least 3 blades in this case before it reaches the outlet. The staggering gives a twist to the block pattern and begins to align with the constricted flow passage to give an ideal grid.

Turbine Blades meshing: a. 2D sectional grid showing the staggered blocks. b. shows the 3D grid with tip clearance. — ***Figure 17: a.*** 2D sectional grid showing the staggered blocks. b. shows the 3D grid with tip clearance.

Case 3: Staggering Across the Blade (two blades)

Figure 18-19, shows another staggering scenario. In Figure 18a the regular periodic-to-periodic blocking with non-orthogonal block-placement at the blade and periodic surfaces is shown.

Turbine blades meshing: Staggered grid. — **Figure 18: a.** Shows the faces to be split to convert regular periodic-to-periodic topology to staggered topology. b. Shows the final staggered wireframe.

Figure 18b presents how a staggering block pattern can be introduced. Staggering not only provides a novel way of approaching blade meshing but also allows the user to have additional features incorporated like the trailing edge enrichment in this case. What this means to the user is, the space constraint is managed well to resolve the meshes in regions where the resolution is needed to capture the physics. Figure 19 shows the grids obtained for the blade with tip-clearance.

Meshing turbine blades: 3D Staggered grid with tip clearance. — **Figure 19:** 3D Staggered grid with tip clearance.

Staggering need not be limited to the above scenarios alone, they could be done from hub to shroud as well. Especially in a marine propeller meshing, it eliminates the skewness and orthogonality issues particularly when they are highly twisted. The staggered blocks in the above case originate on the hub, pass through the blade, and end on the shroud.

Wrapping-Up

Structured multi-block grids are the ideal grids one can think of for meshing turbine blades. Usage of H-O-H topology helps to get good resolution, smooth and orthogonal grids for blades with large camber and rounded leading and trailing edges. Even blades with large camber and high pitch can be effectively meshed by introducing staggering. In such scenarios, the flow passages are very narrow, and this lack of space results in skewed stretched cells and loss in orthogonality. Stagger smartly aligns and adjusts the blocks to get healthy grids.

With this, we come to the end of this first article on the art and science of meshing turbine blades. In the next article, we will look into aspects of the single topology approach for automated gridding.