Which is the optimal Mesh Size for CFD?
Which is the optimal mesh size for CFD?
Understanding the impact of mesh size in Computational Fluid Dynamics (CFD) is essential for achieving accurate and efficient simulations. The choice of mesh size affects both the precision of the results and the computational resources required.
Importance of Mesh Size in CFD
In Computational Fluid Dynamics (CFD) simulations, the choice of mesh size is critical. Mesh size influences accuracy, convergence, and the simulation’s computational cost. A finer mesh can produce highly accurate results but demands substantial computing power and time. Meanwhile, a coarser mesh simplifies computations, potentially sacrificing detail and accuracy, creating a trade-off.
For RANS Models
RANS models quickly predict the time-averaged flow characteristics, suitable for large-scale simulations.
- Standard k-epsilon model: Often used in industrial applications, it benefits from hexahedral meshes due to their accuracy. A base cell size of 225 μm is frequently ideal to ensure balanced accuracy and computational effort.
- Standard k-omega and SST models: These models excel in capturing near-wall turbulence and require fine boundary layer meshes. Using automatic wall treatment can adapt the formulation to the mesh, optimizing accuracy without massive computational efforts. Meshes of around 150-200 μm cater well to these models.
For LES Models
LES resolves larger turbulent eddies while modeling smaller scales, needing a high-resolution mesh.
- Standard LES: Generally, a fine mesh, with cell sizes around 100-150 μm, captures eddies accurately while balancing computation time and cost.
- Hybrid LES/RANS models: Here, mesh considerations need a blend of the above strategies. Near-wall regions can use LES with finer meshes, transitioning to RANS in bulk regions, using coarser meshes.
Specific Applications and Mesh Strategy
For CFD simulations involving complex geometries or intricate flow details, like in pig houses or rotating machinery, combining hexahedral for regular regions and tetrahedral for complex domains is effective.
- Cylindrical and Animal Model Shapes: Ensuring the mesh conforms well to complex geometries without degrading quality. Non-conformal hybrid meshes allow using fine meshes around complex shapes and coarser meshes elsewhere.
- Rotor Blades: For cases like rotor blade simulations, unsteady flow phenomena near blades require meshes that adapt to dynamic conditions. Mesh independence checks are crucial, and meshes around 100 μm to capture detailed vortices without excessive computational costs.
Mesh Types and Their Applications
Hexahedral meshes excel in environments with straightforward geometries. Their uniform shape enables low computational costs while maintaining high accuracy in solution predictions. Hexahedral meshes are particularly effective in regions where the flow is smoothly varying, such as flat plates or aerodynamic surfaces. Their capability for defining cells with high aspect ratios makes them suitable for capturing boundary layers efficiently.
Tetrahedral meshes offer flexibility in handling complex geometries that are impractical for hexahedral grids. These meshes are unstructured, allowing for automatic generation in intricate domains. While tetrahedral meshes adapt well to curved surfaces and sharply varying flows, they generally require a higher number of cells to achieve the same accuracy as hexahedral meshes.
The hybrid mesh approach, incorporating both hexahedral and tetrahedral cells, leverages the strengths of each. This versatility is particularly beneficial in simulations involving a combination of simple and complex geometrical features. Non-conformal hybrid meshes use interfaces to connect hexahedral and tetrahedral regions, simplifying the mesh generation process while maintaining a good balance between computational efficiency and accuracy.
Each mesh type’s suitability depends on the specific requirements of the CFD task at hand:
- Hexahedral meshes are predominant in automotive and aerospace sectors, where clean, streamlined flows are prevalent.
- Tetrahedral meshes find more applications in biomedical simulations, consumer products, and complex architectural designs.
- Hybrid meshes are particularly advantageous in multidisciplinary fields such as environmental engineering simulations of airflow around mountains or buildings.
Selecting the appropriate mesh type is paramount for successful CFD modeling and simulation. The key lies in understanding both the strengths and limitations of each mesh in relation to the specific geometry and flow conditions being analyzed.
Turbulence Models and Mesh Requirements
Different turbulence models inherently demand unique mesh requirements to ensure precision and reliability in CFD simulations:
RANS Models and Mesh Requirements
RANS (Reynolds-averaged Navier-Stokes) models are prevalent for their speed and efficiency in providing time-averaged solutions of turbulent flows. However, the mesh must be sufficiently fine to accurately capture these averaged characteristics without excessive computational cost. For instance:
- Standard k-epsilon model: This model is often coupled with hexahedral meshes for their structured nature, making them ideal for industrial applications involving straightforward geometries. A typical mesh size for regions of high-interest (like boundary layers) is around 225 μm to balance accuracy and computational effort effectively.
- Standard k-omega and SST (Shear Stress Transport) models: These low Reynolds number models excel close to walls, where boundary layers significantly influence flow characteristics. Automatic wall treatment facilitates optimal performance even with variations in mesh density, typically ranging from 150 μm to 200 μm.
LES Models and Mesh Requirements
LES (Large Eddy Simulation) models resolve larger turbulent structures directly while modeling smaller ones. This hybrid approach requires a significantly finer mesh:
- Standard LES: Utilizes a mesh size of approximately 100 μm to 150 μm, ensuring critical turbulent eddies are well-resolved. This fine granularity captures the intricate details of the turbulence, pivotal in applications like aeroacoustics and combustion simulations, albeit with high computational costs.
- Hybrid LES/RANS models: These models merge LES’s ability to resolve large eddies and RANS’s time-averaged approach for near-wall flows. Thus, regions near walls may use even finer meshes (around 100 μm), while bulk flow regions adopt RANS strategies with coarser meshes.
DES Models and Mesh Requirements
DES (Detached Eddy Simulation) models blend LES and RANS methodologies, designed to resolve large-scale turbulent structures away from walls while using RANS formulations near walls. The mesh design for DES must transition smoothly between these regions:
- DES and IDDES: In industrial applications like automotive and rotorcraft aerodynamics, DES meshes need to capture critical flow characteristics around surfaces and in wake regions. With mesh sizes varying according to location, finer meshes (~100 μm) are employed near walls and detailed regions, whereas coarser meshes can be used in free-stream areas.
- DDES (Delayed DES): Ensures better handling of separated flows and adverse pressure gradients by delaying the switch from RANS to LES. This requires refined and adaptive meshes, particularly in regions where flow separation and reattachment happen.
Mesh Selection Guidelines for Accurate Simulations
When selecting a mesh for CFD simulations, consider these guidelines for different turbulence models:
- RANS Models:
- Apply finer meshes near walls and regions with sharp gradients.
- Ensure high aspect ratio cells for boundary layer capture, generally using hexahedral meshes.
- Use automatic wall treatment to balance computational demands and accuracy.
- LES Models:
- Employ extremely fine meshes, particularly in critical turbulence-generating regions.
- Ensure mesh refinement adapts to the scales of the turbulent structures being resolved.
- Check for mesh independence, verifying that further refinement doesn’t significantly alter results.
- DES Models:
- Adapt mesh density based on proximity to walls and flow separation regions, optimizing transition zones.
- Integrate RANS-appropriate coarser meshes for bulk flow areas and LES-fine meshes for near-wall and intricate flow regions.
- Hybrid and Complex Applications:
- Combine hexahedral meshes for regular and transitional regions with tetrahedral meshes around complex geometries.
- Utilize non-conformal hybrid meshes for practical ease in combining different mesh types while retaining fidelity in computational accuracy.
Understanding how mesh size and type influence turbulence model performance is critical for setting up reliable and efficient CFD simulations. Each model dictates specific meshing strategies, demanding careful planning and execution to optimize both accuracy and computational resources.
Mesh Independence and Convergence
In CFD simulations, ensuring mesh independence and achieving convergence are crucial. Mesh independence implies that further refining the mesh does not significantly alter the results, indicating that the solution is sufficiently accurate. Convergence means that the numerical solution stabilizes as iteration progresses, confirming that the algebraic system is being solved accurately.
To verify mesh independence, grid refinement studies are often employed. This involves systematically refining the mesh and comparing the results. Here’s how one can proceed:
- Refinement Process: Start with a coarse mesh and compute the solution. Refine the mesh by increasing the number of cells and recompute the solution. Repeat this process until further refinement results in negligible changes in the solution.
- Grid Convergence Index (GCI): This statistical method quantifies how the solution changes with mesh refinement. The GCI provides a measure of the error relative to the finest grid, aiding in confirming mesh independence.
- Richardson Extrapolation: This technique estimates the error by comparing solutions from different mesh densities. It provides an extrapolated value based on fine and coarse mesh results, offering insights into possible errors in the solution.
- Key Parameters Monitoring: Monitor critical flow parameters such as velocity, pressure, and turbulence quantities at various mesh refinements. Ensure these parameters stabilize, indicating mesh independence.
Ensuring convergence is equally vital, as it guarantees that the iterative solution process is resolving properly. Here are methods to achieve reliable convergence:
- Residuals Analysis: Residuals measure the difference between successive iterations. Aim to reduce residuals several orders of magnitude (e.g., 10-6), indicating that the solution is stabilizing.
- Solution Stabilization: Observe if key physical quantities (such as drag or lift coefficients in aerodynamics) stabilize over iterations. A consistent solution over successive iterations is a sign of convergence.
- Under-relaxation Factors: In iterative solvers, adjusting under-relaxation factors can help achieve convergence. These factors dampen changes between iterations, preventing oscillations and contributing to stability.
- Mesh Quality: Ensure the mesh quality is high, with cells having appropriate aspect ratios and avoiding excessively skewed cells. Poor mesh quality can hinder convergence and lead to inaccurate results.
- Numerical Schemes: Select appropriate numerical schemes for discretization. Higher-order schemes can offer better accuracy but may require finer meshes and higher computational efforts to converge.
Once mesh independence is confirmed and convergence achieved, the CFD simulation results can be considered reliable. These practices of verifying mesh independence and striving for reliable convergence are foundational in producing high-fidelity simulations that reflect real-world phenomena accurately.
Case Studies and Practical Examples
Practical examples and case studies demonstrate the real-world application of mesh size selection principles across different industries. These examples highlight the nuanced decisions engineers must make in various contexts.
In the aerospace industry, a computational study of airflow over a NACA 0012 airfoil using the SST (k – ω) model employed a structured hexahedral mesh with sizes around 175 μm near the airfoil surface. This fine resolution allowed for precise capturing of boundary layers and separation bubbles at high angle-of-attacks, ensuring simulations matched experimental findings accurately.
The automotive sector utilizes strategic mesh adaptation in CFD simulations of airflow around vehicles. Using a hybrid RANS/LES model, engineers selected different mesh sizes to balance computation time and accuracy:
- Near the car’s surface and in critical regions like the grille and underbody: ~150 μm
- Free-stream regions: Coarser mesh
In environmental engineering, simulations of wind flow around urban structures employ non-conformal hybrid mesh approaches. For a high-rise building simulation, engineers used:
- Finer tetrahedral meshes (~150 μm) close to the building facade to capture detailed flow features
- Hexahedral meshes in the broader urban domain for efficiency
Rotor blade simulations in renewable energy applications, such as wind turbines, often employ URANS models with dynamic mesh adjustments. A study of a wind turbine blade used:
- Fine resolution of ~125 μm near the rotating blades to capture detailed vortical structures
- Progressively coarser mesh in the surrounding flow field
In the biomedical field, a simulation of blood flow through an arterial bypass graft used a fine mesh size of around 100 μm in high shear regions where the graft connects to native vessels. This allowed for accurate prediction of flow patterns, shear stress distribution, and potential locations of restenosis.
These case studies exemplify how adjusting mesh resolution to fit specific regions within a simulation can yield accurate, reliable, and practical results while balancing computational efficiency with the need for high-fidelity simulations.
The key takeaway is that selecting the appropriate mesh size is fundamental to balancing accuracy and computational efficiency in CFD simulations. By customizing mesh strategies to specific turbulence models and applications, engineers can achieve reliable and practical results, driving advancements across diverse engineering fields.