Troubleshooting Wall Shear Stress Overestimation in Coronary Artery CFD

 Reproducing benchmark hemodynamics literature often reveals unexpected numerical discrepancies. In healthy coronary arteries, physiological Wall Shear Stress (WSS) typically ranges from 1.0 to 7.0 Pa (10 to 70 dyn/cm²), while localized peak values in severe stenotic throat regions rarely exceed 15–25 Pa. Experiencing a ~60 Pa overestimation indicates a fundamental modeling mismatch rather than a minor mesh discretization error.

Wall Shear Stress is defined mathematically as the product of fluid dynamic viscosity (μ) and the wall-normal velocity gradient:

τ_w = μ · (∂u_t / ∂n)|_wall

A systematic diagnostic workflow is outlined below to isolate the root cause of this severe discrepancy in ANSYS Fluent.

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1. The Geometry Scaling & Unit Conversion Trap

The most common cause of an order-of-magnitude WSS discrepancy in blood flow simulations is an unverified unit import from CAD into the CFD pre-processor.

• Cubic Dependency on Diameter: For a fully developed laminar pipe flow (Poiseuille flow), WSS depends inversely on the cube of the internal vessel diameter (D) for a given volumetric flow rate (Q):

τ_w = (32 · μ · Q) / (π · D³)

• Unit Mismatch Impact: If the CAD model was created in millimeters but imported into Fluent without scaling (treating raw numbers as meters), or if a subtle scaling factor was applied during STL/STEP import, small errors in internal diameter produce massive errors in WSS. Verify geometry dimensions in Fluent under Domain → Mesh → Scale.

2. Blood Rheology & Viscosity Formulation

Blood displays shear-thinning non-Newtonian behavior, particularly in low-shear recirculation zones. However, at high wall shear rates (˙γ > 100 s^-1), blood behaves closely to a Newtonian fluid with dynamic viscosity μ ≈ 0.0035 Pa·s (or 3.5 cP).

• Carreau vs. Casson vs. Newtonian: Verify whether the reference paper used a Newtonian model or a non-Newtonian formulation (such as Carreau-Yasuda or Casson).
• Zero-Shear Viscosity (μ₀): If a Carreau model is used, ensure the zero-shear viscosity limit (μ₀) is not accidentally set an order of magnitude higher (e.g., 0.056 Pa·s instead of 0.0035 Pa·s). Applying high-viscosity parameters to wall-adjacent cells directly multiplies the computed stress tensor.

3. Unintended Turbulence & Spurious Eddy Viscosity (μ_t)

Coronary flow is predominantly laminar (Reynolds number Re ≈ 200–400 under resting conditions). If a RANS turbulence model (e.g., k-ω SST or k-ε) was enabled in Fluent, effective viscosity is evaluated as:

μ_eff = μ_molecular + μ_turbulent

If artificial turbulence is triggered at the inlet or near geometric bifurcations, non-zero eddy viscosity (μ_t) is added to the fluid, resulting in heavily inflated shear stresses. Ensure the solver is explicitly set to Laminar unless severe post-stenotic turbulence is being modeled.

4. Boundary Condition Profiles & Entrance Effects

Uniform (plug) velocity profiles at the inlet produce unphysically steep velocity gradients along the entrance wall before the boundary layer develops.

• Inlet Extension Length: If the inlet boundary is positioned too close to the coronary branch or bifurcation of interest, the artificial entrance length gradient will corrupt the localized WSS. Ensure inlet extensions are at least 5 to 10 vessel diameters (5–10D) long.
• Profile Type: Apply a fully developed parabolic velocity profile or a Womersley profile (for pulsatile flow) using a User-Defined Function (UDF) or Profile File, rather than a flat uniform inlet velocity.

5. Gradient Evaluation Scheme & Boundary Nodal Values

In ANSYS Fluent, the spatial velocity gradient (∂u_t / ∂n) at boundary faces depends on the gradient discretization scheme configured under Solution → Methods.

• Green-Gauss Cell-Based vs. Least Squares: Switch the gradient discretization scheme to Least Squares Cell-Based or Green-Gauss Node-Based. Standard Green-Gauss Cell-Based evaluation on skewed boundary prism meshes can introduce artificial gradient spikes at wall boundaries.
• Near-Wall Mesh Resolution: For laminar CHT/fluid flow, ensure the first cell height provides smooth wall-normal resolution. Excessively high aspect ratio cells combined with high mesh skewness along curved arterial walls can cause Fluent to incorrectly extrapolate node velocities at boundary faces.

Are you modeling coronary flow as steady-state or transient pulsatile? Share your inlet profile setup and solver settings in the comments below!