Example: blood_flow_1d_validation
Figure 7.3 — Example: Blood Flow 1D Validation
Crate: cfd-suite (workspace root)
Run: cargo run --example blood_flow_1d_validation --no-default-features
Source: examples/blood_flow_1d_validation.rs
What This Example Demonstrates
Four literature validation cases for 1D non-Newtonian blood flow, each exercising a different rheology or network model:
| Case | Reference | What is validated |
|---|---|---|
| 1. Poiseuille flow — Casson model | Merrill et al. (1969) | Pressure drop vs analytical |
| 2. Symmetric bifurcation | Murray (1926) | Flow split obeys Murray’s Law |
| 3. Asymmetric bifurcation | Hagen-Poiseuille | Pressure-balanced flow split |
| 4. Fåhræus-Lindqvist effect | Pries et al. (1992) | Viscosity reduction in small tubes |
Key Code Snippet
use cfd_1d::domain::channel::Channel;
// Casson model: √τ = √τ_y + √(μ_∞ · γ̇)
// τ_y ≈ 0.0056 Pa (yield stress, Ht=45%)
// μ_∞ ≈ 0.00345 Pa·s (infinite-shear viscosity)
// Carreau-Yasuda for full shear-rate range:
// μ(γ̇) = μ_∞ + (μ_0 − μ_∞) · [1 + (λγ̇)^a]^((n-1)/a)Physics Background
Blood is a shear-thinning non-Newtonian fluid. At high shear rates (arteries, cardiac cycle peak) it approaches Newtonian behaviour (μ ≈ 3.5 mPa·s). At low shear rates (venules, stenosed vessels) it exhibits:
- Yield stress from rouleaux formation
- Fåhræus-Lindqvist effect: apparent viscosity drops for tube diameter < 300 μm