C-30 · THERMAL & FLUID · CARDIOVASCULAR
Heart valve flow
Watch blood leave the heart through a caged-ball, tilting-disc, bileaflet or natural valve in a live flow simulation in your browser — the flow itself opens and shuts the leaflets. See the jet, its angle, the vortices in the sinus and how much the valve narrows the way out.
| above 0.50 — mild range or no narrowing |
| 0.25–0.50 — moderate range |
| below 0.25 — severe range |
| Case | Reference | This solver |
|---|---|---|
| Channel flow | exact (Poiseuille, Couette) | 10⁻¹³ |
| Pulsatile channel | Womersley | 0.1–0.8 % |
| Turning cylinder | Taylor–Couette torque, exact | 0.01–0.4 % |
| Lid-driven cavity, Re 100 | Ghia, Ghia & Shin 1982 | 0.5 % |
| Cylinder wake, Re 100 | St 0.168–0.172 | 0.1695 |
| Cylinder drag, Re 20 | C_D 2.01–2.22 | 2.22 |
| Moving vs fixed body | same drag | 0.07 % |
| Free cylinder in shear | ω = γ̇/2, Jeffery | 0.75 % |
- For learning and comparison only — not for diagnosis, treatment or choosing a device.
- A two-dimensional slice narrows the way out more than the real three-dimensional valve does: compare the valves with each other, not with patient values.
- The flow solver comes from the same work as Tessera, our own simulation software. See Tessera →
HOW IT'S CALCULATED · WITH YOUR NUMBERS
Step by step, with your numbers
- 01Lattice and fluid
D2Q9 · TRT Λ = 3/16 · ν = 0.012 → τ = 3ν + ½ = 0.536The outflow tract is 50 nodes wide; one node is about 0.5 mm for a 25 mm annulus. - 02Reynolds number
Re = U·D / ν = 0.04 × 50 / 0.012 = 167Peak systole, in two dimensions. A real aorta runs near 4 000. - 03One beat
u_in = U·sin(π t / 0.35T) · T = 16 000 stepsSystole is 35 % of the beat. In diastole the inlet pressure is held below the aorta's by Δp = c_s²·Δρ = 0.0020 (lattice units), and the back-flow shuts the valve. - 04Leaflets moved by the flow
(I + I_a)·θ̈ = M_fluid + I_a·θ̈_prevStops: disc on an eccentric pivot, closed ↔ 70°. Density 2× that of blood; opening limited to 100 % of the travel. - 05Jet
v_jet / v_tract = max|u| / Uafter the first beat - 06Velocity ratio
VR = v_tract / v_jetafter the first beat - 07Effective orifice
EOA / A_tract = VRafter the first beat
References: Krüger et al., The Lattice Boltzmann Method (Springer 2017), ch. 5, 10, 11; Bouzidi, Firdaouss & Lallemand (2001); Wen et al. (2014); Ghia, Ghia & Shin, J. Comput. Phys. 48 (1982); Sarkar & Sarkar, Prog. CFD 10 (2010); Baumgartner et al., EAE/ASE recommendations, Eur. J. Echocardiogr. 10 (2009); Dasi et al. (2009); Sotiropoulos et al., Annu. Rev. Fluid Mech. 48 (2016).
BEYOND A 2D SLICE