Yova's Wind Tunnel

C_d reference

This model

Current geometry—

Published values

00.71.4

Where these come from

White, F. M. Fluid Mechanics, 7th ed., Table 7.3 — bluff-body and streamlined-body drag coefficients.

Hoerner, S. F. Fluid-Dynamic Drag, 1965 — the standard compendium for shape and interference drag.

Hucho, W.-H. (ed.) Aerodynamics of Road Vehicles, 4th ed. — vehicle C_d and frontal-area conventions.

Blevins, R. D. Applied Fluid Dynamics Handbook, ch. 10 — tabulated C_d by cross-section.

Munson, Young & Okiishi. Fundamentals of Fluid Mechanics — Reynolds-number dependence of C_d.

Read this as an estimate. The number on the left is a parametric fit driven by the model's bounding box, incidence, Reynolds number and Mach number — not a solved flow field. Real C_d comes from a wind-tunnel run or a validated RANS/LES solve, and can differ by 20–30% for the same silhouette.

AeroJAX · 2D Navier–Stokes

idle

Simulated with AeroJAX

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Field

Show

Colourmap

Scale 1.0×

Range

Solver setup

Grid

Pressure

Advection

Blockage 30%

Steps/frame 2

Geometry, freestream speed, fluid, angle of attack and model rotation are read live from the tunnel. Press Re-read geometry after you rotate or swap the model.

Solved force coefficients

C_d · corrected —

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C_l · corrected —

—

Strouhal —

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Drag force —

—

C_d / C_l history

C_d C_l

Wake & surface diagnostics

C_p minimum—

peak suction

Wake deficit—

at 2·D downstream

Separation—

fraction of chord

Stagnation—

fraction of height

Cross-check against the parametric estimate

Regime

Physical Re—

from tunnel conditions

Solver Re—

—

Timestep pipeline

Convergence

RMS ∇·u after projection dt

Time integration

dt—

—

CFL—

max |u|·dt/h

Sim time—

—

Throughput—

solver steps/s

The trace viewer reads the solver state after each substep, so the numbers below the equations are the actual residuals for the timestep on screen — not a reconstruction.

What is running

A JavaScript port of the numerical pipeline in AeroJAX, a real-time, differentiable CFD framework by Arno Meijer, built on JAX. github.com/arriemeijer-creator/AeroJAX · LGPL-3.0.

Governing equations

∂u/∂t + (u·∇)u = −(1/ρ)∇p + ν∇²u − (χ/ε)(u − u_s)

∇·u = 0

Incompressible Navier–Stokes with a Brinkman penalisation term. The mask χ is a smoothed Heaviside of the model silhouette; ε is the penalisation parameter — as ε→0 the porous region approaches a rigid no-slip body.

Discretisation

Grid. MAC staggered arrangement — u on vertical faces, v on horizontal faces, p and χ at cell centres. This is what removes pressure–velocity decoupling and the checkerboard modes a collocated grid suffers from.

Advection. Semi-Lagrangian backtrace, Euler / RK2 / RK3, unconditionally stable in the advective term.

Diffusion. Explicit 5-point Laplacian on ν + ν_t, with a Smagorinsky eddy viscosity ν_t = (C_sΔ)²|S|, C_s = 0.17.

Projection. Chorin fractional step: ∇²p = (ρ/Δt)∇·u*, then u = u* − (Δt/ρ)∇p. Poisson solved by geometric multigrid V-cycle, red–black SOR, or Jacobi.

Boundaries. Dirichlet inlet, convective outflow with p = 0, and either free-slip or moving-ground walls.

Time step. CFL- and diffusion-limited, optionally trimmed by a PID controller driven by the divergence residual rather than a fixed CFL number.

Forces

Drag and lift are obtained by integrating the momentum removed by the penalisation term each step, F = Σ χ/ε (u − u_s) dV, then non-dimensionalised on the projected height of the silhouette.

Validation

Know the limits. This is a 2D slice through a 3D body, so it cannot capture trailing vortices, wheel wakes or any spanwise flow — the tunnel's 3D pressure integration and this solver answer different questions. Brinkman penalisation smears the surface over roughly one cell, so C_d and C_l are trend-accurate rather than quantitative. Road-car Reynolds numbers are ~10⁶–10⁷; the solver clamps Re into a range it can resolve and reports both numbers on the Analysis tab.