Alex BlytheAero public guided demoUpdated September 17, 2026

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A CFD case, one step at a time.

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6 steps · At your paceScripted Aero guide · Recorded results

Requirements → Math → CAD → Mesh → Solve → Render

See how Aero turns a question into a CFD workflow.

Start with the nozzle example, or choose another above.

\dot{m} = ρ A V

Mass flow = density × area × velocity

For this nozzle: 0.010 kg/s → 6.762 m/s at the inlet.

Aero

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Requirements conversation

Interactive demo guide

Aero

Describe the engineering decision you need to make. I’ll separate known inputs, assumptions, missing data, success criteria, and what must remain blocked.

Inspect the full math, case data and evidence

Detailed walkthrough / Recorded evidence

Inspect each engineering stage and ask why it passed—or why it remains blocked.

The retained nozzle case below exposes the equations, geometry, mesh, solver telemetry, rendered field, and evidence gates behind the short guided experience.

AEROEngineering workbenchRECORDED RUNCOMPLETEOpenFOAM / rhoSimpleFoam

Engineering notebook

01 Problem

Evaluate steady compressible air flow through the approved converging-diverging nozzle and determine whether pressure drop is stable across the predeclared wall-refined mesh family.

02 Requirements / knowns

Use the fixed rhoSimpleFoam chain, deterministic case template, and every predeclared required gate.

Commanded mass flow: 0.010 kg/sUser input
Reference pressure: 101325 PaCase configuration
Reference temperature: 300 KCase configuration
Unknown fields: p, U, T, rhoCase configuration

03 Assumptions

Steady, compressible perfect-gas air; one-degree axisymmetric wedge; k-omega SST turbulence model; adiabatic no-slip wall; fixed reviewed inlet turbulence quantities.

04 Governing physics

Conservation of mass

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ u) = 0

∂ρ/∂t: density accumulation; zero in the selected steady model
∇·(ρu): net mass flux from a control volume

The evidence harness checks the solver patch-flux balance against this requirement.

Analytical

Ideal-gas reference density

ρ = \frac{p}{R T}

p: absolute reference pressure (Pa)
R: specific gas constant for air (J/(kg K))
T: absolute reference temperature (K)

Provides a reference density for low-speed screening, not a solved density field.

Analytical

Steady mass continuity

\dot{m} = ρ A V

ṁ: mass-flow rate (kg/s)
ρ: density (kg/m³)
A: flow area (m²)
V: area-mean normal velocity (m/s)

Sets an independent inlet velocity scale from case inputs before OpenFOAM is run.

Analytical

Reference Mach number

M = \frac{V}{\sqrt{γ R T}}

M: Mach number
γ: heat-capacity ratio
V: reference mean velocity (m/s)

Screens the expected inlet regime independently of the numerical solution.

Analytical

05 First-order analysis

Reference density 1.1768 kg/m³, inlet velocity 6.762 m/s, Mach 0.0195, and dynamic-pressure scale 26.9 Pa.

These are ANALYTICAL screening values computed before solving. Independent pressure drop is NOT YET ESTABLISHED because the inputs do not justify a fully-developed loss model.

Inputs
- Commanded mass flow: 0.010 User input
- Reference state: 101325 Pa / 300 K Case configuration
- Inlet area: 1.257e-3 Case configuration
Equation
$\dot{m} = ρ A V$
Analytical estimate
6.762 m/s
Expected trend
Increasing mass flow raises reference velocity and Mach linearly and the dynamic-pressure scale approximately quadratically.
Numerical result
NOT YET ESTABLISHED
Comparison
NOT YET ESTABLISHED

06 Geometry

PARAMETRIC GENERATED - deterministic nozzle with 20 mm inlet radius, 8 mm throat radius, 24 mm exit radius, 45 mm converging length, and 110 mm diverging length. This is not unrestricted text-to-CAD.

07 Boundary conditions

Inlet U: flowRateInletVelocity / one-degree mass fractionCase configuration
Outlet p: 101325 PaCase configuration
Inlet T: 300 KCase configuration
Walls: no-slip / adiabaticCase configuration

08 Fidelity / model selection

Steady compressible k-omega SST model. Numerical acceptability and mesh independence passed, while external validation, wall-resolution suitability, and fitness for a design decision remain NOT YET ESTABLISHED.

09 Numerical method

Solver: OpenFOAM rhoSimpleFoamCase configuration
Mesher: CadQuery + Gmsh transfinite wedge, 12,600 cells at Level 4Case configuration
Execution: isolated fixed worker chainCase configuration

10 Predeclared acceptance criteria

Before execution: completion artifacts; mesh quality; residual ≤ 1×10⁻⁴; mass imbalance ≤ 1%; energy imbalance ≤ 2%; outlet-flow variation ≤ 1% over 20 samples.

Readiness additionally requires a validation reference, substantiated fidelity claims, and at least two eligible mesh levels agreeing within 2%. Missing required evidence blocks establishment.

11 Execution

The retained Level 4 run completed 4,200 outer iterations through the isolated worker. Process exit alone was not treated as engineering success; all required numerical evidence was finalized afterward.

12 Evidence

The Aero/cfd/evidence.py contract is authoritative. Residual, conservation, and monitor charts use parsed OpenFOAM telemetry only.

13 Interpretation

Numerical acceptability is PASS and the predeclared 2% pressure-drop mesh-independence gate is PASS. Overall design readiness remains NOT ESTABLISHED because validation and intended-use fidelity are not established.

Pre-solve analytical workspace

First-principles expectations from case inputs, established before OpenFOAM executes.

ANALYTICAL / PRE-RUN

CASE / NOZZLE-WALL-REFINEMENT-V6

First-order flow screening

Analytical

ṁ: 0.010 kg/s
p_ref: 101325 Pa
T_ref: 300 K
r_i: 20 mm
R: 287 J/(kg K)
γ: 1.4

Scope and authority

case inputs \to analytical expectations \neq solver output

\text{case inputs} \rightarrow \text{analytical expectations} \neq \text{solver output}

Every value below is established before solving from the declared reference state and inlet geometry. It is a screening calculation, not validation and not a reconstruction of CFD output.

Inlet reference area

A_{i} = π r_{i}^{2}

A_i = \pi r_i^2

The deterministic nozzle definition supplies the 20 mm inlet radius. The full circular area is used for this independent reference-scale calculation.

Area1.2566e-3 m²

Reference density

ρ_{ref} = \frac{p_{ref}}{R T_{ref}}

\rho_{ref} = \frac{p_{ref}}{R T_{ref}}

Perfect-gas air at the declared reference pressure and temperature provides a pre-solve density scale. This is not the solved density field.

Reference density1.1768 kg/m³

Continuity velocity scale

V_{i} = \frac{\dot{m}}{ρ_{ref} A_{i}}

V_i = \frac{\dot{m}}{\rho_{ref} A_i}

Steady mass continuity converts the commanded mass flow into an inlet mean-velocity scale using only case inputs.

Reference velocity6.762 m/s

Compressibility screen

a_{ref} = \sqrt{γ R T_{ref}}, M_{i} = \frac{V_{i}}{a_{ref}}

a_{ref}=\sqrt{\gamma R T_{ref}},\qquad M_i=\frac{V_i}{a_{ref}}

The reference Mach number screens the inlet regime before choosing and running the numerical model.

Reference Mach number0.01948

Reference speed of sound347.19 m/s

Dynamic-pressure scale

q_{i} = \frac{1}{2} ρ_{ref} V_{i}^{2}

q_i = \frac{1}{2}\rho_{ref}V_i^2

This establishes an order-of-magnitude pressure scale and the expected quadratic response to mass flow. It is not a nozzle pressure-drop prediction.

Dynamic-pressure scale26.91 Pa

What is not established

{Δp}_{analytical} = NOT YET ESTABLISHED

\Delta p_{analytical}=\text{NOT YET ESTABLISHED}

The available inputs do not justify an independent loss model for this converging-diverging turbulent nozzle. Aero therefore does not fabricate an analytical pressure drop or reuse the CFD result as its own prediction.

first-order-screening.texREAD ONLY / GENERATED FROM CASE STATE

% Aero pre-solve first-order screening
% Authority: CASE INPUTS -> ANALYTICAL; no CFD output is used.
\begin{aligned}
A_i &= \pi r_i^2 \\
\rho_{ref} &= \frac{p_{ref}}{R T_{ref}} \\
V_i &= \frac{\dot{m}}{\rho_{ref} A_i} \\
a_{ref} &= \sqrt{\gamma R T_{ref}} \\
M_i &= \frac{V_i}{a_{ref}} \\
q_i &= \frac{1}{2}\rho_{ref}V_i^2 \\
\Delta p_{analytical} &= \text{NOT YET ESTABLISHED}
\end{aligned}

Engineering viewport

Geometry — drag to pan, scroll to zoom

Result fields

Final engineering monitors (11)

Ux final residual: 6.812e-6
Uy final residual: 1.770e-5
Uz final residual: 0.00318672
h final residual: 2.780e-5
k final residual: 8.822e-5
omega final residual: 2.939e-5
p final residual: 3.320e-6
inlet_total_energy_flux: -8.37146
Outlet mass flow: 2.778e-5 kg/s
outlet_total_energy_flux: 8.37989
pressure_drop: 439.613

Solver output

Real solver telemetry

Residual convergence

Mass conservation

Energy conservation

Outlet mass-flow monitor

Aero

Aero The retained Level 4 run passed its required numerical gates, and the frozen Levels 2 / 3 / 4 family passed the predeclared 2% pressure-drop mesh-independence gate. Validation and intended-use fidelity remain not established, so this is not yet design-ready.

Explanations stay tied to structured case and evidence state. A local request can only become an allowlisted mass-flow run, fixed axisymmetric-nozzle schema, or reviewed mesh study; it cannot create commands, paths, arbitrary CAD code, solver dictionaries, or container settings.

Engineering evidence

Execution

StatusCOMPLETE

Solver runtime798.20 s

Request to result829.42 s

Numerical evidence

Numerical acceptabilityPASS

Design readiness

Overall design readinessNOT ESTABLISHED