Pillar III

From quantum features to thrust

Predicting how new biofuel blends behave from their molecules up, then testing those predictions in a small turbojet engine we are designing and building in-house.

The energy ladder

Liquid blend

enthalpy of mixing (van der Waals)

Vaporization

enthalpy of vaporization (van der Waals)

Combustion

enthalpy of combustion (mostly chemical bonds)

Combustion energy comes mainly from chemical bonds; intermolecular forces shape how the fuel mixes and evaporates. Getting both right lets us predict a blend before we burn it.

2 · The mathematics

From bonds to heat release

How we go from a molecule's structure to a prediction of how much energy it releases, and how fast.

ReaxFF total energy

E_{\text{system}} = E_{\text{bond}} + E_{\text{over}} + E_{\text{under}} + E_{\text{val}} + E_{\text{tors}} + E_{\text{vdW}} + E_{\text{Coul}}

A reactive force field: every term depends on bond order, so bonds can break and form during a simulation.

ReaxFF bond order

BO'_{ij} = \exp\!\Big[p_{bo1}\big(\tfrac{r_{ij}}{r_0^{\sigma}}\big)^{p_{bo2}}\Big] + \exp\!\Big[p_{bo3}\big(\tfrac{r_{ij}}{r_0^{\pi}}\big)^{p_{bo4}}\Big] + \exp\!\Big[p_{bo5}\big(\tfrac{r_{ij}}{r_0^{\pi\pi}}\big)^{p_{bo6}}\Big]

Bond order is a smooth function of distance, so energy stays continuous as a C–H bond stretches and breaks.

Enthalpy of combustion (Hess's law)

\Delta H_c^\circ = \sum_{\text{products}} \nu\,\Delta H_f^\circ - \sum_{\text{reactants}} \nu\,\Delta H_f^\circ

For a hydrocarbon: CxHy + (x + y/4) O2 → x CO2 + (y/2) H2O.

Bond-energy estimate

\Delta H_c \approx \sum D_{\text{bonds broken}} - \sum D_{\text{bonds formed}}

A fast first guess from bond dissociation energies (C–H ≈ 413, C=O ≈ 799, O–H ≈ 463 kJ/mol).

Quantum-level prediction

\Delta H_f^{298} = E_{\text{QM}} + \text{ZPE} + \!\int_0^{298}\! C_p\,dT - \sum_{\text{atoms}} \big(E_{\text{atom}} - \Delta H_{f,\text{atom}}\big)

Atomization route from an electronic-structure calculation; feeds Hess's law above.

Blend heating value

\text{LHV}_{\text{blend}} = \sum_i w_i\,\text{LHV}_i \;+\; \sum_{i<j} w_i w_j\,\kappa_{ij}

Mass-weighted mixing with a learned interaction term κ for non-ideal pairs. The engine measures where this breaks.

Computational

These are standard published relations. Our contribution is fitting κ and the force-field terms to blends we then measure.

3 · Alternative biofuels

Which molecules could replace jet fuel?

Each candidate trades energy density against how cleanly it can be made. Values below are published reference figures, not our measurements.

Fuel	Source	Formula	LHV (MJ/kg)	Trade-off
Jet-A (baseline)	Petroleum	$\sim\text{C}_{12}\text{H}_{23}$	43.2	Reference
HEFA-SPK	Used cooking oil, fats	$\text{C}_{9}\text{–C}_{15}\ \text{alkanes}$	44.1	No aromatics; needs blending for seals
Farnesane	Fermented sugar	$\text{C}_{15}\text{H}_{32}$	43.9	Single molecule; costly
n-Butanol	Fermentation	$\text{C}_4\text{H}_9\text{OH}$	33.1	Lower energy, easier to make
Ethanol	Corn, cane	$\text{C}_2\text{H}_5\text{OH}$	26.8	Low energy density; absorbs water

Our question: which blends of these hit Jet-A thrust in a real engine, and can the equations above predict it before we burn it?

Predict → Measure → Choose

Force fields score candidate blends.

The test stand logs thrust, exhaust temperature, fuel flow and RPM.

AI picks the next blend and engine setting.

In design

Goal: find alternative fuel blends that match conventional jet-fuel thrust.

5 · Centerpiece

The Engine Explorer

A KJ66-class model turbojet, the classic open design by Kurt Schreckling and Jesús Artés, named for its 66 mm compressor wheel. Built at true relative scale: 110 mm × 240 mm.

Explode

Cutaway

Component deep-dives

01 · Shaft tunnel

Ø22 bearing pockets bored in two setups. A floating rear spigot allows for thermal growth.

02 · Compressor + diffuser

Air speeds up through the wheel, then slows and pressurizes in the diffuser. Tip gap: 0.2 mm.

03 · Combustion chamber

Fuel flows into 6 vaporizer tubes and burns in a ring.

04 · NGV + turbine

Hot gas turns on the vanes and drives the wheel. Tip clearance matters more than any other tweak.

05 · Bearings + lubrication

A separate oil supply, so oil doesn't confound fuel comparisons.

Test stand

Sensors feed a laptop data logger.

Build timeline

In design

01
CAD + long-lead parts
02
Test stand + data logging
03
Machining: shaft tunnel, rotor, diffuser, combustor, NGV, housing
04
Balancing + spin test
05
Baseline runs
06
Biofuel blend tests

Machined in our workshop. Engine runs only at an approved, safety-planned test site.

Videos

Video coming soon

How a turbojet works in 90 seconds

Video coming soon

Build log

One video per build phase.

Video coming soon

First run

Coming soon.