Source: https://guthlabs.ai/docs/instruments/brayton-cycle-efficiency-calculator/mechanism/

instrument mechanism / verified-clean

# Brayton Cycle Efficiency Calculator mechanism

The inspectable method record for Brayton Cycle Efficiency Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The base simple-cycle efficiency formula is standard, but the specification is incomplete for its claimed outputs and does not define the regenerative efficiency adjustment. Verdict remains NEEDS_REVIEW until the missing work equations, regeneration model, temperature units, input constraints, and zero-denominator behavior are explicitly specified.

- The base formula η=1−1/rp^((γ−1)/γ) is correct only for an ideal simple Brayton cycle with constant γ, isentropic compression and expansion, and no pressure losses.

- No formula is provided for compressor-exit temperature, turbine-exit temperature, compressor work, turbine work, net specific work, or back-work ratio, even though those outputs are claimed.

- The regenerative adjustment is unspecified: effectiveness ε alone does not define η without the regenerator temperature relations and heat-input definition.

- A standard regeneration model must specify T2r=T2+ε(T4−T2), T4r=T4−ε(T4−T2), and η=(wt−wc)/qin, with qin=Cp(T3−T2r).

- Regeneration is physically useful only when T4>T2; otherwise the regenerator should be bypassed or ε should be treated as zero.

- The listed formula does not use turbine/compressor inlet temperatures or Cp, so it cannot by itself produce specific work or back-work ratio.

## Units and conventions

- Temperatures are absolute temperatures in kelvin for all thermodynamic formulas; Celsius or Fahrenheit values must be converted before multiplication or division.

- Pressure ratio rp is dimensionless and means compressor outlet absolute pressure divided by compressor inlet absolute pressure.

- γ is dimensionless and assumed constant, with γ>1; the examples use γ=1.4 for air.

- Cp is assumed constant and expressed in kJ/(kg·K); the examples use Cp=1.005 kJ/(kg·K), so work outputs are in kJ/kg.

- The test vectors use the standard ideal-cycle relations T2=T1·rp^((γ−1)/γ), T4=T3/rp^((γ−1)/γ), wc=Cp(T2−T1), wt=Cp(T3−T4), and wnet=wt−wc.

- For regenerated cases, the standard no-pressure-loss regenerator model and ε between 0 and 1 are assumed.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "rp": 4,
    "gamma": 1.4,
    "T1_K": 288,
    "T3_K": 1400,
    "Cp_kJ_per_kgK": 1.005,
    "regeneration": false
  },
  "expected_outputs": {
    "eta": 0.32705,
    "specific_work_kJ_per_kg": 319.497,
    "back_work_ratio": 0.30569
  },
  "working": "a=(γ−1)/γ=0.4/1.4=2/7. F=rp^a=4^(2/7)=1.485994. T2=T1·F=288·1.485994=427.966 K. T4=T3/F=1400/1.485994=942.130 K. wc=Cp(T2−T1)=1.005·(427.966−288)=1.005·139.966=140.666 kJ/kg. wt=Cp(T3−T4)=1.005·(1400−942.130)=1.005·457.870=460.163 kJ/kg. wnet=wt−wc=460.163−140.666=319.497 kJ/kg. η=1−1/F=1−1/1.485994=0.32705. Back-work ratio=wc/wt=140.666/460.163=0.30569."
}
````

## Failure boundary

- Division by zero occurs for back-work ratio when turbine work is zero, including the rp=1 boundary case.

- The exponent requires γ>1; γ=1 causes a degenerate zero-efficiency result, and γ≤1 is not a valid ordinary ideal-gas Brayton-cycle input.

- rp must be positive; rp=0 is invalid and negative pressure ratios are nonphysical.

- Regenerator effectiveness should be constrained to 0≤ε≤1.

- The regenerator formula requires a specified operating condition such as T4>T2; applying regeneration when T4≤T2 can produce nonphysical heat flow or misleading efficiency.

- If T3≤T2, the heat-addition denominator is zero or negative and efficiency is undefined or nonphysical.

- Celsius inputs used directly instead of kelvin produce incorrect temperatures and work values.

- Cp must be supplied or given a clearly documented default; changing Cp changes specific work but not the ideal simple-cycle efficiency.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/brayton-cycle-efficiency-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/brayton-cycle-efficiency-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/brayton-cycle-efficiency-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`