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| Part | Mass flow [kg/s] | Density [kg/m³] | Inner diameter [mm] | Velocity [m/s] | Re | f (Darcy) | Length [m] | Δp [bar] | Δp/m [Pa/m] | Note |
|---|---|---|---|---|---|---|---|---|---|---|
| Entrance | 3.15e-4 | 528.5 | 0.6 | 2.11 | – | – | 0 | 0.0177 | – | loss K = 0.5 plus acceleration to the liquid velocity |
| Liquid part | 3.15e-4 | 528.5 | 0.6 | 2.11 | 5,280 | 0.0373 | 5.74 | 4.26 | 74,100 | single-phase liquid until the saturation pressure is reached |
| Two-phase part | 3.15e-4 | 28.66 | 0.6 | 38.9 | – | – | 0.13 | 0.759 | 586,000 | vapour fraction 0 → 0.09; density and velocity at the outlet Choked flow at the outlet. |
Entrance: Δp = (1 + K)·G²/(2ρ), K = 0.5Momentum: −dp = f·G²·v/(2d)·dz + G²·dvEnergy: h + w²/2 = constant (minus the heat taken by the suction line heat exchanger)Two-phase: v = (1 − x)·v_L + x·v_V, 1/μ = x/μ_V + (1 − x)/μ_L (McAdams)Choked when (p_i − p_i+1) − G²·(v_i+1 − v_i) ≤ 0Cycle: t₀ and tc are dew points (EN 12900). The liquid leaves the condenser at the bubble point minus the subcooling and enters the capillary at the condensing pressure. The evaporator delivers vapour at p₀ and t₀ + superheat. Properties from CoolProp 8 (reference equations of state; blends with their glide).
Capillary: the homogeneous model described in the ASHRAE Handbook – Refrigeration and by Stoecker & Jones: an entrance loss (K = 0.5), single-phase liquid friction until the pressure reaches the saturation pressure of the liquid, then adiabatic two-phase flow with liquid and vapour at the same speed (h + w²/2 constant), marched in 200 pressure steps with friction and acceleration. Two-phase viscosity after McAdams, friction factor after Churchill (smooth drawn copper).
Choked flow: when the pressure drop no longer gives any length (−dp/dv = G²) the flow is critical; if that happens above the evaporating pressure the tube ends there and the rest of the expansion takes place in the jet into the evaporator – the normal state of a capillary system.
Suction line heat exchanger: calculated from its geometry – the soldered length, where it starts and the inner diameter of the suction line. Heat passes from the capillary to the suction gas in counterflow with UA per metre = 1/(1/(h_i·π·d) + 1/(h_g·π·D)); both film coefficients after Gnielinski (laminar Nu = 3.66), the suction gas side being the dominant resistance, the solder joint left out. The gas is followed cell by cell from the evaporator outlet along the capillary's own temperature profile, and the capillary and the gas are iterated until the return gas temperature and the heat taken from the capillary agree (as in the first-principles models of Hermes, Melo & Gonçalves). A measured return gas temperature can be entered instead. A heat exchanger that keeps the liquid subcooled delays the flashing and makes the tube considerably longer for the same flow.
Limits: the model lets the liquid flash exactly at saturation (no metastable delay), which makes the length somewhat too short when the subcooling is large; oil, bends and coiling are left out. Published comparisons of homogeneous models with measurements show deviations of the order of 10–20 % in mass flow Against the worked examples in the ASHRAE Handbook – Refrigeration 2006, ch. 44, the app gives 4–5 % more flow for an adiabatic R134a tube and about 8 % more with a suction line heat exchanger; always confirm the charge and the superheat in a test run.
Start from the compressor: its mass flow at the design point (evaporating and condensing temperature, subcooling) must pass through the capillary. For every bore the app finds the length that gives exactly that flow; a longer tube passes less, a larger bore more. Choose a bore whose length is practical, typically 1.5–4 m in fridges and freezers.
Calculate it in the tool above ↑
A larger bore with a longer tube is less sensitive to tolerances, dirt and oil than a short tube with a small bore: ±0.02 mm on a 0.6 mm bore changes the flow by about 8 %. Very short tubes (under 0.5 m) are hard to get right; very long ones are impractical. The app recommends the size whose length is closest to the middle of your wanted range.
Calculate it in the tool above ↑
The cold suction gas cools the liquid in the capillary: more cooling capacity per kg, less flash gas, and the suction line does not sweat or frost. The liquid then stays liquid longer and the tube passes more refrigerant per metre, so a soldered tube is longer than an adiabatic one for the same flow. The app calculates the exchanger from the soldered length and the suction line diameter; a measured return gas temperature can be entered instead.
Calculate it in the tool above ↑
The speed of the two-phase mixture rises as it flashes. At a certain point it reaches the critical (sonic) speed: lowering the evaporating pressure further does not raise the flow. Most capillary systems run choked; then the tube length decides the flow and the evaporating pressure only changes the jet at the outlet.
Calculate it in the tool above ↑
Yes, the properties of isobutane and propane come from CoolProp's reference equations of state. Remember that hydrocarbons are flammable (A3): appliance standards limit the charge per circuit, and a capillary system has no receiver, so the charge has to be weighed in exactly.
Calculate it in the tool above ↑HC (A3) refrigerant pipe sizing →
Published comparisons of homogeneous models with measurements on adiabatic tubes show deviations of the order of 10–20 % in mass flow; with a suction line heat exchanger the uncertainty is larger. Against the worked examples in the ASHRAE Handbook (2006, ch. 44) the app is within +4…9 % in mass flow. The bore tolerance alone gives several per cent. Use the result as a starting point and confirm the superheat and the pressures in a test run.