Engineering task and calculation objective
This module calculates the nucleate boiling contribution in flow boiling of saturated pure liquids in vertical tubes per Chapter H3.5.2.1 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). At high heat fluxes, the heat transfer in the evaporator tube is no longer governed by the convection of the two-phase flow but by bubble nucleation at the tube wall; the heat transfer coefficient then depends primarily on heat flux and reduced pressure.
This calculation is needed for the design of vertical evaporator tubes in steam generators and natural and forced circulation evaporators as soon as the heat flux exceeds the onset threshold of nucleate boiling. The method normalizes the heat transfer coefficient to a substance-specific reference value at standard conditions (standard heat flux, standard diameter, reference roughness) and scales it via the reduced pressure p* = p/pc, the ratio q̇/q̇₀, the tube inside diameter, and the arithmetic mean roughness of the tube wall.
Together with the convective contribution from Chapter H3.5.1.1, the governing local heat transfer coefficient along the evaporator tube is obtained; the substance class, flow direction, and boundary condition also enter the evaluation.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the boundary condition, substance class, and flow direction: The selection parameters determine which correlation parameters apply: water, cryogenic fluids, and organic substances have different characteristic values, and the flow direction (upward or downward) influences the bubble removal.
- Form the reduced pressure: From the boiling pressure and the critical pressure of the fluid, p* = p/p_c is calculated; the pressure function of the correlation describes the strong increase of the heat transfer with reduced pressure.
- Normalize the load: The local heat flux q̇ is referred to the standard heat flux q̇₀ and raised to the power of the pressure-dependent heat flux exponent; the standard value of the heat transfer coefficient serves as the substance-specific reference.
- Correct for geometry and surface effects: Deviations of the tube inside diameter from the standard diameter and of the arithmetic mean roughness from the reference roughness are corrected via power functions — rougher surfaces provide more nucleation sites and higher heat transfer coefficients.
- Evaluate the local nucleate boiling contribution: The result is the local nucleate boiling heat transfer coefficient at the position defined by mass flux and vapor quality; it is combined with the convective contribution to give the governing overall value of flow boiling.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Tube inside diameter | di | m |
| Vapour mass fraction | ẋ | -- |
| Mass flux | ṁ | kg/(m²·s) |
| Surface tension | σ | mN/m |
| Density | ρL | kg/m³ |
| Density | ρG | kg/m³ |
| Dynamic viscosity | ηL | mPa·s |
| Dynamic viscosity | ηG | mPa·s |
| Prandtl number | Pr | - |
| Thermal conductivity | λL | W/(m·K) |
| Thermal conductivity | λG | W/(m·K) |
| Specific heat capacity | cpL | J/(kg·K) |
| Specific heat capacity | cpG | J/(kg·K) |
| Reference tube diameter | d0 | m |
| Arithmetic mean roughness height | Ra | m |
| Arithmetic mean roughness height | Ra0 | m |
| Boiling pressure | pS | Pa |
| Critical pressure of the medium | pc | Pa |
| Heat flux | q̇ | W/m² |
| Reference heat flux | q̇0 | W/m² |
| Type of substance | Stoffart | – |
| Reduced pressure (p* = p / pc) | p* | - |
| n | n(p*) = | - |
| (p_*) | F(p*) = | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Heat flux | q̇ | W/m² |
| Heat transfer coefficient (convective boiling) | α(z)K | W/(m²·K) |
| Heat transfer coefficient (nucleate boiling) | q ≥ qonb α(z)B | W/(m²·K) |
| Heat transfer coefficient | α(z) | W/(m²·K) |
| Heat flux at the onset of nucleate boiling | qonb | W/m² |
Calculation options
Type of substance
Non-cryogen · Cryogen
Direction of flow
upwards · downwards
Boundary condition
Constant wall temperature · Constant heat flux
Frequently asked questions
When must I use the nucleate boiling contribution instead of the convective contribution?
Nucleate boiling only sets in above a minimum heat flux that depends on pressure and substance. Below it, the convective contribution governs. In practice, both contributions are calculated and combined per the VDI Heat Atlas procedure; at high q̇ and low vapor qualities, nucleate boiling dominates, at low q̇ and high vapor qualities, convection.
Why does the tube roughness enter the calculation?
Vapor bubbles form at microscopic nucleation sites on the surface. The arithmetic mean roughness Ra is the practical measure of their density: relative to the reference roughness, a rougher wall increases the heat transfer coefficient, a smoother one (e.g. drawn stainless steel tubes) lowers it. If the roughness of the actual tube is ignored, the error can easily reach double-digit percentages.
Does the nucleate boiling contribution depend on the vapor quality?
Much more weakly than the convective contribution. As long as the wall is wetted, bubble formation is governed by wall superheat, pressure, and surface. With increasing vapor quality, however, the convective contribution grows until it suppresses nucleate boiling; beyond the dryout point, the heat transfer collapses regardless of the mechanism.