Thermal Hydraulics & Thermodynamics · C-TH-007

Critical Heat Flux and DNB (CHF) — The Heat-Flux Limit Where Nucleate Boiling Ends and Wall Temperature Jumps

Why a fuel rod's wall temperature jumps once heat flux passes CHF, and how DNB in PWRs differs from dryout in BWRs and CANDU.

Concept C-TH-007

Definition

Critical heat flux (CHF) is the heat flux at which a heated surface loses sustained contact with the liquid and boiling heat transfer starts to deteriorate sharply — in other words, the maximum heat flux at which nucleate boiling can be maintained. When bubbles crowd near the wall and form a vapor film under subcooled-to-low-quality, high-heat-flux conditions, it is called departure from nucleate boiling (DNB); when the liquid film on the wall dries out in high-quality annular flow, it is called dryout.

This note covers the phenomenon and its value (CHF).

Principle and mechanism

Where CHF sits on the boiling curve

For a heated surface immersed in saturated water at 1 atm, raising the wall superheat ΔTe = T_wall − T_sat produces the following sequence. Textbook typical values (flat plate, Zuber family) are listed; actual values depend on the surface and geometry (an experimental curve for a thin heated wire, for example, differs from them).

Region or point	Name	Characteristics	Textbook typical value
A–B	Natural convection	Single phase, low heat transfer coefficient	ΔTe below about 5 °C
B	Onset of nucleate boiling (ONB)	Bubbles start forming in wall cavities; at onset the superheat is released and wall temperature drops to B′ (hysteresis)	ΔTe about 5 °C
B′–C	Nucleate boiling (isolated bubbles)	Bubbles detach and stir the liquid; q″ rises steeply, roughly ∝ ΔTe³	ΔTe about 5–10 °C
C–D	Nucleate boiling (jets and columns)	Bubbles merge into columns and increasingly hinder liquid resupply	ΔTe about 10–30 °C
D	Critical heat flux (CHF)	Maximum heat flux	About 1.26 MW/m², ΔTe about 30 °C
D–E	Transition boiling	Partial vapor film; heat flux falls as ΔTe rises; unstable under heat-flux control	ΔTe about 30–120 °C
E	Minimum film boiling point (Leidenfrost)	Minimum heat flux of film boiling	About 0.02 MW/m², ΔTe about 120 °C
E–F	Film boiling	Conduction through a stable vapor film, with radiation increasing at high temperature	—

Pool-boiling CHF is obtained from the Zuber-type expression of hydrodynamic instability theory:

q″CHF = C · hfg · ρv^1/2 · [σ g (ρl − ρv)]^1/4
C = 0.131 (Zuber's original) or 0.149 (Lienhard). This note uses 0.149 by default. For water at 1 atm, 0.149 gives about 1.26 MW/m² and 0.131 about 1.11 MW/m².

Log–log pool boiling curve of saturated water at 1 atm, heat flux from 0.001 to 10 MW/m² against wall superheat from 1 to 3,000 °C, with regions of natural convection, nucleate, transition and film boiling, points A, B (ONB), C, D (CHF about 1.26 MW/m²), E (minimum film boiling, Leidenfrost) and F, a dashed horizontal jump from D to D′ on the film-boiling branch under heat-flux control, a dashed return from E to E′ on the nucleate branch, and cards giving the Zuber-type equation q″CHF = C·hfg·ρv^1/2·[σg(ρl − ρv)]^1/4 with C 0.131 or 0.149 and about 1.26 MW/m² for water at 1 atm — Boiling curve of saturated water at 1 atm. On a heat-flux-controlled surface such as a fuel rod, exceeding CHF at D causes a jump to D′; lowering the flux returns from E to E′. Curve and D′ are illustrative typical values, not cladding temperatures or PWR 15.5 MPa values.

Why exceeding CHF means a "jump"

A fuel rod is a heated surface whose heat flux is fixed by the fission power (a heat-flux-controlled surface). Once the heat flux exceeds D, it cannot follow the transition-boiling branch. The only state that can pass the same heat flux is D′ on the film-boiling branch, so the wall temperature shoots up to it. In the pool-boiling example, ΔTe at D′ is over 1,000 °C, which is why melting of metal heaters was called burnout. Conversely, when the heat flux is lowered, film boiling persists down to E and then returns to E′. Because of this hysteresis, once DNB occurs, a small reduction in power does not restore nucleate boiling immediately; rewetting requires the wall temperature to fall below the minimum film boiling temperature.

DNB and dryout — same CHF, different mechanisms

DNB (PWR): subcooled to low quality (local equilibrium quality xe around 0 or below) and high heat flux. Bulk liquid is still present, but the bubble layer near the wall crowds and coalesces until a local vapor film covers the wall. Explanatory models include bubble crowding (Weisman–Pei), sublayer dryout beneath bubbles (Lee–Mudawar, Katto) and hydrodynamic instability; there is no single accepted theory. Because it occurs at high heat flux, the wall temperature rise is fast and large.
Dryout (BWR, CANDU): in high-quality annular flow, the liquid film on the wall is exhausted by evaporation and entrainment. It is governed less by local heat flux than by the heat accumulated upstream (local quality, boiling length), so BWRs manage it with the critical power ratio (CPR) instead of a local heat-flux ratio. Steam and droplet cooling remain, so the temperature rise is generally milder than for DNB, though it depends on conditions.

Left: heated vertical channel with flow regimes from single-phase liquid and subcooled boiling through bubbly and slug or churn flow to annular flow as quality rises, with close-ups of DNB (bubble crowding forming a vapor film, PWR, high heat flux, subcooled to low quality) and dryout (wall liquid film depleted, BWR and CANDU, high-quality annular flow). Right: W-3 critical heat flux from 0 to 5 MW/m² against local quality from −0.15 to +0.15 at 15.5 MPa for mass fluxes 2,000, 3,500 and 5,000 kg/m²s, showing CHF falling from 2.17 to 0.95 MW/m², about 56 percent, from xe 0 to 0.15 at G 3,500, and the mass-flux effect reversing near xe 0.094 — DNB and dryout: the same CHF, different mechanisms. The W-3 curves are an example calculation (SI form, 15.5 MPa, De 12.6 mm, inlet enthalpy 1,287 kJ/kg, uniform heat flux, no corrections, range xe ±0.15) — not design values, and not a BWR dryout calculation.

Influencing factors

How CHF changes when one factor increases with the others fixed:

Factor increased	CHF	Reason or caveat
Local equilibrium quality (enthalpy)	Decreases strongly	The strongest factor. In the W-3 example (G 3,500), about 56 % lower from xe 0 to 0.15
Inlet subcooling	Increases	Local quality at the same height is lower
Mass flux G	Increases at low quality	Effect weakens or reverses at high quality (curves cross near xe about 0.1 in the W-3 example)
Pressure	Maximum at intermediate pressure	At fixed quality, water peaks at about 3–7 MPa and decreases toward the critical pressure
Hydraulic diameter	Decreases	CHF rises in smaller channels
Upstream heat-flux concentration (non-uniform axial shape)	Downstream CHF decreases	Upstream bubble layer and enthalpy build-up; corrected by the W-3 F-factor
Mixing-vane spacer grids	Increases	Turbulent mixing breaks up the wall bubble layer

Two pressure effects must be kept apart. In the PWR operating range, a pressure drop lowers the saturation temperature, reduces subcooling and raises local quality, so DNBR falls. That is a different matter from the effect of pressure at fixed quality.

How CHF is determined

CHF is obtained not from theory but from experimental correlations, developed for each fuel design from tests with electrically heated rod bundles that simulate the real fuel.

W-3 (Tong, Westinghouse): a local-conditions, uniform-heat-flux correlation (pressure, G, xe, hydraulic diameter, inlet enthalpy). Range xe ±0.15, pressure about 7–16 MPa, with the non-uniform heat-flux F-factor and grid factors as corrections. The traditional DNBR limit is 1.30.
WRB-1, WRB-2(M): for Westinghouse bundles with mixing-vane grids.
CHF look-up table (Groeneveld 2006): a databank normalized to an 8 mm round tube, covering pressure 0.1–21 MPa, G 0–8,000 kg/m²s and xe −0.5 to 1.0; diameter and bundle correction factors are applied for use in system analysis codes.
BWR: critical-power correlations such as GEXL (boiling length–quality type) are used to evaluate MCPR.

Each correlation has its own database and range of application, and extrapolation outside the range is not allowed. That is why design limits are tied to a specific correlation.

What it means in a plant

Design: beyond CHF the heat transfer coefficient drops by an order of magnitude or more, cladding temperature rises by hundreds of °C, and oxidation and embrittlement accelerate. "No DNB" in normal operation and anticipated operational occurrences (AOOs) is therefore set as a specified acceptable fuel design limit (SAFDL).
PWR (OPR1000, APR1400, etc.): local subcooled boiling in the upper part of the hot channel is allowed, but DNB is not. In CE-type plants the core protection calculator (CPC) low-DNBR trip provides protection; in Westinghouse-type plants, the overtemperature ΔT trip does.
BWR, CANDU: dryout criteria. BWRs use MCPR; CANDU reactors use critical channel power and the regional overpower protection (ROP) trip.
Accidents: loss of flow, RCP shaft seizure and control rod withdrawal are DNB-limited events. Accidents in which CHF is unavoidable, such as a LOCA, are judged against separate criteria such as the peak cladding temperature of 1,204 °C.

Regulatory and design criteria

For example, in the United States:

Basis	Key point
10 CFR 50 App. A, GDC 10 and 20	SAFDLs not exceeded during normal operation and AOOs; automatic actuation of protection systems
NUREG-0800 SRP 4.4 Rev. 2 (2007)	PWR: 95/95 no DNB; BWR: at least 99.9 % of fuel rods avoid boiling transition during AOOs
10 CFR 50.46	ECCS acceptance criteria in a LOCA, including peak cladding temperature 1,204 °C

The CHF phenomenon itself is unchanged; what has evolved is the method of judging it. Instead of a single generic correlation and limit (W-3, DNBR limit 1.30), current designs use a limit set by a fuel-specific correlation and statistical thermal design (for example, KCE-1 with a limit of 1.29 for APR1400).

Easily confused pairs

	DNB	Dryout
Reactor type	PWR	BWR, CANDU
Flow condition	Subcooled to low quality, bubbly flow	High quality, annular flow
Mechanism	Wall bubble crowding → local vapor film	Wall liquid film exhausted by evaporation and entrainment
Governing variable	Local heat flux	Local quality, accumulated power
Margin index	DNBR (MDNBR)	CPR (MCPR), critical channel power

Another pair is ONB and DNB. ONB is where boiling starts (B); DNB is where nucleate boiling ends (D). "DNB = the start of boiling" is a common misconception. Also, heat flux is the heat actually flowing, while CHF is the limit the flow conditions allow; their ratio is the DNBR.

Key points at a glance

Definition: CHF = the maximum heat flux at which nucleate boiling is maintained; beyond it boiling heat transfer deteriorates sharply.
Boiling curve: natural convection → ONB → nucleate boiling → CHF → transition boiling → Leidenfrost → film boiling.
Heat-flux-controlled surface: above CHF, a horizontal jump D → D′ and a sharp wall temperature rise (1 atm example: ΔTe over 1,000 °C).
DNB: subcooled, low quality, high heat flux; wall bubble crowding → vapor film (PWR).
Dryout: liquid film depletion in high-quality annular flow (BWR, CANDU).
Influencing factors: quality↑ → CHF↓ (largest factor); subcooling and G (at low quality)↑ → CHF↑; pressure gives a maximum at intermediate pressure.
Prediction: experimental correlations (W-3, WRB, KCE-1), look-up tables, Zuber equation for pool boiling.
Design meaning: SAFDL, DNBR ≥ correlation-specific limit (95/95); MCPR for BWRs.

Sketch of the boiling curve of log heat flux against log wall superheat with four regions — natural convection, nucleate, transition and film boiling — the CHF point as the nucleate limit, a dashed horizontal jump to D′ under heat-flux control, and the Leidenfrost minimum film boiling point, noting CHF about 1.26 MW/m² at ΔTe about 30 °C and Leidenfrost ΔTe about 120 °C for saturated water at 1 atm — Sketch: the boiling curve with the CHF point and the jump on a heat-flux-controlled surface.