Pressure Drop in Two-Phase Flow: HVAC Design Explained

Leave a Comment / HVAC / By

Views in the last 30 days: 26

Estimated read time: 7 minute(s)

Pressure Drop in Two‑Phase Flow: HVAC Design — Interactive Explainer
Two‑Phase Flow: Pressure Drop & Design

Why two‑phase pressure drop makes or breaks HVAC refrigerant circuits

It governs refrigerant circulation, heat‑exchanger performance, and the energy your compressor or pump must spend to keep things moving.

Total pressure drop ΔPtotal decomposes into ΔPF (friction) + ΔPA (acceleration) + ΔPG (gravity).

Big picture

Two‑phase flow pressure drop is one of the key challenges in HVAC system design because it directly influences the refrigerant circulation, heat exchanger performance, and the overall energy consumption of the system. When liquid and vapor phases coexist in components such as evaporators, condensers, or direct‑expansion coils, the pressure drop becomes a combined effect of friction, momentum change (due to phase change and acceleration), and hydrostatic forces. This complexity means that pressure drop isn’t simply a “loss” term—it affects how much pumping or compression work is needed, which in turn impacts efficiency, sizing, and cost.

How engineers usually split ↓

In two‑phase flows the total pressure gradient (dp/dz) is typically divided into: frictional losses at walls and between phases; momentum (acceleration) effects as vapor forms/condenses; and hydrostatic changes in vertical or inclined runs, where the liquid‑vapor mixture weight matters.

For example, the ASHRAE 2017 Handbook presents this breakdown (see Eq. 29a) and shows how void fraction (vapor fraction by volume) enters the math via mixture density models.

Why it matters in practice

  • Compressor / pump sizing: higher ΔP means more work and energy use.
  • Refrigerant distribution: maldistribution across circuits if branches see different drops.
  • Geometry trade‑offs: microchannels and enhanced fins boost heat transfer but can raise ΔP.

In microchannels, two‑phase multipliers and flow regime depend on channel size, mass flux, and quality—correlations such as Lee & Lee (2001) and Mishima & Hibiki (1996) are commonly used in the literature. For plate‑type exchangers, chevron angles, port losses, and narrow passages add extra components you must account for.

Frictional ΔPF

Wall shear + interfacial shear. Often estimated from a single‑phase liquid drop times a two‑phase multiplier (e.g., Friedel or Lockhart–Martinelli based).

Acceleration ΔPA

Momentum change as quality shifts from xin to xout. Homogeneous‑model estimate uses mixture densities via void fraction.

Gravity ΔPG

Hydrostatic term. Important in vertical risers and downcomers; sign flips with direction of flow.

Try it: two‑phase pressure drop micro‑estimator illustrative

A quick, slip‑free (homogeneous) calculator to feel the relative contribution of each term. Suitable for trend‑sense only—not a design tool.

Friction
–
kPa
Acceleration
–
kPa
Gravity
–
kPa
Total
–
kPa

Assumptions: homogeneous (slip‑free) mixture density, φ² user‑specified for two‑phase friction multiplier, single‑phase ΔPL via Darcy 4fL(L/D)·G²/(2ρl). For real design, use validated correlations and vendor data.

Flow Regime Explorer (visual only)

This animation adds more bubbles as x rises. Rule‑of‑thumb label below is indicative only.

Likely regime: intermittent / slug

Empirical correlations and their role

Because the hydrodynamic and heat transfer aspects of two‑phase flow are not as straightforward as those for single‑phase flow, engineers rely on empirical correlations like the Friedel correlation, Lockhart–Martinelli model, Grönnerud correlation, and the Müller‑Steinhagen & Heck correlation. These correlations provide designers with a means to estimate pressure drops under various operating conditions, though they can sometimes vary by as much as 30–50% from measured values. For example, the Friedel correlation starts with a single‑phase pressure drop and applies a multiplier to account for the additional effects in two‑phase flow.

Designers use these models as approximations, adding safety margins and verifying with experimental or in‑service data to ensure that the system will operate reliably. It’s a classic design trade‑off: increasing the heat transfer area (often through enhanced surfaces) can improve performance but might also result in a higher pressure drop, necessitating a careful optimization balance.

Practical implications for HVAC design
  • Evaluate tube/channel sizes to minimize undue pressure losses.
  • Consider flow‑control devices (valves, distributors, baffles) that alter pressure distribution.
  • Use correlations as guides, then confirm with tests/vendor curves for your refrigerant and geometry.
  • Optimize enhanced surfaces so gains in h don’t get erased by excess ΔP.

Citations (highlighted)

ASHRAE Handbook (2017), Eq. 29a — dp/dz components & void fraction Friedel (1979) — two‑phase multiplier approach Lockhart–Martinelli (1949) — two‑phase flow parameter X Grönnerud (1972) — boiling flow in tubes Müller‑Steinhagen & Heck (1986) — unified friction correlation Lee & Lee (2001) — microchannel pressure drop Mishima & Hibiki (1996) — small‑diameter two‑phase flow
🌀 Flow Patterns in Horizontal Evaporator Tubes 🔥 Critical Heat Flux 🌡️ Nucleate Boiling Explained ♻️ Heat Exchangers in HVAC 🌊 Fluid Properties: Viscosity & Density 🔧 How Flow Loses Energy 🧮 Pipe Design Calculator 💨 Convective Heat Transfer 📈 Psychrometric Calculators
Two‑Phase Pressure Drop Correlations — Presets for HVAC
📘 Two‑Phase Pressure Drop — Correlation Playbook

Major correlations for HVAC applications (with presets)

VRF, tube‑fin, and plate HX presets auto‑fill typical LM C and Chisholm B so readers can explore quickly. Fully namespaced & responsive.

Lockhart–Martinelli (LM)

X^2 = (dp/dz)_L / (dp/dz)_G \u2192 ϕ_L^2 = 1 + C/X + 1/X^2

Workhorse for conventional tubes; moderate accuracy (±30%). C depends on regimes (TT=20, TL=12, LT=12, LL=5).

Chisholm (modified LM)

ϕ_L^2 = 1 + (X^2 − 1)[B·x^0.875(1−x)^0.875 + x^1.75]

Adds channel‑size sensitivity; better for mini/microchannels (±15–20%). B depends on geometry — treat as calibratable.

Presets, selector & micro‑estimator illustrative

Microchannel: Dh < 1 mm Minichannel: 1–3 mm Conventional: > 3 mm
Recommendation: — Preset: —
ϕ² used
–
ΔP2φ,F (kPa)
–
Correlation
–
Notes
–
—

Preset ranges are indicative (for education). Typical spans: LM C ≈ 12–20 depending on regime; Chisholm B ≈ 0.6–1.5 depending on geometry and test fit. Always calibrate against vendor/experimental data.

Flow regime considerations

  • Microchannels (< 1 mm): surface tension dominates; confinement is significant.
  • Mini‑channels (1–3 mm): transition region; use modified correlations.
  • Conventional (> 3 mm): traditional models apply.

Rule‑of‑thumb: bubbly → homogeneous may suffice; slug → Chisholm recommended; annular → use phenomenological or Friedel‑based models with regime checks.

Fluid properties

  • Density ratio ρL/ρG → void fraction & slip.
  • Viscosity ratio → regime transitions & wall friction.
  • Surface tension → crucial in microchannels.

Flow characteristics

  • Mass flux G → primary driver of ΔP.
  • Vapor quality x → phase distribution & void fraction.
  • Saturation temperature → properties & heat transfer.

Geometry

  • Hydraulic diameter → confinement & model choice.
  • Orientation → gravity term significance.
  • L/D → development effects.

Citations (highlighted)

Lockhart & Martinelli (1949) — two‑phase parameter X Chisholm — diameter‑sensitive extension for ϕL² Friedel (1979) — Fr/We based ϕLO² ASHRAE Handbook (2017) — dp/dz components & void fraction
♻️ Heat Exchangers in HVAC — Types & Design 🌡️ Nucleate Boiling — Explained 📈 Psychrometric Calculators 🌀 Duct Design (ASHRAE‑based) 🔁 Continuity Equation: HVAC Duct Flow

Related Posts

Leave a Comment