Mixing

Overview

Mixing of two or more air streams represents one of the most common psychrometric processes in HVAC systems. This adiabatic process occurs whenever return air combines with outdoor air in economizer cycles, exhaust air mixes with outdoor air in energy recovery systems, or zone air streams merge in return plenums. The analysis of mixing processes relies on fundamental conservation principles—mass balance and energy balance—applied to the moisture and dry air constituents.

The mixed air state point lies on a straight line connecting the two inlet air states on the psychrometric chart. The exact location along this line depends on the mass flow rate ratio of the two streams. Understanding mixing processes is essential for economizer control strategies, minimum outdoor air calculations, freeze protection, and energy recovery system design.

Fundamental Principles

Conservation Laws

The mixing process follows two fundamental conservation principles:

Mass Conservation:

Total dry air mass flow rate is conserved
Total moisture mass flow rate is conserved
Volume flow rates do not add linearly (density varies with state)

Energy Conservation:

Total enthalpy flow rate is conserved for adiabatic mixing
No heat transfer occurs with surroundings
Kinetic and potential energy changes are negligible

Graphical Representation

On the psychrometric chart, the mixed air state point lies on the straight line connecting the two inlet states. This linear relationship results from the fact that both dry-bulb temperature and humidity ratio are extensive properties when considering mass flow rates.

The position along the mixing line is determined by the lever rule, which states that the ratio of distances from the mixed point to each inlet point is inversely proportional to the mass flow rate ratio.

Engineering Equations

Two-Stream Mixing Analysis

For two air streams mixing adiabatically:

Mass Balance - Dry Air:

ṁ₃ = ṁ₁ + ṁ₂

Where:

ṁ₃ = mixed air mass flow rate (lb/min or kg/s)
ṁ₁ = stream 1 mass flow rate (lb/min or kg/s)
ṁ₂ = stream 2 mass flow rate (lb/min or kg/s)

Mass Balance - Moisture:

ṁ₃ · W₃ = ṁ₁ · W₁ + ṁ₂ · W₂

W₃ = (ṁ₁ · W₁ + ṁ₂ · W₂) / (ṁ₁ + ṁ₂)

Where:

W = humidity ratio (lb_w/lb_da or kg_w/kg_da)

Energy Balance - Enthalpy:

ṁ₃ · h₃ = ṁ₁ · h₁ + ṁ₂ · h₂

h₃ = (ṁ₁ · h₁ + ṁ₂ · h₂) / (ṁ₁ + ṁ₂)

Where:

h = specific enthalpy (Btu/lb_da or kJ/kg_da)

Dry-Bulb Temperature:

T₃ = (ṁ₁ · T₁ + ṁ₂ · T₂) / (ṁ₁ + ṁ₂)

Where:

T = dry-bulb temperature (°F or °C)

Bypass Factor Formulation

When mixing return air with outdoor air, the equation can be expressed using bypass factor (X):

X = ṁ_oa / ṁ_total

T_ma = (1 - X) · T_ra + X · T_oa
W_ma = (1 - X) · W_ra + X · W_oa
h_ma = (1 - X) · h_ra + X · h_oa

Where:

X = outdoor air fraction (dimensionless)
ma = mixed air
ra = return air
oa = outdoor air

Volumetric Flow Rate Considerations

Volume flow rates do not add linearly because air density changes with temperature and moisture content:

V̇₃ ≠ V̇₁ + V̇₂  (generally not equal)

To convert between mass and volume flow rates:

ṁ = ρ · V̇ = V̇ / v

V̇ = ṁ · v

Where:

ρ = air density (lb/ft³ or kg/m³)
v = specific volume (ft³/lb or m³/kg)
V̇ = volume flow rate (cfm or m³/s)

Corrected Mixed Volume Flow Rate:

V̇₃ = ṁ₃ · v₃ = (ṁ₁ + ṁ₂) · v₃

The specific volume v₃ must be evaluated at the mixed air conditions.

Mixing Line Properties

Linear Relationship

For any property φ that is extensive with respect to dry air mass:

φ₃ = (ṁ₁ · φ₁ + ṁ₂ · φ₂) / (ṁ₁ + ṁ₂)

This applies to:

Dry-bulb temperature (T)
Humidity ratio (W)
Enthalpy (h)
Dew-point temperature (T_dp)

Lever Rule Application

The position of the mixed point divides the mixing line such that:

Distance from point 1 to mixed point     ṁ₂
─────────────────────────────────────  = ────
Distance from point 2 to mixed point     ṁ₁

This graphical relationship provides a quick check of calculations and enables visual estimation of mixed conditions.

Non-Linear Properties

Relative humidity and wet-bulb temperature do NOT follow linear relationships during mixing. The mixed air relative humidity typically falls below both inlet stream relative humidities in the middle portion of the mixing line. This phenomenon occurs because saturation vapor pressure is an exponential function of temperature.

HVAC System Applications

Economizer Mixing

Air-side economizers mix outdoor air with return air to provide “free cooling” when outdoor conditions are favorable.

Control Strategies:

Dry-bulb economizer: Compares outdoor and return air temperatures
Enthalpy economizer: Compares outdoor and return air enthalpies
Differential enthalpy: Uses both temperature and humidity measurements

Minimum Position:

Code-required minimum outdoor air must always be maintained
IMC Section 403.3: Minimum 0.06 cfm/ft² or 15 cfm/person
ASHRAE 62.1: Ventilation rate procedure or IAQ procedure

Maximum Position:

Limited by design outdoor air damper capacity
Typically 60-100% outdoor air depending on system design
Must consider freeze protection for cooling coils

Makeup Air Systems

In applications with exhaust requirements (kitchens, laboratories, industrial processes), makeup air must be provided:

V̇_ma = V̇_exhaust - V̇_relief

Mixed condition depends on:
- Building air temperature and humidity
- Outdoor air conditions
- Infiltration characteristics

Return Air Plenum Mixing

Multiple zones with different conditions merge in return plenums:

T_mixed = Σ(ṁᵢ · Tᵢ) / Σ(ṁᵢ)
W_mixed = Σ(ṁᵢ · Wᵢ) / Σ(ṁᵢ)

This mixed return air then combines with outdoor air at the air handling unit.

Energy Recovery Systems

Air-to-air energy recovery devices create effective mixing processes:

Run-around loops:

Precondition outdoor air using energy from exhaust air
Mixing calculation determines entering coil conditions

Heat wheels and plate exchangers:

Transfer both sensible and latent energy
Effectiveness determines degree of preconditioning

Design Considerations

Freeze Protection

Mixing outdoor air with return air reduces the risk of freezing coil damage, but careful analysis is required:

Critical Conditions:

Outdoor air temperature < 32°F (0°C)
Mixed air temperature < 35-40°F (2-4°C) at coil face
Low load conditions with high outdoor air percentage

Protection Strategies:

Minimum mixed air temperature setpoint (typically 40-45°F)
Preheat coil upstream of mixing plenum
Face and bypass damper arrangements
Glycol addition to chilled water systems

Damper Control Sequences

Typical economizer sequence:

Full mechanical cooling: Minimum outdoor air position
Economizer transition: Modulate outdoor air damper open
Full economizer: Maximum outdoor air position
Integrated economizer: Modulate outdoor air with mechanical cooling

Damper sizing considerations:

Velocity through outdoor air damper: 500-800 fpm typical
Pressure drop across dampers: 0.2-0.5 in. w.g.
Leakage class per AMCA 500-D

Stratification Prevention

Incomplete mixing creates temperature stratification in ducts and plenums:

Factors promoting good mixing:

High velocity differential between streams (> 500 fpm difference)
Turbulent flow conditions (Re > 4000)
Adequate mixing length (minimum 5-7 equivalent diameters)
Baffles or turning vanes to create turbulence

Consequences of poor mixing:

Inaccurate temperature sensor readings
Freezing damage to coil tubes in cold outdoor air streams
Comfort complaints from non-uniform air delivery

Sensor Placement

Temperature and humidity sensors measuring mixed air must be located where complete mixing has occurred:

Minimum distance: 5 duct diameters downstream of mixing point
Prefer locations after fans or coils (enhanced turbulence)
Use averaging sensors or multiple sensors for large ducts
Avoid locations near plenum walls or dead zones

Calculation Methods

Tabular Method

For hand calculations, organize data in tabular format:

Parameter	Stream 1 (OA)	Stream 2 (RA)	Mixed Air
Mass flow rate, ṁ (lb/min)	850	3,400	4,250
Dry-bulb temp, T (°F)	35.0	75.0	-
Humidity ratio, W (lb/lb)	0.0025	0.0095	-
Enthalpy, h (Btu/lb)	11.2	28.8	-

Calculate mixed properties using mass-weighted averages.

Psychrometric Chart Method

Plot both inlet states on psychrometric chart
Draw straight line connecting the two points
Calculate mass flow rate ratio: r = ṁ₁/(ṁ₁ + ṁ₂)
Locate mixed point at fractional distance r along line from point 2 toward point 1
Read mixed air properties from chart

Computer Methods

Psychrometric calculation libraries:

ASHRAE RP-1485 psychrometric libraries
PsychroLib (open source, multiple languages)
Engineering Equation Solver (EES)
MATLAB/Python psychrometric packages

Building energy simulation:

EnergyPlus
TRACE 3D Plus
Carrier HAP
Trane TRACE 700

Standards and References

ASHRAE Standards

ASHRAE Fundamentals Handbook:

Chapter 1: Psychrometrics
Equations 32-34: Moist air property calculations
Figure 1: ASHRAE Psychrometric Chart No. 1

ASHRAE 62.1 Ventilation for Acceptable Indoor Air Quality:

Section 5: Systems and Equipment
Section 6.2: Outdoor Air Intake
Appendix A: Mass Balance Method for multiple zones

ASHRAE 90.1 Energy Standard:

Section 6.4.3.8: Economizer Requirements
Section 6.5.1: Outdoor air damper controls
Table 6.5.1: Economizer high-limit shutoff temperatures

Code Requirements

International Mechanical Code (IMC):

Section 403.3: Minimum ventilation rates
Section 403.3.1: Outdoor air delivery monitoring
Section 606.2: Air economizers

International Energy Conservation Code (IECC):

Section C403.5: Economizers (commercial buildings)
Table C403.3.1: Minimum equipment efficiencies

Worked Examples

Example 1: Economizer Mixed Air Calculation

Given:

Outdoor air: T₁ = 55°F, W₁ = 0.0045 lb_w/lb_da
Return air: T₂ = 75°F, W₂ = 0.0095 lb_w/lb_da
Total supply air flow: 10,000 cfm at mixed conditions
Outdoor air fraction: 40%

Find: Mixed air dry-bulb temperature, humidity ratio, and enthalpy

Solution:

For 40% outdoor air fraction:

X = 0.40

T_ma = (1 - 0.40) × 75 + 0.40 × 55
T_ma = 0.60 × 75 + 0.40 × 55
T_ma = 45 + 22 = 67°F

W_ma = (1 - 0.40) × 0.0095 + 0.40 × 0.0045
W_ma = 0.60 × 0.0095 + 0.40 × 0.0045
W_ma = 0.0057 + 0.0018 = 0.0075 lb_w/lb_da

From psychrometric chart at T = 67°F, W = 0.0075 lb_w/lb_da:

h_ma ≈ 25.8 Btu/lb_da
φ_ma ≈ 52% RH

Alternatively, calculate enthalpy directly:

h₁ = 0.240 × 55 + 0.0045(1061 + 0.444 × 55) = 18.1 Btu/lb
h₂ = 0.240 × 75 + 0.0095(1061 + 0.444 × 75) = 28.4 Btu/lb

h_ma = 0.60 × 28.4 + 0.40 × 18.1
h_ma = 17.0 + 7.2 = 24.2 Btu/lb

(Note: Direct calculation shows slight difference from chart reading due to chart resolution)

Example 2: Minimum Outdoor Air with Variable Flow

Given:

Design outdoor air requirement: 2,000 cfm at 75°F
Current return air conditions: 72°F, 13.5 ft³/lb specific volume
Current outdoor air conditions: 45°F, 12.9 ft³/lb specific volume
Minimum outdoor air damper position maintains constant volume OA

Find: Mixed air temperature when system operates at 75% of design airflow

Solution:

Design outdoor air mass flow rate:

ṁ_oa,design = 2,000 cfm ÷ 13.5 ft³/lb = 148 lb/min

At 75% flow, if outdoor air volume remains constant (damper position fixed):

V̇_oa = 2,000 cfm (constant)
ṁ_oa = 2,000 ÷ 12.9 = 155 lb/min (varies with density)

V̇_total = 0.75 × V̇_design
V̇_design = V̇_oa,design ÷ X_design

Assuming design OA fraction was 20%:

V̇_design = 2,000 ÷ 0.20 = 10,000 cfm
V̇_total,current = 0.75 × 10,000 = 7,500 cfm

X_current = 2,000 ÷ 7,500 = 26.7% (increased OA fraction)

T_ma = 0.733 × 72 + 0.267 × 45
T_ma = 52.8 + 12.0 = 64.8°F

This demonstrates that outdoor air fraction increases at reduced flow when dampers maintain constant position.

Example 3: Three-Stream Mixing

Given: Three zone return air streams merge in return plenum:

Zone 1: 1,500 cfm at 73°F, 50% RH
Zone 2: 2,200 cfm at 68°F, 45% RH
Zone 3: 1,800 cfm at 77°F, 55% RH

Standard air density: 0.075 lb/ft³

Find: Mixed return air temperature and humidity ratio

Solution:

Convert volume flows to mass flows (assuming v ≈ 13.33 ft³/lb for all):

ṁ₁ = 1,500 ÷ 13.33 = 113 lb/min
ṁ₂ = 2,200 ÷ 13.33 = 165 lb/min
ṁ₃ = 1,800 ÷ 13.33 = 135 lb/min
ṁ_total = 413 lb/min

From psychrometric chart:

Zone 1 (73°F, 50% RH): W₁ = 0.0082 lb_w/lb_da
Zone 2 (68°F, 45% RH): W₂ = 0.0065 lb_w/lb_da
Zone 3 (77°F, 55% RH): W₃ = 0.0106 lb_w/lb_da

Mixed temperature:

T_mixed = (113 × 73 + 165 × 68 + 135 × 77) ÷ 413
T_mixed = (8,249 + 11,220 + 10,395) ÷ 413
T_mixed = 29,864 ÷ 413 = 72.3°F

Mixed humidity ratio:

W_mixed = (113 × 0.0082 + 165 × 0.0065 + 135 × 0.0106) ÷ 413
W_mixed = (0.927 + 1.073 + 1.431) ÷ 413
W_mixed = 3.431 ÷ 413 = 0.0083 lb_w/lb_da

Result: Mixed return air is 72.3°F, 0.0083 lb_w/lb_da (approximately 54% RH)

Common Design Errors

Volume Flow Assumption

Error: Assuming V̇₃ = V̇₁ + V̇₂

Impact: Can result in 5-15% error in airflow calculations, affecting fan sizing and energy consumption.

Correction: Always use mass flow rates for mixing calculations, then convert to volume using mixed air specific volume.

Sensor Location

Error: Placing mixed air temperature sensor immediately downstream of mixing dampers

Impact: Sensor reads stratified air, not true mixed temperature, causing control instability and potential freeze damage.

Correction: Locate sensor minimum 5 duct diameters downstream or after fan/coil where turbulence ensures mixing.

Minimum OA at Low Flow

Error: Using constant volume outdoor air damper with variable flow systems

Impact: Outdoor air percentage increases at low flow, causing overcooling, comfort issues, and energy waste.

Correction: Implement airflow tracking or mass balance control to maintain constant OA fraction across operating range.

Freeze Protection Setpoint

Error: Using mixed air temperature setpoint below 40°F

Impact: Risk of coil freezing in coldest portions of non-uniform air stream.

Correction: Maintain minimum 40-45°F mixed air temperature; add preheat if necessary for economizer operation.

Advanced Topics

Psychrometric Mixing with Altitude

At elevations above sea level, use altitude-corrected psychrometric charts or adjust equations for barometric pressure:

W = 0.62198 × (p_w) / (p_atm - p_w)

Where p_atm varies with altitude per standard atmosphere equations.

Mixing with Condensation

If mixed air conditions result in relative humidity > 100%, condensation occurs. The final state lies on the saturation line at mixed air enthalpy:

If φ_calculated > 100%, then:
- Final state: φ = 100% (saturated)
- T_final found at h_mixed on saturation curve
- Condensate mass = ṁ_total × (W_mixed,calculated - W_saturated)

Energy Recovery Effectiveness

For energy recovery devices, the effective mixing considers heat exchanger effectiveness (ε):

T_oa,entering_coil = T_oa + ε × (T_ea - T_oa)
W_oa,entering_coil = W_oa + ε_latent × (W_ea - W_oa)

Where ε_latent may differ from sensible effectiveness.

Summary

Psychrometric mixing analysis forms the foundation for:

Economizer control and optimization
Minimum outdoor air ventilation compliance
Freeze protection strategies
Energy recovery system design
Multi-zone return air management

Proper application of mass and energy balance equations ensures accurate prediction of mixed air conditions, enabling precise HVAC system control and energy-efficient operation. Understanding the graphical representation on psychrometric charts provides intuitive verification of calculations and aids in troubleshooting control issues.

The linear relationship of mixing processes on the psychrometric chart—combined with the lever rule for locating mixed states—makes this one of the most straightforward psychrometric processes to analyze. However, careful attention to mass flow rates versus volume flow rates, proper sensor placement, and stratification prevention remains essential for successful implementation in real HVAC systems.