10.5 Variable Air Volume (VAV) Systems, Terminal Boxes & Space Air Diffusion (ADPI)

10.5 Variable Air Volume (VAV) Systems, Terminal Boxes & Space Air Diffusion (ADPI)

Variable Air Volume (VAV) systems are the predominant air distribution design for modern commercial and institutional office buildings. Rather than varying supply air temperature at a constant flow rate, a VAV system delivers conditioned air at a constant supply temperature (typically $55.0^\circ\text{F}$ / $12.8^\circ\text{C}$) while modulating volumetric airflow rate ($\text{CFM}$) to match dynamic zone sensible thermal loads. On the PE Mechanical: HVAC and Refrigeration exam, VAV and air diffusion problems evaluate terminal box architectures (single-duct, series/parallel fan-powered), dual-maximum reheat sequences, Effective Draft Temperature ($\theta$), Air Diffusion Performance Index (ADPI), diffuser throw selection, and duct static pressure reset algorithms.

---

1. VAV Terminal Box Architectures & Operational Sequences

VAV terminal boxes (often called VAV units) regulate primary cold air entering individual thermal zones from the central AHU supply trunk.

+---------------------------------------------------------------------------------------------------------+
|                                    VAV TERMINAL UNIT ARCHITECTURES                                      |
+---------------------------------------------------------------------------------------------------------+
|                                                                                                         |
| 1. SINGLE-DUCT VAV WITH REHEAT:                                                                         |
|    Primary Air (55°F) ===> [ Airflow Sensor + Damper ] ===> [ Reheat Coil (HW/Elec) ] ===> Diffusers    |
|                                                                                                         |
| 2. SERIES FAN-POWERED VAV (Constant Volume to Space):                                                   |
|    Primary Air (55°F) ===\                                                                              |
|                           [ Continuous Terminal Fan ] ===> [ Reheat Coil ] ===> Diffusers (Constant CFM)|
|    Plenum Return (75°F) ==/                                                                             |
|                                                                                                         |
| 3. PARALLEL FAN-POWERED VAV (Variable Volume to Space):                                                 |
|    Primary Air (55°F) ====================================> [ Reheat Coil ] ===> Diffusers (Variable)  |
|                                                                 ^                                       |
|    Plenum Return (75°F) ===> [ Backdraft Damper + Fan ] ========/ (Fan runs ONLY during Reheat)         |
+---------------------------------------------------------------------------------------------------------+

Detailed Engineering Comparison: Terminal Unit Types

---

2. ASHRAE 90.1 Dual-Maximum Control Logic

Energy conservation standards (ASHRAE Standard 90.1) prohibit simultaneous heating and cooling (reheating primary cold air) unless airflow is throttled to a minimum ventilation baseline.

ASHRAE 90.1 DUAL-MAXIMUM VAV CONTROL SEQUENCE:

 Airflow (CFM)
      ^
 Max  +===============                                               ==============+ Max Heating
 Cool |               \                                             /              | Flow (~50%)
 Flow |                \                                           / (Zone calls   |
      |                 \                                         /   for heat)    |
 Min  |                  \                                       /                 |
 Flow |                   +=====================================+                  |
      |                   |     DEADBAND (No Heat / No Cool)    |                  |
      +-------------------+-------------------------------------+------------------+------> Zone Temp
                         68°F                                  72°F
      [   Cooling Mode   ]        [ Reheat Valve CLOSED ]        [ Heating Mode: Reheat Active ]

1. Cooling Mode ($T_{\text{zone}} > 72^\circ\text{F}$): Reheat coil valve is closed. Primary damper modulates between $V_{\min}$ ($20\%$ to $30\%$ of maximum) and $V_{\max,\text{cool}}$ ($100\%$).
2. Deadband ($68^\circ\text{F} \le T_{\text{zone}} \le 72^\circ\text{F}$): Primary damper stays at $V_{\min}$ to satisfy ASHRAE 62.1 outdoor air ventilation. Reheat valve remains closed.
3. Heating Mode ($T_{\text{zone}} < 68^\circ\text{F}$): As zone temperature drops, the reheat coil modulates open while maintaining $V_{\min}$. If maximum supply water temperature limit is reached ($T_{\text{discharge}} \le 90^\circ\text{F}$ to prevent ceiling thermal stratification), the damper is permitted to increase airflow up to $V_{\max,\text{heat}}$ (typically $50\%$ of cooling max).

---

3. Space Air Diffusion & Air Diffusion Performance Index (ADPI)

Space air diffusion is the aerodynamic process of distributing conditioned air into an occupied room to achieve uniform temperature, humidity, and velocity distribution without generating drafts or stagnant zones.

Occupied Zone Boundaries

ASHRAE Standard 55 defines the occupied zone as the room volume between:

• Floor level to $6.0\text{ feet}$ ($1.8\text{ m}$) above the floor.
• $2.0\text{ feet}$ ($0.6\text{ m}$) inward from perimeter walls or stationary air conditioning equipment.

CEILING AIR DIFFUSER DISCHARGE JET & COANDA ATTACHMENT:

            [ Supply Diffuser ]
  ===================+===================================== Ceiling Surface
                     |  ---> Supply Jet Clings to Ceiling (Coanda Effect)
                     |       Entrains Room Air & Warms Up
                     |
                     |                  Drop (d)
                     \                 / 
                      \               /
                       v             v
  +--------------------------------------------------------+ <--- 6.0 ft Occupied Zone Ceiling
  |                                                        |
  |   OCCUPIED ZONE (-3°F <= Effective Draft Temp <= +2°F) |
  |   Air Velocity: 30 FPM <= Vx <= 70 FPM (Ideal Comfort) |
  |                                                        |
  +--------------------------------------------------------+ <--- Floor Level

Effective Draft Temperature ($\theta$)

Thermal comfort combines air temperature differences and local convective air velocity. The Effective Draft Temperature ($\theta$) is defined by ASHRAE Fundamentals as:

$$\theta = (T_x - T_c) - 0.07 (V_x - 30)$$

Where:

• $\theta$ = Effective Draft Temperature ($^\circ\text{F}$)
• $T_x$ = Local airstream dry-bulb temperature at test point ($^\circ\text{F}$)
• $T_c$ = Average room control dry-bulb temperature ($^\circ\text{F}$)
• $V_x$ = Local air velocity at test point in feet per minute ($\text{FPM}$)

ADPI Comfort Criteria

A test point within the occupied zone satisfies thermal comfort if:

$$-3.0^\circ\text{F} \le \theta \le +2.0^\circ\text{F} \quad \text{and} \quad V_x \le 70\text{ FPM}$$

• If $\theta < -3.0^\circ\text{F}$: Occupants perceive an unacceptable cold draft.
• If $\theta > +2.0^\circ\text{F}$: Occupants perceive stagnant, stuffy conditions.
• If $V_x > 70\text{ FPM}$: Excessive air movement causes draft discomfort regardless of temperature.

Air Diffusion Performance Index (ADPI) Definition

$$\text{ADPI} = \left(\frac{\text{Number of Measurement Points Meeting Comfort Criteria}}{\text{Total Number of Measurement Points in Occupied Zone}}\right) \times 100\%$$

Design Target: A high-performance air distribution system achieves $\text{ADPI} \ge 80\%$ across both full-load and part-load VAV operating conditions.

---

4. Diffuser Throw, Induction & The Coanda Effect

Key Diffuser Aerodynamic Metrics

1. Throw ($T_{150}, T_{100}, T_{50}$): The linear distance from the diffuser face to the point where the discharge jet centerline velocity decays to $150\text{ FPM}$, $100\text{ FPM}$, or $50\text{ FPM}$.
2. Characteristic Room Length ($L$): The distance from the diffuser centerline to the nearest wall or to the mid-point collision line between opposing diffusers.
3. Throw-to-Length Ratio ($T_{50}/L$): The primary engineering sizing ratio for diffuser selection to maximize ADPI.
4. Coanda Effect (Surface Attachment): When cold air is discharged parallel to a ceiling, the constraint of the solid surface prevents ambient air from being entrained from above. This generates a localized low-pressure zone between the air jet and ceiling, causing the jet to cling to the ceiling surface for extended distances. This surface attachment allows cold primary air ($55^\circ\text{F}$) to induce warm room air and temper to $68^\circ-70^\circ\text{F}$ before dropping into the occupied space.

Optimal $T_{50}/L$ Sizing Matrix for Maximum ADPI

---

5. Duct Static Pressure Reset (Trim and Respond)

ASHRAE Standard 90.1 mandates that multi-zone VAV systems with DDC controls implement dynamic static pressure reset.

• Traditional Control: Supply fan modulates VFD to maintain a fixed static pressure setpoint ($1.5\text{ in. wg}$) measured at a static pressure sensor located $2/3$ down the main duct trunk.
• Trim and Respond Algorithm: The building automation system (BAS) continuously monitors all VAV box damper positions. If the most open damper is only $60\%$ open, the AHU fan speed is trimmed downward, dropping the duct static setpoint until at least one critical VAV box damper opens to $90\%$ to $95\%$.
• Energy Impact: Reducing duct static pressure from $1.5\text{ in. wg}$ down to $0.8\text{ in. wg}$ during part-load hours slashes central fan electrical consumption by $30\%$ to $50\%$ while eliminating high-pressure duct hiss.

---

6. Worked Example: VAV Box Mixed Air & ADPI Point Evaluation

Problem: A Series Fan-Powered Terminal Unit (FPU) serves a corner conference room. The terminal fan delivers a constant airflow of $1,200\text{ CFM}$ to four ceiling diffusers. Primary cold air is supplied at $55.0^\circ\text{F}$ ($h_p = 23.22\text{ Btu/lbm}$). Ceiling plenum return air is at $76.0^\circ\text{F}$ ($h_{\text{plenum}} = 28.50\text{ Btu/lbm}$). The room thermostat setpoint is $T_c = 74.0^\circ\text{F}$.

Part A: When the room sensible cooling load is $16,200\text{ Btu/hr}$, calculate:

1. The required supply air temperature ($T_{\text{supply}}$) delivered by the terminal unit.
2. The required primary airflow rate ($\text{CFM}_{\text{primary}}$) and induced plenum airflow rate ($\text{CFM}_{\text{plenum}}$).

Part B: In the occupied zone, air velocity and temperature are measured at two locations:

• Point 1: $T_1 = 72.0^\circ\text{F}$, $V_1 = 45\text{ FPM}$
• Point 2: $T_2 = 69.5^\circ\text{F}$, $V_2 = 80\text{ FPM}$ Calculate the Effective Draft Temperature ($\theta$) for each point and determine whether each point satisfies the ADPI thermal comfort criteria.

Step-by-Step Solution:

Part A: Calculate supply temperature and primary airflow:

$$\dot{Q}_s = 1.08 \times \text{CFM}_{\text{total}} \times (T_{\text{room}} - T_{\text{supply}})$$ $$16,200\text{ Btu/hr} = 1.08 \times 1,200\text{ CFM} \times (74.0^\circ\text{F} - T_{\text{supply}})$$ $$16,200 = 1,296 \times (74.0 - T_{\text{supply}})$$ $$74.0 - T_{\text{supply}} = \frac{16,200}{1,296} = 12.50^\circ\text{F}$$ $$T_{\text{supply}} = 74.0^\circ\text{F} - 12.50^\circ\text{F} = 61.50^\circ\text{F}$$

Now, perform a sensible energy balance across the series mixing plenum ($T_{\text{supply}} = 61.50^\circ\text{F}$):

$$T_{\text{supply}} = \frac{\text{CFM}_p \cdot T_p + \text{CFM}_{\text{plenum}} \cdot T_{\text{plenum}}}{\text{CFM}_{\text{total}}}$$ $$61.50 = \frac{\text{CFM}_p \times 55.0 + (1,200 - \text{CFM}_p) \times 76.0}{1,200}$$ $$61.50 \times 1,200 = 55.0 \cdot \text{CFM}_p + 91,200 - 76.0 \cdot \text{CFM}_p$$ $$73,800 = 91,200 - 21.0 \cdot \text{CFM}_p$$ $$21.0 \cdot \text{CFM}_p = 91,200 - 73,800 = 17,400$$ $$\text{CFM}_p = \frac{17,400}{21.0} = 828.57\text{ CFM} \approx 829\text{ CFM}$$ $$\text{CFM}_{\text{plenum}} = 1,200 - 829 = 371\text{ CFM}$$

Part B: Evaluate Effective Draft Temperatures (theta):

$$\text{Effective Draft Temperature Formula: } \theta = (T_x - T_c) - 0.07 (V_x - 30)$$

Point 1 ($T_1 = 72.0^\circ\text{F}$, $V_1 = 45\text{ FPM}$):

$$\theta_1 = (72.0 - 74.0) - 0.07(45 - 30) = -2.0 - 0.07(15) = -2.0 - 1.05 = -3.05^\circ\text{F}$$

• $\theta_1 = -3.05^\circ\text{F}$ (Fails comfort threshold $-3.0^\circ\text{F} \le \theta \le +2.0^\circ\text{F}$; slight cold draft).
• $V_1 = 45\text{ FPM} < 70\text{ FPM}$ (Velocity acceptable).
• Conclusion for Point 1: FAILS ADPI criteria due to draft.

Point 2 ($T_2 = 69.5^\circ\text{F}$, $V_2 = 80\text{ FPM}$):

$$\theta_2 = (69.5 - 74.0) - 0.07(80 - 30) = -4.5 - 0.07(50) = -4.5 - 3.50 = -8.00^\circ\text{F}$$

• $\theta_2 = -8.00^\circ\text{F}$ (Severe cold draft failure).
• $V_2 = 80\text{ FPM} > 70\text{ FPM}$ (Velocity exceeds maximum comfort limit).
• Conclusion for Point 2: FAILS ADPI criteria.

---

7. NCEES Reference Handbook Navigation & Exam Tips

• Effective Draft Temperature: Look in the Space Air Diffusion section of the Mechanical Reference Handbook for $\theta = (T_x - T_c) - 0.07(V_x - 30)$.
• ADPI Criteria: Remember that a test point passes if and only if $-3.0^\circ\text{F} \le \theta \le +2.0^\circ\text{F}$ AND $V_x \le 70\text{ FPM}$.
• Coanda Throw Rule: For diffusers with surface attachment (Coanda), catalog throw values are approximately $1.4\times$ to $1.5\times$ longer than for non-attached (free jet) discharge.