Air Distribution and Indoor Environment Evaluation

Abstract

This book comprises six chapters covering a range of air movement patterns, mechanisms, parameter correlations, and design methods of attachment ventilation, written to help HVAC engineers design and use attachment ventilation described in this book. This chapter introduces the traditional air distribution methods and the indexes to evaluate ventilation performance. The traditionally used ventilation modes comprise mixed and displaced ventilation. The mixed ventilation is based on the dilution principle, supplying a high momentum flow from the ceiling/upper sidewall to the room, while the displaced ventilation is based on the displacement principle, supplying a low momentum flow from the floor/lower wall area to the occupied zone. This chapter briefly presents their pros and cons. Following this, a novel ventilation mode has been proposed, i.e., vertical wall attachment and column attachment ventilation. The ventilation evaluation indexes, such as vertical temperature gradient, effective draft temperature, air diffusion performance index, ventilation efficiency, and thermal stratification height, are presented.

Air distribution affects air quality, thermal environment, and work efficiency. The goal of ventilation is to provide occupants with clean air for breathing and thermal comfort. In essence, ventilation means controlling air movement in rooms or built environments. It is the science of studying the interaction of natural convection and organized currents of ventilation air. Ventilation affects not only indoor air quality and thermal comfort, but also energy consumption over the building’s life. The air distribution is a result of the complex interaction of different flows. Therefore, room air distribution in space and in time domains should be carefully considered in order to avoid regions of high velocity and low temperature as well as regions of polluted air, which may affect occupants’ comfort and well-being. This book introduces the principle and methods of applying fluid mechanics to predict the air movement along various wall surfaces in a ventilated room. Attachment ventilation (attached ventilation) theory and design methods are put forward.

The air currents induced by production processes or heated objects are diverse in any room, industrial workshop, or any given space. The purpose of ventilation is to meet the required air parameters (such as temperature t, velocity u, and relative humidity RH, etc.) in a given space and guarantee the environmental condition of people’s lives or industrial production. It is essential to control those natural air currents by jets of air supplied, as a result of interaction, eventually achieving specified parameters of the built environment.

The ventilation task is to regulate the air change in a confined enclosure to create the intended temperature, velocity, concentration field, etc. For mechanical ventilation, the air is supplied to given spaces in the form of jets by air diffusers or openings of the air passage. The ventilation jets can dilute or blow thermal air (excessive heat and moisture) or hazardous pollutants to a specific area and then remove them in an ordered manner.

A wide variety of definitions exist in literature for air distribution. ASHRAE defines air distribution as “room air distribution systems are intended to provide thermal comfort and ventilation for space occupants and processes” (ASHRAE 2017). In a broad sense, air distribution is a rationalized and organized air flow process in any given space to meet the requirements of air temperature, velocity, humidity, airflow rate, and human comfort (CIBSE 2016). The “given spaces” comprise ordinary industrial and civil buildings, enclosed and semi-enclosed zones involved in aeronautic and astronautic, transportation, facility agriculture environment, etc.

Up to date, there have mainly been traditionally two kinds of ventilation modes, mixing and displacement ventilation, since the invention of central air-conditioning systems. The former is based on the dilution principle, supplying a high momentum flow from the ceiling or upper sidewall to the room, while the latter is based on the displacement principle, supplying a low momentum flow from the floor or lower wall area into the occupied zone. This chapter briefly presents their pros and cons. Following this, a novel ventilation mode has been proposed, i.e., vertical wall attachment (VWAV) and column attachment ventilation (CAV). The ventilation evaluation indexes are prsented, such as vertical temperature gradient, effective draft temperature, air diffusion performance index, ventilation efficiency, and thermal stratification height.

1.1 Ventilation and Air Distribution

Tracing back to history, creating an intended living environment is closely related to the development and progress of human civilization. As a necessary means of indoor environment control, ventilation has been widely paid attention to. Since ancient times, people have come to realize that a favorable indoor environment can be achieved by rational air movement. That is to say, ventilation always has been a historic and vital topic in the field of heating, ventilation and air conditioning (HVAC) (Cao et al. 2014; Li et al. 2014; Melikov 2004; Lin et al. 2011; Han et al. 2019). Before the development of the electric power industry in the late nineteenth century, natural ventilation through operable windows was the only means of ventilating buildings. It was not until electric power became generally available early in the twentieth century that the desired living environment could be achieved by mechanical ventilation. Even in contemporary society, ventilation is still the primary means of controlling residential and industrial pollutants. So far, there has been a well-accepted research paradigm (Chen 2009; Baturin 1965; Bakhalev and Troyanovski 1965; Li et al. 2010):

$$\begin{aligned} & {\text{Practical}}\;{\text{phenomenon}} \to {\text{Fluid}}\;{\text{mechanics}}\;{\text{and}}\;{\text{heat}}\;{\text{transfer}}\;{\text{model}} \\ & \to \left\{ {\begin{array}{*{20}c} {{\text{Mathematical}}\;{\text{model}} \to {\text{Calculation}}} \\ {{\text{Experimental}}\;{\text{analysis}}} \\ \end{array} } \right\} \to {\text{Law}}\;{\text{of}}\;{\text{nature}}\;{\text{and}}\;{\text{engineering}}\;{\text{application}} \\ \end{aligned}$$

In view of the essence of ventilation’s complexity of turbulent motion and the diversity of boundary conditions in engineering applications, it is foreseeable that ventilation theory and technology will remain hotspots and challenges in the future.

Creating a healthy and comfortable environment in low energy or nearly zero energy consumption is challenging. In other words, the indoor environment control of intended temperature and humidity, good air quality, and low energy consumption is related to a rational cooling and heating source system and directly to air distribution (Zhang et al. 2011; Karimipanah et al. 2007).

The room air distribution is the ultimate manifestation of a series of air handling processes (such as heating or cooling processes) of the environment control system, and it is also the most direct terminal technique for creating a comfortable indoor environment. On the one hand, it is directly related to the ventilation effectiveness of the conditioned zone; on the other hand, it closely influences the required cooling and heating loads of the buildings, i.e., the total energy consumption of ventilation or air-conditioning systems. For instance, traditional mixing ventilation is required to bear the total cooling/heating loads of the entire space, whereas displacement ventilation only needs to remove the local cooling loads of the occupied space.

Ventilation is a complex combination of theory and technology based on the requirement. From the perspective of indoor environment control, when designing ventilation systems, we should comprehensively apply theoretical methods such as mechanics, heat transfer, etc., to the design of airflow paths, air diffuser forms, and locations, forming intended parameters distribution for given spaces (Lu 2007; GB/T 50155-2015; REHVA 2013).

Generally, ventilation involves two broad categories of issues:

• Air movement in a confined space—the confined jet movement mechanisms in spaces with or without obstacles, in other words, the airflow velocity variations with time and space.

• Heat exchange (or pollutants dilution) of a ventilated room—from the consideration of conservation of the convective heat and mass transfer in the jet, the equality of the increments of momentum, buoyancy force, or the temperature (concentration) distribution, that is, airflow temperature (concentration) variations with time and location.

From the perspective of force decomposition, the essence of air distribution is to control the mutual effects of mechanical momentum and thermal buoyancy in ventilation processes. The influencing factors include but are not limited to air supply rate, temperature, air inlet structure, and jet throw. For example, the air supply velocity of the underfloor air distribution (UFAD) system can affect indoor air interacting dynamic characteristics. The air distribution performance is closely related to ventilation efficiency or temperature efficiency.

Since the invention of air conditioners in the early twentieth century, two main indoor air distribution methods have been developed: mixing and displacement ventilation (Li 2000; Awbi 2008; Cao et al. 2014). The simplified diagrams of various air distributions and vertical temperature distributions are demonstrated in Fig. 1.1.

Fig. 1.1

Simplified diagram of various air distributions. a Mixing ventilation, b displacement ventilation (sidewall air supply), c underfloor air distribution (UFAD), d temperature distribution of displacement ventilation with concentrated heat sources on the floor (Zhao and Li 1998)

As is well known, the mixing ventilation theory is based on the dilution principle. Mechanical momentum is the source power to drive the interaction between supplied jets and ambient air, to meet the requirements of designed parameters. The mechanical momentum is generally “opposite” to the thermal plume arising from the buoyancy forces created by temperature differences. The supplied air will incessantly mix with ambient air, and the indoor air temperature of the entire space is uniformly distributed (CIBSE 2016; Rock et al. 1995). Thus, there is no thermal stratification, as shown in Fig. 1.1a. The mixing ventilation mainly aims to remove all of the heating/cooling load of the entire space. The principle behind completely mixing is to dilute the contaminants or “excessive” heat with the supplied air. This goal can be achieved by creating air recirculation, resulting in the same concentrations in occupied zones as the exhaust air. To date, there has been convincing evidence that the mixing air distribution spreads out “flooding-like irrigation” features, and the ventilation efficiency is relatively low (Li 2000; Zhao and Li 1998; Rock et al. 1995; Awbi 2008; Croome and Roberts 1981; Zhao 2008; Ma and Yao 2015). Nevertheless, its advantage lies in that the air supply plenums and duct systems are installed in the upper room zone; accordingly, it saves the occupied zone.

For displacement ventilation, indoor polluted air (excessive heat) is replaced by sidewall or underfloor-supplied air. Starting from the perspective of “acting force”, the synergized effects of thermal buoyancy and mechanical momentum are taken into account in displacement ventilation. There is consistency between the mechanical momentum of supplied air and thermal buoyancy for their direction and magnitude, so seldom or rarely mixing occurs between supplied air and ambient air (ASHRAE 2017), as shown in Fig. 1.1b–d. Better air quality can be obtained under this displacement ventilation mode, and excessive heat in the conditioned zone can be removed effectively, which meets the requirements of the living or production process. The thermal stratification phenomenon occurs in the room accordingly. The interface height of thermal stratification in the vertical direction depends on the relationship among air supply position, total air supply rate, heat load, etc. (Li 2000; Zhao and Li 1998; Rock et al. 1995; Awbi 2008; Croome and Roberts 1981; Zhao 2008; Ma and Yao 2015; Griefahn et al. 2001; Lau and Chen 2006).

For displacement ventilation, a slight temperature difference (2.0–4.0 ℃) exists between the jets and surroundings, and so does the supply air velocity (0.1–0.5 m/s). Therefore, displacement ventilation needs a more significant airflow rate under the same cooling load than mixing ventilation. Accordingly, more terminal energy will be consumed; meanwhile, it also occupies the lower room zone for installing plenums and duct systems (Zhao 2010). In addition, there is a risk of draft sensation with the improper design of air distributions (Seppänen 2008). Displacement ventilation is only used for cooling.¹ It can also be used as a fresh air supply system combined with a radiant heating system in rooms (Awbi 2008). In addition, the plenum duct systems for displacement ventilation are mostly installed beneath the interlayer of floors, as shown in Fig. 1.1c, which suggests that it needs to raise the floor (up to 30–50 cm). Compared to mixing ventilation, its initial investment is relatively higher; therefore, its engineering application is much restricted (Fred 2003, 2006; Yuan et al. 1998).

Over the years, Angui Li and his team have been devoted to developing the theory and design methods for the vertical wall (VWAV) and column attachment ventilation (CAV) (Li 2019; Li et al. 2008, 2015). Figure 1.2 shows the schematic diagram of attachment ventilation. It combines the advantages of both mixing ventilation and displacement ventilation and avoids a series of shortcomings, such as low-temperature efficiency of mixing ventilation and occupying workspaces of displacement ventilation. Attachment ventilation aims to focus on the environmental control of the occupied zone or conditioned zone. A vertical air temperature gradient exists in conditioned spaces, so it only bears the partial cooling load and has higher temperature efficiency than mixing ventilation. Attachment ventilation system is used to supply cool/thermal air or remove contaminants, which has been widely used in various scenarios, such as Xiong’an high-speed railway stations (Li et al. 2021), Zhengzhou subway stations (Sun et al. 2021), hospital wards (Li et al. 2020; Zhang et al. 2022), office buildings (Zheng et al. 2019), etc.

Fig. 1.2

Schematic diagram of the air distribution of attachment ventilation. a Vertical wall attachment ventilation (VWAV), b column attachment ventilation (CAV)

Normally, for the interior layout of buildings, the duct systems of attachment ventilation are laid in the upper room space. The supply air moves along the vertical wall or column, impinges the floor, then turns horizontal, creating a thin layer of the air reservoir or air lake. That is to say, thin-layer air spreads evenly over the floor with low velocity and slight temperature differences. The attachment ventilation delivers high-quality fresh air to the occupied zone through the Coanda effect (CE) and extended Coanda effect (ECE) (Li 2019). It meets the requirements of the air temperature, velocity, and concentration field, etc. for the occupied zone. Attachment ventilation mode can be applied to all kinds of spaces with little or large cooling load, especially suitable for large space environmental control. More importantly, attachment ventilation can be applied to solve the problem that thermal air is difficult to deliver to the occupied zone for large spaces in the winter time.

Compared to mixing ventilation, the temperature efficiency of attachment ventilation has been dramatically enhanced. Taking a standardized subway station as an example, under the premise to ensure indoor comfort requirements, the CAV can reduce the airflow rate by 20%, and the cooling capacity by 31%, compared with traditional mixing ventilation. The synthetical coefficient of performance (SCOP) of the air conditioning system has increased by 17%, demonstrating that attachment ventilation can significantly reduce the initial investment and operating energy consumption for the ventilation and air conditioning system (Liu 2018).

This book systematically summarizes the current research progress on attachment ventilation, covering vertical wall (VWAV), column (CAV), and adaptive attachment ventilations (AAV), etc. The parameter correlations of air distribution and case studies are presented. It provides a set of novel air distribution theories and design methods for the building environment.

1.2 Objective Evaluation of the Indoor Air Environment

A series of evaluation indexes can be used to evaluate the ventilation effect. The objective evaluation indexes for the indoor environment mainly comprise the vertical temperature gradient, effective draft temperature θ_ed, ventilation efficiency (temperature efficiency) E_T, thermal stratification interface height, air diffusion performance index (ADPI), velocity non-uniformity coefficient K_V, temperature non-uniformity coefficient K_T, air age $\tau_{{\text{A}}}$, air exchange efficiency $\eta_{{\text{A}}}$, etc. The primary air parameters include jet centerline velocity, excess temperature, averaged air temperature, averaged velocity, mean radiant temperature, operative temperature, radiant temperature asymmetry, etc.

• 1. Vertical temperature gradient

For air distribution modes, there is usually a vertical air temperature difference in the vertical direction, i.e., vertical temperature gradient, which is generally caused by the air temperature difference between supply air and the conditioned zone, internal heat sources, etc. Attachment ventilation aims to provide occupants with clean air for breathing more effectively. With attachment ventilation, it is possible to utilize buoyancy flows that transfer contaminant from the occupied zone towards the upper room zone and improve the air quality inhaled by occupants. Simultaneously, with better air quality, attachment ventilation creates a vertical temperature gradient in the room, with a higher temperature near the ceiling. Additionally, the vertical temperature gradient is a function of flow rate and load.

Also, the high vertical air temperature difference between the head and ankles can cause discomfort. From the perspective of hygiene and human comfort, it is necessary to keep the vertical air temperature difference within a specific range. For instance, ISO (International Organization for Standardization) (BS EN ISO 7730-2005) specifies allowable differences between the air temperature at head level and ankle level, using categories of Class A, B, and C as follows:

• Class A < 2.0 ℃,

• Class B < 3.0 ℃,

• Class C < 4.0 ℃.

The ANSI/ASHRAE standard (ANSI/ASHRAE Standard 55-2017) states that the vertical air temperature difference between the head and ankles should be less than 3.0 °C (sedentary occupants) or 4.0 °C (standing occupants). It should be noted that the above two standards do not specifically emphasize the ventilation modes, i.e., displacement ventilation or mixing ventilation. Chinese standard Design Code for Heating, Ventilation, and Air Conditioning of Civil Buildings (GB50736-2012) stipulates that for displacement ventilation, the vertical air temperature difference between 0.1 and 1.1 m above the floor should not be greater than 3.0 ℃.

REHVA defines the representative measurement heights for air temperature gradient between the head and ankles as: 0.1 and 1.1 m above the floor for a sedentary person; 0.1 and 1.7 m above the floor for a standing person (REHVA 2002; GB/T50785-2012).

If the vertical temperature difference between the head and ankles is less than 8.0 ℃, the local percentage dissatisfied (LPD) caused by the vertical temperature gradient can be determined using Eq. (1.1) (GB/T50785-2012).

$$LPD = \frac{100}{{1 + {\text{exp}}\left( {5.76 - 0.856\Delta t_{{{\text{a}},{\text{v}}}} } \right)}}$$

(1.1)

where

LPD :

local percentage dissatisfied, %;

∆t_a,v:

vertical air temperature difference between head and ankles, ℃.

• 2. Effective draft temperature θ_ed

The effective draft temperature provides a quantifiable comprehensive comfort index at a discrete point in space by combining the physiological effects of air temperature and air movement on the human body. The effective draft temperature θ_ed (a calculated temperature difference that combines air temperature difference and measured air speed at each test point) can be calculated using Eq. (1.2) for cooling conditions (Fanger et al. 1988).

$$\theta_{{{\text{ed}}}} = t_{{\text{x}}} - t_{{\text{n}}} - 8(u_{{\text{x}}} - 0.15)$$

(1.2)

where

θ_ed:

effective draft temperature, ℃;

t_x:

local airstream dry-bulb temperature, ℃;

t_n:

averaged (control) room dry-bulb temperature, ℃;

u_x:

local airstream centerline velocity, m/s.

When the effective draft temperature falls within the range of −1.5 < θ_ed <  +1.0 (ASHRAE Handbook) (ASHRAE 2017) or −1.7 < θ_ed <  +1.1 (Zhu 2010), and the air velocity u_x < 0.35 m/s, most people feel thermal comfort for sedentary occupants.

• 3. Air diffusion performance index

The air diffusion performance index (ADPI) has been developed as an indicator to quantify the comfort level in heating or cooling for a given space conditioned by a mixed air system. ADPI employs the effective draft temperature collected at an array of points taken within the occupied zone to predict comfort. ADPI is the percentage of points in a given space where the effective draft temperature is between −1.7 and +1.1 K for cooling and −2.2 and +2 K for heating. The acceptable air velocity is less than 0.35 m/s for heating and cooling. In addition, the acceptable vertical temperature gradient should be less than 3 K/m (ASHRAE 2017). In other words, ADPI is defined as the percent of test points in the room where the effective draft temperature and mean velocity (speed) meet the criteria in Eqs. (1.3a, 1.3b). ADPI can also be used to evaluate the air diffusion performance of the occupied zone of displacement and attachment ventilation.

For cooling

$$ADPI = \frac{{{\text{Number of measuring points that meet}}\left( { - 1.7 < \theta_{{{\text{ed}}}} < + 1.1} \right)}}{{\text{Total number of measuring points}}} \times 100{\text{\% }}$$

(1.3a)

For heating

$$ADPI = \frac{{{\text{Number of measuring points that meet}}\left( { - 2.2 < \theta_{{{\text{ed}}}} < + 2} \right)}}{{\text{Total number of measuring points}}} \times 100{\text{\% }}$$

(1.3b)

Acceptable air velocity ≤ 0.35 m/s for heating and cooling. For temporary staying zone, such as subway stations, the acceptable air velocity is ≤ 0.5 m/s.

High ADPI values generally correlate to high space thermal comfort levels with the maximum obtainable value of 100%. Selecting inlets/outlets to provide a minimum ADPI value of 80% generally results in a well-mixed space (ASHRAE 2017; Zhao 2008).

• 4. Ventilation efficiency (temperature efficiency) E_T

Ventilation efficiency (temperature efficiency) can be used to evaluate the ventilation effectiveness of air distribution modes (Zhao 2010; Sandberg 1981). Ventilation efficiency refers to the system’s ability to remove excessive heat or pollutants from sources in a given space. It can be understood as the ratio of the supply airflow rate utilized to dilute the pollutants effectively to the total supply airflow rate in the space. It can be further subdivided into transient ventilation efficiency and steady-state ventilation efficiency.

When the indoor excessive heat load remains stable, the steady-state ventilation efficiency can be used to evaluate the air distribution effectiveness to eliminate the heat load in the occupied zone. In terms of this view, the ventilation efficiency can also be called temperature efficiency (dimensionless excess temperature), which is reciprocal to the heat distribution factor m. It can be determined using Eqs. (1.4a, 1.4b)

$$E_{{\text{T}}} = \frac{{t_{{\text{e}}} - t_{0} }}{{t_{{\text{n}}} - t_{0} }}$$

(1.4a)

or

$$m = \frac{{t_{{\text{n}}} - t_{0} }}{{t_{{\text{e}}} - t_{0} }}$$

(1.4b)

where

t_e:

temperature in the exhaust air terminal, ℃;

t₀:

temperature in the supply air terminal, ℃;

t_n:

averaged air temperature of the occupied zone (conditioned zone), ℃.

The evaluation indexes for ventilation effectiveness cover many factors, such as building space types, heat source forms, ventilation modes, etc. It is always challenging to carry out a systematic quantitative analysis of each factor. As a solution, a comprehensive analysis of multiple factors can be performed based on experiments. Zhao (2010) randomly selected experimental data of air supplied downwards and exhausted upwards air distribution. For ventilated spaces of civil and industrial buildings with low-intensity discrete heat sources (q_v < 50 W/m³), Fig. 1.3 shows the relationship between lg Ar and E_T. The experimental conditions are summarized in Table 1.1. E_T can be calculated by Eq. (1.5)

$$E_{{\text{T}}} = 0.31\,{\text{lg}}\,Ar - 0.01\quad \left( {r = 0.{898}} \right)$$

(1.5)

Fig. 1.3

Ventilation efficiency of different ventilation modes (Zhao 2010)

Table 1.1 Experimental conditions of different ventilation modesFootnote

Note from Zhao HZ (2010) Indoor heat convection and ventilation, China Architecture & Building Press, Beijing, Table 1–3.

where Ar is Archimedes number, which is defined as $Ar = \frac{gH}{{u_{0}^{2} }}\frac{\Delta t}{{T_{0} }}$.

For typical room spaces, the averaged velocity of air distribution with underfloor air supply can be approximated by the ratio of the supply airflow rate G to the room cross-sectional area F_n, that is

$$u_{0} = G/F_{{\text{n}}}$$

(1.6a)

$$\Delta t = Q/\rho c_{p} G$$

(1.6b)

Therefore, for nonisothermal rooms

$$Ar = \frac{{gQHF_{{\text{n}}}^{2} }}{{\rho c_{{\text{p}}} T_{0} G^{3} }} = \frac{{B_{0} HF_{{\text{n}}}^{2} }}{{G^{3} }}$$

where B₀ is buoyancy flux, $B_{0} = \frac{gQ}{{\rho c_{{\text{p}}} T_{0} }}$.

For ordinary offices or residential buildings, the ventilation temperature range is 15–40 ℃, and thus $B_{0} \approx 0.000028Q$.

For displacement ventilation with low-intensity heat sources, the relationship between the seven parameters of Q, G, H, F_n, t₀, t_e, t_w in the ventilated room can be determined according to E_T = f (Ar).

It can be observed from Fig. 1.3 that the E_T of mixing ventilation is about 1, while the E_T of displacement ventilation is 1–2. This indicates that the supply air of mixing ventilation and indoor air are intensively mixed, resulting in the temperature of the occupied zone and the exhaust temperature being almost the same, yet displacement ventilation shows a significant temperature gradient $t_{{\text{e}}} > t_{{\text{n}}}$.

• 5. Thermal stratification interface height

In ventilated or air-conditioned rooms, the temperature increases with height in the lower and upper layers. The air enters the room at a low temperature, and is mixed slightly with the room air and heated by convection from the occupied zone, thus making the air temperature at the floor level higher than the supply temperature. The air temperature increases from the floor level to the ceiling, more or less linearly, because the thermal plume rises to the ceiling due to its buoyancy, while the outer, cooler parts of the plume layer according to their temperature. If the thermal plume flow rate G_H at the exhaust opening exceeds the ventilation air flow rate G, part of the excessive thermal flow will be forced to move downward in the reverse direction, as shown in Fig. 1.4.

Fig. 1.4

Thermal stratification interface of a ventilated room

When the ventilation air flow rate G is equal to the flow G_Y of the buoyant plume at a particular height Y section of the room, G = G_Y, the thermal stratification is formed, and the height Y is defined as the thermal stratification interface height Y_s (Zhao 2010). In this scenario, the velocity component in the vertical direction of the airflow at the thermal stratification interface outside the main plume section is 0. Above the thermal stratification interface, the thermal airflow is a vortex turbulent recirculation mixed flow. The negative pressure gradient affects the airflow in the lower zone and shows a low-speed irrotational flow. The vertical temperature distribution outside the main plume is simplified to the model shown in Fig. 1.5.

Fig. 1.5

Simplified model of buoyancy plume diffusion

If the velocity u in the vertical direction is proportional to the distance from the thermal stratification interface height Y_s, that is

$$u = - k\left( {y - Y_{S} } \right) = - k\tilde{y}$$

(1.7)

where $\tilde{y}$ is the height from the thermal stratification interface, $\tilde{y} = y - Y_{S} \ge 0$.

Based on the one-dimensional steady-state energy equation in a room, the vertical temperature distribution of thermal stratification at any height is derived (Zhao 2010)

$$\left( {t - t_{0} } \right)/\left( {t_{{\text{e}}} - t_{0} } \right) = 0.5\left( {1 + erfH^{*} } \right)$$

(1.8)

where

erfH^*:

Gaussian error function, $erfH^{*} = \frac{2}{\sqrt \pi }\int_{0}^{{H^{*} }} {e^{{ - \eta^{2} }} {\text{d}}\eta }$, $H^{*} = \left( {\frac{{k\tilde{y}^{2} }}{2a}} \right)^{0.5}$;

a:

thermal conductivity, W/m⋅K;

t₀:

air supply temperature, ℃;

t_e:

air exhaust temperature, ℃.

The vertical temperature curve in Fig. 1.6 represents a symmetrical nonlinear distribution (Zhao 2010), with the thermal stratification interface height Y_S as the origin. For y = Y_s, t = (t₀ + t_e)/2, that is, the temperature of the thermal stratification interface is just the averaged value of the supply and exhaust air temperature.

Fig. 1.6

Vertical temperature distribution of thermal stratification

Thermal stratification interface height is an essential characteristic parameter that describes thermal stratification flow features. It is related to factors such as indoor vertical temperature distribution, indoor-outdoor temperature differences, geometric forms, locations, number of heat sources, ventilation modes, and even wall heat transfer. For the thermal stratification interface height of the indoor space with an isolated heat source, substituting ventilation airflow rate G into plume flow rates G_Y of various heat sources to obtain the thermal stratification interface height expression. For heat sources with different shapes or multiple heat sources, the corresponding thermal stratification interface height can be obtained by correcting a single heat source (Zhao 2010).

• 6. Velocity and temperature non-uniformity coefficient

Differences in air velocity and temperature exist in different room space positions. This difference can be evaluated by the non-uniformity coefficient. The velocity non-uniformity coefficient K_v and temperature non-uniformity coefficient K_t are defined as

$$K_{{\text{v}}} = \frac{{\sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {(u_{i} - \overline{u} )^{2} } } }}{{\overline{u} }}$$

(1.9a)

$$K_{{\text{t}}} = \frac{{\sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {(t_{i} - \overline{t})^{2} } } }}{{\overline{t}}}$$

(1.9b)

where

n:

number of sampling points;

u_i, t_i:

velocity, and temperature of each sampling point, respectively;

$\overline{u}$, $\overline{t}$:

arithmetic averaged of velocity and temperature of each sampling point.

• 7. Air age

The concept of air age in indoor air distribution is derived from the experience of the reaction time of chemical kinetics (Wang 1992), which initially refers to the time from the start of the reaction of the material in the reactor to the time when the required conversion rate is reached, that is, the reaction duration. In a continuous flow reactor, the time the material particles enter the reactor until departure is the residence time.

When comparing the air movement process of the indoor air distribution to the flow of materials in the reactor, the concepts of the air age τ_A and air residence time τ_r can be obtained (Fanger et al. 1988; Li et al. 2003; Sandberg and Sjoberg 1983; ASHRAE 2017). The “youngest” air is at the point where outdoor air enters a room by mechanical or natural ventilation, or through infiltration. The “oldest” air may be at some location in the room or in the exhaust air. When the air distribution system’s characteristics are varied, air age is inversely correlated with the quality of outdoor air delivery (ASHRAE 2017).

Obviously, the air age τ_A refers to the time it takes for the air to enter the room until it reaches a certain point A in the room, which is illustrated in Fig. 1.7. The air residence time, τ_r is the time it takes for the air from the entrance until departure. The residual time τ_rl (or life expectancy) is defined as the time required for the air to leave the exit from the current position (Fig. 1.7). For the gas micro-cluster, which are groups of air molecules at a specific location in the room, the relationship between air age, residence time, and residual time is as follows

$$\tau_{{\text{A}}} + \tau_{{{\text{rl}}}} = \tau_{{\text{r}}}$$

(1.10)

Fig. 1.7

Air age, residual time, and residence time at room point A

Essentially, air age reflects the ability of different air distributions to remove pollutants (including thermal pollution), and it can be obtained by experiments. When using the step-down (decay) tracer gas method, fill the room with tracer gas and then supply air (tracer gas concentration is 0) to the room. The initial concentration at point A (any point) in the room is c(0). The time-dependent data of tracer gas concentration c($\tau$) are available by measuring tracer gas concentration at point A at every certain time. The time-averaged air age is defined as

$$\tau = \frac{{\mathop \int \nolimits_{0}^{\infty } c\left( \tau \right){\text{d}}\tau }}{c\left( 0 \right)}$$

(1.11)

The time-averaged air age in the room is defined as the average of the local averaged air age at each point, that is

$$\overline{\tau } = \frac{1}{V}\int\limits_{V} \tau {\text{d}}V$$

(1.12)

where V is the room volume, m³.

The averaged air age of the whole room is 1/2 of the residence time τ_r, that is

$$\overline{\tau } = 1/2\tau_{{\text{r}}}$$

(1.13)

If the ventilation airflow pattern in the room is taking the shape of ideal piston flow, the air residence time is the shortest, which is equal to the nominal time constant, i.e., the room volume to the ventilation volume, τ_n = V/G, that is

$$\tau_{{\text{r}}} = \tau_{{\text{n}}} = V/G$$

(1.14)

Generally, it refers to the airflow inside a room in the concept of air age, and the air age at the room’s entrance is regarded as 0. If the influence of the air handling equipment and the flow process in air supply ducts are taken into account, the concept of air age should be modified. The time that the gas micro-cluster enters the ventilation system from outdoor to a certain point A in the room, can be defined as the modified air age (or total air age), which reflects the air freshness of different ventilation or air conditioning systems.

• 8. Air exchange efficiency

Air exchange efficiency, η_a, is an index used to evaluate ventilation effect: how efficiently room air is replaced by supply air. It is one of the characteristic parameters of air distribution and has nothing to do with pollutants (Zhu 2010). The air exchange efficiency is defined as the ratio between the shortest possible time needed for replacing the air in a room (τ_n) and the average time for whole room air exchange (τ_r). It is a dimensionless number expressing the effectiveness of renewal of the internal air population by the supply air.

$$\eta_{{\text{a}}} = \frac{{\tau_{{\text{n}}} }}{{\tau_{{\text{r}}} }} = \frac{{\tau_{{\text{n}}} }}{{2\overline{\tau }}}$$

(1.15)

According to the relation (1.15), the upper limit for this efficiency is 100%, which occurs for idea flow.

The air exchange efficiency η_a is ≤ 100%. The greater the air exchange efficiency, the better the ventilation performance. The air exchange efficiency of some typical ventilation modes is as follows:

• η_a = 100% for piston flow;

• η_a≈100% for perforated ceiling air supply;

• η_a = 50–100% for lower-supply and upper-exhaust with single air vents.

It should be pointed out, when defining the air exchange efficiency of mechanical ventilation, the influence of envelope airtightness on air age is not considered. A building’s envelope airtightness can be measured with a blower-door test or pressure pulse method (JGJ/T 177-2009). Here, the blower-door test is mentioned by the way. The airflow rate is generally measured at 50 and −50 Pa pressure differences. The envelope airtightness is quantified by Eq. (1.16) by calculating the air change rate.

$$N_{50}^{ \pm } = G/V$$

(1.16)

where $N_{50}^{ + }$, $N_{50}^{ - }$ is the air change rate at pressure differences of 50 and −50 Pa, h⁻¹.