Nonisothermal Attachment Ventilation Mechanisms

Abstract

Under nonisothermal conditions, the heated or cooled supply air jet interacts with indoor convection of heat sources, producing a specific temperature field, velocity field, and concentration field. This chapter deals with the airflow mechanisms of nonisothermal attachment ventilation. It discusses the air movement of nonisothermal attached jets, which provides a theoretical basis for the design of the air distribution system for attachment ventilation. The parameter correlations of temperature and velocity distribution of attachment ventilation, etc., are obtained. The influencing factors of human movement and wall roughness elements on the airflow field have also been discussed.

Under nonisothermal conditions, the heated or cooled supply air jet interacts with the indoor convection of heat sources, producing a specific temperature field, velocity field, and concentration field. This chapter mainly discusses the indoor air movement of nonisothermal attachment ventilation, including VWAV, RCAV, CCAV, etc., which provides a theoretical basis for designing attachment ventilation. The parameter correlations of temperature and velocity distribution of attachment ventilation are established. The influencing factors of human movement and wall roughness elements on the airflow field have also been discussed.

4.1 Nonisothermal Vertical Wall Attachment Ventilation

The jet flow can be divided into thermal plumes, momentum jets, and buoyant jets. The thermal plume refers to the air currents rising from a hot body or descending from a cold body, and buoyancy usually promotes its further movement and diffusion after entering the environment. The momentum jet refers to fluid flows produced by a pressure drop through an orifice or opening. The buoyant jet, also called a forced plume, refers to the flow whose motion is transitioning from a plume to a momentum jet. In fact, it is a kind of modified plume or momentum jet.

Considering the influence of thermal buoyancy caused by the density or temperature difference, the continuity equation, and momentum equation can be expressed in the following forms (see Fig. 3.2b for the coordinate system)

$$\frac{\partial u}{{\partial y^{ * } }} + \frac{\partial v}{{\partial x}} = 0$$

(4.1)

$$u\frac{\partial u}{{\partial y^{ * } }} + v\frac{\partial u}{{\partial x}} = g - \frac{1}{\rho }\frac{\partial p}{{\partial y^{ * } }} + \frac{\partial }{\partial x}\left( { \in \frac{\partial u}{{\partial x}}} \right)$$

(4.2)

Let ρ_n denote the density of the surrounding fluid, and assume the pressure of the surrounding fluid is the static pressure distribution in the vertical direction, so

$$\frac{\partial p}{{\partial y^{*} }} = \rho_{{\text{n}}} g$$

(4.3)

Since the air density difference is slight, the Boussinesq approximation can be adopted. The Boussinesq model neglects density differences except in the gravity term of the momentum equation. In Eq. (4.2), ρ of the pressure gradient term is replaced by ρ_n (except for the natural convection with high temperature difference, the simplification is reasonable), and Eq. (4.2) is written as

$$u\frac{\partial u}{{\partial y^{ * } }} + v\frac{\partial u}{{\partial x}} = \frac{{\rho - \rho_{{\text{n}}} }}{{\rho_{{\text{n}}} }}g + \frac{\partial }{\partial x}\left( { \in \frac{\partial u}{{\partial x}}} \right)$$

(4.4)

For buoyant jets, the specific momentum flux M and the specific buoyancy flux B are two parameters of great significance, which can be used to describe the characteristics of buoyant jets.

In a specific cross-section, the total momentum of the buoyant jet is

$$m = \int\limits_{0}^{\infty } {\rho u^{2} {\text{d}}x}$$

(4.5)

Specific momentum flux is

$$M = \frac{m}{\rho } = \int\limits_{0}^{\infty } {u^{2} {\text{d}}x}$$

(4.6)

The specific buoyancy flux B reflects the initial density gradient between the mixture injection fluid and ambient fluid.

According to the principle of mass conservation, the flux conservation relationship of the density difference ρ − ρ_n can be obtained

$$\int\limits_{0}^{\infty } {u\frac{{\rho - \rho_{{\text{n}}} }}{{\rho_{{\text{n}}} }}g\,{\text{d}}x} = {\text{Constant}}$$

(4.7)

The specific buoyancy flux is

$$B = \int\limits_{0}^{\infty } {u\frac{{\rho - \rho_{{\text{n}}} }}{{\rho_{{\text{n}}} }}g\,{\text{d}}x}$$

(4.8)

Here, the dimensional analysis method is applied to determine the maximum velocity and temperature decay rate.

First, the plume in steady state is considered. Ignore the initial flow rate and initial momentum of the plume, and consider the time-averaged characteristics of the plume as a function of specific buoyancy flux B, axial distance y*, kinematic viscosity ν, and diffusion coefficient k, thus (Rodi 1982)

$$u_{{\text{m}}} = f\left( {B,y^{ * } ,\nu ,k} \right)$$

(4.9)

The dimension of B is L³S^-3. According to dimensional analysis, u_m is given by

$$u_{{\text{m}}} = B^{\frac{1}{3}} f\left( {\frac{{B^{\frac{1}{3}} y^{*} }}{v},\frac{v}{k}} \right)$$

(4.10)

where

$\frac{{B^{\frac{1}{3}} y^{*} }}{v}$:

local Reynolds number;

$\frac{\nu }{k}$:

Prandtl number.

For the fully developed turbulent plume, it can be assumed that the flow is self-similarity with respect to the local Reynolds number (this hypothesis is reasonable and validated by Pera et al. 1971 and Mollendorf and Gebhart 1973), and the molecular characteristics of the fluid are not of great importance, then $f\left( {\frac{{B^{\frac{1}{3}} y^{*} }}{v},\frac{v}{k}} \right)$ tends to a non-zero limit constant K_p. The final formulation of u_m thus reads

$$u_{{\text{m}}} = K_{{\text{p}}} B^{\frac{1}{3}}$$

(4.11)

For the buoyant jet, a characteristic length scale $l_{M} = \frac{{M_{0} }}{{B_{0}^{\frac{2}{3}} }}$ is defined. Here, M₀ is the initial specific momentum flux, and B₀ is the initial specific buoyancy flux. This scale can determine the relative magnitude of momentum and buoyancy. It can be considered that the time-averaged features of the buoyant jet is a function of the initial specific momentum flux M₀, the initial specific buoyancy flux B₀, and the axial distance y^*, thus

$$u_{{\text{m}}} = f\left( {M_{0} ,B_{0} ,y^{*} } \right)$$

(4.12)

where the dimension of M₀ is L³S^-2, dimension of B₀ is L³S^-3. According to dimensional analysis, u_m is given by

$$u_{{\text{m}}} = \left( {\frac{{M_{0} }}{{y^{*} }}} \right)^{\frac{1}{2}} f\left( {\frac{{y^{*} B_{0}^{\frac{2}{3}} }}{{M_{0} }}} \right)$$

(4.13)

When $\frac{{xB_{0}^{\frac{2}{3}} }}{{M_{0} }} \to \infty$, the buoyancy dominates flow, the buoyant jet changes into a plume. According to the previous analysis, we can see that $u_{{\text{m}}} \sim y^{{{*}0}}$, and thus $f\left( {\frac{{y^{ * } B_{0}^{\frac{2}{3}} }}{{M_{0} }}} \right) \to \left( {\frac{{y^{ * } B_{0}^{\frac{2}{3}} }}{{M_{0} }}} \right)^{\frac{1}{2}}$.

If $\frac{{xB_{0}^{\frac{2}{3}} }}{{M_{0} }} \to 0$, the buoyancy effect can be neglected, the buoyant jet changes into a momentum jet. From the analysis in the previous chapters, we can see that $u_{{\text{m}}} \sim y^{{{*} - \frac{4}{3}}}$, and thus $f\left( {\frac{{y^{ * } B_{0}^{\frac{2}{3}} }}{{M_{0} }}} \right) \to \left( {\frac{{y^{ * } B_{0}^{\frac{2}{3}} }}{{M_{0} }}} \right)^{{ - \frac{5}{6}}}$.

From the above analysis, it can be concluded that the exponent of axial distance y^* should be in the range of $- \frac{4}{3}\sim 0$ as a function of centerline velocity u_m of the nonisothermal attached jet, and the specific expression depends on the relative magnitude of $y^{ * } \cdot B_{0}^{\frac{2}{3}}$ and M₀. Since B₀ ≪ M₀ is common in actual conditions, the exponent should be closer to $- \frac{4}{3}$, which is also illustrated in the empirical curve obtained from the experiment, see Fig. 4.1a.

Fig. 4.1

Influence of supply air temperature t₀ and heat flux intensity q on the centerline velocity and temperature in the vertical attachment region (h = 2.5 m, u₀ = 3.0 m/s). a Dimensionless centerline velocity, b excess temperature decay

When Eq. (4.13) is used for nonisothermal attached jets, the exponent functional relationship of the centerline velocity u_m with respect to the axial distance y^* can be determined experimentally.

In engineering applications, the heat load distribution can be considered evenly distributed on the floor with a constant heat flux intensity, as the indoor heat distribution of ordinary offices or residential buildings is scattered, and human movement enhances indoor air uniformity. Taking ordinary office buildings as an example, the influence of supply air temperature t₀ and heat load q (heat flux intensity) is investigated, and detailed information is shown in Table 4.1.

Table 4.1 Cases with different air supply temperature t₀ and heat flux intensity q (h = 2.5 m, u₀ = 3.0 m/s)

The jet centerline velocity and excess temperature decay for the vertical attachment region are shown in Fig. 4.1. As shown in Fig. 4.1a, it is found that for different heat flux intensities and supply air temperatures, there is the similarity of the centerline velocity distributions.

In the condition of 0 ≤ y^*/b ≤ 7.5, the centerline velocity remains unchanged in the initial attachment region, and then the jet enters the main region with the fully developed turbulence. With the increase of supply air throw, the centerline velocity decreases exponentially, which can be regarded as linear decay within a certain distance. When y^*/b > 47.5, in the jet terminal, the centerline velocity decays sharply due to impinging effect. Since the fluid micro-cluster with low momentum in the viscous fluid boundary layer is not enough to resist the increased pressure caused by impinging, the jet separates from the wall (see Fig. 4.1a).

The consistency of the distribution of centerline velocity u_m and centerline temperature t_m is discussed below. The momentum equation and enthalpy difference equation are listed

$$\int\limits_{0}^{\infty } {\rho u^{2} \,{\text{d}}x} = \rho_{0} u_{0}^{2} b$$

(4.14)

$$\int\limits_{0}^{\infty } {\rho uc_{{\text{p}}} \left( {t - t_{{\text{a}}} } \right){\text{d}}x} = \rho_{0} u_{0} c_{{\text{p}}} \left( {t_{0} - t_{{\text{n}}} } \right)b$$

(4.15)

where t_n is the temperature of surrounding air and c_p is the specific heat at constant pressure.

Equations (4.14) and (4.15) lead to the following approximate relationship

$$\frac{{u_{{\text{m}}} }}{{u_{0} }}\sim \frac{{t_{{\text{m}}} - t_{{\text{n}}} }}{{t_{0} - t_{{\text{n}}} }}$$

(4.16)

Some studies have also presented the following empirical correlations of nonisothermal turbulent jets (Ping 1995)

$$\frac{{t_{{0}} - t_{{\text{n}}} }}{{t_{{\text{m}}} - t_{{\text{n}}} }} \approx \left( {\frac{u}{{u_{{\text{m}}} }}} \right)^{{{\text{Pr}}}}$$

(4.17)

For any position y, the temperature profile is wider than the velocity profile. This is because the exponent Pr ≈ 0.7 for air, and $\frac{u}{{u_{{\text{m}}} }}$ is always less than 1.

Thus, as a simplification, it can be approximated that the centerline velocity decay and the excess temperature decay have almost the same form, and the experimental data also support this argument (see Fig. 4.1).

In the horizontal air reservoir region, the centerline velocity profile is almost consistent with excess temperature, as shown in Fig. 4.2. It can be found from experimental results that the jet presents an “elastic effect” in the jet impinging region. The centerline velocity in the horizontal region first rises (x/b ≤ 10 in the jet impinging region) and then falls. The jet centerline temperature almost decreases linearly due to the mixing with the surrounding air. However, outside the range of x/b ≥ 90 –100, the centerline velocity and temperature drop rapidly. It should be noted that in summer conditions, the cold air jet may be heated by floor (t_m ≥ t_n), so the excess temperature is negative in the flow terminal.

Fig. 4.2

Influence of t₀ and q on the centerline velocity and temperature in the horizontal air reservoir region of attachment ventilation. a Centerline velocity distribution, b excess temperature distribution

4.2 Nonisothermal Column Attachment Ventilation

In the vertical attachment region, as shown in Fig. 4.3, the decay of centerline velocity and excess temperature show good similarity. In RCAV, the ambulatory-shaped “▣” air inlet is usually adopted. The mixing properties of the airflow resulting from the interaction of flow due to the rectangular column’s arris is investigated. Researches show that the RCAV’s velocity and temperature decay more quickly than that of VWAV.

Fig. 4.3

Influence of t₀ and q on the centerline parameters in the vertical attachment region of RCAV. a Centerline velocity distribution, b excess temperature decay

Generally, for CCAV, the curvature radius r of the circular column is large enough than the magnitude boundary layer thickness δ, the influence of column curvature can be ignored. In this condition, the experimental study shows that the flow feature of CCAV is similar to that of RCAV.

In the horizontal air reservoir region, the decay of centerline velocity and excess temperature is shown in Fig. 4.4. The dimensionless centerline velocity and temperature distribution in the main regions are self-similarities. However, due to the “arris effect” of rectangular columns, the intersection and superposition of two adjacent attached jets further consume the jet momentum. Compared RCAV and VWAV, the former’s centerline velocity is slightly lower.

Fig. 4.4

Effect of t₀ and q on characteristics of the horizontal air reservoir region of RCAV. a Dimensionless centerline velocity, b excess temperature distribution. The reason for the negative value of excess temperature is that the floor heat sources may cause the centerline temperature t_m to be higher than the indoor averaged temperature t_n, $\frac{{t_{{\text{n}}} - t_{{\text{m}}} }}{{t_{{\text{n}}} - t_{{0}} }} < 0$

As discussed in Chap. 3, the time-averaged velocity distributions have proved to be sufficient in reflecting the fundamental features of attachment ventilation. The time-averaged centerline velocity distribution in the horizontal air reservoir region of CCAV is consistent with that of the RCAV, as shown in Fig. 4.5. That is to say, the centerline velocity increases at the initial stage and then decreases, and the excess temperature decreases exponentially.

Fig. 4.5

Effect of t₀ and q on characteristics of the horizontal air reservoir region of CCAV. a Dimensionless centerline velocity, b excess temperature decay

4.3 Characteristic Parameter Correlations of Nonisothermal Attachment Ventilation

The thermal jet flows of different attachment ventilation modes (including VWAV, RCAV, CCAV, etc.) indicate dissimilarities and similarities. The characteristics of the jet flow field of three types of nonisothermal attachment ventilation under different parameters, including supply air height h and velocity u₀ are compared as follows.

4.3.1 Vertical Attachment Region

The centerline velocity and temperature distribution in the vertical attachment region under different air supply heights (h = 2.5, 6.0, and 8.0 m) are illustrated in Figs. 4.6, 4.7, and 4.8. y^*_max is defined as the maximum attaching length, and it can be expressed by Eq. (4.18).

$$y_{\max }^{*} = 0.92h - 0.43$$

(4.18)

Fig. 4.6

Parameters variations in the vertical attachment region of VWAV. a Centerline velocity, b excess temperature distribution

Fig. 4.7

Parameters variation in the vertical attachment region of RCAV. a Centerline velocity, b excess temperature distribution

Fig. 4.8

Parameters variation in the vertical attachment region of CCAV. a Centerline velocity, b excess temperature distribution

Equation 4.18 is applicable when h ≥ 0.5 m.

With regard to the building space size, noise limitation, and economy, in the range of 0 < y^*/b ≤ 70 of VWAV, Eq. (4.18) would possess better accuracy, and the error is generally no more than 5%. When the air supply height increases from 2.5 to 8.0 m, the separation point rises slightly and lies in the range of 0.5–1.0 m.

The equations shown in Table 4.2 characterize the decay profile of centerline velocity and excess temperature in the VWAV, RCAV, and CCAV.

Table 4.2 Comparison of centerline velocity and excess temperature in the main section of the vertical attachment region

For the engineering application, taking the simple and practical as a principle, the centerline velocity and temperature decay in the vertical attachment region of the VWAV, RCAV, and CCAV can be uniformly expressed by Eqs. (4.19) and (4.20). The correlation equations have high accuracy in the range $y^{*} /b \le 40$, and the error is no more than 5–8% (5% for the vertical attachment region, and 8% for the horizontal air reservoir region, respectively). For nonisothermal attached jets, the arris effect of a rectangular column and the curvature effect of a circular column gradually appear some distance away from the air inlet or opening (see the region of y^*/b > 40 in Fig. 4.9).

$$\frac{{u_{{\text{m}}} (y^{*} )}}{{u_{0} }} = \frac{1}{{0.012\left( {\frac{{y^{*} }}{b}} \right)^{1.11} + 0.90}}$$

(4.19)

$$\frac{{t_{{\text{n}}} - t_{{\text{m}}} }}{{t_{{\text{n}}} - t_{{0}} }} = \frac{1}{{0.01\left( {\frac{{y^{*} }}{b}} \right)^{1.11} + 0.942}}$$

(4.20)

Fig. 4.9

Unified correlations of centerline velocity and excess temperature distributions in the vertical attachment region of three attachment ventilation modes. a Centerline velocity distribution, b excess temperature decay

The arris effect of a rectangular column and the curvature effect of a circular column will influence the flow field. However, with the increase of the rectangular column’s length-to-width ratio or the circular column’s curvature radius, both the airflow patterns of RCAV and CCAV tend toward that of VWAV. The recommended slot inlet widths of attachment ventilation are shown in Fig. 4.10 (Chen 2018). For example, for a circular column with a diameter of 500 mm, the upper and lower bounds of f/F of slot inlet are 0.05 and 0.7, respectively. It is recommended that the slot inlet width should be selected within 30–150 mm.

Fig. 4.10

Slot inlets or air inlets width range of attachment ventilation. a Recommended slot inlet width for CCAV, b geometric parameters of the circular column

4.3.2 Horizontal Air Reservoir Region

The centerline velocity distribution in the horizontal air reservoir region of VWAV, RCAV, and CCAV under different air supply heights are shown in Fig. 4.11. The air supply velocity should be further enhanced for the larger air supply height. The larger air supply height and velocity trigger expanding the impinging region and intensifying the air entrainment rate.

Fig. 4.11

Comparison of centerline velocities in horizontal air reservoir region of three attachment ventilation modes. a Vertical wall, b rectangular column, c circular column

The airflow centerline velocity away from the vertical wall of 1.0 m, which is the boundary of the control zone (more information can be found in Chap. 6), can be calculated by Eq. (4.21) (physically “equivalent” to the air supply velocity of displacement ventilation).

$$\frac{{u_{{\text{m}}} (y_{\max }^{*} )}}{{u_{0} }} = k_{{\text{v}}} \frac{{u_{{{\text{m,1}}{.0}}} }}{{u_{0} }} + C_{{\text{v}}}$$

(4.21)

where

• u_m,1.0 = air velocity in the control boundary, i.e., the airflow centerline velocity in the air reservoir region at a distance of 1.0 m from the vertical wall, m/s;

• u_m(y^*_max) = centerline velocity at the separation point of a wall-attached jet, m/s;

• k_v, C_v = empirical coefficient, which are different for different attached walls. k_v = 1.808, C_v = −0.106 for VWAV; k_v = 1.374, C_v = −0.060 for CAV.

The excess centerline temperature distributions in the horizontal air reservoir region of the VWAV and CAV are shown in Fig. 4.12. The excess centerline temperature decreases linearly in most areas of the horizontal air reservoir region. It can be observed that there is a negative excess temperature. The centerline temperature t_m will increase due to the floor heat sources and is higher than the indoor temperature t_n, so the excess temperature $\frac{{t_{{\text{n}}} - t_{{\text{m}}} }}{{t_{{\text{n}}} - t_{0} }} < 0$.

Fig. 4.12

Effect of air supply heights on centerline temperature in the horizontal air reservoir region. a Vertical wall, b rectangular column

The correlations of jet characteristic parameters of attachment ventilation under isothermal and nonisothermal conditions are summarized in Table 4.3.

Table 4.3 Correlations of characteristic parameters of attachment ventilation under isothermal and nonisothermal conditions

In summary, there are self-similarities for the centerline velocity and excess temperature in the jet’s main regions (regions I and III). The centerline velocity can be uniformly expressed as

$$\frac{{u_{{\text{m}}} (\gamma )}}{{u_{0} }} = \frac{1}{{a_{i} \left( {\frac{\gamma }{b} + b_{i} } \right)^{{\text{m}}} + c_{i} }}$$

(4.22)

The excess temperature in the vertical attachment region can be uniformly expressed as

$$\frac{{t_{{\text{n}}} - t_{{\text{m}}} }}{{t_{{\text{n}}} - t_{0} }} = \frac{1}{{a_{j} \left( {\frac{\gamma }{b} + b_{j} } \right)^{{\text{n}}} + c_{j} }}$$

(4.23)

where $\gamma = y^{*}$ for the vertical attachment region, $\gamma = x$ for the horizontal air reservoir region. $y^{*}$ is the vertical distance from the jet entrance along the flow direction of the vertical wall to a given point, x is the horizontal distance from a given point in the horizontal air reservoir region to the vertical attached-wall surface, and b is the characteristic width scale of the air inlet or opening. In addition, the coefficients a_i, b_i, c_i, and a_j, b_j, c_j are related to the air inlet structures (turbulence coefficient), the air inlet position, etc.

4.4 Air Opening and Control Zone in Rooms

The main elements affecting room air environmental parameters include the air supply velocity and temperature difference. The following factors should also be taken into account.

• (a) form of air openings, such as geometry and location of air inlets, and exhaust outlets;

• (b) interior geometry and room occupied zone;

• (c) heat source’s location, distribution, and heat dissipation, including room surface temperature;

• (d) internal disturbances (such as human activities, industrial production, etc.);

This section analyzes factors such as the shapes of the air opening, the control zone, etc.

4.4.1 Influence of Air Opening Types

In this section, taking the slot inlet used in the RCAV and CCAV as examples, the effects of the circular column diameter and the rectangular column dimension on the attachment ventilation performance are analyzed, respectively.

• 1. Circular column diameter

The velocity distributions under different column diameters are shown in Fig. 4.13. The velocity decay of the attached jet becomes slower as the column diameter d increases from 0.25 to 1.50 m. With the increase of the column diameter, the air inlet area and air supply rate are correspondingly enlarged, the thickness of the air reservoir is increased, and the horizontal jet throw is enhanced. Therefore, large-size columns are required for larger spaces.

Fig. 4.13

Velocity distributions of room longitudinal section with different column diameters. a d = 0.25 m, b d = 0.75 m, c d = 1.00 m, d d = 1.50 m

• 2. Rectangular column side length

Taking the square column as an example, the velocity in the horizontal air reservoir region increases by about 0.1 m/s as the column side length increases from 0.6 to 1.0 m when the air supply velocity is 1.5 m/s, as shown in Fig. 4.14. In the horizontal reservoir zone, the smaller the column’s side length a, the more significant impact of the arris effect on the air movement. The increase of the column’s side length a means the augment of the air supply rate, and decrease of the occupied zone temperature.

Fig. 4.14

Influence of side length of the square column. a Velocity and temperature field in the longitudinal section, b temperature field in the ankle plane

• 3. Plenum

The plenum is a device that converts dynamic pressure into static pressure, and it is used to stabilize the opening airflow, and reduce the airflow turbulence and noise to ensure the slots’ air supply uniformity. The uniformed or low turbulence intensity airflow is the goal of the plenum design. So, the appropriate plenum can improve ventilation or temperature efficiency (Li et al. 2010; Hanzawa et al. 1987).

Here, plenums used for CCAV are presented as examples, which have been installed in Zhengzhou subway station, as shown in Fig. 4.15.

Fig. 4.15

Plenums used for CCAV. a Prototype, b installed in Zhengzhou subway station, c 3-dimensional structure, d plan view of the plenum, e structure and test points, f air velocity testing at the plenum opening

As illustrated in Fig. 4.15, the plenum design parameters for CCAV are as follows:

• Plenum: inner diameter Φ₁ = 1.26 m, outer diameter Φ₂ = 2.10 m, plenum thickness 0.60 m.

• Grille opening on the bottom of the plenum: inner diameter φ₁ = 1.50 m, outer diameter φ₂ = 1.59 m, net area A = 0.16 m².

In this plenum, two pieces of perforated plates with variable aperture sizes are fixed inside the plenum. For instance, when the measured airflow rate is 2000 m³/h, the plenum overall velocity non-uniformity coefficient is 6.8%, with excellent air supply uniformity, as shown in Fig. 4.15e.

4.4.2 Control Zone and Column Spacing

From the view of human comfort, the control zone (occupied zone) is generally within 2.0 m from the floor. While for the industrial environment, the scope of the control zone is related to the service objects.

The jet effective diffusion radius and the jet envelope surface are defined as follows.

• (1) Jet effective diffusion radius for CAV. The horizontal distance from the attached wall to the point where the jet speed decays to 0.25 m/s (allowed air speed). For temporary staying zones, such as airport terminals, subways stations, and other temporary stops of traffic places, the allowed air speed can be taken as 0.5–0.8 m/s. For multiple columns arranged uniformly on the ground, the effective diffusion radius is (l − d)/2, where l is the column center spacing, and d is the column hydraulic diameter.

• (2) Airflow envelope surface. The interface formed by the constant velocity points, where the air velocity is specified by ventilation design. The velocity of the airflow envelope surface can be taken as 0.25–0.5 m/s (JG/T 20-1999). As shown in Fig. 4.16, there are three airflow envelope surfaces with a velocity of 0.5 m/s for different attachment ventilation modes.

  Fig. 4.16

  

  Airflow envelope surfaces of several attachment ventilation modes. a VWAV, b RCAV, c CCAV

• 1. Control zone

Figure 4.17 presents the velocity field distribution for different occupied zone lengths. The occupied zone lengths are 5.4 m (size ratio, i.e., length/height ratio L/h = 2.1) and 2.5 m (L/h = 1.0), respectively, with the same jet inlet height and location. When the length of occupied zone L changes from 5.4 to 2.6 m, the control zone shrinks, the jet flow field “thickens”, and the wall-normal velocity gradient decreases. When L/h = 1.0, the inducing effect of the upper exhaust outlet is more significant, which may cause a short circuit of the airflow path. When the air supply velocity increases from 1.0 to 2.0 m/s, the vortex at the far end of the horizontal air reservoir region becomes remarkably larger. It is recommended that h/L should not exceed 1:1.5.

Fig. 4.17

Influence of size ratios L/h on the flow field. a u₀ = 1.0 m/s, L/h = 2.1, b u₀ = 1.0 m/s, L/h = 1.0, c u₀ = 2.0 m/s, L/h = 2.1, d u₀ = 2.0 m/s, L/h = 1.0

• 2. Column spacing

In HVAC engineering applications, there are usually multiple columns in large spaces. When column attachment ventilation is used, those columns will lead to confluence flow in the air reservoir region (Wu 2019). As shown in Fig. 4.18, the double-column and four-column attached air supply form a “−” shaped and a “+” shaped airflow pattern, respectively. There seems to be an “invisible air wall” between the two columns; thus, the flow field of muti-columns can be regarded as the confined single-column attached airflow. The design of multi-column attachment ventilation can refer to the single-column attachment ventilation design method. However, their throw may be different.

Fig. 4.18

CFD simulation and flow visualization of multi-column attachment ventilation. a, c, e CFD simulation, b, d, f flow visualization

The effective diffusion radius of the RCAV airflow on the horizontal floor is related to the control zone length (column spacing), indicated by the symbol l. The velocity and temperature distribution of the longitudinal section (vertical section) and human ankle cross-section (y = 0.1 m) are shown in Figs. 4.19 and 4.20, respectively, in the conditions of the air supply velocity u₀ = 1.50 m/s, air supply temperature t₀ = 15 ℃, and floor cooling load q = 100 W/m². Although l is different, from 6 to 12 m, there is all apparent vertical temperature stratification, and the temperature gradient in the occupied zone (within 2.0 m above the floor) is approximately 2 ℃.

Fig. 4.19

Velocity and temperature contours of RCAV in the central longitudinal section. a l = 6 m, velocity contour, b l = 9 m, velocity contour, c l = 6 m, temperature contour, d l = 9 m, temperature contour

Fig. 4.20

Velocity and temperature contours of RCAV in the ankle plane (y = 0.1 m) of rectangular column attached air supply. a l = 6 m, velocity contour, b l = 12 m, velocity contour, c l = 6 m, temperature contour, d l = 12 m, temperature contour

4.4.3 Airflow at the Exhaust Outlet

The room airflow distribution is mainly determined by the air jet discharged from the air inlet. The exhaust outlet (suction outlet) has a limited influence due to the rapid decay of airflow velocity near the outlet. For a spherical suction outlet, the radial velocity is approximately inversely proportional to the square of the distance from the air outlet. For the long and narrow slots, the velocity is inversely proportional to their width.

Generally, the width-length ratio of the exhaust outlet is greater than 0.2, and $0.2 \le \frac{x}{d}$ (or $\frac{x}{{1.13\sqrt {F_{0} } }} \le 1.5$), the exhaust outlet velocity decay can be estimated by Eq. (4.24)

$$\frac{u}{{u_{0} }} = \frac{1}{{9.55\left( \frac{x}{d} \right)^{2} + 0.75}}$$

(4.24)

The airflow velocity decays to about 5% of the center velocity at double diameters away from the exhaust outlet. For attachment ventilation, the exhaust outlet can be located at the upper sidewall or the center of the ceiling.

4.5 Effect of Heat Sources on Indoor Airflow

One of the ventilation tasks is eliminating the excessive heat generated by indoor heat sources. The indoor air temperature distribution mainly depends on the heat source distribution form and heat dissipation conditions. The heat sources for different industrial and civil buildings can be classified into the following modes: evenly distributed heat sources on the floor, concentrated plane heat sources, and volumetric heat sources. This section mainly introduces the effects of these three typical heat sources on the wall-attached jet movement.

4.5.1 Evenly Distributed Heat Sources on the Floor

Studies have shown that for the air supplied downwards and exhausted upwards systems with evenly distributed heat sources on the floor, such as the floor radiant heating system, the indoor vertical temperature distribution is a nearly linear profile (except for the air temperature near the floor). It can be deduced that if the full-plane heat source moves upward from y = 0 to a higher position of y + △y, the vertical linear temperature profile will exist above the position of y + △y.

Taking the CCAV as an example, the effect of evenly distributed heat sources on ventilation performance and thermal comfort is analyzed (Yin et al. 2017). Figure 4.21a shows a library reading room with a dimension of 6.0 m × 6.0 m × 4.0 m (length × width × height), in which 8 human models with a height of 1.7 m are evenly arranged. Detailed information can be found in Table 4.4. The vertical temperature gradients of the occupied zone within 2 m and the draft sensation at ankle plane y = 0.1 m are presented in Fig. 4.21b, c, respectively.

Fig. 4.21

Effect of heat sources on indoor thermal environment parameters. a Physical model, b vertical temperature gradient, c draft sensation at ankle plane (y = 0.1 m)

Table 4.4 Parameters of heat sources and circular column attachment ventilation

For a certain supply air rate and temperature, the averaged air speed in the occupied zone increases slightly with the increasing heat source intensity. The main reason is that the momentum of the thermal plume is smaller than that of the mechanical air supply. When the heat source intensity q increases from 80 to 150 W/m², the averaged flow speed in the occupied zone only increases by 0.035 m/s. However, the temperature gradient in the occupied zone remains almost unchanged at 0.45 ℃. The temperature gradient gradually increases above the occupied zone due to the rise of the body’s thermal buoyancy effect, reflecting the temperature distribution effect of the evenly distributed heat sources (Fig. 4.21b).

The intensity of heat sources influences indoor temperature and air speed, affecting human thermal comfort. The draft sensation at the ankle position y = 0.1 m decreases from 20.3 to 12.2% with the heat flux increasing (Fig. 4.21c).

4.5.2 Concentrated Plane Heat Sources

The effect of the plane heat source plume on the attached ventilation flow field is investigated by the 2D-PIV laser test method (Wang 2009). The dimension of the test chamber is 600 mm × 300 mm × 340 mm. The plane heat source is simulated by the electric heating wires evenly coiled on a mica plate, 160 mm × 160 mm, as shown in Fig. 4.22. During the tests, keep the indoor ambient temperature t_n = 24 ℃, and the width of the slot inlet b = 10 mm. Figure 4.23 shows the velocity vector at z = 150 mm under S = 45 mm (S/b = 4.5), and the experimental cases are shown in Table 4.5.

Fig. 4.22

Scheme of the attachment ventilation 2D-PIV test with a plane heat source

Fig. 4.23

Effect of plane heat sources on VWAV, 2D-PIV velocity vector diagram in plane z = 150 mm. a Longitudinal section, u₀ = 0.3 m/s, Q = 1.0 W, b longitudinal section, u₀ = 0.3 m/s, Q = 3.0 W, c horizontal air reservoir region, u₀ = 1.5 m/s, Q = 1.0 W, d horizontal air reservoir region, u₀ = 1.5 m/s, Q = 3.0 W

Table 4.5 Experimental cases of 2D-PIV of attachment ventilation with a plane heat source

Figure 4.23 clearly shows that as the intensity of the plane heat source increases from 1.0 to 3.0 W, the airflow momentum above the heat sources increases significantly, resulting in a flow velocity increase in the horizontal air reservoir region. The mechanical air supply, thermal plume, and the return air work together to produce a “large-recirculation” airflow pattern at a certain height above the floor, which grows larger with increasing heat source intensity.

4.5.3 Volumetric Heat Sources

Volumetric heat sources, such as industrial workshops, ordinary household appliances, and modern electronic equipment, are common in buildings. The thermal plumes generated by these heat sources will affect the air distribution of attachment ventilation (Cui 2010).

• 1. Influence of volumetric heat source intensity on the air reservoir

The influence of volumetric heat source intensity on the air reservoir is investigated by 2D-PIV. The test chamber used has been introduced in Sect. 4.5.2. A volumetric heat source is arranged in the center of the test chamber with a size of 80 mm × 80 mm × 90 mm, as shown in Fig. 4.24. Details of the experiment cases are shown in Table 4.6.

Fig. 4.24

2D-PIV test chamber of attachment ventilation with a volumetric heat source

Table 4.6 Experiment cases of 2D-PIV of attachment ventilation (volumetric heat source)

In view of the symmetry of the chamber, half of the flow velocity field (x = 0–335 mm) is measured by 2D-PIV, as shown in Fig. 4.25. A continuous thermal plume is produced by the buoyancy above the heat source, which has a significant induction effect on the horizontal airflow reservoir. Figure 4.25c, d show a clearly horizontal piston flow similar to the displacement ventilation in the occupied zone. As the heat source intensity increased from 1.0 to 10 W, the induction effect of thermal convection on the upward movement of horizontal piston flow is further strengthened, and a “large-recirculation” flow field is formed in the upper-middle part of the space (Fig. 4.25d).

Fig. 4.25

Velocity vector and streamline diagram, effect of volumetric heat sources on attachment ventilation flow field. a u₀ = 1.0 m/s, Q = 1.0 W, velocity vector, b u₀ = 1.0 m/s, Q = 10 W, velocity vector, c u₀ = 1.0 m/s, Q = 1.0 W, streamline, d u₀ = 1.0 m/s, Q = 10 W, streamline, e u₀ = 1.5 m/s, Q = 1.0 W, velocity vector, f u₀ = 1.5 m/s, Q = 10 W, velocity vector

• 2. Effect of heat source intensity on the vertical attachment region

The influence of volumetric heat source intensity on the airflow in the vertical attachment region is investigated in this section. The decay of the dimensionless centerline velocity u_m/u₀ with dimensionless distance y^*/b is shown in Fig. 4.26 for wall-attached jets under various volumetric heat source intensities. In the vertical attachment region, when u₀ = 1.5 m/s, the centerline velocity distribution of the vertical attachment region presents strong self-similarity under different heat source intensities (Fig. 4.26b). The inertial forces mainly drive the airflow in this region, and the influence of the thermal plume can be negligible. However, the thermal plume affects the centerline velocity when the air supply velocity is lower (u₀ = 0.3 m/s or less). It can be observed that the centerline velocity increases very slowly with a high heat source intensity enhancement. In fact, the jet velocity of u₀ = 0.3 m/s has the same order of magnitude as the velocity of the thermal plume. Therefore, for the air supply velocity of 1–5 m/s, the influence of heat sources on the airflow velocity can be ignored in the vertical attachment region.

Fig. 4.26

Jet time-averaged velocity as a function of volumetric heat sources in the vertical attachment region. a u₀ = 0.3 m/s, b u₀ = 1.5 m/s

• 3. Heat sources off the floor

In a built environment, most of heat sources are usually placed at a certain distance away from the floor, such as office electronics, household electrical equipment, and heat transfer in windows, etc. The normal distance between the heat source bottom and the floor is represented by y (y > 0). With the increase of y, the influence of the heat source is futher weakened on the flow field close to the floor, and the thermal stratification interface height will also rise (Zhao 2010; Yin et al. 2017; Yang 2019) (see Figs. 4.27 and 4.28).

Fig. 4.27

Flow field of AWAV affected by heat sources above the floor. a y = 0 m, b y = 0.5 m, c y = 1.0 m

Fig. 4.28

Temperature field of AWAV affected by heat sources above the floor. a y = 0 m, b y = 0.5 m, c y = 1.0 m

Figure 4.27 shows the effect of y on the indoor air velocity distribution. The air movement path is as follows.

Jet inlet (air inlet) → vertical wall-attached flow → impinging on the floor → horizontal air reservoir → upward movement together with thermal plumes → jet entraining air and moves to the ceiling (exhausted by the return air outlet or air outlet).

The influence of y on the indoor temperature distribution is shown in Fig. 4.28. With the heat source’s elevation, the thermal plume’s induction effect on the lower occupied zone’s airflow gradually decreases. However, the induction effect on the upper room zone’s airflow is gradually increased. The thermal stratification is quite remarkable, and the ventilation efficiency is improved to some extent. We can conclude that it is beneficial to the thermal environment control in the occupied zone to place equipment with high heat intensity at a high position above the floor in a workshop.

4.6 Human Movement Effect on Airflow Field of Attachment Ventilation

Airflow affects the thermal comfort of the human body. Conversely, human activities will also directly impact indoor airflow. This section discusses the effect of human movement on the indoor flow field for VWAV (Cao 2016).

The influence of human movement speeds on the indoor flow field is investigated. The room dimension is 4.0 m × 4.0 m × 2.5 m, the slot inlet size is 1.0 m × 0.05 m, and the exhaust outlet size is 0.2 m × 0.5 m, as shown in Fig. 4.29. The human body is simplified as a cuboid of 1.7 m × 0.3 m × 0.2 m (height × width × thickness) (Zhang and Gu 2009; GB/T 13547-1992). The dynamic grid technique is used to simulate human movement.

Fig. 4.29

Physical model and CFD calculation domain

The walking speeds are taken as 0.9 m/s (slow speed), 1.2 m/s (normal speed), and 1.8 m/s (fast speed) (Han and Wang 2011), and the corresponding human body heat loss is 115 W/m², 150 W/m², and 220 W/m², respectively (Fanger et al. 1988). The floor heat flux intensity is 30 W/m² (Zhao 2010). The detailed information is listed in Table 4.7. For the sake of discussion, the coordinate origin is located in the central section (see Fig. 4.29).

Table 4.7 Human movement speed and relevant parameters

When the human body is stationary (t = 0), the indoor flow field is shown in Fig. 4.30a. The jet velocity decay in the vertical attachment region is almost independent of the human body, and the mean air velocity in the horizontal air reservoir region is about 0.2 m/s. To some extent, the human body is equivalent to a stationary heat source, and the thermal plume with a velocity of 0.3 m/s is formed above the human body.

Fig. 4.30

Influence of human movement on flow field, at room central section, windward walking speed 1.2 m/s. a x = 3.5 m (starting point), stationary, 0 m/s, b x = 2.6 m, c x = 1.7 m, d x = 0.8 m, e x = 0.8 m, 4.0 s after pausing

The indoor flow field changes continuously during human movement. When VWAV air supply velocity is 1.0 m/s, walking speed is 1.2 m/s, and the initial position is x = 3.5 m, the flow fields corresponding to different human movement positions (x = 0.9, 2.6, 1.7, 0.8 m) are shown in Fig. 4.30. In the initial stage of the movement, a large induced wake velocity is formed in the far area behind the human body, reaching 2.0 m/s or more, which is about twice than the speed of human movement. The airflow velocity near the body (3–5 cm) is about 1.2 m/s, the same as the human movement speed. The wake influence further expands when walking close to the air supply side. In the vertical direction, human movement only influences the air velocity in the occupied zone (within 2.0 m above the floor). In the horizontal direction, the influence occurs in front of the human body within 0.6 m.

There is a spherical vortex overhead during human walking. Once the human movement stops, the airflow speed in the occupied zone quickly diminishes to 0.2 m/s (ambient air speed) within 1.0 s. In fact, the influence of human movement on indoor airflow only lasts for a short time, about 1.0–4.0 s. The higher the air change rate, the shorter the recovery time of the flow field.

It is found that there is no significant difference in air speed within the range of human height in the occupied zone, regardless of whether the movement speed is 0.9 m/s or 1.8 m/s. However, outside the occupied zone, a very low air speed exists, approximately 0.2 m/s. Figure 4.31 shows the indoor air velocities under different human motion speeds. It can be concluded that when the human body moves slowly, the affected zone is merely within the scope of the occupied zone, and the flow field can quickly recover once the movement stops. The most important factor affecting the indoor flow field is jet momentum.

Fig. 4.31

Influence of human movement on indoor air speed with different heights. a 0.5 m height, b 1.0 m height, c 1.5 m height, d 2.0 m height. Note See Fig. 4.29, central longitudinal section z = 0 m, height y = 0.5, 1.0, 1.5 and 2.0 m

4.7 Effect of Wall Temperature

The thermal conditions at the jet attached-wall surface are usually approximated with reasonable accuracy to be constant surface temperature or constant surface heat flux. Natural convection heat transfer occurs at the vertical jet-attached surface due to the temperature difference between the wall and the jet. The flow regime in natural convection is governed by the dimensionless Grashof number Gr, which represents the ratio of the buoyancy force to the viscous force acting on the airflow.

$$Gr = \frac{{g\beta \left( {T_{{\text{s}}} - T_{\infty } } \right)L_{{\text{c}}}^{3} }}{{v^{2} }}$$

(4.25)

where

• g = gravitational acceleration, m/s²;

• β = coefficient of volume expansion,1/K;

• T_s = temperature of the surface, ℃;

• T_∞ = indoor air temperature, air far from the surface, ℃;

• L_c = characteristic length of the wall, m;

• v = kinematic viscosity of the fluid, m²/s.

In comparison, the role played by the Reynolds number in forced convection is played by the Grashof number in natural convection. As such, the Grashof number provides the main criterion in determining whether the flow is turbulent or not in natural convection. For vertical walls, the plume is observed to become turbulent at Grashof numbers greater than 3 × 10⁸.

When the vertical wall surface is subjected to the attached jet, this issue involves both natural and forced convection. The relative importance of each mode of heat transfer can be determined by Gr/Re². Natural convection effects can be negligible if $Gr/Re^{2} \ll 1$, free convection dominates and the forced convection effects can be negligible if $Gr/Re^{2} \gg 1$, and both effects are significant and should be considered if $0.1 \le Gr/Re^{2} \le 10$.

When the wall temperature is higher than the indoor air temperature (t_w > t_n), a convective flow along the vertical wall is generated (Fig. 4.32a); when the wall temperature is lower (t_w < t_n), the airflow will move downward due to cooling (Fig. 4.32b). If the thermal convection takes the same direction as the mechanical force, assisting mixed convection is formed; otherwise, opposing mixed convection is generated (Zhang et al. 2001; Rohsenow et al. 1992), as shown in Fig. 4.32c–d.

Fig. 4.32

Natural and mixed convection resulting from the wall temperature difference. a t_w > t_n, b t_w < t_n, c opposing mixed convection, d assisting mixed convection

Here is an example of the wall temperature’s influence on attachment ventilation. The air supply temperature t₀ = 15 ℃, the air supply height h = 4.0 m, and the air inlet size is 2.0 m × 0.05 m. More information is shown in Table 4.8.

Table 4.8 Room wall temperature t_w and air supply parameters of attachment ventilation

Figures 4.33 and 4.34 show the indoor velocity and temperature field under different wall temperatures. With the increase in wall temperature, the indoor air velocity field does not change significantly, whereas the indoor air temperature does increase to a certain extent. It is observed that the temperature stratification takes place obviously in the entire room.

Fig. 4.33

Influence of wall temperature on indoor flow field with u₀ = 1.5 m/s. a t_w = 15 °C, b t_w = 20 °C, c t_w = 30 °C

Fig. 4.34

Influence of wall temperature on temperature stratification with u₀ = 1.5 m/s. a t_w = 15 ℃, b t_w = 20 ℃, c t_w = 30 ℃

Figure 4.35 shows the influence of wall temperature on the jet centerline velocity and temperature. When Gr/Re² ≤ 0.1, due to the larger momentum of mechanical ventilation, the effect of natural convection generated by the nonadiabatic wall can be ignored. The jet velocity in the vertical attachment region is almost identical to that of the adiabatic wall, see Fig. 4.35. It means that if the wall-attached jet flows along the interior wall, the wall temperature’s effect on the supply flow field may be ignored. Otherwise, the wall convective heat transfer should be taken into account.

Fig. 4.35

Effect of wall temperature on the flow field of attachment ventilation (t₀ = 15 ℃). a Centerline velocity, and b excess temperature in the vertical attachment region

4.8 Effect of Wall Roughness

In practical attachment ventilation applications, rough elements or protruding objects may be on the wall surface, so the wall cannot be considered smooth. The relative roughness is represented by k/δ, where δ and k denote the boundary-layer thickness and height of the roughness elements, respectively. The critical point of the flow through a rough wall surface is that the relative roughness k/δ decreases along the wall when k remains constant because δ increases downstream. This circumstance causes the front of the wall to behave differently from its rearward portion as far as the influence of roughness on drag is concerned (Schlichting 1995).

The amount of roughness which is considered “admissible” in engineering applications is that maximum height of individual roughness elements which causes no increase in drag compared with a smooth wall (Schlichting 1995). Turbulent boundary layer roughness has no effect if all protruding objects are contained within the sublayer. However, from the view of ventilation, it seems more convenient to specify a value of relative roughness k/b. We can obtain the allowed value of k/b from the experiments.

Here, a case study about the attachment length and centerline velocity under different roughness heights is presented by the 2D-PIV laser velocity measurement technique. The experimental apparatus is shown in Fig. 4.36 (photo shooting area: x = 10–250 mm, y = 12–330 mm), the test chamber dimension is 600 mm × 300 mm × 340 mm, and the slot inlet width b = 10 mm. The roughness elements are arranged evenly, and the absolute roughness heights k are 0.5 mm, 1.0 mm, and 2.0 mm, respectively. Detailed information can be found in Table 4.9.

Fig. 4.36

Experimental diagram of the room with a rough surface

Table 4.9 Experimental cases for studying the effect of roughness on vertical wall attachment ventilation

• 1. Effect of roughness on attachment length

The attachment length is defined as the distance between the initial jet attachment point y₁ and the separation point y₂. The airflow velocity vector graphs under different roughness heights measured by 2D-PIV are shown in Figs. 4.37 and 4.38. It can be found that with the increase of the roughness height, the attachment point location is little altered, and the separation point moves slightly downwards closer to the floor (see Fig. 4.39). It means that the roughness elements may hinder the Coanda effect. In fact, the stronger the Coanda effect, the longer the vertical attachment region. The experiment shows that the central position of the “recirculating vortex”, in the upper left corner area (at y = 265 mm, see Fig. 4.37; at y = 290 mm, see Fig. 4.38) between the air supply jet and the vertical sidewall, is not significantly affected by the roughness. However, the separation point location y₂ moves further downwards (see Fig. 4.38).

Fig. 4.37

Effect of sidewall roughness on attachment length, u₀ = 0.3 m/s. a k/b = 0.05, b k/b = 0.1, c k/b = 0.2

Fig. 4.38

Effect of sidewall roughness on attachment length, u₀ = 1.0 m/s. a k/b = 0.05, b k/b = 0.1, c k/b = 0.2

Fig. 4.39

Attachment length as a function of roughness and air supply velocities

From the flow field measured by 2D-PIV (Fig. 4.39), we can find that with the increase of air velocity, the roughness elements’ influence on the attachment length will gradually decrease. When u₀ increases to 1.5 m/s, the attachment length is almost irrelevant to the roughness.

• 2. Effect of roughness on centerline velocity

The jet centerline velocities under different k/b are shown in Fig. 4.40. It can be seen that in the range of 0 ≤ k/b ≤ 0.2, the centerline velocity decays of the wall-attached jet are basically identical. The roughness does not significantly influence the centerline velocity.

Fig. 4.40

Centerline velocity measured by 2D-PIV as a function of roughness (S/b = 7.5). a u₀ = 1.0 m/s, b u₀ = 1.5 m/s

For the deflected wall-attached jet, taking S/b = 7.5 as an example, the centerline velocity decay is shown in Fig. 4.40. In the range of y^*/b < 12, the supply air jet has not yet attached to the sidewall, the centerline velocity decays almost as fast as that of the free jet. When the S/b exceeds the extreme attachment distance S_max, the jet fails to attach to the sidewall, leading to poor attachment ventilation performance. Hence, it is recommended that the air supply opening be installed as close as possible to the adjacent wall to ensure the attachment ventilation effectiveness.