Study of underfloor air distribution using zonal model-based simulation and experimental measurements

Energy and Buildings 152 (2017) 96–107

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Study of underfloor air distribution using zonal model-based simulation and experimental measurements Hong Fang a , Dongliang Zhao a,b,∗ , Gang Tan a,∗∗ , Anthony Denzer a a b

University of Wyoming, Laramie, WY, United States University of Colorado Boulder, Boulder, CO, United States

a r t i c l e

i n f o

Article history: Received 28 February 2017 Received in revised form 7 July 2017 Accepted 10 July 2017 Available online 17 July 2017 Keywords: Zonal model UFAD POMA Numerical modeling Mechanical ventilaiton

a b s t r a c t Underfloor air distribution (UFAD) is an effective strategy to provide both ventilation and air conditioning for buildings. To predict indoor airflows and temperature distribution, zonal model has advantages over other methods such as multi-zone model and computational fluid dynamics (CFD) by considering the prediction accuracy and computational cost. In this work, a numerical algorithm for floor-mounted diffuser flows, which calculates the airflow mass conservation and energy conservation separately, was implemented in a newly developed zonal model computer program for UFAD application, based on the established zonal model-pressurized zonal model with air-diffuser (POMA). This computer program was validated by lab experiments under both natural convection condition and mechanical ventilation for a lab-scale mixing UFAD system. Comparisons of zonal model simulation results and experimental measurements for both temperature distributions and air flows in the lab room showed that the newly developed zonal model is a good tool for predicting the indoor thermal environment with UFAD system. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Applied in industry, residential and commercial buildings, the underfloor air distribution (UFAD) system generally sets diffusers in the floor and delivers air bottom up rather than top down. Because it directly supplies fresh air into occupied zones, the UFAD system offers better air quality and thermal comfort to occupants than traditional ceiling-based air distribution systems [1]. Therefore, the UFAD system is generally designed to condition the occupied lower portion of space and leave the upper unoccupied space to function as a stratified displacement region [2]. Compared to conventional air distribution (e.g., overhead), the UFAD system can save 5–10% building height and save 20–30% total energy [2]. The UFAD ventilation is different from displacement ventilation as displacement ventilation generates vertical temperature stratification for the entire space and the air is commonly supplied horizontally at floor level at very low velocities [3]. The UFAD system, especially so-called mixing UFAD, delivers air vertically from the floor with a short throw by applying high mixing rate diffusers [4]. The performance of mixing UFAD is determined by a balance between

∗ Corresponding author at: University of Colorado Boulder, Boulder, CO, United States. ∗∗ Corresponding author. E-mail addresses: [email protected] (D. Zhao), [email protected] (G. Tan). http://dx.doi.org/10.1016/j.enbuild.2017.07.026 0378-7788/© 2017 Elsevier B.V. All rights reserved.

the effects of warm air buoyancy creating a stratified temperature distribution and the mixing momentum effects of airflow forced through diffusers [5]. Since the room air temperature variation in vertical direction and the air movements are critical for designing the UFAD system [6], accurately predicting these critical data can help designers to evaluate their UFAD systems’ performance at design stage. Previous study found that discomfort complains in the rooms with UFAD systems were mainly caused by lack of air movements or drafts [7]. There are a number of tools that can be used to predict airflows and temperature distribution in a space, such as the multi-zone model. The multi-zone model assumes each room is a homogeneous node that connects to other rooms and outside environments [8]. With boundaries of walls, windows and doors and air flowing through the boundaries from the orifices (e.g., doors and windows), the multi-zone model is generally applied to evaluate the homogeneous characteristics such as air temperature and pressure of a node and analyse the bulk airflow relation between nodes [9,10]. Another powerful calculation tool is computational fluid dynamics (CFD) which can provide detailed environmental information of each simulated room [11]. Compared to experimental methods, CFD is much more economical and effective [12,13]. In CFD, turbulence models are applied to capture fluid flow characteristics. The k − ε model is one of the popular models which produced qualitatively satisfactory results for a number of complex flows [14]. For air flows in the room with UFAD system, both k − ε model [15]

H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Nomenclature A b Cp h L m q r x V R  w ␣  

Area of the wall surface (m2 ) Slot height (m) Specific heat of air (kJ/kg K) height of the sub-zone (m) depth of sub-zone (m)Depth of sub-zone (m) Mass flow rate (kg/s) Heat transfer rate (W) Radius of the jet cone (m) Distance from outlet (m) Velocity (m/s) Air gas constant (J/kg K) Difference Width of the sub-zone (m) Convective heat transfer coefficient (W/m2 K) Angular (degree) Air density (kg/m3 )

Superscript/subscript i Initial p Point Return r s Supply Centerline y normal Normal boundary wall-zone Between wall surface and neighbour zone air zone-zone Between two adjacent zones ref Reference

and the Reynolds averaged Navier-Stokes (RANS) model [16,17] are applicable. Due to the simplifications made in the model development, the multi-zone model can only provide bulk temperature of the spaces and bulk airflow across spaces [9,18]; while due to solving NavierStokes equations with turbulence models, CFD simulation requires high computational cost [19,20]. Both methods have their limits when applying to assist the design of UFAD. As an alternative solution, zonal model not only predicts indoor thermal environment with temperature, pressure, and airflow distributions, but also is computationally efficient [21]. The concept of the zonal model was firstly presented by Leburn in 1970 [22]. He used zonal model to study the interaction between the terminal unit and the rest of the room, including the floor and the roof. Following that, Allard and Inard did a thorough survey and evaluation to zonal model tools and utilized the zonal model to investigate the temperature stratification within nonindustrial buildings [23]. Later on, Huang and Haghighat used zonal model to predict airflows, temperature and volatile organic compounds (VOC) distributions within a room [24]. Bozonnet utilized zonal model to investigate the building thermal behavior which is affected by solar radiation [25]. Jiru did an analysis of modeling airflow and temperature in a ventilated double skin facade by applying the zonal model approach [26]. Daoud presented simulations using a zonal airflow model, a radiation model and a humidity model to predict the heat fluxes, the transient airflow patterns, the temperature and the humidity distributions in a three-dimensional section of an indoor ice rink [27]. The zonal model method is able to solve the pressure field to predict airflow and solve energy conservation equations to predict temperature distributions in a building space [28]. In this method, the space is divided into dozens to hundreds of sub-zones where air temperature and density are assumed homogeneous but pressure varies hydrostatically. When dividing sub-zones, the method is dif-

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ferent for various room sizes and types, but a general rule is to make the complexity as low as possible to reduce the computational time [29]. A comprehensive evaluation of zonal model’s capability has been completed by Inard and Buty [30]. Zonal models can predict the temperature variation in vertical direction and air flows with satisfactory precision for horizontal air jet [31]. Different zonal models have been developed for indoor environmental prediction. Bouia [32] presented the use of mass flow in terms of pressure difference between sub-zones for natural ventilation but this zonal model was not applicable to mechanically ventilated spaces. Inard and Buty [30] introduced the zonal model to evaluate airflow patterns caused by the air buoyancy in a room. But the main limitation of this model is that pre-knowledge of the flow pattern is needed. Later, Inard et al. [33] suggested a method that the zones are divided into regular sub-zones and specific flow sub-zones depending on the volume of momentum. The shortage of the model significantly depends on the appropriate behavior law for specific flows [31]. One of the well-known zonal models is the Pressurized zOnal Model with Air diffusers (POMA), developed by Lin [34]. The advantage of POMA is that it can solve more general-purpose airflow pattern and temperature distribution within a room. The definition of sub-zones can be general and the number/geometry of sub-zones are flexible and simple. POMA models the driving forces in a general way so that this zonal model can be applied to all kinds of driving forces [34]. POMA is a model that uses pressure differences to trigger airflows in the room. In the model, four assumptions have been made: (1) inviscid air, (2) uniform air temperature and density in each sub-zone, (3) hydrostatically varying pressure along the vertical direction in each sub-zone while flow resistance throughout the sub-zone concentrated at the interface where two sub-zones connect, and (4) mass and energy conservation principles applied to all sub-zones. In POMA, the normal boundary that does not involve any forced air movements is generally categorized into three types: (1) horizontal air-to air boundary, (2) vertical air-to-air boundary, and (3) wall surface boundary. The first two types of air-to-air boundaries are the focus of airflow calculation. The third one, wall surface boundary, is defined for heat transfer calculation. In jet flow boundary, POMA applied jet flow equation to calculate mass flow rate. However, POMA’s original research was focused on horizontal jet flows delivered at top level of the room, not applicable to mixing UFAD system. Based on POMA’s methodology, this work further incorporated an algorithm for vertical jet flows from raised floor and newly developed a zonal model-based computer program to simulate airflows and temperature distribution in a lab-scale mixing UFAD system. 2. Zonal model algorithm redevelopment The newly developed zonal model program was based on POMA [34]. This project contributed several updates to the method applied in POMA, including the mass flow rate through the vertical interface that falls within the jet region. In this new calculation process, both the mass and energy conservation equations of the jet flows were treated as non-isothermal for achieving better accuracy when computing the air flowrate and temperature distribution. The new algorithm regarding air mass flow rate calculation in jet flow boundary is described below. 2.1. Airflow through the horizontal air-to-air interface perpendicular to the jet trajectory As shown in Fig. 1, there has 6 defined sub-zones and an upward mixing jet flow supplied from diffuser simplified point ‘O’, the

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H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 1. Illustrative sketch of vertical jet boundary.

velocity V at distance r (e.g., r = LAD = LBD in Fig. 1) can be estimated as below: 1

V = Vy 10− 3.3



r r0.5



(1)

where, r0.5 represents one half of the radius of the jet cone (e.g, r0.5 = LCD = LDE in Fig. 1). Experiments showed that the conical angle for r0.5 is approximately one-half of the total angle of a jet divergence [35]. Vy is the centerline velocity in same cross-section plane as V. Regenscheit [36] examined the decay of maximum velocity of non-isothermal vertical jets. The equation of the velocity at centerline is given as:



Vy =

xi + x

 

Ar /k







2.83

x/xi − 1

Vs

(2)

where xi is length of jet core; x represents distance from outlet; k = b/xi and b is the slot height; Vs is the velocity at supply diffuser, and Ar is the Archimedes number which is, Ar =

g



As T

(3)

Ts Vs2

where g is gravity acceleration, As is a reference area usually taken to be the effective area of the supply diffuser, isTs the air temperature of the supply diffuser, and T is the temperature difference between the neighbouring sub-zones. Therefore, we have,



r0.5 = LCD = LDE =



w 2

tan 2

+h

tan

 4



(4)

Substitute Eq. (2) into (1) and integrate from A to B (see Fig. 1), the mass flow rate through the entire jet horizontal interface (A-B) can be obtained as follows:

B mAB =

1 − 3.3

flow Vy 10



r r0.5

2 Ldr

(5)

A

2.2. Air flow through mixed interface Mixed boundary contains jet boundary and normal boundary such as the boundary (H–J) as shown in Fig. 1. The range from K to J is jet horizontal interface. The mass flow rate can be obtained by using Eq. (5) but integrating from K to J. The range from H to

K is normal boundary. The mass flow rate of the normal boundary part in the mixed interface can be obtained by using the following equation: mH−K =

LHK normal m LHJ H−J

(6)

is mass flow rate of air flow through normal boundwhere mnormal H−J ary of H to J under natural convection. The total mass flow rate of air through the mixed interface (H–J) is: mH−J = mH−K + mK−J

(7)

2.3. Heat flux through boundaries As in the method proposed by POMA, radiation heat transfer is neglected in this work. Only convection heat transfer between air and walls and heat carried by airflows are accounted. The convection heat transfer between air and walls can be described as: q = ˛ATwall−zone

(8)

where, q is heat transfer rate, ␣ is convective heat transfer coefficient, A is area of the wall surface, and Twall−zone is temperature difference between wall surface and neighbor sub-zone air. The heat carried by air flow is described as: q = Cp mTzone−zone

(9)

where, m is mass flow rate, Cp is specific heat of air, and Tzone−zone is air temperature difference between two adjacent sub-zones. 2.4. Airflow through the vertical air-to-air interface parallel to the jet trajectory The mass flow rate in the vertical interface is equal to one half of the difference of the mass flow rate between the bottom horizontal interface and the upper horizontal interface. Taking sub-zone 5 in Fig. 1 as an example, the mass flow rate mIQ from the diffuser can be collected in experiment. The mass flow rate mFG can be obtained by Eq. (5). Therefore, the mass flow rate through the vertical interface (F-I) and (G-Q), assumed to be the same, is written as, mFI = mGQ =

 1 mIQ − mFG 2

(10)

H. Fang et al. / Energy and Buildings 152 (2017) 96–107

2.5. Jacobian matrix for vertical jet Since each sub-zone has its mass and energy conservation equation, the number of mass conservation equations for the sub-zones shown in Fig. 1 is 5. A general mass conservation equation for steady state condition is written as:



mi,j = 0

(11)

j

where mi,j represents the rate of mass flow from sub-zone i to subzone j. The mass conservation equation for zone 2 is presented, for example, as below, m1,2 − m2,3 + m5,2 = 0

(12)

The general energy conservation equation is described as following,



qi,j = 0

(13)

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Jacobian matrix non-zero terms. This study presents partial differential terms that will be incorporated into the Jacobian matrix when developing a zonal model-based computer program to simulate mixing UFAD. For the case shown in Fig. 1, the unknown variable vector, or the X vector for Newtonian method seen in Eq. (15), contains 11 variables, comprising of 5 sub-zone pressure unknowns (except the reference pressure set in sub-zone 6) and 6 sub-zone temperature unknowns. Also, the residual vector, or the F vector seen in Eq. (15), consists of residuals from calculations of 5 mass conservation equations (i.e., the n-1 rule) and 6 energy conservation equations. To derive the Jacobian matrix, sub-zone 5, involving with the jet flow and neighboring with sub-zones 2, 4, and 6, is taken as an example to demonstrate the partial differential terms in Jacobian matrix under mixing UFAD condition. The pressure of sub-zone 5 associates with the fifth row of the Jacobian matrix, as illustrated below,

   0 ∂F5 0 ∂F5  ∂Pref 2 ∂Pref 4

∂F5 ∂Pref 5

∂F5 0 ∂T2

∂F5 ∂F5 ∂T4 ∂T5

0



∂F5  (17) ∂T6 

j

where qi,j represents rate of energy transfer from sub-zone i to sub-zone j. The energy conservation equation for zone 2 is presented as an example, Cp m1,2 T1 + Cp m5,2 T5 − Cp m2,3 T2 + ˛A (Twall−zone − T2 ) = 0

(14)

where Cp is the specific heat of air, Ti (i=1, 2, and 5 here) is the air temperature of a specific sub-zone under uniform zonal temperature assumption, ␣ is the convection heat transfer coefficient between the wall surface and the air in the neighbor sub-zone, Twall-zone is the wall surface temperature, and A is the interface area between the wall and the neighbor sub-zone. Since the mass flowrate between two neighbor sub-zones is a function of the static pressure difference between the two subzones and the temperatures in the sub-zones, four pressures and four temperatures for the four sub-zones involved in Eq. (14) will be obtained when solving the mass and energy conservation Eqs. (12) and (14). To evaluate pressures in sub-zones, a reference pressure (Pref ) is set at the bottom interface of sub-zone 6 as shown in Fig. 1, which is the basis of pressure calculations for other zones as pressure varies hydrostatically. For sub-zones involved the vertical jet in mechanical mixing UFAD, solving the mass and energy conservation equations becomes more complicated and requires iterative calculations. For the case shown in Fig. 1, the solutions eventually yield five pressures for sub-zones 1–5 as sub-zone 6 has the reference pressure and six temperatures for the six sub-zones. In particularly, to solve these aforementioned nonlinear equations (e.g., the nonlinear relationship of mass flowrate and pressure difference), same as POMA, Newtonian method is applied. Fi (X + X) = Fi + JX

∂Fi ∂xj

−2 ∂F5 = ∂Pref 5 RT5 + gh 2

G Vy 10





2Pref 5 RT5 +

gh 2

2

r r0.5

Ldr

(18)

F

2Pref 5 R ∂F5 =  2 ∂T5 RT5 + gh 2

−



1 − 3.3

G



1 − 3.3

Vy 10

r r0.5

2 Ldr

F

∂ ∂T5

G Vy 10

1 − 3.3



r r0.5

2 Ldr

(19)

F

where R is the gas constant for air and h is the height of the subzone. The temperature of sub-zone 5 associates with the tenth row of the Jacobian matrix, as shown in below,

   0 ∂F10 0 ∂F10  ∂Pref 2 ∂Pref 4

∂F10 ∂Pref 5

∂F10 0 ∂T2

∂F10 ∂F10 ∂T4 ∂T5

0



∂F10  ∂T6  (20)

The two partial differential terms directly relevant to sub-zone 5 in this row are given as: −2CP T5 ∂F10 = ∂Pref 5 RT5 + gh 2

G Vy 10



1 − 3.3

r r0.5

2 Ldr

(21)

F

(15)

where X is the vector which contains unknown variables such as pressures Pref1 , Pref2 . . . Prefn-1 for the n-1 sub-zones and temperatures T1 , T2 . . . Tn. for the n sub-zones; Fi is the residual vector calculated from the mass and energy conservation equations; and J is the Jacobian matrix. The general form of the Jacobian matrix is: Ji,j =

The two partial differential terms directly relevant to sub-zone 5 in this row are given as:

2Pref 5 RCP T5 ∂F10 =  2 ∂T5 RT5 + gh 2

−

(16)

Where xj is the j element of the unknowns in the equations. The vertical jet flow from diffuser is different from horizontal jet flow handled in POMA [34], resulting in a completely new set of

2CP Pref 5 RT5 +

 −

G

gh 2

Vy 10

1 − 3.3

Vy 10



r r0.5

2 Ldr

F

1 − 3.3



r r0.5

2 Ldr

F

2CP Pref 5 T5 RT5 +

G

gh 2



∂ ∂T5

G

1 − 3.3

Vy 10 F



r r0.5

2 Ldr

(22)

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H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 2. Experimental lab with UFAD (a) the experimental room and (b) plan view of the thermocouple grid planes (i.e. long plane and short plane).

Fig. 3. Locations of thermocouples (a) and anemometers (b) along the short plane.

3. Experimental setup The mixing UFAD experiments were conducted in the Architectural Engineering (ARE) Research Laboratory located at University of Wyoming, USA. The size of the experimental room is 4.63 m long by 3.62 m wide by 2.41 m high, as shown in Fig. 2a. With the raised floor, the space height above the floor plenum is 2.09m. The experimental room was isolated from adjacent spaces (see Fig. 2b) by using Benzene boards. A mixing UFAD system provided air conditioning to the room through plenum beneath raised tiles. A single-layer ASHRAE type B diffuser [35], 0.50 m by 0.19m, was fixed in the center of the raised floor throughout this work. Consisting of a Trane XV 80 furnace and a XR13 air-conditioner with a constant speed supply fan, the mechanical system was installed in the northern closet. A single layer bar type return grille, with 30◦ deflection and a size of 0.81 m by 0.46m, was installed in the north wall at 1.68 m above the raised floor to draw air back to the air conditioning system. In this work, the experimental room was divided into 160 sub-zones (8 × 5 × 4 along the L × W × H dimensions) and sub-zone overlapping was avoided for the zonal model study. When dividing sub-zones, we imposed a sub-zone to cover the floormounted diffuser. The boundary of the air jet was symmetric in the sub-zone immediately above the diffuser. In particular, along the central sectional planes of the experimental room (see Fig. 2), 20 sub-zones were created for the short plane and 32 sub-zones were made for the long plane, as shown in Figs. 3 and 4. In experiments, 52 thermocouples were installed in the centers of the sub-zones along the central sectional planes, as shown in Fig. 2b, to measure temperature distributions in the room. Detailed thermocouple locations, marked with identifiers such as “T1” or “T2”, are shown in Figs. 3 a and 4 a. The thermocouples used in this study have a measurement accuracy of 0.1 ◦ C. To evaluate air movements in the space, the ComfortSense anemometers 54T33 of Dantech Dynamics were used to measure air velocities crossing interfaces

Fig. 4. Locations of thermocouples (a) and anemometers (b) along the long plane.

between sub-zones, as shown in Figs. 3 b and 4 b. The 54T33 temperature compensated omnidirectional probe has specifications of 0.5–10.0 m/s velocity measuring range and velocity accuracy of ±2%

H. Fang et al. / Energy and Buildings 152 (2017) 96–107

101

Fig. 5. Interior surface temperatures of ceiling, floor and walls (a) East-west direction. (b) North-south direction.

or 0.02 m/s for 0–1 m/s and ±5% for 1–5m/s. Experiments for both natural convection and mechanical convection conditions were conducted, where natural convection was used for model validation. All the experimental measurements lasted for at least 30 min to ensure steady state was obtained.

Table 1 Experimental settings for mixing UFAD under heating condition. Indoor temperature (thermostat) setpoint, ◦ C

Temperature of supply air, ◦ C

Temperature of return air, ◦ C

Air supply mass flow rate, kg/s

29.4

36.1

29.5

0.02

4. Mesurement and simulation results Experiments were carried out both under natural convection condition, for which the mechanical system was shut off but heat transfer still happens between the walls and the sub-zone air; and under mechanical ventilation condition, for which the room was heated by the UFAD system through the floor mounted diffuser. The work in this study was focused on the indoor air movements caused by the diffuser supplied air and the convection heat transfer between the air and the wall/ceiling surfaces with UFAD system. Experimental data has been used to verify the application of the newly developed zonal-model based computer program for indoor environmental prediction, especially for the UFAD system. During the experimental study, the interior building fac¸ade surface temperature was measured to provide boundary conditions to zonal-model calculation. As shown in Fig. 5, in mechanical ventilation experiment, the interior surfaces of northern and western walls were measured at 26.3 ◦ C while the interior surfaces of the eastern and southern walls were at 27.2 ◦ C. At the same time, the ceiling surface temperature was 15 ◦ C and the floor temperature was 27.5 ◦ C. 4.1. Indoor temperature distribution under natural convection When the UFAD system was shut off and the diffuser/grille were sealed, indoor air movements in the experimental room were driven by natural convection, caused by the warm and cold building fac¸ade surfaces. In this experiment, the interior surfaces of north and west walls were measured at 20 ◦ C while the interior surfaces of the east and south walls were at 13 ◦ C. At the same time, the ceiling surface temperature was 15 ◦ C and floor temperature was 14 ◦ C. These interior surface temperatures were the only boundary inputs to the zonal model; indoor air temperature distribution was calculated. Results from the zonal model based numerical calculation and experimental measurements for indoor air temperature distribution are compared in Figs. 6 and 7. For example, the monitoring points of S-column 1 along the short plane are corresponding to T1, T6, T11, and T16 as shown in Fig. 3a. In the long plane, the monitoring points of L-column 1 are corresponding to T1, T9, T17 and T25 as shown in Fig. 4a. Temperature trends from the zonal model showed a good agreement with experimental measurements. This com-

parison has validated the newly developed zonal model computer program; it can accurately predict the indoor thermal environment for a natural convection condition where there is no mechanical ventilation. However, when the temperature is relatively low, some discrepancies can be observed between the simulation results and experimental measurements, especially for some points in Scolumns 1 and 5 along the short plane. This is because these two columns are located next to the walls. The temperature difference between the indoor air and the interior wall surface is small, which results in calculation error when the Jacobian matrix is approaching singular. 4.2. Indoor temperature distribution under mixing UFAD Laramie, Wyoming has cold and dry weather conditions. The winter heating season is very long (usually from September to May). Therefore, this experiment was conducted under heating conditions. To enlarge the buoyancy effect and examine the zonal model’s capability to capture the ventilation characteristics under strong buoyancy force, the indoor temperature setting point was set at a relatively warm temperature of 29.4 ◦ C (85 ◦ F) to force the system suppling even warmer air streams (e.g., 36.1 ◦ C in the experiment) and thus achieve stronger convection heat transfer between room air and wall/ceiling surfaces. Table 1 describes the experimental settings. As shown in Figs. 3 and 4, there was only one diffuser installed in the middle of the raised floor. Figs. 8 and 9 compare indoor air temperatures along the short plane and the long plane between zonal model simulation results and experimental measurements under UFAD ventilation. In these two figures, the horizontal axis represents a dimensionless temperature, denoted as below, TDimensioness =

TP − TS Tr − TS

(23)

where, TP is the temperature of measuring points; TS is the supply air temperature from diffuser; and Tr is the return air temperature at the return grille. From Figs. 8 and 9, it can be seen that the newly developed zonal model can accurately predict indoor air temperatures under mixing UFAD ventilation. For this heating experiment, the indoor air temperature generally decreases with the space height and there

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H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 6. Temperature comparison between zonal model simulation results and experimental measurements for natural convection condition along the short plane. “S” in the titles stands for along the short plane.

is an obvious thermal stratification in the vertical direction. Since the air in lower portion is warmer than the air in upper portion, the air temperatures in the space demonstrate a clear mixing effect due to the use of this specific type of diffuser. The temperature distribution in the vertical direction produced temperature variations of 0.4 ◦ C to 1.0 ◦ C along the short plane and the long plane, respectively. The simulation results agree well with the experimental data. Furthermore, simulation results agree well with the temperature stratification trend along the height.

4.3. Airflows crossing sub-zone interfaces During the mixing UFAD experiment, anemometers recorded air flow velocities for the locations shown in Figs. 3 b and 4 b. The anemometers at A12 and A18 were used to measure the supply air velocity for volumetric flow rate along the short plane and the long plane respectively, adopted as inputs in zonal model calculation. The air flowrate between two neighboring sub-zones can be

obtained from air flow velocities, either through measurements or zonal model calculations, using following formula, mi,j = Vi,j i A

(24)

where mi,j represents the mass flow rate from sub-zone i to subzone j; Vi,j is the air flow velocity across the interface between subzone i and sub-zone j; i is the air density of sub-zone i, and A is the interface area. Figs. 10 and 11 show 11 and 17 airflow rates individually compared between the zonal model simulation results (second row, red) and the experimental measurements (third row, black). The black percentages at the fourth row are the difference between simulation results and the experimental measurements, Difference =

|Experimental data − Simulation results| × 100% Simulation results

(25)

The differences between the experimental measurements and the results simulated by the newly developed zonal model com-

H. Fang et al. / Energy and Buildings 152 (2017) 96–107

103

Fig. 7. Temperature comparison between zonal model simulation results and experimental measurements for natural convection condition along the long plane. “L” in the title stands for along the long plane.

puter program varies in a range between 11.6% and 18.9%, with an average difference of 15.7% along the short plane. In the long plane, the calculation results vary between 7.65% and 16.64%, with an average difference of 11.75%. Part of the discrepancy can be attributed to velocity measurements using Omnidirectional probes that may not be perfectly perpendicular to the air flow direction. However, the difference is a good demonstration of the zonal model’s prediction capability for airflows in mixing UFAD system. In

particular, the results from zonal model are acceptable in industrial application. 5. Discussion/conclusion This work applied a vertical non-isothermal jet flow algorithm, targeting towards mixing UFAD application, into a newly developed zonal model program based on the methodology developed

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H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 8. Temperature comparison of zonal model simulation results and experimental measurements for mechanical ventilation along the short plane.

by POMA. The newly developed zonal model program has been validated for both natural convection and mechanical ventilation conditions. In particularly, the validation of the zonal model program under natural convection examined the accuracy of the fundamental simplifications and assumptions made in zonal model development, as well as the accuracy of Newtonian method for solving the mass and energy conservation equations. This validation ensures a solid foundation for the zonal model applicable to mechanical ventilation. The calculation results showed that the newly developed model can accurately predict air temperature distribution in the laboratory room. Compared to temperature prediction for mechanical ventilation, the discrepancy between the simulated air tempera-

tures and experiment measured air temperatures appears greater under natural convection condition. This is possibly caused by the reversed Jacobian matrix approaching to singular when the air flowrate is relatively small for pure buoyancy driven air movements under natural convection. Airflow measurements have been used to evaluate the airflow prediction from the re-derived zonal model. Although the airflow rates from model calculation for the lab-scale mixing UFAD showed an acceptable agreement with experimental measurements, the discrepancy between the experimental measurements and simulation results for airflow rates are more significant than that for temperatures, which may be due to the limits of the measurement instrument.

H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 9. Temperature comparison of zonal model simulation results and experimental measurements for mechanical ventilation along the long plane.

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H. Fang et al. / Energy and Buildings 152 (2017) 96–107

Fig. 10. Comparison of airflows [kg/h] between zonal model simulation and experimental measurement along the short plane.

Fig. 11. Comparison of airflows [kg/h] between zonal model simulation and experimental measurement along the long plane.

In summary, the zonal model can predict indoor thermal environment in the scenario of the experiments, for both temperature and air movement, under mixing UFAD, with more accurate details than multi-zone model and less computational cost than CFD simulation. The experimental case studied in this work involved only one diffuser. It is highly possible to deal with multiple diffusers in future application. The newly developed model can be expanded to multiple-diffuser situation with inclusion of a jet flow overlapping model [37].

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