A study on density stratification by mechanical extraction displacement ventilation

International Journal of Heat and Mass Transfer 110 (2017) 447–459

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A study on density stratification by mechanical extraction displacement ventilation Y.J.P. Lin ⇑, J.Y. Wu Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43 Section 4, Keelung Rd., Taipei 106, Taiwan

a r t i c l e

i n f o

Article history: Received 11 November 2016 Received in revised form 14 March 2017 Accepted 16 March 2017

Keywords: Displacement ventilation Extraction sink Flow stratification Intermediate stratified layer

a b s t r a c t The purpose of this study is to investigate the stratified flow driven by mechanical extraction displacement ventilation and compare the effects of the supply source and the extraction sink on the flow in the ventilated space. The extraction sink effect, which has rarely been addressed in the previous research, is discussed in this paper. This study investigates the flow stratification, the thickness of the intermediate stratified layer and their relationships with the suction, buoyancy and inertia forces in the space. The saltbath technique was employed to conduct experiments simulating mechanical extraction displacement flow by using an acrylic reduced-scale model. According to the connection opening area on the partition, experiments were categorized into two series, denoted as Ex(I) and Ex(II). Experimental results show that as the extraction flow rate increases, the distance between the plume source and the interface height increases and the reduced gravity of the dense layer decreases as predicted by the two-layer stratification model. The stratification stability highly depends on the magnitude of the force ratio in the ventilated space. Similar to the previous research, the inflow inertia force has a clear influence on the formation of the intermediate stratified layer. The strong suction force in this study seems to aid the flow stratification and diminish the intermediate stratified layer thickness. The linear fit relationship between the intermediate stratified layer thickness and the force ratio gives a close result to the previous study. Similar to the previous study on displacement ventilation, the density in the dense layer is observed to be uniform when the extraction flow rate is small. The density distribution along a horizontal level with a certain non-zero gradient in the dense layer is clearly identified when the flow rate is high and the location is near the extraction sink, an observation that is very different from the previous study on displacement ventilation. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Ventilation (cooling and heating) in buildings consumes a large amount of energy nowadays. According to Refs. [1,2], nonindustrial buildings account for 30–50% of all primary energy consumption in Organization for Economic Cooperation & Development countries, and ventilation operation consumes as much as 50% of the amount attributed to the non-industrial buildings section. Building ventilation is an important issue, because of the needs for improving the indoor air quality and providing a comfortable environment for occupants. It is essential to adopt an appropriate ventilation strategy to achieve the purposes of energy saving and a comfortable indoor environment. Building ventilation is usually classified as natural and mechanical ventilation systems according to the driving forces. The driving ⇑ Corresponding author. E-mail address: [email protected] (Y.J.P. Lin). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.03.053 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

force of mechanical ventilation depends on the mechanical equipment, such as fans or jet flow producing devices. The ventilation flow rate could be easily adjusted according to the demand for the space using mechanical ventilation. Displacement ventilation has been used over the past few decades as an energy-efficient approach compared to conventional overhead mixing systems. Displacement ventilation is an approach that utilizes flow stratification in space to provide more efficient heat transfer than the traditional well mixing ventilation. Different stratification distributions result in distinct flow rates and ventilation efficiencies in the space [3,4]. This stratification is one of the most beneficial factors of displacement ventilation over conventional mixing-type ventilation, because the displacement ventilation systems only take account of a part of the total load considered in the mixing ventilation systems. Furthermore, the displacement ventilation systems improve indoor air quality in the lower level by separating contaminated air from clean air through stratification. Therefore, energy savings

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Nomenclature Aj ax Bo C Cj cp FB FI FS g g0 g 0f g 0p ðHÞ H hf I I0 l Mj Q Q p ðHÞ Q ex R1 R2 r u V Wo x z

jet flow source opening area (m2) opening area at location x (m2) buoyancy flux of the plume source (m4 s3) universal constant of the plume (–) universal constant of the jet (–) specific heat at constant pressure (J kg1 K1) buoyancy force on the outlet opening (N) inertia force at the inlet opening (N) suction force on the outlet opening (N) gravitational acceleration (m s2) reduced gravity (m s2) reduced gravity in the buoyant layer (m s2) reference reduced gravity for normalization (m s2) height of the room (m) interface level of the buoyant layer (m) light intensity (–) light source intensity (–) distance away from the jet virtual origin (m) Q2 jet specific momentum, Ajj (m4 s2) volumetric flow rate (m3 s1) reference volumetric flow rate for normalization (m3 s1) extraction volumetric flow rate (m3 s1) constant coefficient (–) constant coefficient (–) radius distance away from the extraction sink (m) flow velocity at the opening (m s1) velocity (m s1) heat flux of the heat source (J s1) horizontal coordinate (m) vertical coordinate with the origin at the source level (m)

as well as good indoor air quality can be controlled efficiently by the use of displacement ventilation. Many researchers have reported the advantages of displacement ventilation theoretically and experimentally for different HVAC applications [5–7]. Displacement ventilation has its potential advantages of indoor thermal comfort (ITC) and indoor air quality (IAQ). In a space using the displacement ventilation system, the conditioned fresh air is directly delivered to the occupied zone, and thermal stratification is established in the space. The thermal stratification performance is critical to the ITC and IAQ. Lin and Xu [8] studied the effect of a point heat source at different levels in a space with natural displacement ventilation and found that the stratification performance of natural displacement ventilation is different from that of mechanical displacement ventilation having the same heat source condition which was investigated by Park and Holland [9]. Lin and Lin [10] studied the stratified flow in the space using mechanical or natural displacement ventilation and used a reduced-scale model in a water tank to conduct laboratory experiments. Their experimental results showed that the stability of flow stratification is highly dependent on the force components in the space and the high flow rate provided by mechanical displacement ventilation may result in serious disturbance on the flow stratification. The previous research on mechanical displacement ventilation mostly address it with one or more controllable flow supply sources, and this type could be categorized as mechanical supply displacement ventilation (hereinafter referred to as MSDV). In this study, the flow in a ventilated enclosure due to a localized source having a constant buoyancy flux, Bo , combined with

Dimensionless parameters g^0f dimensionless reduced gravity in the buoyant layer g 0f ) (=g0 ðHÞ p h ^ dimensionless interface level of the buoyant layer (= Hf ) h f b Q dimensionless volumetric flow rate (=Q pQðHÞ) ^d dimensionless thickness (=Hd ) Greek symbols a entrainment constant of the plume (–) b coefficient of thermal expansion (K1) D magnitude of the difference (–) d thickness of the intermediate stratified layer (m) q density (kg m3) rg deviation on the reduced gravity rh deviation on the interface level Subscripts ex experimental result th theoretical prediction a exterior environment f the buoyant layer in inlet opening j jet o real plume source out outlet opening p inside the plume s extraction sink th o theoretical plume origin v virtual origin correction

the mechanical extraction displacement ventilation system having a flow rate, Q ex , as shown in Fig. 1 is investigated. According to a review paper by Linden [11], the heat flux W o released by a heat source is equivalent to the imposed buoyancy flux, Bo in the flow

Bo ¼

gbW o ; qc p

ð1Þ

where g is the gravitational acceleration, b is the coefficient of thermal expansion of the fluid, q is the density and cp is the specific heat at constant pressure. The configuration in Fig. 1 is fixed to investigate the relative influence of different force components, namely the suction, buoyancy and inertia forces, on the flow in the space. The ventilated space is divided into two connected chambers, denoted as the forced and unforced rooms, by a partition with an opening. The forced room has a constant buoyancy source inside

Qex

Qp(hf ) z

Q Q

H hf

Bo

Fig. 1. A schematic diagram showing mechanical extraction displacement ventilation of two connected chambers.

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it and the unforced room only functions as the pathway of supply flow. This paper focuses on the steady-state stratified flow in the forced room, and stresses the effect of the extraction sink, which has rarely been addressed in previous research. This study investigates the stratified flow in a space using mechanical extraction displacement ventilation and compare the effects of the supply source and the extraction sink on the flow in the ventilated space. Theoretical analysis and experimental results are presented in this paper. The theoretical analysis on the stratified flow is introduced in Section 2. Section 3 shows the experimental setup and two experimental series. Experimental results and theoretical predictions regarding mechanical extraction displacement ventilation are shown in Section 4. The conclusions of this study are given in Section 5.

in Fig. 2(a). Assuming that the stratification consists of two stable layers, the density of each layer is homogeneous respectively. For a constant plume source, the buoyancy flux is constant in the room as

2. Theoretical analysis

Based on the buoyancy conservation, the reduced gravity of the buoyant layer in the steady state is expressed as

Based on the driving force, mechanical displacement ventilation can be classified as the supply and extraction types. The supply type is presented in the previous study by Lin and Lin [10], along with natural displacement ventilation. This paper focuses on discussing the flow in a room having a plume source and using mechanical extraction displacement ventilation, as shown in Fig. 2. The theoretical analysis is divided into four parts: the displacement ventilation model without considering the intermediate stratified layer, the jet model, the sink model and the intermediate stratified layer between two layers. The two-layer stratification displacement ventilation model is based on the point plume theory by Morton et al. [12] and the conservation equations. The jet model is presented to show the inflow effect, and the sink model is introduced to represent the influence of extraction outflow. The formation of the intermediate stratified layer is considered to be dependent on the ratio of the force at the outlet to that at the inlet.

Bo ¼ g 0o Q o ;

ð2Þ g 0o

where Bo is the buoyancy flux, is the reduced gravity, and Q o is the volumetric flow rate of the plume source. The density difference between the ambient fluid and the plume source is expressed as Dq ¼ qa  qo . When Dq is small compared to the density of ambient fluid qa , i.e. Dq  qa , the Boussinesq approximation can be applied to the flow and the reduced gravity of the plume source is presented as



g 0o ¼ g

g 0f ¼



qa  qo Dq : ¼g qa qa

ð3Þ

Bo ; Q ex

ð4Þ

where Q ex is the extraction volume flow rate. According to the point plume theory [12], the reduced gravity in a plume at the steady-state interface level is presented as

g 0p ðhf Þ ¼

1 23 53 Bo hf ; C

ð5Þ

 9 13 2 where C ¼ 0:1428 is the plume constant and C ¼ 65 a 10 a p3 , which is related to the plume entrainment constant a. The entrainment pffiffiffi constant of a ¼ 0:083  2 ¼ 0:117 (refer to Turner [14]) is used in this study. The reduced gravity in the buoyant layer in Eq. (4) is equal to that presented in Eq. (5) in the steady state, and this relationship gives 3

2.1. Two-layer stratification model for displacement ventilation

hf ¼

Referring to the classical natural displacement flow as shown by Linden et al. [13] or the MSDV system without considering interfacial mixing by Lin and Lin [10], the two-layer stratification model is introduced in this section. The theoretical model of mechanical extraction displacement ventilation in the forced room is shown

Qex

g^0f ¼

H-hf

Qp(hf)

Q Bo

(a)

:

ð6Þ

g 0f g 0p ðHÞ

¼

Q p ðHÞ 1 Bo 1 ¼ ¼ b Q Q g 0p ðHÞ Q

hf Bo

(b)

Fig. 2. (a) The schematic of the two-layer stratification model without considering the intermediate stratified layer, and (b) the schematic of the intermediate stratified layer with the thickness, d, in the forced room using mechanical extraction displacement ventilation. The thickness of the intermediate stratified layer is considered to be dependent on the ratio of the total force, including the suction and buoyancy forces, at the outlet opening to the inertia force at the inlet opening.

ð7Þ

and 3

thickness δ

FI

1

5 ^ ¼ hf ¼ Q 1 ¼ h f 3 1 H C 5 B5 H o

Qp(hf) hf

3

C 5 B5o

The two-layer model without considering the intermediate stratified layer is similar to that presented in Lin and Lin [10]. Therefore, the interface height is mainly controlled by the flow rate in the space, and also slightly by the buoyancy source strength. For the purpose of general use, Eqs. (4) and (6) are normalized to be equations of dimensionless parameters as follows:

Fs+FB

H-hf

Q ex 5

!35

Q 1 3

CBo H

5 3

 ¼

Q Q p ðHÞ

35

b 35 ; ¼Q

ð8Þ

where H is the height of the room, Q p ðHÞ and g 0p ðHÞ are respectively the volumetric flow rate and the reduced gravity in the plume with a constant buoyancy source strength, Bo , at the level H. 2.2. The jet model There must be at least one flow supply source in a ventilated space. A jet flow with a constant source of momentum M j and flow rate Q j is considered here. The schematic of the non-swirling jet model is shown in Fig. 3(a). The virtual origin of the jet flow is the theoretical origin where the radius is assumed as zero. As the jet flow develops, the jet velocity is approximated as

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F B ¼ qg 0f ðH  hf Þaout :

l

ð12Þ

The suction force at the exit opening is represented as

Virtual origin

 2 Q ex F S ¼ qQ ex uout ¼ q aout ; aout

Vj

where ain and aout are the opening areas of the inlet near the floor level and the outlet on the ceiling level respectively, and H  hf is the thickness of the buoyant layer. These forces, as shown by Eqs. (11)–(13), change with the flow rate. The terms g 0f and hf in the

Real source opening

(a)

expression for the buoyancy force, as shown in Eq. (12), are dependent on the flow rate as shown in Eqs. (4) and (6). Previous experimental results by Lin and Lin [10] showed that there is a transition region between the fresh ambient and polluted buoyant layers in the laboratory experiment, rather than a clearcut interface level. This transition region is denoted as the intermediate stratified layer in this study. The ratio of the sum of the suction and buoyancy forces at the exit opening to the inertia force at the entrance opening is represented as

r Vs

 FS þ FB ¼ FI

(b)

V j ¼ C j Mj l

1

¼ Cj

Q 2j Aj

!12

1

l ;

Q ex aout

2

þ g 0f ðH  hf Þ aout :  2 Q ex ain a

ð14Þ

in

Fig. 3. Schematics of (a) the non-swirling jet flow from the inlet opening on the side wall, and (b) the flow induced by the extraction sink of the outlet opening.

1 2

ð13Þ

This force ratio is considered to be related to the thickness of the intermediate stratified layer, d (see Fig. 2(b)), and experimental results in Section 4.2 confirm this.

ð9Þ 3. Laboratory experiments and the data processing approaches

where C j is the empirical constant for the jet flow and the top-hat profile with C j = 3.5 as shown in Lee and Chu [15] is applied in this research, Aj is the jet source opening area and l is the distance away from the jet virtual origin. 2.3. The sink model The schematic of the sink model is shown in Fig. 3(b). The outlet opening with the extraction device is considered as a point sink, and the induced flow velocity V s away from the extraction sink is presented as

Vs ¼

Q ex ; 2pr 2

ð10Þ

where Q ex is the extraction volumetric flow rate and r is the radial distance away from the extraction sink. Here the outlet opening, as an extraction sink, is at the center of the flat face, and 2pr 2 is the curved surface area of a hemisphere. 2.4. The intermediate stratified layer The inertia force due to the inflow and the suction and buoyancy forces at the outlet opening of the forced room play their individual roles on the stratified flow in the space using mechanical extraction displacement ventilation. The suction force tends to draw the fluid out of the space through the outlet opening. The buoyancy force tends to stratify the fluid and bring the buoyant fluid to the ceiling where the outlet opening is located. The inertia force of the inflow from the inlet opening near the floor tends to mix the fluid inside it. The inertia force due to the inflow is represented as

 2 Q F I ¼ qQ ex uin ¼ q ex ain : ain

ð11Þ

Using the two-layer stratification model to estimate the buoyancy force exerting on the exit opening results in

The experimental setup and experimental series are introduced in this section. The data processing approaches, including the light intensity and density analysis approaches, are the same as those in Lin and Lin [10]. The salt-bath technique was employed to simulate the flow in the space, and the orientation of the experiments was reverse vertically to that of the theoretical model with a heat source as shown in Section 2. Fresh water was used as the ambient fluid, and the dense brine with dye represented the buoyant fluid. This experimental arrangement makes the flow visible. The experimental setup for this research was similar to that employed by Lin and Lin [10] to study MSDV, but a few changes were made in order to conduct mechanical extraction displacement ventilation experiments. Experiments were conducted a tank, which was identical to that used by Lin and Lin [10]. A Plexiglas reduced-scale model of 38.5 cm long, 17 cm wide and 17 cm high, which was divided into two chambers, the forced room and the unforced room, by a partition wall. There were two series of experiments marked by Ex(I) and Ex(II) (see Fig. 4(a) and (b)), and two partition walls with individual connection opening sizes of p and 51 cm2 (see Fig. 5(a) and (b)) were used. Each series only used one of the partition walls, and the opening on the partition wall functioned as the inlet opening of the forced room. A shield screen, as shown in Fig. 5(c), was placed in the forced room between the partition wall and the plume nozzle in order to prevent the plume from being disturbed by the inflow coming from the unforced room. Fig. 6 shows a sketch of the experimental arrangement. This reduced-scale model was placed in a large cubic Plexiglas tank of 83 cm long, 83 cm wide and 83 cm deep, which was maintained at a constant ambient fresh water density while the experiment was running. Fresh water was used as the ambient fluid and replenished in each experiment. The plume source nozzle was placed at the center of the ceiling in the forced room, and supplied by constant-density brine with a

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salt water supply

fresh water supply

(0, 0)

z

x

(192.5, 0) screen

(385, 0)

(192.5, 35)

(235, 170) (0, 170)

Unit: mm

Extraction device (a)

(0, 0)

x

fresh water supply

salt water supply screen (192.5, 0) (385, 0)

z

30

(235, 170) (0, 170)

Unit: mm

Extraction device (b)

Fig. 4. Schematics of experimental series in this research include (a) Ex(I) and (b) Ex(II).

constant head. A flow meter regulated a constant flow rate of salt water, Q o = 2.4 cm3 s1, into the forced room in each experiment. The density of the source brine qo , ranging from 1.11827 to 1.11967 g cm3, gave the source reduced gravity g 0o , ranging from 117.81 to 119.18 cm s2, and the source buoyancy flux Bo , ranging from 282.74 to 286.03 cm4 s3, in all experiments.

The extraction device was connected with an opening on the floor in the forced room by using a mechanical pump to take the fluid out of the reduced-scale model. The opening had a diameter of 2 cm, i.e. an area of p cm2. The ambient fresh water in the environmental tank flowed through an opening on the ceiling in the unforced room to displace the drained fluid in the reduced-scale model as shown in Fig. 4, and the opening also had a diameter of 2 cm. Two series of experimental conditions are summarized in Table 1, and each series includes four different extraction flow rates, i.e. Q ex = 1, 2, 3 and 4 LPM (liters per minute), i.e. 16.67, 33.33, 50 and 66.67 cm3 s1. Because the flow rate through the pump was greater than the extraction flow rate of each experiment, the pump had to be connected with another pipe to extract some additional fluid from the large environmental tank to balance the two flow rates. The extraction flow rate of the reduced-scale model in the experiment was controlled by a flow meter as shown in Fig. 6. Fig. 8 shows the experimental image acquisition arrangement. The flow patterns were observed by applying the lightattenuation flow visualization technique, as described in Allgayer and Hunt [16]. The light intensity data were derived from images of the flow with dye concentration. The relationship between the solution density and the light intensity was used to transform the light intensity profile of the image into the density profile in the flow by using the Lambert-Beer law. Experimental images were recorded via the UniqVision UP900DS-CL CCD camera and the Bitflow Neon-CLB frame grabber directly into the computer hard disk. The DigiFlow program (refer to [17]) was used to control the camera and analyze the intensity data of experimental images. The resolution of each recorded image was approximately 2 pixels per millimeter. The light intensity range was normalized from 0 to 1. The light intensity value near the interface height changed significantly in the vertical direction, and therefore the interface level was defined as the location having the maximum slope. The window for determining the interface level ranged from (x; z) = (355 mm, 15 mm) to (356 mm, 155 mm). The solution samples were measured by a DMA 4500 M laboratory density meter (Anton Paar), which had an accuracy of up to 5  105 g cm3. A series of sampling syringes were placed on the side wall of the forced room, from 1.5 cm to 15.5 cm at every 2 cm interval between two consecutive measurement points, for a total of 8 measurement locations in the reduced-scale model. The solution at each sampling location was taken once every 1000 s. Density measurements were used to confirm the results

3 cm

3.5 cm

17 cm

2 cm

17 cm

(a)

8.5 cm

partition (II)

partition (I)

5.5 cm

17 cm 14 cm

17 cm

(b)

0.5 cm

(c)

Fig. 5. Schematics of two interior partitions: (a) partition (I) for Ex(I) series and (b) partition (II) for Ex(II) series, and (c) a shield screen between the partition and the turbulent plume in the forced room for all experiments.

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Constant Pressure Head (Salt Water) Siphon pipe

Faucet

Environmental Tank

Reduced-scale Model

drain

83 cm 17 cm

38.5 cm

Rotameter

Pump

83 cm drain Fig. 6. Experimental arrangement of the reduced-scale model using mechanical extraction displacement ventilation in the laboratory.

Table 1 Experimental conditions for a reduced-scale model using mechanical extraction displacement ventilation. Experimental runs Series (I)

Ex(I)_1

Ex(I)_2

Ex(I)_3

Ex(I)_4

Q ex (cm3 s1) Bo (cm4 s3)

17.33 282.74

33.03 286.03

49.40 284.21

66.43 284.14

Series (II)

Ex(II)_1

Ex(II)_2

Ex(II)_3

Ex(II)_4

Q ex (cm3 s1) Bo (cm4 s3)

17.13 285.36

33.53 283.75

49.82 282.86

67.27 283.54

1.02

1.016

1.012

diffusive screen

model environment tank

3

ρ (g/cm )

light source

ρ = 0.9981 - 0.0068 ln (I / I0) Coefficient of Determination : 0.9492

1.008

1.004

CCD camera

1

flow images camera control

0.996 -1.6

-1.4

-1.2

-1

-0.8

-0.6

ln (I / I0)

-0.4

-0.2

0

0.2

PC (hard disk)

Fig. 8. Top view of the experimental image acquisition arrangement.

Fig. 7. The measured density against the light intensity for Ex(I)_4.

obtained with the light-attenuation technique. The relationship between the density and the intensity was established by using the Lambert-Beer law as



q ¼ R1 þ R2 ln

  I ; I0

ð15Þ

where R1 ; R2 are constant coefficients determined by experimental results, and I0 is the light intensity of the fresh water in the reduced-scale model. The dye and the salt were added into the water and mixed well to make the brine source solution before running the experiment. The dye concentration is supposed to be propositional to the salinity or the density of the brine solution lin-

Y.J.P. Lin, J.Y. Wu / International Journal of Heat and Mass Transfer 110 (2017) 447–459

453

Fig. 9. Experimental images of (a) Ex(I)_1 and (b) Ex(I)_4 in the steady state.

early. The results of the measured density, q, of the sampled solution against the light intensity I for Ex(I)_4 are presented in Fig. 7. In laboratory experiments, the plume source has a finite volume flux and momentum flux at its nozzle outlet, contrary to the pure plume theory, which assumes that the plume is a source of buoyancy only. Therefore, the real plume source in the experiment is adjusted to fit the plume theory by using the virtual origin. According to Hunt and Kaye [18], the distance between the virtual and real plume sources, denoted as the virtual origin correction zv , is dependent on the bulk properties of plume source. The virtual origin, zth o , is above the real source, zo = 0 cm, in this experimental arrangement. 4. Results 4.1. Two-layer model Experimental images of the two cases with individual flow rates of 1 and 4 LPM, or 16.67 and 66.67 cm3 s1, in Ex(I) series, Ex(I)_1 and Ex(I)_4, are shown in Fig. 9 and in Ex(II) series, Ex(II)_1 and Ex (II)_4, are shown in Fig. 10. Two-layer stratification was observed in the experimental cases with small flow rates, as shown in Figs. 9 (a) and 10(a), although there was some slight flow disturbance in Ex(I) series as shown in Fig. 9(a). When the flow rate increased, this stable two-layer stratification was significantly disturbed in Ex(I) series of experiments, as shown in Fig. 9(b), but still maintained quite well in Ex(II) series of experiments, as shown in Fig. 10(b).

The magnitude of the inertia force of the inflow is considered to be the cause of the flow disturbance. This inflow inertia force in Ex(I) series is much larger than that in Ex(II) series at the same flow rate, because of their different connection opening sizes. Therefore, the flow disturbance is stronger and a more noticeable intermediate stratified layer is formed between the fresh and dense layers due to the inflow from the unforced room in Ex(I) series, especially for the high flow rate case as shown in Fig. 9(b). The two-layer stratification model gives estimation formulae for the reduced gravity in the dense layer and the interface level between the fresh and dense layers in the steady state, as shown in Eqs. (4) and (6). Theoretical prediction using the average buoyancy flux, Bo = 284.08 cm4 s3, and the virtual origin correction, zv = 1.75 cm, in experiments results in the reference volumetric flow rate Q p ðHÞ = 124.23 cm3 s1 or the reference reduced gravity g 0p ðHÞ = 2.29 cm3 s1 for calculation of the dimensionless reduced gravity in the dense layer, as shown in Eq. (7). Fig. 11 shows experimental results and theoretical prediction regarding the dimensionless reduced gravity of the dense layer against the dimensionless flow rate for two experimental series. The reduced gravity varies inversely as the flow rate for the constant buoyancy flux condition. The reduced gravity of the dense layer shows good agreement between experimental results and theoretical prediction. Fig. 12 shows experimental results and theoretical prediction regarding the dimensionless interface level between the two layers against the dimensionless flow rate for two experimental series.

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Fig. 10. Experimental images of (a) Ex(II)_1 and (b) Ex(II)_4 in the steady state.

Qp(H) = 124.23 cm3/s; H = 17 cm

hf

g’f / g’p(H)

Qp(H) = 124.23 cm3/s; g’p(H) = 2.29 cm/s2

Qex/Qp(H) Fig. 11. Experimental results of the dimensionless reduced gravity of the dense layer against the dimensionless flow rate for two experimental series, Ex(I) and Ex (II), along with theoretical prediction.

Qex/Qp(H) Fig. 12. Experimental results of the dimensionless interface level between two layers against the dimensionless flow rate for two experimental series, Ex(I) and Ex (II), along with theoretical prediction.

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Y.J.P. Lin, J.Y. Wu / International Journal of Heat and Mass Transfer 110 (2017) 447–459 Table 2 Comparisons between theoretical prediction by using the two-layer stratification model and experimental results. hf ex (cm)

hf th (cm)

Deviation of hf (%)

g 0f ex (cm s2)

g 0f th (cm s2)

Deviation of g 0f (%)

Ex(I)_1 Ex(I)_2 Ex(I)_3 Ex(I)_4

4.62 7.46 9.40 11.67

4.01 6.71 9.03 11.13

3.59 4.41 2.18 3.18

14.21 7.85 5.63 4.41

16.32 8.66 5.75 4.28

1.79 0.68 0.10 0.11

Ex(II)_1 Ex(II)_2 Ex(II)_3 Ex(II)_4

3.01 6.61 9.37 10.25

3.96 6.80 9.10 11.23

5.59 1.12 1.59 5.76

14.43 7.73 5.22 4.05

16.66 8.46 5.68 4.21

1.88 0.62 0.39 0.14

Exp.

0

0 3000 s

2

2

4

4 6

8 10

z (cm)

z (cm)

6

thickness δ

8 10

12

Top limit hf Bottom limit

12

7.5% ΔIntensity

14

14

ΔIntensity

16

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

16

Intensity

3000

4000

Fig. 13. The light intensity profile of Ex(I)_4 in the steady state. The notation d represents the thickness of the intermediate stratified layer.

rh ¼

hf ex  hf th  100%; H

ð16Þ

and the deviation on the reduced gravity is defined as

rg ¼

 0  g f ex  g 0f th g 0o

 100%:

6000

7000

(a) 0 2

Top limit hf Bottom limit

4 6

z (cm)

Theoretical prediction uses Eq. (8) to estimate the dimensionless interface level. The distance between the plume source and the interface level increases with the flow rate to the power of 35. Experimental results for the interface level agree well with theoretical prediction. The two-layer stratification model generally gives good results in mechanical extraction displacement ventilation to estimate the basic parameters, such as the reduced gravity and the interface level, in the space having a given volumetric flow rate. Theoretical prediction and experimental results of this study are summarized in Table 2. The deviations on the interface level between theoretical prediction and experimental results are less than 6%, and the deviations on the reduced gravity are less than 2%. The deviation on the  interface level  is defined as

5000

Time (s)

8 10 12

ð17Þ

However, as the flow rate increases, the incoming flow disturbing stable flow stratification becomes more noticeable and the sharp interface between the two homogeneous layers changes to an intermediate stratified layer with a certain thickness. 4.2. Formation of the intermediate stratified layer The same procedure as that presented in Lin and Lin [10] to determine the quantitative thickness of the intermediate stratified

14 16

3000

4000

5000

Time (s)

6000

7000

(b) Fig. 14. Experimental results of the top and bottom limits of the intermediate stratified layer and the interface level against the time for Ex(I) series, (a) Ex(I)_1, and (b) Ex(I)_4.

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layer was applied in this study. Fig. 13 shows the light intensity profile derived from one of the recorded flow images of Ex(I)_4. In order to determine the thickness of the intermediate stratified layer d, a specific intensity slope value is chosen as the threshold value. Because either of the ambient and buoyant layers has a similar intensity magnitude inside its core region, the intensity slope value is less than the threshold value inside either of two layers. The first level from the ceiling or floor having the intensity slope larger than the chosen threshold value is regarded as the boundary level of the core region of the ambient or buoyant layer. The core regions of the ambient and buoyant layers are marked in Fig. 13. Then the average magnitudes of light intensity, Ia and If , inside

^

456

0 2 4

Qex/Qp(H)

z (cm)

6

Fig. 16. Experimental results of the dimensionless thickness of the intermediate stratified layer against the dimensionless flow rate in two series of mechanical extraction displacement ventilation.

8 10

Top limit hf Bottom limit

12 14 16

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4000

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Time (s)

6000

7000

(a) 0 2

Top limit hf Bottom limit

4

the core regions of the ambient and buoyant layers are determined. The intensity difference DI ¼ Ia  If is used to determine the top and bottom levels of the intermediate stratified layer, which has the top boundary level with the intensity value of Ia  0:075DI and the bottom boundary level with the intensity value of If þ 0:075DI. Fig. 14(a) and (b) shows the corresponding thicknesses and interface levels of Ex(I)_1 and Ex(I)_4, whose experimental images are presented in Fig. 9(a) and (b), and Fig. 15(a) and (b) shows those results for Ex(II)_1 and Ex(II)_4, whose experimental images are presented in Fig. 10(a) and (b). When the flow rate was small and the buoyancy force dominated the flow, i.e. F B  F I and F B  F S , the thickness of the intermediate stratified layer was less pronounced as shown in Figs. 14(a) and 15(a). As the flow rate increased, the change in the intermediate stratified layer thickness in Ex(I) series of

δ

δ

z (cm)

6 8 10 12 14 16

3000

4000

5000

Time (s)

6000

7000

(b) Fig. 15. Experimental results of the top and bottom limits of the intermediate stratified layer and the interface level against the time for Ex(II) series, (a) Ex(II)_1, and (b) Ex(II)_4.

log [(FB+FS) / FI ] Fig. 17. Experimental results of the dimensionless thickness of the intermediate stratified layer against the logarithm of the force ratio in two series of mechanical extraction displacement ventilation.

Y.J.P. Lin, J.Y. Wu / International Journal of Heat and Mass Transfer 110 (2017) 447–459

0.5

0.4

∧ δ

0.3

0.2

0.1

0

0

0.1

0.2

0.3

Q/Qp(H)

0.4

0.5

0.6

Fig. 18. Experimental results of the dimensionless thickness of the intermediate stratified layer against the dimensionless flow rate in two series of experiments, respectively, with mechanical extraction displacement ventilation and MSDV.

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experiments, as shown in Fig. 14 was more apparent than that in Ex(II) series as shown in Fig. 15. This was because the inflow inertia force in Ex(I) series was much stronger than that in Ex(II) series, and their buoyancy force magnitudes were similar for a given flow rate. Similar to MSDV, the inflow inertia force in this study had a clear influence on the formation of the intermediate stratified layer. It is quite interesting to compare the formation of the intermediate stratified layer in the two experimental cases of Ex(I)_1 and Ex(II)_4 as shown in Figs. 14(a) and 15(b). Both cases had similar inflow inertia force magnitudes and Ex(I)_1 even had a stronger buoyancy force, but the intermediate stratified layer in Ex(I)_1 was thicker than that in Ex(II)_4. Therefore, the stronger suction force in Ex(II)_4 was expected to aid the flow stratification and diminish the intermediate stratified layer thickness. Fig. 16 shows the dimensionless thickness of the intermediate stratified layer against the dimensionless extraction flow rate for two series of experiments. In general, the thickness of the intermediate stratified layer increased with the flow rate for both series. However, Ex(I)_3 and Ex(I)_4 were observed to have similar thicknesses, although the flow rate of Ex(I)_4 was higher than that of Ex (I)_3. In these two experimental cases, the suction and inertia forces had similar magnitudes and the buoyancy force was much less than these two forces, i.e. F S  F I  F B . Therefore, the stratified

Fig. 19. Light intensity contours of experimental images of (a) Ex(I)_1 and (b) Ex(I)_4 in the steady state.

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flow was mainly dominated by the suction and inertia forces, and using Eq. (14) to calculate the force ratio gave close results for the two cases. The thickness of the intermediate stratified layer in Ex(I) _3 or Ex(I)_4 was expected to be the maximum limit for Ex(I) series, because the case with an even higher flow rate in this series still had a similar force ratio to that in Ex(I)_3 or Ex(I)_4, i.e. ðF S þ F B Þ=F I  1, and should lead to a similar thickness. Fig. 17 shows the relationship between the force ratio and the thickness of the intermediate stratified layer, and the force ratio is calculated by using Eq. (14). The thickness of the intermediate stratified layer is considered to be dependent on the ratio of the force at the outlet to that at the inlet for mechanical extraction displacement ventilation, and this hypothesis is identical to that for MSDV. The linear fit equation between the dimensionless thickness and the logarithm of the force ratio for the mechanical extraction displacement ventilation in this research gives the relationship as

  ^d ¼ d ¼ 0:3  0:17 log F S þ F B : H FI

ð18Þ

This linear fit relationship and experimental results are shown in Fig. 17. This linear fit result is close to that presented in Lin and Lin [10], and they show the linear fit relationship due to MSDV as

  ^d ¼ d ¼ 0:218  0:126 log F B : H FI

ð19Þ

Comparing the formation of the intermediate stratified layer in experiments with mechanical extraction displacement ventilation and MSDV, Fig. 18 shows the dimensionless thickness of the intermediate stratified layer against the dimensionless flow rate for two series of experiments, respectively, using two types of displacement ventilation. The main difference between two types of displacement ventilation is the presence or absence of the suction force in the flow. Fig. 18 shows that a significant suction force clearly diminishes the intermediate stratified layer by comparing Ex(I)_4 and MSDV(I)_4, which both have the same flow rate of 4 LPM, or 66.67 cm3 s1. The effect of the suction force on the thickness of the intermediate stratified layer is even more obvious when comparing Ex(II) and MSDV(II) series of experiments. With a given flow rate, any one experimental case in Ex(II) series always has a thinner intermediate stratified layer than that in MSDV(II) series. Only Ex(II)_1 and MSDV(II)_1 have similar scales of the intermediate stratified layer thickness, because both have a strong buoyancy force compared with the suction force in the flow. The increasing rate of the intermediate stratified layer thickness in Ex(II) series is clearly less than that in MSDV(II) series, as shown in Fig. 18.

Fig. 20. Light intensity contours of experimental images of (a) Ex(II)_1 and (b) Ex(II)_4 in the steady state.

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4.3. Contours of light intensity in the dense layer The light intensity of the experimental images could be interpreted as the density in the flow as presented in Section 3. The contour of light intensity in the dense layer could be regarded as the density contour, or the corresponding temperature contour in the buoyant layer of the space with a heat source, as presented in Section 2. The light intensity in the dense layer was almost uniform when the extraction flow rate was small, such as Ex(I)_1 and Ex(II)_1 shown in Figs. 19(a) and 20(a), and their contours of light intensity were generally horizontal and almost concentrated near the interface level. This observation is similar to that in MSDV or natural displacement ventilation. The contour of light intensity in the dense layer was generally horizontal when the flow rate was moderate or the location was away from the extraction sink. When the flow rate became high and the location approached the extraction sink, the contour of light intensity in the dense layer would bend toward the location of the extraction sink as shown in Figs. 19(b) and 20(b) for Ex(I) _4 and Ex(II)_4. The gradient of the light intensity along a horizontal level with a certain non-zero constant value in the dense layer was clearly identified, and it indicated that the density distribution along the horizontal level was non-uniform. The density near the extraction sink was less than that away from the extraction sink at the same horizontal level in the dense layer. This observation regarding the density gradient performance in the dense layer is very different from that in the previous study on displacement ventilation, and is a very unique feature of mechanical extraction displacement ventilation. To the best knowledge of the authors, this experimental observation is the first reported in the literature on displacement ventilation. 5. Conclusions This study investigates the steady-state stratified flow in a room having a plume source and using mechanical extraction displacement ventilation, emphasizing the effect of the extraction sink on the flow. The two-layer stratification displacement ventilation model is applied to calculate the design parameters in the ventilated space and has good agreement with experimental results. As the flow rate increases, an intermediate stratified layer with a certain thickness is observed and becomes noticeable. Experimental observations similar to the previous research, the inflow inertia force has a clear influence on the formation of the intermediate stratified layer. However, the strong suction force in this study shows to aid the flow stratification and diminish the intermediate stratified layer thickness. The force ratio in a ventilated space plays a key role in the formation of the intermediate stratified layer. The linear fit relationship between the dimensionless thickness and the

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logarithm of the force ratio in this study agrees closely with the previous study. The density in the dense layer is generally uniform when the flow rate is moderate or the location is away from the extraction sink. However, when the flow rate is high and the location is near the extraction sink, the density distribution along the horizontal level with a certain non-zero gradient in the dense layer is clearly identified, which is a unique feature of mechanical extraction displacement ventilation. Acknowledgments The authors like to acknowledge the financial support of this research work from the National Taiwan University of Science and Technology (NTUST), and Taiwan Ministry of Science and Technology, the grant of MOST 105-2221-E-011-062. The authors like to acknowledge Mr. Lo, Chi-Hao for the help of redrawing some figures in this paper. References [1] M.W. Liddament, M. Orme, Energy and ventilation, Appl. Therm. Eng. 18 (1998) 1101–1109. [2] L. Perez-Lombard, J. Ortiz, C. Pout, A review on buildings energy consumption information, Energy Build. 40 (2008) 394–398. [3] M. Sandberg, What is ventilation efficiency?, Build Environ. 16 (2) (1981) 123– 135. [4] K. Lee, Z. Jiang, Q. Chen, Air distribution effectiveness with stratified air distribution systems, ASHRAE Trans. 115 (2) (2009) 322–333. [5] E. Mundt, Displacement ventilation systems – convection flows and temperature gradients, Build. Environ. 30 (1) (1995) 129–133. [6] P.V. Nielsen, Velocity distribution in a room ventilated by displacement ventilation and wall-mounted air terminal devices, Energy Build. 31 (3) (2000) 179–187. [7] H. Xing, H.B. Awbi, Measurement and calculation of the neutral height in a room with displacement ventilation, Build. Environ. 37 (10) (2002) 961–967. [8] Y.J.P. Lin, Z.Y. Xu, Buoyancy-driven flows by a heat source at different levels, Int. J. Heat Mass Transfer 58 (2013) 312–321, http://dx.doi.org/10.1016/j. ijheatmasstransfer.2012.11.008. [9] H.J. Park, D. Holland, The effect of location of a convective heat source on displacement ventilation: CFD study, Build. Environ. 36 (7) (2001) 883–889. [10] Y.J.P. Lin, C.L. Lin, A study on flow stratification in a space using displacement ventilation, Int. J. Heat Mass Transfer 73 (2014) 67–75. [11] P.F. Linden, The fluid mechanics of natural ventilation, Annu. Rev. Fluid Mech. 31 (1999) 201–238. [12] B.R. Morton, G.I. Taylor, J.S. Turner, Turbulent gravitational convection from maintained and instantaneous sources, Proc. Roy. Soc. London A 234 (1196) (1956) 1–23. [13] P.F. Linden, G.F. Lane-Serff, D.A. Smeed, Emptying filling boxes: the fluid mechanics of natural ventilation, J. Fluid Mech. 212 (1990) 309–335. [14] J.S. Turner, Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, 1973. [15] J.H.W. Lee, V.H. Chu, Turbulent Jets and Plumes, Kluwer Academic Publishers, 2003. [16] D.M. Allgayer, G.R. Hunt, On the application of the light-attenuation technique as a tool for non-intrusive buoyancy measurements, Exp. Therm. Fluid Sci. 38 (2012) 257–261. [17] S.B. Dalziel, DigiFlow User Guide, DL Research Partners, version 1.1, 2006. [18] G.R. Hunt, N.G. Kaye, Virtual origin correction for lazy turbulent plumes, J. Fluid Mech. 435 (2001) 377–396.