Numerical investigation of the flow behavior of an isothermal impinging jet in a room

Building and Environment 49 (2012) 154e166

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Numerical investigation of the flow behavior of an isothermal impinging jet in a room H.J. Chen a, b, *, B. Moshfegh a, b, M. Cehlin a a b

Department of Building, Energy and Environmental Engineering, Faculty of Engineering and Sustainable Development, University of Gävle, 801 76 Gävle, Sweden Division of Energy Systems, Department of Management and Engineering, Linköping University, Linköping, Sweden

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 August 2011 Received in revised form 26 September 2011 Accepted 27 September 2011

The impinging jet concept has been proposed as a new ventilation strategy for use in office and industrial buildings. The present paper reports the mean flow field behavior of an isothermal turbulent impinging jet in a room. The detailed experimental study is carried out to validate the numerical simulations, and the predictions are performed by means of the RNG k
ε and SST k
u model. The comparisons between the predictive results and the experimental data reveal that both of the tested turbulence models are capable of capturing the main qualitative flow features satisfactorily. However, it is worth to mention that the predictions from the RNG k
ε model predicts slightly better of the maximum velocity decay as jet approaching the floor, while the SST k
u model accords slightly better in the region close to the impingement zone which is crucial for spreading of the jet inside the room. Another important perspective of this study is to investigate the influence of different flow and configuration parameters such as jet discharge height, diffuser geometry, supply airflow rate and confinement from the surrounding environment on the impinging jet flow field with the validated model. The obtained data are presented in terms of the jet dimensionless velocity distribution, maximum velocity decay and spreading rate along the centerline of the floor. The comparative results demonstrate that all the investigated parameters have certain effects on the studied flow features, and the diffuser geometry is found to have the most appreciable impact, while the supply airflow rate is found to have marginal influence within the moderate flow range. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: Impinging jet ventilation Measurement Numerical simulation Parametric study

1. Introduction The method of distributing fresh air from the supply diffuser into the enclosed space has a significant impact on the generated airflow pattern, which is essentially related to the condition of the indoor environment. A good air distribution system not only promotes a comfortable and healthy environment for occupants, but also contributes to energy conservation [1]. Within the last two decades, the principle of impinging jet has been applied to air conditioning and ventilation, and developed as a new ventilation strategy, i.e., impinging jet ventilation (IJV) [2,3]. Due to the potential for providing better air distribution and energy-efficient operation, as well as its flexibility for both cooling and heating purposes, IJV has received increasing attention, and developed as an alternative to conventional ventilation systems, i.e., mixing and

* Corresponding author. Department of Building, Energy and Environmental Engineering, Faculty of Engineering and Sustainable Development, University of Gävle, 801 76 Gävle, Sweden. Tel.: þ46 739128884; fax: þ46 26 648828. E-mail address: [email protected] (H.J. Chen). 0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.09.027

displacement ventilation systems, used in office environments and industrial premises [4,5]. In the impinging jet ventilation system, a high momentum air jet is discharged downwards, strikes the floor and spreads over it, thus distributing the fresh air along the floor in the form of a very thin shear layer. This method enables the air jet to overcome the buoyancy force generated from heat sources and reach further regions. Therefore more efficient ventilation in the occupied zone can be achieved compared to a displacement ventilation system [6]. However, the draught sensation must be taken into account when designing such systems, since the high velocity might occur in the occupied zone. Therefore, the flow behavior of IJV system should be investigated carefully to enable proper design to achieve better thermal comfort environment. Impinging jet has been widely studied with various flow configurations. The flow field of impinging jet is characterized as the combination of three regions d free jet region, impingement region and wall jet region, as illustrated in Fig. 1. A number of comprehensive reviews of the flow characteristics of jet impinging on a flat plate can be found in the literature [7e11]. Gaunener et al. [7] made an extensive literature survey on the flow field of a single impinging jet, presenting the methods for determining the

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

Fig. 1. Flow regions of an impinging jet.

pressure and velocity profiles in each region; Copper et al. [8] experimentally investigated the characteristics of the velocity field of a turbulent circular impinging jet, where the axial velocity decay, jet growth rate and the radial velocity distributions were analyzed; Knowles and Myszko [9] examined the effects of the nozzle heights on the thickness of the wall jet after the impingement region; Rajaratnam et al. [10] reviewed the impact of the nozzle geometry on the development of a three-dimensional wall jet, where various nozzle shapes (circular, square, rectangular, elliptic and triangular) were considered. The non-dimensional velocity profiles were found similar in all cases at a distance 10 times greater than the nozzle height. A recent study by Xu and Hangan [11] summarized the effects of Reynolds number, nozzle geometry and the confinement of surrounding boundaries on the behaviors of the mean and turbulent flow field of an orthonormal impinging jet. They found that the effect of Reynolds number is provoked in the surface flow field below a critical Re, i.e., the relative maximum velocity increases and the height of the maximum decreases by increasing the Reynolds number. The investigated range of Reynolds number is from 27,000 to 190,000. They also pointed out the influence of the jet discharge height h on the velocity profiles, i.e., the position of the maximum velocity as well as its half maximum velocity decreases with increasing h, which is due to the increased suppression of the axial component. Even though most of the work reported in the literature review is focused on the theory and fundamental perspective, they still lead us to investigate the effects from various supply conditions on the characteristics of the impinging jet flow field in a room. As an alternative approach to scale model or full-field experimental method, computational fluid dynamics (CFD) is being extensively used as a fast and cost-effective tool to predict air distribution and design ventilation systems. With the advantages of CFD, such as the ability to provide detailed information on environmental parameters as well as the flexibility to perform large number parametric studies [12e16], the application of CFD to room airflow prediction has met with considerable success [17e21]. Most of the numerical studies on ventilation flow adopt the method of Reynolds Average NaviereStokes (RANS) modeling, which requires economic computer power and is suitable for indoor environment study. The turbulence model is being emphasized as a crucial factor for the accuracy of ventilation flow prediction, and the performance of various turbulence models has been reviewed by many authors, some of which are cited here [22e28]. Chen [22] examined five k
ε models in the prediction of 2D ventilation flow, where natural, forced, and mixed convection and impinging jet flow in rooms were considered. The results revealed that the tested models were able to predict the mean velocity accurately, but none of them could

155

capture the fluctuating velocity satisfactorily due to the isotropic turbulence assumption. In addition, he recommended the use of RNG k
ε model for indoor airflow simulation. Chen further evaluated [23] the three Reynolds stress models (RSM) and standard k
ε model to predict the airflow distribution for the same case as studied in 1995 [22]. It was found that the three RSM models were able to predict the existence of the secondary recirculation within the room airflow, which could not be obtained from the twoequation turbulence models. However, RSM is more complex and requires more computing effort compared to two-equation turbulence models, which might impose some limitations on the building environment simulation. Luo and Roux [24] tested the accuracy of RNG k
ε model in the prediction of a wall jet discharged from a complex nozzle, where good consistency with measurement was observed together with the local mesh refinement. Stamou and Katsiris [25] applied the SST k
umodel to predict the velocity and temperature distributions in a model office; the predictive results showed the best agreement with experimental data compared to standard k
ε and RNG models. Zhai Z et al. summarized the prevalent turbulence models in the applications to indoor environments and evaluated their performance for the predictions of various indoor airflow scenarios [26,27]. A recent study by Cao et al. [28] used the CFX SST k
umodel to simulate the velocity distribution of a ceiling attached plane jet after its impingement on the opposite wall. The presented results showed good agreement with measurements in terms of the maximum velocity decay at low-Reynolds numbers. In addition to above cited two-equation eddy-viscosity models and the RSM, a multiple-equation eddy-viscosity model named v2
f model was developed by Durbin in 1991 [29]. This model has shown satisfactory performance for a range of flow types especially for the impinging jet flow, see e.g. Rundström and Moshfegh [30] and Behnia et al. [31]. Besides the satisfactory performance from v2
f model, the SST model was also shown to have good agreement with the results predicted by v2
f model, as reported by Esch and Menter [32]. The study presented by Zuckerman and Lior [33] also indicated that the SST model may perform as well as the v2
f model does for the impinging jet problem and it was recommended due to lower computational cost. In the current investigation, RNG k
ε and SST k
u model are implemented to predict the mean flow field structure of an isothermal impinging jet in a room. The reason of choosing this two turbulence models is due to the good compromise between computational speed and accuracy, as revealed from the previous study presented by Chen and Moshfegh [34] as well as shown from other researchers’ investigations [22,25,28,32]. The performance of the employed models is examined with the accompanied measurement as well as the previous study [3]. After validation, the aspects of jet discharge height, diffuser geometry, supply airflow rate and the confinement from the surrounding boundaries are investigated further to examine the influence on the consequent flow. By identifying the impact from the supply conditions on the flow structure, detailed knowledge of the impinging jet flow mechanism can be obtained and contributed to further optimization. 2. Computational set-up and numerical scheme 2.1. Physical model The physical model under consideration is a semi-confined room with the dimensions 5.76  3.04  3 m, see Fig. 2. There are three openings inside the room, two of which are 1 m high and 5.76 m long located beneath two side walls, while the other one is placed at the end of the room and designated the door opening, 3 m

156

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

Fig. 2. Computational domain.

high and 1.32 m wide. The air enters the room through a 1.51 m long semi-elliptic pipe, and is discharged from the outlet with the area of 0.0166 m2 at the height h of 0.6 m above the floor. The geometry and dimension of the supply diffuser at outlet are also presented in Fig. 2.

2.2. Governing equations The airflow field inside the room is assumed to be steady-state, three-dimensional, incompressible and turbulent. Based on these assumptions, the continuity and time-averaged NaviereStokes equations are given by:

vUi ¼ 0 vxi

(1)

!
 v U j Ui 1 vP v vU n i
u0i u0j ¼
þ r vxi vxj vxj vxj

(2)

Where u0i u0j is the unknown and called the Reynolds stress. To close the equation system, this term must be appropriately modeled. The most popular model to approximate the Reynolds stress is based on the Boussinesq hypothesis, which assumes the Reynolds stress tensor is proportional to the strain rate tensor and expressed by:


u0i u0j

¼ nt

vUi vUj þ vxj vxi

!


2 kd 3 ij

(3)

where nt is the eddy viscosity, k is turbulent kinetic energy defined as k ¼ u0i u0j =2, and dij is the Kronecker delta. The eddy viscosity nt is expressed as the product of the velocity scale and turbulent length scale together contributing to the dimension of m2/s. The common methods to derive nt are to combine the turbulent kinetic energy k with the dissipation rate ε through nt ¼ Cm k2 =ε or with the specific dissipation rate u through nt ¼ k=u, accordingly two additional transport equations for k, ε or u are required to be solved in order to close the above described setting of equations.

2.3. Turbulence models In the present study two turbulence models are implemented, i.e., the RNG k
ε and SST k
u model. Explicit mathematical descriptions of the two models are given below. 2.3.1. The RNG k
ε model In the RNG k
ε model, the transport equations for the turbulent kinetic energy k and dissipation rate ε are given below:

"
  # v Uj k n vk v nþ t þ Pk
ε ¼ sk vxj vxj vxj

(4)

"
  # 2 v Uj ε n vε v ε  ε nþ t þ Cεl Pk
Cε2 ¼ sε vxj vxj k vxj k

(5)

Pk represents the rate of the turbulent kinetic energy production and is expressed as:

Pk ¼ nt

vUi vUj þ vxj vxi

!

vUi ¼ nt Sij Sij vxj

(6)

Where Sij is the mean rate-of-strain tensor defined as:   2 1 vUi vUj  ε introduces an additional source term ; Cε2 Sij ¼ þ k 2 vUj vUi that makes the RNG model superior for responding to the effect of rapid strain and streamline curvature to standard k
ε model, which is given by:

 Cε2

ε2 ¼ Cε2 þ k

  Cm h3 1
h=h 0

1 þ bh3

(7)

k Where h ¼ S , denotes the ratio between the time scales of the ε turbulence and mean flow. The constants appearing in the RNG k
ε model are listed below: Cm ¼ 0.0845, Cε1 ¼ 1.42, Cε2 ¼ 1.68, sk ¼ sε ¼ 0.7194, b ¼ 0.012, h0 ¼ 4.38.

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

2.3.2. The shear-stress transport (SST) k
u model SST k
u model by Menter [35] including the low-Reynolds correction is used in this study. This model is formulated based on two existing models, i.e., the standard k
u and k
ε model, in which the former is activated in the inner region of the boundary layers, and the latter is used in the outer wake region and in free shear flows. SST k
u model performs similarly to the standard k
u model, but it avoids the strong sensitivity of u-equation to the free-stream properties [36,37]. To utilize the advantage of standard k
ε in the freestream, the k
ε model needs to be converted into a k
u formulation. The switch between the two models is controlled by blending functions F1 and F2, which appears in the u-equation and the modified turbulent eddy viscosity formulation, respectively; for details see ANSYS Fluent [38]. SST k
u model shows major improvements in the prediction of adverse pressure gradient and separating flows. The transport equations for k and u in SST k
u model are expressed as follows:

"
  # v Uj k nt vk ~
b ku þ v n ¼ P þ k sk vxj vxj vxj

(8)

"
  # v Uj u a~ nt vu v 2 bu n ¼ P
þ þ su vxj nt k vxj vxj þ 2ð1
F1 Þsu2

1 vk vu u vxj vxj

(9)

~ ¼ minðP ; 10rb kuÞ, F1 is the blending function Where P k k designed to be one inside the boundary layer (activating k
u model), and equal to zero away from the surface (activating k
ε model). All the constants in the SST k
u model (denoted by 4) are computed based on the corresponding values in the k
u model (denoted by 41 ) and the k
ε model (denoted by) via the relation of. The values of the model constants are: b1 ¼ 0.075, b* ¼ 0.090, sk1 ¼ 1.176, su1 ¼ 2.000, a1 ¼ 0.31, b2 ¼ 0.0828, sk2 ¼ 1.000, su2 ¼ 1.168. 

2.4. Boundary conditions The boundary conditions are specified as follows: At the inlet (the jet discharged section), the measured y-component velocity profile, V, is imposed, the distributions of turbulent kinetic energy k, and dissipation rate ε or specific dissipation rate u are determined by using the following formula [39]:

kin ¼ 1:5ðVin Tu Þ2

(10)

3=4

157

εin ¼ Cm k3=2 =l

(11)

1=4 uin ¼ k1=2 =Cm l in

(12)

Where, V is the y-component velocity at the inlet, Cm is the empirical constant specified in the turbulence model with a proximate value of 0.09, and l is a length scale given by, dh is the hydraulic diameter for the jet discharged section. At the openings, the pressure outlets are used assuming the gauge pressures are zero. All the surfaces are set as non-slip walls. 2.5. Grid independency and numerical details ANSYS Workbench 13.0 [40] is used to construct the threedimensional configuration and generate the mesh. To cover the whole computational domain efficiently, non-uniform grid distribution is used, i.e., finer mesh is placed adjacent to the inlet, outlet and walls as well as the region expected to have the steep velocity gradient. Three different grid densities, i.e., 2,503,372, 4,991,480 and 6,171,052 hexahedral cells have been tested by RNG k
ε and SST k
u model. By comparing the predictions from the three grids, the last two grids present fairly similar results for both tested turbulence models, which show a slight improvement on the first grid compared to measurements. Therefore, the grid with 4,991,480 cells in total and 3562 cells at the inlet boundary surface is considered sufficient for use in the current study. The mesh is refined enough near the solid walls by keeping the yþ to be less than one in order to solve the all boundary layer with a two-layer model. Fig. 3 illustrates the mesh configuration. The finite-volume solver Fluent 13.0 [39] is used to numerically simulate the flow field of an impinging jet ventilated room. The governing equations are solved with a segregated scheme and the pressure-velocity coupling is controlled by SIMPLE algorithm. The discretization schema with respect to the non-linear and pressure terms as well as the viscous terms are chosen as the second-order upwind and second-order central scheme. The simulation was declared converged when the two consecutive iterations for any local variable and the error of the overall mass unbalance were reduced less than the criteria of 10
04 and 0.03%, respectively. The simulations were performed on a computational node with two Intel Xeon 3.00 GHz processors, each with four cores. The total internal memory is 16 GB. 3. Experimental procedure The measurements were performed at the Laboratory of Ventilation and Air Quality at the Centre of Built Environment,

Fig. 3. Mesh configurations in the computational domain: (a) perspective view; (b) side view.

158

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

Fig. 4. (a) Measuring lines in the vertical middle plane; (b) corresponding positions in detail.

University of Gävle, Sweden. The test room was located in the main laboratory and with the approximate identical set-up as studied in CFD. To create better inlet boundary conditions for numerical simulation, an extra pipe 1.0 m long was used to connect the supply duct with the IJ device to deliver a more uniform flow. The supplied airflow rate was regulated to 0.020 m3/s and measured by orifice plate, with accuracy of 5%. The detailed flow field measurements were conducted at different locations within the center plane of the room, including the regions beneath the outlet and along the floor. The typical measuring lines are displayed in Fig. 4. A 3D traversing system was used to enable the complete point measurements by switching or moving the sensor along the desired direction. The velocity measurements were performed using a 5 mm platinumcoated tungsten sensor and a Dantec 56C01 anemometer system with a 56C17 bridge. It included a small thermistor positioned close to the anemometer probe but with the minimum effect on the measured air due to the heated wire. In order to avoid the error induced from the natural convection, the probe was operated at the working temperature of 120  C. The hot-wire was calibrated in the velocity range 0.2e2.5 m/s and the data were fit to a 4th order polynomial. Calibration was performed at two different temperatures thus allowing for temperature correction of the velocity data. The velocity was measured over 2 min with the sampling rate of 100 Hz. The accuracy for velocity measurement is estimated to 5%

or 0.03 m/s, whichever is greatest. During the measurement, the average room air temperature was around 20  C, and the temperature difference between the inlet and the room was controlled less than 1  C. In addition, to provide the accurate descriptions of the flow at the exit section for CFD study, the mean velocity, V, and turbulence intensity, Tu, profiles were captured by traversing the sensors through the region 4 mm beneath the supply exit section and covering the whole supply projected area. 4. Case studies In this paper, different cases concerning the model validation and a series of parametric studies are carried out; the detailed case specifications and the relevant CFD set-up are listed in Tables 1 and 2. 5. Results and discussion In this section, detailed comparisons regarding the numerical validation as well as the extensive results obtained from parametric study, in the case of an isothermal impinging jet flow in a room as illustrated in Fig. 2, are presented. First, the accuracy of the tested turbulence models are validated against two reference cases, i.e., accompanied experiment as well as Karimipanah and Awbi’s finding [3]; second, the results obtained from parametric studies

Table 1 Parameters used in different case studies. Case

Diffuser geometry

Discharge height (m)

Supply airflow rate (m3/s)

Confinement on side walls

Boundary conditions

Validation with measurement

Semi-elliptic

0.60

0.020

No

Profiles for Uin, k, and ε or u

Discharge height

Semi-elliptic

0.30 0.60 0.95

0.020

No

Uin ¼ 1.2 m/s Tu ¼ 10% dh ¼ 0.1265 m

0.60

0.020

No

Uin ¼ 1.2 m/s Tu ¼ 10% dhc

0.60

0.010 0.020 0.030

No

Uin ¼ 0.6, 1.2 and 1.8 m/s Tu ¼ 10% dh ¼ 0.1265 m

0.60

0.020

Diffuser geometry

a

Supply airflow rate

Confinement

a b c

Semi-elliptic square Rectangular 1 (ARb ¼ 2.5) Rectangular 2 (AR ¼ 10.0) Semi-elliptic

Semi-elliptic No Yes

Uin ¼ 1.2 m/s Tu ¼ 10% dh ¼ 0.1265 m

Diffuser geometry effect is based on the identical outlet area that the semi-elliptic pipe has, and all the diffusers are designed with the value of 0.0167 m2. AR represents the aspect ratio of width to height, denoted by a/b, as marked in Fig. 2. dh see Table 2.

H.J. Chen et al. / Building and Environment 49 (2012) 154e166 Table 2 Details of diffuser dimensions. Geometry

a (m)

b (m)

Hydraulic diameter dh (m)

Semi-elliptic Square Rectangular 1 Rectangular 2

0.2044 0.1291 0.2044 0.4088

0.1035 0.1291 0.0816 0.0408

0.1265 0.129 0.117 0.074

are presented to assess the effects of the different flow and configuration parameters on the flow behavior of the impinging jet, and particular attention is focused on the wall jet region developed after a certain distance from the impingement zone. 5.1. Numerical validation with measurement 5.1.1. Comparison of jet mean velocity distribution The jet velocity distributions calculated from RNG k
ε and SST k
u model are compared with experimental measurements in Figs. 5 and 6. The results are analyzed at various locations in the vertical middle plane, including the regions below the inlet and along the floor, as detailed in Fig. 4. The velocity profiles are presented in non-dimensional form, where the jet velocity is normalized by its local maximum velocity Vmax or Umax, and the location x or y is scaled by the hydraulic diameter dh of the pipe with the value of 0.1265 m. As shown in Fig. 5, the predicted jet profiles exhibit good consistency compared with experiential data in the region beneath the inlet, and over most compared regions, the predictions from the two tested turbulence models are quite similar. It is worth mentioning that at the height of y ¼ 0.065 m, the predicted velocity profiles present small velocity peaks near the inlet wall x ¼ 0, which is due to the influence of the recirculation flow caused by jet impingement on the floor, and the difference of the small peak is related to the size of the recirculation zone. However, due to the limitation of the measurement, the small velocity peak was not captured. Besides comparing the jet profiles below the inlet, analyzing the wall jet behavior along the floor is more substantial for validating the turbulence model. The comparisons are made at four downstream distances from the inlet wall and presented in terms of the mean velocity distribution, as shown in Fig. 6. At the location of

1.2

5.1.2. Comparisons of jet maximum velocity decay In order to further validate the reliability of numerical modeling, the dynamics of jet with regards to the maximum velocity decay in the regions below the exit and along the floor are investigated. Concerning the process as the jet approaches the floor, the predicted decaying trends from the two turbulence models are similar to the experimental findings, as presented in Fig. 7a in which the velocity profiles proceed from right (close to inlet) to left (near the floor). It can be seen that over most of the compared region the velocity decays slowly; this is because the jet is mainly affected by the turbulent shear stress. Within this region,

1.2

0.8

SST k-ω

0.6 0.4

RNG k-ε

0.8

SST k-ω

0.6 0.4 0.2

0.2

0

0 0

0.5

1.2

1 1.5 x/d h, y=0.545 m

0

2

V/Vmax

SST k-ω

0.6

2

RNG k-ε

0.8

SST k-ω

0.6

0.4

0.4

0.2

0.2

0

1 1.5 x/d h, y=0.225 m

Experiment

1

RNG k-ε

0.8

0.5

1.2

Experiment

1 V/Vmax

Experiment

1

RNG k- ε V/V max

V/Vmax

x ¼ 0.3 m, rather good agreement is noticed between the results from SST k
u model and measurement, while the RNG k
ε model does not seem to predict the velocity development in the same manner, i.e., the velocity is under-predicted in the lower part, but over-predicted at the higher region. Moving farther from the inlet wall, the predicted velocity profiles from both tested turbulence models appear to deviate from the experimental data, and larger discrepancy is observed at the location of x ¼ 0.7 m and 1.0 m. The presented deviations can be explained partly due to the overpredicted maximum velocity resulting in the lower velocity outside the inner region (where U ¼ Umax), and partly due to the instability of the flow causing the variation of the wall jet edge. The unstable feature of the flow over the floor has been analyzed in the study by Cehlin and Moshfegh [41], where they identified that the instability can cause the stream position to vary from time to time, and this time-dependent condition can not be captured by the steady-state numerical simulation. In addition, Cehlin and Moshfegh also emphasized that the accuracy of measurement should be taken into account when evaluating the accuracy of prediction results; large measurement uncertainty might be provoked in a region that has high turbulence intensity (>30%). In this study, high turbulence intensity is observed outside the inner region of the wall jet, which is due to the generated shear stress between wall jet and ambient air. Therefore, the errors from the simulation and measurement both contribute to the exhibited larger discrepancy. In general, the velocity predictions from both implemented turbulence models show good agreement compared with measurements, and better consistency is observed from the SST k
u model in the region close to the impingement zone.

Experiment

1

159

0 0

0.5

1 1.5 x/d h, y=0.125 m

2

0

0.5

1 1.5 x/d h, y=0.065 m

2

Fig. 5. Comparisons of non-dimensional velocity profiles at different locations below the inlet (see Fig. 4b), where dh ¼ 0.1265 m.

160

H.J. Chen et al. / Building and Environment 49 (2012) 154e166 0.8

0.8 Experiment

Experiment

0.7

0.6

RNG k- ε

0.6

RNG k-ε

0.5

SST k- ω

0.5

SST k- ω

y/d h

y/dh

0.7

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0 0

0.2

0.4

0.6

0.8

1

1.2

0

0.2

0.8

y/dh

0.6

RNG k-ε

0.5

SST k- ω

y/d h

Experiment

0.7

0.4 0.3 0.2 0.1 0 0

0. 2

0. 4

0. 6

0. 8

0.4

0.6

0.8

1

1.2

U/Umax , at x=0.5 m

U/Umax , at x=0.3 m

1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1. 2

Experiment RNG k- ε SST k- ω

0

0. 2

U/Umax , at x=0.7 m

0. 4

0. 6

0. 8

1

1. 2

U/Umax , at x=1.0 m

Fig. 6. Comparisons of non-dimensional velocity profiles at different locations along the centerline of the floor (see Fig. 4b), where dh ¼ 0.1265 m.

a

1.4

b

1

1

Umax /Uin

Vmax /Vin

1.2

0.8 0.6

Experiment

0.4

RNG k- ε

0.2

SST k- ω

Experiment

0.8

RNG k-ε

0.6

SST k-ω

0.4 0.2 0

0

0

1

2

3

4

5

y/dh

0

2

4

6

8

10

x/d h

Fig. 7. Comparisons of jet maximum velocity decay: (a): below the inlet; (b): along the centerline of the floor, where dh ¼ 0.1265 m.

the predictions from both turbulence models are quite close, but they are slightly over-predicted according to the experimental findings. Below the height of y/dh ¼ 1.54, jet begins to decelerate from the wall damping effect exerted by the floor, and the maximum velocities predicted by the RNG k
ε model show slightly closer agreement with measurement compared to that from the SST k
u model. After the jet impinges on the floor, the flow turns and follows the impinging surface. At a further downstream distance from the impingement point, the flow spreads parallel along the floor and decelerates in the form of a thin shear layer. Fig. 7b presents the comparisons between the simulation results and experimental data regarding the jet maximum velocity decay along the centerline of the floor. According to Fig. 7b, both of the tested turbulence models show good agreement with experimental data, despite the maximum velocity is slightly over-predicted for the farther region. Based on the above analyzed results concerning the accuracy of the numerical predictions for the velocity profiles and jet maximum velocity decay, it appears that both RNG k
ε and SST k
u model are capable of capturing the mean flow field of an isothermal impinging jet in a room satisfactorily, and the predictions from both tested turbulence models are quite similar. In this article, SST k
u model is used to perform the parametric study; the reason is partly due to the satisfactory performance as discussed in section 5.1, and partly due to the proved success from the literature reviews [25,28,32].

5.2. Numerical validation with the previous study In addition to the validation based on the current experimental study, the model is verified further with the previous study by Karimipanah and Awbi [3]. In their study, the air distribution of an isothermal wall impinging jet ventilated room was experimentally investigated, in which an outlet velocity of 1.60 m/s and supply height of 0.95 m were used. To compare with their experimental findings, the case based on the semi-elliptic pipe with the outlet velocity of 1.20 m/s and jet discharge height of 0.95 m was simulated by the SST k
u model. The predicted results are compared with those given by the formula reported in study [3] with regards to the jet maximum velocity decay and spreading rate along the centerline of the floor, as presented in Fig. 8. Considering the fact that the derived equations in their study are based on the measured pffiffiffi locations from x= Az 4 to 10, the comparison results are mainly focused on that range. As shown, the SST k
u model reproduces the jet behavior quite well; the predictions of the maximum velocity decay and the jet spreading rate show a goodpconsistency ffiffiffi according to their findings within the range of 4 < x= A < 10. 5.3. Numerical parametric study In this section, the effects from the jet discharge height, diffuser geometry, supply airflow rate and the confinement from the surrounding environment on the generated airflow pattern are presented, and the results are analyzed with respect to the non-

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

a

161

b

Fig. 8. Comparisons with Karimipanah and Awbi’s study [3] at the discharge height of 0.95 m: (a) jet maximum velocity decay; (b) jet spreading rate along the centerline of the floor, where ¼ 0.129.

dimensional velocity distribution, maximum velocity decay and the jet spreading rate along the centerline of the floor. 5.3.1. Effect from the jet discharge height In order to explore the impact of the jet discharge height on the resulting airflow distribution, three discharge heights of 0.30, 0.60 and 0.95 m are studied. First, the effect on the similarity of the velocity profiles along the centerline of the floor is examined by plotting U/Umax against y/y0.5. No appreciable influence is observed, for which reason attention is focused on the impact on the development of velocity distribution. As noted in Fig. 9, the smaller jet discharge height leads to greater velocity and thinner shape close to the diffuser, i.e., at x ¼ 0.4 and 0.7 m, which is attributed to the reduced air entrainment and less jet diffusion resulting in the more conserved momentum before jet strikes on the floor. However, the differences in terms of the magnitude of the velocity and the shape of the velocity profiles are diminished when moving farther from the inlet wall, and all the profiles coincide at the end of the compared region, i.e., x ¼ 2.0 m. As stated above, jet issued at a lower level has the potential to conserve more momentum and therefore contributes to the higher velocity within the inner region when the jet is spreading over the floor. This finding is confirmed by the presented maximum velocities at different downstream distance from the inlet wall, as shown

0.07

in Fig. 10a. It is also found that in the region close to the inlet wall jet discharged at a lower level tends to decay faster compared to that from higher levels, but as jet penetrates into the room all the decaying tendencies appear similar. Besides, it is noticed that at a sufficient distance from the inlet wall, i.e., at the location of x/ dh z 12, the maximum velocities decay linearly with the downstream distances in the three studied cases. However, the effect of jet discharge height on jet width growing is hardly detected; all the jets spread at a similar rate along the centerline of the floor, as presented in Fig. 10b. 5.3.2. Effect from the diffuser geometry To investigate the effect from the diffuser geometry on the generated flow pattern, four types of diffusers are studied, i.e., semi-elliptic, square, rectangular 1 (AR ¼ 2.5) and rectangular 2 (AR ¼ 10.0); for details see Tables 1 and 2. All the diffusers are designed based on the identical outlet area 0.0167 m2 and with different dh. First, the velocity distributions of wall jets produced from different types of diffusers are presented in Fig. 11. As shown, the velocity profiles from the semi-elliptic and square diffusers are relatively close to those from the rectangular ones. As the diffuser aspect ratio increases from 1 (square) to 10 (rectangular), the magnitude and shape of the velocity profile tend to become larger

0.07

h=0.30m h=0.60m h=0.95m

0.04

0.03

0.02

0.02

0.01

0.01 0 0

0 0.2

0.4 0.6 0.8 U/Uin, at x=0.4 m

0.07

1

1.2

0.2

0.4 0.6 0.8 U/Uin, at x=0.7 m

0.07

h=0.30m

0.06

1

1.2

h=0.30m

0.06 h=0.60m

0.05

y/H

0.03

0.02

0.02

0.01

0.01 0.4

0.6

0.8

U/Uin, at x=1.0 m

1

1.2

h=0.95m

0.04

0.03

0.2

h=0.60m

0.05

h=0.95m

0.04

0 0

h=0.95m

0.04

0.03

0

h=0.60m

0.05

y/H

y/H

0.05

y/H

h=0.30m

0.06

0.06

0

0

0.2

0.4

0.6

0.8

1

1.2

U/Uin, at x=2.0 m

Fig. 9. The effect of the jet discharge height on velocity development along the centerline of the floor, where H ¼ 3.0 m, Uin ¼ 1.2 m/s.

162

H.J. Chen et al. / Building and Environment 49 (2012) 154e166 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

b

h=0.30m

2

h=0.60m

1.5

h=0.95m

y 0.5/d h

Uamx /Uin

a

1 h=0.30m 0.5

h=0.60m h=0.95m

0 0

5

10

15

20

0

25

5

10

15

20

25

x/d h

x/d h

Fig. 10. The effects of jet discharge height on (a) maximum velocity decay and (b) jet spreading rate along the centerline of the floor, where dh ¼ 0.1265 m.

0.07

0.05

Semi-elliptic Square Rectangular AR=2.5 Rectangular AR=10

0.06 0.05

0.04

y/H

y/H

0.07

Semi-elliptic Square Rectangular AR=2.5 Rectangular AR=10

0.06

0.03

0.04 0.03

0.02

0.02

0.01

0.01 0

0

0

0.2

0.4

0.6

0.8

0

1

0.2

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0.05

0.04 0.03

0.03 0.02

0.01

0.01

0

0.2

0.4 0.6 U/Uin, at x=1.0 m

1

0.04

0.02

0

0.8

Semi-elliptic Square Rectangular AR=2.5 Rectangular AR=10

0.06

y/H

y/H

0.05

0.6

0.07

Semi-elliptic Square Rectangular AR=2.5 Rectangular AR=10

0.06

0.4

U/Uin, at x=0.7 m

U/Uin, at x=0.4 m

0.8

0

1

0

0.2

0.4 0.6 U/Uin, at x=2.0 m

0.8

1

Fig. 11. The effect of diffuser geometry on the velocity developments along the centerline of the floor, H ¼ 3 m, Uin ¼ 1.2 m/s.

and thicker, as depicted in Fig. 11. The comparative study reveals that the momentum in the axial direction x is influenced to a great extent by the diffuser shape and aspect ratio. Second, the influence of the diffuser geometry on the variations of jet maximum velocity decay and spreading rate with the axial distance x are presented in Fig. 12, in which x is scaled by its own dh, and the compared positions correspond to the locations of x ¼ 0.4, 0.5 through 1.0 (in increments of 0.1), and continuing with x ¼ 1.2, 1.5, 2, 2.5 and 3 m. For each diffuser type the fully developed region is identified, which is based on the definition of the fully developed region where the centerline velocity decreases inversely with the distance from the supply opening [6], i.e., Umax fx
1 . In Fig. 12a, the

a 0.9

Square

0.7

Rectangular AR=2.5

0.6

Rectangular AR=10.0

2

0.5 0.4

1.5 1

0.3 0.2

Semi-elliptic Square Rectangular AR=2.5 Rectangular AR=10.0

0.5

0.1 0 0

3 2.5

y 0.5/d h

Umax /Uin

b

Semi-elliptic

0.8

whole compared region is identified as the fully developed region for the semi-elliptic, square and rectangular 1 (AR ¼ 2.5) diffusers, and the presented maximum velocity decay rates are fairly similar. For the rectangular 2 (AR ¼ 10.0) diffuser, the fully developed flow state appears late, beginning approximately at the location of x/ dh ¼ 20. Therefore the jet from the rectangular diffuser with AR ¼ 10.0 decays lower compared to others in the beginning, while within the fully developed region all the jets decay at a similar rate. Concerning the jet growth rate along the floor, the spreading rate y0.5/x from the rectangular diffuser with AR ¼ 10.0 is found to have a relatively small value compared to others due to its non-fully developed flow property, as shown in Fig. 12b.

10

20

30

x/d h

40

50

0 0

10

20

30

40

50

x/d h

Fig. 12. The effects of diffuser geometry on (a) maximum velocity decay and (b) jet spreading rate along the centerline of the floor, the values of dh see Table 2.

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

In the preceding paragraphs the effects from the diffuser geometry have been presented by the plotted velocity distribution, maximum velocity decay and jet spreading rate in the direction normal to the floor, whereas the growth feature of jet in the transverse direction was not analyzed. The velocity contour plots with the iso-surface of 0.25 m/s for the four investigated diffuser geometries are shown in Fig. 13. As illustrated, the generated airflow pattern is strongly dependent on the diffuser geometry and aspect ratio. According to Fig. 13, in the region close to the inlet wall, the semi-elliptic diffuser tends to distribute air in a radial direction, while the square diffuser appears to spread the jet approximately equally in the longitudinal and lateral directions. The wall jets developed from both rectangular diffusers have a stronger tendency to distribute air longitudinally, especially for the one with larger aspect ratio. Based on the indicated jet spreading mechanisms from different diffusers we might conclude that jet is more directed along the longitudinal direction when the lateral movement is weak, as a result of the mass conservation. Therefore, the greater conserved momentum, particularly at the initial development of the jet, could contribute the greater velocity along the floor and the longer penetrated distance into the room. It is clear from Figs. 11e13 that the diffuser configuration plays a significant role in determining the flow pattern over the floor. When designing HVAC systems to achieve efficient air distribution while maintaining energy conservation, the configuration of the diffuser should be chosen based on each applied ventilated environment, i.e., for office ventilation, the diffusers with the semielliptic shape and the rectangular one with the comparable aspect ratio are appropriate for delivering fresh air both in the longitudinal and lateral direction, while for industrial premises,

163

a rectangular nozzle with a larger aspect ratio (e.g., AR ¼ 10) can be more suitable for enabling the air to penetrate longer distance. 5.3.3. Effect from the supply airflow rate The wall jet behavior is investigated further with respect to the supply airflow rate, in which the cases of jet issued from the semielliptic nozzle and discharged at a height of 0.6 m with the three supply airflow rate, i.e., 10 l/s, 20 l/s and 30 l/s are considered, see Table 1. Fig. 14 presents the velocity distributions from the three studied airflow rates. In the region close to the inlet wall, all the velocity profiles exhibit the same character, and at the farther downstream locations, i.e., x ¼ 1 and x ¼ 2 m, a slight difference of the velocity profile appears within the inner region, i.e., the lower velocity is presented from the smaller airflow rate at the same compared position. This is due to the fact that the higher supply airflow rate provides more momentum, therefore larger velocity is observed as jet spreading into the middle of the room. The impacts of the supply airflow rate on the trends of maximum velocity decay and jet growth rate along centerline of the floor are depicted in Fig. 15. Note that the flow behavior is nearly independent of the investigated supply airflow rates within the moderate range, except that some marginal difference is observed. 5.3.4. Effects from the confinement of the room In the field of indoor environment, the application of jet is mainly encountered within an enclosed space. Because the present study is carried out in a semi-confined room, it is essential to assess the effect of room confinement on the characteristics of the airflow field. The condition of the closed room is achieved by changing the CFD boundary settings from the pressure outlets on both side walls

Fig. 13. Contour plots of iso-velocity with 0.25 m/s for four studied diffuser geometries: (a) semi-elliptic; (b) square; (c) rectangular with AR ¼ 2.5; (d) rectangular with AR ¼ 10.0.

164

H.J. Chen et al. / Building and Environment 49 (2012) 154e166 0.07

0.07 10 l/s

0.06

0.04

20 l/s

0.05

30 l/s

y/H

Y/H

0.05

10 l/s

0.06

20 l/s

30 l/s

0.04

0.03

0.03

0.02

0.02

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0.01 0

0 0

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0

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U/Uin, at x=0.4 m 0.07

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1

0.07 10 l/s

0.06

20 l/s

0.05

y/H

30 l/s

0.04

10 l/s

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20 l/s

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y/H

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U/Uin, at x=0.7m

30 l/s

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1

0

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U/Uin, at x=1.0 m

0.4

0.6

0.8

1

U/Uin, at x=2.0 m

Fig. 14. The effect of supply airflow rate on the velocity developments along the centerline of the room, where H ¼ 3 m, Uin ¼ 0.6, 1.2 and 1.8 m/s corresponding to the supply airflow rate of 10, 20 and 30 l/s.

a 0.8

10 l/s

b 1.8

0.6

20 l/s

1.4

0.5

30 l/s

1.6 1.2

y 0.5/d h

Umax /Uin

0.7

0.4 0.3

1 0.8 10 l/s

0.6

0.2

0.4

0.1

0.2

0 0

5

10

15

20

0

25

20 l/s 30 l/s

0

5

10

y/d h

15

20

25

x/d h

Fig. 15. The effect of supply airflow rate on (a) maximum velocity decay and (b) jet spreading rate along the centerline of the floor, where dh ¼ 0.1265 m.

0.07

0.07 Semi-conf ined

0.06

0.05

Conf ined

0.04

Conf ined

0.04

0.03

0.03

0.02

0.02

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0.06

y/H

y/H

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1

0

0.2

U/Uin, at x=0.4 m 0.07

0.6

0.8

1

0.07 Semi-conf ined

0.06 0.05

Semi-conf ined

0.06 0.05

Conf ined

0.04

y/H

y/H

0.4

U/Uin, at x=0.7 m

0.03

0.03

0.02

0.02

0.01

0.01

0

Conf ined

0.04

0 0

0.2

0.4

0.6

U/Uin, at x=1.0 m

0.8

1

0

0.2

0.4

0.6

0.8

1

U/Uin, at x=2.0 m

Fig. 16. The effect of confinement on the velocity development along the centerline of the floor, where H ¼ 3 m, Uin ¼ 1.2 m/s.

H.J. Chen et al. / Building and Environment 49 (2012) 154e166

a 0.8

b 1.8 1.6

Semi-conf ined

0.7

1.4 1.2

Conf ined

0.5

y 0.5/d h

Umax /Uin

0.6 0.4 0.3

1 0.8 0.6

0.2

0.4

0.1

0.2

0

0

0

165

5

10

15

20

25

0

Semi-conf ined

Conf ined

5

x/d h

10

15

20

25

x/d h

Fig. 17. The effects of confinement on (a) maximum velocity decay and (b) jet spreading rate along the centerline of the floor, where dh ¼ 0.1265 m.

Fig. 18. Contour plots of iso-velocity with 0.10 m/s under two room configurations: (a) semi-confined room; (b) confined room.

to the solid walls, and the calculated flow field is compared with the one under the situation of the semi-confined room. Both cases are based on the discharge height 0.6 m and from the semi-elliptic diffuser with the airflow rate of 20 l/s. The comparisons of velocity profiles at four downstream stations under semi- and fully confined spaces are presented in Fig. 16. A slight difference appears at the location far from the inlet wall, i.e., at x ¼ 2.0 m the velocity under the semi-confined situation is greater than that in the confined case for the outer region of the wall jet. However, the confinement effect is hardly detected for the maximum velocity decay, as shown in Fig. 17a, while the impact becomes clear for the jet spreading rate at the farther region, i.e., x/ dh z 20 and 25, the vertical spreading rate from the semi-confined room is greater than from the confined room, as indicated in Fig. 17b. To explain the difference resulting from the confinement effect on the velocity characteristic, the contour plots of iso-surface of 0.10, 0.15 and 0.25 m/s are analyzed. Fig. 18b illustrates the general airflow pattern with the iso-velocity of 0.1 m/s under the confined room, i.e., the air distribution toward the x-axial direction is relatively flat, which is due to the fact that jet can not penetrate the side wall. As a result the remaining momentum forces the jet to stretch and move along the z-axial direction. However, the air distribution in an unconfined room along the x-axial direction is somewhat stronger than that in z-axial direction, as indicated in Fig. 18a. Therefore, the lower velocity and the smaller spreading rate in the direction normal to the floor from the confined case is observed, which is a consequence of the enhanced jet spreading in the z-axial direction compared to the semi-confined case. Due to the observed nearly identical flow patterns for the iso-velocities of 0.15 and 0.25 m/s, the contour plots are not presented here. It is worth mentioning that the confinement effect mainly influences the

farther region from the inlet wall, where the flow field is dominated by the small velocity, i.e., U ¼ 0.1 m/s.

6. Conclusion In the present study, the flow behavior of an isothermal impinging jet in a room has been investigated. First, the validation of the two implemented turbulence models of RNG k
ε and SST k
u model is performed, and the results indicate that both of the tested turbulence models are capable of capturing the main flow feature satisfactorily according to the experimental findings. However, it is worth to mention that the predictions from the RNG k
ε model predicts slightly better of the maximum velocity decay as jet approaching the floor, while the SST k
u model accords slightly better in the region close to the impingement zone which is crucial for spreading of the jet inside the room. Second, a number of parametric studies are carried out with the validated model (SST k
u), and different aspects of the jet discharge height, diffuser geometry, supply airflow rate and the confinement from the room are studied. By analyzing the jet nondimensional velocity distribution, maximum velocity decay and spreading rate along the floor, it has been observed that all the investigated parameters have certain effects on the generated flow pattern, in which the diffuser geometry is found to have the most appreciable impact, and the supply airflow rate is identified to have marginal influence under the investigated moderate flow range. On the whole, the current study is a step toward a better understanding of the characteristics of turbulent impinging jet flow in a ventilated room, and the acquired knowledge will contribute to future work on ventilation system design and optimization.

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Acknowledgment The authors greatly acknowledge the financial support from KK Foundation, Formas, Fresh Air AB, Ny Kraft Sverige AB, University of Gävle and Linköping University. The authors sincerely thank Mr. Hans Lundström for his technical assistance on measurements at the University of Gävle, Gävle, Sweden.

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