response surface models for cfd predictions of air diffusion performance index in a displacement...

Fp

ga

r, Lo

r D

. 7,

olog

d fo

me

Energy and Buildings xxx (200

+ Models

ENB-2319; No of Pages 8Performance Index (ADPI) in a displacement-ventilated office is presented. By adopting the technique of Computational Fluid Dynamics (CFD),

the new ADPI models developed are used to investigate the effect of simultaneous variation of three design variables in a displacement ventilation

case, i.e. location of the displacement diffuser (Ldd), supply temperature (T) and exhaust position (Lex) on the comfort parameter ADPI. The RSM

analyses are carried out with the aid of a statistical software package MINITAB. In the current study, the separate effect of individual design

variable as well as the second-order interactions between these variables, are investigated. Based on the variance analyses of both the first- and

second-order RSM models, the most influential design variable is the supply temperature. In addition, it is found that the interactions of supply

temperature with other design variables are insignificant, as deduced from the second-order RSM model. The optimised ADPI value is

subsequently obtained from the model equations.

# 2007 Elsevier B.V. All rights reserved.

Keywords: Response Surface Methodology (RSM); Computational Fluid Dynamics (CFD); Air Diffusion Performance Index (ADPI); Thermal comfort; Air

ventilation

1. Introduction

The cooling of occupied spaces, which is generally

accomplished by mechanical ventilation, consumes a huge

amount of non-renewable fossil energy in the world that leads

to the pollution of atmospheric environment. Therefore, in

order to minimise the energy usage while enabling good

thermal comfort condition to be achieved, effective distribution

of fresh air within an occupied space is of practical importance.

For a long time, the heating, ventilating and air conditioning

(HVAC) engineers and researchers have been realising that in

order to optimise the comfort condition in an occupied space,

efficient quantitative models that establish the relationship

between a large group of independent parameters (design

variables) and output variable (response) are highly desirable.

This can be accomplished by both the experimental and

numerical approaches.

In order to study the relationship between the response and

independent design variables, a large number of experiments

are undoubtedly required. This has reflected on the increased

total cost of the study, which is particularly true in the case of

employing physical experimentations. Therefore, numerical

experiments such as those accomplished by CFD have been

gaining immense popularity within the HVAC industry since

the past few decades. Despite the fact that it is not totally free

from errors, it serves as a practical design tool for building

engineers nowadays. For example, by using pure numerical

approach, Haghighat et al. [1] have investigated the relationship

between the concentration level in a partitioned room and

various positions of door, supply and exhaust. Lee and Awbi [2]

have studied the effect of partition on ventilation effectiveness

due to its location and gap underneath. Lim et al. [3] have

determined the optimum position of an air-conditioned unit for

achieving good thermal comfort condition (based on the

* Corresponding author. Tel.: +60 389286227; fax: +60 389212116.

E-mail addresses: [email protected] (K.C. Ng),

[email protected] (K. Kadirgama), [email protected] (E.Y.K. Ng).1 Tel.: +60 389287255, fax: +60 389212116.2 Tel.: +65 67904455, fax: +65 67911859.

0378-7788/$ see front matter # 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.enbuild.2007.04.024Response surface models for C

performance index in a dis

K.C. Ng a,*, K. Kadira Department of Research & Applications, O.Y.L. R&D Cente

Sungai Buloh, Selangob Department of Mechanical Engineering, Universiti Tenaga Nasional, Km

c School of Mechanical and Aerospace Engineering, Nanyang Techn

Received 29 January 2007; received in revise

Abstract

Based on the Response Surface Methodology (RSM), the developPlease cite this article in press as: K.C. Ng et al., Response surface m

displacement ventilated office, Energy & Buildings (2007), doi:10.1016D predictions of air diffusion

lacement ventilated office

ma b,1, E.Y.K. Ng c,2

t 4739, Jalan BRP 8/2, Taman Bukit Rahman Putra, 47000,

arul Ehsan, Malaysia

Jalan Kajang-Puchong, 43009 Kajang, Selangor Darul Ehsan, Malaysia

ical University, 50 Nanyang Avenue, Singapore 639798, Singapore

rm 22 March 2007; accepted 13 April 2007

nt of first- and second-order models for predicting the Air Diffusion

www.elsevier.com/locate/enbuild

7) xxxxxxodels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

Predicted Mean Vote) in a typical studio-type apartment. Very

recently, by employing the commercial CFD code (FLUENT),

Ooi et al. [4] have studied the temperature and velocity

distributions in an air-conditioned room for various positions of

the air conditioner blower. Based on the results of three blower

positions simulated, the best position is then selected for

maximum comfort of an occupant. In addition, some

recommendations have been given by Bojic et al. [5], based

on the pure CFD analyses (FLOVENT), the optimum

placement of a window-type air conditioner in a residential

bedroom in order to achieve minimum draft subjected to the

calculation of Air Diffusion Performance Index (ADPI). It can

be noted in general, however, most of the numerical studies

focus on the one-factor-at-a-time design, without having any

idea on the behaviour of response variable when two or more

design variables are varied at the same time. The current paper

intends to consider this particular issue that involves making

design decision based on several design variables, which is

practically desirable.

In order to demonstrate the method, the authors have

considered the effect of simultaneous variations of three design

variables in a displacement-ventilated office (refer to Fig. 1),

i.e. location of the displacement diffuser (Ldd), supply

temperature (T) and exhaust position (Lex) on the behaviour

of response variable (ADPI). The case considered here is taken

from He et al. [6], in which detailed numerical and

experimental studies have been performed to investigate the

efficiency of contaminant removal for several ventilation

systems. Here, the CFD model developed is firstly validated

with the experimental data provided by He et al. [6], prior to

ion

be

K.C. Ng et al. / Energy and Buildings xxx (2007) xxxxxx2

+ Models

ENB-2319; No of Pages 8Fig. 1. Configuration of the mockup office equipped with a displacement ventilat

4A. Exact dimensions and locations of the obstacles and measurement points canorigin O, (a) isometric view and (b) top view.

Please cite this article in press as: K.C. Ng et al., Response surface m

displacement ventilated office, Energy & Buildings (2007), doi:10.1016system investigated by He et al. [6]. The measurement points are 1A, 2A, 3A and

found in He et al. [6]. The design variables (Ldd and Lex) are measured from theodels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

Bui

+ Models

ENB-2319; No of Pages 8running the response surface analyses. It has been recently

noted by Abou-El-Hossein et al. [7] that RSM is one of the

statistical techniques that saves cost and time in conducting

experiments by reducing the total number of required tests.

Furthermore, RSM helps to identify, with great accuracy, the

effect of the interactions of different design variables on the

response when they are varied simultaneously. In spite of this,

within the community of building engineering, only a few

research works based on RSM are reported, such as those by

Klemm et al. [8] for multicriteria optimisation and Valencia

et al. [9] for model development to predict asphalt pavement

properties.

In this study, based on RSM, the first- and second-order

models for the comfort parameter ADPI are developed for a

displacement ventilation case illustrated in Fig. 1. Based on the

received RSM models from the CFD simulation, the most

influential design variable is determined and the corresponding

interactions between the design variables are subsequently

identified. Also, based on the model equations obtained, one

can easily identify the optimum design combination to achieve

good thermal comfort condition based on the ADPI value,

which is frequently used as a reference value for indoor airflow

studies [10].

2. Introduction to response surface methodology

Response Surface Methodology (RSM) is a collection of

mathematical and statistical techniques for empirical model

building. By careful design of experiments, the objective is to

optimise a response variable (output variable), which is

influenced by several independent design variables (input

variables). An experiment is a series of tests, called runs, in

which changes are made in the input variables in order to

identify the reasons for changes in the output response.

Originally, RSM has been developed to model experimental

responses and then migrated into the modelling of numerical

experiments. The difference is in the type of error generated by

the response. In physical experiments, inaccuracy can be due to

measurement errors whereas in numerical experiments, errors

may due to incomplete convergence of the iterative process,

round-off errors and the discrete representation of continuous

physical phenomena. In RSM, the errors are assumed to be

random.

RSM is a methodology of constructing approximations of

the system behavior using results of the response analyses

calculated at a series of points in the design variable space.

Optimisation of RSM can be solved in the following three

stages:

Design of experiment. Building the response surface model. Solution of minimization/maximisation problem accordingto the criterion selected.

The concept of a response surface involves a dependent

variable y called the response variable and several independent

K.C. Ng et al. / Energy anddesign variables x1, x2, . . ., xk. If all of these variables are


displacement ventilated office, Energy & Buildings (2007), doi:10.1016assumed to be measurable, the response surface can be

expressed mathematically as:

y f x1; x2; . . . ; xk (1)For practical design purpose, the goal is to optimise the

response variable y, subjected to certain combination of design

variables. In what next, the ADPI model in the form of Eq. (1)

will be expressed.

3. Model of air diffusion performance index

Draft is a frequent concern when designing indoor

environments [11]. In order to account for the presence of

draft, which is defined as any localised feeling of coolness or

warmth of any position of the body due to both air movement

and air temperature, the ADPI parameter is used in the current

study. ADPI presents the percentage of locations where values

are taken that meet specifications for effective draft temperature

(1.7 K < u< 1.1 K) and air speed (WS < 0.35 m/s). If ADPIreaches its maximum value, i.e. 100%, the most desirable

condition is thereby achieved [5]. The effective draft

temperature is expressed as:

u Tx Tc aWS b (2)where Tx is the local dry bulb temperature for air (8C), Tc theaveraged room dry bulb temperature (8C) and WS is the airspeed (m/s). The constants a and b are taken as 8 K s/m and

0.15 m/s, respectively.

With reference to RSM, where the response variable is ADPI

in the current study, the relationship between the investigated

three design variables and the response variable can be

represented by the linear Eq. (3):

y1 b0x0 b1x1 b2x2 b3x3 (3)Here, y(1) is the first-order prediction model for ADPI and b is

the model parameter. x0 is dummy variable (x0 = 1) and b0 is anarbitrary constant. The design variables such as x1, x2 and x3 are

the location of the displacement diffuser (Ldd), supply tem-

perature (T) and exhaust position (Lex), respectively.

In most of the practical cases, the response surface

demonstrates some curvature effects in most ranges of the

design variables. Therefore, it would be more useful for a

designer to consider the second-order model. The practical

importance of second-order model is to help one to understand

the second-order effect of each design variable separately and

the two-way interaction amongst these design variables. This

second-order model y(2) can be represented by Eq. (4), in

general, for three design variables:

y2 b0x0 b1x1 b2x2 b3x3 b11x21 b22x22 b33x23 b12x1x2 b13x1x3 b23x2x3 (4)

Here the two indices (subscripts) of variable b represent the

interaction between the corresponding variables. For example,

b12 represents the significance of interaction between design

ldings xxx (2007) xxxxxx 3variable 1 and 2.

odels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

4. Research methodology

4.1. CFD simulation

The ADPI models, as discussed in the previous section, are

determined numerically in the current work. The CFD package

used has been constantly verified with the available experi-

mental measurement and reference solution (see [12,13]). Here,

prior to performing the sensitivity study based on RSM, the

flow model is validated with the experimental data given by He

et al. [6]. The ADPI values for various design combinations

(obtained from the BoxBehnken method to be discussed later)

are then determined by the validated CFD model.

The flow solver is based on the finite-volume formulation

on structured meshes using the cell-centered approach. It uses

a non-staggered variable storage technique, which is more

robust as compared to the traditional staggered arrangement

[14]. Therefore, in order to avoid the pressure oscillations

steady when the percentage difference of the successive

change between the variables at current and previous time

steps is less than 0.01%.

The configuration of the displacement ventilation flow case

has been illustrated in Fig. 1. The design variables in this

particular design combination (based on that of [6]) are:

Ldd = 1.5550 m, T = 15.9 8C and Lex = 2.33 m. Figs. 2 and 3compare the predicted speed and temperature profiles with the

available experimental data at four locations (see 1A, 2A, 3A

and 4A in Fig. 1). In general, the predicted speed and

temperature variations match the measurements and, by

considering the coarseness of the mesh system employed

(30 25 16), the agreements can be considered satisfacto-rily. The discrepancies between the predicted and measured

speed profiles may due to, partly, the low speed values

associated in most of the space in which the hot-sphere

anemometers may fail to give accurate results [6]. For the

temperature profiles, all the predictions follow the similar

in a


+ Models

ENB-2319; No of Pages 8arisen due to the non-staggered arrangement, the pressure

interpolation technique similar to the one proposed by Rhie

and Chow [15] is adopted here. The issue of pressurevelocity

decoupling associated with the current incompressible flow

equations is resolved via the SIMPLE algorithm of Patankar

[16]; more recent details of SIMPLE algorithm can be found

in Jasak [17]. The Bi-Conjugate Gradient (Bi-CGSTAB)

method proposed by Van der Vorst [18] has been used to solve

the sparse matrix system arisen from the discretised flow

equations. In the current study, the first-order upwind

differencing scheme for convective discretisation is adopted

for robustness purpose. This is acceptable in the current

context due to the fact that trend analysis deduced from the

simulation results of various designs is more important here.

In order to model the flow turbulence, the RNG ke equationsare adopted. Buoyancy is modelled via the Boussinesq

approximation. In order to promote numerical stability of the

buoyant flow simulation, a transient approach has been used

with a time step size of 0.1 s. The results are assumed to be

Fig. 2. Comparison of speed profiles on mesh 30 25 16 at four locations

prediction.


displacement ventilated office, Energy & Buildings (2007), doi:10.1016trends of those measured. Here, the predicted and measured

temperature profiles have shown clear stratification associated

with the displacement ventilation system.

4.2. Experimental design for RSM

With the validation of the current CFD model, the ADPI

models, i.e. Eqs. (3) and (4), are now readily to be determined.

The model parameter b is calculated from the least square

method, in which the calculation is performed by adopting the

commercial statistical software, MINITAB. In order to reduce

the total number of numerical tests and allow simultaneous

variation of the three independent design variables, the

numerical procedure has to be well designed.

In the current study, the BoxBehnken design method,

which is based on the combination of the factorial with

incomplete block design, has been adopted. The attractive part

of this method is that it does not require a large number of tests

as it considers only three levels (lowest 1, middle 0 and

displacement ventilated room. H = 2.26 m. ^: Experiment [6], : currentodels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

ns i

erim

K.C. Ng et al. / Energy and Buildings xxx (2007) xxxxxx 5

+ Models

ENB-2319; No of Pages 8Fig. 3. Comparison of temperature profiles on mesh 30 26 16 at four locatiosupply temperature (15.9 8C), Te is the exhaust temperature (24.8 8C). ^: Exp

Table 1

Levels of design variables

Design variable Coding of levels

1 (lowest) 0 (middle) 1 (highest)Location of the displacement 0.700 1.905 3.110highest 1) of each design variable. The maximum and

minimum levels (constraints) of each design variable are

normally determined based on the recommendations given by

the manufacturer as well as users preferences. The levels of the

three design variables are given in Table 1. The BoxBehnken

design is normally used for non-sequential experimentation,

where a test is conducted only once, which in turn allows

efficient evaluation of the model parameters in the first- and

diffuser, Ldd [m]

Supply temperature, T [8C] 13 16 19Exhaust position, Lex [m] 0.00 2.36 4.72

Table 2

CFD simulation conditions according to BoxBehnken design and the predicted A

Test number Location of the displacement

diffuser, Ldd [m]

Supply temperature,

T [8C]

1 3.110 16

2 3.110 16

3 1.905 13

4 0.700 19

5 1.905 19

6 1.905 13

7 3.110 13

8 0.700 16

9 3.110 19

10 0.700 16

11 0.700 13

12 1.905 16

13 1.905 16

14 1.905 16

15 1.905 19


displacement ventilated office, Energy & Buildings (2007), doi:10.1016second-order models. By using MINITAB, the simulation

conditions of 15 tests are generated, as shown in Table 2. Based

on these testing conditions, the comfort parameter (response

variable), ADPI is then computed from the in-house CFD

package as described earlier. The CFD-predicted ADPI values

are plotted in Fig. 4 for different test numbers, on top of those

predictions based on RSM, which will be discussed in the next

section.

5. Results and discussions

5.1. Development of first-order ADPI model

After performing the 15 numerical tests using CFD, the

ADPI simulated is used to find the model parameters appearing

in the postulated first-order model (see Eq. (3)). In order to

n a displacement ventilated room. H = 2.26 m. T* = (T Ts)/(Te Ts). Ts is theent [6], : current prediction.perform the calculation of these parameters, the least square

method is used with the aid of MINITAB. The first-order linear

DPI models based on CFD and RSM

Exhaust position,

Lex [m]

ADPI (%)

CFD 1st-order RSM 2nd-order RSM

4.720 36.23 34.27 35.42

0.000 35.70 33.72 35.14

4.720 22.87 24.99 23.33

2.360 40.96 43.13 40.62

4.720 42.21 43.45 42.00

0.000 22.77 24.44 22.99

2.360 21.92 24.76 22.26

4.720 35.02 34.17 35.58

2.360 42.59 43.23 43.62

0.000 33.97 33.62 34.78

2.360 26.08 24.66 25.06

2.360 35.04 33.95 35.71

2.360 35.04 33.95 35.71

2.360 35.04 33.95 35.71

0.000 41.72 42.90 41.25


/j.enbuild.2007.04.024

locations of the displacement diffuser (Ldd) and the exhaust

(Lex) do not contribute much to the variation of the ADPI. In

general, the increase of all the design variables will cause

the ADPI to become larger, which is desirable from the

design point of view. Chung and Lee [10] have performed a

similar trend analysis on ADPI based on different values of

inlet air temperature. It is worth to mention here that, as

illustrated in Fig. 5, the current predicted model agree


+ Models

ENB-2319; No of Pages 8Fig. 4. Comparison of ADPI models against CFD predictions.model for predicting the ADPI can be expressed as:

ADPI1 15:6377 0:0241Ldd 3:0770T 0:1153Lex(5)

From this linear expression, by examining the values of

the coefficients, one can easily deduce that the response

variable ADPI is significantly affected by the supply

temperature (T). Also, it is interesting to note that the

Fig. 5. Comparison of ADPI model based on supply temperatures. For RSM,

Ldd is 3.11 m and Lex is 4.72 m.

Table 3

Analysis of variance (ANOVA) for first-order equation (from MINITAB)

Source of variation Degree of freedom (d.f.) Sum of sq

Regression 3 682.312

Linear 3 682.312

Residual error 11 45.991

Lack-of-fit 9 43.324

Pure error 2 2.667

Total 14 728.303


displacement ventilated office, Energy & Buildings (2007), doi:10.1016qualitatively well with that of Chung and Lee [10], in which

the ADPI values increase as the supply temperature

increases.

As seen from Fig. 4, the predicted ADPI values obtained

from the first-order model agree well with the CFD values. The

adequacy of the first-order model is verified by using the

analysis of variance (ANOVA). At a level of confidence of 95%,

the model is checked for its adequacy. As shown in Table 3, the

P-value of 0.236 (> 0.05) is not significant with the lack-of fitand F-ratio is 3.61. This implies that the model can fit and it is

adequate [19].

5.2. Development of second-order ADPI model

Here, the second-order model is formulated to describe the

effect of the three design variables investigated on the ADPI,

given by MINITAB:

ADPI2 82:2641 6:2873Ldd 12:3392T 0:3862Lex 0:0074L2dd 0:3143T2 0:0875L2ex 0:4004LddT 0:0452LddLex 0:0143TLex (6)

Similar to the first-order model, by examining the

coefficients of the first-order terms, the supply temperature

(T) has the most dominant effect on the ADPI. The contribution

of exhaust location (Lex) is the least significant here. Also,

owing to the P-value of interaction is 0.248 (>0.05), one caneasily deduce that the interactions of distinct design variables

are not significant here. In other words, the most dominant

design variable T has minimum interaction with others in the

current context.

As seen from Fig. 4, the predicted ADPI using the second-

order RSM model is able to produce values close to those

computed using CFD, and, as it should be the case, it exhibits

better agreement as compared to those from the first-order RSM

model. The ANOVA shown in Table 4 indicates that the model

is adequate as the P-value of the lack-of-fit is not significant

(>0.05).

uares Mean squares F-ratio P-value

227.440 54.400 0.000

227.440 54.400 0.000

4.181

4.814 3.610 0.236

1.333odels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

Table 4

Analysis of variance (ANOVA) for second-order equation (from MINITAB)

Source of variation Degree of freedom (d.f.) Sum of sq

Regression 9 720.851

Linear 3 682.312

Square 3 30.050

Interaction 3 8.489

Residual error 5 7.452

Lack-of-fit 3 4.785

Pure error 2 2.667

3

K.C. Ng et al. / Energy and Bui

+ Models

ENB-2319; No of Pages 85.3. Design optimisation

With the ADPI models obtained, the optimised response

variable (ADPI) can then be determined. Here, the goal is to

maximise the ADPI from the correct combination of the design

variables.

For optimisation purpose, the response variable is trans-

formed using a specific desirability function shown in Fig. 6.

The weight defines the shape of the desirability function for the

response, which can be selected from 0.1 to 10.0 to emphasise

or de-emphasize the target value (set to 100%). Aweight can be

Less than one (minimum is 0.1) places less emphasis on thetarget, or

Equal to one places equal importance on the target and thebounds, or

Greater than one (maximum is 10.0) places more emphasis onthe target, which is the main concern of the current work.

Therefore, the weight is set to 10.0.

From the second-order ADPI model, the optimized ADPI

value is 43.41% (calculated from MINITAB), subjected to the

following combination of the design variables:

Ldd 3:11m; T 19 C; Lex 4:6487m: (7)In order to verify the optimised ADPI value predicted from

RSM, the CFD simulation is performed again, by adopting the

combination of design variables shown in Eq. (7). The ADPI

computed is 42.68% (%difference = 1.71%), and it is worth to

mention here that it is indeed the highest ADPI value as

compared to those from the previous 15 CFD tests (see Table 2).

Apparently, all the design variables are approaching their

Total 14 728.30maximum values (level = 1) in the case of maximum ADPI

value is desired. This condition holds true even for the first-

Fig. 6. Desirability function for maximising the response.


displacement ventilated office, Energy & Buildings (2007), doi:10.1016order model, in which the linear model has recommended the

ceiling values of those design variables in order to achieve the

most desirable comfort condition, by maximising the ADPI

value in the current context.

6. Conclusion

CFD studies have been applied extensively to the simulation

of indoor/outdoor airflow. However, most of the numerical tests

are based on a one-factor-at-a-time design, without having any

idea about the behaviour of an output parameter (response)

when two or more design variables are varied simultaneously.

The current study focuses on the effect of simultaneous

variations of three design variables in a displacement-ventilated

office, i.e. location of the displacement diffuser (Ldd), supply

temperature (T) and exhaust position (Lex) on behaviour of the

response variable (air diffusion performance index).

In the current work, the response surface methodology has

been proven to be a successful technique to perform the trend

analysis of air diffusion performance index with respect to

various combinations of three design variables. By using the

least square method, the first- and second-order models have

been developed based on the test conditions in accordance with

the BoxBehnken design method. The models have been found

to accurately representing the ADPI values with respect to those

simulated using CFD. The equations have been checked for

their adequacy with a confidence interval of 95%.

Both RSM models reveal that the supply temperature is the

most significant design variable in determining the ADPI

response as compared to the others. In general, within the

working range of the supply temperatures considered here,

ADPI increases as the supply temperature increases. Based on

uares Mean squares F-ratio P-value

80.095 53.740 0.000

227.44 152.610 0.000

10.017 6.720 0.033

2.830 1.900 0.248

1.490

1.595 1.200 0.485

1.333

ldings xxx (2007) xxxxxx 7the second-order RSM model, the supply temperature does not

interact much with the remaining design variables. Therefore,

one may exclude both locations of displacement diffuser and

exhaust for indoor comfort design purpose (based on ADPI) in

the current design case. With the model equations obtained, a

designer can subsequently select the best combination of design

variables for achieving optimum comfort condition.

Acknowledgements

The first author would like to express his sincere

appreciation to his former colleague, Dr. T.K. Lim (now in

AMD, Singapore) for his recommendation. We also acknowl-


/j.enbuild.2007.04.024

edge Mr. W.M. Chin (OYL R&D, Malaysia) for showing

consistent interest and support on the current work. The

software facilities provided by Universiti Tenaga Nasional

(UNITEN) are greatly appreciated. Also, special thanks to Mr.

Anuar (UNITEN), for developing the Graphical User Interface

of the current CFD package.

Reference

[1] F. Haghighat, Z. Jiang, J. Wang, A CFD analysis of ventilation effective-

ness in a partitioned room, Indoor Air 4 (1991) 606615.

[2] H. Lee, H.B. Awbi, Effect of partition location on the air and contaminant

movement in a room, in: Proceedings of Indoor Air 99, vol. 1, Edinburgh,

August 813, (1999), pp. 349354.

[3] T.K. Lim, Y.L. Ong, M. Hamdi, Locating the Optimum Position to Place

an Indoor Air Conditioner in Studio-Type Apartment to Achieve Good

Thermal Comfort, FLOVENT Technical Paper, Paper V45, total number

of pages: 7, 2005.

[4] Y. Ooi, I.A. Bahruddin, P.A.A. Narayana, Airflow analysis in an air

conditioning room, Building and Environment 42 (3) (2007) 1531

1537.

[5] M. Bojic, F. Yik, T.Y. Lo, Locating air-conditioners and furniture inside

residential flats to obtain good thermal comfort, Energy and Buildings 34

(2002) 745751.

[6] G. He, Z. Yang, J. Srebric, Removal of contaminants released from room

surfaces by displacement and mixing ventilation: modelling and valida-

tion, Indoor Air 15 (2005) 367380.

[7] K.A. Abou-El-Hossein, K. Kadirgama, M. Hamdi, K.Y. Benyounis,

Prediction of cutting force in end-milling operation of modified AISI

P20 tool steel, Journal of Materials Processing Technology 182 (2007)

[8] K. Klemm, W. Marks, A.J. Klemm, Multicriteria optimisation of the

building arrangement with application of numerical simulation, Building

and Environment 35 (2000) 537544.

[9] L.E.C. Valencia, A.M. Ramirez, G.L. Barcenas, E.A. Guzman, Modelling

of the performance of asphalt pavement using response surface method,

Building and Environment 40 (8) (2005) 11401149.

[10] K.C. Chung, C.Y. Lee, Predicting air flow and thermal comfort in an

indoor environment under different air diffusion models, Building and

Environment 31 (1) (1996) 2126.

[11] J. Toftum, Air movement-good or bad? Indoor Air 14 (Suppl. 7) (2004)

4045.

[12] K.C. Ng, Multigrid solution using high-resolution NVF differencing

schemes for solution-adaptive unstructured meshes, Ph.D. Thesis,

Department of Mechanical Engineering, Universiti Tenaga Nasional,

Malaysia, 2006.

[13] K.C. Ng, M.Z. Yusoff, E.Y.K. Ng, Higher-order bounded differencing

schemes for compressible and incompressible flows, International Journal

for Numerical Methods in Fluids 53 (1) (2007) 5780.

[14] J. Zhu, On the higher-order bounded discretisation schemes for finite

volume computations of incompressible flows, Computer Methods in

Applied Mechanics and Engineering 98 (1992) 345360.

[15] C.M. Rhie, W.L. Chow, Numerical study of the turbulent flow past an

airfoil with trailing edge separation, AIAA Journal 21 (1983) 15251532.

[16] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere,

Washington, DC, 1981.

[17] H. Jasak, Error Analysis and Estimation for the Finite Volume Method

with Applications to Fluid Flow, Ph.D. Thesis, Imperial College, Uni-

versity of London, UK, 1996.

[18] H.A. Van der Vorst, BI-CGSTAB: a fast and smoothly converging variant

of BI-CG for the solution of nonsymmetric linear systems, SIAM Journal

of Scientific and Statistical Computing 13 (2) (1992) 631644.

[19] C.R. Hicks, Fundamental Concepts in the Design of Experiments, fourth

ed., Oxford University Press, USA, 1993.


+ Models

ENB-2319; No of Pages 8241247.Please cite this article in press as: K.C. Ng et al., Response surface m

displacement ventilated office, Energy & Buildings (2007), doi:10.1016odels for CFD predictions of air diffusion performance index in a

/j.enbuild.2007.04.024

Response surface models for CFD predictions of air diffusion performance index in a displacement ventilated officeIntroductionIntroduction to response surface methodologyModel of air diffusion performance indexResearch methodologyCFD simulationExperimental design for RSM

Results and discussionsDevelopment of first-order ADPI modelDevelopment of second-order ADPI modelDesign optimisation

ConclusionAcknowledgementsReference

response surface models for cfd predictions of air diffusion performance index in a displacement...

Documents