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A numerical approach for air velocity predictions in front of exhaust flanged slot openings

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Building and Environment 39 (2004) 9–18www.elsevier.com/locate/buildenv
A numerical approach for air velocity predictions in front of exhaustanged slot openings
Vittorio Betta
a
, Furio Cascetta
b
;
∗
, Pierluigi Labruna
a
, Adolfo Palombo
a
a
DETEC, University of Naples, Federico II, Piazzale Tecchio 80, 80125 Naples, Italy
b
DIAM, Second University of Naples, Via Roma 29, 81031 Aversa, Italy
Received 13 December 2001; received in revised form 9 June 2003; accepted 12 July 2003
Abstract
Nowadays the computational uid dynamics (CFD) simulation represents an important tool for the performance analysis of the localexhaust ventilation (LEV) systems. In this paper air velocity eld in the proximity of a free-standing anged slot having a 6:1 aspectratio is investigated by such an approach. Numerically calculated velocities both in centreline and o the hood axis are compared with thevelocities obtained by the most popular experimental and theoretical formulas available in literature. Simple equations are with a commonmathematical structure, which are provided for all the numerically simulated velocity trends.
?
2003 Elsevier Ltd. All rights reserved.
Keywords:
Computational ow dynamic (CFD) simulation; Local exhaust ventilation (LEV) systems; Design guidelines
1. Introduction
In the industrial workrooms and laboratories, indoor air quality (IAQ) control must comply with a double request:to provide healthy working conditions and to protect, fromdamages, the industrial products. In order to satisfy theserequirements, important design instructions and guidelinesare dened [1]. In this direction, particular attention is paid
to the air ventilation, widely used to contain the airbornecontaminants concentrations to suciently low levels. Thelocal exhaust ventilation (LEV) systems [2] achieve thisaim by generating, towards the exhaust opening, an airoweldthatremovestheairbornecontaminantsdecreasingtheir spreading over the workplace air.The Navier–Stokes equations describing the airow eldinduced by an exhaust opening [3] are complex and ex-
act analytical solutions are provided only in very simplecases. Hence, the classic design practices for LEV systemsare mainly based on empirical relationships that do not pro-vide deeper insight into the underlying physical phenomena.Despite this limitation, the experimental analyses today arestill an eective tool in the LEV systems investigation [4,5],
∗
Corresponding author. Tel.: +39-817682290; fax: +39-812390364.
E-mail addresses:
fcascett@unina.it (F. Cascetta), palombo@unina.it(A. Palombo).
often required in order to calibrate and validate the the-oretical results. An alternative approach is based on po-tential ow models for LEV systems [6,7]. Here, some
ideal hypotheses are considered such as incompressible,irrotational ow and negligible uid viscosity. Althoughmodels of this kind satisfactorily simulate the unobstructedow eld in front of the exhaust openings, they are unableto describe the ow behaviours where turbulent stressescannot be disregarded. More realistic models are obtained by the equations describing the uid ow and the rela-tive turbulence eects. Thanks to the computer technologydevelopment and advances in applied mathematics, suchequations are implemented and solved by suitable com- putational uid dynamics (CFD) codes. Nowadays theCFD approach is largely diused in the simulation of theLEV systems [8 – 11]. Both simple and complex geome-
tries can be analysed. CFD is often adopted to assessthe LEV systems performance and to dene new designguidelines.The rectangular long hood, often called slot, is largelydiused since it induces a wide capture action towards largecontaminant sources. It is usually adopted as exhaust rimat large tanks or exhaust hood in high velocity low volumeLEV systems. A ange is often assembled on its edge inorder to reduce the suction from the hood rear and fromother non-signicant areas.
0360-1323/$-see front matter
?
2003 Elsevier Ltd. All rights reserved.doi:10.1016/j.buildenv.2003.07.004
10
V. Betta et al./Building and Environment 39 (2004) 9–18
Nomenclature
A
area of the slot opening, m
2
A
C
area of the slot ange, m
2
a
length of the slot opening, m
b
width of the slot opening, m
C
width of the slot ange, m
D
h
hydraulic diameter of the slot opening, m
s
area of the suction duct, m
2
Greek symbols
;;;
parameters
angle of the convergent in a tapered hoodThe aim of this paper is to investigate the performanceof a anged free-standing slot opening with 6:1 aspect ratiousing a commercial CFD code (FLUENT 5.5 [12]).Theairvelocityeldsinfrontoftheslotarecomputedandthe numerically predicted velocities in centreline and o thehood axis are compared with those obtained by the popular experimental and theoretical formulas reported in literature.In order to give some design guideline, simple equations aresuggested, which are provided for all the simulated velocitytrends in the function of the hood distance. Finally the pre-dicted velocity contours in front of this slot are presented todisplay the velocity eld in the whole hood air capture area.
2. Modelling and simulation
A anged 6:1 slot opening having length (a) and width(b) of 0.600 and 0
:
100 m, respectively (Fig. 1) is modelled by the grid generator GAMBIT [13]. Reference is made
to an orthogonal three-dimensional system located at the
Fig. 1. The considered 6:1 anged slot, the portion of the simulationcontrol volume close to the hood opening and the relative mesh.
hood face centre with the
x
-axis directed outbound, the
y
-axis parallel to the slot length and the
z
-axis parallel to theslot width. A simulation control volume is dened in the air zone inuenced by the hood running. It includes the air re-gion where the sucking eect is weak, the region where theair velocities are higher and the hood duct. A portion of thiscontrol volume close to the hood opening is shown in Fig. 1.Such modelled volume domain is suitably divided into alargenumberofelementarythree-dimensionalcells,formingthe computational mesh. The size of the elementary cells istaken to resolve the velocity gradients of air due to hoodinteraction. The higher these gradients in the investigatedregion are, the smaller the cells and the closer the mesh aredesigned here.In the centre of each cell a grid point is identied. In thiscase their total number is about 1
×
10
5
. A xed pressure boundary condition is assigned at the free-stream surface of the control volume. The hood ange and the hood duct aresimulated as walls. A constant velocity condition is givento the downstream surface of the conduit.The air sucked by the slot is assumed to be an incompress-ible uid. The airow considered is unobstructed, isother-mal and without buoyancy eects. The adopted turbulencemodel is the Renormalization Group (RNG)
k
–
model [14].
The solving system, based on the fully turbulent ow as-sumption, srcinates from the Reynolds-averaged Navier– Stokes equations. The continuity time-averaged equation ina Cartesian reference system (using tensor notation) is
@
u
i
@x
i
= 0
;
(1)while the time-averaged momentum one is
u
j
@
u
i
@x
j
=
−
@
p@x
i
+
@@x
j
(2
S
ij
−
u
i
u
j
)
:
(2)Direct reference can be made to FLUENT manual [12], so
all model details can be omitted, for the sake of clarity.The control-volume method is applied. The previousequations of mass conservation and momentum (Eqs. (1)and (2)), and the transport equations of turbulent kinetic
energy and dissipation of turbulent kinetic energy [12] are
discretized on each elementary cell of ow calculation do-main [12]. The discretized equations are then solved for
each variable iteratively until a convergent solution is ob-tained. It is assumed that sucient convergence is achievedwhen the dimensionless residual term of each system equa-tion is less than 10
−
3
.
3. Results and discussion
The three-dimensional CFD simulation of the mod-elled 6:1 anged slot is related to an exhaust ow rate of 0
:
14 m
3
=
s. The corresponding
Re
number (based on the slothydraulic diameter) is 2
:
7
×
10
4
. The performance resultsare reported as air velocity elds due to the hood sucking
V. Betta et al./Building and Environment 39 (2004) 9–18
11
eect. Although simulation is performed on the whole mod-elled volume, particular attention is paid to reporting andanalysing the predicted velocities for the air region, out of the opening, where the suction eect is remarkable.The simulation results can be applied to other slots hav-ing similar geometries as well [15]. Therefore the velocity
values are non-dimensionalized with respect to the averagevelocity inside the exhaust duct,
V
av
:
V
∗
=
V=V
av
; V
av
=
•
V =A;
(3)where
A
is the hood opening area (
A
=
ab
)
;
•
V
is the air volume ow rate, and
V
is the velocity module dened as
V
=
u
2
+
v
2
+
w
2
(4)
u;v
and
w
being the velocity components, respectively, inthe
x;y
and
z
directions.For the same reason, the distances from the consideredCartesian reference system srcin are made dimensionlesswith respect to
√
A
:
x
∗
=
x=
√
A; y
∗
=
y=
√
A; z
∗
=
z=
√
A:
(5)In Fig. 2 the numerical predicted centreline velocities andthoseobtainedbythepopularformulasofEngelsandWillert[16], Garrison and Byers [17,18], Silverman [19] and Tya-
glo and Shepelev [2,20] are plotted vs. the dimensionless
Table 1The most popular formulas for the prediction of the centreline velocity in anged rectangular hoodsFormula Application eld Author and basic hypothesis
V
(
x
)
V
av
= 1
:
351
:
35 + (4
x=D
h
)
1
:
45
V
(
x
)
V
av
= 11 + 0
:
5 + (4
x=D
h
)
1
:
9
0
6
x D
h
6
0
:
50
:
5
6
x D
h
6
3
:
5
ab
not specied
A
C
= 2
:
3 A
A s
not specied
not speciedEngels and Willert(experimental study)
V
(
x
)
V
av
= 1
:
07(0
:
22)
x=b
V
(
x
)
V
av
= 0
:
277
xb
−
0
:
867
V
(
x
)
V
av
= 0
:
277
xb
−
1
:
3
0
6
xb
6
0
:
50
:
5
6
xb
6
11
6
xb
6
3
:
301
6
ab
6
10
C
=
√
A
not speciedGarrison and Byers
;
Garrison(experimental study)
V
(
x
)
V
av
=
b
2
:
8
x x
not specied
ab
¿
5
C
not speciedSilverman(experimental study)
V
(
x
)
V
av
= 2
arctan
ab
2
x
√
4
x
2
+
a
2
+
b
2
0
6
x
√
A
6
1
:
61
6
ab
6
16
C
√
A
¿
1Tyaglo and Shepelev(three
−
dimensional potential ow)
Centreline, y* = 0, z* = 0
-0.50.00.51.01.52.0V*0.00.51.0
Eng
el and WillertGarrison and ByersSilvermanTyaglo and ShepelevNumerical Simulation
x*
Fig. 2. Experimental and theoretical predicted centreline velocities.
x
∗
-distance from the hood face, on the centreline axis. Suchempirical and theoretical relationships for the anged slotsare shown in Table 1 together with their elds of application.Taking a rst look at the graph reported in Fig. 2, it isobserved that the trend shape of the numerically predictedvelocity decay is in general very similar to that given bysuch formulas. By a deeper analysis of these curves severaldierences vs. the numerically predicted velocity trend can
12
V. Betta et al./Building and Environment 39 (2004) 9–18
x* z*
01.63 0.08161.220.8160.4080.163
y*
0.245
Fig. 3. Positions on the hood face are where the reported velocities progress.
bedetected.Suchdierencescanbeexpressedbytherelativevelocity percentage deviations, dened as follows:
EW
=
V
∗
−
V
∗
EW
V
∗
EW
×
100
;
GB
=
V
∗
−
V
∗
GB
V
∗
GB
×
100
;
S
=
V
∗
−
V
∗
S
V
∗
S
×
100
;
TS
=
V
∗
−
V
∗
TS
V
∗
TS
×
100
;
(6)where
EW
;
GB
;
S
and
TS
are the percentage devia-tions between the numerical simulation predicted veloci-ties and those obtained by the above mentioned formulas.
V
∗
EW
; V
∗
GB
; V
∗
S
and
V
∗
TS
are the relative dimensionless veloci-ties.Theresultsofthenumericalsimulationoverestimatetheexperimental data of Engels and Willert in all the displayedrange. In particular, the relative deviations are almost alwayshigher than 10%. For
x
∗
¿
0
:
7 they exceed the threshold of 20%, while they become higher than 50% where the suc-tion eect is weaker. The same overestimating behaviour isachieved against the formula of Garrison and Byers. Herethe deviation values are in general lower than the previouscase, particularly in the air zone far from the hood. Alsoin this case the relative deviations are almost always higher than 10%, but they exceed the threshold of 20% only in fewcases. The FLUENT results are always lower than Silver-man’s experimental data. In the air region very close to theopening the Silverman’s formula appears unreliable havingan asymptotical trend (
x
∗
→
0
; V
∗
→ ∞
). Furthermore,where the velocity gradients are still high, the relative devi-ations are less than 20%. In the air region where the suctionis weak they are larger than 40%. Some of the deviations between the previous experimental results and the presentones could be due to several geometrical dierences in therelative exhaust hoods and hood ducts. As an example, theexperimental results refer to tapered hoods while the numer-ical simulation to a hood with a duct having constant crosssection. The lowest deviations are reached between the nu-merical simulation and the potential ow solution of Tya-glo and Shepelev: for
x
∗
¿
0
:
4, the velocities are practicallycoincident. Note that the potential ow approach is unableto describe the physical phenomena occurring very close tothe hood opening since in this region the basic hypothesesof this model are not valid [6].
Thecentrelinesimulationresultsand,ingeneral,theavail-able experimental formulas do not account for airborne con-taminants located o the hood axis and, in general, for widecontaminant sources. For this reason the o-axis velocityeld and even that beyond the hood opening are also in-vestigated. The results are reported as predicted velocity vs.the dimensionless
x
∗
-distance from the slot face, on several
x
∗
-parallel lines, whose projections (points) on the
y
∗
–
z
∗
plane are displayed in Fig. 3. Having obtained for the slot a
symmetric behaviour of the velocity eld with respect to thegeometric symmetry planes, the results are reported only for a quarter of its domain. This hypothesis allows a simpliedapproach even though it is experimentally demonstrated thatin an exhaust slot opening occurs at a certain degree of uid
V. Betta et al./Building and Environment 39 (2004) 9–18
13
x*
-0.50.00.51.01.52.0
V*
0.00.51.0
y* = 0.816, z* = 0(y = 0.2 m, z = 0 m)y* = 1.22, z* = 0(y = 0.3 m, z = 0 m)y* = 1.63, z* = 0(y = 0.4 m, z = 0 m)Correlation equation plot
Fig. 4. Numerically predicted velocities out of the hood axis. The considered axes cross the hood face in:
y
∗
= 0
:
816
; z
∗
= 0;
y
∗
= 1
:
22
; z
∗
= 0;
y
∗
= 1
:
63
; z
∗
= 0.
x*
-0.50.00.51.01.52.0
V*
0.00.51.0
y* = 0.816,z* = 0.163(y = 0.2 m, z = 0.04 m)y* = 1.22, z* =0.163(y = 0.3 m, z = 0.04 m)y* = 1.63, z* =0.163(y = 0.4 m, z = 0.04 m)Correlation equation plot
Fig. 5. Numerically predicted velocities out of the hood axis. The considered axes cross the hood face in:
y
∗
= 0
:
816
; z
∗
= 0
:
163;
y
∗
= 1
:
22
; z
∗
= 0
:
163;
y
∗
= 1
:
63
; z
∗
= 0
:
163.
dynamic asymmetry due to unavoidable constraints (fan ef-fect, presence of solid surrounding surfaces, etc.). Note thatthese point locations belong both to the hood face domainand to the hood ange one.In Fig. 4, the dimensionless predicted velocity is plotted
vs.
x
∗
along the axes crossing (Fig. 3): the hood opening at
y
∗
= 0
:
816
; z
∗
= 0, the slot face edge at
y
∗
= 1
:
22
; z
∗
= 0and the ange at
y
∗
= 1
:
63
; z
∗
= 0. In the brackets of thegure legend are also reported the dimensional positions of such axes for the modelled slot (0
:
6 m length, 0
:
1 m width).The simulation results are reported for the air region closeto the hood opening only (in Figs. 4 – 8 some solid curves
are also plotted representing the correlation equations, thatare presented later in the paper).The highest velocity trend obviously belongs to the lineclosest to the
x
∗
axis. From the duct region, represented bythe negative
x
∗
-zone, the velocity decreases at rst steeplyand then smoothly towards the air region distant from thehood opening. Note that in this case for
x
∗
¿
1 results
V
∗
¡
0
:
1, i.e. the air velocity is lower than 10% of the aver-age one (see Eqs. (3)). Moving laterally to the line locatedon the border of the hood opening, it is observed that the predicted air velocity is obviously null for
x
∗
= 0, growsup to a maximum located approximately in
x
∗
= 0
:
1 where

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