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98 The Open Mechanical Enginee ing Jou nal, 2013, 7, 98-107
1874-155X /13 2013 Ben ham Open
Open Access
Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex
Tube when he Inle Pa ame e s a e Va ied
E. To ella1, J. Pa iño2, D. Sánchez2, R. Llopis2 and R. Cabello*,2
1Depa men o Applied The modynamics, Camino de Ve a, 14. Poly echnic Uni e si y o Valencia, E-46022 Valencia,
Spain
2Depa men o Mechanical Enginee ing and Cons uc ion, Campus de Riu Sec. Jaume I Uni e si y, E-12071 Cas ellón,
Spain
Abs ac : The pape p esen s he analysis o he ene gy pe o mance o an ai o ex cooling ube unde a ia ions o he
ai inle p ope ies, wi h h ee independen expe imen al es s alida ed h ough he ene gy balance in he de ice.
The expe imen al analysis includes he ollowing a ia ions o he inpu condi ions: Fi s , he e ec o he ai inle
p essu e o he o ex ube, ocused on he analysis o empe a u e a ia ions in he ou pu cold s eam and in he cooling
capaci y when he cold low ac ion a ies. Second, we s udied ai inle empe a u e a ia ions o he o ex ube unde
di e en cold low ac ions, which is an analysis no ound in he li e a u e. And inally, is s udied he pe o mance o he
o ex ube when he insula ion is p o ided o in absence o insula ion.
Keywo ds: Vo ex ube, e ige a ion sys em, ene gy analysis.
1. INTRODUCTION
The Vo ex e ec was i s obse ed by Ranque [1] while
obse ing he mal di ision in a cyclone sepa a o , being his
design imp o ed by Hilsch [2]. Kassne and Knoe nschild
[3] pe o med a heo e ical s udy based on he assump ion
ha he e ec was due o adiaba ic expansion, which led o a
low empe a u e in he low p essu e a ea nea he axis o he
ube. Subsequen ly, o he esea che s ha e p oposed
di e en heo ies o explain he ene gy sepa a ion p ocess,
some o he mos impo an e e enced in ch onological
o de a e: Webs e [4], Ful on [5], Shepe [6], Ha ne e al.
[7], Lay [8,9], Deissle e al. [10], Reynolds [11], Lewellen
[12], Linds om [13], Ku osaka [14], Ami ani e al. [15],
S ephan e al. [16], A buzo e al. [17], Gu sol e al. [18],
Lewis e al. [19], Ahlbo n e al. [20], T o imo [21] and
Colga e [22]. No wi hs anding hese e o s, a heo y which
sa is ac o ily explains he en i e p ocess has no been
de eloped ye . Despi e he abo e s a emen and he low
ene gy e iciency o he o ex ube, hey a e
comme cialized o di e en applica ions when
compac ness, eliabili y and low cos a e he main ac o s
and when ene gy e iciency becomes less impo an .
Cu en ly, hey a e used o cool pa s o machines,
dehumidi y gas samples, cool elec ical panels, lique y
na u al gas (Fin’ko [23, 24]), cool unde ad e se condi ions
(Baz e al. [25, 26]), chill labo a o y en i onmen s in
*Add ess co espondence o his au ho a he Depa men o Mechanical
Enginee ing and Cons uc ion, Campus de Riu Sec. Jaume I Uni e si y, E-
12071 Cas ellón, Spain; Tel. +34 964 728135; Fax: +34 964 728106;
E-mail: [email protected]
explosi e a mosphe es (B uno [27]), in hype ba ic chambe s
(Baz e al. [28]), sepa a e pa icles (Riu e al. [29]), in
nuclea magne ic esonance (NMR) (Ma in e al. [30]),
pe o m apid PCR (Polyme ase Chain Reac ion) wi h eal-
ime op ical de ec ion [31]. Fu he mo e, o ex ubes
ope a e as suc ion de ices (Alhbo n e al. [32]) and as
expande s in ansc i ical CO2 cycles (Sa ka e al. [33]).
Recen ly, Sachin e al. [34] and O han e al. [35] s udied
di e en geome ies o he cold end o imp o e he ene gy
pe o mance o he o ex ube.
In con as o he exis ing expe imen al analysis o ai
o ex ubes, which mainly ocuses on s udying hei
pe o mance unde a ia ions o he cold low ac ion wi h
cons an inle empe a u e p ope ies, he objec i e o his
wo k is o analyse he incidence o he ai low inpu
pa ame e s (inle p essu e and inle empe a u e) on i s
ene gy pe o mance. Speci ically, we analyse he ou le
empe a u e o he cold s eam, he cooling capaci y p o ide
and he COP eached by he e ige a ing de ice.
Acco dingly, his wo k p e ends o con ibu e o he
unde s anding o he eal pe o mance o ai o ex ubes.
2. EXPERIMENTAL TEST BENCH AND ANALYSIS
The expe imen al es bench de eloped o his wo k is
shown in Fig. (1). This expe imen al se up inco po a es an
EXAIR BP3215 o ex ube (maximum olume ic low a e
0,007078 m3/s in s anda d condi ions a 690 kPa o inle
p essu e). The assembly is he mally isola ed om he
comp essed ai en ance in he cold and ho ou le s.
We measu e empe a u e wi h K- ype he mocouples and
p essu e wi h piezoelec ic ansduce s placed a he inle and
ho and cold exi s. The unce ain ies, calib a ed using
Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 99
ce i ied e e ences, a e o ± 0.5 ºC o he he mocouples
and o ± 0.1% o he ull scale ange (0-1000 kPa) o he
p essu e ansduce s. We measu e empe a u e on he ou e
su ace o he ubes, since acco ding o Ahlbo n [36], o
measu e he empe a u e o mo ing luids, a de ice mo ing
a he speed o he low should be used so as o achie e
he mal equilib ium.
We use wo mass low me e s, one o he inle ai (Tes o
6441, wi h p ecision ± 0,3 % o ull scale) and o he o he
ho exi ai (B onkho s model EL-Flow F112AC, wi h
p ecision ±0.1% ull scale). The signals a e ga he ed by an
AGILENT 34970A da a acquisi ion sys em.
3. VORTEX TUBE CHARACTERIZATION
The main pa ame e s ha cha ac e ize he ope a ion o a
o ex ube a e he ollowing:
3.1. Cold Flow F ac ion
Cold low ac ion a io is he a io be ween cold low
and inle low:
=mc
min
; 0 ! !1
(1)
3.2. COP
As o any e ige a ion plan , COP is he a io be ween
he cooling capaci y p oduced and he powe consump ion
equi ed in he ins alla ion, as p esen ed by equa ion (2).
COP =Q0
PCs
(2)
whe e he cooling capaci y is calcula ed in he same way as
in he case o a hea exchange , aking in o accoun he
ene gy abso bed o cool he cold s eam (3).
Q
0
=m
c
!c
p
!(T
in
"T
c
)
(3)
Supply o comp essed ai , in he case o o ex ubes, is
usually p o ided by an independen ai comp esso , making
i di icul o es ima e he powe consump ion o compu e he
COP i a wa me e is no a ailable o i he ai comp essed
is no used exclusi ely in he o ex acili y.
Acco ding o Boswell [37], he powe equi ed o
comp ess ai om a mosphe ic condi ions, assuming an
isen opic p ocess, can be calcula ed acco ding o exp ession
(4), whe e he subsc ip s “2” and “1” indica e he comp esso
ou pu and inpu condi ions.
PCs =
!
!
"1#min #R#(T2"T1)
(4)
Using he ela ionships inhe en in an adiaba ic
comp ession p ocess (5) and (6),
T
2
T
1
=p
2
p
1
!
"
#$
%
&
'
(1
'
(5)
R!
"
"
#1=c
p
(6)
and conside ing ha ai is cooled un il p ac ically o an
a mosphe ic empe a u e (T1), wha means ha his is he
o ex inle empe a u e “Tin”, he exp ession o powe
consump ion can be w i en as de ailed by exp ession (7).
P
Cs
=m
in
!c
p
!(T
2
"T
1
)
(7)
Ob aining “T2” by means o (5), he inal exp ession o
calcula ing he COP wi h expe imen al da a, easible
measu able, is shown in equa ion (8)
COP =Q
0
P
Cs
= !(T
in
"T
c
)
T
in
!p
in
p
1
#
$
%&
'
(
(
)
"1)/
)
"T
in
#
$
%
%
&
'
(
(
= !(T
in
"T
c
)
T
in
!p
in
p
1
#
$
%&
'
(
(
)
"1)/
)
"1
#
$
%
%
&
'
(
(
(8)
Fig. (1). Tes bench and senso s loca ion.
100 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al.
4. EXPERIMENTAL ANALYSIS
The wo ks a ailable in li e a u e demons a e ha he
main magni udes which a ec he ene gy pe o mance o a
o ex ube a e he inle p essu e (pin) and he low a io ( ).
The e o e, we e alua e he ene gy pe o mance o he o ex
ube wi h a se ies o ials in which he low a io a ies
inside he ope a ing ange o he de ice.
4.1. Expe imen al Tes Range
We conside h ee di e en expe imen s o e alua e he
pe o mance o he o ex ube. Fi s , i was pu h ough
h ee di e en inle p essu e le els, condi ions a e de ailed in
Table 1. Second, he in luence o he inle ai empe a u e
was e alua ed, a ied using a he mos a ic wa e ba h (as
shown in Fig. 1) by using a small hea exchange placed in
he inpu cu en . The e alua ion ange o he o ex ube in
his es is shown in Table 2. Finally, he e ec o he
he mal insula ion o he o ex ube was e alua ed o
cons an ai inle condi ions, as de ailed in Table 3.
4.2. Valida ion o Expe imen al Measu emen s
Fi s , o check he alidi y o he expe imen al esul s we
analyse he ene gy balance on he o ex ube, i exp essed
by ela ion (9). In he ene gy balance he hea ans e o he
en i onmen is neglec ed and po en ial ene gies a e
conside ed equal o he inpu and ou pu cu en s ( ue in he
expe imen al plan ).
Pin =min !(hin +Ec,in )=mc!(hc+Ec,c)+m !(h +Ec, )=Pou
(9)
As i is illus a ed by Fig. (2), he expe imen al es s
co obo a e he ene gy balance o equa ion (9). As can be
obse ed in Fig. (2), o e all ene gy balance shows a
de ia ion o ± 5% be ween he o al powe o he de ice
inpu and ou pu . The h ee cloud o poin s co espond o he
h ee inle p essu e le els (Table 1). The he modynamic
p ope ies o he ai we e e alua ed using Re p op ou ines
[38] neglec ing he mois u e o he inle ai , since i
p esen ed a low mois u e a io.
4.3. Inle P essu e Va ia ion Tes
Fi s , we p esen he analysis o he expe imen al
pe o mance o he o ex ube o he inle p essu e
a ia ion es (Table 1).
In Fig. (3), he measu ed ai ou le empe a u es o he
o ex ube a e depic ed. The expe imen al e olu ions a e
consis en wi h p e ious expe imen al s udies, such as hose
o P om onge [39] and Saidi [40]. As i can be obse ed in
he e olu ion o he ou le cold low in Fig. (3), a minimum
in empe a u e exis s in each es . This minimum in
empe a u e is ansla ed o wo coinciden minimums in he
powe o he cold low a he o ex ou le , p esen ed in Fig.
(4). In Fig. (4), we p esen he o al powe and he
con ibu ion due o he p oduc o he mass low by i s
speci ic en halpy. The di e ence be ween hem is he
p oduc o he mass low by he kine ic ene gy.
In Fig. (5), we depic he alues o cold mass low and i
speci ic en halpy o he s eady-s a e co esponding o he
highes p essu e in he es . I can be deduced om Fig. (5)
ha he cause o he minimum in he ou le empe a u e o
he cold ai and in he ou pu powe s is he ou le mass low
e olu ion o he cold low.
Table 1. Inle P essu e Va ia ion Tes Range
Tes
A e age pin
[kPa]
Va ia ion pin
[%]
A e age Vin
[m3/h]
Va ia ion Vin
[%]
A e age Tin
[ºC]
Va ia ion. Tin
[%]
A e age min
[kg/h]
Va ia ion. min
[%]
HP
563.35
-0.27 ÷ 0.22
16.35
-5.13 ÷ 3.31
20.08
-2.48 ÷ 3.00
109.45
-4.96 ÷ 3.23
MP
409.22
-0.76 ÷ 0.76
11.33
-2.97 ÷ 3.41
21.08
-2.60 ÷ 1.20
54.91
-2.48 ÷ 3.68
LP
256.86
-0.74 ÷ 0.88
6.19
-4.77 ÷ 3.35
21.61
-0.65 ÷ 0.84
18.79
-4.24 ÷ 2.77
Table 2. Inle Tempe a u e Va ia ion Tes Range
Tes
A e age pin
[kPa]
Va ia ion pin
[%]
A e age Vin
[m3/h]
Va ia ion Vin
[%]
A e age Tin
[ºC]
Va ia ion. Tin
[%]
A e age min
[kg/h]
Va ia ion. min
[%]
HT
572.93
-0.46 ÷ 0.28
16.22
-5.84 ÷ 3.59
38.98
-1.57 ÷ 1.01
103.75
-6.05 ÷ 3.93
MT
549.15
-0.46 ÷ 0.57
16.02
-6.14 ÷ 2.90
19.33
-0.56 ÷ 0.60
104.8
-6.00 ÷ 2.98
LT
550.42
-0.63 ÷ 0.73
15.89
-6.17 ÷ 4.22
14.37
-8.87 ÷ 2.67
105.95
-5.21 ÷ 3.85
Table 3. Tes Condi ions wi h and wi hou Insula ion
Tes
A e age pin
[kPa]
Va ia ion pin
[%]
A e age Vin
[m3/h]
Va ia ion Vin
[%]
A e age Tin
[ºC]
Va ia ion. Tin
[%]
A e age min
[kg/h]
Va ia ion. min
[%]
WITH
575.06
-7.72 ÷ 10.4
16.12
-5.47 ÷ 11.7
20.98
-1.66 ÷ 1.25
109.96
-11.48 ÷ 20.78
WITHOUT
577.14
-9.05 ÷ 11.07
16.41
-10.02 ÷ 8.94
21.56
-1.68 ÷ 1.39
112.17
-13.50 ÷ 18.28
Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 101
On he o he side, ega ding he ene gy pa ame e s, we
p esen he cooling capaci y in Fig. (6) and he COP in Fig.
(7) o he h ee inle p essu es o he o ex ube conside ed.
They ha e been ep esen ed e sus he low a io (1).
As can be obse ed in Fig. (7), a maximum in COP exis s
o each inle p essu e le el. This is because he exis en
ela ion be ween he cooling capaci y and he empe a u e o
he cold ou le low (equa ion 3). None heless, he alue o
he low a io ‘ ’ co esponding o he minimum empe a u e
Fig. (2). Ini ial check. O e all ene gy balance in he o ex ube.
Fig. (3). Ai ou le empe a u es o he cold and ho s eams s low a io o he inle p essu e a ia ion es .
0
2
4
6
8
10
12
0
P
ou
[Kw]
2 4 6
P
in
[Kw]
810
-5%
+5%
12
200
220
240
260
280
300
320
340
360
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
T
ou
[K]
T_OUTc HP T_OUTc MP T_OUTc LP
T_OUTh HP T_OUTh MP T_OUTh LP
102 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al.
o he ou le cold low does no coincide wi h he alue o
he low a io ‘ ’ co esponding o he maximum cooling
capaci y, since a a ia ion o he mass low exis s.
De eloping equa ion (3),
Q
0
=m
c
!c
p
!(T
in
"T
c
)= !m
in
!c
p
!(T
in
"T
c
)
(10)
de i ing (3) wi h espec o he low a io ‘ ’,
dQ
0
d =m
in
!c
p
!(T
in
"T
c
)" !m
in
!c
p
!dT
c
d
(11)
and equalling o ze o,
(T
in
!T
c
)= "dT
c
d
(12)
Exp ession (12) es ablishes he alue o he low a io ‘ ’
which maximizes he cooling capaci y. F om a de ailed
obse a ion o equa ion (12), i can be said ha he alue o
‘ ’ which maximizes he cooling capaci y di e s om he
alue o ‘ ’ which minimizes cold exi empe a u e, since i
hey we e he same he alue o he di e en ial
dTc
d
would
be equal o ce o. Acco dingly, he alue o ‘ ’ which
minimizes he cold exi empe a u e is lowe han he alue
HP = 563.35 kPa
5
5.5
6
6.5
7
7.5
8
8.5
9
0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95
P [kW]
PT_ou ,c
m_ou ,c * hou ,c
Fig. (4). Ou pu powe s o he p essu e es .
HP = 563.35 kPa
0
5
10
15
20
25
30
0.75 0.77 0.79 0.81 0.83 0.85 0.87 0.89 0.91 0.93 0.95
m
ou ,c
[kg/s]
285
287
289
291
293
295
297
299
h
ou ,c
[kJ/kg]
m_ou ,c h_ou ,c
Fig. (5). Mass low a e and speci ic en halpy o he cold ou pu cu en s low a io o he maximum p essu e alue.

Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 103
o ‘ ’ which maximizes he cooling capaci y. This easoning
can be obse ed on he ep esen a ion o he cooling capaci y
and cold exi empe a u e dependence on he low a io ‘ ’ on
Figs. (3, 6) espec i ely.
Rega ding he COP e olu ions p esen ed in Fig. (7), i
needs o be men ioned ha hei alues a e highe han hey
would be in an ac ual ins alla ions, since he cooling capaci y
has been ela ed wi h an ideal powe o he comp ession
p ocess, which in his assay is conside ed o be cons an o
each inle p essu e.
4.4. Inle Tempe a u e Va ia ion Tes
The second expe imen al analysis which is pe o med
wi h he o ex ube co esponds o he empe a u e a ia ion
o he ai inle (Table 2). This analysis has no been ound in
li e a u e, acco dingly his sec ion aims o highligh he
0
0.2
0.4
0.6
0.8
1
1.2
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Q
0
[kW]
Q0 HP
Q0 MP
Q0 LP
Fig. (6). Cooling capaci y s low a io o he p essu e a ia ion es .
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
COP
COP HP
COP MP
COP LP
Fig. (7). COP s low a io o he h ee inle p essu es.
104 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al.
impac o he ai inle empe a u e on he ene gy
pe o mance o he de ice.
Fi s , in Fig. (8), we p esen he e olu ion o he cold
ou le empe a u e o h ee di e en ai inle empe a u es
e sus he low a io. I can be obse ed ha he cold ou le
empe a u e is as lowe he ai inle empe a u e is. The
abo e discussed minimum empe a u e o a gi en low a io
exis s in he expe imen al e olu ions.
Rega ding he cooling capaci y, we p esen i s e olu ion
in Fig. (9) o he h ee inle empe a u es e sus he low
a io. A ligh inc ease on he cooling capaci y wi h he
inc ease o he ai inle empe a u e o he o ex ube can be
240
250
260
270
280
290
300
310
0.7 0.75 0.8 0.85 0.9 0.95 1
Tou ,c [K]
HT MT LT
Fig. (8). Cold ou le empe a u e s low a io in he inle empe a u e a ia ion es .
0
0.2
0.4
0.6
0.8
1
1.2
0.7 0.75 0.8 0.85 0.9 0.95 1
Q
0
[kW]
Q0 HT
Q0 MT
Q0 LT
Fig. (9). Cooling capaci y s low a io o he inle empe a u e a ia ion es .
Expe imen al E alua ion o he Ene gy Pe o mance o an Ai Vo ex Tube The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 105
obse ed. Tha is because he di e ence be ween he inle
empe a u e and ha a he cold ou le is highe when highe
he ai inle empe a u e is.
4.5. Insula ion Tes
Finally, we analyse he e ec o he insula ion in he
o ex ube. We e alua e his e ec by compa ing he ene gy
pe o mance o he o ex ube wi h insula ion and wi h no
unde simila inle condi ions (Table 3).
We p esen he expe imen al e olu ion o he cooling
capaci y in Fig. (10) and he COP in Fig. (11).
F om he analysis o he expe imen al e olu ions, i can
be a i med ha no app eciable di e ence exis s be ween he
esul s wi h and wi hou insula ion, and he li le di e ences
can be associa ed wi h small de ia ions o he es
condi ions.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Q
0
[kW]
Q0 WITH
Q0 WITHOUT
Fig. (10). Cooling capaci y s low a io wi h and wi hou insula ion.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
COP
COP WITH
COP WITHOUT
Fig. (11). COP s low a io wi h and wi hou insula ion.
106 The Open Mechanical Enginee ing Jou nal, 2013, Volume 7 To ella e al.
5. CONCLUSIONS
We p esen a es bench o an ai o ex ube in he
p esen wo k. I allows o modi y he inle condi ions o he
ai in o de o analyze hei in luence in he ene gy
pe o mance o he de ice.
The pape p esen s he expe imen al e alua ion o he ai
o ex ube unde inle p essu e and empe a u e a ia ions
o he inle ai o e a wide ange o a ia ion o he cold and
ho lows, i. e., a ia ion o he low a io. We alida ed all
he expe imen al esul s wi h he o e all ene gy balance in
he de ice, ob aining an e o below 5%.
We obse ed a minimum in he ou pu empe a u e o he
cold low in he inle p essu e a ia ion es . This minimum
was al eady e idenced in p e ious wo ks, as well as i s
ans e o he COP alues, howe e , his pape analyses he
causes which p oduce his minimum. We concluded ha i is
associa ed wi h he a ia ion o he mass low a e o he
cold ou pu cu en . Fu he mo e, we analyse he alues o
he low a ios a which he minimum in empe a u e and
cooling capaci y a e ob ained.
We s udied expe imen ally he in luence o he inle
empe a u e o he ai o he o ex ube, and conclude ha
he ou le empe a u e o he cold low is lowe as lowe he
inle empe a u e is. Addi ionally, he cooling capaci y is
highe when highe he inle empe a u e is, since he
di e ence in empe a u e be ween he inle ai and he cold
ou le ai is highe .
Finally, we e alua ed he e ec o he insula ion o he
o ex ube o cons an inle condi ions, and we concluded
ha he insula ion does no modi y app eciably he ene gy
pe o mance o he de ice.
NOMENCLATURE
COP = Coe icien o pe o mance
cp = Speci ic hea a cons an p essu e, kJ·kg-1·K-1
Ec = Speci ic kine ic ene gy, J·kg-1
h = Speci ic en halpy, J·kg-1
m = Mass low a e, kg·s-1
p = P essu e, kPa
PC = Comp ession powe consump ion, kW
Q0 = Cooling capaci y, kW
R = Gas cons an
= Gold low ac ion
T = Tempe a u e, K
G eek Symbols
ΔT = Tempe a u e di e ence
γ = Speci ic hea a io
Subsc ip s
c = Cold low
in = Inle low
h = Ho low
ou = Ou le Flow
s = Isen opic p ocess
CONFLICT OF INTEREST
The au ho s con i m ha his a icle con en has no
con lic o in e es .
ACKNOWLEDGEMENTS
The au ho s a e indeb ed o he Spanish Minis y o
Educa ion and Science (CTM2008-06468-C02-02/TECNO)
and o he Spanish Minis y o he En i onmen and Ru al
and Ma ine A ai s (200800050084716) o hei economic
suppo o his wo k.
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