CALIFORNIA S'TATE UNIVERSITY, NORTHRIDGE
AN INVES'I'IG.trriON OF l1. DEVICE
·ro
REDUCE THE
\I
·EXHAUST PRESSURE O.F' AN
I~'TERNAL
COMBUSTION ENGINE
A graduate project submitted tn partial satisfaction of
the requirements for the degree of Master of Science in
En.e:ineerin.,..
<J
0
by
DwaynfJ Herbert
~ut.scher
The graduate project of
California State Univsrsity, Northridge
ii
·TABLE OF' CONTENTS
Number
I
II
III
Chapter
List of Figures
iv
Notation
v
Abstract
vii
Introduction
1
Venturi Theory
4
Venturi Analytical Hodel
11
Hodel Results
12
IV
Water Table Testing
19
v
Wind Tunnel Testing
2_5
Venturi Summary
29
VI
VII
VIII
Interne;~
Combustion Eng:i.ne Tbeory
31
Eng.ine Analytical Model.
Model Results
IX
Conclusions
40
42
LIST OF FIGURES
Number
Figure
Fag~
i
Venturi Device
2
2
Venturi Cut.avray
5
Venturi Flovr vs. Free stream Velocity, U....
13
Throat Pressure vs. Freestream
Velocity, U....,
13
-·r.:;
Freestream Diffusion vs. Exit Diffuser
Angle
14
6
Freestream Diffusion vs. Inlet Area
15
7
Capture Ratio vs. Throat Width
16
8
Throat Pressure vs,. Throat Width
16
9
Capi:.ure rlatio vs. Diffuser Recovery
Coefficient (Exh;o~ust Pipe Removed)
18
10
Venturj_ Inlet Strearnline.s
22
11
Venturi Diffuser Streamlines
23
12
Venturi Streamlines (Exhaust Pipe .Removed) 24
1.3
Capture Ratio vs. Freestre2m
Velocity (With Exhaust Pipe)
26
1 I,
•'T
Capture Ratio vs. Freestream
Velocity (Exhaust Pipe Removed)
2'/
15
Indicated Horsepower Decrease for
a 4.4 PSI Back Pressure Increase
16
Volumetric Efficiency vs.
Venturi Throat Pressure
''7
I f
Indicated Horsepower Increase vs.
Venturi Throa'.;
ecsure
iv
.3'7
39
NOTATION
A = area
BHP ·- brak.e horsepov1er
c =
n
\.J
p
any constant
-· diffuser recovery coefficient
d = diameter
ev
= volumetric
efficiency
evi -· ideal volmnetric efficiency
e vt -- constant volumetric efficiency
F - fuel-air ratio
FHP
:::
fl"iction horsepov1er
F
::
Froud.
r
number
g -- gravitational constant
h
H
= water
- total
depth
p1'essure
HP = hor ser;ovrer
IHP -· indicated horsepower
IMEP
,J
= indicated
= mechanica]
mean effective pressure
equivalent of heat
k - tcleal gas constant
ki-t = inlet loss coefficient
L ::: perimeter
HPH ·- miles per b. our
N
= diffuser
length
P - static pressu:cs
Q - volumetric flow rate
v
Qc
r
rc
= heat of
= radius
co~bustion
= compression
per mass of fuel
ratio
RPH = revolutions per minute
s
·- piston sneed
u -- velocity
w
.::
throat wiclth
0(.::: diffuser half angle
~
or*
~
=
inlet half angle
-- boundary l<::::..yer thickness
= thermal
efficiency
t> = density
e=
one dimensional case angle
Subscripts·
b
e
= exhaust
= exit
h -
back pressure
hyd:cc:~uli,c
i - inlet
piston
p
t
-:::
throat
1
-·
any locati.o:r1
2
= any Iocatj.o:n
= infin].ty
oo
Superscripts
0
'".: degrees
vi
ABSTRACT
AN DTVESTIGATION OF A DEVICE TO REDUCE THE
EXHAUST PRESSuRE OF AN INTERNAL COHBUSTION ENGINE
by
DvJayne Herbert Deutscher
:Master of Science in Engineering
December, 197L!.
The device under jnvestigation seeks to lower the
exhaust bade pressv..re of
e11
internal combustion eng.ine.
It does thi.s by emersing a VPnturi ina freestream and
capturing some of the flow.
The pressu:t'e at the throat
of the ventrui is lowered due to the acceleration of the
flow :Ln the convergi.r:g inlet.
the exhaust pipe i.s placed.
the ven.tur:L throat
cylinder-~
pressure~
At the tbx·oat the exit of
Tb.e pipe
E:xj.t
pressure is
and therefo.re the eng:i_ne
s, ·;:Jack lH'Gssure will be
lowered~
A theoretical treatment of the venturi is presented.
'11h8 equat::i_rJrtS are de>Ie1oped for the flOW as
and flows tru'ough the venturi.
developed
fro~
j_ t
approach8f:3
An analytical model i.s
these equations to predict the venturi 1 s
vii
this ,'ffialytical model a..re presented.
The results of
water table a11d vrind tunnel testing a.r-ce presented.
'l'he resv.l ts o:f the analytical predictions and testing
are compared ru1d explained.
An analytical model of an internal combustion engine
is developed from theoretical equations presented.
genel:'al ·results from
:~.,:i.d.s
model arE premrnted.
The
Finally
the results from testing and the venturi analytical model
are incorporated into the engine model &'1d the overall
performance of the device is presented.
v:uJ.
I. IN'TRODUC'fiON
This report covers the results of an analytical and
experimental investigation of a device designed to lower
the exhaust back pressure of a.n internal combustion engine.
The devj_ce is patented and the inventor, 11r* Ben Venturi,
requested that California State University, Northridge
School of Engineering test and evaluate the dev:Lce.
The device, referred to as venturi in this report,
is a two dimensional, converging-diverging nozzle.
mounted on the engine's exhaust pipe.
the throat of the venturi.
It
~s
rrhe pipe
The device is shown in figure 1.
When the automobile is moving, the venturi \Hill capture
sorne of th.e freestrearn aj_r, accelerate it to 1Nard the
t.l-t?~oe..
t
(therefore lowering the static pressure), and then reexpand the flovr in a diffuser.
The exhaust pipe exit
pressure will be the static pressure at the venturi throat.
The engine cylinders will, therefore, have a lovrer back
pressure.
Decreasing the back presstrre increases the
vollmletric effi.c:iency and cEgine power.
, rrhe _problem arle.l;y-zed c ons].ste6. of several pa_rts:
1.
Determine the volume nf air captured by
the \rerrt uri.
Determine what effect lowering the cylinder
back preEJsure actually had on engir:e power.
3~
Determine the effect of the exhaust ::=-·ipe
flow being added to the venturi
flo~.
2
3
4.
Optimize the venturi if the actual design,
provided by the inventor, proved not to be
optimDiflo
While a venturi used in a closed piping system is
a common device, and a converging-diverging nozzle is
also common in freest:rE.d.Jil supersonic flow, a search of
available literature revealed nc data or application for
a venturj_ emersed in a subsonic,
free stream .flow.
The
theoretical approach was, therefore, to divide the venturi
into flow regimes that could be analyzed.
Equations aJ..'e
written for each of these regimes and summed to determine
the overall performance O .l the venturi.
L'
Testing was begun
by modeling ·the venturi on a wa:ter table and visually
observing the flow
pat~erns.
Ccncnr-reDtly an analytical
mode1 vms developed, using the theoreti.cal equations, to
predict the VE!nturi's perfo:r·mance.
Also, a.n analyticaJ.
model was developed to predict the effects on tte internal
combustion engine.
Testing was concluded by testing two
variations o:l' thG device in tb.e low speec1 0r:Lnd tunnel.
Th~.Ls
re:port YJill discuss the result.s of tests con-
. ducteci, c:md VIill compare these results to analytical
prediet1.m1s, attempting to explain anomalj_es
ex1st.
~vhere
they
Some opinions will be given as to the merit of such
a device along vJ:Lth suggestions of aro.::ts for future study
and refi.nement.
I I. VENTURI 'J.1HEORY
The behavior of t.hs flovr throughout the venturi
and immediately u.pstream can be analyzed by using
Bernoulli's equation (equation l) with the appropriate
Equations 1, 2, c?Jld 3 a:ce
1oss coefficients added..
vvritten in their general form and stations 1 and 2 refer
to any two theoret.ical locations that the equation is
being applied betv:een.
(l)
D
"'"2
This basic form of Bernoulli 1 s equation can
in
tsr~s
bE~
re-written
of areas and volumetric flo·N rate, Q.
=
(2)
aJ1d re-arra:1z;ed i.nto the form:
p
1
_,
.,
'
\
21
I) - t'(~., )2 Ii 1 (A
2 .-
'J
n
c:.. 1:'-2
I
I
I
I-
(3)
21
-· I
~
lc,;_
---
.
-!
6
-•]
I
-~
The total flo'N of the venturi is consta.nt
fror1~
a point
ahead of the inlet (infinity) to the exit, with the
exception of the addition of exhaust flmv at the throat.
The treatment of this mass addition will be discussed
later in this
sec~1on.
The change in pressure, P
"l.s deterrn:Lned by t11(7 a.reD.s, A and A •
2
1
/,
'i~
If A2 /A
1
1
>
- P2 ,
1 there
t
Pt
At
Q
,/
Figure 2: Venturi Cutaway
is a static pressure decrease from station l to station 2s
If A /A < 1 the opposite j_s true, P - P2 , is positive
1
2 1
and there is a static pressure rise or diffusion.
Shown in figure 2 are the actual ventur1 sto.tions
th~t
will be referred to in this report.
Bernoulli's
equation i.s "\vritten between these points ,g_nd corr·esponding
presmu'es e:<.re calculated basod on the vent uri flow.
Ahead of the venturi the air velocity is that of
the automobile.
The streamlines e-J:·e assumed. to be
par:-3.11el to each otlw:c and perpendicular to the venturi
p_
=
H -
P Uoo
2
(4)
2
As the flow approaches the inlet it isentropically
diffuses from a point upstream (infinity) to the inlet.
It diffuses because all the flow is not captured by the
venturi.
If all the flow were captured, the losses
throughout the venturi would have to be zero.
It is convenient now to define capture ratio:
Capture Ratio
Actual Flow Through Venturi
Frontal Flow Based on Ai
= Total
=Q
-
(5)
Consider a mass which is captured by the venturi when
it is at infinity.
It has velocity
area Aco and therefore flow Q
= U,x;
u~
l
Aoo •
crossectional
This control
mass approaches the inlet and diffuses to Ai-} . Uj_.
capture ratio
Q
Q....
can
=
The
now be shown to be:
Ua.oA..a
U.~o Ai
=
A"""::.
(6)
A-'..L-
Writing Bernoulli's equation in the form of equat:i.on 3
from infin:L ty to the inlet the presstrre change is proportion:3.l to the capture ratio A oa /A-".
J.
.?:i. -
Po....,.,
(7)
I]
(
A oo /A. is less than one, therefore, a pressure rise
l
from infinity to the inlet.
From the i.nlet to the throat the flow goes through
a contraction (A.< A.) and there is a corresponding
"C
l
decrease in static pressure.
Also there is·a non-
recoverable pressure loss due to the geometric change
Equation 8 defines the resulting
in the flow passage.
pressure at the throat.
-P
·j
-
=
E'
~Q \} 2 lll
---
2 A_,
.L,
- Ai ) 2] - k~
If
-
J.
,_A_
\
t
.
~~
- i-~1~--,)
! 2;'
\
( Q, \ 2
'--)
\ A.l. I
'J'
(8)
1
As shown before the first term on the right side of
equation 8 will yield a c:ecrease in pressure sine";
Ai/At
> l.
The second term:. the nori~·recoverable loss,
also causes a presstrce decrea.se.
of a loss coeffi.cient k.
The second term COl'H3.ists
. times the downstream ( tlE.,os.t)
l-"C
velocity head.
Data for this loss C()efficient was tel{en
(reference 1).
Reference I is for a one dimensional,
symmetr:ic convergence case.
T'he data is :Ln terms of total
convergence angle 28, downstream corner :tadius r and
downstream diameter d.
Tl:te venturi 1 s t'vvo dimensional
contraction has a half angle of {J
= 45
degrees.
To
correlate this convergence it is assumed that the venturi
is symmetrtca1 about the centerline.
hD.f:;
one
strr::J.:.g:::.~~
The contract:Lon
VJC:?,ll (the exhaust pipe) and one
con~~
8
verging wall.,
based on
~
A rate of change of area
== L15 deg.1:?0}es.
calculated
~:vas
Using this rate of cho.nge the
equj_valent 28 1.-rc.:.ts calculated for the one dimensional
case..
The
equiYGJ~ent
2& is
53.1 degrees.
To correlate
the r/d relati.onship the downstream radius on the convergent wall
,,:;;.;u3
used and a hydraulic di.ameter was
calculated f.:c·cm reference 1.
=
(9)
4A,_L.
1
From the t1::troat to the exit the flow diffuses.
The
exit :pressure is calculated from the following equation:
+ p
(10)
t
The static pr_•,.;::;ssu.re recovery coefficient; C , data was
p
taken from a :pa_per on tvm dimensional diffusers by
Renea.u, Johnston and Kline of Stanford University
(reference 2).
The data is presented in terms of the
total_ diverge?J:ce angJe 29 and a non-cJ.im.enslonal length
correlatio?J
"t~r<:.:u:;
employed as in the case of the inlet
loss coefficient.
The jet from the exl1aust pipe is
assur::zed to prov.ide one strc:dgbt wall.
·J:he recc:)v'"·e:r·y plots of reference 2 are also in terms
of a throat, non,-dimer:..sion.al, boundary layer thickness
9
diffuser j_nlet area blocl:ed by the boundary
The
layer~
a
data used fm:: the ventm:-j_ application VIas taken from
·· ' 11 a t.uri.)U
·
- l__ enc' b: ounc1ary _-.ayer
l
' ' · 1
2 co
p l o-c' vrrc
-cnlCi;:ness,
o. 015.
*/1·,:/r
--
rrhis is the thinnest boundary layer for which
there \'las dc:rta available for the entire range of
considered :c:r this paper.
N/W' s
The venturi bounda..:.."'y layer
develop only along the exhaust pipe.
is assumed
The
other side o::;: the throat has a sharp convergence with
e.lmost no fiovr on that VJall.
1<-"'..ter vrith t1w
experiment.?~-
A conclusion di.scussed
work.
The ventu:-ci boundary
layer thickness at the throat is
W = 0.188,
o(_
= 15 degrees and U c.o
for
= 55
111PH.
'l'he
trt:.:...nnel~
the boundary· layer thickness, the higher the recovery
the recovery· coefficients are Lased on a mass
velocity at the di.ffuser inlet.
a·~i~rage
A thicker boundary
layer cause.:'• a higher cure velocity at the throat and
the r•3cov-e:cy :is not as laTge.
SumrJ.a·cizing the ven tul'i flow regimes:
1..
1
~. he
freest.ream :flcrw that is captured by the
vesnturt diffuses from a point ahead of the
V(~ntu.rl
2.~
~:r:~e
to the ir:tlet vlith a resul tc:mt static
flew then accelerates to the throat, The
st,atj~c
:oressure decreases and there is a non·-
10
3~
The flmv is diffused from the throat to the
exit, but with another loss proportiona.l to
( l - CD) •
.t
At the exit the pressure, Pe' must be equal to the freestream static pressure, Poo
For this to be true, the
pressure rise of :cegir.1e one must equal the pressure
losses of regimes two cmd three.
1.1 he flmv rate that
satisfies these conditions is the flovv the venturi will
capture~
III. VENTURI ANALYTICAL HODEL
The preceeding equations and assumptions are the
I~ivdel
basis for an analytical
developed to determine
the amount of flow captured by the
venturi~
computations a capture ratio i.s assumed.
in
pl~essure
'The changes
a.re calculAted resulting in an exit pressure.
If p e is less
The calculated P e is compared
to Poe
.
...
than Pea
To begin
, the losses were too large, there was too much
flow assumed.
~Che
progra..ra now iterates the flmv rate
until the absolute value of the differen.ce in pressures,
Absolute [ \-e
lp
- _o,()
p
)/ p .,..,
J
'
is less than 10-8.
The IJ1).rr)ose of the lJrogram was to:
1) predict
ana.lytically t:he resul·cs th;:;t wou.ld later be measured
in testing; and 2) optimi.ze the geometry of the ven t.~:t.:ci.,
As a basis for the geomet.ric parameters the inlet c'Jnvergence angle and exit o...::re& used by the
imrento:.:.~
werr.:;
held constant •. rrhe throat area (in terms of W) and
. diffusj_on c:mgle
were
d.
~v-aried..
For each V! 2.:.11d
the
o<.
combination f.i vo freestreaJTI velocity cases, · 25 HPII tc
65 HPH
VJ·Ere
ca1c.:u}ated.
held c onsto...:l "s, reducj_ng
diffuser length ?L
1\T/VT
"
1·
=
L·!·./
t:'
· ·
.,
~,
.. o
anct
G
"[:)
Ac
S].nce the ex:i..t arGa has bGen
ex
d ... =
-- (). 71 ..
that at N/!f = L:-8, C
p is
results in
0.11
inc:c<::as:Lng
15 degrees and if:! = 0.188,
Reference 2 yields the result
';~rays
less than 0. 70.
These
conditions ther2fore yield very close to the m.s.xi.nn.lm C
p
1. 1
' '
12
Two inlet loss coefficients were considered,
considered.
l--c = o.oo
would only be
k ..
A zero loss coefficient
and.
ssible if there was very little flow
=
convergence.
0. 05 is the coefficient tal:en from
reference l.
HODEl, RESULTS
Figure 3
sl1.!J'NS
the increase in flow rate through
the venturi as tJ:w velocity is increc:tsed.
constant velocity, Q increases as
e1..
Also, at
dec::'eases.
This
corresponds to 2.:n j_ncreasing recovery coefficient, CD,
.1:
thus reducing t.tte total venturi losses.
between curves at U t>O
.,
=
The dj_stance
constc;mt j_s proportional to th9
. cp•·
cnange ln
Cp changes O. 08e.
degrees C
p
~:he
=
30 degrees and
o<.
-
20
changes 0.22.
In figure.
shown.
Betvieen oc
Z;.
the effects on throat presm. rre are
res'.'l.1t.s are proport,ional to those shovm in
figure .3 since e::n increase in flow will re.sult in a
lower
'\
.l +·.
'.....
Here :it j.s seen that sm.eJ.ler
tX 1
s result in
lower throat p:r.·esr::;ures ..
IJ'l::e amoun.t of diffusion from infinity to the inlet
l'
..,
C'
This is significant because, as
expla.:Lnc·d before, this pressure 1·ise VJill equal the
venturi pressure
losses~
The greater the diffusion)
the greatGr the JD.llowablo losses in tne venturL
13
w= 0.188 inch
Q
0.32
rt3/sec
0.,28
~--~~-~1__-J~--~~---~_J
45
U-.?
55
65
!VLPH
Fig. J: Venturi Flow vs. Freestream Velocity, u_
14.68 [
14.64.
·o
.. t
14.60
PSI
14 .. 56
·' 4
.l.
~
r
!
t:;':l 1.·--""'
-
Uca MPH
Fig. 4, Throat Pressure
vs~
Freestream Velocity,
U~
14
-------UoO=
------
- - - - - - - - - U<>O =
65 NPH
55
JYlPH
w = 0 o 188 inch
- - - Uoa =
0.021
45 l•:i.PH
- - - - - - - - - - - - - - Uoa == 35 MPH
0.020
25
0(
35
45
degrees
Figure 5: Freestream Diffusion vs. Exit Diffuser Angle
At
c<-
equal a constant., diffusion increases as velocity
increases&
This allo>:Js more flmv as shown in figure
Of interest is the sl5.ght j_nCJ'ease in diffusion as
increases.
mig~t
is
ot...
This does not result in a flow increase, as
be expected, becc_use the .recovery coefficient
decreasi~g
to
The effect: of :i_nc.l'easing
li:lOre
l'he plot iE
diffusion c.o
tal.;;~e
non-dimr~nsionalizecl
1
.,,
cp
at a faster rate.
The arnount of freestream diffusion is
allr>rr.L7.'.g
3~
propol~tional
A.l and thereby
place is shown j_n figm:e 6.
by dividing the amou..nt of
d.i ~f ftts1.cJn ( .r.'-· :i - P ca) by the freestrean1 velocity head (H - P oo ) •
15
1,.000
0 .. 998
w
0.996
= 0.188
lJ..o=
inch
55 MPH
0.994
P1-Pc.o
H-Poc
0.992
0.990
0.988
0.986
~
0.981
b-------~--------~·--------J
1
2
3
________
_J
4
times P, 1
Figure 6: Freestream Diffusion vs. Inlet Area
Total diffusion to zerc vcloci ty, rmuld have a Y<'l1-ue ') f ot:,_e.
The plot shows that diffusion can be increased by increasing the inlet e..rea.
The effect is actually less dramatic
thc:m the plot indicates sinc8 in ,:;_11 cases diffusion vras
unchanged (A-; "' 1).
--'-
The prograr.:1 :i::"f;sults showed tho.t
j_ncreasiDg the area four times increases the flovr less
than 0.01 percent.
}'j_gure 7 shows tho capture. ratio as a
and c<..
It is
approxima~~ely
funct~ion
of \'!
consta11t for all freestrec::m
16
~--~---LL--~--~--~--~1--,-L_~
.19
.25
o)l
.J8
w inch
·Figure 7: Capture Ratio vs .. Throat Width
\
c.(=
\
U
15°
=55
------
--
'\...~--------'•
.
MPH
w irtch
Figure 8: Throat Pressure vs. Throat Width
17
velocj_ties considered.
capture ratio.
area.
'J1 he smallest o<.. has the greatest
Captm,e ratio also increases with throat
This is because tho losses are based on the
Increasing the a:cea reduces the
throat veloci_t:.y head.
veloeity head c;md the losses.
Figure 8 shows the throat pressure as a fnnction
of throat area.
It is seen that the lo·west pressure i,s
attained at 1J - 0.188
inch~
Only
0(..
=
15 degrees is
plotted since 'this has already been shoVJn to be the
optimum angle considered.
The lowest Pt does not corres-
pond to the higher flow rates attained at lal'ger throat
areas..
It is a tra.deoff between high velocity hea.ds
(lo·wer static :presSl..JJ::'es) at the throat and reducing
the
T..-entu:;.~i
]_o:sses (lower throat velocity head,s) ~
?~w
=
0.188
bet"l.~reen VJ =
sharp fall of the curve
is due to a
r;::.~:pid
-
rise ]_n Cp •
0.13 and W
At W = 0~ 1~;
- the N/VJ ratio
exceoded the naximm11 discussed earlier a.nd. C
p
clecTea:::>:':Hi
rapidly.,
The CEJ.se
calcu.lated.
'.fOI'g't:"IllCO
l"!i th
the
exhaur..:d~
pipe removed vras alEiO
T!J.e venturi :novr has a 90 cleg:.cee :i.nlet con-
and a 90 degree
diffuser~
rrwo dimensional
dj_ffnser literature suggested that some recovery vrould
exist for a 90 degree diffu8er.
pred:JJ:;t,::d
Figure 9 shows the
th<3 independent
variable~
Two t.-td.et J..oss coe:f'fj_cients are plotted. lr.l--c. . . . () ~ 08
j __ s
18
0.28
0.27
A~
Ai
0&26
--- -
kl-t =
o.oo
=
0.08
0 .. 25
Cp
Figure 9: Capture Ratio vs. Diffuser Recoverv
Coefficient (Exhaust Pipe Removed)v
the loss coefficient ta1-;:en from reference 1 using the
hydraul.ic di.c:1!lietsr corr'ela.tio~1::1 discuss8d before.
IV. '.'lATER TABLE rrESTIHG
The investigation on the water table YJas undertaken
to gain an e::-:lpirj_ca1 understading of y.;hat was happening
to the flow stream as it approached and flowed through
the venturi ..
The uater table. prov:Ldes a means of
visualizing the floD.
A one dimensional model is con-
structed on the surface of the table.
The water, when
As the
undisturbed, flows in a sheet of constant depth.
water approaches the venturi model some of the f'reestrE)<"u'11
flovr diverges and goes cLround the Inodel and sm"1"' is
captured.,
Styrofoam balls are dumped into the freestream
flow ahead of the model.
The balls follovr the st.rean1-
By u.sing ti-c:1e lo.pse photography the str·eamlines
are seen.
The improtant non-dimensional modeling para-
meter is the Froud number, defined in equation
u
11~
(11)
(g X h)~­
11he Froud mrrn1)er is the ratio of the velocity to the 1.vave
t .
propagavlOn
..1.
•
'
V8~0Cl~Ya
nh
.t d
l_e macnl·u,e
"-' ~r
,
]·_ndl. ca_·tes
0~
71
-
different flo.w behaviors, similar to the behav:Lor of
compressible flou as Jndicated by
}~ch
number.
(For
Froud number less the:m one the flow accelerates in an
area contractj_on and decelerates in an area expax1.sion,
t.he saHe as for flow vrith Hach number less than one. )
The ven-'curi i.B operc.,ting subsonically so the Froud number
on UJ.e nater table vras fj_xed at. less than one.
19
The tests
20
Vlere conducted at F,.. = 0.55, the l.mvest Fr that could be
attained.
as F
Reynolds number effects are not as iEJ.portant
if the Reynolds number is high enough.
r
To increase
the Reynolds number the model was constructed at three
times scale.
This produced a Reynolds number greater
than 2 x 10~-.
Several geometric variations of the same
basic device v:ere tested ru1d the results photographically
documented.
Figure 10 shovrs the freestrear.a flow ahead of the
venturi inlet.
The streamlines are seen to diverge as
they approach the inlet producing the freestream
diffusion discussed earlier.
It was originally believed
that by observing which strear.alines vrere
forc~3d.
a:r·ound
the venturi. and which streamlines went into tlH3 ven-turi
a capture ratio could be determined.
This method pro-
duced capture ratios of 22 percent to 33 percent,
significantly hj_gher than predicted by the analytical
model~
Closer observation shovls that there is a lo.rge
stagnation ar·ea (encircled in figure 9) in -the ven.turi
j_nJ.et~.
~~he
ro.ass of·
f]_u~id.
in t-h.is crree. j_.s n1ostl:r stagnant
although some mc:Lss is ent.rained by the flow near the
strait~ht
VJalJ.ed exhaust pipe..
a.nce o:f .flow being capttiT'ed.
This produces the appearThe streamlines do xiot con-
verge in the inlet as they should if the flow were being
accelerated torrard the
~~e
throat~
Also the styrofoan balls
seen to be held motionless on the inlet walls.
21
Dovmstream of the throat almost no lines can be seen.
This suggests that very fevf balls are actually captured
and go through the throat.
Figure 11 shows the flow from the exhaust pipe
mixing with the flow through the venturi.
The flovJ in
the exhaust pipe is flovring at approximately the saJ.Ile
velocity as the freestream.
A large number of balls
were dumped into the venturi flow just upstream of the
throat.
the
The exhaust flow is seen diverging as it leaves
pipe~
The divergence angle j_ncreased as the exhaust
flovv rate was increased.
This produced
a.
smaller effec- ·
tive diffuser angle than was assumed in the anaJ.,ytical
(lJ.'he analytical model assumed the exhe..vst flow
formed one straight wall of the diffuser.)
The jet,
exhaust flow is actu.ally entraining the venturi flow
along their boundary layer.
'I'he venturi flmv is approxi-·
mately stagnant along the stationary diffuser vmll.
Figure 12 shows the streamlines with the exhaust
pipe reEJ.OVed.
the venturi.
rrhe flow j_s primarily stra:i..ght through
There is only a small ;:..::.>·:1ount of
convergence~
A sit1ilar amount. of diffusion is seen downstrerun of the
22
0
23
~--=
24
(\.)
V. \'liND
TUNNT~L
TESTING
Two configurations were tested in the low speed wind
tunnel.
The first configu.ration tested vras provided by
the inventor.
It had an inlet convergence angle
degrees and diffuser angle
width is 0.13 inches.
~:he
o< ::;: Lt.5 degrees.
@ = 1+5
The throat
exhaust pipe extends approxi-·
mately four inches upstream of the inlet.
r:L1he
pipe VJaG
left open to capture some oi' the freestream fl.ovJ.
r.rhe
second configuration tested had the same venttu'i geometry
but had the exhau.st pipe :rem.ovedo
this
conf~~_gm'ation
is 1 .. 5 incheso
The throat v1idth for
Both configurations
were te.sted over a range of freestre.sun velocities from
l t 6 '!fDH
l'1l: ,. t 0
11 ''P,.,.
ll+9 r.l
.ti.
While most of thir:; range is faster
than the venturi's normal oper-:-1ting vel;)ci ty, the capture
ratio ha,s been shown to be approximately independent of
freestream v-elocity.
To determine the a,mount of flmv
captured, the inlet side of the model
wa£~
instrumented
with static pressure taps at three locations:
l) the
inle·:::; 2) h,"SL""'.f 'Nc..y bct·ween +,hs i:nlet ar:td the thz·oat;
an~3)
the throat.
As the flow converges, due to the
area change, the static pressure docrer-o.sE;se
The quantity
of fJ.ovJ can be ca.lculated knm'ring the ch,s.nge in aJ:'ea and
preL:>:::>u.rc~
.A
foi~m
of equation 3, r\0Nr:Ltten here for
26
0.067
G.
o.o66
A._
0.065
Ai
0.064
0.,06.3
U00
MPH
Figure 13: Capture Ratio vs. Freestream
Velocity (With Exhaust Pipe)
(3a)
The models were also tufted along the inlet and exit wall
to visually observe the flow.
·The capture ratio :for the venturj_ with the exhaust
pipe is shovm i.n fj_gu:re l.'3.
"
02:,. A<:><:>
/"Ai
vE:locity at
n/'"5 •
= ("'J_,uo
t..
cayft.-Ure
r:·'
rne
.
a.
It has .:m B.ri th.metic average
.
t'
ra·1.0
.
lncreases
_c;
·.c.h
vrJ_Ld-
2."at.e of ::; .. 6 x 10 " percent per :H:PH.
of A <.?0/A.l
smaJ.l deviab.on f:com t:he aE;sum])tion
. to the :increased exhau.st flow.
This
= constant
The open
exhau;:>t Fipe was capturi..ng more flovv at highez' velocities.
The incr;s.str3ed exhaust flmv \'i:Lll change the operaU.on of
the vent uri dif fuE,er..
.f'>. t
al.rca.dy bEH·:n. srwvm th.::;t
decreases, thus a
hi~her
hi.gher exhau.st flovrs it has
~~-1J.e
eff'ecti ve diffuser angle .
rocovery coefficient.
A higher
2?
G
G
0.2.3
~--~~~._--~--~--~--~~--L-~~--~---J
120
U00
140
MPH
Figure 14: Capture Ratio vs~ Freestream
Velocity (Exhaust Pipe Removed)
C
p
wi.l1 allo·w 1nore flov1 to be captured.
Also diffuser
recov-ery may :improve with increased flow, a result of
highe.r freestrea.m velocities.
r:L'he tufts along the inlet
wall showed :rw flow· at all over the entire range of
velocities tested.
~ehe
tuft.s along the exit wall showed
separation pr:;:;.sent over the entire range of velocities.
The back flow aj)pea..red to increase as the free.strean1
velocity was. lncreased.
'l'b.e
con:Jtj_gul~ation
with the exb.aust pipe removed was
tested and t.l:u.:; eapture ratio data is shovm in figure 14.
The ari thmet.i.c average of this data :Ls A oo /A. = Oe2Gl.
l
is
d:i~avvn
capture ratio increases at a rate of
per HPH.
'rhe data points also have
on
28
wide fluctuations from the fared curve.
'11hese fluctua-
tions are probably a result of fluctuations in Cp.
Reference 2 indicates unsteady recovery with diffuser
angles in the r2.nge of
Lf-0
to 50 degrees.
With 28 = 90
degrees larger fluctuations can be expected.
'l'he fact
that A oa /A-; increases and the fluctuations become less
-'-
suggests, as before, that the diffuser performcu"'1Ce is
improving as velocity is increased.
VI. VENTURI SUNHARY
The test data and Cillalytical model both predict a
small 11e.rcentage of the freestream flon vrill be captured
by the venturi.
The capture ratio is just slightly
greater th&'1 the throat to inle·t aTe a ratio, At/Ai
0. 0505 for the ventu..ri with the exlw.w3t pipe.
yielded A o.a /Ai
A~/A.
l
= 0. 065
= o.c)606.
=
rr:est data
c;md the analytical model predicted
The area ratio ·without the e:xb.aust pipe
is At/Ai = 0.24 and test data gives _A.oa /Ai
=
()~,26L
If there were no recovery, the capturE.' ratio would be
equal to the throat to inlet area ratio since P.L ... P
t-
p CoO
e
=
•
The proceeding capture ratios quoted for the
analytical model are based on an inlet loss coefficient
k.l - ·t = 0. 0.
This vms concluded since with a
s1~1all
flow.•
only a. small contraction is required from the inlet to
the throat.
l'Uso
supporting this conclusion is the
observa.nce, cl"uring viind bmnel and water table testing,
of little or· no flovi along the inlet
wall~
<-_The fact that tests yield a la_rger captm'e ratio
than tl1e analyticB.l model cc:m be explainod for several
reaso.:1.s.
'rhe exr1aust flow actually entrains some of the
venturi flovi along their boundary.
This has the effect
of st.1.ckin.c; flov.J through the vent uri.
flow widens out after it exits the
Also, the exhaust
pipe~
The analytical
model assumed the exhaust flow to provide one straight
30
VIall.
This fanning out decreases the a.rea rate of change.
For a decreased area rate of change a higher diffuser Cp
should be used. The higher recovery coefficient would
allmv more flow th.rough the venturi.
Both of these
phenomena, which are not j_n.cludecl in the analytical model,
will increase the computed flow.
Also, as mentioned
be.fore, the throat boundary 1aye.r thj_ckness is thinner
than the assm::1ed thic1<:...ness.
layer the higher
cp •
The thinner the boundm:·y
Co:c.1paring test data to the plots
of figure 6 suggests thai:: the effective diffuser a.ngle
is e.pproxirflately 35 degrees.
This would give a C
p
=
0.35 instead of Cp = 0.25, which was used in the analysis.
The captur·e ratio, from wind tunnel testing, for
the venturi vlitb
110
exhaust pipe is 0. 261.
If again
k.l.- t is assumed to be zero, figure 9 shows the recovery
coefficient to be
shovm some
0.155.
ex~n<::. :nsion
'rhe vrater table test, figure :U2,
dovmst.ream of the throat.
. .1
VII. INTERNAL COMBUSTION ENGINE
~CHEORY
The power output of an internal combustion engine
is directly proportional to it's volumetric efficiency.
The volumetric effj_ciency, e v , is a function of variables
such as engine heat transfer, inlet manifold Mach number,
fuel to air ratio, general engine design, valve capacity,
timing, compression .ratio, exhaust pressure and many
more.
The exhaust pressure, while just one variable,
has a very large effect on volumetric efficiency.
Reference 3 states that
11
tests indicate a decrease of
about ll percent in power for an increase of
back. pressure".
4.4 PSI in
It is this exhaust pressure that the
vent.u.ri device t:-;eeks to r-ed.uce. ·Reducing Pb will increase
110 determine the effect of lowering the back pressure
an analytical model of an j_:riternal combustion engine was
developed.
e~gi~e
ThA basis for this model is the assumption
variabJos.
t hefx i so I ated.
The
e~fect
of Pb on e v and pmver was
F'or purposes of c ompB.r:.Lson the indicated
horsepower 1 IHP, :Ls calcula.ted.
Brake horsepower, as
defined .in equation 12, is usually of interest in engi.ne
I
per fO!.'DJcmc e a:rta.Ly si. s.
32
Brake HP
BHP
=
(12)
In di_c at Ed RP -· Friction HP
=
HIP
FHP
It is seen that if friction horsepower, FHP, is assumed
constant, an increase in IHP will produce an equal
increase in BHP.
FHP
approximately constant at con-
stant RPN.
A useful concept i,n the ru:u:a.lysis of internal combustion engines is mean effective pressure.
It is equal.
to that constant pressure whj_ch, if exerted on the
piston for the whole outward stroke, vioulcl. yield
equal to the work of the cycle.
wol~k
In the case of IHP the
equivalent mean effective pressure is Indicated Mean
EffecLi_ ve Pressure, D1EP.
IMEP = J x p x e
v
(13)
None of the var::i.ables on the r:Lght side of equation 13
is a function of back pressure except ev, so they are
Equation 13 then reduces to a
assumed to be constant.
constant times ev.
C x ev
Reference 3 also states
11
(14)
H1EP is reduced one pound for
each po 1J.nd the back pressure is above atmospheric because
of the extra work done by tb.e piGton during the exhaust
strol\e 11 •
Equatio:n. 15 accounts for this change in pressu:re:
(1_5)
cSJ.se of
The
pressure change is added directly to the IMEP.
The power is now calculated from equation 16:
1
IHP = +..,. x IHEP x Ap x S x 550
(16)
Ap is the area the IMEP is doj_ng work on.
S, the piston
speed, ls a function o:f RPM and stroke length.
A
p
and
S
Both
are constant for .the same engine geometry and
RPM.
The volumetric efficiency determines the c:tmov.nt of
fresh fuel and air charge that will flow into tile cylinder.
To eyaluate the overall voluritetric efficiency it i3
assumed to be composed of two parts.
= e v:L.
X
(17)
G
vt
evt takes into account all the variables that were
e v:L. is the ideal
previously assumed to be constant.
val umetr::Lc e fficif.:mcy.
(18)
k
l
p
Eq. u.!~ t i
011
.J.c)'
of e
on
F~.
u
V
k (rc - 1)
from reference
As R
D
~'
shows the dependence
is increased e . is decreased.
Vl
insr8ases the clearance gases left in the
cylirlder, therefore allowing le.ss fresh .;;dr and fuel
By eBsuming r
mixture into
k. = L lr,
for
air~
c
and taking
i.cka1 vel umetric e f'ficienc ies are
calculated as a f'unct:Lon Gf Pf_/P_,.
.. }
.L
\rVhelJ.
e..
·,r e. . ~L u.e
fc;x"' e .
if
t
is assumed, the ov·erall volumetric efficiency may be
calculated.
value for e
later,
0. 958.
evt
Reference L suggests that a representative
v
J .. s
CJ:.. 3Li··
Assuming, for reasons discussed
PSI and r C = 10.5~ e Vl. is equal to
Using these tvw values for ev a..nd evi yieJ.ds
Pb
= 21
= 0.877.
Equation
eV
17
now becomes:
= 0.8'77
(17a}
x e Vl.
Equati.on 17a is the equation used i.n the analytice.l
model to compute IMEP.
The inlet
ar.ud
efficiency varies ..
back pressures vary as the volumetric
means an increased
v
flow o:f fresh in]_et charge and exhaust gases. As the
flow increases P.
:L
An increased e
decreaseso
There is a higher pressure
drop from the eng::ine inlet. to the intake valves.
An
increase in exhm.Lst flOw means an increase in P, , there
0
is a higher nressure loss in the exhaust pipe.
11he
flo'N rate in terilfts of ev is:
(19)
VIII. ENGINE ANALYTICAL HODEL
The analytical model assumes a flow rate to begin computations.
Inlet and back pressures are calculated.
these pressures ev is calculated.
rate is calculated.
assumed flow.
From
Knovring ev' a new flow
This new flow i.s compared to the
If the ne\v flow j_s larger than the assumed
flow, ev was too large.
The flow is increased so the
ratio Pb/P i is increased and the nex:t ev calc:J.lated will
be smaller.
Conversely, if the nevr flow was smaller than
the assumed flow
·'
e
v
vras too small and the flovv is reduced.
The program continues to iterate flow l'ate unt.il the
change
~i.n
flow rate from one :Lteration to the next is
less than 10-8 •
When this criteria has been met IMEP
and IHP are calculated and printed.
The thermodynamic data for the program was taken
from reference 4.
The engine data used is for a Pontiac
engine used by the California State University, Northridge
School of Engineering in thGir fluids laboratory.
These
numeri.cal vaJ.uGs are not discu.ssed here since of i.nterest,
:Ln this
p."J..}JC-;r)
is the potential increases in pow·er not
the actual engine's output.
HODEL RESULTS
The model predicts the Pontiac engine's output to
be 3LJ-6 ~ 4 HP at 5, 000 RP£.1.
'J:h:Ls
compm-es closely to its
rated horsepower of 350 HP at 5,000 RPM.
35
36
IHP
Decrease
%
0.82
\
~~-~'----L----~--J--~~~~-~---~·--~-----J
10
20
RPM
30
50
40
x100
Figure 1): Indicated Horsepower Decrease for
a 4.4 PSI Back Pressure Increase
..,
•
~1gure
·i
c:
~J
'
t,ne d ecrease
'' PSI
snows
1n power · or a 4-· ~
increase in P,.
~~
· . £ >
J.
At 2,200 RPM the model predicts the ll
percent decrease quoted in reference 3.
Figure
lt
shows the variation of volumetric effie-
iency with exhaust pipe exit pressure and RPH.
di.cted by equation
decreased
As pre-
18, ev increases a..s Pt and consequently
(RP~1 =
noted at lower RP.i'1' s.
constant).
Higher efficiencies are
This does not produce highe.r power
outpu.Ls since power· is aJ..so proportional to engine speed.
37
RPN
2000 RPM
.3000 RP.l\1
4000 RPivl
5000-RPM
.
'----~-- ._--~£~--~·----~--~---~
10.0
12.0
Pt
14.0
PSI
Figure 19: Volumetric Efficiency vs.
Venturi Throat Pressure
Heducing the exhacJ.Dt bach. prussure has a larger effect
on the higher RPM's.
Reducing Pt increases e v , at 5,000
RPYl} at a rate of approximately -0.02 percent per PSI.
The same Pt redttetion, for l~PN :::: 1,000, increased ev
at a. .rate of -0 ~ 0045 percent per PSI.
38
Figure 17 sho·'I!S the DO'!Ier increase versus exhaust pipe
exit pressure..
IHP increase is defined in equation 20.
(D
IEP Increase= r'D
Ii.c
J:t re d_uce d)
IHP (Pt
(20)
= 14.696)
As the pressure decreases the higher RPM's show larger
increases.
T·llm pressuresj
also calculated.
Pt
=
1~-·
:from venturi results, were
6001 is the throat pressure
for the inventor's geometry (W
= 0.13
and
t>l
= 45 degrees).
Th5_s pressure ·was attained at a free stream veloci.ty
IHP increases of 0.10 percent to 0.33
percent resurt>ed.
To operate a vehicle at 65 MPH the
in the range of 2, 500
engine •·s RPH would probably be
to 3,500 RPH...
from
0~
Ther-efore power increases could be expected
23 per{; en t to 0. 29 percent from the inventor' 3
geometry.
Th~:;
second pressure, I\
= 14. 4'+79
PSI, repre-
sents the low-est throat pressure attaj_ned by ahy gemnei::ry
(W
= 0.188 and.
0(
= 15
degrees).
to O.B6 percmxt resulted.
as be fore,
a!:;
:U
~
Power i.ncreases of 0. 26
This pressure was attained,
Again, the probable
increases wou:.Ld be in the mid RPN range or 0. 60 to
0.76 percent ..
'
1.2T "-~·' ,
1,201
"'-...,~
.
'
.......
<!:
1 ,,
4, '"''·
tll
!
1 .. 14~
IBP
INCREASE
1.12~
. ._
'""
"""
~
1,061
~
"'~
~
!1PM
.;000 RPM
""vy //
~2000
//
//
~
RPM
r-1000 RPM
'
,-,~
'
;/~~
~~
~
1.0~~
8 .. 0
-
~
~~
t.o4f1.,00?
~ ~000
.
'-....
1.10~
1,08~
/-5000 RPM
.
""~
1 .. 18 [
-
7
. i. •01-···..
9.'
•
. I .. 0
10
·--··'
11 .. 0 ..
Pt
12.0
I
lJ.O
.
14,0
15.0
PSI
Figure 17& Indicated Horsepowe:r: Inorea:..1a vs., Venturi Throat Pressure
\..N
\.0
IX. CONCLUSIONS
1.
No venturi device, in a freestream application,
captures an appreciable percentage of the freestream
flovv.
'rhe actual capture ratio being only sl.ig;h.tly
larger than the inlet to throat area ratio.
not produce signifi.cc;rr1t decreases in throat
2.
This does
pressure~
The optimum venturi geometry optimizes the
diffuser recovery coefficient Cp •
minimum expansion angle ( ot...
= 15
This was attained at
degrees).
The
optimum throat width was W = 0.188 inch.
3~
The inlet area and convergence geometry are
close to optimum.
Increasing the inlet area had little
effect on the capture ratio.
4.
The interaction of the exhaust flow and the
venturi flow is not well defined.
A study of this inter-
action may account for the differences betvreen the
a:nalyti.cal model's predictions and test results.
5~
The power increasc:::s attained do not wc-,_rrant use
of this device on automobiles.
It should be noted that
evei1 the small decree.ses in pressurt) INere under optimum
condit·.ions.
to the inlet.
An u.ndisturbed freestream flow perpendj_cular
Tbj_s :is a condition that may not be
poss:Lble when installed on a
<:,-;:
6.
vehicle~
S:Lgnificant increases in po·wer can be attained
if the back pressure is lowered enough.
This suggests
41
that it is worthwhile to investigate potential methods
of reducing the cylinder back pressure.
If a source of
flow were available and forced through a venturi, povv-er
increases could be attained.
BIBLIOGRAPHY
1.
The SAE
J~er::.Q::.S~Ja.c_e
Ap-olieq Thermodynamics Manua1,,
Society of Automotive Engineers, Nevr York,
pp.
2.
A-45
'1965,
and A-L~6.
1. B. Ren,3au, J. P. Johnston, and
s.
J. Klin2,
"Performance and Design of Straight, Two-Dimensional,
Diffusers", Jottrnal of Basic En_g,ineerinp;, Trans.
AS£1E, Series D, Vol.
3.
89, March 1967,
pp.
141-150.
:Lester C.. Lichty, Internal Combustion Engine_§,,
NcGraw-H]_ll Book Co.,
Theorv
a~d
pp285.
Practice, The MIT Press,
---~--.. ·~-
PP~ 147-c~ 1 0 ..
1951:
.
.
1966,