Design of a Tuned Intake Manifold - H. W. Engelman (ASME paper 73-WA/DGP-2)

The Society shall not be responsible for statements or aptmans advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications . Discussion is printed only if the paper is published in an ASME ;ournal or Proceedings . Re lea sed for general publication upon presentation. Full credit should be given to ASME, the Professional Division, and the author (s).

$3.00 PER COPY I TO ASME MEMBERS

~~f;~·c;~-11 RESEM~CH STP.FF FORD MOfOH COMPM.'Y

Design of a Tuned Intake Manifold H. W. ENGELMAN Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio Mem. ASME

This paper summarizes a long-term study of intake manifold tuning. It includes the results of several graduate research projects. A ration al mathematical model is developed which defines the modes of resonance in a manifold for up to four cylinders, and affords a method of design for peak ram supercharge at a desired engine speed. A specific example of the design of a manifold is included.

Contributed b y the Diese l & Gas Engine Power Dh•ision of th e American Society of '\1eehanieal Engineers for presentation at the Winter Annual Meeting, Detroit, Michigan, November 11 - 15, 1973. Manuscript r ece i,•cd at ASME H eadquarte r s .Jul y 18, 1973 . Copies will be available until August I, 1974 .

... ,

....

t AfiERICAN SOCIETY OF MECHANICAl. ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK. N.Y. 10017

·Design H.

of a Tuned Intake Manifold

w. ENGELMAN

ABSTRACT This paper summarizes a long-term study of intake manifold tuning. It includes the results of several graduate research projects . A rational mathematical model is developed which defines the modes of resonance in a manifo ld for up to four cylinders, and affords a · method of design for · peak r am supercharge at a desired engine speed. A specific example of the design of a manifold is included . BACKGROUND Improved breathing wi ll almost always improve the combustion in a diesel engine. It is not uncommon to f ind that a better air su pply may actually reduce peak pressure at a given power level. This paper describes an accurate mathematical model for the design of certain multicyli nder intake manifolds to get the best possible breathing, using the resonances which are always present to obtain some supercharge. The fact that air, like all gases, is compressible, or e l astic , means that resonances will exist . Just as crankshafts and valve trains have resonances, so does every intake manifold. However, in cran kshaf ts and valve trains we seek to avoid resonant oscillation~, whereas in manifolds, the oscillations can be extremely beneficial. It is not generally possible to say j ust how much gain can be achieved in a particular engine by intake tuning. It will be of the order of a twenty percent increase i n charge flow over the open port, for a typical engine. However, since any manifold on the engine will have resonances, some tuning effects will exist and may produce some supercharge. The tuned design may not be much better . It is not at al l unusual to encounter air distribution problems in a new engine development. These are most commonly resona nce effects, but not recognized as such . It would be well to define just what a properly tuned manifold is or does. Give n an eng ine, a welltuned intake manifold will give maximum torque at some desired value of rpm by utilizing resonance effects to produce supercharge. The air flow and charge density will be above the values for the engine with open ports over a speed range greater than two-to-one. The greatest percentage increase will be in the middle of the range, and the peak will not be sharp . The design calculations set forth in this paper are the result of a very long-term study. A Ph.D. study at th e University of Wisconsin (1)1 resulted in a paper (2) presented to this division in 1953, when ll.umbers in parentheses designate References at end of Paper .

it was still the Oil and Gas Power Division. That initial work established the Helmholtz resonator as a model of the cylinder and its intake pipe with t he valve open dur ing the intake stroke . Previous analyses were all based on organ-pipe theory, which simply does not provide a way to inc lude the effect of pipe area and cylinder volume. Thus th e Ricardo patent (3) sets forth equations which bracket the optimum length within a ratio of 3 to 1. Less indefinite is the equation given in the Pla tn er patent (4), which gives the tolerance in inches, but even this may be twenty percent plus or minus . The reason for these t olerances is simple: variations of pipe area or cylinder volume do affect the optimum pipe length, and the equations do not include them. PRINCIPLES The basic Helmholtz reso nator is shown in Figure 1. The characteristic feature of this resonator is that its dime nsions are small compared with the wavelength of a sound at its resonant frequency . At ics fundamental res onance, the air in the pipe is the osci llating mass, and the air in the cavity volume is the spring of a simple spring-mass system .

Fig. 1

Helmholtz Resonator

The cylinder of an engine with its intake pipe with the valve open constitutes just s uch a Helmholtz resonat or as shownin Figu re 2. A principal finding o f the original work (1,2) was how piston movement affected the resonance. For the fixed resonator of Figure 1, th e resonant frequency, f 0 , is given by fo = Cs •

~

21T " ~

(1)

wltere, in consis tent units, cs A L v

velocity of sound pipe c r oss-sectional area pipe length cavity volume

I

The e f fec t ive engine cylinder volume is that at mid-stroke (1), one-half the displacement plus the c l earance volume. Thus VD 2

( ~)

(2)

R - l

i

where K is the ratio of frequencies , and may vary from 2.0 to over 2 . 5 depending largely o n valve timin g . For metric units the constant is 1348. This study also cover ed the effect of standing waves in the organ pipe mode when the valve closed, and showed that the effect is not large unless the pipe itself is quite large . The study also included th e effects of bends, and pipes consisting of two sections of diff erent c ross-sectional area. An important result is that the composi t e pipe may be treated on the basis that

(~L)

eff

11 = A 1

(5)

where VD R

piston dis placement compression r atio

Substitution of this Veff fo r V i n Eq uation (1) gives the resonant f r equency of the cylinder and pipe with a moving piston, where the end of the pipe is open .

~I

Fig. 2 Cylinder and Intake Pipe a Helmholt z Resonator .

Modeled as

The second principal fi nd i ng of the original work is that the tuning peak will occur wh e re the nat ural Helmholtz resonan ce of cylinder and pipe is roughly doub le the piston frequency . That is, the pe riod of a resonant cycle takes approximately 180 degrees of crank rotation. From these findings the equation published in 1953 (1, 2) is

Np

77C s

~ ~~ ~ "'V

LVD "'V R + 1

where the subscripts refer to the individual sections of the pipe . A manifold was then built for a V-8 gasoline engine and t es ted as an undergraduate laboratory experiment in The Ohio Sta t e University Internal Comb ustion Engine Laboratory . The stock two-barrel carb uretor was used, each barrel feeding fou r cylinders which fire at uniform intervals . The improvemen t in economy and l ow-end torque led Ka uff ma nn (7 ) to undertake th e r eduction of gasoline engine emissions by application of tuned manifolds as his Ph.D. dissertation. Unfortunately, the Clean Air Act of 1970 was passed during his i nvestigation. A treme ndous improvement whe n he started , suddenly was not ha lf good enough as of December 31, 1970 . However , Eberhard and Schwallie in the M.Sc. theses (8 , 9) i nvestigated the tuning of manifolds. The basic concept is present ed in the early work (1) but without 1 experimen tal confirmation . Eber hard studied threecylinder groups a nd Schwa llie studied the four-cylinder manifold . The basic acoustical model of three-cylinder and four-cylinder manifolds is shown in Figure 3 . For simplici ty, the cylinder on its intake s troke is denoted by vl, and i ts pipe to the branch point has dimensions 1 1 a nd A1 . The idle pipes with their closed valves simply comprise a volume de noted by v 2 . Their organ pipe mode resonance frequencies will be substantially higher than the tuning or Helmholtz frequency . Consequently, their effect is that of a plenum at the branch point . Flow e nters the bra nc h point through a feed pipe of dimens i ons L2 a nd A2 . In a gasoline engine, the carburetor would comprise par t of L2 /A 2 .

(3)

where Np is the rpm at which the tuning peak occurs, Cs is t he velocit y of sound in t he pipe in fps, and A, L, and v are in inches. The cons t a n t, 77 , provides 0 for convers1on of units and sets the Helmholtz resonance a t 2 . 1 times piston frequ e ncy . The constant is 642 for metric units , wh ere C i s in M/sec a nd A, L, I and V are in cent imeters. s ~hompson at The Ohio State University in his M.S c . ! Fig . 3 Acoustical Model of I ntake Manifo ld thesis (5) continued the st udy of singl e pipes and the r esults were presented in a DGP paper (6) in 1969 . The acoustical model can now be hand l ed easily by Equation (3) is rewritten (for English units) a mathematical method used for electrical resonant circuit s . The elect rical analog is shown in Figure 4. Np = 162 C Resonant electrical circuits , especially in communi(4) cations wo rk , are generally treated in terms of resonant K sl ~l~ freq uency or freque ncies , a nd a factor Q wh ich i s essen-

~ r;::-: ~

2

. -tially the reciprical of the losses. It is quite convenient to treat the tuned manifold in the same way. The frequency of the tuning peak is quite independent of the losses. The losses reduce the gain, or supercharging, but their elimination is quite separate from the design for a particular Np.

and the two frequencies are found t o be

(ab+a+l) + 2abL

211

f

Electrical Analog of Intake Manifold.

To design a manifold having certain frequency characteristics it i~ not necessary to carry any loss or resistance terms in the calculations . According l y , Figure 4 shows no resistances in the electrical analog. c1 corresponds to the effective cylinder volume, 1 1 to the L/A of th e intake pipe, c2 to the volume of the other intake pipes and log at the branch, and 1 2 to the L/A of the inlet, including the carburetor, if any. It should be pointed out that this analog is valid only if the intake periods have little or no overlap, generally up to four cylinders only. It is readily shown that the electrical analog in Figure 4 has two resonant frequencies, and further, that one of these will be higher a nd one lower tha n the resonant frequency of 1 1 and c1 taken alone. At the lower frequency, the voltages on c and Cz are in phase, 1 while at the higher frequency the voltages are of opposite phase . Similarly, in the tuned manifold there are two resonances, one higher than and one lower than that calculated for Np from e quations (3) or (4) using Vl, A1, and L1. At the lower resonance the pressures i n the cylinder and at the branch point are in phase, and at the higher resonance they are out of phase . The solution for the resonant frequencies is re adily carried out on the basis of series r esonance, such that the voltage across the current source in the analog is zero. To simplify the solution, an inductance ratio is defined for both the analog and the acoustical model: (L/A) 1

1

(L/A)

2

(6)

1

Similarly, a capacitance ratio is defined

v2 2(R-l) VD

~ (ab+a+l/ c

(8)

- 4ab (9)

1 1

where f is the lower and f the higher resonant fre1 2 quency. The resonant frequency of L c alone is 1 1

'1 4

4ab

211

1

Fig.

~ (ab+a+l ) 2 -

(ab+a+l) -

l

(R+l)

Then the characteristic equation for the ana log circuit becomes 0

(10)

p

which is analogous to equation (1) . Then two frequenc y ratios may be defined for the analog circuit (11)

and (12)

For the intake manifold, X

1

Nl = -

N

(13)

p

and (14)

Figures 5 and 6 give the values of x and x respective1 2 ly for the ratios a and b most likely to be encountered. It should be emphasized that these equations do not define engine performance or performance gained by tuni ng. It is recognized that the designer want s to be able to predict the performance of the engine on his drawing board, and needs the e quations which will e nabl e him to do so . What the equations presented here will do instead is also useful, however. With this mathematical model, the designer can define the manifold configuration which optimizes resonance for his operating conditions. The fact that any flow losses will degrade breathing is well known, but the designer may elect to accept a l oss to obtain swirl in the cylinder in a diesel e ng ine, or t o accept the losses due to high runne r velocity for mixture d istribution in a gasoline engine . As will be shown, this mathematical model pre dict s the re so nan ces ver y well, in terms of the freq uencies that will be found. It should therefore be a very useful de s ign tool . The confirmation of this model is considered the mos t important of th e experimental results whi ch f ollow. The ide nti f i cation of the r esonances was emphasized in the expe rime ntal work, rather than specific prediction of e ngine performance .

3

1. 0

0. 9

i

I

0 .7

...

0.6

:

I

I

"

\\\~'\ ~ ).__

I

I

i

i

! :

,

\\\1'\1'\.j ~

l

I ,

I

I

I 0 I "N ~ ~ I ~'\.'\."l""' "'~""-~ ~"'-1 T-- 1"--.L

t; ili o.•

I

:

J ;-- rl-

-----...::: :::::f:::±::-- ~r- t-

I 0. ~

1-~~

I

I

0. 2

i

I

'

•

i ' 0 .4

0 .6

I

I

!

i

I

0 .2

j

I

I

120

I

I

. 0

I

I

~~ '-...~t---.. N-.. I lr-~ --...__.,...._--:. "t--l-... ......

I

o. 1

I I

I CA.PACI'I'AlfC! RATIO b\

N

- - \\\V