Strojni{ki vestnik 50(2004)1,55-65 Journal of Mechanical Engineering 50(2004)1,55-65 ISSN ISSN UDK : UDC

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1 Strojni{ki vestnik 50(2004),55-65 Journal of Mechanical Engineering 50(2004),55-65 ISSN ISSN UDK : UDC : Strokovni ~lanek (.04) Kozarac D., Mahalec I., Luli} Z.: Metode za dimenzioniranje Seciality - Design aer Methods (.04) Metode za oblikovanje elementov sesalnega zbiralnika batnega motorja z notranjim zgorevanjem Design Methods for the Intake-Manifold Elements of Recirocating Internal Combustion Engines Darko Kozarac - Ivan Mahalec - Zoran Luli} V uvodu risevka so rikazane metode oblikovanja sesalnih zbiralnikov, ki omogoèajo oveèanje rostorninskega izkoristka zaradi dinamiènih srememb tlaka. Predstavljene so analitiène metode za otimiranje remera in dolžine sesalnih cevi glede na vrtilno frekvenco motorja ter metode, ki uoštevajo resonanco v sesalnem zbiralniku. V osrednjem delu risevka je redstavljena analiza uèinkovitosti osameznih metod, ki je bila izvedena s simulacijo na modelu štirivaljnega motorja z notranjim zgorevanjem. Pri simulaciji so bili uoštevani fizikalni in kemièni uèinki od trenutka, ko ride zrak v sesalni zbiralnik, do trenutka, ko izušni lini zaustijo izušni zbiralnik. V risevku je rikazan tudi naèin uorabe enorazsežnega modela za analizo vliva izbranega elementa sesalnega sistema na rostorninski izkoristek motorja ter za izbiro otimalne rešitve ri danih zahtevah Strojniški vestnik. Vse ravice ridržane. (Kljuène besede: motorji z notranjim zgorevanjem, zbiralniki sesalni, otimiranje, simuliranje, metode analitiène) Methods for intake-manifold design that will lead to an increase in volumetric efficiency by using dynamic changes of ressure, are resented in the introductory art of this aer. Analytical methods for tuning the intake-ie length and diameter to a secific engine seed, and methods dealing with the resonance in the intake manifold are considered. The main art of the aer comrises an analysis of these methods that was conducted on a simulation model of a four-cylinder sark-ignition engine. Physical and chemical rocesses are considered in the model, from the moment the air enters the intake system until the combustion gases leave the exhaust ie. It is also shown how one-dimensional simulation calculations can be used for the analysis of a single intake-system element s influence on the volumetric efficiency of the engine, and for the selection of the otimal solution for given demands Journal of Mechanical Engineering. All rights reserved. (Keywords: internal combustion engines, intake manifold, otimization, simulation, analytical methods) 0 UVOD Na tok lina skozi motor z notranjim zgorevanjem v glavnem vlivajo sesalni in izušni sistem ter konstrukcija in krmiljenje ventilov. Lahko torej reèemo, da je sesalni sistem zelo omemben del motorja, katerega oblika in izmere vlivajo na rostorninski izkoristek motorja, orabo goriva in hru. Med delovanjem motorja rihaja v sesalnem sistemu do dinamiènih srememb, kar vodi do sremembe njegove uèinkovitosti v odvisnosti od vrtilne frekvence motorja. S sremembo geometrijske oblike sesalnega sistema je ri dani vrtilni frekvenci motorja mogoèe oveèati njegov rostorninski izkoristek. Sesalni sistemi tekmovalnih motorjev so rilagojeni doseganju najveèjega rostorninskega 0 INTRODUCTION Fluid flow through an internal combustion engine is mainly influenced by the intake system, the exhaust system and by the valve mechanism. Therefore, the intake system is an imortant engine element whose shae and dimensions influence the volumetric efficiency, fuel consumtion, and noise ollution. During the engine s oeration, dynamic changes occur in the intake manifold, which leads to a change in its efficiency with the change of the engine s seed. With a change to the geometry of the intake system, it is ossible to increase the engine s volumetric efficiency at a secific engine seed. The intake systems of racing engines are tuned to roduce maximum volumetric efficiency at a high engine stran 55

2 izkoristka ri visokih vrtilnih frekvencah motorja, ri veèini reostalih motorjev a doseže sesalni sistem najveèji rostorninski izkoristek ri nižjih vrtilnih frekvencah motorja. Za zmanjšanje vliva geometrijske oblike sesalnega zbiralnika na obnašanje motorja so bili razviti sesalni zbiralniki s sremenljivko geometrijsko obliko. S sreminjanjem dolžine sesalnih cevi dosežemo oveèanje rostorninskega izkoristka motorja v širokem obmoèju vrtilnih frekvenc. Za doloèitev izmer takšnega sesalnega sistema a moramo oznati vliv geometrijske oblike na rostorninski izkoristek in seveda tudi same metode za izraèun izmer sesalnega sistema. IZRAÈUN GEOMETRIJSKE OBLIKE SESALNEGA ZBIRALNIKA Za izraèun geometrijske oblike sesalnih zbiralnikov je bilo razvitih veè metod, ki jih lahko razdelimo tri razdelimo v tri skuine:. Analitiène metode za izraèun otimalne vrtilne frekvence ri danih izmerah sesalnega zbiralnika. 2. Enorazsežne numeriène simulacije za izraèun izmenjane kolièine lina med delovanjem motorja. 3. Trirazsežne numeriène simulacije za izraèun izmenjane kolièine lina med delovanjem motorja. Metode, ki sadajo v tretjo skuino, so èasovno zelo otratne, zato niso rimerne za analizo celotnega sesalnega zbiralnika, temveè le za osamezne manjše dele, nr. za simulacijo toka lina skozi sesalni ventil. Zaradi tega metode v tretji skuini ne bodo oisane bolj odrobno.. Analitiène metode Sesalne zbiralnike, ki vodijo do oveèanja rostorninskega izkoristka motorja, lahko razdelimo v dve skuini: v otimirane in resonanène sesalne zbiralnike. Otimirani sesalni zbiralniki dosežejo tlaèno konico ri doloèeni vrtilni frekvenci motorja kar vodi do najveèjega rostorninskega izkoristka. Raziskave so okazale, da je rostorninski izkoristek najveèji v rimeru, èe doseže tlak v sesalnem zbiralniku najveèjo vrednost v obmoèju zasuka glavne gredi 20 do 50 stoinj red zartjem sesalnega ventila. Vrtilna frekvenca motorja, ri kateri ride do najveèje vrednosti, imenujemo otimalna vrtilna frekvenca. Po [] lahko na odlagi redostavke o oteku tlakov v sesalnem zbiralniku red sesalnim ventilom doloèimo nihajni èas, ko so sesalni ventili odrti t, oziroma teèe lin v valj, in èas, ko so ventili zarti t 2, oziroma ni retoka. Na odlagi teh dveh nihajnih èasov izraèunano dolžino l in rerez A seed, whereas with most other engines, the intake systems roduce maximum volumetric efficiency at a lower engine seed. To overcome different intake-manifold geometry effects on the engine behaviour, variable intake manifolds are being develoed. The increase in the volumetric efficiency over a broad range of engine seeds is achieved by varying the intake runner. In order to determine the dimensions of such a manifold, it is necessary to be familiar with the influence of the intake-manifold geometry on the volumetric efficiency, as well as with some methods for calculating the manifold dimensions. INTAKE-MANIFOLD GEOMETRY CALCULATIONS In the ast a large number of exressions and methods for calculating the dimensions of intake manifolds have been develoed. They can be divided into three main grous:. Analytical exressions that calculate the tuning engine seed using manifold dimensions. 2. One-dimensional simulation calculations, which calculate the amount of fluid that is exchanged during the engine s oeration. 3. Three-dimensional simulation calculations, which calculate the amount of fluid that is exchanged during the engine s oeration. This third grou of methods is not suitable for the entire intake manifold because these methods consume a considerable amount of time for the model design and calculation. But they are useful for the simulation of individual small arts, such as the flow through the intake valve. Therefore, this grou of methods will not be described in more detail.. Analytical exressions The intake manifolds that result in an increase of engine s volumetric efficiency can be divided into tuned intake manifolds and resonant intake manifolds. At some engine seed a tuned intake manifold causes a ressure trace in the manifold that leads to the maximum volumetric efficiency. Research has shown that if the ressure in the intake manifold is a maximum in the eriod of crank angle degrees (CA deg) before the intake valve closes, then the maximum volumetric efficiency is obtained. The engine seed at which this maximum occurs is called the tuned engine seed. According to [], from the assumed ressure trace in the intake manifold in front of the intake valve, the oscillation time eriod when the valves are oen t, and when the valves are closed t 2 are determined. With these time eriods, the length l, and a cross-sectional area A of the rimary intake ie are stran 56

3 glavne sesalne cevi o enaèbah () in (2): V n A c kjer so: c v m/s hitrost zvoka; n v min - vrtilna frekvenca motorja; t ivo =a ivo /(6. n) in t ivc =a ivc /(6. n), s èas ko je sesalni ventil odrt oz. zart.; V c v m 3 rostornina valja; a ivo in a ivc, - zasuk glavne gredi, ko je sesalni ventil odrt oz. zart; k o =t ivo /t in k c =t ivc / t 2 razmerje med èasom odrtja/zartja sesalnega ventila in riadajoèim nihajnim èasom. Posledica sreminjanja tlaka v sesalni cevi v èasu, ko so sesalni ventili odrti, so tlaèna nihanja, ki se ohranijo tudi o trenutku, ko se sesalni ventil zare. Po [2] lahko ta reostala tlaèna nihanja v sesalni cevi še dodatno oveèajo rostorninski izkoristek, èe se najveèji tlaèni vrh reostalega nihanja ujame z zgornjo mrtvo lego (ZML) ri sesalnem taktu. Enaèba za ois omenjenega stanja je naslednja: calculated using Eq. () and (2): 720 -áivo l = c, m 24 ê n 2 ð ê o c é 720 -á ivo = tan ê90 ê, m áivo ë êc áivo c ù 2 (2), o ú û where: c, m/s seed of sound; n, rm engine seed; t ivo =a ivo /(6. n) i t ivc =a ivc /(6. n), s time during which the intake valve is oen or closed; V c, m 3 cylinder volume; a ivo i a ivc, deg - crankshaft angle during which the intake valve is oen or closed; k o =t ivo /t i k c =t ivc /t 2 ratio of the valve timings with oscillation time eriods. As a result of ressure changes in the intake ie during the time the intake valves are oen, the ressure in the ie continues to oscillate after the intake valve closes, and these oscillations are called residual waves. According to [2], if a eak ressure of the residual wave from the revious cycle occurs at the to dead centre (TDC) of the intake stroke, an additional imrovement in the volumetric efficiency is obtained. From this aroach, the following equation is derived: () ( k ) t d 2 - è + è = 720 (3), kjer je: q t =(2. n. l )/c v stoinjah zasuk glavne gredi za èas otovanja tlaènega vala od valja do sesalne cevi in nazaj; q d v stoinjah zasuk glavne gredi za èas sesalnega ulza v sesalni cevi. Po [4] izraèunamo otimalno vrtilno frekvenco motorja kot: * è c n = q 24 l s where: q t =(2. n. l )/c, CA deg time eriod of wave travel from the engine cylinder to the ie end and back; q d, CA deg time eriod of a suction ulse in the intake ie. Ref. [4] roosed a slightly modified, simler exression for calculating the tuned engine seed: -, min /rm (4), kjer so: q s - število celih tlaènih valov v reostalem where: q s - the number of comlete residual wave tlaènem nihanju; q * =540+q ivc v stoinjah zasuk oscillations; q * =540+q ivc, CA deg eriod in which glavne gredi, v katerem ta reostala tlaèna nihanja residual waves exist; q ivc, CA deg angle of intake obstajajo; q ivc v stoinjah zasuk glavne gredi ri valve closure after BDC. zartem sesalnem ventilu o sodnji mrtvi legi (SML). At a defined engine seed the resonant Pri resonanènem sesalnem zbiralniku vliva intake manifold causes an increase in the volumetric efficiency due to the corresondence of na oveèanje rostorninskega izkoristka motorja ujemanje tlaènih nihanj z resonanèno frekvenco the ressure disturbance frequency with the intake manifold resonant frequency, or one of its sesalnega zbiralnika ali enega izmed njegovih delov. Najveèji rostorninski izkoristek onovno dosežemo arts. le ri doloèeni vrtilni frekvenci motorja. Ref. [4] concluded that ressure oscillations V viru [4] so tlaèna nihanja v sesalnem in the intake manifold are comrised of two basic zbiralniku razdeljena na dva osnovna tlaèna vala. Prvi waves. One wave, which is influenced by the shae tlaèni val je osledica oblike glavne sesalne cevi in ima of the rimary intake ie, has a short oscillation kratko eriodo, medtem ko na drugi tlaèni val z daljšo eriod, and the other, which has a longer oscillation eriodo vliva oblika celotnega sesalnega zbiralnika. eriod, is influenced by the whole intake manifold. It Tam so bili izeljani tudi izrazi za izraèun resonanène also derived exressions for calculating the resonant frekvence w (rad/s) sesalnega zbiralnika s štirimi frequency w (rad/s) of the intake manifold with four osamiènimi glavnimi sesalnimi cevmi (sl. ): individual rimary intake ies (Fig.): w l cos = 0 c (5) A s w s cos l w V w = Sb + 4 tan l (6), A c A c c stran 57

4 kjer so: A s v m 2 rerez vstone sesalne cevi; l s v m dolžina vstone sesalne cevi (to je cev, ki je red zbirnim rostorom sesalnega zbiralnika); V Sb v m 3 rostornina zbirnega rostora sesalnega zbiralnika. Vir [5] a je doolnil zgornja izraza še z uoštevanjem vliva rostornine valja. Enaèba (7) odaja resonanèno frekvenco za glavno sesalno cev, enaèba (8) a resonanèno frekvenco za celoten sesalni zbiralnik: kjer sta: A c v m 2 rerez valja, l c v m dolžina valja (definirana kot olovica delovnega giba bata). Z uorabo zaisanih enaèb je mogoèe izraèunati izmere otimalnega resonanènega sesalnega zbiralnika v zelo kratkem èasu. Žal a te enaèbe ne uoštevajo vseh vlivnih dejavnikov, nr: sremembo rostornine valja, vliv krmiljenja ventilov, srememb v rerezu sesalnih cevi, vliva hitrosti in tlaka lina na tlaènem valu, vliv tlaènih nihanj od reostalih valjev ri motorju z veè valji, vliv izušnega zbiralnika, vliv segrevanja lina zaradi segrevanja samega sesalnega zbiralnika, vliv tlaènih uorov v sesalnih ceveh itn. Poleg tega a omenjeni avtorji ne odajajo enaèb za izraèun rostorninskega izkoristka motorja. Ac w l c tan tan A c c where: A s, m 2 cross-sectional area of the secondary intake ie; l s, m length of the secondary intake ie (the ie that is located before the manifold lenum); V Sb, m 3 intake manifold lenum volume. Ref. [5] considered the influence of the cylinder volume. With Eq.(7), the resonant frequency w that is related to the rimary intake ie is calculated, whereas by Eq.(8) the resonant frequency related to whole intake manifold is calculated: w l = (7) w l w lc + Ac tan w l 3 tan (8), w l w lc c tan tan c c where: A c, m 2 cross-sectional area of the cylinder; l c, m length of the cylinder (set to be equal to half of the iston stroke). With all these equations it is ossible to calculate the dimensions of a tuned or resonant intake manifold, for the defined engine seed, in a short eriod of time. These equations, however, do not take into account all the relevant factors, such as: cylinder volume change, influence of valve timing, influence of valve lift, change in ie cross-sectional area, influence of gas velocity and gas ressure on the wave seed, the influence of waves from other intake ies in a multi-cylinder engine, the influence of the exhaust manifold, the influence of gas heating, the influence of the friction resistance in the ies, etc. Moreover, these equations do not give the value of the volumetric efficiency. A tan As w ls w Vsb cot = + c c + A c A c c A -A.2 Enorazsežne numeriène simulacije.2 One-dimensional simulation calculations Z enorazsežnimi numeriènimi simulacijami lahko izraèunamo èasovni otek tlaka, temerature, masnega retoka, hitrosti lina itn. v sesalnih ceveh, ki so nadalje namenjeni za izraèun rostorninskega izkoristka motorja za izbrane robne ogoje oz. razored. Otimizacijo sesalnega zbiralnika izvedemo s onavljanjem izraèunov ri razliènih robnih ogojih. Osnova za izraèune so enaèbe enorazsežnega toka neviskoznega lina: Kontinuitetna enaèba: ( ) r r v r v da + + = 0 gibalna enaèba: t x A dx momentum equation: 2 2 ( r v) ( r v + ) r v da r v v f = 0 t x A dx D in zakon o ohranitvi energije: energy equation: [ r v h] ( r e0) 0 r v h0 da r q = 0 t x A dx One-dimensional simulation calculations calculate the time trace of ressure, temerature, mass flow, gas velocity, etc. in the intake ie, and with these results they calculate the volumetric efficiency for a redetermined intake-manifold configuration. The otimisation of the intake manifold can be conducted by analysing these results for several different manifold configurations. The bases for these calculations are the equations of one-dimensional inviscid flow: Continuity equation: (9) (0) (). stran 58

5 Pri reševanju sistema enaèb enaèimo stanje lina s stanjem idealnega lina, kar je za otrebe izraèunov ri sesalnih zbiralnikih v veèini rimerov zadovoljivo [6]: Enaèbe (9), (0) in () redstavljajo sistem arcialnih diferencialnih enaèb v èasu t in legi x, ki analitièno niso rešljive. Za reševanje se zato uorabljajo numeriène metode, ki z naredkom raèunalništva dajejo vedno natanènejše rešitve. RT r = For concluding the equation set, the gas roerties are related by an ideal-gas state equation, which is usually sufficiently accurate for engine manifolds [6]:. (2). Equations (9), (0) and () reresent a system of artial differential equations relating to the time t and the longitudinal coordinate x, and they cannot be solved analytically. For solving these equations, a numerical method must be emloyed. With the develoment of comuters, more comlex methods have been derived, so today it is ossible to find very comlex and very accurate numerical methods for solving these equations. 2 RAÈUNSKI MODEL Raèunski model temelji na štirivaljnem štiritaktnem vrstnem motorju z vžigalno sveèko, katerega osnovne izmere so odane v reglednici. V analizi je uorabljen sesalni zbiralnik s štirimi glavnimi sesalnimi cevmi in štiritoèkovnim vbrizgom goriva (sl. ). Otimalna vrtilna frekvenca motorja je bila izraèunana z enaèbami () do (8), za nekaj razliènih razoredov sesalnega zbiralnika. Za identiène razorede so bile izvedene tudi enorazsežne numeriène simulacije, na odlagi katerih so bili dobljeni nekateri sklei. Da bi bili rezultati numeriènih simulacij èim bolj natanèni, so bili oleg uorabe redostavke o idealnem linu uoštevani naslednji vlivi: izraèun dogajanja v valju, vžig, retok lina mimo ventilov, retok lina skozi omejilnike retoka, izraèun dogodkov v zbiralnem rostoru in ovezave le tega s sesalnimi cevmi. 2 CALCULATION MODEL The calculation model is based on a four-cylinder, four stroke, in-line, sark-ignition engine, whose basic dimensions are shown in Table. The intake manifold with four individual rimary intake ies and multioint injection shown in Fig. is used in the analysis. The resonant or tuned engine seeds are calculated for several different intake-manifold arrangements, with Eqs.() to (8), and the results are shown in the next section (Table 2). For the same intake-manifold arrangements, the one-dimensional simulation calculations are conducted, and with the results from these calculations some conclusions are obtained. In order for the simulation calculations to be as accurate as ossible, the calculation model, besides a one-dimensional inviscid flow calculation, comrises the following: in-cylinder rocess calculation, combustion, valve flow calculation, calculation of flow through flow restrictions, calculation of rocesses in lenums and at lenum with ie connections. In this manner, a large number of influences is taken into account. Preglednica. Osnovne izmere motorja Table. Basic engine dimensions tlaèno è razmerje e comression ratio remer valja D bore D delovni gib bata H stroke H dolžina ž ojnice con. rod length L odrtje sesalnega ventila intake valve oens zartje sesalnega ventila intake valve closes odrtje izušnega ventila exhaust valve oens zartje izušnega ventila exhaust valve closes 8,8 80 mm 55,5 mm 0,2 m 40 stoinj red ZML 40 deg CA before TDC 82 stoinj o SML 82 deg CA after BDC 79 stoinj red SML 79 deg CA before BDC 30 stoinj o ZML 30 deg CA after TDC stran 59

6 l ds V Sb l s d Sl.. Sesalni zbiralnik raèunskega modela (d remer glavne sesalne cevi, l dolžina glavne sesalne cevi, d s remer vstone sesalne cevi, l s dolžina vstone sesalne cevi, V Sb rostornina zbirnega rostora zbiralnika) Fig.. Intake manifold of calculation model (d rimary ie diameter, l rimary ie length, d s secondary ie diameter, l s secondary ie length, V Sb lenum volume) Znano je, da ima oblika izušnega zbiralnika velik vliv na rostorninski izkoristek motorja in da dinamiène sremembe tlaka v izušnem zbiralniku neosredno vlivajo tudi na dinamiène sremembe tlaka v sesalnem zbiralniku v èasu, ko se odrtje sesalnega in izušnega ventila rekrije. Omenjeni vliv ri izraèunu ni bil uoštevan, kar je bilo zagotovljeno z izbiro robnega ogoja nesremenljivega tlaka takoj za izušnim ventilom. Na koncu risevka so za rimerjavo odani še rezultati izraèuna brez zanemaritve vliva izušnega zbiralnika. 3 REZULTATI ANALIZ It is well known that the exhaust manifold configuration has a significant influence on the volumetric efficiency, and that dynamic changes of ressure in the exhaust ie affect the dynamic changes of ressure in the intake manifold when there is valve overlaing. The exhaust manifold has not been included in the calculation model in order to neglect its influence. Instead, a boundary condition with constant ressure has been set just behind the exhaust valve. At the end of the aer, for the urose of comarison, the calculation of the whole model is made. 3 ANALYSIS OF THE RESULTS Enaèbe () do (4) neosredno ovezujejo otimalno vrtilno frekvenco z izmerami sesalnega zbiralnika n v min -, medtem ko enaèbe (5) do (8) odajajo resonanèno frekvenco sesalnega zbiralnika w res v rad/s in z njo ovezano resonanèno vrtilno frekvenco motorja n res v min - : Slika rikazuje najomembnejše izmere sesalnega zbiralnika. Za vsako od teh izmer so bile izbrane tri razliène vrednosti in izraèunani otimalna in resonanèna vrtilna frekvenca motorja. Pri sreminjanju ene izmere so bile reostale izmere doloèene kot srednja vrednost izbranih treh vrednosti. Primer: za analizo vliva dolžine glavnih sesalnih cevi je bila otimalna in resonanèna vrtilna frekvenca izraèunana za tri razliène dolžine glavnih sesalnih cevi l =250, 500 in 750 mm, medtem ko so bile reostale izmere nesremenljive: d =35 mm, l s = 200 mm, d s =50 mm in V Sb =8,5 dm 3. Rezultati izraèunov so rikazani v reglednici 2. Razvidno je, da razliène enaèbe dajo zelo razliène rezultate. Na odlagi velikega števila enaèb, ki so bile dokazane kot ravilne, velja, da se s oveèevanjem dolžine glavnih sesalnih cevi resonanèna vrtilna frekvenca motorja zmanjšuje, kar a ne velja za n res = Eqs.() to (4) directly link the dimensions of the intake manifold with the tuned engine seed n (rm), while with Eqs.(5) to (8) it is ossible to calculate the intake manifold s resonant frequency w rez (rad/ s), and with it, it is ossible to calculate the resonant engine seed n res : 5 wres (3). ð Fig. shows the most significant dimensions of the model intake manifold. For each dimension three different values were used for calculating the tuned or resonant engine seeds. While changing the value of one dimension, other dimensions are set to the middle of three values. For examle, in order to analyse the influence of the length of the rimary intake ie, the tuned and resonant engine seeds are calculated for three different rimary ie lengths l =250, 500 and 750 mm, while the other dimensions were as follows: d =35 mm, l s = 200 mm, d s =50 mm i V Sb =8.5 dm 3. The results of these calculations are shown in Tab.2. From the results it is clear that different equations give significantly different results. According to a large number of equations that have roven to be accurate, by increasing the length of the rimary-intake ie, the resonant engine seed decreases. An excetion to this is Eq. 2. The influence of the rimary ie s diameter stran 60

7 enaèbo (2). Vliv remera glavne sesalne cevi se tudi razlikuje, saj se o enaèbah (2) do (4) in (7) s oveèevanjem remera oveèuje tudi resonanèna vrtilna frekvenca motorja, medtem ko se o enaèbah (6) in (8) le ta zmanjšuje. Enaèbe () in (5) ne uoštevajo remera glavne sesalne cevi. Nadaljnji izraèuni kažejo, da veliko enaèb ne uošteva remera vstone sesalne cevi, njene dolžine in rostornine zbirnega rostora ri izraèunu resonanène vrtilne frekvence motorja. Enorazsežne numeriène simulacije so bile izvedene s rogramom AVL Boost. Rezultati izraèuna rostorninskega izkoristka motorja ri vseh vrtilnih frekvencah motorja za vse analizirane modele (regl. 2) so rikazani na sliki 2. Kakor je razvidno iz reglednice 2, imamo sedem razliènih razoredov sesalnega zbiralnika, ki so razdeljene s onavljanjem v et skuin, vsaka s tremi razliènimi razoredi. Na sliki 2(a) so rikazane krivulje rostorninskega izkoristka za tri razliène dolžine glavnih sesalnih cevi. S oveèevanjem njihove dolžine se rostorninski izkoristek motorja ri majhnih in srednjih vrtilnih frekvencah oveèa, ri višjih vrtilnih frekvencah a se zmanjša. Pri razoredu sesalnega zbiralnika z najdaljšo cevjo ima rostorninski izkoristek ri vrtilni frekvenci 3600 min - izrazit vrh, kar lahko razložimo s ojavom resonanènega olnjenja. Primerjava teh rezultatov s tistimi iz reglednice kaže najveèje ujemanje z enaèbo (7). differs according to different equations. Eqs. (2) to (4) and (7) show that when the ie diameter increases the resonant engine seed also increases, whereas Eqs.(6) and (8) show that when the diameter is increased, the resonant engine seed decreases. Eqs.() and (3) to (5) do not take the rimary intake ie s diameter into account. Further calculations show that a large number of the equations shown do not take into account the secondary ie diameter, the secondary ie length and the lenum volume when calculating tuned or resonant engine seeds. One-dimensional simulation calculations were conducted with the AVL Boost rogram, and for each intake manifold configuration (shown in Table 2), the volumetric efficiency across the whole seed range is calculated. It is clear from Table 2 that there are eleven different intake manifold configurations, which are, with reetition, collected in five grous, each with three different combinations. Fig.2(a) shows the volumetric efficiency curves for three different lenghts of the rimary intake ie. With an increase in the lenghth of the rimary intake ie, the volumetric efficiency at low and mid engine seed is imroved, whereas at high engine seeds the volumetric efficiency is deteriorated. The model with the longest intake ie has a considerable volumetric efficiency eak at 3600 rm, which can be considered as resonant charging. The comarison of these results with the results from Tab. shows that the best corresondence is obtained with Eq.(7). Preglednica 2. Otimalne in resonanène vrtilne frekvence motorja, izraèunane z uorabo analitiènih metod Table 2. Tuned and resonant engine seed calculated with analytical exressions l mm d mm l s mm d s mm V Sb mm Vrtilne frekvence motorja (v min - ), izraèunane è o enaèbi è Engine seed (rm) calculated with equation () (2) (3) (4) (5) (6) (7) (8) d = 35 mm l s = 200 mm d s = 50 mm V Sb = 8,5 dm 3 l = 500 mm l s = 200 mm d s = 50 mm V Sb = 8,5 dm 3 d = 35 mm l = 500 mm d s = 50 mm V Sb = 8,5 dm 3 d = 35 mm l = 500 mm l s = 200 mm V Sb = 8,5 dm 3 d = 35 mm l s = 200 mm d s = 50 mm l = 500 mm stran 6

8 l L=250 mm l L=500 mm l L=750 mm d =35 mm l s =200 mm d s =50 mm V Sb =8.5 l Vrtilna frekvenca Engine (min seed - )/Engine (rm) seed (rm) (a) d d=25 mm mm d d=35 mm mm d d=45 mm mm l =500 mm l s=200 mm d s=50 mm V Sb=8.5 l Vrtilna frekvenca Engine (min seed - )/Engine (rm) seed (rm) (b) Sl. 2. Vliv dolžine glavne sesalne cevi (a) in remera (b) na rostorninski izkoristek štirivaljnega motorja Fig. 2. Influence of the rimary ie length (a) and diameter (b) on the volumetric efficiency of a four-cylinder engine Na sliki 2(b) so rikazane krivulje rostorninskega izkoristka za tri razliène remere glavnih sesalnih cevi. Z zmanjševanjem remera se rostorninski izkoristek motorja ri nižjih vrtilnih frekvencah motorja oveèuje, ri višjih vrtilnih frekvencah a se zmanjšuje. Razvidno je tudi, da se lokalni vrh rostorninskega izkoristka z manjšanjem remera glavnih sesalnih cevi omika v smeri manjših vrtilnih frekvenc. Primerjava rezultatov z rezultati iz reglednice onovno kaže najboljše ujemanje z enaèbo (7). Vliv dolžine vstone sesalne cevi na rostorninski izkoristek je razviden iz diagramov na sliki 3a. Pri visokih vrtilnih frekvencah srememba dolžine vstone sesalne cevi nima vliva na vrednost rostorninskega izkoristka, ri nizkih vrtilnih frekvencah a se kaže v majhnih sremembah strmine krivulje rostorninskega izkoristka motorja. Vliv dolžine vstone sesalne cevi je bolj izrazit, èe je rostornina zbirnega rostora kolektorja manjša, kar je razvidno s slike 4. Vliv remera vstone sesalne cevi je razviden iz diagramov na sliki 3b. Sreminjanje remera Fig.2(b) shows the volumetric efficiency for three different rimary-ie diameters. With a decrease in the diameter of the rimary ie, the volumetric efficiency at lower engine seeds increases, while at the same time at high engine seeds it decreases. In addition, the local maxima of the volumetric efficiency curve shift to lower engine seeds with a decrease in the diameter of the rimary ie. The comarison of these results with the results from Table also shows that the best corresondence is obtained with Eq.(7). The influence of the length of the secondary intake ie on the volumetric efficiency is shown in Fig. 3(a). The change in the length of the secondary intake ie does not cause a change in the volumetric efficiency at high engine seeds, while at low engine seeds it causes very small changes to the shae of the curve. The influence of the secondary intake ie on the volumetric efficiency would be greater if the lenum volume were smaller (shown in Fig.4). The influence of the diameter of the secondary intake ie can be seen in Fig.3(b). The change lls=00 s mm lls=200 s mm lls=500 s mm d =35 mm l =500 mm d s =50 mm V Sb =8.5 l Vrtilna frekvenca Engine (min seed - )/Engine (rm) seed (rm) (a) Ds=30 d s mm Ds=50 d s mm Ds=70 d s mm d =35 mm l =500 mm l s =200 mm V Sb =8.5 l Vrtilna frekvenca Engine (min seed - )/Engine (rm) seed (rm) (b) Sl. 3. Vliv dolžine vstone sesalne cevi (a) in remera (b) na rostorninski izkoristek štirivaljnega motorja Fig. 3. Influence of the secondary ie s length (a) and diameter (b) on the volumetric efficiency of a fourcylinder engine stran 62

9 VVsb=6 Sb l VVsb=8.5 Sb l VVsb= Sb l l =500 mm d =35 mm l =500 mm d =35 mm l s =200 mm d s =50 mm l s =200 mm d s =50 mm Vrtilna frekvenca Engine (min seed )/Engine (rm) seed (rm) Vrtilna frekvenca Engine (min seed )/Engine (rm) seed (rm) (a) (b) Sl. 4. Vliv rostornine zbiralnega rostora sesalnega zbiralnika na rostorninski izkoristek motorja ((a) razmeroma velika rostornina; (b) majhna rostornina) Fig. 4. Influence of the intake manifold s lenum volume on the volumetric efficiency ((a) relatively large lenum volume; (b) lowered lenum volumes) VVsb=0.55 Sb l VVsb=. Sb ll VVsb=6 Sb l l of the secondary intake ie s diameter does not change the volumetric efficiency at high engine seeds, but at low engine seeds it changes the shae of the curve. If the secondary intake ie s diameter is decreased too much, then this ie becomes the lace of choking, and the volumetric efficiency is lowered throughout the whole seed range. At higher engine seeds, the lowering of the volumetric efficiency is greater than at lower engine seeds. Fig.4 shows the results of simulation calculations for several different intake-manifold lenum volumes. When the lenum volume is relatively big in comarison with the dislacement volume of the engine, a small change in the lenum volume will not change the volumetric efficiency curves. (Fig.4(a)). But if the lenum volume is reduced to a value around the dislacement volume or smaller, then changes in the volumetric efficiency curve occur. It should be noted that small changes to the small lenum volumes do not result in significant changes in the volumetric efficiency, but in comarison with the results obvstone sesalne cevi ne vliva na rostorninski izkoristek motorja ri visokih vrtilnih frekvencah motorja, ri nižjih vrtilnih frekvencah a se kaže v sremembi oblike krivulje rostorninskega izkoristka. Èe zmanjšamo remer vstone sesalne cevi reveè, deluje le ta kot dušilo, kar zmanjša rostorninski izkoristek v celotnem obmoèju vrtilnih frekvenc. Zmanjšanje je bolj izrazito z veèanjem vrtilnih frekvenc motorja. Na sliki 4 so rikazani rezultati izraèunov za nekaj razliènih rostornin zbiralnega rostora sesalnega zbiralnika. Èe je rostornina zbiralnega rostora razmeroma velika roti delovni rostornini motorja, majhne sremembe rostornine zbiralnega rostora nimajo vliva na rostorninski izkoristek motorja (Sl. 4b), toda èe rostornino zbiralnega rostora zmanjšamo ribližno na vrednost delovne rostornine motorja se ojavijo razlike v krivuljah rostorninskega izkoristka motorja. Te razlike so razmeroma majhne, toda v rimerjavi z razlikami ri Engine seed (rm) Vrtilna frekvenca (min - ) Engine seed (rm) Sl. 5. Prostorninski izkoristek štirivaljnega motorja Fig. 5. Volumetric efficiency of four-cylinder engine model Primary intake ie length (mm) Dolžina glavne sesalne cevi (mm) Primary intake ie length (mm) stran 63

10 veèji rostornini zbiralnega rostora sesalnega zbiralnika mnogo izrazitejše (sl. 4b). Z manjšanjem rostornine zbiralnega rostora se vliv elementov red tem rostorom na rostorninski izkoristek motorja (nr. vhodna sesalna cev) oveèuje. Prikazani diagrami so ridobljeni z numeriènimi simulacijami brez uoštevanja izušnega zbiralnika. Èe bi želeli doloèiti izmere sesalnega zbiralnika na redstavljeni naèin, bi bilo treba tudi izušni zbiralnik vkljuèiti v izraèun ter izvesti izraèun za celoten motor. Sreminjanje rostorninskega izkoristka v odvisnosti od vrtilne frekvence motorja in dolžine glavne sesalne cevi je razvidno iz diagrama na sliki 5, na odlagi katere lahko dolžino glavne sesalne cevi toèno doloèimo. 4 SKLEPI Èe želimo doloèiti izmere sesalnega zbiralnika s sremenljivo geometrijsko obliko, je treba natanèno doloèiti izbrane izmere za vsako obratovalno toèko. Predstavljene analitiène enaèbe sicer dajo rezultate hitro, vrašljiva a je rav njihova toènost. Nobenega dvoma ni, da ne bi trirazsežne numeriène simulacije dale mnogo boljši ogled na dogajanje v valju, toda za njihovo uorabo je treba mnogo veè vhodnih odatkov. Poleg tega a je zmogljivost današnjih namiznih raèunalnikov oz. delovnih ostaj še remajhna, da bi bili izraèuni oravljeni v srejemljivem èasu. Poiskati je torej treba oravnavo med toènostjo in otrebnim èasom izraèuna oz. oiskati naèin, kako otimalno uorabiti vse omenjene metode. V rvi fazi uorabimo za okvirno doloèitev izmer sesalnega zbiralnika analitiène enaèbe. Nadaljnjo otimizacijo dosežemo z uorabo enorazsežnih numeriènih simulacij, kar je bilo tudi rikazano in ki v veèini rimerov dajo dovolj natanène rezultate. Z uorabo trirazsežnih numeriènih simulacij je mogoèe ridobiti nekatere stalnice, ki jih nadalje uorabimo v hitrejših enorazsežnih numeriènih simulacijah za doseganje še bolj toènih rezultatov. Na zaèetku so lahko ti modeli zelo rerosti - z le nekaj elementi motorja, na koncu ostoka a morajo zagotovo vsebovati vse elemente motorja. Na odlagi rezultatov takih analiz je že mogoèe toèno doloèiti izmere sesalnega zbiralnika, ki bi dale najveèjo zmogljivost motorja v dani toèki delovanja. tained with large lenum volumes, the change is considerable (Fig. 4(b)). When lowering the intake-manifold lenum volume, the influence of elements that are located before the lenum on the volumetric efficiency (for instance, the secondary intake ie) is increasing. The charts shown are obtained from the simulation calculations of a model without an exhaust manifold. If the dimensions of the intake manifold are to be determined with this kind of simulation calculation, it is necessary to include the exhaust manifold in the model and to conduct the calculations for the whole engine model. The change in the volumetric efficiency caused by a change of one intake-manifold dimension over the whole engine seed range can be shown with a three-dimensional chart (Fig.5), from which this dimension can be recisely selected. 4 CONCLUSION If an intake manifold with variable geometry is to be designed, then its dimensions must be very recisely determined for every engine working oint. The resented analytical equations give results very quickly, but they may not be sufficiently accurate. There is no doubt that three-dimensional simulation calculations would give a much better insight into the charging of the cylinder, but they would require a large amount of inut data, and with currently available comuters the calculations would last too long. Therefore, it is necessary to find a comromise between accuracy and the time necessary to obtain the result in the design rocess, and to find a way how to otimally use all the mentioned methods. In the first hase, the analytical equations will be useful for determining the aroximate intake-manifold dimensions. Further otimisation can then be achieved, as has been shown, using one-dimensional simulation calculations, which in most cases give very accurate results. One-dimensional calculations have roblems with the flow through shar bends, ie junctions and oet valves. Using three-dimensional calculations on these elements, it is ossible to obtain more accurate constants that will be used in simler and faster one-dimensional models, for even more accurate results. In the beginning these models can be simle, with only a few engine elements, but at the end of the rocess they must be comlete, i.e. they must contain all the engine elements. From the results of these calculations it is ossible to select the dimensions of the intake-manifold elements that would give the best engine erformance at a defined working oint. 5 LITERATURA 5 REFERENCES [] Fiala, E., H.P. Willumeit (967) Schwingungen in Gaswechselleitungen von Kolbenmaschinen. MTZ 4(967) Stuttgart, [2] Broome, D. (969) Induction ram, art, 2 &3. Automobile Engineer (969) London, Aril issue, 30 33, May issue, 80 84, June issue, stran 64

11 [3] Yagi, S., A. Ishizuya, and I. Fujii (970) Research and develoment of high seed high erformance, small dislacement Honda engines. SAE aer [4] Ohata, A.,Y. Ishida (982) Dynamic inlet ressure and volumetric efficiency of four cylinder engine. SAE aer [5] Ohata, A., H. Saruhashi, I. Matsumoto, Y. Imamura (985) Acoustic control induction system six cylinder engines. JSAE rev. August issue, 8-5. [6] Winterbone, D.E., R.J. Pearson (2000) Theory of engine manifold design. Professional Engineering Publishing, London, ISBN [7] Winterbone, D.E., R.J. Pearson (999) Design techniques for engine manifolds. Professional Engineering Publishing, London, ISBN X. Naslov avtorjev: Darko Kozarac rof.dr.ivan Mahalec dr. Luliæ Zoran Univerza v Zagrebu Fakulteta za strojništvo in ladjedelništvo Ivana Luèiæa Zagreb, Croatia fsb.hr fsb.hr fsb.h Autors Address: Darko Kozarac Prof.Dr.Ivan Mahalec Dr. Luliæ Zoran University of Zagreb Faculty of Mechanical Eng. and Naval Architecture Ivana Luèiæa Zagreb, Croatia fsb.hr fsb.hr fsb.hr Prejeto: Srejeto: Odrto za diskusijo: leto Received: Acceted: Oen for discussion: year stran 65