Gas exchange process for IC-engines: poppet valves, valve timing and variable valve actuation
Topics Analysis of the main parameters influencing the volumetric efficiency in IC engines: - Valves and valve timing - Dynamic effects - Turbocharging
Introduction At the end of each cycle, in an IC engine the burned gases have to be replaced by new charge of air/fuel and (often) recycled exhaust gases. The gas exchange process is quite complex since it involves many time-dependent phenomena, such as: unsteady and compressible flows, frictional losses, heat transfers, area changes and complex geometrical paths. During the gas exchange process, because of the cyclic operation of cylinders, the flows through each component are pulsating and strongly influenced by inertia effects and wave actions, and hence difficult to be analyzed.
Layout of the intake and exhaust systems for a 4- stroke, TC, SI engine.
Volumetric efficiency or filling coefficient Volumetric efficiency (ηv) or filling coefficient (λv), defined as: ma: trapped air mass per cycle mt: theoretical amount of mass that can fill the cylinder displaced volume ρa: air density at reference conditions V: cylinder displaced volume
The filling coefficient measures the engine capability to fill its displacement with air. For this reason, it is defined as the ratio between the trapped air mass per cycle and the theoretical amount of mass that can fill the engine displacement at reference conditions.
The actual air mass, ma, aspirated inside the cylinder at the end of the single cycle, is different from the ideal one mt, for different reasons:
1) Burned gases inside the combustion chamber Vc at the end of the exhaust process, have a pressure pr which is higher than the atmospheric pressure pa. Therefore, burned gases expand, at the beginning of the induction stroke, filling part of the displacement Vd (that, instead, should be filled by fresh charge).
2) Pressure inside the cylinder at the end of the induction stroke is lower than pa, because energy must be spent to overcome frictional losses along the induction system and to accelerate the fluid through the inlet ports. The inlet valve does not close at BDC (point 1), but somewhat later at the beginning of the compression stroke (point i), where is pi> pa. However, the available volume Vi for fresh charge is then lower than V1, hence the loss in filling is evident.
3) During the intake exchange process, heat is exchanged between the hot engine walls and the entering fresh fluid, increasing the temperature of the new charge and hence decreasing the air density inside the cylinder at the end of the induction process.
4) The gas exchange process is influenced by dynamic effects, due to unsteady flows and pressure wave actions, which can improve or hinder the cylinder filling, depending on whether the geometry of the induction system is tuned or not with available times. To overcome this limitation, some car engines use now induction systems of variable geometry with the rotational speed.
5) For reasons of simplicity, cost and reliability, the conventional engines are equipped with a fixed angular valve timing. This means that the crank angles of valve opening and closing does not vary with the engine rotational speed n. For this reason, times available for the exchange process decrease when the engine speed increases. Hence fixed timings (with fixed geometry) can be optimized just for a limited engine speed range.
A first estimation of the filling coefficient (λv) can be achieved by applying the energy conservation to the intake process: which, after some manipulation, can lead to the following expression:
Numerical fluid dynamic models are needed for more accurate predictions.
Dependency of the volumetric efficiency from the engine speed: 1) CURVE A: Non- dependent speed effects (like fuel vapour pressure) drop ηv below 100% 2) CURVE B: Charge heating in the manifolds and cylinder drops curve A to curve B. It has a greater effect at lower engine speeds, due to the longer gas residence times. 3) CURVE C: Frictional flow losses increase as the square of the engine speed, and drop curve B to curve C. 4) CURVE D: At higher engine speeds, the flow into the engine during at least part of the intake process becomes chocked. Once it occurs, further increases in speed do not increase the flow rate significantly, so volumetric efficiency decreases sharply (curve C to curve D). 5) The induction ram effect, at higher engine speeds, raises curve D to curve E. Late inlet valve closing, which allows advantage to be taken of increased charging at higher speeds, results in a decrease of ηvat low engine speeds due to backflow (curves C and D to F). Finally, intake and/or exhaust tuning can increase the volumetric efficiency (often by a substantial amount) over part of the engine speed range, curve F to G.
Poppet Valves In a four-stroke engine, the most significant flow restriction, along all the intake and exhaust systems, is usually located in the poppet valves. For this reason, the flow through these engine components has to be analyzed. Modern four-stroke engines usually control the opening and closing of the intake and exhaust ports of the cylinders by poppet valves. They offer: - Minimum fluid-dynamic losses - High sealing ability and good reliability while subjected to high accelerations (and hence inertia forces).
The quantity of heat absorbed by the valve when heat is released from the products of combustion amounts roughly to 70% by conduction through the valve head when it is closed, and 30% by conduction through the fillet underside of the valve when it is open and the exhaust gas is escaping through the exhaust port. When the valve is closed, about 76% of the total heat input from the heat released by combustion is transferred by conduction to the cylinder head coolant by way of the valve seat, and only 24 % of the total heat input to the valve is conveyed through the valve stem to the cylinder head coolant via the valve guide. High operating temperatures due to incorrect ignition timing and mixture strength raise the valve head temperature until the valve head becomes the focal point for pre-ignition. A portion of the valve head then becomes the point of ignition which again leads to further heating of the valve head until eventually the valve seat distorts. Consequently, the poor seating of the valve during the combustion phase provides an escape route for some of the burning gases and, as a result, causes excessive local overheat and burning in the valve rim and seat region.
If large quantities of combustion products accumulate around the valve seat they will eventually become dislodged due to the repeated valve closing impact, some of the break-away deposits will then provide exit passages for the burning gases. The partial radial tunnelling around the valve seat when it is closed will therefore cause the valve seat to overheat as the gas escapes, since the heat flow path around the head is interrupted. This may result in severe carburization and oxidation of the valve seat surface, and ultimately it may burn a semiconcave groove into and around the valve seat. The name 'guttering' is derived from the top face contour of house guttering.
Flow coefficient Flow through a valve is mainly influenced by the available area and the pressure head across cylinder and pipe. The valve flow area (both exhaust and intake) is rapidly varying with time, or better it is a function of crank angle θ, which is proportional to time, for a given shaft rotational speed ω.
The pressure upstream the valves changes continuously with time, therefore the flow through the valve results highly unsteady. It is also turbulent, and some useful information can be drawn from flow tests in steady-state conditions. The figure illustrates the main device used in these flow tests.
Direct flow (from the manifold to cylinder): through the actual port-valve group (or a preliminary model), air is aspirated by a fan located in the cylinder, to simulate the piston effect. Reverse flow (from the cylinder to the pipe): in this case, the fan is pressuring the cylinder.
In both cases, the lift is kept constant and, at steady flow conditions, actual air mass flow rates are measured, for different valve lifts and pressure heads Δpv across the valve. To derive more general information about the flow, that may be extended to other engines operating at similar fluid-dynamic conditions, the measured actual air mass flow rate values are made dimensionless by dividing them by the ideal mass flow rates that would pass through a reference area Avref under the same Δpv in an iso-entropic expansion.
This is the valve flow coefficient C: ma = measured air mass flow rate mid = ideal air mass flow rate that would pass through a reference area Avref under the same Δpv in an iso-entropic expansion. Avref = is the reference area, set to be constant and equal to the inner seat area:
The flow coefficient for fully turbulent flow is independent on Re. where a01 is the total speed sound in 1 and the compressible flow function is:
m* is the critical or sonic mass flow.
The flow coefficient includes not only the typical losses of the actual flow (friction, heat exchange, energy dissipation, etc.), but also effects of continuous change in geometric flow area. Since the flow is fully turbulent, the effect of Δpv is negligible, and typical values of C are usually plotted as function of l/dv (non-dimensional valve lift). C is increasing with l/dv since the geometric flow area increases, but it do not reach values near unity because the ideal flow rate is referred to Avref, that is greater than the actual one, even at lmax. C values for reverse flow are lower than for direct flow due to higher energy losses.
To avoid complex calculations, it is useful to refer to the following areas, which are simple to be determined:
The lateral surface Aca of the cylinder of base diameter dv and height l, called curtain area and expressed by:
The area Av of the cross section of the valve seat, or seat area, expressed by:
The curtain area is not the minimum flow area, but it varies linearly with lift, including its effect in the change of flow section. It is therefore useful to consider the following ratio Γ:
The coefficient Γ reaches unity when is l/dv = 0.25, showing that it is useless to increase the lift beyond the value that makes the curtain area equal to the seat area, because then the seat area (and no more the curtain area) becomes the minimum section of flow control. For this reason, also the flow coefficient reaches the maximum value around l/dv = 0.25. In each case, it becomes possible to quantitatively assess how much can be gained, in terms of effective flow area, by further increasing the maximum lift, and to compare this advantage with the draw-back of higher accelerations, that are amplified with the ratio of minimum lifts.
The flow coefficient increases with l/dv, since the geometric flow area increases, but it does not reach values near unity, because the ideal flow is referred to an area greater than then actual one, even at the maximum lift. The effective geometric flow area is the lateral surface of a cylinder whose diameter is equal to dv and height equal to the valve lift l. The C values are lower for reverse flow than for direct flow, due to higher energy losses, since the poppet valve does not follow the air flow as efficiently as in the direct flow:
Port design significantly affects the discharge coefficient performances, which can approach the isolated valve values in case of well designed conditions.
Flow Area The motion of a poppet valve is usually designed in order to avoid the oscillations superimposed to the basic lift trend, driven by the cam, and the problems of lubrication and wear. These conditions determine the shape of its acceleration and velocity diagrams. The maximum valve lift is generally the only parameter that can be utilized to improve the cylinder filling. In this optimization process, it is necessary to understand that the minimum flow area is a complex function of lift as well as valve and seat dimensions.
The cross-sectional area varies continuously with the valve lift and it is a function of the crank angle θ: h/dv = h/dv(θ) The flow coefficient is function of valve lift: C=C(h/dv) and finally the (instantaneous) effective area is a function of the crank angle.
The effective area is the one in correspondence of the vena contracta of the flow. If the flow coefficient is equal to 1 (ideal condition), the effective available cross sectional area for the flow over the reference area will have this slope: Aeff/Aref, where Aref = valve seat area.
Flow Coefficient The value of C and the choice of reference area are linked together: their product, C Aref, is the effective flow area of the valve assembly Ae. Several different reference areas have been used, depending on the scope.
Valve Diameter The higher the effective flow areas opened by the valves are and the better the filling process is. There is a minimum value of this area, necessary to avoid that the flow reaches the sound velocity a in the minimum restriction. When this happens (the flow becomes chocked during the process) the gas exchange in the cylinder may substantially deteriorates, since fluid velocities can no more increase beyond the sound velocity. Chocking is particularly critical in the intake valve, because it blocks any further raise of mass flow rate, needed to increase the rotational speed of the engine, which then becomes gulped.
Filling coefficients, measured on a large set of engines and intake valve designs, correlates quite well with a sort of mean inlet Mach Number, called inlet Mach index or gulp factor Z:
Vfmi is an appropriate fluid mean velocity during the inlet process, given by the mean piston speed up, amplified by the ratio between the cylinder cross section Acyl and the seat valve area Av(reduced by the mean flow coefficient during the inlet process, Cmi)
A simple model of inlet chocking process allows to correlate the volumetric efficiency with Z by the following relation:
The volumetric efficiency is rapidly decreasing after a critical value Zcrit (0.5 according to experiments, 0.75 according to a simplified model), because of choking process in the inlet flow area. The following expression allows to determine the minimum inlet area Av,min, necessary to avoid choking in all the operating range of the engine:
The geometry of the combustion chamber limits the area of the valve seats. Examples: flat cylinder head with 2 and 4 valves.
They are just theoretical values since the valve seats should be spaced adequately (for strength reasons, insertion of refrigerant passages, placing of spark and/or fuel injector…).
The intake valve diameter div is usually larger than the exhaust one dev. Usually, div=1.1 dev. This is because fluid dynamic losses during the intake stroke influences more heavily the filling process.
The area available in the cylinder head is better exploited when more than two valves per cylinder are used. If two valves are used for the intake and two for the exhaust, the ratio between the overall flow area Aov and the cylinder section Acyl is now:
The area rise is 30% compared to the case when only one valve is used. When more than one valve per cylinder are used: - Each valve is smaller, offers a lower inertia and is easily cooled. - The valve-train is more complex, since four valves have to be driven.