# On discharge from poppet valves: effects of pressure and system dynamics

## Abstract

Simplified flow models are commonly used to design and optimize internal combustion engine systems. The exhaust valves and ports are modelled as straight pipe flows with a corresponding discharge coefficient. The discharge coefficient is usually determined from steady-flow experiments at low pressure ratios and at fixed valve lifts. The inherent assumptions are that the flow through the valve is insensitive to the pressure ratio and may be considered as quasi-steady. The present study challenges these two assumptions through experiments at varying pressure ratios and by comparing measurements of the discharge coefficient obtained under steady and dynamic conditions. Steady flow experiments were performed in a flow bench, whereas the dynamic measurements were performed on a pressurized, 2 l, fixed volume cylinder with one or two moving valves. In the latter experiments an initial pressure (in the range 300–500 kPa) was established whereafter the valve(s) was opened with a lift profile corresponding to different equivalent engine speeds (in the range 800–1350 rpm). The experiments were only concerned with the blowdown phase, i.e. the initial part of the exhaustion process since no piston was simulated. The results show that the process is neither pressure-ratio independent nor quasi-steady. A measure of the “steadiness” has been defined, relating the relative change in the open flow area of the valve to the relative change of flow conditions in the cylinder, a measure that indicates if the process can be regarded as quasi-steady or not.

## 1 Introduction

*R*is the specific gas constant. If the flow is choked \(p_\mathrm{T}/p_0\) becomes constant

Whilst these assumptions seem reasonable, their validity has not been unambiguously confirmed. Previous studies on the subject are relatively few and contradictory in their support or rejection of the assumptions.

The effect of high pressure ratios, using a steady flow bench with pressure ratios up to \(p_{0_{\mathrm{cyl}}}/p_{\mathrm{port}}\approx\) 4.8 (\(p_{0_{\mathrm{cyl}}}\) is the cylinder total pressure and \(p_{\mathrm{port}}\) is the exhaust port static pressure) was investigated by Woods and Khan (1965). It was found that for low lifts (\(\ell /d<0.04\), \(\ell\) is the valve lift and *d* is the port diameter) the effective area was independent of the pressure ratio. For larger valve lifts (\(\ell /d>0.04\)), at pressure ratios \(p_{0_{\mathrm{cyl}}}/p_{\mathrm{port}}<2\), the effective area either increased or decreased, depending on the geometry. For \(p_{0_{\mathrm{cyl}}}/p_{\mathrm{port}}>2.2\) the effective area was shown to become constant for any given valve lift, partially supporting the assumption of pressure ratio insensitivity.

Decker (2013) investigated the values of \(C_\mathrm{D}\) of two different geometries under “blowdown-like” conditions. The experimental setup consisted of a pressurised cylinder, which was fitted to a cylinder top, exhausting to the atmosphere. When a pressure ratio (\(p_{0_{\mathrm{cyl}}}/p_{\mathrm{atm}}\)) of approximately nine was reached, the valve was quickly opened to a fixed lift and the cylinder was allowed to discharge (two valve lifts were tested, \(\ell /d\approx\) 0.03 and 0.06). The mass-flow rate was determined from the cylinder pressure (a similar method is used in the present study) and \(C_\mathrm{D}\) was evaluated from when the valve reached the desired lift, until a given pressure threshold (\(p_{\mathrm{cyl}}=200\) kPa), giving an approximate pressure-ratio range from 2.0 to 7.5. In that study, \(C_\mathrm{D}\) was shown to decrease as the cylinder pressure increased. The study also showed that a modified port geometry, which gave a 6–7 % increase in \(C_\mathrm{D}\) for steady measurements, actually showed a decrease of 1–3 % in \(C_\mathrm{D}\) when measured during the more realistic “blowdown-like” conditions. This suggests that neither the quasi-steady nor the pressure ratio insensitivity assumptions are valid.

An alternative approach to using a discharge facility is to use a pulsating flow, as Bohac and Landfahrer (1999) did. They investigated the quasi-steady assumption by comparing the mass flow measured on a pulsating flow bench (with a pulsation frequency equivalent to 6000 rpm) to the mass flow calculated using 1D-simulations, using \(C_\mathrm{D}\)-values obtained through steady measurements. The measurements were performed at fixed valve lifts, at pressure ratios of approximately 1.06. For the valve lifts they claim to be most important to the engine performance (\(0.12\le \ell /d\le 0.28\)), the mass flow obtained through simulations were within 0.5–2.5 % of the measured values. They assert that the quasi-steady assumption is reasonable and can be used for engine simulations.

With the development of computing power it is now also possible to do large eddy simulation (LES) of the exhaust process. Semlitsch et al. (2014) used LES to compare \(C_\mathrm{D}\) for steady conditions to \(C_\mathrm{D}\) under pulsating conditions (equivalent to 1500 rpm). In the simulations a fixed valve lift (\(\ell /d\approx 0.12\)) was used. Large differences in the flow-field were found between the steady and pulsating cases and the addition of pulsation resulted in a 2 % decrease in \(C_\mathrm{D}\) and they recommend measuring \(C_\mathrm{D}\) under pulsatile conditions.

In another study Semlitsch et al. (2015) investigated how valve and piston motion affects the exhaust process, again using LES. In this study, they performed simulations on a double exhaust-valve cylinder top. Three different types of valve and piston motions were investigated: (i) Moving valves (\(0.08\le \ell /d\le 0.36\)) and a moving piston, (ii) initially moving valves which stopped at \(\ell /d=0.12\) (\(0.08\le \ell /d\le 0.12\)) with the full piston motion and (iii) steady flow with fixed valves. The simulated engine speed was 1200 rpm and the initial pressure ratio (\(p_{\mathrm{cyl}}/p_{\mathrm{port}}\) at \(\ell /d=0.08\)) was 1.77. For case study (i) the flowfield at the end of a discharge period (when the valve had returned to \(\ell /d=0.08\)) was used for the initiation of the flow at the start of each cycle. The study showed large differences in flow-field characteristics between the different case studies. However, they claim that the small differences, that could be noted in \(C_\mathrm{D}\), represent an “error” and that the piston and valve motion can be neglected when performing low order modelling, i.e. implying that the discharge can be considered as quasi-steady.

Benson (1959) compared \(C_\mathrm{D}\) for a two-stroke engine (where the exhaust port opening is determined from the piston motion) under steady and dynamic conditions. In the dynamic experiments pressurised air was supplied to a mechanically driven engine. The release pressure ratio was approximately \(p_{\mathrm{cyl}}/p_{\mathrm{atm}}=4\) and the engine speed varied from 324 to 654 rpm. The mass flow out of the cylinder was calculated from the cylinder pressure trace and the release temperature of the gas in the cylinder. It was shown that the \(C_\mathrm{D}\) measured during dynamic conditions was considerably lower than those measured under steady conditions, indicating that the quasi-steady assumption is invalid.

The quasi-steady assumption was also investigated by Woods and Khan (1967), who compared pressure measurements from a dynamically discharging fixed volume cylinder and pressures calculated using 1D simulations with \(C_\mathrm{D}\) values obtained through steady flow experiments. The initial pressure ratio was in the range of \(1.89\le p_{\mathrm{cyl}}/p_{\mathrm{port}}\le 3.52\) for engine speeds in the range of \(407\le n\le 808\) rpm. They conclude that even though \(C_\mathrm{D}\) depends on both valve lift and pressure ratio, the pressure ratio can be neglected in the unsteady flow calculations. They reasoned that \(C_\mathrm{D}\) was independent of pressure ratio at low valve lifts and at higher valve lifts (where \(C_\mathrm{D}\) is more sensitive) the pressure ratio change is small. By comparing the measured pressures (in the cylinder and a flow restriction located downstream of the port) with the simulated pressures they also concluded that the process could be modelled as quasi-steady.

As the review of the previous studies highlights, there is no clear picture regarding the validity of the quasi-steady assumption or the assumption that \(C_\mathrm{D}\) is insensitive to pressure ratio. This motivates the present study, wherein these assumptions are directly tested by comparing \(C_\mathrm{D}\) obtained through steady flow experiments to \(C_\mathrm{D}\) measured on a discharging cylinder. The present experiments focus on the blowdown phase of the exhaust stroke, i.e. the initial part of the exhaustion where the pressure ratios are high and the limiting flow area is located around the valve head. Because of this the investigated valve lifts are limited to \(\ell /d\le 0.2\) (\(\ell \le 7\) mm).

In Sect. 2 the static and dynamic experimental setups, the geometry of the valve and seat as well as the method to determine the time-resolved mass flow rate are described. Section 3 shows the experimental results both for the static and dynamic tests for the one-valve cases, whereas Sect. 4 discusses a suggested new measure of unsteadiness, i.e. when the flow can be considered quasi-steady. In this section, also results from the double-valve experiments are shown indicating that dynamic effects are even stronger here, in agreement with the new measure of unsteadiness. Finally, Sect. 5 summarises the results and gives some conclusions drawn from the work.

## 2 Experimental method

The experiments can be divided into two types: static and dynamic. In the static experiments the valve was mounted in a cylinder setup, with a fixed lift and a steady flow exhausted through the valve using a gas stand (Sect. 2.1) with air at room temperature. The dynamic experiments used a moving valve, through which air, initially at room temperature, was discharged from a pressurised cylinder of similar size as a heavy-duty engine cylinder (Sect. 2.2). The key components (i.e. valve, seat, port and cylinder dimensions) are common to both the static and dynamic rigs. Both the valve and the valve seat are taken from a Scania diesel engine. In Sect. 2.3 the geometry of the valve/seat opening is shown especially with reference to the smallest area, whereas Sect. 2.4 describes the method used to determine the time-resolved mass-flow rate.

### 2.1 Static-valve rig setup

The setup of the static rig consisted of a 2 l cylinder with a diameter of \(B=\) 120 mm and length \(S=\) 177 mm that was connected to the 7\(^\circ\) conic diffuser through flanges. The cylinder had two taps for Pitot pressure-probes (or static pressure measurements) and two axially co-located taps for total temperature probes (located 0.25 and 0.5*S* from the top plate). In the flange, connecting the cylinder and diffuser, a holder crosses the pipe that allows for the valve actuation rod (VAR) to be locked at any fixed valve lift (Fig. 4 show the dynamic setup, but the connection between the VAR and the valve was similar in both cases).

*d*), whereas the valve had an outer diameter of \(\phi =41\) mm and an angle of 45.5\(^\circ\) (see Fig. 3).

The port connected to a 35 mm diameter straight outlet pipe (approximately 15*d* long) that exhausted to the atmosphere. The outlet pipe also hosted two 1 mm pressure taps that were located 2*d* and 2.5*d* downstream of the cylinder top. Slightly downstream of the pressure taps the outlet pipe had a tripod guide that fixed the valve stem to the centre of the pipe. To decrease the aerodynamic blockage the leading and trailing edges of the 1 mm thick tripod arms and the guide tube (which has a wall thickness of 2 mm) were filed at an angle of 30\(^\circ\) with respect to the major axis of the setup.

Although most experiments were made in a single-valve setup an additional top plate was designed and manufactured to accommodate a double-valve geometry since four valves per cylinder, i.e. two inlet and two outlet valves, is the most common configuration in engines today. The centre-to-centre distance between the valves was 45.5 mm and each valve had its own outlet of the same length as in the single-valve geometry.

All data in the static experiments were acquired with a sampling frequency of 16 kHz for 5 s, using a 16-bit National Instrument PCI-6250 A/D-converter using a LabView program.

The mass-flow rates were set to cover the range of mass flows obtained in the dynamic experiments for a given valve lift.

### 2.2 Dynamic valve rig

For the dynamic valve experiments a cylinder with the same dimensions as in the static valve case (\(B=120\) mm; \(S=\) 177 mm) was clamped and sealed between two 20 mm thick plates (see Fig. 4). The “top plate”, where the valve/seat assembly was located, was the same as in the static experiments. The cylinder had three pressure taps (placed 0.25, 0.5 and 0.75*S* from the cylinder top) and three axially co-located ports for temperature probes. Initial testing of the setup showed negligible difference between the three different cylinder pressure mountings, thus it was decided to use only the centrally placed tap in the experiments. All pressures were measured using Kistler 4045A5 piezoresistive transducers (500 kPa range), which have a quoted linearity \(\le 0.1\) % of full scale output. The temperature was measured using a T-type thermocouple and a Fluke 51-II thermocouple reader, which has an accuracy better than about \(\pm 0.3\) K. The cylinder was charged prior to exhaustion from a compressed air supply through a solenoid-controlled valve, located near the bottom of the cylinder. The air pressure at start of the exhaustion was varied in the range 300–500 kPa.

The top and bottom plate had stadium-shaped sinks (5 mm deep), in which the cylinder was fitted. This allowed the location of the valve to be moved relative to the cylinder wall, thus allowing the radial position of the valve to be changed. For the experiments in this study the valve was centrally placed in the cylinder. However it was shown that a radial displacement of the valve did not show any significant effect on the outflow characteristics.

To increase the sealing ability in the dynamic experiments, the valve was painted with a rubber spray-paint. This was necessary since obtaining a perfect seal between the valve and the seat is (nearly) impossible without machining the seat to the right shape in situ. The rubber coating had a thickness less than 0.1 mm.

The valve was connected to a LinMot P10-70x320U electromagnetic linear motor, using the valve actuation rod (VAR), which allowed the valve position to be controlled. The VAR passed through the bottom plate via a guide and was sealed using a spring-loaded circular seal. In order for the linear motor to cope with the large forces required to actuate the valve when the cylinder is pressurized, the bottom plate and the VAR compressed a spring during valve closing. The spring generated a force of approximately 300 N when the valve is fully closed (about half of the force on the valve caused by the pressure difference between the cylinder and the outlet at a cylinder pressure of 500 kPa). The valve position was measured using a Novotechnik TE1-0025 linear transducer that was connected to the slider of the linear motor. The quoted repeatability of the linear transducer is 2 \(\upmu\)m and the linearity is ± 0.2 % of full scale output (FSO = 25 mm).

*p*is the pressure that one is trying to measure (the seat pressure in this case), \(\zeta\) is the damping ratio of the setup and \(\omega _{0}\) is the natural frequency (in radians per second) of the setup. The natural frequency of the setup can be estimated with good accuracy using the following relation (see e.g. Bajsić et al. 2007):

*a*is the speed of sound, \(L_\mathrm{p}\) is the length of the pressure port, \(A_\mathrm{p}\) is the cross sectional area of the pressure port and

*V*is the end-volume connected to the sensor. The damping ratio is more complicated to estimate, and here it has been determined experimentally. This was done using a bursting membrane to generate a pressure step, details of these experiments are given in Winroth (2017b).

When running an experiment, the valve was closed and the cylinder slowly pressurized to the desired initial pressure (\(p_{0i}\)). When the temperature had stabilized the linear motor was triggered and the valve thereby actuated according to a pre-programmed partial sinusoidal lift-profile equivalent to the lift profile of an engine at a given engine speed (*n*). The experiments were controlled through LabView and the data were acquired with a sampling frequency of 25 kHz. Each case was repeated 8 times and the data were later ensemble averaged.

The initial pressure was varied from \(p_{0i}=300\) kPa to \(p_{0i}=500\) kPa, in steps of 50 kPa, and the tested equivalent engine speeds ranged from 800 to 1350 rpm.

### 2.3 Geometric minimum flow area

*s*):

When the valve initially lifts from the seat the location of the throat moves from the seat-valve contact point to the back of the conic section of the valve and connects orthogonally to the conical section of the seat. For valve lifts \(0.014<\ell /d<0.17\) the throat moves upstream towards the seat leading edge connecting to the back of the valve conic section. By further increasing the lift in the range \(0.17<\ell /d<0.198\) the location of the throat is fixed at the leading edge of the seat-conic section and the back of the valve-conic section. In this range only the angle of the frustum is changing. As the lift is increased further, the position of the throat “jumps” back to the trailing edge of the conic section of the seat and now starts to move downstream on the valve. Figure 7 shows the location of the throat for five valve lifts in the range \(0.114\le \ell /d\le 0.229\). Finally, at \(\ell /d\ge 0.354\) the minimum area is at the valve guide in the outlet pipe.

Since the location of the throat is changing, it is not possible to measure the true throat pressure with only one pressure tap at a fixed position. This means that the throat area cannot be used for \(C_\mathrm{D}\) calculations for subsonic flows. It also implies that the seat pressure (\(p_\mathrm {\mathrm{seat}}\)), which is measured 0.9 mm from the leading edge of the conic section of the seat, cannot be directly used as a “check” to decide if the flow is choked or not.

### 2.4 Time-resolved mass-flow measurements

To compute \(C_\mathrm{D}\) for the dynamic valve system, it is necessary to temporally resolve the mass flow during the discharge process. Time-resolved mass-flow measurements in pipe flows can be done by traversing a hot-wire probe over the cross sectional area of the pipe (Laurantzon et al. 2012) or by using a vortex-shedding meter (Ford et al. 2016). However, if \(C_\mathrm{D}\) is to be correlated to a certain lift, it is necessary to place the mass-flow meter very close to the valve itself. This is because the density may vary along the outlet pipe, and thus the time lag of the measurement relative to the lift becomes unknown.

*m*is the mass of the air in the cylinder,

*V*is the cylinder volume,

*p*and

*T*are the pressure and temperature of the air in the cylinder, respectively. To be able to use Eq. (9) directly it is necessary to measure both the time-resolved pressure as well as temperature. Although measuring time-resolved pressure is considered an easy task (with a flush-mounted pressure sensor), measuring temporally resolved temperature is not. This is usually accomplished using a cold-wire resistance thermometer, which can have a relatively high roll-off frequency (dependent on the wire length and diameter, Arwatz et al. 2013). When the temperature change is large, however, as in the present experiments (\(\Delta T \approx 100\) K) the thermal inertia of the prongs significantly influences the measurement accuracy, rendering cold-wire anemometry unusable for the present case.

## 3 Results

The results of the static single-valve experiments are presented in Sect. 3.1. In Sect. 3.2 the data from the dynamic single-valve experiments are presented and discussed.

Since there is no piston in the setup, the model experiments are only valid during the blowdown phase. Thus, the analysis will only consider \(\ell /d\le 0.2\), corresponding to \(\ell <7\) mm, for which typically the piston is near the bottom-dead centre, i.e. there is no pumping work done. In figures with lifts \(\ell /d>0.2\), the region where \(\ell /d>0.2\) is shaded to indicate that this region is not part of the main focus of the analysis.

### 3.1 Static single-valve experiments

In the experiments the position of the minimum geometric area (i.e. the throat position) moves as a function of the valve lift. Therefore, it is not possible to monitor the corresponding throat pressure. However, if the flow is choked, the ratio of total to throat pressure is fixed at \(p_0/p_T=1.89\). Thus, the isentropic mass flow, for choked conditions, can be calculated without measuring the throat pressure (see Eq. 4). This means that the flow must be choked when using the minimum geometric flow area as the reference area for calculations of \(C_\mathrm{D}\).

To check if the flow is choked the seat pressure was studied. If the flow is choked the pressure ratio \(p_0/p_\mathrm {\mathrm{seat}}\) should be constant. The pressure ratio is determined by the ratio of local flow area at the measurement location to the minimum flow area (Anderson 2004). Any change in this ratio is associated with an upstream change in effective area (total pressure loss or change in flow topology, such as the appearance of separation bubbles).

### 3.2 Dynamic single-valve experiments

The dynamic experiments are carried out by first filling the cylinder with air to the desired pressure, wait until the temperature stabilise whereafter the valve rod is actuated with the desired lift profile. For each parameter setting (pressure and equivalent rotational speed) the experiments were repeated eight times. To demonstrate the repeatability of the experiments, and to give the reader an impression of the signal-to-noise ratio, the raw pressure signals of the eight trials, for three different initial pressures, for an equivalent engine speed of 1350 rpm are shown in Fig. 11. Valve lift measurements, corresponding to engine speeds of 900 and 1350 rpm at an initial cylinder pressure of 400 kPa are shown in Fig. 12. Although some small-scale noise persists, the profiles are consistent and repeatable. This noise originates from electrical interference, generated by the linear motor used to actuate the valve. To improve the signal-to-noise ratio, for each case 8 trials were ensemble averaged.

The normalised demand lift profile is the same for all engine speeds. Evaluating the difference \(\epsilon =(\ell _{d}-\ell )/d\), where \(\ell _{d}\) is the demanded lift, it is possible to compare the different engine-speed lift profiles. Evaluating \(\epsilon\) for all test cases it is found \(-\,0.032\le \epsilon \le 0.027\) for \(\ell /d\le 0.2\), indicating that the different engine speeds have similar (though not perfectly matched) normalised lift profiles.

As discussed in Sect. 3.1 a condition for the calculations of the isentropic mass flow is that the flow is choked. Determining if the flow is choked is non-trivial in the dynamic experiment, since the local flow area at the seat pressure measurement is continuously changing. Instead the measured pressure ratio \(p_{0_{\mathrm{cyl}}}/p_{\mathrm{seat}}\) can be compared to the pressure ratio estimated from the ratio of the minimum geometrical area and the area at the seat measurement position. The case which should reach sub-critical condition at the lowest valve lift is the \(p_{0i}=300\) kPa case at an equivalent engine speed of \(n=800\) rpm. Figure 14 shows the measured pressure ratio of the different engine speeds for an initial cylinder pressure of \(p_{0i}=300\) kPa. This figure show a discrepancy between the measured pressure ratio and the pressure ratio estimated from the geometry. However, this deviation is mainly a result of the “installation” of the pressure sensor.

The setup for the seat-pressure measurement was found to be overdamped. The damping was found to be \(\zeta =3.5\) and the eigenfrequency \(\omega _0=5400\) rad/s (Winroth 2017b). Using these values and Eq. (5) the pressure measurement can be corrected to better reflect the pressure in the seat, see Fig. 15. Since Eq. (5) depends on both the first and second time-derivative of the pressure measurement signal noise is amplified. This means that the corrected seat-pressure is not suitable as a quantitative indicator of the seat pressure, but it is still useful for determining if the flow is choked.

To clearly illustrate the changes in flow physics between the static and dynamic cases Fig. 18 shows the pressure ratio of the cylinder pressure and the back pressure measured in the outlet pipe for various cylinder pressures with \(\ell /d=0.143\). The figure shows results both for the steady case as well as for the four different engine speeds used in this study. In the steady case a transition is clearly seen at a cylinder pressure around 240 kPa, where the back pressure becomes small and the ratio becomes constant independent of the cylinder pressure, indicating a supersonic flow at the position of the pressure tap. This pressure ratio of about 14 indicates a Mach number of about 2.4 and an area ratio of 2.3 if the flow was isentropic. However, for \(\ell /d=0.143\) the area ratio between the exhaust pipe area at the position of the pressure tap and the open valve seat area is 1.72 which would give a Mach number of 2.0. This difference may be explained by losses (such as oblique shock waves) in the flow giving a lower total pressure in the outlet pipe than the isentropic one.

## 4 Discussion

### 4.1 A measure of steadiness

To understand why the dynamic and static cases differ, it is necessary to reapproach the problem. Clearly the exhaust process is not quasi-steady as a dependence on *n* exists. However, as the faster *n* cases yield increased \(C_\mathrm{D}\) values it is also apparent that considering the valve motion alone (relative to some characteristic velocity) does not provide a complete picture of the problem. This calls into question the conventional reasoning that the process is quasi-steady because \(d \ell / d t<< \sqrt{\gamma RT}\). Further it raises the questions, what is governing the exhaust process? Is there another way to determine if the process is quasi-steady or not?

To understand the exhaust process, let us first consider the differences between a dynamic and static experiment. One of the major differences between the static and the dynamic experiments is that in the dynamic experiment the air in the cylinder will accelerate from nominally stagnant conditions, whereas in the static experiments the air flow is steady. This means that the inertial effects from accelerating the flow will be different in the two types of experiments. However, if this was the sole cause of the change in \(C_\mathrm{D}\), increasing engine speed should decrease \(C_\mathrm{D}\), which clearly it does not.

The conventional approach assumes the discharge process to be quasi-steady because the valve speed [\(\mathcal {O}(1)\) (m/s)] is much smaller than the characteristic flow speed [\(\mathcal {O}(10^2)\) (m/s)]. Hence, the flow essentially perceives the valve as stationary.

The relation between the characteristic speeds, used in the conventional approach, is a necessary requirement. However, that approach neglects the dynamics of the flow conditions, which are (for a cylinder discharge process) also continuously changing.

*p*,

*T*) are dictated by the amount of air in the cylinder and the associated time scale can thus be expressed as \(\tau _{\mathrm{c}} = m/\dot{m}\). Here, \(\dot{A}_\mathrm{T}\) is the time-derivative of the minimum area. The time scales associated with these values may be used to establish an additional criterion for the validity of the quasi-steady assumption, for dynamic exhaustion processes

For a large ratio \(V/A_\mathrm{T}^{3/2}\) the flow is expected to be quasi-steady. If the flow area is small only a small amount of air will leave the cylinder for a given lift. Likewise, if the volume is large the discharged air (at any given valve lift) will only have a small effect on the (cylinder) conditions.

In the experiments performed in this study a fixed volume is used. Thus, it is expected that the initial part of the exhaust process is most likely to be quasi-steady (as the flow area scales with valve lift).

Figure 20 shows \(Q_\mathrm{S}\) as a function of valve lift, for an initial pressure \(p_{0i}=500\) kPa. It can be seen that \(Q_\mathrm{S}\) rapidly decreases with increasing valve lift and that \(Q_\mathrm{S}<10^2\) at \(\ell /d>0.029\) for all engine speeds tested in this campaign. Referring to Fig. 17 it can be seen that the static and dynamic \(C_\mathrm{D}\) have similar values at high \(Q_\mathrm{S}\)-numbers, i.e. at small \(\ell /d\). The \(Q_\mathrm{S}\)-number increases with engine speed, a trend that also can be seen in Fig. 17 where higher engine speeds moves the obtained \(C_\mathrm{D}\) curves towards the one obtained from steady measurements. This indicates, somewhat surprisingly, that at high engine speeds the flow becomes “more quasi-steady”.

### 4.2 Double-valve experiments

Dynamic exhaustion experiments for the double-valve setup were performed at an equivalent engine speed of \(n=1350\) rpm. Considering the definition of the \(Q_\mathrm{S}\)-number (see. Eq. 14): when two valves are used instead of one, the time scale of the geometry is unchanged (\(2\dot{A}_\mathrm{T}/2A_\mathrm{T} = \dot{A}_\mathrm{T}/A_\mathrm{T}\)). However, the time scale of the flow conditions (\(m_\mathrm{c}/\dot{m}\)) will be affected, as a larger \(A_\mathrm{T}\) allows for a larger \(\dot{m}\). This means that the cylinder can discharge faster and that the time scale of the flow conditions should decrease, hence reduce the \(Q_\mathrm{S}\)-number relative to the single valve.

In Fig. 24 \(C_\mathrm{D}\) for both the double (dashed) and single (solid) valve experiments are plotted as a function \(\ell /d\). It can be seen that the double-valve setup in general displays a lower \(C_\mathrm{D}\) than the corresponding single-valve experiment. The double-valve setup also exhibits a larger dependency on initial pressure than for the single valve. These results support the observation that a more unsteady process has lower \(C_\mathrm{D}\) and higher pressure ratio dependency.

## 5 Summary and conclusions

An experimental investigation, focussing on the blowdown phase of the exhaust process of an internal combustion engine, has been carried out. The assumptions, i.e. that the flow can be modelled as quasi-steady and that it is pressure-ratio independent, usually made when using 1D/0D simulations for engine optimisation, have been examined through a series of experiments. Most of the experiments were done with a single valve, although the effect of a double-valve configuration was also studied. The experiments included evaluating the discharge coefficient (\(C_\mathrm{D}\)) under both steady conditions, using a fixed valve, and by emptying a cylinder volume with a dynamically moving valve. The steady flow experiments were made using a high-pressure flow bench, with inlet total pressures up to 500 kPa and mass flow rates up to 0.5 kg/s. The dynamic estimation of \(C_\mathrm{D}\) were made by analysing the exhaustion of a pressurised (fixed volume) cylinder. The dynamic setup allowed the initial cylinder pressures and valve opening speeds (equivalent to different engine speeds) to be varied.

Dynamic determination of \(C_\mathrm{D}\) reveals a dependency on pressure ratio, where an increase in cylinder pressure results in a decrease of \(C_\mathrm{D}\). This was not anticipated from the static measurements where \(C_\mathrm{D}\) was rather insensitive to the cylinder pressure. It has also been shown that an increase in engine speed increases the value of \(C_\mathrm{D}\) as well as decreases the sensitivity to initial cylinder pressure. The dynamic values of \(C_\mathrm{D}\) are always significantly lower than those for steady flow at equivalent lift. Also the fact that \(C_\mathrm{D}\) is a function of engine speed suggests that the quasi-steady assumption is not valid.

A measure of the dynamics of the exhaustion process, the quasi-steadiness number (\(Q_\mathrm{S}\)), was formulated. This measure relates the time scale of the geometry change to the time scale of the change in flow conditions. The \(Q_\mathrm{S}\)-number has been used to show why the blowdown phase of a typical engine exhaust stroke cannot be considered as quasi-steady. It was observed that as \(Q_\mathrm{S}\) decreased (indicating a higher level of unsteadiness) the overall value of \(C_\mathrm{D}\) decreased and the dependency on initial cylinder pressure increased.

As a final conclusion the present experiments show that results of the \(C_\mathrm{D}\) obtained from static measurements can not be viewed as accurate if implemented in 1D/0D simulations. When doing simulations one should be aware of this fact and, although rather complicated, strategies for how to use more realistic values of \(C_\mathrm{D}\), determined from dynamic experiments at relevant pressure ratios, should be pursued.

## Notes

### Acknowledgements

This work was funded by the Competence Center of Gas Exchange (CCGEx) at KTH Royal Institute of Technology, Sweden, a centre supported by the Swedish Energy Agency, Scania CV, Volvo CARS, Volvo Powertrain, Borg Warner and KTH. The workshop staff (Rune Lindfors and Jonas Vikström) of the KTH Fluid Physics Laboratory are gratefully acknowledged for their technical support.

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