Experimental study on the forcing design for an intermittent injection

Intermittent jets injected into a cavity are rather common in widely different applications; ranging from the injection of blood into and from the heart ventricles to the fuel injection into internal combustion engines. Understanding their behaviour is becoming more and more crucial. As an example, heavy duty vehicles (HDV) and cars are responsible for around \(5\%\) (European Commission 2007) and \(12\%\) (European Commission 2014) respectively of total EU emissions of carbon dioxide (CO\(_2\)), the main greenhouse gas. In view of these facts, the European Commission pursues firmly the policy of reducing the environmental impact of transports and disciplining automotive engines emission requirements. This is one of the reasons why engines innovation, seeking to improve their performance and efficiency, has become a key task in mechanical engineering, technology and research.

Combustion in modern internal combustion engines is a complex phenomenon that depends on the mixing of the fuel with air and is associated with turbulent conditions. Turbulence may intensify combustion but it may also quench the flame. In the case of spray combustion, the injection process is the phase which has most potential to improve combustion, by enhancing mixing in the short time between injection and combustion. In addition, this mixing by pulsed injection is relevant also in several different areas, such as liquid/liquid and gas/liquid dispersions in chemical and chemical engineering applications or processing and treatment of radioactive waste and in general pollutant dispersion.

Many previous studies have clarified that a more efficient entrainment of bulk ambient fluid and an increased jet mixing rate can be attained by unsteady, e.g. pulsatile instead of continuous, injection (Tanaka 1984; Bremhorst and Hollis 1990; Johari and Paduano 1997; Nathan et al. 2006). This has led to the design of the so called common rail injectors in modern diesel engines: the injectors can be steered electronically with respect to duration and frequency of injection (Doudou 2005).

In addition, both older and recent studies (Borée et al. 1997; Musculus 2009; Hu et al. 2012; Grosshans et al. 2015) have shown that, during and after a deceleration phase, pulsed jets experience better mixing. Musculus (2009) has investigated analitically the genesis of a wave of increased entrainment, related to the deceleration phase, which travels downstream at twice the jet penetration rate. The simplified model was later on extended to include full numerical simulations. For example Grosshans et al. (2015) used LES in their numerical study of intermittent jet mixing. The entrainment at the head of the jet is found to be lower (in the accelerating phase) as compared to the entrainment at the tail of the injected jet during the deceleration phase. Additionally, as the initial speed of the tail of the jet is larger than the speed of its head, the shape of the jet and thereby the mixing is enhanced as the jet bulb travels downstream.

The concept of entrainment wave, as introduced by Musculus (2009), derives from a simplified version of the integral momentum transfer equation in jetsIt is a nonlinear first-order wave equation where \(\beta\) is a positive coefficient and M is the integral momentum. So, a deceleration transient \(\left( \frac{\partial {\dot{M}}}{\partial t} < 0 \right)\) generates a positive momentum flux spatial gradient \(\frac{\partial {\dot{M}}}{\partial x}\) and therefore an increased entrainment rate. More details can be found in Musculus (2009).

This paper aims, through experiments, to shed light on the influence exerted on the flow field by the jet temporal profile. In particular we aim to study the effects that the deceleration phase has on the generated flow field and mixing. In a combustion engine, prior and during the combustion, there are substantial pressure and temperature gradients. Hence baroclinic and dilation effects may be equally important as vortex stretching in vorticity and turbulence dynamics. In order to isolate the latter effects, in our experiments we exclude compressibility effects, whereby only the effects of vortex stretching in the enhancement of vorticity and in the transfer of turbulent energy to smaller scales (assuming that viscous effects are small) is considered. The experimental set-up uses injection of liquid into liquid (water into water), and focuses only on the effect of the temporal shape of some injection profiles.

Intermittent injection implies the additional formation of vortex rings. Their formation dynamics can be characterized through a dimensionless timescale based on the formation process energy, i.e. \(\hat{T}\approx 4\) (Gharib et al. 1998) (\(\hat{T}=\frac{L}{D}\) in a piston–cylinder apparatus) with piston motion along a length of L and diameter D. When vortex generation durations are shorter or equal to the limiting value \(\left( \hat{T}\le 4 \right)\), all the vorticity is collected by the initial, leading vortex ring. Whereas for larger injection times, all the vorticity induced starting from \(\hat{T}\approx 4\) is generated at the trailing jet vortex, although unable to nourish the main vortex with additional vorticity. Krueger (2001) was able to demonstrate that such limiting time corresponded to the maximum normalized time-averaged thrust; Dabiri and Gharib (2004) found that a vortex ring can contain up to 65% of entrained fluid fraction; Olcay and Krueger (2008) revealed through a PLIF study that the time variation of injection velocity along with the formation number timescale \(\hat{T}\) affects the initial and terminal entrainment rates; while Querzoli et al. (2010) related the limiting time in gradually varying velocity flows, representative of real flows in nature, to the time when the positive acceleration ends, that is when \(u^{*}=\frac{L(t)}{t}\) is maximum, \(u^{*}\) being the velocity of the ejected fluid and L the piston stroke length.

The paper is organized as follows: Sect. 2 describes the experimental setup and the measurement techniques. Section 3 is devoted to the experimental results in terms of flow statistics, entrainment ratio and triple decomposition (phase dependent) of the velocity field. Finally, in Sect. 4 our conclusions are presented.

The experimental setup includes the pumping system and the measurement system, as depicted schematically in Fig. 1. The pumping system is basically a hydraulic circuit originating from an auxiliary tank and driven by a piston-like system. The motion of the piston is driven by a programmable servo motor and can be defined arbitrarily by the user. A ballscrew mechanism transforms this rotational motion into linear and transmits it to a piston/cylinder. A fully-pulsed jet condition (only blowing and no-flow phases, no suction phase) is obtained thanks to a membrane chamber located downstream to the cylinder and equipped with check valves to dissociate the flowing water from the pumping mechanism. A flow-rectifying pipe connects this plastic chamber to the nozzle, downstream to which the pulsed jet is injected into a water tank (18 cm \(\times\) 18 cm \(\times\) 50 cm). Originally, this rig was constructed as a phantom setup in order to measure the diastolic function of the human heart, a more detailed description thereof can be found in Töger et al. (2015).

Planar PIV measurements are performed in the vertical plane at the centreline of the water tank/nozzle.

PIV is a proven technique (c.f. Adrian 2005) which allows to obtain spatial information on the velocity field in a plane illuminated by a laser. Consequently the acquisition system is composed of a Nd:Yag pulsed laser (25 mJ/pulse) and of a Flowmaster 3s Camera (12 bit, 1280 pixel \(\times\) 1024 pixel resolution). The camera had a 6.7 \(\upmu\)m sensor pixel size and was equipped with a 50 mm focal length objective set at an aperture equal to \(f_{\#}=2\). The water was seeded by glass hollow beads having a density of 1.05–1.15 g/cm\(^3\) and a diameter around 10 \(\upmu\)m. The average particle image size was around 2.52 pixels. The particle image densities, evaluated as number of particles per pixel \((N_\mathrm{{ppp}})\), was at all times about 0.04. These values are close to the optimal value prescribed by Willert and Gharib (1991) \((N_\mathrm{{ppp}}=0.035)\) and in agreement with the recommendations of Raffel et al. (2007) and Cierpka et al. (2013) \(\left( 0.03< N_\mathrm{{ppp}} < 0.05\right)\). The magnification factor M was about 11 pixel/mm (roughly 0.09 mm/pixel). The light beam generated by the laser was converted by a cylindrical and spherical lenses optics set into a light sheet having a thickness of about 1 mm. The image mapping parameters, providing the relation between the positions \((x_\mathrm{{obj}},y_\mathrm{{obj}},z_\mathrm{{obj}})\) in the object domain and the corresponding positions in the image plan \((x_\mathrm{{im}},y_\mathrm{{im}})\) (see Soloff et al. 1997), have been determined inserting a dual plane calibration target in the object domain (laser sheet plane), illuminated with an incoherent white light source instead of the laser, to avoid speckle pattern on the surface that compromise the contrast of the calibration image (Adrian and Westerweel 2011). The locations of the target’s markers are reconstructed by a cross-correlation operation between calibration and template images in addition to a peak-finding algorithm (Willert 2006).

Acquired images have been processed by a digital cross-correlation analysis (Willert and Gharib 1991). A multi-grid/multi-pass algorithm (Soria 1996), with an iterative image deformation (Scarano 2001; Huang et al. 1993; Jambunathan et al. 1995; Nogueira et al. 1999) was used to compute the instantaneous velocity fields. The algorithm was based on two steps on a larger window size (64 \(\times\) 64 pixels) and four steps on a smaller (32 \(\times\) 32 pixels) with an overlap factor of 50%. Moreover, to eliminate spurious vectors, a vector validation algorithm, based on a regional median filter ( Westerweel and Scarano 2005), with kernel region of 3 \(\times\) 3 vectors, and group removing, is applied.

It has been shown that the size of the framed area can affect PIV results. For a fully developed turbulent flow, it was discovered that the size of the acquired region should not exceed a limiting value around 40 Taylor microscales (Lacagnina and Romano 2015). This condition depends on the size of the array used to record the PIV images, so the same limit value is not applicable in this case. Moreover, in the current measurements, the flow is not turbulent intermittently and even then it is not fully developed. Anyhow, one may estimate the “Taylor microscale” \(\lambda\) in this situation by the auto-correlation function. This estimate gives a value of approximately \(\lambda =3.2\,\times \,10^{-3}\) m (\(Re_{\lambda }\approx 650\)) and therefore the framed area (11 cm \(\times\) 9 cm) is slightly lower than the limit \(40\lambda\).

In this study three different time-dependent injection strategies have been chosen (as shown in Fig. 2), and they differ in terms of how the velocity changes along the pulse cycle. The first one is a square (on/off) profile characterized by extremely strong acceleration and deceleration, separated by a constant injection velocity phase. This strategy is depicted by the ratio between two time-sequences: namely the injection time \(T_1\) and the rest (no-injection) time \(T_2\). A value of \(\frac{T_1}{T_2}=0.5\) has been chosen as reference, while the values 0.2 and 0.85 have been studied for comparison. The second injection strategy is based on an isosceles triangular velocity profile in time, with an acceleration phase equal in modulus to the deceleration phase. Finally a scalene triangular velocity profile, having a deceleration larger in modulus (stronger) as compared to the acceleration (LAHD, low acceleration high deceleration). The three injection schemes have the maximum velocity at the cylinder in common and it is equal to 0.3 m/s. Obviously, the largest acceleration/deceleration occurs in the square (on/off) case and the mildest deceleration is in the isosceles triangular case, see Table 1. The injection profiles defined here vary in the injected momentum/mass. However, the different injection profiles have in common the mass flow rate, being close to 0.08 g/s, and the volume flow rate, in the range 4–5 L/min, as shown in Table 1. These values are not so different from the real ones for high duty diesel engine fuel injectors (2–2.5 L/min) and anyhow constrained from our setup. Moreover, as we are focusing on the mixing, we can assume that the required amount of injected fluid or its momentum, can be accounted for by, for example, multiple injectors. Here, we aim at comparing different injections strategies with given injection rates during a given injection time.

Moreover, in order to study the effect of the Reynolds number on jet features, three different nozzle diameters have been installed: \({D_0}= 25\) mm, \({D_1} = \frac{D_0}{2} = 12.5\) mm and \({D_2} = \frac{D_0}{3} = 8.3\) mm. Keeping the volume flow rates constant, the variation in the cross section is balanced by an increased inlet velocity corresponding to Reynolds numbers in the range \(Re=11{,}000{-}34{,}000\), see Table 2.

The measurement section was located two \(D_0\) diameters downstream to the nozzle edge on its symmetry axis (x, see Fig. 3) and it extends along roughly four diameters \(D_0\). The origin of the coordinate system is in center of the nozzle section, in correspondence to its lip. Therefore the u velocity component is along the streamwise direction (X axis) of the jet and the v component along the vertical direction (Y, r axis). Each injection cycle was subdivided into twenty periods and fifty PIV images (double frame) were acquired in correspondence to each phase.

This work is focused on an experimental study on the influence that the design of injection strategies have on the flow field and mixing potentiality of pulsed jets, paying a specific attention on the deceleration phase of the forcing. The attention is on the modifications of the velocity field investigated by means of the particle image velocimetry (PIV) technique. Three different injection velocity strategies have been used, namely square, isosceles triangle and high deceleration scalene triangle (LAHD). It has been shown that the square injection strategy has the highest values of entraining inward radial velocity to which does not correspond a high mass entrainment, potentially due to its extremely abrupt deceleration. While the LAHD strategy has a large inward radial velocity which does correspond to a high mass entrainment, possibly sustained by the entrainment wave triggered by the strong but not abrupt deceleration. The steep deceleration of the square strategy is anyhow able to develop the highest values of turbulent mixing as reflected by the magnitude of the turbulent fluctuations. This effect increases while the vortex moves forward to the far field.

Among the square injection strategies, it has been found that a shorter injection to rest ratio \(\frac{T_{1}}{T_{2}}\) is able to deliver a higher mass entrainment. Moreover, the vortex ring in these cases is able to travel downstream more rapidly, as predicted by the model of Musculus (2009).

The organized systematic variations in velocity, associated with the periodic flow, have been discriminated from the chaotic or turbulent ones, by means of a Triple Decomposition, and the two contributions have been contrasted for the different injection strategies.