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ILASS-Americas 30th Annual Conference on Liquid Atomization and Spray Systems, Tempe, AZ, May 2019

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*Corresponding author: [email protected]

Influence of K-factor on Cavitation Suppression for a Heavy-duty Diesel Injector Operating with Straight-run Gasoline

R. Torelli*, G. M. Magnotti, and S. Som

Argonne National Laboratory Lemont, IL 60439-4801, USA

Y. Pei, M. Traver

Aramco Services Company: Aramco Research Center – Detroit Novi, MI 48377-1732, USA

Abstract

The occurrence of cavitation inside injectors is generally undesirable since it can cause material erosion and result in deviations from the expected operating conditions and performance. Previous numerical work employing an injector geometry measured with x-ray diagnostics and operating with a high-volatility straight-run gasoline has shown that: (1) most of the cavitation is generally observed at low needle lifts, (2) needle motion is responsible for asymmetric structures in the internal flow as well as large pressure and velocity gradients that trigger phase transition at the orifice inlets, and (3) cavitation affects the injector discharge coefficient and distribution of injected fuel. To explore the potential for material damage within the injector orifices due to cavitation cloud collapse, the cavitation-induced ero-sion risk assessment (CIERA) tool has been applied for the first time to the realistic geometry of a heavy-duty injector using the CONVERGE software. Critical locations with high erosive potential matched qualitatively well with x-ray scans of an eroded injector sample that underwent a durability test with straight-run gasoline. This motivated a CFD exploration of orifice design modifications, using a nominal reconstruction of the realistic geometry and an automated procedure for fast generation of modified surface files. In this work, the influence of the orifice K-factor on the inten-sity and duration of cavitation structures was investigated. Quantitative and qualitative analyses highlighted the im-portance of this parameter in limiting or suppressing cavitation inside the injector orifices and provided useful insights and design guidelines for injectors operating with high-volatility fuels.


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Introduction According to long term projections, the growing

global economy will drive an increase in the transport of both people and commercial goods. At the same time, higher internal combustion engine efficiency and the growing presence of electric vehicles will lead to a peak and subsequent decrease in light-duty vehicle energy de-mand [1]. This is expected to result in decreasing de-mand for gasoline products while that of diesel and mid-dle distillates continue to rise [1, 2]. This scenario sug-gests that gasoline could become an attractive alternative fuel for commercial vehicle users if the total cost of own-ership becomes competitive compared to traditional die-sel vehicles. Gasoline compression ignition (GCI), a more thermodynamically efficient combustion type than traditional spark ignition, could provide such a solution. GCI allows the fuel to be burned under low temperature combustion (LTC) conditions while increasing fuel effi-ciency and reducing criteria pollutant emissions [3, 4]. In recent studies, the use of a straight-run gasoline (SRG) has been explored as a potential candidate for prelimi-nary testing. SRG is characterized by diesel-like chemi-cal reactivity and physical properties similar to market gasoline [3, 4], which make this fuel the ideal intermedi-ate step towards the use of conventional gasoline in com-pression-ignited engines.

Typical gasoline injection systems are commonly designed for spark-ignited engines and for maximum in-jection pressures of 250-300 bar. However, it has been shown that in order to achieve simultaneous mixing-con-trolled GCI operation and particulate emission benefits (compared to diesel), the injection pressure should be in excess of 1000 bar [3, 5, 6]. On the other hand, some researchers concluded that the high fuel pressure require-ment could be relaxed by developing low temperature and partially premixed GCI [7, 8]. Nevertheless, higher diesel-like injection pressures might still be needed in or-der to minimize particulate emissions under peak load engine operation [9].

It is reasonable to assume that under operating con-ditions typical of diesel fuel injection, the behavior of gasoline-like fuels might deviate from that of diesel fuel due to considerable differences in their thermodynamic and transport properties. Previous work by the authors provided a detailed analysis of the physical properties of SRG and specifically compared viscosity, density, and saturation pressure against those of other diesel-like fuels such as n-dodecane [10]. For internal nozzle flow applications, fuel density and viscosity were found to be the main factors in determining the total amount of fuel that the injection system was capable of delivering. Computational fluid dynamics (CFD) simulations showed that SRG’s lower viscosity (one order of magni-tude lower than diesel’s) enabled higher velocities and

volumetric flow rates inside the injector orifices that par-tially compensated for the SRG’s lower density. How-ever, the higher saturation pressures, typical of gasoline-like fuels, enhanced the occurrence of cavitation inside the injector. The phase change due to cavitation typically occurred at the needle seat and at the inlet of the injector orifices where strong velocity and pressure gradients were more likely to develop [10-12]. The presence of cavitation resulted in perturbations to the internal flow field and caused considerable deviations from the ex-pected performance of the injector.

Subsequent work from the authors pointed out that another major cause for strong flow field disturbances is the occurrence of eccentric injector needle motion during the injection event [13, 14]. In their work, the authors showed that the fuel’s tendency to flow along preferen-tial paths inside the injector is tightly connected with the radial motion of the needle. Using CFD simulations, it was shown that, as a consequence of the interaction with the needle, the flow formed asymmetric and high veloc-ity jet-like structures which would originate on one side of the needle seat, cross the injector sac, and enter the orifices located on the opposite side. This would cause strong flow separation and intense cavitation at the lower edge of the orifice inlets, contributing to non-negligible orifice-to-orifice variability [13].

Another potential concern about using gasoline-like fuels in GCI applications is connected with the reliability and durability of the injection system, especially if the hardware was originally designed to operate with diesel fuel. Tzanetakis et al. [15, 16] recently performed a se-ries of durability studies in which they employed SRG in the same diesel injection system from which the injector simulated in this work was obtained. In [16], x-ray im-aging was performed to evaluate the injector geometry following a series of durability studies. The x-ray images indicated significant cavitation damage to the injector or-ifices after only 200 hours of operation with SRG. Dam-age to the injector was observed to accelerate as the in-jector reached 400, 600, and eventually 800 hours of op-eration.

Several authors have numerically and experimen-tally investigated the effect of injector design on the in-ternal flow and ensuing spray. Morgan et al. [17] com-pared valve-covered orifice (VCO) and mini-sac injec-tors in an experimental study and found that, under sim-ilar operating operations, VCO nozzles provided a better atomization and evaporation, together with a lower rate of penetration than those of mini-sac injectors, likely due to different internal flow structures. Blessing et al. [18] employed a not-scaled, transparent single-hole diesel in-jector and performed optical measurements of the inter-nal flow with maximum injection pressures of 800 bar. Using three different injector tips with K-factors of -2.5, 0.0, and 2.5 respectively, Blessing et al. [18] studied the


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impact of K-factor on cavitation development, where K-factor is defined as follows:

𝐾𝐾 =𝑑𝑑𝑖𝑖𝑖𝑖[𝜇𝜇𝜇𝜇] − 𝑑𝑑𝑜𝑜𝑜𝑜𝑜𝑜[𝜇𝜇𝜇𝜇]

10 (1)

where 𝑑𝑑𝑖𝑖𝑖𝑖 and 𝑑𝑑𝑜𝑜𝑜𝑜𝑜𝑜 are the orifice inlet and outlet

diameter expressed in µm. Blessing et al. showed that cavitation inside the orifice was strictly correlated with the K-factor value. Indeed, large cavitation structures were observed for the divergent and straight orifice (i.e., with K-factors of -2.5 and 0.0 respectively), while the convergent design (K-factor of 2.5) allowed for complete suppression of the cavitation inside the orifice. Blessing et al. [18] also observed a strong correlation between the occurrence of cavitation inside the orifice and changes in global spray characteristics. It was observed that in the presence of cavitation inside the orifice, a wider spray cone angle and a shorter liquid penetration were rec-orded. Conicity and hydro-grinding (i.e., orifice inlet ra-dius of curvature) were investigated by Som et al [19] who concluded that these parameters can significantly help to reduce cavitation and turbulence levels inside the orifice, and in turn slow down primary breakup and lead to larger droplets. Som et al. [19] also showed that spe-cific injector design choices can have direct conse-quences on the spray in terms of increased penetration and more limited liquid dispersion. Hence, with conical and hydro-ground injectors, the evaporation rate and fuel air mixing could be reduced, allowing for ignition to oc-cur further downstream.

For some applications, cavitation has been found to improve injector performance, specifically with respect to issues such as coking. Argueyrolles et al. [20] pro-posed a criterion to define the minimum cavitation inten-sity required to avoid coking risk. They concluded that, by means of their method, it seemed possible to optimize a diesel injector geometry in terms of orifice diameter, conicity factor, and hydro-grinding level with the most suitable trade-off between engine performances (power and emissions) and robustness with respect to coking.

Although much work has been performed to under-stand the impact of injector orifice design on cavitation development and spray formation under conventional diesel injection operating conditions, there is a lack of understanding of how fuel properties may impact the se-lection of an optimal injector design. This question is of critical importance when focusing on how to improve the design of existing heavy duty injection systems for off-design fuels, such as high-volatility fuels.

The findings from Tzanetakis et al. [16] motivated the current study to better understand the potential for cavitation-induced erosion within heavy-duty fuel injec-tors operating with gasoline-like fuels. To link multi-

phase flow predictions with the progress towards mate-rial erosion, the cavitation-induced erosion risk assess-ment (CIERA) tool developed by Magnotti et al. [21] was employed in this computational study. The present work constitutes the first application of CIERA to a re-alistic geometry of a production heavy-duty diesel injec-tor.

The outcome of CIERA provided another strong jus-tification to pursue the study presented in this work. In order to better understand how cavitation can be con-trolled and potentially suppressed, the K-factor was var-ied across its range of validity to assess its impact on suppressing cavitation. The findings from this work can then be used to inform design guidelines when consider-ing the use of high-volatility fuels in heavy-duty injec-tion systems.

The manuscript is outlined as follows: first, the CFD framework is introduced, followed by a description of the cavitation erosion model employed in this study. Next, the geometry modification tool is described and the results on varying the K-factor are presented. Finally, the main findings and conclusions of the study are sum-marized.

CFD Modeling Framework and Setup All the simulations reported in this manuscript were

conducted with the CONVERGE CFD code [22]. An un-steady Reynolds-Averaged Navier-Stokes (URANS) formulation closed by the standard k-ε turbulence model [23] was used for the design exploration part of the study. The large eddy simulation (LES) one-equation dy-namic structure model [24] was used for the initial part of the work in which the erosion potential associated with the use of SRG was investigated. In the cavitation erosion studies, the use of an LES turbulence model was necessary to capture the pressure and velocity fluctua-tions that lead to cavitation shedding and fuel vapor cloud collapse. As noted in the work of Magnotti et al. [25], the high numerical viscosity characterizing URANS formulations limits their ability to predict cavi-tation-induced erosion. On the other hand, a URANS for-mulation was preferred for the design exploration study as the computational demands of LES and the number of simulations performed would have required computing resources not compatible with the scope of this work.

The homogenous mixture model was employed to describe the multiphase nature of the flow field. All phases (i.e., liquid, vapor, and non-condensable gases) were modeled as compressible. A perfect gas assumption was used for the gaseous species, while the liquid was modeled as a barotropic fluid. Bilicki and Kestin’s ho-mogenous relaxation model (HRM) [26] was employed to predict the cavitation-induced phase change. The physical properties used to represent SRG have been


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published in the authors’ previous work [10, 13]. The op-erating conditions were identical to those published in [14], i.e., injection pressure of 1000 bar, back pressure of 100 bar, with fuel and ambient temperatures of 358 K. The injector geometry used for the simulations was ob-tained through x-ray tomography experiments that were performed at the 7-BM beamline of the Advanced Pho-ton Source (APS) at Argonne National Laboratory [27]. The injector needle motion, used as the boundary condi-tion for the moving parts of the CFD domain, was rec-orded at the 32-ID beamline of the APS [28] and was first presented in a previous study from the authors [14]. Further details on the experimental setup can be found in [13, 14]. The mesh and numerical setups used in the pre-sent work have been validated in the authors’ previous work [13] in which predictions of mass flow rate of Ul-tra-Low-Sulfur diesel (ULSD) fuel under several injec-tion pressures had been compared against experiments. A constant minimum mesh size of 10 µm was imposed in the eight orifices and in conical regions immediately downstream of the orifices, which extended for 5 diam-eter lengths. The minimum cell size in the sac was 20 µm. The minimum grid sizes at the needle seat ranged between 5 and 20 µm at any given time according to the minimum gap resulting from the radial motion of the needle with respect to the seat. This ensured an improved solution of the flow at the needle seat at all times (i.e., a prescribed minimum number of cells between the seat and the needle was always guaranteed). A full view of the computational domain is shown in Figure 1.

Figure 1. Full view of the computational domain.

The orifices are visible in the middle and are colored by their reference number.

Predictions of Erosion Potential In order to better understand the experimentally ob-

served erosion in the x-ray measurements from Tzane-takis et al. [16] and explore the possible causes for ma-terial erosion, multiphase flow predictions were com-pared with experimental images. Figure 2 shows a slice of the predicted distributions of three multiphase flow quantities of interest, namely fuel vapor volume fraction, velocity magnitude, and pressure, which are overlaid on the experimental x-ray images. The multiphase flow pre-dictions indicated the formation of strong velocity and pressure gradients at the inlet of orifice 3, which pro-vided the conditions for cavitation formation. Down-stream of this region, condensation of the cavitation clouds was predicted to occur. These locations were con-sistent with the regions in the injector orifice where ma-terial erosion was observed in the durability tests per-formed by Tzanetakis et al. [16].

Figure 2. Instant contours of Fuel Vapor Volume

Fraction (top), Velocity (middle) and Pressure (bottom) overlaid with x-ray scans of the injector analyzed in [16]. Courtesy of C. Powell and coworkers at the APS, Ar-gonne National Laboratory.

In order to link multiphase flow predictions with the potential and severity of material erosion, the CIERA tool developed by Magnotti et al. was employed in this work. A detailed description of the model formulation can be found in [21], but the salient details are summa-rized here. Through the use of a user-defined function (UDF) implemented in the CONVERGE code, an energy balance is performed at the fluid-solid interface to esti-mate the energy absorbed by the material following a hy-drodynamic impact. By treating the solid surface as a bi-linear material, the solid is assumed to behave elastically for impact stresses below the material yield stress, and


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no impact energy is assumed to be absorbed. For impact pressures above the material yield stress (assumed as 300 MPa, carbon steel), the impact energy is assumed to be completely absorbed and stored by the material. After re-peated impacts, the local stored energy increases in time until a critical threshold is reached, which would mark the end of the incubation period and the point at which material erosion would occur. In this work, the stored en-ergy metric was employed as a qualitative measure of progress towards material failure. Future investigations will explore the use of CIERA to relate the predicted stored energy to injector material properties and quantify the expected incubation period.

The predicted stored energy distributions on the in-ternal surfaces of the injector are shown in Figure 3. Within orifice 3, potential sites for erosion were pre-dicted, which coincide with the regions identified in the experimental measurements, shown in Figure 2. Upon closer inspection, some deviations are observed between the measured and predicted locations. There are several factors which may contribute to this discrepancy. First,

it is important to note that the simulation was only per-formed for a single injection with a nominal duration of 0.7 ms. No single injection event can replicate the range of conditions encountered during the durability tests, which represent the cumulative result of numerous injec-tions over 200-800 hours of operation. Within this simu-lated period of time, the statistics describing the hydro-dynamic impacts within the injector orifices may not have converged and may not have the ability to represent the average cavitation cloud collapse behavior. Second, during the durability tests, the injection conditions were allowed to vary in terms of injection duration and pres-sure, where peak injection pressures approached 2500 bar. It is expected that the erosion potential and severity will increase with shorter injection durations and larger injection pressures. To better understand the impact of injection conditions on the potential and severity of cav-itation erosion, future work will explore higher injection pressure conditions and their influence on predicted ero-sion sites and stored energy magnitude.

Figure 3. Stored energy distribution at 0.440 ms. The red circle highlights the stored energy due to cavitation

cloud collapse in orifice 3.

Geometry Definition and Modification In order to investigate the effect of the K-factor on

the internal flow development, a “nominalized” repre-sentation of the x-ray scanned injector was created. Fig-ure 4 shows a comparison of the orifice inlet and sac re-gions for the x-ray geometry (Figure 4, left) and the re-constructed “nominalized” baseline geometry (Figure 4, right).

The baseline nominal geometry was characterized by an orifice outlet diameter of 186 µm, a K-factor of

2.0, and an inlet radius of curvature of 50 µm. The K-factor was then varied between a minimum value of 1.5 and a maximum value of 3.5 while keeping the other two parameters unchanged. Five surfaces were generated, al-lowing for a comprehensive evaluation of the influence of K-factor on the duration and intensity of cavitation.

The variation of the K-factor was achieved by morphing the baseline geometry surface through a newly developed tool implemented in Matlab [29]. The ar-rangement of the points constituting the triangulated sur-face of the nominal geometry was such that the points


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could be displaced to accommodate the input specified by the user. Therefore, by simply indicating the desired numerical values of the K-factor, the user is able to gen-erate a new surface file, bypassing the involvement of any computer-aided drawing (CAD) tools.

Figure 5 shows the capability of the surface genera-tion tool by reporting two views of the surfaces obtained by assigning the minimum and maximum K-factor val-ues.

Figure 4. Close-up views of the sac and orifice inlets surface. X-ray scanned (left, from [13, 14]) vs. “nominal-

ized” baseline geometry (right).

Figure 5. Close-up view of two injector geometries characterized by the minimum (left) and maximum (right)

values of K-factor.

Effect of K-factor on Cavitation Suppression Figure 6 shows the results of the evaluation of the

K-factor influence on cavitation suppression. The data are plotted as a function of time from left to right and as a function of the K-factor value from top to bottom. Five cases in total were run for this part of the study, but only four are shown in Figure 6 for the sake of brevity.

From the analysis of Figure 6, it is apparent that in-creasing the K-factor had a clear beneficial effect on cav-itation reduction. A more effective pressure recovery was observed as the inlet area and the conicity of the or-ifice increased (not shown here). This resulted in reduced

intensity, duration, and extent of cavitation as the K-fac-tor grew from 1.5 to 3.5. In the case with the largest K-factor, the pressure recovery was so effective that super-cavitation was avoided, i.e., fuel vapor was prevented from crossing the orifice outlet. Similarly, the velocity contours reported in Figure 6 highlighted that the veloc-ity magnitude and gradients were smaller as the K-factor increased, implying less severe pressure jumps and smoother transitions between the flow inside the sac and the one in the orifice. The lack of super-cavitation can be seen as a positive outcome from an injector performance standpoint. Indeed, by preventing the occurrence of su-per-cavitation, it is guaranteed that only liquid fuel will


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cross the orifice outlet. This translates to higher orifice discharge coefficients and, potentially, more limited dis-turbances to the ensuing spray in the near nozzle region. On the other hand, with large K-factors, the condensation of the fuel vapor generated through cavitation occurred inside the orifice, as opposed to those cases with lower K-factors where it occurred outside of the injector. As shown by Magnotti et al. [21], changing operation in

cavitation regime from super-cavitation to developing cavitation can affect the likelihood of a given cavitation erosion mechanism and possibly enhance its erosive po-tential. In light of this, future work will focus on linking these results back to cavitation erosion predictions to identify the best trade-off between performance and risk of material erosion connected to the cavitation suppres-sion design strategy.

Figure 6. Effect of orifice K-factor on Fuel Vapor Volume Fraction (top four rows) and Velocity Magnitude

distributions with streamlines (bottom four rows) in Orifice 3 during the 0.1-0.2 time interval.


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Conclusions This study evaluated the ability of a specific injector

design parameter to suppress or limit cavitation occur-rence inside a multi-hole heavy-duty diesel injector run-ning with a high-volatility straight-run gasoline. Previ-ous durability tests indicated the potential for cavitation-induced erosion to occur within the injector orifices. The first part of the study utilized a detailed multiphase flow simulation to explore the potential causes for cavitation-induced erosion. Multiphase flow predictions were found to correlate well with the experimentally measured locations for material erosion. The application of the CI-ERA tool allowed for multiphase flow predictions to be linked to the potential and severity of erosion. This pre-liminary study indicated good correlation between pre-dicted erosion sites and experimentally observed regions of damage within the injector orifices.

In order to identify design parameters that could suppress cavitation formation and reduce the potential and severity of cavitation-induced erosion, a design study was carried out. In particular, the ability of the or-ifice K-factor to suppress cavitation was investigated. A nominal reconstruction of the x-ray scanned geometry used for the preliminary study on the erosion potential was generated and a novel geometry morphing tool de-signed in Matlab was employed for fast and automated generation of modified geometries. The results of the parametric design studies revealed that the K-factor was an influential parameter in its ability to suppress cavita-tion formation. Increasing the K-factor via changes in the inlet area and conicity of the orifice allowed for a more effective pressure recovery, which resulted in reduced intensity, duration, and extent of cavitation. In the case with the largest K-factor, the occurrence of super cavita-tion was suppressed entirely.

This study is intended to help guide initial design improvements for heavy-duty fuel injectors operating with high-volatility fuels. Future work will focus on sim-ultaneously involving multiple design parameters such as the inlet radius of curvature and the orifice inlet shape (elliptical vs. circular), and testing several designs under more challenging operating conditions, namely higher injection pressures, which are expected in typical opera-tion. The results will be linked back to cavitation erosion predictions to identify effective design guidelines for re-ducing cavitation erosion.

Acknowledgments The submitted manuscript has been created by

UChicago Argonne, LLC, Operator of Argonne National Laboratory (Argonne). Argonne, a U.S. Department of Energy Office (DOE) of Science laboratory, is operated under Contract No. DE-AC02- 06CH11357. The U.S. Government retains for itself, and others acting on its be-

half, a paid-up nonexclusive, irrevocable worldwide li-cense in said article to reproduce, prepare derivative works, distribute copies to the public, and perform pub-licly and display publicly, by or on behalf of the Govern-ment.

The authors wish to thank: • Blues and Bebop High Performance LCRC

cluster facilities at Argonne National Labora-tory; and

• Convergent Science Inc., for providing the CONVERGE CFD software licenses.

Nomenclature d injector orifice diameter K K-factor Subscripts in inlet out outlet

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