Numerical investigation of diesel fuel spray in a nozzle with counter-swirling jets

. Nozzle prototype for a diesel fuel reformer was investigated using numerical simulation. The main goal was to increase the rate and degree of fuel evaporation, as well as to improve the mixing characteristics between diesel fuel and superheated steam. A nozzle design was proposed with two internal regions, in which jets with opposite swirl directions were created. The simulation of mixing and evaporation of liquid fuel droplets and steam jets was performed in a finite volume formulation. The results of simulations show good uniformity of the mixture concentration downstream the nozzle exit, as well as high degree of evaporation, which is important for catalytic processes.


Introduction
In recent years, demand for the amount of electricity generated has grown strongly due to the increase in consumption.At the same time, the growing environmental requirements are pushing the industry to development of new methods of generating energy without carbon dioxide emissions, which contribute to climate change and lead to global warming.A promising method of clean energy conversion is building power plants based on hydrogen fuel cells.One of the main problems of the distribution of such power plants is their high cost and low availability of fuel for them.At the moment, the development of fuel processors is being actively carried out.These devices are based on catalytic processes for converting various types of fuel into syngas.
There is a need to create energy converters operating on diesel fuel.Diesel fuel is easily transportable and already has a developed logistics network.The design of an effective fuel processor for the conversion of diesel fuel into syngas depends on several important parameters.For a catalytic reaction to occur in the reactor chamber, it is important to ensure a uniform distribution of fuel droplets in the working volume, therefore, there is a need to design a novel type of the injector nozzles for these tasks to ensure uniform liquid fuel atomization and mixing.The development of additive technologies makes it possible to create nozzles of arbitrary shapes with complex internal geometry, which opens up new possibilities for design.
In industrial applications related to fuel atomization (combustion chambers, power plants), nozzles optimized for high fuel consumption with high Weber and Reynolds numbers are mainly used.In these areas the nozzles are optimized for a high net fuel flow rate.
On the other hand, in applications, such as catalytic reforming of fuel into syngas and hydrogen [1][2][3], it is necessary to optimize the atomization process for regimes with low fuel flow rate, limited by the effective area of the catalyst.In such applications in is needed to ensure a high degree of mixture homogeneity, which is necessary for the correct operation of the catalyst.For these applications, it is necessary to develop new types of nozzles that take into account the regime of the operation of these devices.
In [1], the design of the diesel fuel reformer was proposed and its operation was studied.This reformer was studied by a numerical method in [2], however, such aspects as the uniformity of the fuel spray and its evaporation were not reported.Similar studies were carried out for other reformers [3][4].The conclusion is that in low fuel-consumption modes there is a problem in the production of centrifugal injectors with the necessary pressure drop due to very small dimensions of the nozzle outlet and high precision required for its manufacture.An alternative approach is the use of "airblast" type nozzle in which the atomization occurs due to interaction of a steam jet with the liquid fuel.As applied to diesel reformers, such injectors have been poorly studied.
In this work, an experimental model of a nozzle for a diesel fuel reformer used to produce synthesis gas was studied numerically.The nozzle has two steam supply channels, creating two volumes inside the nozzle with different directions of swirl (Fig. 1a, b).Superheated water vapor with a temperature of 450 o C is supplied through these channels.Fuel is supplied through a coaxially arranged channel of smaller diameter located inside the steam supply channel before its splitting.The diameter of the supply channels for steam is 0.8 mm; the diameter of a fuel supply channel is 0.5 mm.This E3S Web of Conferences 459, 04018 (2023) https://doi.org/10.1051/e3sconf/202345904018XXXIX Siberian Thermophysical Seminar configuration leads to formation of a layer with strong shear on the separating edge between the regions with opposite swirl, which contributes to the generation of turbulence and increased mixing and evaporation rate of diesel fuel droplets.
The flow rate of water vapor was set equal to 350 g/h.The fuel (modelled by n-heptane) flow rate was 150 g/h.The simulation was carried out in the open-source package OpenFoam [5] (www.openfoam.com)with a solver sprayFoam.For the gas phase, Navier-Stokes equation was solved in a compressible formulation.Due to a small Reynolds number in the flow (~2000), the simulation was carried out without explicitly specifying the turbulence model.The liquid phase was modelled as a monodisperse droplet flow in a Lagrangian representation.

Nozzle geometry
In this paper, in order to achieve uniform spraying and mixing of fuel, a nozzle model was proposed, with two steam supply channels bifurcating from a larger tube (Fig. 1a).These channels lead to cylindrical cavities in each of which a swirling flow is created.The signs of swirl are mutually opposite in these two regions.The two cylindrical regions are separated by a thin wall (Fig. 1b).After passing the wall edge the flows parts with opposite swirl start to interact with each other creating tangential shear.Further downstream a recirculation zone is created followed by a narrowing nozzle outlet.The simulated nozzle is connected to a 30 o conical surface simulating the initial part of internal chamber of a fuel processor.
This nozzle design allows to achieve a high amplitude of tangential shear, which leads to the generation of turbulence, which increases the effective diffusion, and, as a result, increases the intensity of mixing, secondary atomization and evaporation of fuel droplets inside the nozzle.The swirl of the flow also lengthens the trajectories of the droplets, thereby increasing the residence time of the liquid phase droplets inside the nozzle, which enhances the processes of heat transfer, mixing and evaporation.

Computational details
The flow inside the nozzle was studied numerically using an open-source computational fluid dynamic code OpenFoam [5].
The simulation was carried out taking into account variable density and temperature of the mixture.The thermodynamic properties of the mixture were determined as weighted average depending on the local mass fraction of the mixture components.
The evolution of two Euler components of the mixture was simulated: superheated water vapor and diesel fuel vapor (heptane vapor), as well as the evolution of Lagrangian particles (heptane droplets).
For the Euler phase, the following model equations were solved: ( ) ( ) Where Equation 1 ).Equation 4is the continuity equation.
The right-hand sides of equations (1-4) are the sources/sinks (Sm, Sh, SY, Sev) associated with the interaction with the Lagrangian phase (fuel drops).
Due to small Reynolds numbers (~2000), the turbulence model was not used to solve the equations.For the discretization of spatial derivatives, central difference schemes (second order of accuracy) were used.For time derivatives, implicit Crank-Nicolson scheme (second order of accuracy) was used.
For the liquid phase, each Lagrangian parcel modelled an individual spherical drop, for which the following evolutionary equation of motion was solved: Where FD and FP denote the drag and pressure gradient force acting on the droplet; up denotes the droplet velocity and mp the droplet mass.The drag force was set in the following form: Where urel is the gas velocity in the droplet reference frame;  is the dynamic viscosity of the gas; p is the density of the liquid phase; d is the droplet diameter; CD is the drag coefficient; Rep is the local Reynolds number for the droplet.The drag coefficient for a spherical drop was set according to [6].
The effect of the pressure gradient in the gas on the droplet was calculated as: The change in the droplet mass due to evaporation was taken into account as follows (using the Rantz-Marshall model [6] for the Sherwood number).

( ) (
) Where Sc is the Schmidt number for fuel vapor; Dvap is the kinematic viscosity of fuel vapor, sat is the density of saturated vapor on the droplet surface, inf is the density of fuel vapor in a given computational cell.
The heat balance for a droplet was calculated according to the following equation (the Ranz-Marshall model [6] was also used, but for the Nusselt number Where cp is specific heat of the droplet; Tp is the temperature of the droplet; A is the surface area of the droplet, T is the temperature of the gas in the computational cell containing the droplet; and hw is the specific enthalpy of the phase transition. Between the Eulerian and Lagrangian phases, the two-way exchange of momentum (friction), heat, and matter (evaporation) was simulated.The computational domain (Fig. 1) was the nozzle itself with an outlet connected to a cone simulating the initial part of the diesel fuel processor working domain (cone with an angle of 30 o ).Grid convergence on grids with different resolutions was studied.It was found that a grid with a number of cells of 6 million (Fig. 2), with refinement to solid surfaces, is sufficient for the convergence of the results with resolution.
The steam velocity at the inlet was ~200 m/s which converts to a Reynolds number of ~2000, while the Weber number at the inlet was ~300.A simple estimate from the critical Weber number (Wec = 12) shows that the equilibrium droplet size under these conditions is ~50 µm.The droplets of 100 µm were used in the simulation to emphasize the effect of the nozzle on the largescale side of the droplet spectra, which is the most problematic for evaporation.

Simulation results
Distributions of mean velocity components are presented in Figure 3.According to the simulation results, it can be seen that intense shear stress in the flow is concentrated in the cylindrical channels with opposite swirl and in the zone where the two counter-rotating jets are mixed together.The main source of the shear is the azimuthal velocity component (Fig. 3c); and the shear direction is radial.Azimuthal velocity component in its peak magnitude is several times larger than the longitudinal one.These two effects (strong shear and high swirl rate) are positive for diesel fuel atomization as they increase mixing and lengthen the droplet trajectories.there is also a central jet.This is also a positive effect for the flow mixing with environment as no large recirculation zone is formed outside of the nozzle which might induce a stagnation zone in the flow with slow mixing between the flow components.This effect is a consequence of compensation of azimuthal velocities between the counter-rotating jets.Due to non-equal pathways of inner and outer jet, the outer jet tangential velocity decays slower and some amount of positive swirl is present at the nozzle outlet.
The distribution of velocity fluctuations magnitude is shown in Figure 4.It can be seen that a noticeable turbulence of the flow occurs inside the nozzle due to non-stationary effects, which improves the effective diffusion inside the mixture.The largest magnitude of fluctuations is observed in tangential velocity in the region of the mixing of counter-rotating jets.This confirms the efficiency of mixing intensification by generation of high tangential shear.
Different components of fluctuations show a somewhat different distributions inside the which could be interpreted as non-homogeneous or coherent mode of vortex interactions.Further downstream, after the flow exits the nozzle, the fluctuations become more isotropic due to a more stochastic way of vortex interactions.Figure 5 shows the simulated distribution of mass fraction of the vapor phase of diesel fuel.The distribution is averaged over a 0.0025 s period from the start of fuel injection.At the moment of fuel injection the steam flow fields were already established.It can be seen how the fuel vapour is distributed in the working volume.For the flow rates under study, the equilibrium mass fraction of fuel is 0.3.Thus, the closer the vapor concentration to this value, the greater amount of the liquid phase has already evaporated.
Inside the nozzle a slight nonuniformity in the fuel vapor mass fraction (higher values of Y C7H16 in the inner jet) is observed.This is because of unequal number of droplets getting into inner and outer channels.It can be seen that a lot of fuel is evaporated before exiting the separated jets domains.Downstream, inside the nozzle, the jets are effectively mixed.
Near the outlet of the nozzle, an almost equilibrium concentration of the vapor phase of the fuel is achieved, which indicates the effectiveness of the proposed nozzle design.In the future, it is necessary to simulate the process of initial atomization of the spray and calculate the evaporation rates for realistic droplet diameter spectra.The simulations carried out in this work show that the proposed nozzle model is effective for evaporating liquid diesel fuel and mixing it with superheated water vapor.The counter-rotation of flows occurring inside the nozzle leads to the formation of areas of intense shear and turbulence of the flow, which makes it possible to effectively break the liquid jet into droplets without using high pressure to supply fuel.Further experimental study of this nozzle model in the prototype of the operating diesel fuel reformer is expected with the model validation studies.
The study was funded by the grant of President of Russian Federation (MD-157.2022.4).
is the momentum balance equation for a mixture (u is the mixture velocity,  is the density of the mixture ( =  is gas pressure,  is dynamic viscosity of the mixture ( =  2 determines the enthalpy balance (hs is specific enthalpy,  is thermal conductivity of the mixture.Equation 3 determines the balance of mass fractions of the mixture components (water vapor Y H2O , and diesel fuel vapor Y C7H16

Fig
Fig 3c shows the distribution of the longitudinal velocity component, it can be seen that a recirculation zone is formed inside the nozzle, the interaction of which with the main flow leads to the generation of instabilities and turbulent fluctuations in the flow.At the