A high-fidelity simulation of the primary breakup within suspension high velocity oxy fuel thermal spray using a coupled volume of fluid and discrete phase model

Highlights

• Coupled VOF and DPM model employed to model the primary breakup for combustion applications.

• Investigated the effect of a co-annular liquid injector for suspension.

• Investigated the effect of the injection Weber number.

• Comparison of Sauter mean diameter to experimental measurements within literature.

Abstract

In the suspension high velocity oxy fuel (SHVOF) thermal spray, a suspension is injected into the combustion chamber where the jet undergoes primary and secondary breakup. Current knowledge of the primary breakup within the combustion chamber is very limited as experimental investigations are impeded due to direct observational inaccessibility. Numerical methods are also limited due to the computational costs associated with resolving the entire range of multiphase structures within SHVOF thermal spray. This paper employs a coupled volume of fluid and discrete phase model, combined with a combustion model, to simulate primary breakup at a fraction of the cost of a fully resolved simulation. A high-fidelity model is employed within this study to model the combustion chamber; the model shows a backflow region that will contribute to clogging within the nozzle. This study modifies the injector type for SHVOF thermal spray by introducing a co-flow around the liquid injection to reduce clogging within the combustion chamber. This study shows that introducing a co-flow of gas at a velocity of 200 m/s around the liquid injection reduces the backflow region by 40% within the combustion chamber. The addition of a gas co-flow results in a smaller region of backflow. Small suspension droplets with insufficient momentum are unable to overcome the backflow and will likely deposit themselves onto the wall of the combustion chamber. The deposition of the particles on the walls causes clogging of nozzles often seen in SHVOF thermal spray. The addition of a gas co-flow results in an increase in the velocity of droplets formed during primary breakup. The greater droplet velocity allows for small droplets to overcome the small backflow region near the liquid injection. The Sauter mean diameters predicted from the numerical model are compared to experimental measurements available within the literature and shows good agreement.

Introduction

The breakup of liquid jets has been extensively studied both experimentally and computationally due to the wide range of applications that utilise atomization of liquid jets. The breakup of liquid jets plays a fundamental role within diesel engines, suspension thermal spray, gas turbines and rocket engines to name a few (Xiao et al., 2014; Tian et al., 2015; Ghiji et al., 2017). Breakup investigations within a suspension high velocity oxy fuel (SHVOF) thermal spray combustion chamber through experimental methods are very limited due to the direct observational inaccessibility of the combustion chamber. Additionally, there are several challenges when trying to measure dense regions of flow. The liquid is surrounded by gases undergoing combustion; visualizing into the centre of the chamber where the suspension is injected is impeded by radiation emitted from combustion. Owing to the size of the combustion chamber (22 mm length) instrumentation must be placed outside of the chamber. Additionally, the liquid jet rapidly disintegrates into droplets of a few microns; experimental techniques must have sufficient temporal and spatial resolution to capture the breakup process (Xiao et al., 2016). Hence, computational investigations provide an invaluable tool to investigate primary breakup.

SHVOF thermal spraying is used to deposit nanostructured coatings from powdered feedstocks too small to be processed by mechanical feeders. SHVOF thermal spray allows for the formation of nanostructured coatings with improved density and mechanical properties (Murray et al., 2016). Current approaches in modelling the injection of suspension within the combustion chamber fail to account for the primary breakup of the suspension (Esther Dongmo et al., 2009; Jadidi et al., 2016). Traditionally, the blob method is employed to model the injection of suspension into the combustion chamber (Chadha et al., 2019b; Chadha et al., 2019a). For the blob method the jet is simplified to an injection of discrete droplets that can undergo secondary breakup. The suspension is typically injected as a set of discrete droplets using the discrete phase model (DPM) that can undergo secondary breakup, evaporation, heating and acceleration. The DPM framework provides a robust treatment for droplet tracking away from the dense regions of the flow; however, in dense regions of the flow such as near the liquid column; this approach is flawed.

Traditional means of modelling primary breakup in CFD using methods such as interface reconstruction methods are unfeasible to resolve the full scale of droplet structures within SHVOF thermal spray. The most popular interface reconstruction method, the volume of fluid (VOF) model, requires a mesh fine enough to resolve the smallest droplet structures. Droplets formed from the primary breakup of jets occupy a wide range of scales and are of orders of magnitude smaller than the injector diameter (Tomar et al., 2010). Hence, it would be computationally expensive to resolve the breakup phenomenon from large scale structures down to the smallest scale droplets. Within recent years there has been a growing body of literature looking to couple the VOF and DPM models together. Here, the primary breakup is modelled using the VOF model and the droplets formed from primary breakup are then transferred to a DPM framework. The small-scale structures that require the most computational resources within the VOF framework can then be modelled at a lower computational cost using the DPM framework. This allows for large scale structures such as the liquid core, ligaments and large droplets to be resolved whilst allowing the small-scale droplet structures to be modelled without significantly impacting the computational cost of the model.

Early attempts to couple the VOF model with the DPM model had to address the criteria of conversion of droplets from a VOF framework to a DPM framework. Grosshans et al. (2011) utilised a “coupling layer” where VOF droplets are converted into DPM droplets as they pass through a plane known as the coupling layer. One of the challenges in employing a coupled VOF and DPM model for breakup investigations is the different mesh requirements within the VOF and DPM frameworks. With the implementation of a coupling layer suitable meshes can be employed within the respective zones. For the VOF framework droplets must be of an order larger than the mesh size. Whilst for the DPM framework the mesh should be of an order larger than the droplets. The coupling layer approach however is significantly more expensive than later alternative approaches that have been employed to couple the two frameworks. Adeniyi et al. (2017) developed a coupled DPM to VOF framework for bearing chamber applications using the commercial CFD code Ansys Fluent. Within this implementation, droplets were modelled using the DPM framework and the film formation on the bearing chamber walls was modelled using the VOF framework. The criteria for conversion between DPM and VOF was the proximity of DPM droplets to the interface. Tomar et al. (2010) employed a two-way coupled VOF and DPM framework to model jet breakup. The conversion of VOF droplets to DPM droplets was determined by the diameter of the VOF droplets. If the droplets were smaller than the specified diameter then the droplets would convert to DPM. This approach can offer greater savings in computational cost over the coupling layer method as the droplets can be switched from a VOF framework to a DPM framework as soon as the droplets are formed. The conversion of droplets from DPM to VOF was based on the proximity of the droplets to an interface. If the droplets are close enough to an interface the DPM droplets will be deleted and a spherical secondary phase structure is patched in its location. Kim et al. (2014) and Kim et al. (2007) employed a coupled VOF and DPM approach to model the atomization of fuel within a gas turbine injector. Within this study droplets were converted from a VOF framework to a DPM framework if two criteria were met. The first criterion was based on the droplet volume and if the droplets were smaller than a specified volume, they were converted from VOF to DPM. The second criterion was based upon the droplet sphericity and if the droplets were sufficiently spherical the droplets were converted from VOF to DPM. Shinjo and Umemura (2019) and Umemura (2016) extended the application of the coupled VOF and DPM model to include the effects of combustion for a diesel jet. They investigated four cases: diesel jet in cold flow, diesel jet in hot flow, with the inclusion of a single step reaction and finally the inclusion of a multistep reaction. The multistep reaction demonstrated good agreement in predicting the ignition delay with existing literature.

The aim of this paper is to apply the coupled VOF and DPM model to investigate the primary breakup of water within a combustion chamber for SHVOF thermal spray application. The injector design within this study is varied from the standard SHVOF configurations by including a co-flow around the liquid injection. There are several non-dimensional parameters that describe the flow in coaxial jets these include the gas Reynolds number, Re_g, the liquid Reynolds number, Re_l, the momentum flux ratio, MR, and the Ohenesorge number, Oh. This paper investigates the impact of the Weber number (Eq. (1)) by varying the co-flow velocity on the primary breakup within SHVOF thermal spray. The Weber number controls the tendency for breakup (Xiao et al., 2014; Pai et al., 2009) and characterises the relative importance of the fluid inertia to its surface tension (Xiao et al., 2016). The terms in Eq. (1) refer to liquid density, ρ_l, gas velocity, U_g, liquid velocity, U_l, diameter of injector, d, and the surface tension, σ. The addition of a co-flow provides a significant design change for thermal spray.

$$We=\frac{{\rho }_l{\left|U_g-U_l\right|}^{2}d}{\sigma }$$

This paper has employed a multiscale modelling approach for a real-world engineering application. Prior numerical models within this field of application ignore the primary breakup which is a key physical process in the combustion chamber. The detailed insight into the flow physics within the combustion chamber for the current application is new and has been previously unknown. This simulation approach utilised here has never before been used for a practical combustion application such as SHVOF. The approach can be employed on modest HPC facilities for design and optimization studies within a combustion chamber and also for a wide array of multiphase combustion applications. An injection of water into the combustion chamber is considered to provide useful and highly detailed information on the physical processes for the current application. This paper uses the Coupled VOF and DPM model in the commercial CFD software Ansys Fluent V19.3 (Pennsylvania, USA).