Simulation study of fuel spray dynamics in a constant volume combustion chamber

ABSTRACT

The OpenFOAM computational fluid dynamics code was used to investigate the performance characteristics of spray jet in a constant volume combustion bomb. The total duration of fuel spray was approximately $1.25\times {10}^{-3}$ second, and the total mass of fuel sprayed was $6.0\times {10}^{-6}$ kilogram. The results show that there was a positive and somewhat positive qualitative correlation between the profiles of the number of parcels and the mass flow rate of the injected fuel at between $0\le t\le 4.4\times {10}^{-4}$ second. Furthermore, at between $9.1\times {10}^{-4}\le t\le 1.3\times {10}^{-3}$ the number of parcels experienced a sharp rise while the injected mass flow rate was decreasing, see Figure 6. The results of the present study show that the spray droplet sizes vary from $0.25\text{mum}$to $150\text{mum}$ which were found to be reasonably representative of measurement data that are usually observed at the top dead centre position of internal combustion engine test bed experiments. Furthermore, the results of the study show the contour plots of pressure and temperature. The pressure rise varies from the initial value of 50 bar to 75 bar at the end of combustion while the temperature rose from ${550}^{\circ }K$ to its final value of ${2800}^{\circ }K$. The specific details of the results from this study are summarised in the conclusion section.

KEYWORDS:

• Spray droplet break-up
• turbulent flow
• effective surface tension
• Sauter mean diameter

Nomenclature

$B_d$	=	Spalding mass transfer number
$C_D$	=	Drag coefficient
${C_1}_{\epsilon }$, ${C_2}_{\epsilon }$, and ${C_3}_{\epsilon }$	=	Constants
$C_{\mu }\hspace{0.17em}$	=	Constant
${C_3}_{\epsilon }$	=	Degree to which $\epsilon$ is affected by the buoyancy
$d$	=	Droplet diameter
$d_d$	=	Particle diameter
$D_{pq}$	=	Characteristic diameter with dissimilar orders of $p$ and $q$
$D_v$	=	Vapour diffusivity in the gas
$D10,D32$ and $D32$	=	Mean diameter, Sauter mean diameter (SMD) and maximum diameter
$E$	=	Energy
$F$	=	Additional acceleration (force/unit droplet mass) term
$F_D$	=	Drag force per unit droplet mass
$F_{vm}$	=	Virtual mass force
$F_{pg}$	=	Pressure gradient in the fluid
$G_b$	=	Generation of turbulence kinetic energy due to buoyancy
$G_k$	=	Generation of turbulent kinetic energy due to the mean velocity gradients
$g_i$	=	Component of the gravitational vector in the $ith$ direction
$h$	=	Sensible enthalpy
$J_j$	=	Diffusion flux of species $j$
$k$	=	Turbulent kinetic energy
$k_{eff}$	=	Effective conductivity $\left(k+k_t\right)$
$k_t$	=	Turbulent thermal conductivity
$L$	=	Latent heat of vaporisation
$Ma$	=	Mach numbers
$M_t$	=	Turbulent Mach number
$M{W}_s$ and $M{W}_v$	=	Molecular weights for the surrounding gas, and for the vapour respectively
$N{u}_d$	=	Nusselt number
$Oh$	=	Ohnesorge number
$P{r}_d$	=	Droplet Prandtl number
$p$	=	Pressure
$P{r}_t$	=	Turbulent Prandtl number for energy
$q_h$	=	Convective heat transferred to the drop
$\vec{r}$	=	Macroscopic coordinates of space $\left(x,y,z\right)$
$Re$	=	Relative Reynolds number
$R{e}_d$	=	Droplets Reynolds number
$S$	=	Modulus of the mean rate-of-strain tensor
$S_m$	=	Source term
$S_k$ and $S_{\epsilon }$	=	Source terms for the turbulent kinetic energy and dissipation rate respectively
$S{c}_d$	=	Droplet Schmidt number
$S_d$	=	Surface area
$S_h$	=	Heat of chemical reaction and any other volumetric heat sources
$L$	=	Latent heat of vaporisation
$T$	=	Temperature
$t$	=	Macroscopic coordinates of time
$T_L$	=	Lagrangian integral time
$u_i^{\prime }$	=	Fluctuating of velocity in the $ith$ direction $\left(i=1,2,3\right)$
$u_j^{\prime }$	=	Fluctuating of velocity in the $jth$ direction $\left(j=1,2,3\right)$
$u_i$	=	Velocity component in the $ith$ direction
$u_j$	=	Velocity component in the $jth$ direction
${\bar{u}}_p$	=	Mean piston speed
$U_{rel}$	=	Relative velocity between the gas and the droplet
$u$	=	Fluid phase velocity
$u_d$	=	Particle velocity
$\vec{u}$	=	Velocity field
$v$	=	Velicity field
$W{e}_g$	=	Weber gas number
$Y\left(\vec{r},t\right)$	=	Mass fraction
$Y_M$	=	Contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate
$Y_j$	=	Mass fraction of species $j$
$Y_v$	=	Vapour mass fraction
$Y_v^{\ast }$	=	Vapour mass fraction on the drop surface
Greek Symbols	=
$\beta$	=	Coefficient of turbulent buoyancy
$\epsilon$	=	Rate of dissipation of turbulent kinetic energy
$\lambda$	=	Mean free path of the molecule
$\mu$	=	Molecular viscosity of the fluid
${\mu }_l$	=	Liquid molecular viscosity
$\sigma$	=	Surface tension
$\mathrm{\partial }$	=	Partial derivative symbol
${\mu }_t$	=	Coefficient of turbulent kinetic energy
${\delta }_{ij}$	=	Kronecker delta
$\rho$	=	Fluid density
${\rho }_d$	=	Droplet density
${\rho }_g$	=	Surrounding gas density
${\sigma }_k$ and ${\sigma }_{\epsilon }$	=	Turbulent Prandtl numbers for $k$ and $\epsilon$, respectively
$\tau eff$	=	Shear stress tensor
$\phi$	=	Relaxation factor

Acknowledgements

The work reported herein was graciously supported by Augustine University, Ilara-Epe, Lagos, Nigeria and Texas Southern University, Houston, Texas, USA. The authors wish to express their sincere thanks to their colleagues and reviewers for their insightful and constructive remarks which led to improving the clarity of this paper considerably.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are available from the corresponding author, [LA], upon reasonable request. [LA].

Additional information

Notes on contributors

Lucky Anetor

Lucky Anetor Professor Anetor received his Bachelor of Science degree (First Class Honors) in Mechanical Engineering from the University of Lagos, Nigeria and a Master of Science degree in Marine Engineering from the University of London, United Kingdom. Professor Anetor utilized the Canadian Commonwealth Scholarship to study for his doctoral program in Mechanical Engineering (specialization in Internal Combustion Engines and Computational Fluid Dynamics) at the University of British Columbia, Vancouver, Canada. Dr. Anetor also obtained a Master of Arts degree in Mathematics from the University of Houston, Texas, USA. Dr Anetor was the pioneer Dean, Faculty of Engineering, Nigerian Defence Academy, Kaduna, Nigeria. He was also a former Professor of Mechanical Engineering at Kwara State University, Nigeria. He was an Adjunct Faculty at the ITT Technical Institute, Houston, Texas, where he taught undergraduate courses in Information Systems Security, Network Engineering Design, Power Plant Engineering and Industrial Control Systems. He is actively engaged in research and consulting in the areas internal combustion engines, thermo-fluids and industrial control systems (ICS). Dr Anetor has published in local and international journals. He has also consulted widely, delivered lectures and seminars to Fortune 500 petrochemical, medical and process automation enterprises which are located in Israel, Canada and the USA. Professor Anetor is a Licensed Professional Engineer (PE) in the State of Texas, USA.

Edward E. Osakue

Dr. Edward E. Osakue is a Professor in the Department of Industrial Technology, Texas Southern University, Houston; Texas, USA with a concentration in Design Engineering and Technology. He is also graduate Faculty and the coordinator of the Design Technology concentration at the Department. Dr. Osakue joined the Faculty at Texas Southern University in 2005. He worked previously at ITT Technical Institute, Houston South campus as Education Supervisor and Program Chair for CAD Program and School of Design from 1999 to 2005. Dr. Osakue was a Faculty member in the Department of Production Engineering, University of Benin from 1984 to 1992.Dr. Osakue received his doctoral degree in mechanical engineering from the University of New Brunswick, Fredericton, Canada, in 1999. He obtained his Bachelor of Engineering degree in 1983 from the University of Benin, Benin City, Nigeria. His research interests include economical design of mechanical, structural, and piping systems, internal combustion engines, renewable energy, low-velocity impact with friction, and effective curriculum delivery methods. Dr. Osakue is a frequent attendee and presenter at National and International conferences. He is a member of several professional organizations including American Society of Mechanical Engineers (ASME) and American Society for Engineering Education (ASEE).

Christopher Odetunde

Professor Christopher Odetunde is the current Vice Chancellor of Augustine University, Ilara, Epe Lagos State, Nigeria. He was formerly the Dean of the Faculty of Engineering at the Kwara State University, Malete, Kwara State, Nigeria. Professor Odetunde obtained his Bachelor of Science degree in Aeronautical Engineering from Embry-Riddle Aeronautical University and his Master of Science degree in Aerospace/Mechanical Engineering from Iowa State University both in the USA. Furthermore, he bagged his Doctor of Philosophy degree in Aerospace Engineering from Texas A&M University, College Station, Texas, USA. Professor Odetunde also has a Master of Science degree in Project Management which was conferred on him by the Southeastern Institute of Technology, Huntsville, Alabama, USA. Dr. Odetunde’s areas of research interest includes but not limited to, Thermo-Fluids, Combustion, Orbital and Attitude Control, Subsonic, Aircraft structure, Transonic, Supersonic and Hypersonic Aerodynamics, Aviation Safety, Unmanned Aerial Vehicle (UAV), Transportation Methods and Theory. Professor Odetunde is a registered professional engineer with the Council for the Regulation of Engineering in Nigeria (COREN). He is also a Member of Board of trustees of Aviation Accreditation International, AABI. Dr. Odetunde has more than 35 years of aerospace/aviation and management experience.