95 FIGURE 57:VOF RESULTS;(A)ISO-SURFACE OF LIQUID;(B)CROSS SECTION OF LIQUID TO GAS VOLUME RATIO. 101 FIGURE 60: FLUID SIMULATION VOLUME, CROSS SECTION OF FLUID ANGLE FROM CENTERLINE OF (A) RADIAL GROUP (B).
INTRODUCTION
Objectives and outline of the thesis
Likewise, in several cases cavitation leads to its sudden increase and also forces the fluid within the behavior of the spray plumes. RANS simulation of a multi-hole injector provides very useful insight into the air entrainment in the spray cone and jet-to-jet interactions.
Overview of thesis chapters
In contrast, the spray plumes are well separated in the case of the 3-hole injector. 6 (XL, YL, ZL) are the local coordinates, in the direction of the stream flow.
TURBULENCE AND SPRAY MODELLING
Conservation equation
- The total mass conservation equation
- Momentum conservation equation for fluid mixture
- Energy conservation equation
A general conservation equation governing the motion of a fluid in the Eulerian frame, based on the concepts of divergence theorem and Reynolds transport theorem, has been represented in equation (1). In the equation above, a rate of change of physical quantity (X) is balanced by the production term P, supply term S and flux term F.
Turbulence modelling
- Carrier phase equations
- Reynolds Average Navier Stokes
- Large Eddy Simulation
- Liquid phase equations
- Two way coupling, effect of droplets on the gas phase
The average part is obtained from the ensemble mean, which is the average of a set of realizations of the given quantity being averaged. And τ is the Reynolds stress term which is unknown and must be modeled in order to close equations (15) and (16).
Spray modelling
- Liquid injection model
- Secondary droplet breakup model
- Stochastic droplet dispersion model
- Droplet tracking model
- Droplet collision model
- Evaporation and heat transfer models
The coefficient represents the characteristic viscous damping time of the droplet and is proportional to the droplet surface area. The frequency of droplet oscillation is found from the restoring force constant as
Conclusion
Moreover, the heat transfer between the two phases can be easily obtained from the convection equation.
REYNOLDS AVERAGE NAVIER STOKES SIMULATIONS
Turbulence Model
The equation for turbulent kinetic energy and dissipation rate are presented in equations (70) and (71).
Numerical setup and Operational conditions
- Numerical solver
- Numerical schemes
- Two phase numerics
- Computational domain
- Injector Design
- Mass flow rate profile
- Operating conditions
The gas between the two jets is pushed downwards in the upper half of the spray cone (near the injection point). Additionally, a second difference was observed in the 6-well spray compared to 3-well spray on the lower half of the spray cone (far away from the injection needle). But as the spray progresses, the vapor concentration in the center of the spray cone increases.
The distance between the injector holes, denoted Ld in Figure 32, plays a critical role in spray collapse under flash boiling conditions. The slower opening speed injector produces more droplets in the center of the spray cone and the overall spray cone appears to be thicker. The Fft of the excitation signal is shown in Figure 37 (b) in terms of Strouhal number.
Results & Discussion
- Basic validations
- Non-evaporating conditions
- Evaporating conditions
- Jet-to-jet interactions
- Spatial evolution of vapour phase
- Axial gas velocity
- Comparison of spray angles
- Radial gas velocity
- Flux Balance
Flash Boiling
- Modelling of the radial expansion of the spray, “Bell Shape”
- Results and discussion
- Improvement in spray shape
- Temporal evolution of the spray collapse
- Role of injector design parameters in flash boiling conditions
The shadow plot and Mie images in Figure 25 of the spray from a 6-hole injector under flash boiling conditions show the following: (Mojtabi, 2011; Wood, Wigley, & Helie, 2013). An improvement in the atomization modeling of the spray-in-vortex injector under flash boiling conditions has also been reported by (Chang, Lee, & Fon, 2005) using a simplified bubble growth model. This means that the radial expansion of the spray cannot be neglected in the lagrangian spray simulation of the flashing spray.
It is clear in Figure 33 (from left to right) that a small decrease in the distance between the injection holes leads to dramatic collapse of the spray.
Conclusion
- Spray behaviour under non-flashing conditions
- Spray behaviour under flashing conditions
The increase in hole-to-hole distances reduces spray plume interactions close to the injector, and the injection orifice velocity keeps the spray plume separated further downstream.
LARGE EDDY SIMULATIONS OF HIGH PRESSURE SPRAY
Large Eddy Simulations Modelling
- Carrier phase; Subgrid viscosity models
- Lagrangian equations
- Two phase coupling models
- Two phase Subgrid models
- Two-way subgrid scales coupling
- Rarefaction and Compressibility Effect
In equation (81), the velocity of the gas "seen" by the particle is unknown, as it is typically the velocity at residual (or unresolved) scales. The loss of the turbulent kinetic energy of the carrier phase depends on the transfer of fluid fluctuating energy to the particle fluctuating energy and viscous dissipation (Loth, 2008). The loss of TKE due to the viscous losses can be simply thought of as the dissipation of the energy on the Kolmogorov scale, η.
Both mechanisms contribute to the dissipation of the fluid kinetic energy at the subgrid scale, together with the change of the effective density in the subgrid scale viscosity.
Numerical Approach
- Numerical Solver
The effect of rarefaction is quite obvious until is about 10, where drag is reduced for all Mach numbers. 71 For the carrier phase, the solver solves the filtered compressible Navier-Stokes equations as described in section 2.1. Backward implicit scheme, second order accurate in time and depends on the courant number for the stability is chosen for the time discretization.
Pressure rate coupling of the carrier phase is achieved by a PISO-like algorithm (Demirdžić, Lilek, and Perić, 1993) with two iterations of a PISO loop for the prediction correction.
Initial tests
- Initial Tests Setup
- Geometry
- Liquid injection
- Test cases
- Results & discussion
- Input excitations
- Carrier phase Subgrid model effect
- Injection profile effect
- Instabilities and transition
- Developed turbulence
- Comparison of Simulation and experimental data
This signal is then placed on the inlet as the variation of the injection angles of droplets as shown in Figure 37 (a). At the inlet of the nozzle, the Stokes number is defined as the ratio of droplet relaxation time to the injection time scale = / is 68. The results of spatial distribution of the subgrid scale viscosity, µt normalized by the laminar viscosity are presented in Figure. 41.
The results of subgrid-scale viscosity are confirmed on the profile of the streamwise velocity fluctuations in Figure 43.
Conclusion
96 In the experiments, there is a certain probability of finding droplets with negative radial velocities, indicating that the droplets actually go inside the scattering cone, which are not detected by the simulation results. The finding of droplets with negative radial velocities in the center of the spray plume in PDA measurements may be due to jet flapping. Since GDI sprays strongly depend on the internal flow of the injectors, it is necessary to develop an approach that could relate information about the internal flow of the injector to the inlet conditions of the spray.
LES OF SINGLE SPRAY PLUME OF GDI INJECTOR
Nozzle Flow Dynamics
However, the mean fluid velocity distribution appears to be nearly constant, independent of the fluid density distribution. The rms fluid velocity is about 5% of the maximum fluid velocity in the region where there is a high probability of fluid presence. The liquid in the center of the nozzle will have a small angle compared to the droplets on the periphery of the nozzle.
From Figure 62 it can be seen that there is a high probability that the largest droplet sizes will be found in the center of the nozzle, and smaller droplets will be found further away from the center of the nozzle.
Coupling of VOF and lagrangian simulation
In addition, there is some probability that you will find the largest droplets on the cavitation side as well, but here the probability of finding liquid is quite low, which means that larger droplets will be rare on the cavitation side.
Studied Cases and numerical setup
Steady State Results
- Comparison of PDA and LES data
- Probability Density Function comparison of LES and PDA at 100 bar
- Joint Probability Density Function comparison of LES and PDA at 100 bar
- PDF comparison of LES and PDA at 200 bar
- JPDF comparison of LES and PDA at 200 bar
- Centreline gas velocity profile
- Charecterization of Spray half width
- Spray half width evolution
- Mean velocity profiles
- RMS Fluctuations of Carrier Phase
- RMS fluctuations of dispersed phase
- Anisotropy
- Stokes Numbers
Compared to the experiments, the simulation again shows similar trends in the periphery of the spray plume. As expected, a higher density of smaller droplets can be observed at the periphery of the spray plume. The central gas velocity profile shown in Figure 71 shows the rapid decay of the spray plume.
Streamwise rms fluctuations without and with subgrid scale fluctuations of the gas field at the injection pressure of 100 bar and 200 bar are shown in Figure 79.
Unsteady state results
- Temporal spray evolution and dynamics
- Spray Penetration and plume angle
The penetration curves start at 0.433 ms at 100 bar injection pressure, while 0.492 ms for the 200 bar box due to the injector opening delay and electrical signal. 133 stage, the penetration curve increases steadily in both cases due to the sidestream being much faster than the spray cavitation side. The main jet eventually catches the side current at 1.8ms which is illustrated by the flattening of the penetration curve.
As soon as the main jet overtakes the side jet, the penetration curve begins to increase linearly again.
Conclusion
The initial parameters such as injection angle, injection droplet size usually have to be adjusted empirically in the absence of the experimental data. But this kind of iterative process of running a number of simulations to get good results can be computationally expensive in LES, especially in the absence of the experimental results. The internal flow simulation results used in the present work only deal with the steady state injection i.e.
In the experiments it is observed that the instability in the spray comes from both the initial movement of the needle and cavitation.
Experimental set-up of PDA test bench
Experimental set-up of PIV test bench
To get the PIV plane between the two nozzles, a laser sheet enters the test cell at the window at the bottom of the chamber using a 45° mirror. The laser sheet illuminates a vertical plane in the test cell from the bottom of the chamber to the chamber roof in the direction of the injector tip, as shown in Figure 1.
Experimental setup high zoom shadowgraphy
Volume Of Fluid Large Eddy MAGIE project on the same nozzle input of the distributed spray LES. The process captures local thickness evolution, complex shape and the value at the limit of the ligament as shown in Figure 95. a) Initial instantaneously filed (b) distance function (c): derived arithmetic mean of the expected droplet size on this field ( before wave analysis here). The numerical calculations require discretization of the ensemble-averaged Navier-Stokes equations in RANS and averaged Navier-Stokes equations over an assumed filter in LES.
150 A global description of the numerical schemes based on a general transport equation was presented here.
Spatial Discretisation of the terms
- Convection term
- Convection differencing scheme
- Diffusion Term
- Source Terms
Especially in the case of LES, in order to maintain the high accuracy of the solution, it is necessary to use the discretization scheme of the same order as the order of the equation. The face values of the variables must be calculated by some kind of interpolation scheme that will be described later. The limiter used with the central difference scheme is the Sweby limiter (Sweby, 1984) which is presented in more detail in (Jasak, 1996).
In the case of the non-orthogonal mesh, equation (102) is no longer second-order accurate in space and thus a term-splitting operation. applies, which can be represented by: 105).
Time Discretisation
- Euler Implicit Scheme
- Backward Implicit Scheme
This feature allows us to understand the influence of the dominant modes on the flow arrangement. The strong pulsations of the first few modes drastically change the shape of the flow at the output, e.g. POD analysis provides detailed features of the flow that are hidden in the LES data.
Large recirculation zones form in the first few modes and carry much of the energy.