2.1. Three-Dimensional Numerical Model of High-Pressure Marine Fuel Injection Pump
The structural study looks at the barrel distortion and plunger below the maximum supply pressure induced by fuel oil compression. The most significant loss in clearance caused by the deformation was also calculated. Furthermore, the thermal fluid–solid analysis simulation required 4–5 h for each scenario. The PC utilized for the investigation was equipped with an AMD Ryzen 5 2.10 GHz CPU and 8 GB of RAM. Deformation occurs at high pressure during the compression stage of the cycle, and clearance is reduced when the magnitude of the plunger deformation exceeds that of the barrel in a specific location. Commercial software is used to compute the computational domain and the magnitude of the deformation (ANSYS 19.2). The most significant clearance reduction was utilized as a design limit to avoid metal-on-metal contact due to deformation.
The dimension detail shown in
Figure 2 illustrates the proposed marine fuel injection pump, especially the plunger and the barrel parts. To make it different from other models in the literature [
5,
7,
11,
12,
14], the proposed model modified the plunger diameter to 23.9 mm and the plunger stem taper to 1.5° × 30 mm. Moreover, the mesh (tetrahedral shape) of
Figure 3a depicts the computational model, and fine grids with a tetrahedral element were implemented in the region.
Figure 3b illustrates the constraints and disassembly of the barrel, plunger, and fluid domain. In the areas impacted by compressed fuel oil, the plunger’s bottom half was fixed in all directions, and the ultimate supply pressure was implemented. The barrel top and side were fixed in anticipation of twisting in the x and y directions, and the highest supply pressure was also supplied to the compressed fuel oil-affected areas.
2.2. Computational Fluid–Solid Thermal Coupling Theory and Governing Equations for Marine Fuel Injection Pump
The fluid–solid thermal coupling problem pertains to the fundamental issue of a system wherein the fluid field, solid field, and temperature field coexist and mutually influence one another. Furthermore, the essential variables concurrently computed are fluid flow, solid deformation, and temperature change. The resolution of the flow, solid, and temperature fields in the energy fuel pump necessitate the utilization of fundamental flow equations for the fluid domain [
22,
24], a thermal performance [
25], a thermal equation [
26], and mechanical equations [
27] in the solid domain, along with consistent boundary conditions at the fluid–solid interface [
26,
27,
28]. Besides, different temperatures and pressure loads can affect model deformation [
29,
30,
31]. This paper employs the method of calculating unidirectional fluid–solid thermal coupling.
In fluid dynamics, the computational domain of the fluid is commonly treated as an incompressible flow subject to the fundamental equations of fluid motion. These equations comprise the conservation of mass, momentum, and energy conservation. The continuity equation can be defined as follows:
The equation governing momentum can be expressed as:
In different directions, we have
X momentum:
The standard
k-ε equation is used to describe turbulence models [
32,
33]:
The energy equation is as follows:
The equation governing the solid field is derived from the three fundamental laws of elastic mechanics: the deformation continuity law, the stress–strain relationship, and the law of motion, as well as the principle of energy conservation.
The thermal conductivity differential equation is as follows:
The equation of force for every direction (
x,
y, and
z) is expressed as:
The constitutive equation is as follows:
The geometric equation is as follows:
The continuity condition must be upheld at the fluid and solid phases’ interface. The principle of energy continuity is kept at the point of the coupling interface, wherein the temperature and heat flow exhibit continuity.
The interface coupling satisfies both kinematic and mechanical conditions, precisely the continuity of displacement and pressure.
The present study establishes a numerical calculation model for the fluid–solid thermal coupling of the energy plunger/barrel utilizing ANSYS 19.2. Initially, a conventional three-dimensional turbulent flow model is employed to resolve the flow and temperature fields of the energy conduit. The Fluent 19.2 solution is integrated with the thermal and structural modules to exchange temperature and pressure loading data. Ultimately, the computation of the solid structure domain is predicated upon the outcomes mentioned above.
The plunger and barrel of the reciprocating fuel pump were subjected to structural analysis. The mathematical model for the structural numerical analysis is depicted in
Figure 4. The barrel was attached to the housing, and the plunger moved in a linear reciprocating motion. The plunger’s reciprocating action compressed the gasoline. The elastic modulus of the barrel and plunger was 200 GPa with a Poisson’s ratio of 0.3, and more parameters are listed in
Table 1.
Figure 4 depicts a flowchart of the structural analysis simulation. The plunger’s head eccentricity ratio was then used to assess whether there was contact.
Deformation occurs when there is high pressure during the compression stage of the cycle, and clearance is reduced when the amplitude of plunger deformation exceeds that of the barrel in some locations. Finite element method (FEM) commercial software was used to compute the deformation and meshing amplitudes. The most significant decline in clearance was utilized as the design limit to avoid metal-to-metal contact caused by deformation.
Solving the Navier–Stokes equations in the Eulerian frame, the continuous gas phase was handled as a continuum. In contrast, the dispersed phase was addressed by tracking many particles through the flow field [
34]. Particles in the dispersed phase can transfer mass, energy, and momentum to the gas phase. In this investigation, the authors neglected these particle–particle interactions. Instead, the authors used a practical k-model of turbulence that included a different formulation of turbulent viscosity and a separate transport equation for the dissipation rate. This realizable k-model outperforms the traditional k-model, incorporating vortices, rotation, and a significantly streamlined curvature [
35].
Dimethyl ether (DME) is a substitute for diesel due to its equal cetane number, hydrogen content, self-ignition temperature, and calorific value [
36]. The difference in emissions stems from the fact that diesel is not an oxygenated fuel, whereas DME is. As such, diesel produces soot when burned, whereas DME does not. Because of the similarities in cetane between the two fuels, DME may also be utilized in diesel engines with minor modifications to the fuel injection system. LPG and DME qualities are pretty similar, and DME can be utilized as a replacement for LPG because of these similarities [
37]. DME and LPG have comparable physicochemical features and handling conditions. When storing DME, it is necessary to use moderate pressurization instead of LPG, which is stored as a liquid. DME has a volumetric energy density as a liquid believed to be 80% of that of propane, a part of LPG. The table shows the similarities in DME and LPG characteristics.
Table 2 shows the properties of diesel fuel, propane, and DME.
2.3. Description and Modeling of High-Pressure Common Rail Fuel Injection System in AMESim
A high-pressure commonrail fuel injection system’s efficiency is influenced by various factors, including fuel leakage between components, elastic deformation of the high-pressure fuel pipe, diesel compressibility at high pressures and temperatures, and flow rate loss as the fuel passes through cross-sections of various sizes. Its matching architecture is shown in
Figure 5a.
Some assumptions were made based on the system characteristics. First, the fuel temperature disparity was not considered during operations to ensure the pressure could represent the system state. The fluid dynamic development associated with the flows over the pipes is ignored, the cylinders and low-pressure pump volumes are assumed to be infinite, and the pressure is stable. The electrohydraulic valve was expressed as a variable.
The fuel’s compressibility is modeled by the bulk modulus of elasticity (E), Equation (21) [
38]:
where an increase in
dP generates a decrease in the quantity of a unit amount of liquid—
dV. Here,
dV/V is a quantity of dimensionless. From Equation (21), fuel pressure as a function of time is:
V denotes the chamber’s simultaneous volume, and
dV/
dt represents the volume variations induced by mechanical components, the piston, and the inlet and exit flows. Given that the factors influence the fuel’s volume change, Equation (22) can be reformulated as follows:
This is the essential formula for pressure dynamics in each control volume. In Equation (23),
Qin denotes the intake flow,
Qout represents the outlet flow, and
dV0/dt will be provided for the common rail pipe, the high-pressure pump, and the injector, respectively. This symbol indicates the rate of volume change caused by the mechanical piston. All the components of HPCRIS (except for the high-pressure pump) have a constant volume. The respective intake and outtake fluxes
Qin and
Qout can be represented using the energy conservation law as Equation (24):
Here, sign(ΔP) denotes the flow direction sign function, ρ is the dual density, S0 represents the orifice section, µ is the discharge coefficient, and ΔP is the fuel pressure variation through the orifice.
Three identical hydraulic rams share the same shaft in this high-pressure pump, rotating at 120° out of phase with one another. Because the camshaft drives the pump, its development is affected by engine speed. It is linked to the low-pressure circuit by a tiny aperture and to the high-pressure channel through a transmission valve with a conical seat. The pressure dynamics of the high-pressure pump, corresponding to Equation (23), can be represented as follows:
where
Qp is the input fuel flow,
Qpcr is the common rail outlet fuel flow,
Qpl is the fuel leakage flow, and
Pp is the high-pressure pump fuel pressure.
Vp, the volume of the high-pressure pump, fluctuates with camshaft motion, which can be written as
where
Sp is the plunger’s sectional area,
Sp = 𝜋
dp2/4,
hp is the plunger lift,
dp is the diameter of the plunger,
θ is the camshaft angle, and
ωrpm is the camshaft rotational speed.
Qpcr denotes the flow from a high-pressure pump to a common rail, and it is determined by:
where
µp is the coefficient of discharge, which varies with the pressure ratio in a steady-state diesel engine, but it is treated as a constant in this study.
Pcr is the common rail fuel pressure,
Spcr is the high-pressure pump cross-sectional area of the outlet port, and the sign function in Equation (27) is:
When
Pp ≤ Pcr, the check valve (one-way valve) between the rail and the high-pressure pump closes, preventing fuel from flowing back to the pump.
Qpl, the fuel leakage flow, may be considered a constant. As a result of merging Equations (25)–(28), Equation (25) may be expressed as:
The film parameter is defined by Equation (30) as proportional to the ratio between surface roughness and the minimum film thickness. Equation (31) calculated the surface roughness from the barrel and plunger surface roughness [
5,
14]. R
q1 and R
q2 have values of 0.065 μm.
Figure 5b demonstrates the AMESim simulation block, which presents the HP piston pump sub-system, the solenoid injector sub-system, and the injector body and nozzle sub-system. The parameter setting in the AMESim model is shown in
Table 3.
2.5. Grid Independence Test and Model Validation
The paper employs a unidirectional fluid–solid thermal coupling calculation method to compute the pressure and temperature distributions within the fluid region. The boundary conditions for the stress field in the solid region are determined by loading the fluid pressure and temperature in the barrel/plunger interface onto the inner wall of the barrel/plunger. To simulate 3D models of the barrel, plunger, and fluid domain involved in thermal fluid–solid interaction (TFSI),
Table 1 displays the 3D modeling design parameters. The physical finite element model and the boundary conditions are depicted in
Figure 3a,b, respectively, based on the data given in the literature [
7]. Grids defined each structure, including the plunger, barrel, and fluid domain, mostly tetrahedral. The type of mesh/grid is conforming mesh suitable for the solid and fluid domains by sharing their topology and avoiding interface problems.
Table 4 lists the grid sizes and numbers for the various constructions. For network independence verification, multi-parameter and multi-node verification are used. The key points at the plunger stem are used to compare the displacement under different grid numbers.
Figure 6a displays the differences in plunger/barrel displacement sections as a function of the number of grids.
Additionally, the displacement changes in the five different grid numbers have the same value for grid numbers 4 and 5, which is 0.00266 mm. The fluid–solid thermal solution is thus obtained in the model using a grid number of 14,363,772 to maximize simulation time efficiency. The fluid flow generates pressure and temperature loading in unidirectional fluid-solid thermal coupling. These loadings are used as boundary parameters in the solid mechanic’s equation. The plunger displacement was evaluated using a fluid–solid coupling model and compared to the reference result for validation [
7].