The purpose of this work was to show that kiva4 is more accurate than kiva3vr2 under different ignition timings. The numerical accuracy of kiva4 was compared with the numerical results obtained by other researchers who used kiva3vr2 as the simulation code. The combustion characteristics of gasoline under different ignition timings are obtained using the kiva4 code. For achieving this, two cases were investigated; a complete engine cycle was successfully simulated using a four-valve pent-roof engine and a comparison was made with experimental results by other researchers. At a constant speed of 600 rpm, a BASF (Badische Anilin-und Soda Fabrik) octane rating engine-single cylinder was used where ignition timing was changed in the range of 4 ° BTDC to 18 ° BTDC. Kiva4 generates more accurate results than kiva3vr2. The experimental results were more in agreement with kiva4 than kiva3vr2 results. The average temperature and pressure in kiva4 were 640 K and 16.48 bars while in kiva3vr2 were 600 K and 14.83 bars, the peak temperature and pressure in kiva4 were 2316.3 K and 21.5 bars while in kiva3vr2 were 2171.5 K and 19.4 bars. The peak temperature and pressure increase with increasing spark advance until the most favorable instant time is determined. Best performance was achieved when the ignition time was set to 10 degrees before top dead center.
Internal combustion engines have been in use for more than a century and have undergone tremendous changes in design and performance. In the past decades, research efforts have been focused largely on a better spark ignition engine, from the perspective of reducing the pollutant emissions without sacrificing performance and fuel economy.
Simulations based on the KIVA-3 code are widely used to predict diesel combustion. Several advanced sub-models have been developed using the KIVA-3 based code. However the numeric in Kiva4 has been generalized to unstructured mesh and it has the potential to enhance mesh structure flexibility while Kiva3vr2 has low mesh flexibility because of employing a structured mesh [
Kiva4 | Kiva3vr2 |
---|---|
squishnodes = 2 | flfluid = 1.0 |
domenodes = 3 | flface = 2.0 |
bowlnodes = 5 | flbowl = 3.0 |
topbowlnodes = 7 | flsqsh = 4.0 |
portnodes = 11 | fldome = 5.0 |
axisnodes = 37 | flhead = 6.0 |
inoutflownodes = 41 | |
presnodes = 43 | |
movingnodes = 47 | |
movingnodesvalve = 53 | |
solidnodes = 59 | |
solidhnodes = 61 | |
solidbnodes = 67 |
length of all the 12 edges of a cell, all the nodes are identified first and then the distance nodes on various combination have to determined using the x, y, z co-ordinates and this procedure has to be repeated every time length of the edge which is required. But in KIVA-4, the edges associated with each cell are stored in an array and the length of those edges can also be retrieved from the array directly [
Although KIVA-4 still includes the i1tab, i3tab and i8tab bookkeeping arrays, the algorithm below clearly shows that KIVA-4 has a new approach to locate a node of the fluid (gird) cell. It is important to know that, for each computational cell, KIVA-4 no longer uses left, bottom, and front faces for surface area and outward normal vector identification.
In recent years, however, ignition timing has also brought increased attention to the development of advanced SI engines for maximizing performance. The performance of spark ignition engines is a function of many factors. One of the most important ones is ignition timing. Also it is one of the most important parameters for optimizing efficiency and emissions, permitting combustion engines to conform to future emission targets and standards [
Kiva4 | Kiva3vr2 |
---|---|
do i4c = 1, ncellsa | do i4 = ifirst, ncells |
i1= nodes (1, i4c) | i1 = i1tab (i4) |
i3 = nodes (3, i4c) | i3 = i3tab (i4) |
Enddo | Enddo |
that has enough voltage and energy to ensure combustion of the fuel mixture. Be able to reliably accomplish these goals throughout a variety of rpm, load, temperatures and conditions [
Optimization of the engine design and operating variables requires extensive engine testing. Therefore, engine modeling codes are generally preferred for assessing initial designs. Computer models of engine processes are useful tools for analysis and optimization of engine performance and allow exploration of many engine design alternatives in an inexpensive method [
The use of statistical techniques based on experimental data to evaluate the behavior of engines and fuels has been increasing in recent years. For example Christopher J. Rutland et al. Studied Effect of mesh structure in the KIVA4 code with a less mesh dependent spray model for DI diesel engine simulations, the predicted heat release rate using the gas-jet model showed good mesh independency and good agreement with the experiment while that using the standard KIVA spray model calculated with KIVA-4 show significant mesh dependency [
The fuel used in both cases is gasoline and it was manufactured by MOL specification EN-95.The in-cylinder pressure was measured by a piezo-electric pressure transducer of the Type: Kistler 600. Top Dead Center (TDC) and engine piston speed, RPM, was determined by an optical encoder Type: Hengstler RI 32-0/1024.ER.14K. Fuel flow rate was measured using the AVL 7030 Dynamic fuel consumption measuring equipment. The fuel balance works on the gravimetric measuring principle. Fuel is supplied to the engine from a measuring vessel inside the instrument where the weight of the fuel is continuously measured. This instrument enables the highest temperature stability of the fuel conditioning system with measuring accuracy of 0.12%; including self-calibration according to ISO 9001 [
Two different cases were investigated, in both cases kiva4 and kiva3vr2 were compared in order to show the numerical accuracy of the kiva4 code.
Case A: From ref. [
Case B: Siwale et al. Performed experiments on a BASF (BadischeAnilin-und Soda Fabrik) octane rating single cylinder engine. The engine performance parameters are indicted in
The schematic diagram of the octane rating test BASF octane rating engine used for experiments is as shown in
In this study, fluid flow simulation was carried out using the latest version of Los
Description | Value |
---|---|
Model | 100198 4-valve pent-roof |
Bore [mm] | 92 |
Stroke [mm] | 85 |
Squish [mm] | 1.15 |
Connecting rod length [mm] | 147 |
Speed [rpm] | 1500 |
Thsect [degs] | 360 |
Cafin [CAD] | 720 |
ATDC [CAD] | −10 |
Presi (initial pressure) [Pa] | 9.9000e+5 |
Tempi (initial temperature) [K] | 293.15 |
Tspmas (fuel mass flow rate) [g] | 0.0186 |
Ca1ign (start of spark ignition) [CAD] | 346.5 |
Ca1inj (start of fuel injection) [CAD] | 5 |
Description | Value |
---|---|
Model | BASF Prufmotor 368/64, (1994) |
bore [mm] | 65 |
Stroke [mm] | 100 |
Displacement [cm3] | 332 |
Maximum power at full load and 600 rpm [kw] | 0.6 |
Maximum fuel consumption [g/h] at 600 rpm | 400 |
Orifice diameter [mm] | 0.6 |
Mixture heater [w] | 750 |
Compression ratio | 10:1 |
Speed [rpm] | 600 |
Ignition timings | 40 btdc to 180 btdc |
Pressure transducer | Kistler 6051 B (error 1%) |
Spark plug | Kistler 6517 BCD |
Alamos National Laboratory (LANL) CFD code, KIVA-4. KIVA-4, a transient, three-dimensional, multiphase, and multi-component code for the analysis of chemically reacting flows with sprays has been under development at LANL for several years. The code uses an Arbitrary Lagrangian Eulerian (ALE) methodology on a staggered grid, and discretizes space using the finite-volume technique. The code uses an implicit time-advancement with the exception of the advective
terms that are cast in an explicit but second-order monotonicity-preserving manner. Also, the convection calculations can be sub-cycled in the desired regions to avoid restricting the time step due to Courant conditions [
The column in
Fuel | CF | n1 | n2 | n3 | n4 | AEf | AEo |
---|---|---|---|---|---|---|---|
Gasoline | 4.6 × 1011 | 4 | 49 | 32 | 34 | +0.25 | +1.50 |
[
Chemical equation
4C8H17 + 49O2 → 32CO2 + 34H2O (1)
The Case A: Kiva4 package includes a basic grid generator, K3PREP that writes a file called itape17 conforming to the specifications of the engine [
Pre-processing
A pre-processor is a program that processes its input data to produce output that is used as input to another program like a compiler; in this case K3PREP is that program. K3PREP is a pre-processor that generates the mesh for the given geometry in form of an output file called otape17 and that given geometry comes from a file called IPREP file that needs to be built manually. An IPREP file is a file that contains all the necessary information to generate the geometry. The geometry is built following the description of the quantities on the input data file “IPREP” in the order in which they appear using the epilogue file found in the K3PREP directory [
An IPREP file was used by other researchers to generate a structured mesh using kiva3vr2, the mesh is as shown below in
The same IPREP file was used in kiv4 to produce an unstructured mesh. In order to accomplish this, there were a few modifications or changes that had to be made in order for the file to work in kiva4. Changes made to IPREP file are indicated in
After all the modification is done, the file is now ready to be compiled by the program K3PREP. The IPREP file should be placed in the same folder as the executed K3PREP program. On the command line the program is run with the command./K3prep. After the program has finished running, otape17 and otape11 are generated.
Itape17 to Kiva4grid Convertor
The file otape17 is renamed to itape17 and otape11 to itape11. A convertor (convertor.f) for converting kiva3vr2 mesh files to kiva4 format is provided in the main directory. It is compiled by a fortran compiler and will convert itape17 to kiva4grid [
Modification/parameter | Kiva4 | Kiva3vr2 |
---|---|---|
Always start with Title, | K3PREP/100198 4-valve | K3PREP/100198 4-valve |
Align the engine configurations in order, and make sure that each Configuration quantity that follow is close and in line with each other, the last letter and number in line with the previous and next quantity. | Bore engine Stroke Squish configuration thsect | Bore engine Stroke Squish configuration thsect |
Alignment | wedgeflag 00 translate 44 | wedgeflag 00 translate 44 |
Reshape.f requires seven values either 0s or 1s, set ifixed to 0s | nblk1, nblk2, index1 index2, intrp, irelax and ifixed | nblk1, nblk2, index1 index2, intrp and irelax |
in the same folder. In the same directory the exe file is run with the command./Convertor.exe and Kiva4grid will be generated. Below is the generated kiva4grid unstructured mesh in
After all the input files are edited and generated, kiva4 is run in the command terminal with the command: ./kiva4.
Case B: Kiva4 package includes a basic grid generator, K3PREP that writes a file itape17 conforming to the specification. In order to reduce computational time, a 45˚ asymmetrical mesh was created based on the symmetry of the combustion chamber of the BASF octane rating engine-single cylinder as shown in
In computational solutions of partial differential equations, meshing is a discrete
representation of the geometry that is involved in the problem. Essentially, it partitions space into elements (or cells or zones) over which the equations can be approximated. Zone boundaries can be free to create computationally best shaped zones, or they can be fixed to represent internal or external boundaries within a model. The mesh quality can be conclusively determined based on the following factor [
Solution precision
A better mesh quality provides a more precise solution. For example, one can refine the mesh at certain areas of the geometry where the gradients are high, thus increasing the fidelity of solutions in the region. Also, this means that if a mesh is not sufficiently refined then the precision of the solution is more limited. Thus, mesh quality is dictated by the required precision [
Viewing mesh refinement in Ensight
Ensight is a software program for visualizing, analyzing, and communicating data from computer simulations and/or experiments. In numerical analysis, adaptive mesh refinement, or AMR, is a method of adapting the accuracy of a solution within certain sensitive or turbulent regions of simulation, dynamically and during the time the solution is being calculated [
Procedure
To view mesh refinement, the global attribute is turned on and the color set to black. Available parts are hidden in order to view the mesh in the fluid domain. The fluid domain is clipped and the times set to a value were the mesh refinement is able to be viewed.
Quantifying the size of the elements
Element size calculates variables such as the volume/Area/Length for 3D/2D/1D elements respectively at each element creating a scalar, element-based variable.
Procedure
The option for calculator is selected in the fluid domain on the tabs. Elesize (element size) is searched on the calculator and evaluated for selected parts.
The clip is colored with elesize and the palette changed (set range to selected part max/min).
There are many more ways and functions in Ensight that are designed to give the quantification of the grid. EleMetric is another function which calculates an elements mesh metric, at each element creating a scalar, element-based variable depending upon the selected metric function. Elemetric is searched on the calculator and other parameters called metric functions appear. In order to understand what each function does, the question mark is selected on the calculator which brings up the page for the user manual that explains what elemetric is, what each function does and what are the element types it applies to. Some of the examples of the elemetric functions are element type, facecount, centroid etc.
Gradient of the velocity
Gradient of the velocity is one of the physical quantities that the solver uses to
identify which parts of the solution have to be refined. Gradient of the velocity is calculated. The designer selects the mesh configuration.
Procedure
The fluid domain is used when calculating the gradient of the quantity. The algorithm is used in each value of the cell and the true level of the neighboring cells to calculate the gradient. Selecting as a parent part 2D plane brings information that comes from the neighboring 2D cells but the solution in the solver used the 3D domain.
Grad is searched on the calculator. The scalar or vector velocity is selected and evaluated for selected parts. The clip plane is colored with GradV and the palate is edited in order to identify some features. The scale was set to logarithmic and the range was decreased from zero until it gave the required results as shown below in
increase in temperature. The average temperature and pressure for kiva4 is 640 K and 16.48 bars while that for kiva3vr2 is 600 K and 14.83 bars. Combustion takes place when ignition occurs at 346.5 CA causing the piston to move from top dead center to bottom dead center. As seen from kiva4 graphs, both the isosurface and clipboard are completely red indicating high pressure and temperature. The average pressure before combustion in kiva4 shows 16.48 bars.
A comparison is made in this section between the measured values derived from the experimental investigation and the ones calculated by kiva4 and kiva3vr2.
Combustion is a process formed when there is a source of fuel, air (oxidizer) and heat [
the combustion chamber and burns the premixed gasoline-air mixture. The fuel is injected at 5˚ ATDC during the intake stroke when the piston is moving from top dead center to bottom dead center. The piston moves from bottom dead center to top dead center. The air-fuel mixture is compressed isentropically through the compression ratio, in this case 10:1. Heat is added to the working fluid during compression process at constant volume. The temperature and pressure slowly increases as the piston moves from bottom dead center to top dead center. Combustion occurs when the temperature and pressure of the air-fuel mixture is high enough to ignite at 4˚ CA, 8˚ CA, 10˚ CA and 18˚ CA before top dead center. This is called the ignition phase at 356˚ CA as seen from Figures 11(a)-(d). When combustion takes place, the piston moves from TDC to BDC with a greater amount of force and work is done by the system. The peak temperature is above 2000 K and the peak pressure is above 20 bars. Kva4 results are closer to the experiment than kiva3vr2. Figures 11(a)-(d) shows a variation of pressure with time during the combustion of gasoline-air mixture where the pressure is in bars and the time is in crank angle degrees [CAD]. The initial pressure Presi and temperature Tempi are 1.929802218e+6 Pa and 400 K. The calculations begin at 60 degs btdc and finishes at 540 degs atdc. The simulation results in kiva4 agree with the experimental results. The average pressure is 19.56 bars in kiva4 and 18.2115 bars in kiva3vr2 while for the experiment the pressure is 18.8756 bar. Kiva3vr2 generates slightly lower pressure results than Kiva4 due to the changes made in kiva4.
After testing Kiva4’s performance and accuracy, simulations are performed based
on the input parameters of the experimental cases for the ignition timing of 4˚ CA, 8˚ CA, 10˚ CA and 18˚ CA BTDC at 600 rpm. When the calculations begin at 60 degs BTDC, the response of the pressure and temperature is slow and uniform. During the compression stroke at 180 CAD the pressure and temperature in the cylinder begins to build up until it is high enough for combustion to occur. The ignition timing in crank angle degrees (CAD) is (a) 356 CAD, (b) 352 CAD, (c) 350 CAD and (d) 342 CAD as shown in
Parameters | Values |
---|---|
Presi (initial pressure) [Pa] | 1.929802218e+6 |
Tempi (initial temperature) [K] | 400.0 |
Tspmas (fuel mass flow rate) [g] | 0.0116 |
ca1ign (start of spark ignition) [CAD] | 356.0, 352.0, 350.0 and 342.0 |
ca1inj (start of fuel injection) [degs] | 5.0˚ btdc |
When Combustion occurs, the volume of the burned gasoline ? air mixture expands. The expansion of the burning mixture starts at the center and travels in the outward direction towards the cylindrical vessel wall. This movement created a combustion wave that causes a rise in pressure (Lewis & Elbe, 1987) [
The results show that increasing spark advance increases the peak temperature and peak pressure in the combustion chamber.
The objective of this study was to show that kiva4 is more accurate than kiva3vr2 under different ignition timings. The numerical accuracy of kiva4 was compared with the numerical results obtained by other researchers who used kiva3vr2 as the simulation code. The combustion characteristics of gasoline under different ignition timings are obtained using kiva4 and the following conclusions are drawn.
1) After mesh refinement, very fine meshes were obtained with Kiva4 with the highest gradient of 1202 thus had increased fidelity of solutions in the regions.
2) An unstructured mesh was used in Kiva4 and a structured mesh in Kiva3vr2. More accurate results were obtained in Kiva4 than in Kiva3vr2. The average temperature and pressure in kiva4 were 640 K and 16.48 bars while in kiva3vr2 were 600 K and 14.83 bars, the peak temperature and pressure in kiva4 were 2316.3 K and 21.5 bars while in kiva3vr2 were 2171.5 K and 19.4 bars.
3) Peak temperature and pressure increase with late timing of the spark before top dead center. The peak temperature and pressure increase with increasing spark advance until the most favorable instant time is determined. Best performance was achieved when the ignition time was set to 10 degrees before top dead center.
The authors declare no conflicts of interest regarding the publication of this paper.
Lungu, J., Siwale, L. and Luwaya, E. (2018) Numerical Accuracy of the Kiva4 Code under Different Ignition Timing on the Combustion Characteristics of Gasoline in a Spark Ignition Engine. Journal of Power and Energy Engineering, 6, 87-110. https://doi.org/10.4236/jpee.2018.611008
MFB: Mass Fuel Burned (%)
BTDC: Before Top Dead Centre
BDC: Bottom dead center
TDC: Top Dead Centre
CAD: Crank Angle Degrees
CR: Compression Ratio
LHV: Lower heating value (MJ/kg)
IMEP: Indicated Mean Effective Pressure (bars)
FID: Flame Ionization Detection
CA: Crank Angle
EOC: End of Combustion
IBP: Initial Boiling Point
RVP: Absolute vapor pressure (kPa, psi) measured above liquid petroleum products at 37.8˚C by Reid method determined by ASTM D323
VP: Vapor pressure
λ: ratio of actual air-to-fuel-ratio to stoichiometric air-to-fuel ratio
ECU: Electronic control unit
SI: Spark Ignition