{
  "TopNotes": "Sigma 1.6L Engine Analysis\nGraphical Results\nGenerated: 07-Mar-2026 23:08:56\nDominic walton\n2404454\nThermodynamics and combustion\nACHA5011\nDr Owen Williams\n",
  "Figure 1": "This graph shows cylinder volume changing as the piston moves through the engine cycle. The shape is determined purely by engine geometry—stroke, bore, connecting rod length, and crank offset. The simulated line and given data line overlap almost perfectly because volume isn't modeled or guessed; it's calculated directly from these fixed geometric inputs. There's no combustion, heat release, or tuning involved—just math. If the two lines didn't match, it would mean the engine geometry in the simulation doesn't match the real engine, but here the overlap confirms the simulation is working from the correct physical dimensions.\n\n",
  "Figure 2": "The differences in these pressure traces come down to energy release. In the \"without combustion\" case, pressure rises and falls solely because the piston compresses and then expands the air—like a spring being pushed and released. With combustion, its shown that the peak pressure is around the point where the crank angle hits 20 degrees after top dead centre to maximise the force on the expansion stroke",
  "Figure 3": "This PV diagram shows pressure versus cylinder volume, tracing the engine’s work cycle. \nIn the “without combustion” case, the curve simply goes up and down along the same path compression and expansion are nearly symmetric because no energy is added, so the piston gives back almost the same work it took to compress the gas. \nWith combustion, the pressure stays much higher during expansion, creating a wider loop. That extra area represents the net work output from burning fuel. The curve shows the lowest pressure is right at the highest cylinder volume, and right when the cylinder volume hits around 40cc is when combustion happens and shoots the pressure up by around 50 bar\nThe “given data” trace follows a similar loop, confirming that the simulated combustion is releasing energy at the right time and magnitude to produce realistic power.\n",
  "Figure 4": "This log-log PV diagram highlights the compression and expansion exponents—essentially how smoothly energy transfers during the cycle. In the “without combustion” case, the compression and expansion lines are nearly straight and parallel, because the gas behaves like a simple spring—compressing and expanding with no added heat. With combustion, the expansion line stays higher and shifts outward, reflecting the extra pressure from burning fuel pushing the piston down. The “given data” follows a similar path, confirming that the simulated combustion is adding energy at the right rate and that the model captures real gas behaviour under fire.",
  "Figure 5": "This graph tracks the polytropic index throughout the engine cycle, showing how heat behaves during compression and expansion. During compression (roughly -180° to 0°), the line holds steady around 1.33 because pressure and volume follow a consistent relationship with no combustion. During expansion (0° to 180°), it settles around 1.27—slightly lower because heat is leaving the gas as it pushes the piston down.\nThe spikes at the ends happen when the piston slows at top or bottom dead center, disrupting the normal pressure-volume proportionality. The same occurs when the exhaust valve opens—pressure drops suddenly while the piston moves slowly, throwing off the calculation. These deviations don't mean anything is wrong; they just show where the simple pressure-volume relationship no longer applies\n",
  "Figure 6": " \nThis graph shows how quickly pressure is rising or falling at each point in the engine cycle—essentially the “violence” of combustion and gas motion. Before top dead center, you see a positive spike: that’s pressure building rapidly as combustion ignites and flames race through the cylinder. The sharper and higher that peak, the faster the energy is being released. After TDC, you get a negative spike as pressure drops just as quickly when the piston moves down and expansion takes over. If this trace were flat, it would mean no combustion happening—just smooth compression and expansion. Comparing this to real engine data helps confirm that the simulated burn rate matches reality, not too slow (weak power) and not too fast (engine knock).\n",
  "Figure 7": " \nThis graph shows how the torque delivered to the crankshaft varies throughout a single engine cycle at different engine speeds. Early in the cycle (negative crank angles), torque is negative—that’s the work required to compress the gas, which pulls energy from the crankshaft. After top dead center, torque spikes positive as combustion forces the piston down, pushing power back into the crankshaft. As engine speed increases, the peak torque tends to shift slightly later and sometimes drop in magnitude, because there’s less time for the fuel to burn completely and for pressure to fully act on the piston before it moves away. The shape and timing of these curves help validate whether the combustion model is capturing the right burn duration and gas dynamics across the engine’s operating range.\n",
  "Figure 8": " \nThis graph shows how quickly the air-fuel mixture is burning at each point during combustion—essentially the burn rate. The curve starts low, then rises sharply as the flame front develops and spreads through the cylinder. The peak represents the point where the most mass is burning at once, typically just after top dead center. After that, the rate drops off as the remaining unburned mixture shrinks and the combustion event ends. The shape and timing of this curve tell you whether the model’s combustion is realistic: too early or too sharp could mean knock, too late or too spread out could mean incomplete burning and lost power.\n",
  "Figure 9": "Mass Fraction Burned Rate vs Crank Angle\nThis graph shows how quickly the air-fuel mixture burns at each point during combustion. The burn rate starts near zero because the flame kernel is just forming and has little contact with the mixture. It peaks sharply around top dead center when the flame front is fully developed and consuming the largest volume of fuel at once. It then drops back to zero as the remaining unburned charge shrinks and combustion finishes. This shape reflects how flames actually behave in an engine—accelerating as the flame spreads, then decelerating as available fuel runs out.\nWibe Cumulative Function and Mass Fraction Burned Rate Table\nThis table tracks combustion progress numerically over crank angle degrees. The \"Mass Fraction Burned Rate\" column follows the same rise-and-fall pattern as the graph, confirming that burn speed peaks near TDC where flame propagation is fastest. The \"Wibe Cumulative Function\" column represents the total fraction of fuel burned up to that angle, following a characteristic S-curve. It grows slowly at first while the flame establishes, then rises rapidly through the middle as the flame sweeps through most of the charge, and finally levels off as only small fuel pockets remain. This S-shaped profile matches real combustion behavior and confirms the simulation uses a realistic burn model.\n",
  "Figure 10": " \nThis burn rate curve follows the Wiebe function, which produces a specific shape: slow at first while the flame kernel establishes, then rapid as the flame front expands and consumes more mixture, then slow again as the remaining fuel runs out. The parameters controlling this shape are chosen to mimic real combustion behavior, so the curve reflects how pressure builds and fuel burns in an actual engine.\n",
  "Figure 11": " \nThis graph shows how cylinder temperature evolves over the engine cycle. The blue dashed line (without combustion) rises and falls smoothly—temperature increases only from compression, then drops as the piston expands and cools the gas. The red line (with combustion) spikes much higher and faster because burning fuel dumps chemical energy directly into the gas, heating it well beyond compression alone. The green dotted line (given data) follows a similar path, confirming that the simulated combustion is releasing heat at the right time and intensity. The difference between the curves comes down to one thing: adding heat. Compression heats the gas, but combustion is what drives temperatures toward peak values, which directly affects pressure, work output, and emissions formation.\n",
  "Figure 12": " \nThis graph shows cylinder pressure over an engine cycle when no combustion occurs—essentially a motored condition where the engine is spun over without fuel. The pressure rises smoothly as the piston compresses the trapped air, peaking at top dead center where the volume is smallest. After TDC, the pressure drops just as smoothly as the piston moves back down and the air expands. The curve is symmetric because no energy is added; the air behaves like a spring, giving back almost the same work it took to compress it. This shape serves as a baseline—any deviation from it in a firing engine tells you exactly how much additional pressure comes from combustion.\n",
  "Figure 13": " \nThis graph compares three different pressure traces to highlight how combustion modeling choices affect results. The \"Simple Non-Combustion\" line rises and falls smoothly—just compression and expansion with no heat added, like a spring. The \"Ideal Otto Cycle\" line shows a near-instantaneous pressure spike at top dead center, because it assumes combustion happens instantly at constant volume, which isn't physically realistic but serves as a theoretical limit. The \"Detailed Combustion\" line falls between them—pressure rises faster than the non-combustion case but more gradually than the ideal Otto, reflecting a real burn rate where the flame takes time to propagate. The differences exist because each model treats heat release differently: none, instantaneous, or realistic. The detailed trace is what you'd expect from an actual engine, balancing the ideal and the inert.\n",
  "Figure 14": "",
  "Figure 15": "This set of graphs compares three pressure traces to show how combustion changes cylinder pressure and how well the simulation matches real data.\nThe \"Without Combustion\" trace rises and falls smoothly—pressure builds only from compression and drops during expansion, with no energy added. It's symmetric and serves as a baseline.\nThe \"With Combustion (Simulated)\" trace rises faster and peaks much higher because the model adds heat release from burning fuel. The shape is sharper, showing how combustion rapidly increases pressure beyond what compression alone can achieve.\nThe \"Given Data\" trace represents real measured pressure from an actual engine. Its shape closely follows the simulated combustion trace, which tells you the model is capturing the timing, magnitude, and duration of heat release accurately.\nIn the \"All Comparisons\" plot, you can see all three together: the low symmetric baseline, the high sharp peak from simulation, and the real data confirming that peak is realistic. The differences exist because combustion adds energy—and the close match between simulated and given data shows the model is doing it about right.\n"
}