Thermal Engg Lab (ME-306) - Unit 2 Short Notes

UNIT 2: PERFORMANCE TESTING OF INTERNAL COMBUSTION ENGINES & SYSTEMS

2.1. Fundamental Performance Parameters & Definitions

2.1.1. Key Engine Parameters

• Bore (D): Diameter of the cylinder.

• Stroke (L): Distance traveled by the piston from TDC to BDC.

• Compression Ratio (r): $$\displaystyle r = \frac{\text{Total Cylinder Volume}}{\text{Clearance Volume}} = \frac{V_s + V_c}{V_c} $$

• Displacement Volume (Swept Volume, $$\displaystyle V_s $$): Volume swept by piston in one stroke. $$\displaystyle V_s = \frac{\pi}{4} D^2 L \times \text{No. of cylinders} $$.

• Clearance Volume ($$\displaystyle V_c $$): Volume above piston at TDC.

2.1.2. Performance Metrics

• Brake Power (BP): Actual usable power output at the crankshaft. Measured by dynamometer.

$$ BP = \frac{2\pi N T}{60} \text{ (W)} \quad \text{or} \quad BP = \frac{W \times V}{t} \text{ (W)} \quad \text{(for rope brake)} $$

*Where N = rpm, T = torque (N-m), W = load (N), V = spring balance displacement (m), t = time (s).*

• Indicated Power (IP): Power developed inside the cylinder from combustion pressure.

• Frictional Power (FP): Power lost in overcoming friction (piston, bearings, etc.). $$\displaystyle FP = IP - BP $$.

• Mechanical Efficiency ($$\displaystyle \eta_m $$): $$\displaystyle \eta_m = \frac{BP}{IP} $$. Always less than 1.

2.1.3. Fuel & Air Metrics

• Fuel Consumption Rate ($$\displaystyle \dot{m}_f $$): Mass of fuel consumed per unit time. $$\displaystyle \dot{m}_f = \frac{\text{Mass}}{\text{Time}} $$ (kg/s or kg/h).

• Specific Fuel Consumption (SFC): Fuel consumed per unit power output per unit time.

$$ \text{BSFC} = \frac{\dot{m}_f}{BP} \text{ (kg/kW-hr)} \quad \text{(Brake SFC)} $$

$$ \text{ISFC} = \frac{\dot{m}_f}{IP} \text{ (kg/kW-hr)} \quad \text{(Indicated SFC)} $$

• Volumetric Efficiency ($$\displaystyle \eta_v $$): Ratio of actual air intake to theoretical air volume (at ambient conditions) per cycle.

$$ \eta_v = \frac{\text{Mass of air drawn}}{\text{Density of air} \times V_s} \times 100\% $$

2.1.4. Thermal Metrics

• Brake Thermal Efficiency ($$\displaystyle \eta_{bth} $$): Overall efficiency based on BP.

$$ \boxed{\eta_{bth} = \frac{BP}{\dot{m}_f \times CV} \times 100\%} \quad \text{(CV = Calorific Value of fuel)} $$

• Indicated Thermal Efficiency ($$\displaystyle \eta_{ith} $$): $$\displaystyle \eta_{ith} = \frac{IP}{\dot{m}_f \times CV} \times 100\% $$

• Heat Balance Sheet: Energy input (fuel) = Useful output (BP) + Losses (Exhaust gases, Cooling water, Radiation).

2.1.5. Emission Metrics

• Key Pollutants: Carbon Monoxide (CO), Unburned Hydrocarbons (HC), Oxides of Nitrogen (NOx), Smoke/Opacity.

• Measurement: NDIR (CO/CO2), FID (HC), CLD (NOx), Opacimeter/Smoke meter (Smoke).

2.2. Experimental Setup & Instrumentation

2.2.1. Engine Test Rig Components

• Engine: Petrol (SI) or Diesel (CI), 4-stroke/2-stroke.

• Dynamometer: Loads the engine & measures output.

  • Hydraulic: Uses water brake; torque from reaction.

  • Eddy Current: Non-contact; torque from magnetic drag.

  • Electrical (DC/AC): Acts as generator; measures electrical output.

• Systems: Cooling (radiator, thermostat), Lubrication (pump, filter), Fuel supply (tank, pump, filter).

2.2.2. Measurement Devices (Summary Table)

2.2.3. Data Acquisition Systems (DAS)

• Function: Converts analog sensor signals (voltage, resistance) to digital data.

• Components: Sensors → Signal Conditioning (amplification, filtering) → Analog-to-Digital Converter (ADC) → Computer/Software for logging & display.

[!TIP]

Common Pitfall: Not allowing engine to reach steady-state before taking readings. Always wait for temperatures and pressures to stabilize.

2.3. Standard Engine Performance Tests (Procedure & Calculations)

2.3.1. Full Load Test (Variable Speed / Constant Speed)

• Procedure: Set governor (if any) for max fuel. Vary engine speed (no load to full load) or keep speed constant and vary load. Record BP, fuel cons., temperatures, etc.

• Key Output: Performance maps (BP, SFC, $$\displaystyle \eta_{bth} $$ vs. Speed or Load).

2.3.2. Part Load Test

• Procedure: At a fixed speed (usually rated), apply loads at 25%, 50%, 75%, 100%. Record parameters.

• Key Output: Characteristic curves at a specific operating point.

2.3.3. Heat Balance Sheet Preparation

1. Energy Input: $$\displaystyle Q_{in} = \dot{m}_f \times CV $$ (kW)

2. Useful Output: $ BP $ (kW)

3. Losses:

   • Exhaust Loss: $$\displaystyle Q_{exh} = \dot{m}_{exh} \times C_p \times (T_{exh} - T_{amb}) $$

   • Cooling Water Loss: $$\displaystyle Q_{cool} = \dot{m}_w \times C_{pw} \times (T_{out} - T_{in}) $$

   • Radiation & Unaccounted: $$\displaystyle Q_{rad} = Q_{in} - (BP + Q_{exh} + Q_{cool}) $$

4. Check: $$\displaystyle Q_{in} \approx BP + \sum \text{Losses} $$

2.3.4. Morse Test (Multi-cylinder Engines)

• Aim: Determine Frictional Power (FP) and Individual cylinder Indicated Power.

• Procedure (for 4-cyl):

  1. Run all cylinders, note BP₁.

  2. Stop cylinder 1 (spark/ fuel cut), run others, note BP₂.

  3. Repeat for cylinders 2, 3, 4 → BP₃, BP₄, BP₅.

• Calculations:

  • IP of each cylinder (running) = BP₁ - BP (when that cylinder is off)

  • Total IP = Σ (IP of each cylinder)

  • FP = Total IP - BP₁ (when all running)

  • $$\displaystyle \eta_m = \frac{BP_1}{\text{Total IP}} $$

2.3.5. Willan's Line Test

• Aim: Determine Frictional Power (FP) graphically.

• Procedure: Run engine at constant speed. Vary load from zero (motoring) to full. Plot BP (y-axis) vs. Fuel consumption rate (x-axis).

• Result: Straight line. Intercept on BP-axis (at $$\displaystyle \dot{m}_f = 0 $$) gives FP. (FP is the BP required to overcome friction when no useful work is done).

2.3.6. Retardation Test (for Frictional Power)

• Aim: Determine Frictional Power (FP) by measuring deceleration.

• Procedure:

  1. Run engine at high speed, cut off fuel & ignition.

  2. Measure time t for speed to fall from N₁ to N₂ (using tachometer).

  3. Calculate angular deceleration $$\displaystyle \alpha = \frac{2\pi (N_2 - N_1)}{60 \times t} $$ (rad/s²).

• Calculation:

$$ FP = I \times \alpha \times \frac{2\pi N_{avg}}{60} $$

*Where I = Mass moment of inertia of rotating parts (known), $$\displaystyle N_{avg} = \frac{N_1+N_2}{2} $$.*

2.4. Combustion Analysis & Emission Testing

2.4.1. Pressure-Volume (P-V) Diagram

• Instrumentation: Engine Indicator (mechanical/digital) or pressure transducer + crank angle encoder.

• From Diagram:

  • Area ∝ Work done per cycle.

  • Mean Effective Pressure (MEP): Hypothetical constant pressure that would produce same work.

$$ IMEP = \frac{\text{Net Work/cycle}}{V_s} \quad (\text{for 4-stroke, work/cycle = IP} \times \frac{120}{N}) $$

$$ BMEP = \frac{BP \times 120}{V_s \times N} \quad \text{(for 4-stroke, 4-cyl)} $$

*   **Indicated Power:** $$\displaystyle IP = \frac{IMEP \times V_s \times N}{2 \times 60} $$ (4-stroke)

2.4.2. Pressure-Time (P-θ) Diagram

• Analysis: Identifies combustion phases:

  • Ignition Delay (CI) / Flame Initiation (SI)

  • Rapid Combustion / Flame Propagation

  • Afterburning

• Peak Pressure Position: Indicator of combustion phasing (optimal near TDC for CI, slightly after for SI).

2.4.3. Exhaust Gas Analysis & AFR Calculation

• Measured: %CO, %CO₂, %O₂, %HC (ppm).

• Air-Fuel Ratio (AFR) from Orsat/Exhaust Gas Analyzer (for hydrocarbon fuel CₓHᵧ):

$$ AFR = \frac{4.76 \times (\%CO_2 + \frac{\%CO}{2} + \frac{\%H_2O}{2} + \frac{\%O_2}{2}) \times 28.97}{\%C \text{ in fuel} \times 12 + \%H \times 1} \times \frac{100}{\text{Carbon % in exhaust}} $$

*Simpler approximate formula (dry basis, neglecting H₂O):*

$$ AFR \approx \frac{4.76 \times (\%CO_2 + \frac{\%CO}{2} + \frac{\%O_2}{2}) \times 28.97}{(\%C \text{ in fuel}) \times 12} \times \frac{100}{\%CO_2 + \%CO + \%HC} $$

*Where 28.97 = molecular weight of air.*

2.4.4. Smoke Density Measurement

• Principle: Light extinction through a smoke sample.

• Opacimeter: Measures percentage of light absorbed. Smoke Number (SAE/BOSCH): Correlates opacity to a standard scale (0 = clean, 10 = very smoky).

2.5. Performance Curves & Characteristic Analysis

2.5.1. Plotting & Interpretation

• BP vs. Speed: Bell-shaped curve. Peak BP at rated speed.

• SFC vs. BP/BP vs. SFC: U-shaped curve. Minimum SFC at ~75-80% of max load.

• Thermal Efficiency vs. BP: Rises with load, peaks, then may drop.

• Exhaust Temp vs. Load: Increases with load (more fuel, less complete combustion at high load?).

2.5.2. Comparative Analysis (SI vs. CI)

2.5.3. Effect of Variables

• Compression Ratio: ↑ CR → ↑ thermal efficiency (Otto/Diesel cycle), ↑ NOx risk.

• Ignition Timing (SI): Advance → ↑ power & efficiency (up to limit), risk of knocking. Retard → ↓ power, ↑ exhaust temp.

• Injection Timing (CI): Advance → ↑ pressure & temp → ↑ efficiency & NOx, risk of knocking. Retard → ↓ efficiency, ↑ smoke.

2.6. Engine Tuning & Optimization Experiments

2.6.1. Effect of Air-Fuel Ratio (λ or AFR)

• Stoichiometric AFR: Theoretical perfect mix (λ=1). For petrol ~14.7:1.

• Rich Mix (λ<1, AFR↓): More fuel. ↓ SFC? ↑ CO, HC, smoke. ↑ power? (up to a point for CI).

• Lean Mix (λ>1, AFR↑): Less fuel. ↑ SFC? ↑ NOx, ↓ CO, HC. Risk of mis-fire, high exhaust temp.

• Optimum: Usually slightly rich for max power (SI), lean for best economy (CI).

2.6.2. Ignition Timing Variation (SI Engine)

• Procedure: Adjust spark advance/retard in increments (e.g., 5° BTDC to 15° ATDC).

• Observe: BP, SFC, exhaust temp, knocking tendency.

• Optimum: MBT (Maximum Brake Torque) timing – spark advance that gives max BP for given load/speed.

2.6.3. Injection Timing Variation (CI Engine)

• Procedure: Adjust fuel pump timing (advance/retard injection start).

• Observe: BP, SFC, peak pressure, exhaust smoke, noise.

• Optimum: Timing that gives best trade-off between efficiency (early) and smoke/noise (late).

2.7. Safety, Error Analysis & Reporting

2.7.1. Laboratory Safety Protocols

• Fuel Handling: No smoking, fire extinguisher nearby, proper storage.

• Rotating Parts: Guard all shafts, couplings. Loose clothing prohibited.

• High Temperature: Use gloves for exhaust, coolant, oil. Allow engine to cool before maintenance.

• Exhaust Gases: Ensure proper ventilation; CO is lethal.

• Electrical: Proper grounding of DAS, dynamometer.

2.7.2. Sources of Error

• Instrumental: Calibration drift, parallax error (analog gauges), resolution limit.

• Procedural: Inaccurate timing (fuel/stopwatch), not reaching steady-state, incorrect manometer reading.

• Environmental: Ambient temperature/pressure changes affecting air density & correction factors.

2.7.3. Uncertainty Analysis (Simple Propagation)

For a calculated parameter $$\displaystyle Z = f(x, y, z) $$, the maximum possible error:

$$ \Delta Z = \left| \frac{\partial Z}{\partial x} \right| \Delta x + \left| \frac{\partial Z}{\partial y} \right| \Delta y + \left| \frac{\partial Z}{\partial z} \right| \Delta z $$

Example for BP (from torque & speed):

$$ BP = \frac{2\pi N T}{60} \Rightarrow \frac{\Delta BP}{BP} = \frac{\Delta N}{N} + \frac{\Delta T}{T} $$

2.7.4. Lab Report Structure

1. Title & Objective

2. Apparatus & Specifications (Engine, Dynamometer, Instruments with ranges/accuracy)

3. Schematic Diagram of setup

4. Procedure (Step-by-step)

5. Tabulation (Raw readings in a table)

6. Calculations (Sample calculation for one load point, formulas used)

7. Graphs (Plotted curves with labeled axes)

8. Discussion (Interpret curves, compare with theory, explain anomalies)

9. Conclusions (Summarize key findings: e.g., "Max efficiency of 32% achieved at 75% load")

10. Sources of Error & Precautions

[!TIP]

Exam Focus: Be prepared to derive/explain formulas for BP, IP (from IMEP), SFC, thermal efficiency. Know the difference between Morse & Willan's test (Morse for multi-cyl FP & individual IP; Willan's graphical for any engine FP). Always state units in final answers.