UNIT 3: Advanced Engine Performance & Emissions Testing
3.1 Performance Parameters & Definitions
Core Engine Performance Metrics:
| Parameter | Symbol | Definition | Key Formula |
|---|---|---|---|
| Brake Power | BP | Useful power output at the crankshaft (shaft power). | $$\displaystyle BP = \frac{2\pi N T}{60} $$ (W) or $$\displaystyle BP = \frac{W \times N}{60} $$ (W) |
| Indicated Power | IP | Power developed inside the cylinder from gas pressure. | $$\displaystyle IP = \frac{p_m A L N}{60} $$ (W) |
| Friction Power | FP | Power lost to friction (piston, bearings, etc.). | $$\displaystyle FP = IP - BP $$ |
| Brake Thermal Efficiency | $$\displaystyle \eta_{bth} $$ | Ratio of BP to heat input from fuel. | $$\displaystyle \eta_{bth} = \frac{BP}{\dot{m}_f \times CV} $$ |
| Indicated Thermal Efficiency | $$\displaystyle \eta_{ith} $$ | Ratio of IP to heat input. | $$\displaystyle \eta_{ith} = \frac{IP}{\dot{m}_f \times CV} $$ |
| Mechanical Efficiency | $$\displaystyle \eta_m $$ | Ratio of BP to IP (fraction of IP delivered). | $$\displaystyle \eta_m = \frac{BP}{IP} = 1 - \frac{FP}{IP} $$ |
| Specific Fuel Consumption | SFC | Fuel consumed per unit power output per hour. | $$\displaystyle SFC = \frac{\dot{m}_f}{BP} $$ (kg/kW-hr) |
| Specific Air Consumption | SAC | Air consumed per unit power output per hour. | $$\displaystyle SAC = \frac{\dot{m}_a}{BP} $$ (kg/kW-hr) |
| Volumetric Efficiency | $$\displaystyle \eta_v $$ | Ratio of actual air intake to theoretical volume at ambient conditions. | $$\displaystyle \eta_v = \frac{\dot{m}_a}{\rho_a V_d N/2} $$ |
| Relative Efficiency | $$\displaystyle \eta_{rel} $$ | Ratio of actual thermal efficiency to air-standard efficiency. | $$\displaystyle \eta_{rel} = \frac{\eta_{actual}}{\eta_{air-standard}} $$ |
| Fuel-Air Ratio | f/a | Mass of fuel per mass of air. | $$\displaystyle f/a = \frac{\dot{m}_f}{\dot{m}_a} $$ |
| Air-Fuel Ratio | A/F | Mass of air per mass of fuel. | $$\displaystyle A/F = \frac{\dot{m}_a}{\dot{m}_f} $$ |
[!TIP] Exam Focus: Be prepared to derive relationships between BP, IP, FP, and $$\displaystyle \eta_m $$. Know which efficiency is always the highest: $$\displaystyle \eta_{ith} > \eta_{bth} $$.
3.2 Experimental Determination of Engine Power
A. Morse Test (Variable Load, Constant Speed)
-
Principle: Engine runs at constant RPM. Load (BP) is varied in steps. For each load, fuel consumption is measured. IP is calculated from indicated diagram (mean effective pressure) at each point. FP is found as $IP - BP$. Plot Willans line (BP vs. Fuel consumption/hr).
-
Apparatus: Engine, hydraulic/dynamometer, tachometer, fuel measuring setup, stopwatch.
-
Procedure:
-
Warm up engine to desired constant speed.
-
Apply load in increments, record BP (from dynamometer reading), fuel consumption for fixed time, RPM.
-
At each load, take indicator diagram to find $$\displaystyle p_m $$ and calculate IP.
-
Compute FP = IP - BP.
-
-
Willans Line: Straight line plot of Fuel consumption rate (kg/hr) vs. BP (kW).
-
Y-intercept = Fuel consumption at BP=0 → Idling fuel consumption (proportional to FP).
-
Slope = SFC (kg/kW-hr) at that speed.
-
$$FP \propto \text{Y-intercept} \quad \text{and} \quad \eta_m = \frac{BP}{IP} = \frac{BP}{BP + FP}$$
B. Retardation (Deceleration) Test
-
Principle: Engine is run at a speed, then cut off from load and fuel supply. The time taken for the engine to decelerate from $$\displaystyle N_1 $$ to $$\displaystyle N_2 $$ is measured. FP is calculated from the kinetic energy loss.
-
Apparatus: Engine, tachometer, stopwatch, fuel cut-off arrangement.
-
Procedure:
-
Run engine at constant speed $$\displaystyle N_1 $$.
-
Suddenly cut off fuel and load.
-
Measure time ($t$) for speed to drop to $$\displaystyle N_2 $$.
-
-
Calculation:
Let $I$ = total moment of inertia of rotating parts (engine + dynamometer).
$$\text{Loss in KE} = \frac{1}{2} I (\omega_1^2 - \omega_2^2) = FP_{avg} \times t$$
$$\therefore FP_{avg} = \frac{I (\omega_1^2 - \omega_2^2)}{2t}$$
(Where $$\displaystyle \omega = 2\pi N/60 $$)
> [!CAUTION] Requires accurate knowledge of **total system inertia (I)**. Measures **average FP** over deceleration range.
C. Willans Line Method (Graphical)
-
As described in Morse test, the line is obtained by varying load at constant speed.
-
From the graph: At any BP, total fuel consumption $$\displaystyle F_T $$ is read.
-
Fuel for IP ($$\displaystyle F_i $$) = $$\displaystyle F_T - F_0 $$ ($$\displaystyle F_0 $$ = intercept at BP=0).
-
$$\displaystyle \eta_m = \frac{BP}{IP} = \frac{BP}{BP + (F_0 \times CV/\eta_{ith})} $$ (using relations).
-
3.3 Heat Balance Sheet Preparation
Concept: Application of First Law of Thermodynamics (Energy Conservation) to the engine. Energy In = Energy Out
| Energy Input (100%) | Energy Output (Useful + Losses) |
|---|---|
| Heat from Fuel | 1. Brake Power (Useful Work) |
| $$\displaystyle Q_{in} = \dot{m}_f \times CV $$ | $BP$ (kW) |
| 2. Heat Losses | |
| a) Cooling Water: $$\displaystyle Q_{cw} = \dot{m}_{cw} C_p (T_{out} - T_{in}) $$ | |
| b) Exhaust Gases: $$\displaystyle Q_{eg} = \dot{m}_{eg} C_p (T_{eg} - T_{amb}) $$ | |
| c) Unaccounted: Radiation, convection, incomplete combustion, etc. | |
| $$\displaystyle Q_{loss} = Q_{in} - BP - Q_{cw} - Q_{eg} $$ |
Step-by-Step Procedure:
-
Measure: $$\displaystyle \dot{m}_f $$, $CV$, $$\displaystyle \dot{m}_{cw} $$, $$\displaystyle T_{cw,in/out} $$, $$\displaystyle \dot{m}_{eg} $$ (or calculate from air/fuel), $$\displaystyle T_{eg} $$, $$\displaystyle T_{amb} $$, BP.
-
Calculate: All $Q$ terms in kW or %.
-
Tabulate: Standard format showing Input (100%) and distribution of Output (BP% + Losses% = 100%).
-
Significance: Identifies major loss paths (often exhaust & cooling). Guides improvement efforts (e.g., turbocharging reduces exhaust loss).
[!TIP] Common Pitfall: Forgetting that $$\displaystyle \dot{m}_{eg} = \dot{m}_a + \dot{m}_f $$. Always use correct mass flow for exhaust gas enthalpy.
3.4 Engine Mapping & Performance Characteristics
-
Engine Map: 3D plot of a parameter (e.g., BTE, SFC) vs. Engine Speed (N) and Load (BP/Torque).
-
Key 2D Curves (at constant speed or load):
-
Torque Curve (T vs. N): Rises to peak, then falls. Diesel: flatter peak. Petrol: narrower peak.
-
Power Curve (BP vs. N): Increases with N, peaks, then may drop.
-
SFC Curve (SFC vs. BP/N): Minimum SFC at medium/high loads. Poor at idling & very high loads.
-
BTE Curve ($$\displaystyle \eta_{bth} $$ vs. BP/N): Similar trend to SFC (inverse). Peak BTE at ~70-80% of max load.
-
-
Effect of Varying Load at Constant Speed:
- BP ↑ → SFC ↓ (initially), BTE ↑ (to a max), then SFC ↑, BTE ↓ at very high loads (due to friction, incomplete combustion).
-
Effect of Varying Speed at Constant Load (e.g., full load):
-
BP may peak at an intermediate N (volumetric efficiency drop at high N, friction losses at low N).
-
BTE and SFC typically have optimum at medium N.
-
-
Optimal Operating Range: Region of low SFC / high BTE (usually medium load, medium-high speed). Engine maps define this for fuel economy.
-
Petrol vs. Diesel:
-
Petrol: Higher max speed, lower max torque, narrower torque curve, higher SFC at part load (throttling losses).
-
Diesel: Higher torque at low speed, flatter torque curve, better part-load efficiency (no throttling).
-
3.5 Emissions & Smoke Measurement
Major Pollutants & Sources:
-
CO & HC: Incomplete combustion (rich mixture, poor mixing, low temp).
-
NOx: High combustion temperature (Zeldovich mechanism).
-
Smoke (Particulates): Rich zones, incomplete combustion of heavy hydrocarbons (diesel dominant).
Measurement Principles:
| Pollutant | Instrument | Principle |
|---|---|---|
| CO, HC | NDIR Analyzer | Non-Dispersive Infrared: Gas absorbs specific IR wavelengths. |
| NOx | Chemiluminescence Analyzer | NO + O₃ → NO₂* → NO₂ + hν (light). Intensity ∝ NOx. |
| Smoke | Smoke Meter (Opacity) | Light extinction: $$\displaystyle Opacity = (1 - T/T_0) \times 100\% $$ |
| Hartridge Smoke Unit (HSU) | Calibrated scale based on light absorption by soot. |
Test Procedure:
-
Warm up engine and analyzer.
-
Place sampling probe in the exhaust pipe (typically 10-20x pipe diameter downstream of exhaust manifold, upstream of any expansion chamber).
-
Stabilize engine condition (speed/load).
-
Sample exhaust gas, condition (filter, dry, cool), analyze.
-
Record stabilized readings. Influence of λ (Air-Fuel Ratio):
-
Rich (λ<1): ↑ CO, HC, Smoke.
-
Lean (λ>1): ↑ NOx (up to a point), ↓ CO/HC/Smoke.
-
Stoichiometric (λ≈1): Catalyst optimum, but NOx peak. Emission Norms: Bharat Stage (BS-VI), Euro norms set limits for g/km or g/kW-hr.
3.6 Advanced Diagnostic & Measurement Techniques
-
Cylinder Pressure Measurement:
-
Sensor: Piezoelectric pressure transducer (mounted in cylinder head).
-
Output: P-θ diagram (Pressure vs. Crank Angle). Replaces mechanical indicator.
-
Use: Calculate $$\displaystyle p_m $$, $IP$, heat release rate.
-
-
Combustion Analysis:
-
From P-θ diagram, compute Rate of Pressure Rise (dP/dθ) and Heat Release Rate (dQ/dθ) using first law.
-
$$\displaystyle dQ_{net}/d\theta = \frac{\gamma}{\gamma-1} p \frac{dV}{d\theta} + \frac{1}{\gamma-1} V \frac{dp}{d\theta} - Q_{ht} $$
-
Identifies combustion phases (ignition delay, premixed, diffusion).
-
-
Vibration & Noise Measurement:
-
Accelerometer: Mounted on engine block → measures vibration amplitude/frequency (firing order, imbalance, bearing faults).
-
Sound Level Meter: Measures overall noise (dB) and spectrum. Sources: combustion, intake/exhaust, mechanical.
-
-
Blowby Measurement:
-
Principle: Measure gas leaking past piston rings into crankcase.
-
Procedure: Connect crankcase ventilation to a calibrated flow meter or orifice plate. Measure blowby flow rate at different loads.
-
Significance: Indicator of piston ring/wear condition. High blowby → reduced compression, increased oil dilution.
-
3.7 Data Analysis, Reporting & Error Estimation
Data Handling:
-
Systematic Tabulation: All raw observations (time, fuel volume, temperatures, pressures, speeds) in a master table.
-
Calculations: Use consistent units (SI). Apply formulas from 3.1 to derive BP, IP, FP, efficiencies, SFC.
-
Graphical Representation:
-
BP, Torque vs. RPM.
-
SFC, BTE vs. BP or RPM.
-
Willans line (Fuel rate vs. BP).
-
P-θ diagram (if available).
-
Error Analysis:
-
Sources:
-
Instrument precision (stopwatch, thermometer, pressure gauge, tachometer).
-
Heat loss assumptions (unaccounted losses in heat balance).
-
Steady-state assumption (fluctuations in readings).
-
Assumed values (CV of fuel, $$\displaystyle C_p $$ of gases, moment of inertia I).
-
-
Uncertainty Estimation: Use root-sum-square (RSS) method for functions of multiple variables.
Example for BTE: $$\displaystyle \eta_{bth} = f(BP, \dot{m}_f, CV) $$
$$\frac{\delta \eta}{\eta} = \sqrt{ \left(\frac{\delta BP}{BP}\right)^2 + \left(\frac{\delta \dot{m}_f}{\dot{m}_f}\right)^2 + \left(\frac{\delta CV}{CV}\right)^2 }$$
*Report final result as:* $$\displaystyle \eta_{bth} = 35.2\% \pm 1.5\% $$ (95% confidence).
Lab Report Structure:
-
Aim & Objective
-
Theory & Formulas (concise)
-
Apparatus & Schematic Diagram
-
Procedure (step-by-step)
-
Observations & Raw Data (tabular)
-
Calculations & Results (with sample)
-
Graphs
-
Discussion (interpret results, compare with theory, explain anomalies)
-
Conclusion (summary of key findings)
-
Error Analysis & Sources
-
References (if any)
[!TIP] Exam Winning: In viva, be ready to explain the physical significance of each curve on the engine map and justify the placement of the exhaust gas sampling probe.