Thermal Engineering and Gas Dynamics (ME-601) - Unit 1 Short Notes

UNIT 1: THERMAL ENGINEERING AND GAS DYNAMICS

(Based on RGPV Past Paper Analysis)

I. STEAM GENERATORS (BOILERS)

A. Classification of Steam Generators

High-Pressure Boilers (Water-tube type for power plants):

1. Lamont Boiler: Forced circulation, uses centrifugal pump to circulate water through evaporator tubes. High pressure (up to 150 bar), high capacity.

2. Velox Boiler: Uses gas turbine to supply forced draught. Very high evaporation rate (∼100 kg/m²·h), compact.

3. Benson Boiler: Once-through, no drum. Pressure up to 250 bar. Uses in-line superheater.

4. Loeffler Boiler: Steam circulation, avoids salt deposition. High pressure (∼175 bar).

[!TIP]

Exam Focus: Distinguish forced circulation (Lamont) vs. once-through (Benson). Velox is unique for its gas turbine-driven fan.

B. Detailed Study: Lamont & Velox Boilers

1. Lamont Boiler

• Working: Feed water is pressurized by a centrifugal pump (∼2-3 bar above steam pressure) and forced through evaporator tubes (lined with fins) in the furnace.

• Key Parts:

  • Economiser: Preheats feed water.

  • Superheater: In-line type.

  • Steam Separator: Removes moisture from steam.

  • Draught System: Forced draught fan.

• Water/Flue Gas Path:

  Water → Pump → Economiser → Evaporator Tubes → Steam Separator → Superheater → Steam

  Air → FD Fan → Furnace → Economiser → Chimney

2. Velox Boiler

• Significance: Achieves very high evaporation rate (5–6 times conventional) due to high gas velocity (∼60 m/s) from gas turbine-driven fan.

• Working:

  Air → Gas Turbine (driven by exhaust gases) → Combustion Chamber → Evaporator Tubes (bent) → Superheater → Chimney

  Water circulates by natural circulation due to high temperature difference.

• Advantage: Compact, fast response, suitable for peak load plants.

[!DIAGRAM]

DiagramSEARCH: "Lamont boiler schematic water flow path"

DiagramSEARCH: "Velox boiler gas turbine driven draught"

C. Boiler Draught

Definition: Draught is the small pressure difference required to maintain steady flow of air through the grate and flue gases through the boiler. Purpose: To supply combustion air and remove flue gases.

1. Natural Draught (Chimney)

• Theory: Hot flue gases + cold outside air create density difference → pressure difference.

• Draught Pressure Equation:

$$ H_w = 0.00052 \, H \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \quad \text{(in mm of water)} $$

Where:

• $H$ = chimney height (m)

• $$\displaystyle T_1 $$ = average temperature of flue gases (K)

• $$\displaystyle T_2 $$ = outside air temperature (K)

• Effect: Draught ∝ $H$ and $\Delta T$.

2. Artificial Draught

[!TIP]

Numerical Focus: Draught problems often involve finding air-fuel ratio or chimney height. Use:

$$ > \text{Mass of air} = \frac{\text{Draught pressure} \times \text{Area} \times \text{Density of air}}{\text{Pressure drop across grate}} > $$

D. Boiler Mountings & Accessories

Essential Mountings (Safety & Operation):

1. Safety Valve: Releases steam when pressure exceeds safe limit.

2. Water Level Indicator: Shows water level in boiler.

3. Pressure Gauge: Indicates steam pressure.

4. Fusible Plug: Melts at low water level → warns operator.

5. Steam Stop Valve: Isolates boiler from steam pipe.

Essential Accessories (Efficiency & Economy):

1. Feed Pump/Injector: Supplies feed water.

2. Economiser: Recovers heat from flue gases to preheat feed water → increases efficiency.

3. Air Preheater: Recovers heat to preheat combustion air → reduces fuel consumption.

4. Superheater: Increases steam temperature (improves turbine efficiency, prevents condensation).

E. Boiler Performance & Heat Balance

1. Heat Balance Sheet

2. Equivalent Evaporation

• Definition: Amount of steam (kg) generated from feed water at 100°C to dry saturated steam at boiler pressure.

• Formula:

$$ \boxed{E = \frac{m_s (h - h_{f1})}{2257}} $$

Where:

• $$\displaystyle m_s $$ = actual steam generated (kg/h)

• $h$ = enthalpy of steam generated (kJ/kg)

• $$\displaystyle h_{f1} $$ = enthalpy of feed water at 100°C (≈ 419 kJ/kg)

• 2257 = latent heat at 100°C (kJ/kg)

3. Boiler Efficiency

• Direct Method (Input-Output):

$$ \eta_b = \frac{m_s (h - h_{f1})}{m_f \times \text{HHV}} \times 100\% $$

• Indirect Method (Loss Method):

$$ \eta_b = 100 - (\text{Losses in %}) $$

[!TIP]

Common Pitfall: In equivalent evaporation, always use 2257 kJ/kg (latent heat at 100°C, 1 atm), not local latent heat.

II. STEAM POWER PLANT CYCLES (RANKINE CYCLE & MODIFICATIONS)

A. Basic Rankine Cycle

• Processes:

  1. 1–2: Isentropic compression in pump (s₁ = s₂).

  2. 2–3: Constant pressure heat addition in boiler (P₂ = P₃).

  3. 3–4: Isentropic expansion in turbine (s₃ = s₄).

  4. 4–1: Constant pressure heat rejection in condenser (P₄ = P₁).

• Thermal Efficiency:

$$ \eta_{th} = \frac{(h_3 - h_4) - (h_2 - h_1)}{h_3 - h_2} = \frac{W_{net}}{Q_{in}} $$

• Diagram:

  DiagramCANVAS: "T-s diagram of Rankine cycle with labeled processes 1-2-3-4"
  DiagramCANVAS: "P-v diagram of Rankine cycle"

B. Effect of Operating Parameters on Efficiency

[!TIP]

Key Insight: Efficiency ↑ with higher Tₕ and lower Tₗ. Superheating improves efficiency and protects turbine blades from erosion.

C. Regenerative Rankine Cycle

• Principle: Use extracted steam from turbine to preheat feed water → reduces Q_in.

• Feedwater Heaters:

  | Open-Type (Direct Contact) | Closed-Type (Surface) | |--------------------------------|----------------------------------------| | Steam mixes directly with water. | Steam heats water via tubes (no mixing). | | e.g., Deaerator. | e.g., L.P. & H.P. heaters. |

• Regeneration: Increases efficiency by reducing fuel consumption. Closed system more common in power plants.

• Open vs. Closed Feed System:

  Open = feed water heated by direct contact (requires pump between heaters).

  Closed = feed water heated in shell-and-tube exchangers (no direct contact).

D. Reheat Rankine Cycle

• Working: Steam expanded in HP turbine → reheated to initial T → expanded in IP/LP turbines.

• T-s Diagram: Shows two constant pressure heat additions (boiler + reheater).

• Advantages:

  • Reduces moisture content at final turbine stage.

  • Increases average Tₕ → higher efficiency.

  • Allows higher boiler pressure.

• Combined Reheat-Regenerative: Used in modern power plants (e.g., 150 bar, 550°C, reheat at 40 bar).

E. Overall Plant Efficiency & Metrics

• Overall Efficiency:

$$ \eta_{overall} = \eta_b \times \eta_t \times \eta_g $$

Where:

• $$\displaystyle \eta_b $$ = boiler efficiency

• $$\displaystyle \eta_t $$ = cycle (turbine) efficiency

• $$\displaystyle \eta_g $$ = generator efficiency (∼0.95–0.98)

• Steam Rate:

$$ \text{Steam rate} = \frac{3600}{W_{net}} \quad \left( \frac{\text{kg}}{\text{kWh}} \right) $$

($$\displaystyle W_{net} $$ = net work output per kg steam in kJ/kg)

• Heat Rate:

$$ \text{Heat rate} = \frac{1}{\eta_{overall}} \times 3600 \quad \left( \frac{\text{kJ}}{\text{kWh}} \right) $$

F. Advanced Cycles

• Binary Vapour Cycle: Uses two working fluids (e.g., Mercury-water). Mercury cycle operates at high T, exhaust heats water/steam cycle. Higher efficiency but mercury toxicity limits use.

• Vapour Carnot Cycle: Two isothermal + two isentropic processes. Theoretical maximum efficiency but impractical due to:

  • Isothermal heat addition impossible in single-phase.

  • Large pump work for liquid-vapour mixture.

  • Requires infinite heat exchanger area.

III. STEAM TURBINES

A. Fundamentals & Classification

Compounding: To reduce blade speed (avoid centrifugal stresses) and improve efficiency.

• Velocity Compounding: Multiple stages of fixed + moving blades (Curtis turbine).

• Pressure Compounding: Multiple nozzles in series (Rateau turbine).

B. Analysis of Steam Engine Cycles (Modified Rankine)

• Modified Rankine Cycle: Assumes constant volume heat rejection (4–1) instead of constant pressure.

• Efficiency (neglecting clearance):

$$ \eta_{mod} = 1 - \frac{1}{r} \left( \frac{r_c^{\gamma-1} - 1}{\gamma (r_c - 1)} \right) $$

Where:

• $r$ = cut-off ratio ($$\displaystyle V_3/V_2 $$)

• $$\displaystyle r_c $$ = compression ratio ($$\displaystyle V_1/V_4 $$)

• $\gamma$ = adiabatic index

• Numerical Approach: Use steam tables for actual enthalpies at:

  • Admission (P₁, x₁)

  • Cut-off (P₂, V₃ = r·V₂)

  • Release (constant volume: V₄ = V₃, P₄)

  • Back pressure (P₅ = P₁)

C. Turbine Performance & Losses

• Stage Efficiency ($$\displaystyle \eta_{stage} $$): Ratio of work output to enthalpy drop in one stage.

• Overall Efficiency ($$\displaystyle \eta_{turbine} $$): $$\displaystyle \frac{\text{Actual work output}}{\text{Isentropic enthalpy drop}} $$.

• Governing: Methods to maintain constant speed under varying load.

  • Throttle governing: Control valve at inlet (common).

  • Nozzle governing: Separate nozzles controlled individually.

  • Bypass governing: Steam bypassed to later stages.

IV. AIR COMPRESSORS

A. Classification

B. Reciprocating Compressors (Detailed)

1. P-V Diagram with Clearance

• Clearance Volume ($$\displaystyle V_c $$): Volume at TDC when piston is at top.

• Indicated Work (per cycle, single-acting):

$$ W_i = \frac{n}{n-1} P_1 V_1 \left[ \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} - 1 \right] $$

Where $n$ = polytropic index (1.2–1.4).

2. Volumetric Efficiency ($$\displaystyle \eta_v $$):

$$ \eta_v = 1 + C - C \left( \frac{P_2}{P_1} \right)^{\frac{1}{n}} $$

Where $$\displaystyle C = \frac{V_c}{V_s} $$ (clearance ratio).
Effect: ↑ Clearance → ↓ $$\displaystyle \eta_v $$ (less fresh charge per stroke).

3. Efficiencies:

• Isentropic Efficiency:

$$ \eta_{isen} = \frac{\text{Isentropic work}}{\text{Actual work}} = \frac{W_s}{W_a} $$

• Isothermal Efficiency:

$$ \eta_{iso} = \frac{\text{Isothermal work}}{\text{Actual work}} $$

• Mechanical Efficiency:

$$ \eta_m = \frac{\text{Indicated work}}{\text{Brake work}} = \frac{W_i}{W_b} $$

[!TIP]

Numerical Sequence: For compressor problems:

1. Find $$\displaystyle P_2 $$, $$\displaystyle T_2 $$ from polytropic relation.

2. Calculate $$\displaystyle W_i $$ → Power = $$\displaystyle W_i \times \text{rpm} \times \text{cylinders}/60 $$.

3. $$\displaystyle \eta_v $$ from clearance formula.

4. Delivery $$\displaystyle T_2 $$ from $$\displaystyle T_2 = T_1 \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} $$.

C. Multistage Compression with Intercooling

• Advantages:

  • ↓ Work input (closer to isothermal).

  • ↓ discharge temperature.

  • ↑ volumetric efficiency.

• Minimum Work Condition (perfect intercooling, $$\displaystyle T_2 = T_1 $$):

$$ W_{min} = 2 \cdot \frac{n}{n-1} P_1 V_1 \left[ \left( \frac{P_3}{P_1} \right)^{\frac{n-1}{2n}} - 1 \right] $$

Where $$\displaystyle P_3 $$ = final pressure, and intermediate pressure $$\displaystyle P_2 = \sqrt{P_1 P_3} $$.

• Heat Rejected in Intercooler:

$$ Q_{rej} = m C_p (T_2 - T_1) \quad \text{(per kg air)} $$

D. Rotary Compressors: Centrifugal Type

• Principle: Dynamic compression – kinetic energy from high-speed impeller → pressure rise in diffuser.

• Velocity Diagram:

  • $U$ = blade speed, $V$ = absolute velocity, $$\displaystyle V_r $$ = relative velocity.

  • Energy transfer per unit mass: $$\displaystyle W = U_2 V_{w2} - U_1 V_{w1} $$ (often $$\displaystyle U_1 V_{w1} \approx 0 $$).

• Advantages over Reciprocating:

  • Smooth, continuous flow.

  • No valves, less maintenance.

  • High capacity, moderate pressure ratio (3–4:1 per stage).

• Disadvantages:

  • Sensitive to foreign matter.

  • Lower efficiency at part load.

  • Requires high speed (∼15,000–30,000 rpm).

V. FUNDAMENTALS OF GAS DYNAMICS (COMPRESSIBLE FLOW)

A. Basic Concepts & Mach Number

• Mach Number:

$$ M = \frac{V}{a} = \frac{V}{\sqrt{\gamma R T}} $$

Where $a$ = local speed of sound.

• Flow Regimes:

  • Subsonic: $$\displaystyle M < 1 $$ (disturbances propagate upstream).

  • Sonic: $$\displaystyle M = 1 $$ (choked flow).

  • Supersonic: $$\displaystyle M > 1 $$ (disturbances confined to Mach cone).

  • Hypersonic: $M \gg 1$ (typically $$\displaystyle M > 5 $$).

• Stagnation Properties (isentropic relations):

$$ \frac{T_0}{T} = 1 + \frac{\gamma-1}{2} M^2, \quad \frac{P_0}{P} = \left( 1 + \frac{\gamma-1}{2} M^2 \right)^{\frac{\gamma}{\gamma-1}} $$

B. One-Dimensional Isentropic Flow

• Area-Velocity Relation:

$$ \frac{dA}{A} = (M^2 - 1) \frac{dV}{V} $$

• $$\displaystyle M < 1 $$: $dA \uparrow \Rightarrow dV \uparrow$ (subsonic diffuser).

• $$\displaystyle M > 1 $$: $dA \uparrow \Rightarrow dV \downarrow$ (supersonic nozzle).

• $$\displaystyle M = 1 $$: $$\displaystyle dA = 0 $$ → throat condition.

• Critical Conditions (at throat, $$\displaystyle M=1 $$):

$$ \frac{A}{A^*} = \frac{1}{M} \left[ \frac{2}{\gamma+1} \left(1 + \frac{\gamma-1}{2} M^2 \right) \right]^{\frac{\gamma+1}{2(\gamma-1)}} $$

Where $$\displaystyle A^* $$ = throat area.

C. Flow Regimes & Wave Propagation

• Mach Angle:

$$ \mu = \sin^{-1} \left( \frac{1}{M} \right) $$

• Zone of Action: Region within Mach cone where disturbances from a point are felt.

• Zone of Silence: Region outside Mach cone where disturbances are not felt (supersonic flow).

D. Diffusers

• Function: Decelerate flow, increase pressure.

• Subsonic Flow: Convergent diffuser (like nozzle in reverse).

• Supersonic Flow: Convergent-Divergent diffuser (shock waves may form).

• Effect: $V \downarrow$, $P \uparrow$, $T \uparrow$ (total pressure loss if shocks present).

VI. FLOW THROUGH NOZZLES

A. Nozzle Types & Choked Flow

• Convergent Nozzle: For $M \leq 1$ (subsonic flow only).

• Divergent Nozzle: For $M \geq 1$ (supersonic flow only).

• C-D Nozzle: Convergent → throat → divergent. Accelerates subsonic → sonic → supersonic.

• Critical Pressure Ratio ($$\displaystyle \left( \frac{P^*}{P_0} \right)_{isentropic} $$):

$$ \left( \frac{P^*}{P_0} \right) = \left( \frac{2}{\gamma+1} \right)^{\frac{\gamma}{\gamma-1}} $$

For steam ($\gamma \approx 1.3$): $\approx 0.546$; for air ($$\displaystyle \gamma=1.4 $$): $\approx 0.528$.

• Maximum Mass Flow Rate (choked flow, $$\displaystyle M=1 $$ at throat):

$$ \dot{m}_{max} = \frac{P_0 A^*}{\sqrt{T_0}} \sqrt{\frac{\gamma}{R}} \left( \frac{2}{\gamma+1} \right)^{\frac{\gamma+1}{2(\gamma-1)}} $$

B. Friction & Nozzle Efficiency

• Effect of Friction:

  • ↓ Exit velocity.

  • ↑ entropy (irreversibility).

  • May cause supersaturation in steam nozzles.

• Nozzle Efficiency:

$$ \eta_n = \frac{V_{actual}^2 / 2}{h_0 - h_e} = \frac{V_{actual}^2}{V_{ideal}^2} $$

Where $$\displaystyle h_0 $$ = stagnation enthalpy, $$\displaystyle h_e $$ = actual exit enthalpy.

C. Supersaturated Flow (Metastable Flow)

• Conditions:

  • Rapid expansion in nozzle (high $$\displaystyle \frac{dP}{dx} $$).

  • Lack of nucleation sites (very clean steam).

  • Insufficient time for condensation.

• Difference from Isentropic:

  | Isentropic Flow | Supersaturated Flow | |--------------------------|---------------------------------------| | Equilibrium condensation. | Metastable (supercooled vapour). | | Wilson line at saturation. | Wilson line below saturation. | | $$\displaystyle s = \text{const} $$. | $$\displaystyle s > s_{isentropic} $$ (entropy ↑). |

• Effect:

  • Discharge mass flow rate: Same as isentropic (depends on throat conditions).

  • Heat drop: Less than isentropic (some energy used for supersaturation).

  • Exit quality: Lower than isentropic (more moisture if condensation occurs later).

• Wilson Line: Empirical curve on T-s diagram showing limit of supersaturation for steam.

D. Numerical Problems

1. Exit velocity (isentropic): $$\displaystyle V_e = \sqrt{2 (h_0 - h_e)} $$.

2. With friction: $$\displaystyle V_e = \eta_n \times V_{isentropic} $$.

3. % reduction = $$\displaystyle (1 - \eta_n) \times 100\% $$.

4. Quality at exit (if wet): $$\displaystyle x = \frac{h_e - h_f}{h_{fg}} $$ at exit pressure.

VII. CONDENSERS

A. Classification

B. Jet Condensers (Detailed)

Low-Level Jet Condenser (Counter-Flow)

• Construction: Vertical cylindrical vessel. Steam enters at top, cooling water sprayed from top → counter-flow.

• Working:

  1. Steam from turbine enters top.

  2. Cooling water sprayed through nozzles.

  3. Steam condenses on water droplets.

  4. Condensate + water collected at bottom → air pump removes non-condensibles.

  5. Hot water pumped to cooling tower or river.

• Sketch:

  DiagramSEARCH: "low level jet condenser counter flow diagram"

• Advantages: Simple, cheap, good heat transfer.

• Disadvantages:

  • Water wastage (condensate lost).

  • Low vacuum (due to air binding).

  • Requires large water flow.

C. Air Leakage into Condensers

Sources:

1. Leaky joints in condenser, pipes, turbine exhaust.

2. Sealing failure in turbine shaft.

3. Non-condensibles in steam (from boiler water treatment).

Effects:

• ↑ Condenser pressure (↓ vacuum) → ↓ turbine work output.

• ↓ heat transfer coefficient (air film on tubes).

• ↑ pumping power for air removal.

• ↓ overall plant efficiency.

Air Removal:

• Steam jet air ejector or mechanical vacuum pump.

• Two-stage system: First stage removes bulk air, second stage maintains deep vacuum.

VIII. MISCELLANEOUS PERFORMANCE CALCULATIONS & CONCEPTS

A. Steam Power Plant Performance

Overall Thermal Efficiency:

$$ \eta_{overall} = \frac{\text{Power output (kWh)}}{\text{Fuel energy input (kWh)}} $$

From given data:

1. Boiler output: Steam generated per hour → $$\displaystyle Q_{in} = m_s (h_3 - h_{f,feed}) $$.

2. Turbine output: $$\displaystyle W_{net} = (h_3 - h_4) - (h_2 - h_1) $$.

3. Generator output: $$\displaystyle W_{elec} = W_{net} \times \eta_g $$.

4. Overall: $$\displaystyle \eta = \frac{W_{elec}}{m_f \times \text{HHV}} $$.

Steam Rate:

$$ \text{Steam rate} = \frac{m_s}{W_{elec}} \quad \left( \frac{\text{kg}}{\text{kWh}} \right) $$

B. Properties of Steam (Applied Problems)

Given: Mixture at $T$, $V$, $$\displaystyle m_{liquid} $$.

1. Pressure: From steam tables at given $T$ → $$\displaystyle P_{sat} $$.

2. Quality ($x$):

$$ x = \frac{v - v_f}{v_{fg}} \quad \text{or} \quad x = \frac{m_{vapour}}{m_{total}} $$

3. Specific volume: $$\displaystyle v = v_f + x v_{fg} $$.

4. Enthalpy: $$\displaystyle h = h_f + x h_{fg} $$.

5. Entropy: $$\displaystyle s = s_f + x s_{fg} $$.

6. Internal energy: $$\displaystyle u = u_f + x u_{fg} $$ or $$\displaystyle u = h - Pv $$.

C. Gas Turbine Cycle (Brief)

** Brayton Cycle with Reheat & Regenerator**:

• Reheat: ↑ $$\displaystyle W_{net} $$ (same $$\displaystyle T_{max} $$ limit).

• Regenerator: Recovers exhaust heat → ↓ $$\displaystyle Q_{in} $$.

• Conditions for Maximum Output:

  1. Reheat pressure ratio ($$\displaystyle r_{reheat} $$) chosen so that T₃ after reheat = T₄ before reheat (optimal).

  2. Regenerator effectiveness ($\epsilon$) → maximize $\epsilon$ (ideal = 1).

  3. Pressure ratio for max $$\displaystyle W_{net} $$: $$\displaystyle r_p = \left( \frac{T_{max}}{T_{min}} \right)^{\gamma/(2(\gamma-1))} $$ for simple Brayton.

END OF UNIT 1 NOTES
Focus on derivations, diagrams, and numerical methods from past papers. Practice: Draught calculations, compressor work, nozzle flow, Rankine efficiency.