Thermal Engineering and Gas Dynamics (ME-601) - Unit 4 Short Notes

UNIT 4: Thermal Engineering and Gas Dynamics - Short Notes

1. Steam Generators (Boilers)

Classification of Steam Generators:

• Fire-tube vs. Water-tube:

  • Fire-tube: Hot gases pass through tubes surrounded by water. (e.g., Lancashire, Cochran). Low/medium pressure, smaller capacity.

  • Water-tube: Water passes through tubes heated by external gases. (e.g., Babcock & Wilcox). High pressure, large capacity.

• Pressure: Low (< 15 bar), Medium (15-32 bar), High (> 32 bar).

• Firing: Internally fired (furnace inside shell), Externally fired (separate furnace).

Velox Boiler:

• Significance: High-pressure (40-50 bar), high evaporation rate due to forced circulation and high heat transfer.

• Working Principle:

  1. Air-gas mixture from forced draft fan enters combustion chamber.

  2. Water from steam drum via downcomer to header, then to tubes.

  3. High gas velocity (≈ sonic) ensures rapid evaporation.

  4. Steam-water mixture returns to drum for separation.

• Key Components: Combustion chamber, tube bank (evaporator), steam drum, superheater, economizer.

Diagram:

DiagramSEARCH: "Velox boiler cross-section showing forced circulation"

Lamont Boiler:

• Construction: High-pressure (100-150 bar) forced circulation water-tube boiler.

• Water Path: Steam drum → centrifugal pump → distributing header → small-bore tubes (evaporator) → return to drum.

• Flue Gas Path: Furnace → superheater → evaporator tubes → economizer → chimney.

• Important Parts: Steam drum, centrifugal pump, evaporator (small tubes), superheater, economizer.

Diagram:

DiagramSEARCH: "Lamont boiler schematic water and gas path"

Boiler Mountings & Accessories (Functions):

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

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

3. Pressure Gauge: Indicates steam pressure.

4. Fusible Plug: Melts at low water level to warn operator.

5. Feed Check Valve: Allows feedwater entry, prevents backflow.

6. Blow-off Cock: Removes sediments by blowing down water.

2. Boiler Draught

Definition & Purpose:

• Draught: Pressure difference (negative gauge) that moves flue gases from furnace to chimney.

• Purpose: Supply combustion air, remove flue gases, maintain stable flame.

Natural Draught:

• Created by chimney height.

  Draught pressure:

$$ H = \frac{\rho_a - \rho_g}{\rho_a} \times H_{ch} \quad \text{(in m of water)} $$

where $$\displaystyle \rho_a $$, $$\displaystyle \rho_g $$ = densities of air and flue gas.

Artificial Draught:

• Steam Jet:

  • Induced: Steam jet in chimney base entrains flue gases.

  • Forced: Steam jet in air supply duct.

• Fan Draught:

  • Induced Draft (ID) Fan: After furnace, draws gases.

  • Forced Draft (FD) Fan: Before furnace, supplies air.

• Advantages: Independent of weather, higher rates, controllable.

• Disadvantages: Power consumption, cost, maintenance.

Chimney Draught Calculation (Air per kg fuel):

Given: $$\displaystyle H_{ch} $$, $$\displaystyle T_g $$, $$\displaystyle T_a $$, $$\displaystyle P_{atm} $$, draught $h$ (mm water).

1. Find mass of flue gases $$\displaystyle m_g $$ from:

$$ h = H_{ch} \left( \frac{\rho_a}{\rho_g} - 1 \right) $$

with $$\displaystyle \rho = P/(RT) $$.

2. Air-fuel ratio:

$$ \text{Actual air/kg fuel} = \frac{m_g}{1 + \text{excess air}} \times \frac{\text{air in } m_g}{\text{total } m_g} $$

(Assume 20% excess air if not given).

3. Steam Properties and Thermodynamic Tables

Use of Steam Tables:

• Saturated: Given $P$ or $T$, find $$\displaystyle v_f $$, $$\displaystyle v_g $$, $$\displaystyle h_f $$, $$\displaystyle h_{fg} $$, $$\displaystyle h_g $$, $$\displaystyle s_f $$, $$\displaystyle s_{fg} $$, $$\displaystyle s_g $$, $$\displaystyle u_f $$, $$\displaystyle u_g $$.

• Superheated: Given $P$, $T$ (superheat), find $v$, $h$, $s$.

Determination of State Properties (Saturated Mixture):

Given: Mass $m$, Volume $V$, $T$ or $P$.

1. Specific volume: $$\displaystyle v = V/m $$.

2. At given $P$ (or $T$), find $$\displaystyle v_f $$, $$\displaystyle v_g $$.

3. Dryness fraction: $$\displaystyle x = (v - v_f)/(v_g - v_f) $$.

4. Then:

$$ v = v_f + x v_{fg}, \quad h = h_f + x h_{fg}, \quad s = s_f + x s_{fg}, \quad u = u_f + x u_{fg} $$

Dryness Fraction from Specific Volume/Enthalpy:

• From $v$: $$\displaystyle x = (v - v_f)/v_{fg} $$.

• From $h$: $$\displaystyle x = (h - h_f)/h_{fg} $$.

4. Steam Power Cycles

4.1 Rankine Cycle

• Processes (T-s diagram):

  1-2: Isentropic expansion in turbine.

  2-3: Constant pressure heat rejection in condenser.

  3-4: Isentropic pumping.

  4-1: Constant pressure heat addition in boiler.

• Thermal Efficiency:

$$ \eta = \frac{(h_1 - h_2)}{(h_4 - h_3)} \approx \frac{(h_1 - h_2)}{(h_1 - h_4)} \quad \text{(since $$\displaystyle h_4 \approx h_3 $$)} $$

Diagram:

DiagramSEARCH: "Rankine cycle p-v and T-s diagram"

Modified Rankine Efficiency (Steam Engine):

Considers:

• Cut-off at $$\displaystyle r_c $$ (fraction of stroke).

• Release at constant volume.

• Back pressure $$\displaystyle P_b $$.

Work per cycle:

$$ W = (P_1 V_1 - P_2 V_2) + P_2 (V_2 - V_3) - P_b (V_1 - V_3) $$

Efficiency: $$\displaystyle \eta = W / (P_1 V_1 \ln(V_1/V_c)) $$ (assuming hyperbolic expansion to cut-off).

4.2 Effect of Boiler & Condenser Pressures (T-s Diagram)

• Increasing Boiler Pressure:

  ↑ Average $$\displaystyle T_{heat\ addition} $$, ↑ efficiency.

  ↓ Moisture content at turbine exhaust (problem for blades).

• Decreasing Condenser Pressure:

  ↓ Heat rejection, ↑ efficiency.

  ↑ Pump work (negligible), ↑ moisture at exhaust.

4.3 Reheat Cycle

• Schematic: HP turbine → Reheater → IP/LP turbine.

• T-s Diagram: Shows two expansion stages with constant pressure reheat.

• Advantages:

  ↑ Turbine output, ↓ exhaust moisture, allows higher boiler pressure.

4.4 Regenerative Cycle

• Open Feedwater Heater (Deaerator):

  Steam from turbine mixes with feedwater, leaves as saturated liquid at that pressure.

• Closed Feedwater Heater:

  Shell-and-tube; steam condenses on tube side, heating feedwater (no mixing).

• T-s Diagram: Shows feedwater line crossing steam expansion line at multiple points.

• Efficiency Improvement: Preheats feedwater, reduces heat input needed.

4.5 Binary Vapour Cycle

• Working: Two fluids (e.g., mercury-steam). High-boiling fluid (Hg) expands in HP turbine, rejects heat to low-boiling fluid (water/steam) which expands in LP turbine.

• Advantages: Better temperature matching in heat addition, higher overall efficiency than simple Rankine.

4.6 Vapor Carnot Cycle

• Processes:

  1-2: Isothermal heat addition (evaporation).

  2-3: Adiabatic expansion.

  3-4: Isothermal heat rejection (condensation).

  4-1: Adiabatic compression.

• T-s Diagram: Two isotherms, two adiabatics.

• Limitations:

  • Isothermal heat transfer requires infinite area/slow process.

  • Wet compression causes blade erosion.

  • Low specific volume → large compressor size.

4.7 Gas Turbine Cycle with Reheater & Regenerator

• Cycle: Compressor → Combustor → HP turbine → Reheater → LP turbine → Regenerator (preheats air).

• Maximum Output Condition:

  For two-stage turbine with regenerator effectiveness $\epsilon$:

$$ \text{Optimal pressure ratio per stage: } r_p = \left( \frac{T_3}{T_1} \right)^{1/(2n)} $$

where $n$ = number of stages, $$\displaystyle T_3 $$ = max cycle temp, $$\displaystyle T_1 $$ = inlet temp.

Regenerator effectiveness: $$\displaystyle \epsilon = (T_5 - T_2)/(T_3 - T_2) $$.

5. Steam Turbines

Impulse vs. Reaction:

Compounding:

• Velocity Compounding: Multiple moving blade rows separated by fixed blades (e.g., Curtis turbine).

• Pressure Compounding (Rateau): Multiple nozzle rings and moving blade rows (e.g., Parsons turbine).

• Velocity-Pressure Compounding: Combination.

• Need: Reduce rotor speed (< 3000 rpm for 50 Hz), avoid excessive blade velocity and erosion.

Losses in Steam Turbines:

• Nozzle friction, blade friction, leaving loss (kinetic energy loss), tip leakage, disk friction, wetness loss.

6. Condensers and Feedwater Heaters

6.1 Condensers

• Types:

  • Surface: Shell-and-tube; steam and cooling water separate.

  • Jet: Direct contact; steam mixed with cooling water.

• Low-Level Jet Condenser (Counter-flow):

  Cooling water enters top, flows down; steam enters bottom, rises counterflow. Condensate collected at bottom.

  Diagram:

  DiagramSEARCH: "low level jet condenser counter flow sketch"

• Air Leakage Sources:

  Joints, gland packing, non-condensables in steam, vacuum break.

• Effect of Air Leakage:

  ↑ Partial pressure of air → ↑ condenser pressure → ↓ vacuum → ↓ turbine output ↑ pumping work.

6.2 Feedwater Heaters (FWH)

• Open-Type: Direct mixing (deaeration); e.g., deaerator.

• Closed-Type: Indirect; shell-and-tube (steam outside tubes, feedwater inside).

• Working Principle: Regenerative heat exchange; steam from turbine bled to heat feedwater.

• Role in Efficiency: ↑ Feedwater temperature → ↓ heat input in boiler → ↑ cycle efficiency.

7. Fundamentals of Gas Dynamics

7.1 Basic Concepts

• Mach Number ($M$):

$$ M = \frac{V}{a} $$

where $$\displaystyle a = \sqrt{\gamma R T} $$ (ideal gas).

• Subsonic: $$\displaystyle M < 1 $$, Sonic: $$\displaystyle M = 1 $$, Supersonic: $$\displaystyle M > 1 $$, Hypersonic: $M \gg 1$.

• Examples: Commercial jet $M \approx 0.8$, Concorde $M \approx 2.2$.

• Velocity of Sound in Steam:

$$ a = \sqrt{\frac{\gamma P}{\rho}} \quad \text{or} \quad a = \sqrt{\gamma R T} $$

• Mach Cone: For $$\displaystyle M>1 $$, disturbance confined to cone with angle $$\displaystyle \mu = \sin^{-1}(1/M) $$.

  • Zone of Action: Inside cone (affected by source).

  • Zone of Silence: Outside cone (unaffected).

7.2 One-Dimensional Isentropic Flow

• Governing Equations (Steady, Inviscid, Adiabatic):

  Continuity: $$\displaystyle \rho A V = \text{const} $$

  Momentum: $$\displaystyle dP + \rho V dV = 0 $$

  Energy: $$\displaystyle dh + V dV = 0 $$

• Area-Velocity Relation:

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

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

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

• Stagnation Properties (Isentropic):

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

7.3 Diffusers

• Function: Decelerate flow, convert kinetic energy to pressure rise.

• Effect:

  • Subsonic: Divergent duct ($$\displaystyle dV<0 $$, $$\displaystyle dP>0 $$).

  • Supersonic: Convergent-divergent with normal shock (if required).

• Design: Gradual divergence to avoid separation, minimize losses.

8. Flow of Steam Through Nozzles

Nozzle Types:

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

• Convergent-Divergent: For $$\displaystyle M > 1 $$ (supersonic).

Isentropic Flow Assumptions:

Use steam tables or Mollier chart; $$\displaystyle s = \text{const} $$.

Critical Pressure Ratio & Critical Pressure:

• For steam:

  Saturated: $$\displaystyle (P_2/P_1)_{\text{crit}} \approx 0.577 $$

  Superheated: $$\displaystyle (P_2/P_1)_{\text{crit}} \approx 0.546 $$

• At critical pressure, $$\displaystyle M=1 $$, mass flow maximum.

Maximum Discharge Condition:

Mass flow rate:

$$ \dot{m} = C_d A_t \sqrt{2 \rho_1 (h_1 - h_2)} $$

Maximum when $$\displaystyle P_2/P_1 = \text{critical pressure ratio} $$.

Nozzle Efficiency:

$$ \eta_n = \frac{V_{\text{actual}}^2/2}{h_1 - h_{2s}} = \frac{V_{\text{actual}}^2}{V_{\text{isentropic}}^2} $$

Effect of Friction:

↓ Exit velocity, ↑ entropy, ↓ efficiency, ↑ pressure at exit (for given mass flow).

Supersaturated Flow of Steam:

• Conditions: High initial superheat, large pressure drop, rapid expansion (no time for condensation nuclei).

• Effect:

  • Discharge: Slightly higher than isentropic (due to lower density).

  • Heat drop: Lower than isentropic (entropy increases).

• Comparison: Non-equilibrium, metastable state; eventually condenses with shock wave.

9. Air Compressors

9.1 Classification

• Reciprocating: Single/multi-stage, single/double-acting.

• Rotary: Centrifugal, axial, screw, vane.

9.2 Single-Stage Reciprocating Compressor

• Working: Suction (intake), compression, delivery (discharge).

  P-V diagram includes clearance volume expansion.

• Clearance Volume & Ratio:

  $$\displaystyle V_c $$ = volume at TDC, $$\displaystyle V_s $$ = stroke volume.

  Clearance ratio: $$\displaystyle c = V_c / V_s $$.

• Work Input without Clearance:

  Polytropic ($$\displaystyle PV^n = C $$):

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

• Work Input with Clearance:

  Net work = compression work - expansion work from clearance.

• Mean Effective Pressure (MEP):

$$ \text{MEP} = \frac{\text{Net work per cycle}}{V_s} $$

9.3 Performance Parameters

• Volumetric Efficiency:

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

• Isothermal Efficiency:

$$ \eta_i = \frac{\text{Isothermal work}}{\text{Actual work}} $$

• Isentropic Efficiency:

$$ \eta_s = \frac{\text{Isentropic work}}{\text{Actual work}} $$

• Mechanical Efficiency:

$$ \eta_m = \frac{\text{Indicated work}}{\text{Shaft work}} $$

• Power Required:

  Single-acting:

$$ P = \frac{W_{\text{cycle}} \times N}{60 \times \eta_m} $$

Double-acting: Multiply by 2.

9.4 Multistage Compression

• Advantages:

  ↓ Work input (vs single-stage at same $$\displaystyle P_{out} $$), ↓ discharge temperature, ↑ efficiency.

• Perfect Intercooling:

  Minimum work when pressure ratio per stage equal:

$$ \frac{P_2}{P_1} = \frac{P_3}{P_2} = \cdots = \left( \frac{P_{out}}{P_{in}} \right)^{1/N} $$

• Work Done & Heat Rejected:

  Total work = sum of polytropic works per stage.

  Heat rejected in intercooler = $$\displaystyle c_p (T_{intercool} - T_{in}) $$ per kg.

9.5 Rotary Compressors

• Centrifugal Compressor:

  Air enters axially, accelerated by impeller, decelerated in diffuser (pressure rise).

  Velocity diagram: Inlet whirl velocity $$\displaystyle V_{w1} \approx 0 $$, outlet $$\displaystyle V_{w2} = U_2 - V_{r2} \cos \alpha_2 $$.

• Comparison with Reciprocating:

  • Continuous flow vs pulsating.

  • Higher flow rates, lower pressure ratios per stage.

  • Less maintenance, no valves.

10. Performance Evaluation of Steam Power Plants

Heat Balance Sheet (Tabular):

Equivalent Evaporation ($$\displaystyle m_e $$):

Steam generated from and at 100°C per kg fuel.

$$ m_e = \frac{m_s (h - h_{f1})}{2257 \ \text{kJ/kg}} $$

where $$\displaystyle h_{f1} $$ = enthalpy of feedwater at boiler inlet.

Overall Thermal Efficiency ($$\displaystyle \eta_{\text{overall}} $$):

$$ \eta_{\text{overall}} = \eta_{\text{boiler}} \times \eta_{\text{turbine}} \times \eta_{\text{generator}} \times \eta_{\text{cycle}} $$

• $$\displaystyle \eta_{\text{boiler}} = \frac{\text{Heat absorbed by steam}}{\text{Heat input from fuel}} $$

• $$\displaystyle \eta_{\text{turbine}} = \frac{\text{Actual work}}{\text{Isentropic work}} $$

• $$\displaystyle \eta_{\text{generator}} = \frac{\text{Electrical output}}{\text{Mechanical input}} $$

• $$\displaystyle \eta_{\text{cycle}} = \frac{\text{Net work output}}{\text{Heat input}} $$

Steam Rate:

$$ \text{Steam rate} = \frac{\text{Steam consumed (kg)}}{\text{Electrical output (kWh)}} $$

Specific Steam Consumption (SSC) = Steam rate. Lower SSC = better.

[!TIP] Exam Focus Areas from Past Papers:

• Diagrams: Velox boiler, Lamont boiler, Rankine cycle (p-v & T-s), low-level jet condenser, velocity diagram of centrifugal compressor.

• Numericals: Chimney draught (air per kg fuel), modified Rankine efficiency, multistage compressor work with perfect intercooling, nozzle velocity with friction, overall plant efficiency (given condensate rate).

• Derivations: Conditions for maximum discharge in nozzles, minimum work in multistage compression, maximum output in gas turbine with reheater/regenerator.

• Definitions: Mach number, nozzle efficiency, critical pressure ratio, volumetric/isothermal/isentropic/mechanical efficiencies.

• Comparisons: Impulse vs reaction turbines, open vs closed FWH, reciprocating vs rotary compressors, supersaturated vs isentropic nozzle flow.