Computer Aided Engineering (ME-603 (B)) - Unit 1 Short Notes

UNIT 1: TURBOMACHINERY AND FLUID POWER SYSTEMS

I. Thermodynamic and Fluid Dynamic Foundations

Application of First and Second Laws to Turbomachinery:

• First Law (Energy Conservation): For a steady-flow turbomachine, the net work output ($$\displaystyle W_{net} $$) equals the change in total energy (enthalpy $h$, kinetic energy $$\displaystyle \frac{V^2}{2} $$, potential energy $gz$) of the fluid.

$$W_{net} = \dot{m} \left( h_{in} + \frac{V_{in}^2}{2} + gz_{in} - h_{out} - \frac{V_{out}^2}{2} - gz_{out} \right)$$

For most turbomachinery, potential energy change ($\Delta gz$) is negligible.

• Second Law (Entropy & Irreversibility): Introduces the concept of isentropic efficiency ($$\displaystyle \eta_{isen} $$). It compares the actual work output to the ideal work output for an isentropic (reversible, adiabatic) process between the same inlet and outlet pressures.

$$\eta_{isen} = \frac{\text{Actual Work Output}}{\text{Isentropic Work Output}} = \frac{h_{in} - h_{out,actual}}{h_{in} - h_{out,isentropic}}$$

> [!TIP] **Exam Focus:** The Second Law defines the theoretical maximum efficiency. All real machines have $$\displaystyle \eta_{isen} < 1 $$ due to friction, shock losses, and heat loss.

Steam Generators:

• Equivalent Evaporation ($E$): The amount of steam (in kg) that would be generated from feedwater at 100°C to dry saturated steam at the same pressure, per kg of fuel burnt.

$$E = \frac{(h_{steam} - h_{feedwater})}{2257 \ \text{kJ/kg}}$$

where 2257 kJ/kg is the latent heat at 100°C and 1 atm.

• Boiler Types:

  • Water Tube Boiler: Water flows inside tubes, hot gases outside. (High pressure, high capacity).

  • Fire Tube Boiler: Hot gases flow inside tubes, water outside shell. (Low/medium pressure).

Dimensional Analysis & Similarity (Buckingham Pi Theorem):

For efficiency $$\displaystyle \eta = f(\rho, \mu, \omega, D, Q) $$:

1. List dimensions: $$\displaystyle [\eta]=1, [\rho]=ML^{-3}, [\mu]=ML^{-1}T^{-1}, [\omega]=T^{-1}, [D]=L, [Q]=L^3T^{-1} $$.

2. Choose repeating variables: $\rho, \omega, D$.

3. Form dimensionless Pi groups:

   • $$\displaystyle \Pi_1 = \eta $$ (itself dimensionless)

   • $$\displaystyle \Pi_2 = \frac{Q}{\omega D^3} $$ (Flow coefficient, $\phi$)

   • $$\displaystyle \Pi_3 = \frac{\rho \omega D^2}{\mu} $$ (Reynolds number, $Re$)

4. Result: $$\displaystyle \eta = \phi(\phi, Re) $$.

   [!TIP] Common Pitfall: Efficiency is already dimensionless. The theorem shows it depends on two other dimensionless groups: Flow Coefficient ($\phi$) and Reynolds Number ($Re$).

II. Fundamental Theoretical Frameworks

Moment of Momentum Principle (Angular Momentum):

The torque ($\tau$) exerted on a rotor equals the rate of change of angular momentum of the fluid passing through it.

$$\tau = \dot{m} (r V_{\theta,out} - r V_{\theta,in}) = \dot{m} (U_2 r_2 V_{\theta,2} - U_1 r_1 V_{\theta,1})$$

For axial machines ($$\displaystyle r_1 \approx r_2 = r $$): $$\displaystyle \tau = \dot{m} r (V_{\theta,2} - V_{\theta,1}) $$.

Euler's Turbine Equation (Derivation & Significance):

From moment of momentum, power $$\displaystyle P = \tau \omega = \dot{m} \omega r (V_{\theta,2} - V_{\theta,1}) $$.

Since blade speed $$\displaystyle U = \omega r $$:

$$\boxed{P = \dot{m} U (V_{\theta,1} - V_{\theta,2})}$$

• Physical Significance: The work done per unit mass ($$\displaystyle \Delta h_0 $$) is directly proportional to the change in the tangential (whirl) component of absolute velocity and the blade speed.

$$\Delta h_0 = U (V_{\theta,1} - V_{\theta,2})$$

> [!TIP] **High Frequency:** This is the **most fundamental equation** in turbomachinery. All velocity diagram analyses use it to calculate work and efficiency.

Euler's Energy Equation for Reaction Turbines:

For a Parsons (50% reaction) turbine, the enthalpy drop is equally shared between fixed and moving blades. The relative velocity magnitude is constant ($$\displaystyle V_{r1} = V_{r2} $$). Euler's equation remains $$\displaystyle U(V_{\theta,1} - V_{\theta,2}) $$, but velocity diagram relationships change.

General Expression for Power Developed:

$$P = \dot{m} \Delta h_0 = \dot{m} U (V_{\theta,1} - V_{\theta,2})$$

This is the diagram power (power transferred from fluid to rotor). Shaft power = Diagram power × Mechanical Efficiency.

III. Velocity Diagrams and Blade Geometry Analysis

Key Definitions:

• $V$: Absolute velocity.

• $U$: Blade (tangential) velocity.

• $$\displaystyle V_r $$: Relative velocity (velocity of fluid w.r.t. blade).

• $$\displaystyle V_\theta $$: Tangential/Whirl component (contributes to work).

• $$\displaystyle V_a $$: Axial component (contributes to axial thrust).

• $\alpha$: Absolute flow angle.

• $\beta$: Blade (relative) angle.

[!TIP] Vector Addition Rule: $$\displaystyle \vec{V} = \vec{U} + \vec{V_r} $$. Always draw $\vec{U}$ horizontally from origin, then add $$\displaystyle \vec{V_r} $$ tip-to-tail to get $\vec{V}$.

1. Velocity Diagram for Impulse Turbine (e.g., De Laval):

• Assumptions: No pressure change in rotor, $$\displaystyle V_{r1} = V_{r2} $$ (if frictionless), $$\displaystyle V_1 = V_2 $$.

• Construction:

  1. Draw $U$ (horizontal).

  2. From tip of $U$, draw $$\displaystyle V_{r1} $$ at blade inlet angle $$\displaystyle \beta_1 $$ (usually symmetric, $$\displaystyle \beta_1 = \alpha_2 $$).

  3. Complete triangle: $$\displaystyle \vec{V_1} = \vec{U} + \vec{V_{r1}} $$.

  4. For exit, since $$\displaystyle V_{r2} = V_{r1} $$ and $$\displaystyle \beta_2 = -\beta_1 $$ (symmetric), draw $$\displaystyle V_{r2} $$ symmetrically opposite to $$\displaystyle V_{r1} $$.

  5. $$\displaystyle \vec{V_2} = \vec{U} + \vec{V_{r2}} $$.

• Shockless (Aerodynamic) Inflow Condition: $$\displaystyle \alpha_1 = \beta_1 $$ (inlet relative velocity is aligned with blade). This minimizes incidence loss.

2. Velocity Diagram for Reaction Turbine (Parsons Type):

• Assumptions: $$\displaystyle V_{r1} = V_{r2} $$, fixed and moving blades have same shape ($$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle \beta_1 = \alpha_2 $$). Pressure drop occurs in both sets.

• Construction: Symmetric about the vertical axis through the tip of $U$. Inlet and exit triangles are mirror images.

  • $$\displaystyle \alpha_1 > \beta_1 $$, $$\displaystyle \alpha_2 < \beta_2 $$.

  • $$\displaystyle V_{\theta,1} > V_{\theta,2} $$.

3. Vector Diagram for Centrifugal Compressor:

• Inlet (Axial): $$\displaystyle V_{a1} = \text{constant} $$, $$\displaystyle \alpha_1 \approx 90^\circ $$, $$\displaystyle V_{\theta,1} \approx 0 $$.

• Rotor Exit: $$\displaystyle V_{r2} $$ at angle $$\displaystyle \beta_2 $$ (backward, radial, or forward curved). $$\displaystyle U_2 $$ is large.

$$\vec{V_2} = \vec{U_2} + \vec{V_{r2}}$$

• Diffuser: Converts kinetic energy ($$\displaystyle V_2^2/2 $$) to pressure rise. $$\displaystyle V_3 \approx V_{a3} $$ (axial), $$\displaystyle V_{\theta,3} \approx 0 $$.

4. Vector Diagram for Axial Flow Compressor:

• Multiple Stages: $U$ increases slightly along stages, $$\displaystyle V_a $$ is constant.

• Rotor & Stator: Each stage has a rotor (adds energy) and stator (turns flow axially, recovers pressure).

  • Rotor Exit: $$\displaystyle V_{r2} $$ at $$\displaystyle \beta_2 $$.

  • Stator Exit: $$\displaystyle V_3 $$ at $$\displaystyle \alpha_3 $$, designed so $$\displaystyle \alpha_3 = \beta_{next} $$ for next rotor's shockless entry.

IV. Forces, Work, and Efficiencies

Tangential Force on Blades ($$\displaystyle F_t $$):

From Euler's equation: $$\displaystyle P = \dot{m} U (V_{\theta,1} - V_{\theta,2}) = F_t \cdot U $$.

$$\boxed{F_t = \dot{m} (V_{\theta,1} - V_{\theta,2})}$$

Axial Thrust ($$\displaystyle F_a $$):

$$F_a = \dot{m} (V_{a,1} \pm V_{a,2})$$

(+ for opposite directions, - for same).

Work Done per Unit Mass & Diagram Power:

• Work Input/Output: $$\displaystyle \Delta h_0 = U(V_{\theta,1} - V_{\theta,2}) $$.

• Diagram Power (Blade Power): $$\displaystyle P_d = \dot{m} \Delta h_0 $$.

Diagram Efficiency (Blade Efficiency, $$\displaystyle \eta_b $$):

Ratio of useful work (change in fluid energy) to energy supplied.

$$\eta_b = \frac{\Delta h_0}{\text{Energy Supplied}}$$

• For Steam Turbine (Nozzle supplies energy): $$\displaystyle \eta_b = \frac{U(V_{\theta,1} - V_{\theta,2})}{V_1^2/2} $$.

• For Compressor: $$\displaystyle \eta_b = \frac{U(V_{\theta,2} - V_{\theta,1})}{V_2^2/2 - V_1^2/2} $$.

Stage Efficiency ($$\displaystyle \eta_{stage} $$):

Includes nozzle efficiency ($$\displaystyle \eta_n $$) and blade efficiency ($$\displaystyle \eta_b $$).

$$\eta_{stage} = \eta_n \times \eta_b$$

For reaction turbine, stage efficiency = blade efficiency (since pressure drop is in blades).

Polytropic Efficiency of Compressors ($$\displaystyle \eta_p $$):

For multi-stage compressor, it's the efficiency of an infinitesimal stage. It's constant for a given machine and is a better indicator of performance than overall isentropic efficiency.

$$\eta_p = \frac{\text{Actual differential work input}}{\text{Isentropic differential work input}} = \frac{dh_{actual}}{dh_{s}}$$

Relationship with isentropic efficiency $$\displaystyle \eta_{isen} $$ for $n$ stages:

$$\eta_{isen} = \frac{r_p^{(n-1)/n} - 1}{r_p^{(\gamma-1)/(\gamma \eta_p)} - 1}$$

where $$\displaystyle r_p $$ = pressure ratio.

Various Efficiencies:

Effect of Blade and Nozzle Losses on Vane Efficiency:

• Nozzle Loss: Reduces $$\displaystyle V_1 $$ from its isentropic value. $$\displaystyle V_1 = C_v \sqrt{2 \Delta h_n} $$.

• Blade Friction Loss: Reduces $$\displaystyle V_{r2} $$. $$\displaystyle V_{r2} = K V_{r1} $$, where $$\displaystyle K < 1 $$ (velocity coefficient).

• These losses directly reduce the numerator ($$\displaystyle U(V_{\theta,1} - V_{\theta,2}) $$) and/or increase the denominator ($$\displaystyle V_1^2/2 $$) in $$\displaystyle \eta_b $$, lowering vane efficiency.

V. Key Performance Parameters

Degree of Reaction ($R$):

• Definition: Ratio of static enthalpy drop in the rotor blades to the total static enthalpy drop in the stage.

$$R = \frac{\text{Enthalpy drop in rotor}}{\text{Enthalpy drop in stage}} = \frac{h_{2} - h_{3}}{h_{1} - h_{3}}$$

(For stage: inlet=1, after fixed blades=2, after moving blades=3).

• Significance: Indicates how the total pressure drop is distributed between stator and rotor.

  • $$\displaystyle R=0 $$: Pure impulse (all drop in nozzle).

  • $$\displaystyle R=0.5 $$: 50% reaction (Parsons turbine). Equal drop in fixed & moving blades. $$\displaystyle V_{r1}=V_{r2} $$, $$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle \beta_1 = \alpha_2 $$.

  • $$\displaystyle R=1 $$: Pure reaction (all drop in rotor, not practical).

• 50% Reaction Turbine: Symmetric velocity diagram. $$\displaystyle \alpha_1 = \beta_2 $$, $$\displaystyle \beta_1 = \alpha_2 $$, $$\displaystyle V_{r1} = V_{r2} $$. Most common for steam turbines.

Specific Speed ($$\displaystyle N_s $$):

• Definition: The speed at which a geometrically similar turbine would develop unit power (1 kW) under unit head (1 m).

• Derivation (for Turbine): From similarity laws:

$$P \propto N^2 D^5, \quad H \propto N^2 D^2$$

Eliminate $D$: $$\displaystyle P \propto H^{5/2} / N^2 $$ or $$\displaystyle N^2 P / H^{5/2} = \text{constant} $$.

$$\boxed{N_s = \frac{N \sqrt{P}}{H^{5/4}}}$$

($N$ in rpm, $P$ in kW, $H$ in m).

• Significance: A dimensionless index to classify turbine type and select design.

  • Low $$\displaystyle N_s $$ (~10-50): Pelton (Impulse, high head, low flow).

  • Medium $$\displaystyle N_s $$ (~50-300): Francis (Reaction, medium head/flow).

  • High $$\displaystyle N_s $$ (~300-1000): Kaplan (Reaction, low head, high flow).

• For Pumps: $$\displaystyle N_s = \frac{N \sqrt{Q}}{H^{3/4}} $$ (Q in m³/s, H in m).

Manometric Head ($$\displaystyle H_m $$):

The head against which a pump or turbine operates, accounting for all losses (friction, kinetic energy correction). For a pump, it's the total head developed including suction and delivery heads.

Optimization of Blade Efficiency in Impulse Turbines:

For symmetric impulse blades ($$\displaystyle \beta_1 = \beta_2 = \beta $$), blade efficiency is:

$$\eta_b = \frac{2 U (V_1 \cos \alpha_1 - U)}{V_1^2}$$

Maximize $$\displaystyle \eta_b $$ w.r.t. $$\displaystyle U/V_1 $$:

$$\frac{d\eta_b}{d(U/V_1)} = 0 \quad \Rightarrow \quad \boxed{\frac{U}{V_1} = \frac{\cos \alpha_1}{2}}$$

This gives maximum efficiency $$\displaystyle \eta_{b,max} = \cos^2 \alpha_1 $$.

[!TIP] Exam Problem: Given $$\displaystyle \alpha_1 $$, find optimal $U$ and max $$\displaystyle \eta_b $$.

VI. Steam Turbines: Design, Operation, and Analysis

Classification:

• Impulse: Pressure drop only in nozzles, constant blade radius.

• Reaction: Pressure drop in both nozzles and blades.

• Mixed-Flow: Combination (e.g., Curtis wheel).

Compounding:

• Velocity Compounding: Multiple rotor blades on same shaft (Curtis turbine). Used for very high velocity steam. Reduces blade speed requirement.

• Pressure Compounding: Multiple stages with separate nozzles and blades (Rateau turbine). Each stage has small pressure drop. Most common for large turbines.

Losses in Turbines:

1. Nozzle Loss: Friction, incomplete expansion.

2. Blade Friction Loss: Surface friction on blades.

3. Leaving Loss: Kinetic energy of steam ($$\displaystyle V_2^2/2 $$) not recovered.

4. Friction (Disk) Loss: Windage, bearing friction.

5. Regenerative Loss: Heat carried away by exhaust steam (in condensing turbines).

Factors Affecting Performance & Condition for Max Efficiency:

• Factors: Steam condition, blade speed ratio $$\displaystyle U/V_1 $$, nozzle angle $$\displaystyle \alpha_1 $$, blade friction, exhaust pressure.

• Max Efficiency Condition: For impulse turbine, $$\displaystyle U/V_1 = \cos \alpha_1 / 2 $$. For reaction, depends on $R$ and $$\displaystyle \alpha_1 $$.

Reheat Factor ($$\displaystyle R_f $$) & Multi-Stage Efficiency:

• Reheat Factor: Ratio of total isentropic enthalpy drop to stage enthalpy drop (based on average exhaust conditions).

$$R_f = \frac{\sum \Delta h_{s,stage}}{\Delta h_{s,total}}$$

• Improvement in Efficiency: In multi-stage turbines, steam is reheated between stages (in actual plant). This increases average temperature of heat addition, improving cycle efficiency (Rankine cycle). $$\displaystyle R_f > 1 $$ accounts for the effect of moisture and reheat on the total available enthalpy drop.

  [!TIP] Key Point: Reheat factor explains why a multi-stage turbine with same stage efficiency has higher overall efficiency than a single-stage turbine. It's due to the recovery of kinetic energy and reheating between stages.

Governing of Steam Turbines:

• Purpose: Maintain constant speed under varying load.

• Methods:

  1. Throttle Governing: Control steam flow via throttle valve (nozzle). Simple, inefficient at part-load.

  2. Nozzle Governing (Group Governing): Open/close groups of nozzles. Better for large turbines.

  3. Throttle-Nozzle Combined: For wide load range.

  4. Bypass Governing: Bypass steam to intermediate stages.

Nozzle Flow:

• Critical Pressure Ratio: For maximum mass flow (choked flow).

  • Supersaturated (Dry): $$\displaystyle (p^*/p_0)_{critical} = \left( \frac{2}{\gamma+1} \right)^{\gamma/(\gamma-1)} $$. For steam ($$\displaystyle \gamma=1.3 $$), $$\displaystyle p^*/p_0 \approx 0.546 $$.

• Mass Discharge: $$\displaystyle \dot{m} = C_d A_n \sqrt{2 \rho_0 \Delta h_0} $$.

• Effect of Friction (Coefficient of Velocity $$\displaystyle C_v $$): Reduces exit velocity. $$\displaystyle V_{actual} = C_v V_{isentropic} $$, where $$\displaystyle C_v < 1 $$.

VII. Hydraulic Turbines

Pelton Wheel (Impulse Turbine):

• Design Calculations:

  1. Power Available at Nozzle: $$\displaystyle P_{avail} = \rho g Q H $$

  2. Jet Velocity: $$\displaystyle V_j = C_v \sqrt{2gH} $$ ($$\displaystyle C_v \approx 0.98 $$).

  3. Bucket Speed: $$\displaystyle U = \phi \sqrt{2gH} $$ (Optimal $\phi \approx 0.45$ for max efficiency).

  4. Hydraulic Efficiency: $$\displaystyle \eta_h = \frac{2 U V_j (1 + \cos \beta) \cos \alpha}{V_j^2} $$. For $$\displaystyle \beta \approx 165^\circ $$, $$\displaystyle \alpha \approx 0^\circ $$: $$\displaystyle \eta_h \approx \frac{2U}{V_j} $$.

  5. Runner Diameter: $$\displaystyle D = \frac{U}{\pi N} $$.

  6. Jet Diameter: From $$\displaystyle \dot{m} = \rho A_j V_j $$, $$\displaystyle A_j = \frac{\dot{Q}}{V_j} $$, $$\displaystyle d_j = \sqrt{\frac{4A_j}{\pi}} $$.

  7. Jet Ratio ($m$): $$\displaystyle m = \frac{D}{d_j} $$ (typically 10-16).

Draft Tube:

• Function: Converts kinetic energy at turbine exit to pressure head, increases net head, provides a path for discharge.

• Principle: Acts as a diffuser. Pressure recovery: $$\displaystyle p_{exit} + \frac{1}{2}\rho V_3^2 = p_{tailrace} + \text{losses} $$.

• Types:

  1. Conical (Straight): Simple, less efficient.

  2. Elbow: Saves height, common.

  3. Simple (Cylindrical): For low specific speed.

Cavitation:

• Phenomenon: Formation and collapse of vapor bubbles in a liquid when local pressure falls below vapor pressure.

• Causes in Turbines: High suction lift, high rotational speed, poor inlet design → low $$\displaystyle NPSH_{available} $$.

• Effects: Pitting, erosion, vibration, noise, loss of performance, damage to blades.

• Prevention: Ensure $$\displaystyle NPSH_{available} > NPSH_{required} $$ (given by manufacturer). Use low specific speed turbines, pressurize suction.

Specific Speed of Hydraulic Turbines ($$\displaystyle N_s $$):

$$N_s = \frac{N \sqrt{P}}{H^{5/4}}$$

Same formula as steam turbine, but used to select type:

• $$\displaystyle N_s < 10 $$: Pelton

• $$\displaystyle 10 < N_s < 60 $$: Francis

• $$\displaystyle N_s > 60 $$: Kaplan

VIII. Pumps

Centrifugal Pump: Main Parts & Working:

• Parts: Impeller (rotor), Casing (volute or diffuser), Suction pipe, Delivery pipe, Foot valve, Strainer, Priming device.

• Working: Impeller rotates, fluid enters axially at eye ($$\displaystyle V_{a1} $$), gains kinetic energy and pressure via centrifugal force ($$\displaystyle U_2 V_{\theta,2} $$). Volute converts kinetic energy to pressure.

Positive Displacement Pumps:

• Principle: Traps a fixed volume of fluid and forces it into the discharge pipe.

• Types: Reciprocating (piston, plunger), Rotary (gear, vane, lobe).

• Characteristic: High pressure, low flow, self-priming, pulsating discharge.

Advantages of Centrifugal Pump over Reciprocating Pump:

IX. Compressors and Fans

Surging and Choking:

Comparison of Axial Flow and Centrifugal Compressors:

Surging and Efficiency of Axial Flow Compressors:

• Efficiency is high at design point but drops rapidly off-design.

• Surging limit defines the minimum stable flow. Operating too close to surge causes stall, rotating stall, and efficiency collapse.

Polytropic Efficiency of Compressors: (See Section IV)

Centrifugal Blower:

• Similar to centrifugal compressor but for low pressure rise (typically < 0.5 bar).

• Used for ventilation, combustion air supply, pneumatic conveying.

• Often has forward-curved blades for higher flow at lower pressure.

X. Power Transmitting and Fluid Power Devices

Torque Converter:

• Working Principle: Hydraulic device that transmits and multiplies torque. Uses three main elements:

  1. Pump/Impeller: Connected to engine, drives fluid.

  2. Turbine: Connected to load, driven by fluid.

  3. Stator: Stationary, redirects fluid returning from turbine to pump, providing torque multiplication.

• Torque Multiplication: Occurs at low turbine speed (vehicle start). Ratio = (Turbine Torque) / (Pump Torque) > 1.

• Slip: Difference between pump and turbine speeds. At coupling speed (1:1), stator locks (lock-up clutch in autos).

• Sketch: Show three elements in a toroidal casing, fluid flow path: Pump → Turbine → Stator → Pump.

Fluid Coupling:

• Working Principle: Simple hydraulic coupling with only pump and turbine. No stator.

• Slip ($s$): $$\displaystyle s = \frac{N_p - N_t}{N_p} = 1 - \frac{N_t}{N_p} $$, where $$\displaystyle N_p $$, $$\displaystyle N_t $$ are pump and turbine speeds.

• Torque Transmission: $$\displaystyle T_t = T_p \times (1-s) $$. Torque reduces as slip increases.

• Efficiency ($\eta$): $$\displaystyle \eta = \frac{N_t}{N_p} = 1 - s $$. Efficiency = speed ratio.

• Applications: Soft start for conveyors, crushers, protect motors from overload.

Hydraulic Intensifier:

• Function: Increases pressure of a hydraulic fluid using a large-area, low-pressure piston to drive a small-area, high-pressure piston.

• Principle: $$\displaystyle P_1 A_1 = P_2 A_2 $$ (neglecting friction). $$\displaystyle P_2 = P_1 (A_1/A_2) $$.

• Construction: Two cylinders in line, large-diameter ram (low pressure) connected to small-diameter plunger (high pressure). Used in hydraulic presses where high pressure is needed but pump capacity is limited.

Industrial Applications of Power Transmitting Devices:

• Torque Converter: Automobiles, marine propulsion, industrial drives (conveyors, crushers).

• Fluid Coupling: Belt conveyors, fans, pumps, mills (soft start, overload protection).

• Hydraulic Intensifier: Forging presses, clamping systems, test rigs requiring high pressure from a low-pressure source.

XI. Integration with CAE (Computer Aided Engineering)

• CFD (Computational Fluid Dynamics):

  • Simulate 3D flow through complex blade passages.

  • Predict velocity diagrams, pressure distribution, loss mechanisms (boundary layer, separation).

  • Analyze cavitation inception and bubble dynamics.

  • Optimize blade profile for shockless inflow and minimal losses.

• FEA (Finite Element Analysis):

  • Stress and deformation analysis of blades under centrifugal, fluid, and thermal loads.

  • Modal analysis for natural frequencies (avoid resonance).

  • Fatigue life prediction.

• Design Optimization Tools:

  • Parametric modeling of blade geometry.

  • Multi-objective optimization (efficiency vs. stress vs. cost).

  • Automated search for optimal blade angles, degree of reaction, stage stacking.

• Simulation of Transient Operations:

  • Governing: Simulate throttle/nozzle control response to load changes.

  • Surging: Model rotating stall inception and surge cycle in compressors.

  • Start-up/Shutdown: Thermal stress analysis in steam turbines.

[!TIP] CAE Context in Exams: While theory is primary, be ready to mention how you would use these tools. E.g., "To analyze a Pelton wheel's performance, CFD can model the jet-bucket interaction to optimize bucket shape and reduce splashing losses."