8.5 Water Conveyance Structures

8.5 Water Conveyance Structures

Introduction to Water Conveyance Structures

Water conveyance structures form the critical link between the headworks and the powerhouse in a hydropower scheme. This system transports water, often over long distances and through challenging terrain, with the objectives of minimizing head losses and ensuring hydraulic stability. The design must account for steady-state flow efficiency, structural integrity under various loads (water pressure, rock pressure, earthquakes), and control of transient pressure surges. This section covers the key components: tunnels, forebays, surge tanks, penstocks, and the phenomenon of water hammer.

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1. Hydraulic Tunnels: Cross-sections, Hydraulic Design

Hydraulic tunnels convey water from the intake (or settling basin) to the forebay or directly to the penstock. They are classified as headrace tunnels (free-flow or low-pressure) and tailrace tunnels (returning water to the river).

1.1 Tunnel Cross-sections

The choice of shape is dictated by geology, construction method, and hydraulic efficiency.

1. Horseshoe Section:

   • Shape: Curved roof and vertical sidewalls with a curved invert.

   • Advantages: Good structural stability in rock, especially in vertical stress fields. Easy to excavate using drill-and-blast. Provides a flat floor for construction traffic.

   • Disadvantages: Slightly less hydraulically efficient than circular.

   • Application: Most common for headrace tunnels in rock.

2. Circular Section:

   • Shape: Perfect circle.

   • Advantages: Most hydraulically efficient (largest area for a given perimeter, minimizing friction loss). Uniformly resistant to external (rock/water) pressure. Ideal for Tunnel Boring Machine (TBM) excavation.

   • Disadvantages: Requires full support (lining) in weak rock. Less stable for an unsupported span during excavation by drill-and-blast.

   • Application: Pressurized tunnels, soft ground tunnels, TBM-driven tunnels.

3. D-Shaped (or Modified Horseshoe):

   • Shape: Flat invert with a curved roof and walls.

   • Advantages: Provides a flat floor for drainage and construction. Good for moderate rock conditions.

4. Rectangular Section:

   • Application: Typically used for cut-and-cover sections or in very competent rock.

1.2 Hydraulic Design: Velocity and Sizing

The primary goal is to minimize head loss while avoiding sediment deposition and keeping construction cost in check.

1. Design Velocity Criteria:

   • Lower Limit: Must be sufficient to prevent sedimentation of fine particles. Typically > 0.6 m/s.

   • Upper Limit: Controlled by economics and abrasion. High velocity increases head loss (energy loss). For unlined tunnels in rock, velocity is often limited to 2.5 - 3.5 m/s to avoid erosion of joints. For lined tunnels, velocities of 3 - 5 m/s are common.

   • Optimum Economic Velocity: The velocity that minimizes the sum of capitalized energy loss cost and tunnel construction cost. Often lies in the 2.5 - 4.0 m/s range.

2. Sizing (Determining Diameter):

   • Based on the design discharge ($Q$) and selected velocity ($v$). $A = \frac{Q}{v}$ Where $A$ is the required cross-sectional area.

   • The corresponding diameter (for circular) or dimensions (for horseshoe) are then determined.

   • Head Loss Check: Calculate friction head loss using the Manning's or Darcy-Weisbach equation to ensure it is within acceptable limits for the project economics.

     • Manning's Equation: $v = \frac{1}{n} R_h^{2/3} S^{1/2}$

     • Darcy-Weisbach Equation: $h_f = f \frac{L}{D} \frac{v^2}{2g}$ Where $n$ is Manning's roughness, $R_h$ is hydraulic radius, $S$ is slope, $f$ is friction factor.

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2. Tunnel Lining

Lining is applied to the tunnel perimeter to serve one or more functions.

2.1 Purposes of Lining

1. Structural Support: To stabilize the tunnel against rock loads, especially in weak or fractured rock.

2. Hydraulic Smoothness: To reduce roughness ($n$ or $f$) and consequent head losses.

3. Waterproofing: To prevent water leakage from the tunnel (loss of water) or into the tunnel (which can cause instability in the surrounding rock).

4. Protection: To prevent erosion of rock or deterioration due to water contact.

2.2 Types of Lining

1. Unlined Tunnel:

   • Used in excellent quality, massive rock with no stability or seepage issues.

   • Head loss is higher due to rock roughness.

2. Shotcrete (Gunite) with Rock Bolts:

   • Shotcrete: Sprayed concrete applied to the rock surface.

   • Rock Bolts: Steel bars grouted into drill holes to reinforce the rock mass.

   • Provides structural support and some smoothing.

3. Concrete Lining (Cast-in-place):

   • The most common permanent lining for hydraulic tunnels.

   • Reinforced Concrete: Used where high internal water pressure or significant external rock loads are expected.

   • Plain Concrete: Used for smoothing and moderate support.

   • Installed using formwork after excavation.

4. Steel Liner (Penstock in Tunnel):

   • A steel pipe placed within a larger excavated tunnel and grouted into place.

   • Used for very high-pressure sections (pressure shafts/tunnels) where concrete cannot resist the hoop stresses.

2.3 Design Considerations for Concrete Lining

• Internal Water Pressure: The lining must be designed for the maximum static and transient pressure.

• External Loads: Rock pressure, grouting pressure, groundwater pressure.

• Construction Sequence: Lining is often placed in segments with contraction joints.

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3. Design of Forebay and Surge Tanks

3.1 Forebay

1. Function: A small regulating pond located at the end of the headrace tunnel and before the penstock.

   • Provides a constant water level at the penstock inlet.

   • Allows sediment settling (secondary settling after the main basin).

   • Provides a location for the spillway to dump excess water.

   • Houses the penstock intake with trash racks.

2. Design Features:

   • Size: Volume should provide a few minutes of flow at plant discharge to allow for operational adjustments.

   • Spillway: An overflow weir to safely pass flows when the turbine load is suddenly reduced.

   • Penstock Intake: Bell-mouthed entrance with trash racks to protect the penstock.

3.2 Surge Tanks

1. Purpose: To protect the headrace tunnel/pressure shaft from water hammer overpressures caused by sudden changes in turbine load (load rejection or acceptance).

   • It does this by providing a "free water surface" close to the powerhouse, which absorbs and reflects pressure waves.

2. Location: Situated between the headrace tunnel (which has low velocity) and the penstock/pressure shaft (which has high velocity), as close to the powerhouse as topography allows.

3. Types:

   • Simple Surge Tank: A vertical shaft of constant cross-section. Most basic type.

   • Restricted Orifice Surge Tank: The connection to the headrace has a constricted orifice. This dampens the surge oscillations more quickly but creates higher initial pressure spikes.

   • Differential Surge Tank: Has an internal riser connected to the penstock and an outer tank connected to the headrace. Combines benefits of simple and restricted orifice types. Most common for large plants.

   • Gallery-Type Surge Chamber: A horizontal tunnel/chamber used in low-head plants or where vertical excavation is difficult.

4. Key Design Parameters:

   • Thoma's Criterion for Stability: Ensures surge oscillations dampen out after a disturbance. $A_{surge} > \frac{A_{tunnel} L}{2g \rho H_0}$ (Simplified form) where $A_{surge}$ is tank area, $A_{tunnel}$ is tunnel area, $L$ is tunnel length, $H_0$ is static head.

   • Maximum Up-surge and Down-surge: Calculated using mass oscillation equations (e.g., rigid water column theory or method of characteristics) to ensure the tank does not overflow or empty air into the penstock.

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4. Design of Penstocks and Pressure Shafts

These are pressurized conduits that deliver water under high head to the turbines.

4.1 Penstocks

1. Definition: Exposed or buried steel pipes running from the forebay/surge tank to the powerhouse.

2. Design Loads:

   • Internal Pressure: Static head + water hammer pressure.

   • External Pressure: For buried pipes, soil/rock load and groundwater pressure.

   • Weight of Water and Pipe.

   • Temperature Stresses: Expansion/contraction.

   • Earthquake Loads.

3. Wall Thickness Design: Governed by hoop stress due to internal pressure. $\sigma_h = \frac{p D}{2t}$ Where $p$ is internal pressure, $D$ is internal diameter, $t$ is wall thickness.

   • Using the allowable stress ($\sigma_{allow}$), the required thickness is: $t = \frac{p D}{2 \sigma_{allow} \phi}$ where $\phi$ is joint efficiency factor.

   • Additional thickness is added for corrosion allowance.

4.2 Pressure Shafts

1. Definition: Vertical or steeply inclined tunnels that serve the same function as penstocks but are excavated in rock.

2. Types of Linings:

   • Unlined: In excellent, massive rock with high in-situ stress (to resist bursting).

   • Concrete Lined: For structural support and hydraulic smoothness. Concrete alone cannot resist very high pressures.

   • Steel Lined: A steel cylinder placed and grouted into a concreted tunnel. Used for high-pressure sections where rock cannot carry the load. Design is similar to a penstock.

3. Economic Choice: The decision between a surface penstock and a pressure shaft is based on topography, geology, cost, and environmental impact.

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5. Hydraulic Transients: Water Hammer

5.1 Phenomenon

• Definition: The rapid change in pressure (overpressure or underpressure) in a closed conduit caused by a sudden change in flow velocity (e.g., valve closure/turbine shutdown = load rejection; valve opening/turbine start-up = load acceptance).

• Cause: The kinetic energy of the moving water column is converted into pressure energy. The pressure wave travels at the speed of sound in water (acoustic wave speed, $a$), reflecting back and forth.

5.2 Key Parameters

1. Wave Speed ($a$): $a = \frac{\sqrt{K/\rho}}{\sqrt{1 + \frac{K D}{E t} c}}$ Where $K$ is bulk modulus of water, $E$ is Young's modulus of pipe material, $c$ is a factor for pipe support condition.

   • Typical values: 1000 - 1400 m/s for steel pens stocks.

2. Critical Time ($T_c$): $T_c = \frac{2L}{a}$ The time for a pressure wave to travel to the point of reflection (reservoir, surge tank) and back.

   • Rapid Closure ($T_{close} < T_c$): Produces maximum water hammer pressure (Joukowsky's equation).

   • Slow Closure ($T_{close} > T_c$): Produces lower, attenuated pressure rise.

5.3 Joukowsky's Equation (for Instantaneous Valve Closure)

• Gives the maximum theoretical pressure rise ($\Delta H$) due to an instantaneous change in velocity ($\Delta v$). $\Delta H = \frac{a \Delta v}{g}$

  • The corresponding pressure rise is $\Delta p = \rho g \Delta H = \rho a \Delta v$.

• This highlights that higher wave speed ($a$) and larger velocity change ($\Delta v$) lead to more severe water hammer.

5.4 Analysis and Mitigation

1. Analysis Method: The Method of Characteristics (MOC) is the standard numerical method for simulating transient flows in complex systems.

2. Mitigation Measures:

   • Surge Tanks: As described, are the primary protection for headrace systems.

   • Pressure Relief Valves (Surge Anticipator Valves): Installed on the penstock near the turbine. They open rapidly on load rejection to divert flow and limit pressure rise.

   • Slow-Closing Valves/Turbine Governors: Increasing the closure/opening time ($T_c$) to make it "slow" relative to $T_c$.

   • Flywheels: Increase the rotational inertia of the turbine-generator unit, slowing down the rate of speed increase during load rejection and giving the governor more time to act.

   • Air/Vacuum Valves: To prevent collapse under negative pressure.

Conclusion: The water conveyance system is the arterial network of a hydropower project. Its design requires a delicate balance between hydraulic efficiency (minimizing head loss) and structural safety (withstanding static and transient pressures). The integration of tunnels, surge tanks, and penstocks, coupled with a thorough understanding and control of water hammer phenomena, is essential for creating a reliable, safe, and economically optimized conduit that delivers energy potential from the source to the turbine.