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The open feedwater heater is a component in power plants that plays a quintessential role in enhancing the efficiency of the steam cycle. When steam from a turbine is used to preheat the boiler feedwater, it's incorporated directly into the water, thereby mixing the two. This type of feedwater heater operates at the same pressure at which steam is extracted from the turbine, and as a result, the feedwater exits the heater at the saturation temperature associated with that pressure.

The primary advantage of open feedwater heaters lies in their simplicity and lower initial costs. However, this type of system can generate losses due to increased entropy when the steam and feedwater mix, which is often a trade-offs between efficiency and economy.

In contrast to its open counterpart, the closed feedwater heater enhances the thermal efficiency of power plants while minimizing direct contact between the steam and the feedwater. It incorporates a heat-exchanging surface that allows for the transfer of heat from the steam to the feedwater without mixing the two fluids. Consequently, closed feedwater heaters enable operation at temperatures that can exceed the saturation temperature.

Closed feedwater heaters, due to their heat-exchanging surface, often lead to a more efficient heat transfer process. The efficiency gains come with increased complexity and higher costs associated with the additional equipment required, such as heat exchangers and supplementary feed pumps. Moreover, the design of the heat-exchanging surface requires meticulous planning to ensure optimal heat transfer and longevity of the equipment.

The heat-exchanging surface within a feedwater heater is fundamental to the transfer of thermal energy between steam and the feedwater in closed systems. This surface is typically made up of tubes or plates designed to maximize contact with the steam and water, therefore, enhancing the heat transfer efficiency.

The design of the heat-exchanging surfaces, like the choice between tube and plate, is critical and depends on factors such as the desired thermal performance, the properties of the fluids being used, and material considerations for durability and maintenance. It is through the careful design of these surfaces that closed feedwater heaters achieve their efficiency, allowing for higher temperature operation without the direct mixing that characterizes open feedwater heaters.

Turbine extraction refers to the process of removing a portion of the steam from a turbine at some intermediate point in its expansion process. This extracted steam is then used for heating the feedwater in either type of feedwater heater—open or closed. The act of extraction plays a significant role in improving the thermodynamic efficiency of the power plant by reducing the amount of steam that must be condensed in the condenser.

This process utilizes the energy of the steam that would otherwise be partially wasted, optimizing the energy output of the plant. Turbine extraction is a classic example of how energy can be recycled within a system to maximize efficiency, demonstrating a key principle of thermodynamics and energy conservation. Equally important is managing the pressure and temperature conditions of the extraction to ensure that the integration with the feedwater heater is seamless and effective.