Question

Design a steam power cycle that can achieve a cycle thermal efficiency of at least 40 percent under the conditions that all turbines have isentropic efficiencies of 85 percent and all pumps have isentropic efficiencies of 60 percent. Prepare an engineering report describing your design. Your design report must include, but is not limited to, the following: (a) Discussion of various cycles attempted to meet the goal as well as the positive and negative aspects of your design. (b) System figures and \(T\) -s diagrams with labeled states and temperature, pressure, enthalpy, and entropy information for your design. \((c)\) Sample calculations

Short answer

Question: Describe the steam power cycle design that meets the required criteria of having a cycle thermal efficiency of at least 40% while considering the isentropic efficiencies of turbines (85%) and pumps (60%).

Step-by-step solution

Identify Possible Steam Power Cycles

Some common steam power cycles are: 1. The Rankine cycle 2. The reheat Rankine cycle 3. The regenerative Rankine cycle Each cycle can be analyzed individually to determine its efficiency and viability.

Analyze and Compare Different Cycles

Analyze the three cycles mentioned above and compare their positive and negative aspects. Determine which cycle can meet the required thermal efficiency while considering turbine and pump efficiencies.

Develop the Chosen Cycle Design

Once the cycle that can meet the criteria is chosen, develop the design by specifying the following: 1. Operating pressures and temperatures at all states of the cycle 2. Calculate enthalpy and entropy at all states of the cycle

Create System Figures and T-s Diagrams

Draw system figures for the chosen cycle showing all components, such as turbines, pumps, and heat exchangers. Also create the T-s diagram for the cycle with labeled states and pressure, temperature, enthalpy, and entropy information.

Perform Sample Calculations

Perform sample calculations to show that the chosen cycle meets the required criteria, i.e., the cycle thermal efficiency of at least 40%. Include calculations related to: 1. Isentropic efficiencies of turbines and pumps 2. Actual enthalpy changes in turbines and pumps 3. Heat added and removed in the cycle 4. Total work output/input and the overall cycle thermal efficiency

Engineering Report Preparation

Prepare an engineering report including the following: (a) Discussion of various cycles attempted to meet the goal, as well as their positive and negative aspects. (b) System figures and T-s diagrams, with labeled states and pressure, temperature, enthalpy, and entropy information for the chosen-design. (c) Sample calculations to prove that the chosen design meets the required cycle thermal efficiency of at least 40%, considering the given isentropic efficiencies of turbines (85%) and pumps (60%). Once the analysis is complete, and the engineering report is prepared, the student should have a clear understanding of the steam power cycle design process and the selected cycle that meets the targeted thermal efficiency of at least 40%.

Key concepts

Rankine Cycle Efficiency

The Rankine cycle is a common steam power cycle widely used in power plants to convert heat energy into mechanical work. The efficiency of a Rankine cycle is crucial because it indicates how effectively the cycle converts heat into work.

To target a cycle thermal efficiency of at least 40%, it's vital to maximize the temperature at which heat is added and minimize the temperature at which it's rejected. However, the efficiency also depends on the limitations imposed by turbine and pump isentropic efficiencies. For instance, with turbine isentropic efficiencies of 85% and pump isentropic efficiencies of 60%, the cycle efficiency will be less than the isentropic cycle efficiency. This means that actual devices don't perform as ideally as the isentropic model suggests.

In designing an efficient Rankine cycle, one must carefully select the operating pressures, temperatures, and configurations that optimize efficiency while considering these real-world device efficiencies.

Isentropic Efficiency

Isentropic efficiency is a measure of the performance of a turbine or pump relative to its ideal, isentropic performance. Isentropic processes are theoretically perfect, meaning no energy is lost due to friction or turbulence within the device. However, in the real world, machines are not 100% efficient, and isentropic efficiency provides a realistic measure of how a device is likely to perform.

The isentropic efficiencies of 85% for turbines and 60% for pumps, given in the exercise, suggest that we must account for some loss in efficiency due to non-ideal behavior. During the cycle design, actual enthalpy changes based on these efficiencies must be calculated to assess the real performance of the system. Higher isentropic efficiencies would yield a more efficient power cycle, so choosing components with the best possible efficiencies is a key part of the design process.

Thermodynamic Cycle Analysis

Thermodynamic cycle analysis involves studying the changes in energy that occur during the heat engine cycle. This scientific assessment helps engineers design and optimize power plants and other systems where thermal energy is converted into work. Analyzing thermodynamic cycles such as the Rankine cycle reveals factors like operating pressures and temperatures, work done in each process, and the overall energy conversion efficiency.

In the case of the exercise, comparing cycles like the simple Rankine, reheat Rankine, and regenerative Rankine cycles against the desired thermal efficiency is paramount. These cycles have differing levels of complexity and efficiency, influenced by their distinct configurations and the isentropic efficiencies of the turbines and pumps used. Through analysis, engineers can determine the most appropriate cycle to achieve the 40% thermal efficiency target by balancing the positive and negative aspects of each design.

T-s Diagram

A Temperature-Entropy (T-s) diagram is an essential thermodynamic chart used to visualize changes in temperature and entropy throughout a thermodynamic cycle. It's incredibly helpful when designing and understanding steam power cycles like the Rankine cycle.

The diagram graphically represents the various processes of the cycle, such as isentropic expansion in the turbine and isothermal heat addition from the boiler. This visual tool assists in identifying each state's properties, like pressure and specific volume, to evaluate the cycle’s performance. For the exercise, drawing a T-s diagram with labeled states, pressure, and temperature, along with enthalpy and entropy data, allows clear understanding of where the cycle can be optimized for greater efficiency.

Enthalpy and Entropy Calculations

Enthalpy and entropy are fundamental thermodynamic properties that quantify energy in a system and the irreversibility of processes, respectively. Precise calculations of these properties are essential for the analysis and design of any thermodynamic cycle.

In a steam power cycle, the enthalpy of the working fluid changes as it absorbs heat, expands through the turbine, is compressed in the pump, and rejects heat. Entropy measures how spread-out or dispersed energy is within a system during these processes. By calculating the changes in enthalpy and entropy across each component of the cycle, engineers can determine the heat added, the work done, and the overall efficiency of the cycle, as required in the exercise. These calculations also reveal areas where efficiency can be improved in alignment with the isentropic efficiencies provided for turbines and pumps.