ME328 (Spring 08) - Take-home Quiz 2 - Cogeneration ---- Name____________________

In an effort to decentralise the power grid and utilise the waste heat which accompanies power generation, the Athenai Power Consulting Corp. has proposed a Cogeneration system for O'Bleness Hospital to provide both 500kW electric power and hot water at 70°C. The basic approach to this unique design is shown in the following schematic diagram:

A unique aspect of the power plant is that the turbine output is at 100kPa close to 100°C. This high pressure output both eliminates the need for an open feedwater-heater/deaerator and the condenser will be able to directly heat the water to the required 70°C. The induced draft cooling tower shown will allow a minimal effect on the environment. As a young engineer at Athenai your purpose is to complete the basic design and evaluate and discuss its effectiveness.

Notice that a number of stations are not completely defined, in particular the high pressure and temperature at the inlet to the turbine. Athenai would like this to be a simple low pressure system without reheat or regeneration, using an available turbine that has an adiabatic efficiency of close to 90%, and not allowing the quality of the steam at the turbine outlet to go below 90%. You should use both the P-h (pressure-enthalpy) and h-s (enthalpy entropy) diagrams provided to neatly sketch and evaluate various options in order to suitably specify the system. Once this is done then use the Steam Tables to determine the following:

• a) Neatly sketch the final complete cycle on the P-h diagram provided, indicating clearly stations (1), (2), (3), and (4) on the diagram.
• b) Determine the mass flow rate of the steam through the cycle required in order to provide the required turbine output power of 500kW.
• c) Determine the overall thermal efficiency h_th of this power plant. (Recall that thermal efficiency is defined as the net work done divided by the total heat supplied externally to the boiler.
• d) Determine the cooling power in the condenser required to condense the steam exiting the turbine at station (2) and subcool the condensed steam to 60°C.
• e) Assuming that the condenser coolant water is heated from 25°C to 70°C, determine the required mass flow rate of the condenser coolant water.
• f) The induced draft cooling tower will need to cool the coolant by evaporation from 70°C at station (7) to 25°C in the water reservoir. With the aid of the Psychrometric Chart provided determine the mass flow rate of the dry air through stations (8) - (9), as well as the mass flow rate of the makeup water. Determine also the volumetric flow rate of the inlet air at station (8), Clearly mark and label the relevant values on the Psychrometric Chart, including the values of enthalpy (h), relative humdity (f) and specific humidity (w) of stations (8) and (9) respectively.
• g) Discuss the proposed system with respect to its environmental impact and feasibility.

Justify all values used and derive all equations used starting from the basic energy equation for a flow system, mass flow rate equations similar to those developed in the Cooling Tower web page, the basic definition of thermal efficiency h_th, and the definition of adiabatic efficiency h_T of a Turbine. You may either determine the values of enthalpy and specific volume in the Cooling Tower directly from the Psychrometric Chart or from the equations developed in the Mixtures and Solutions web page.

________________________________________________________________________________________
Declaration of Honesty - I hereby declare that this take-home quiz is my own work, and that I did not collaborate with or receive help from anyone else while doing it.

(Signed)___________________________ (Date)______________________