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hw_1 - J Buongiorno Spring 2007 22.313J 2.59J 10.536J...

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J. Buongiorno / Spring 2007 22.313J, 2.59J, 10.536J THERMAL-HYDRAULICS IN POWER TECHNOLOGY Homework Set 1 Question 1 – Basic Parameters in Two-phase Flow 1.1 Prove that the volumetric flow fraction, β , is related to the flow quality, x, by the following expression: x x 1 1 1 v ρ ρ + = β l 1.2 Prove that for homogeneous flow (i.e., v = v v ), the following equations are valid: a) α = β b) m m ρ = ρ + c) m m h h = +
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J. Buongiorno / Spring 2007 Question 2 – Conservation Equations for Two-phase Flow The boiler of a coal-fired power plant consists of a tube bundle surrounding the combustion chamber. The tubes are vertical (10-m length) and round (2-cm inner diameter). The operating conditions for the boiler are as follows: Pressure: 10 MPa (corresponding to a saturation temperature of 311 ° C) Water inlet temperature: 300 ° C Water mass flow rate (per tube): 0.57 kg/s Wall heat flux: 300 kW/m 2 (axially and circumferentially constant) 2.1 Write the steady-state mixture mass, momentum and energy conservation equations for a boiler tube.
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