Nozzles in gas turbine electrical generators accelerate the combustion gases to
ID: 1849993 • Letter: N
Question
Nozzles in gas turbine electrical generators accelerate the combustion gases to higher velocities by burning a fuel. The combustion products (M = 28 kg-kmol-1, cP = 1.009 kJ-kg-1-K-1) in a natural gas fueled electrical generator enter the nozzles with a negligible velocity at 3.61 MPa, 400 C. They leave at 2 MPa, 327 oC through an exit area of 0.1 m2.What is the velocity at the outlet of the nozzles?
What is the mass flow rate through the nozzles?
The increase in the flow work of the combustion products is:
Explanation / Answer
is this short enough? A turbine is a rotary engine that extracts energy from a fluid flow. Claude Burdin (1788-1873) coined the term from the Latin turbo, or vortex, during an 1828 engineering competition. Benoit Fourneyron (1802-1867), a student of Claude Burdin, built the first practical water turbine. The simplest turbines have one moving part, a rotor assembly, which is a shaft with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they rotate and impart energy to the rotor. Early turbine examples are windmills and water wheels. Gas, steam, and water turbines have a casing around the blades that contains and controls the working fluid. Credit for invention of the modern steam turbine is given to British Engineer Sir Charles Parsons (1854 - 1931). A device similar to a turbine but operating in reverse is a compressor or pump. The axial compressor in many gas turbine engines is a common example. Contents [hide] * 1 Theory of operation * 2 Types of turbines o 2.1 Other * 3 Uses of turbines * 4 Shrouded tidal turbines * 5 See also * 6 Notes * 7 External links [edit] Theory of operation A working fluid contains potential energy (pressure head) and kinetic energy (velocity head). The fluid may be compressible or incompressible. Several physical principles are employed by turbines to collect this energy: Impulse turbines These turbines change the direction of flow of a high velocity fluid jet. The resulting impulse spins the turbine and leaves the fluid flow with diminished kinetic energy. There is no pressure change of the fluid in the turbine rotor blades. Before reaching the turbine the fluid's pressure head is changed to velocity head by accelerating the fluid with a nozzle. Pelton wheels and de Laval turbines use this process exclusively. Impulse turbines do not require a pressure casement around the runner since the fluid jet is prepared by a nozzle prior to reaching turbine. Newton's second law describes the transfer of energy for impulse turbines. Reaction turbines These turbines develop torque by reacting to the fluid's pressure or weight. The pressure of the fluid changes as it passes through the turbine rotor blades. A pressure casement is needed to contain the working fluid as it acts on the turbine stage(s) or the turbine must be fully immersed in the fluid flow (wind turbines). The casing contains and directs the working fluid and, for water turbines, maintains the suction imparted by the draft tube. Francis turbines and most steam turbines use this concept. For compressible working fluids, multiple turbine stages may be used to harness the expanding gas efficiently. Newton's third law describes the transfer of energy for reaction turbines. Turbine designs will use both these concepts to varying degrees whenever possible. Wind turbines use an airfoil to generate lift from the moving fluid and impart it to the rotor (this is a form of reaction). Wind turbines also gain some energy from the impulse of the wind, by deflecting it at an angle. Crossflow turbines are designed as an impulse machine, with a nozzle, but in low head applications maintain some efficiency through reaction, like a traditional water wheel. Turbines with multiple stages may utilize either reaction or impulse blading at high pressure. Steam Turbines were traditionally more impulse but continue to move towards reaction designs similar to those used in Gas Turbines. At low pressure the operating fluid medium expands in volume for small reductions in pressure. Under these conditions (termed Low Pressure Turbines) blading becomes strictly a reaction type design with the base of the blade solely impulse. The reason is due to the effect of the rotation speed for each blade. As the volume increases, the blade height increases, and the base of the blade spins at a slower speed relative to the tip. This change in speed forces a designer to change from impulse at the base, to a high reaction style tip. Classical turbine design methods were developed in the mid 19th century. Vector analysis related the fluid flow with turbine shape and rotation. Graphical calculation methods were used at first. Formulas for the basic dimensions of turbine parts are well documented and a highly efficient machine can be reliably designed for any fluid flow condition. Some of the calculations are empirical or 'rule of thumb' formulae, and others are based on classical mechanics. As with most engineering calculations, simplifying assumptions were made. Velocity triangles can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity Va1. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is Vr1. The gas is turned by the rotor and exits, relative to the rotor, at velocity Vr2. However, i
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