For a machine handling a perfect gas a different set of functional relationships is often more useful. The latter procedure is preferred here as it provides a useful exercise. As a concrete example consider an adiabatic compressor handling a perfect gas. The isentropic stagnation enthalpy rise can now be written C p T 02s - T 01 for the perfect gas. This compression process is illustrated in Figure 1. The equiva- lent process for a turbine is shown in Figure 1.
If, in addition, the machine operates at high Reynolds numbers or over a small speed range ,Re can also be dropped. Under these conditions eqn. The ideal adiabatic change in stagnation conditions across a turbomachine. Figures 1. Notice that for both machines subscript 1 is used to denote conditions as inlet. How the position of the operating line is selected is a matter of judgement for the designer of a gas turbine and is contingent upon factors such as the maximum rate of acceleration of the machine.
The term stall margin is often used to describe the relative position of the operating line and the surge line. Overall characteristic of a compressor. The choked regions of both the com- pressor and turbine characteristics may be recognised by the vertical portions of the constant speed lines.
No further increase in m. Overall characteristic of a turbine. Aphysical situation considered by Greitzer is the axial compressor rotor as depicted in Figure 1. References Cumpsty, N. Compressor Aerodynamics. Dean, R. Basic Eng. Douglas, J. Fluid Mechanics.
Fluid Mechanics and Thermodynamics of Turbomachinery - S. Larry Dixon - Google книги
Greitzer, E. Japikse, ed. International Standards Organisation, Paris. Pearsall, I.
The design and performance of supercavitating pumps. Acoustic detection of cavitation. Symposium on Vibrations in Hydraulic Pumps and Turbines. Comparison of cavitation noise with erosion. Cavitation Forum, 6—7, Am. Quantities, Units and Symbols Reynolds, O. Manchester Lit. Ryley, D. Hydrostatic stress in water. Shames, I. Mechanics of Fluids. Shepherd, D. Principles of Turbomachinery. Taylor, E. Dimensional Analysis for Engineers. The International System of Units HMSO, London. Wislicenus, G. Fluid Mechanics of Turbomachinery. Young, F. Problems 1. Determine the axial air velocity of the model so that dynamical similarity with the full-scale fan is preserved.
The effects of Reynolds number change may be neglected.
The viscosity of the air is independent of pressure and the temperature is maintained constant. At what pressure must the model be tested? A water turbine is to be designed to produce 27 MWwhen running at A model turbine with an output of Calculate the model speed and scale ratio. It is estimated that the force on the thrust bearing of the full-size machine will be 7.
For what thrust must the model bearing be designed? Derive the non-dimensional groups that are normally used in the testing of gas turbines and compressors. Acompressor has been designed for normal atmospheric conditions In order to economise on the power required it is being tested with a throttle in the entry duct to 22 Fluid Mechanics, Thermodynamics of Turbomachinery reduce the entry pressure.
At what speed should the compressor be run? Referring to Figure 2. The units of heat and work in eqn. During a change of state from 1 to 2, there is a change in the property internal energy, 2. Figure 2. Flow across an element of area.
In the general case positive heat transfer takes place at the rate Q. Apart from hydraulic machines, the contribution of the last term in eqn. For work producing machines turbines W. In the study of turbomachines many appli- cations of the momentum equation can be found, e.
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- Fluid Mechanics, Thermodynamics of Turbomachinery.
- Fluid Mechanics, Thermodynamics of Turbomachinery.
- Fluid Mechanics and Thermodynamics of Turbomachinery, 5e?
Control volume showing sign convention for heat and work transfers. Considering a system of mass m, the sum of all the body and surface forces acting on m along some arbitrary direction x is equal to the time rate of change of the total x- momentum of the system, i. By shear forces being absent we mean there is neither fric- tion nor shaft work.
However, it is not necessary that heat transfer should also be absent. Integrating this equation in the stream direction we obtain 2. Thus eqn. This form is of central impor- tance in the analysis of the energy transfer process in turbomachines. For a control volume the law of moment of momentum can be obtained. Thus, combining eqns. After some rearranging of eqn. Control volume for a generalised turbomachine. Thus, the rothalpy can be written generally as 2. The second law of thermodynamics—entropy The second law of thermodynamics, developed rigorously in many modern thermo- dynamic textbooks, e.
An important and useful corollary of the second law of thermodynamics, known as the Inequality of Clausius, states that for a system passing through a cycle involving heat exchanges, 2. If the process is adiabatic, dQ. In this book only those considered to be important and useful are included.www.hiphopenation.com/mu-plugins/wiki/white-guy-dating-a.php
Fluid mechanics, thermodynamics of turbomachinery
Thus, Mechanical energy losses occur between the turbine rotor and the output shaft cou- pling as a result of the work done against friction at the bearings, glands, etc. A detailed consideration of the mechanical losses in turbomachines is beyond the scope of this book and is not pursued further. Line 1—2 represents the actual expansion and line 1—2s the ideal or. Fluid Mechanics and Thermodynamics of Turbomachinery, 5e.
Thumbnails Document Outline Attachments. SI static enthaipy rise in the rotor divided by the static enthalpy rise in the stage, i. From the velocity diagram the maximum relative velocity is wI and the corresponding relative Mach. IV gives. Using the equation iii , can be determined as follows,. Substituting values into eqn. Each stage of an axialfloloY compressor is of 0. The mean now coefficient is constant for all stages at 0.