This paper describes the derivation of an optimum inlet Mach Number for the first stages-of an axial-flow compressor based on free vortex design. The optimum Mach Number is related to the given inlet conditions, dimensions, and tip speed and specifies the maximum amount of work that can be done on the fluid and the corresponding free vortex velocity diagrams at any radius in a stage where Mach Number effects are critical.A graphical method is described for simplifying the construction of free vortex velocity triangles for a stage at any radius of flow. This method is derived from the definition of free vortex flow.It is shown that it is possible to design several successive stages using the same rotor blade form and the same stator blade form by merely changing the spacing and root stagger angle. This may be done without compromising the desired load distribution among stages and without violating the laws of free vortex flow. LIST OF SYMBOLS a = acoustic velocity, ft. per sec. ao = acoustic velocity at stagnation conditions, ft. per sec. c m = axial component of velocity, ft. per sec. C p = profile pressure coefficient-dimensionless -(p -&)+ [(p/2) Wl »J (C p )o = profile pressure coefficient at zero Mach Numberdimensionless (C p ) m = profile pressure coefficient at Mach Number = Mdimensionless c u i -tangential component of c\, ft. per sec. c U 2 = tangential component of c 2 , ft. per sec. Acn -vector change in velocity, ft. per sec. c\ -absolute velocity entering stage (entering rotor), ft. per sec. Ci -absolute velocity leaving rotor, ft. per sec. Cz -absolute velocity leaving stage (leaving stator), ft. per sec. D -diameter of flow section, ft. Do = diameter of flow section where velocity diagram is symmetric, ft. D t -inside diameter of casing, ft. g = acceleration of gravity, 32.2 ft. per sec. 2 H = isentropic total enthalpy rise of one stage, ft.lbs. per lb. K -radial parameter-dimensionless = D/Do Mi = Mach Number of flow entering stage--dimensionless M e -critical Mach Number-dimensionless N = revolutions per minute p = static pressure, lbs. per sq.ft. pi = static pressure in front of cascade, lbs. per sq.ft. Q = flow volume entering stage, ft. 3 per sec. r = radius of flow section, ft. U = peripheral velocity of rotor blade, ft. per sec.
The over-all duty of a turbomachine with respect to fluid-friction effects is measured by the machine Reynolds number, UD/ν. Experimental data are presented for several types of turbomachines which show the variation in over-all efficiency with UD/ν when all other dimensionless parameters are held constant. The results are conclusive for the ranges of data reported, and should be useful to design, application, and operating engineers confronted with unfamiliar UD/ν values.
The effect of flow through compressor valve restrictions on the efficiency of the cylinder is well known. This paper provides a method of predetermining these pressure losses from the geometry of the valve design and the application conditions of the compressor stage. The model analysed is that of flow through multiple restrictions in series. The end result is a derived quantity, the ‘equivalent area’, which is the effective area of a single restriction equivalent to the total effect of the actual multiple restrictions. The relationships involving the effects of equivalent area and all other compressor parameters on compressor performance is presented in non-dimensional form. Tests are described which determined actual values of equivalent area for several valve designs and the correlations are presented, which confirm the ability to predict performance of an untested valve from its design and application. Reliability criteria are hypothesized based on considerations of the motion characteristics of the valve elements. Experimental observations of valve motion are described, and the desired characteristics defined from which the quantitative criteria are obtained. Correlations between criteria limits and field experience are presented.
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