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RESEARCH PAPERS

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):473-476. doi:10.1115/1.3446036.

The uncertainty of average measurements has been investigated, and a generalized formula for the standard deviation of spacial and time average measurements has been derived. The special cases of spacial averages and time averages have been considered resulting in recommendations concerning choice of instrumentation and the number of time independent measurements needed. A simplified procedure for estimating the number of additional measurements required to reduce the uncertainty interval to a certain level is also presented.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):477-483. doi:10.1115/1.3446037.

The phenomenon of surge in an axial flow compressor has long eluded the analytical fluid dynamist. In the recent years, a growing degree of improvement and sophistication in the design of axial flow compressors to achieve higher pressure ratios has resulted in increasingly narrow domains of stable operation. A search for improving stability margins revealed the importance of the blade tip region and casing treatments. The authors have approached the problem by both experimental and analytical methods. The results are mutually confirming. Important new inroads have been made in understanding the flow in the blade tip region, operation of casing treatments and the mechanism of the onset of surge. Some significant conclusions in the selection and design of casing treatments and their effects on the stability margin are presented and explained on the basis of experimental and theoretical results.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):484-491. doi:10.1115/1.3446038.

Power plant safety and relief value vent stacks have generally been sized according to the methods and design criteria published by Max W. Benjamin in the 1940s. Although the method might have been satisfactory at that time utilizing basic flow dynamics, it not only requires laborious calculations, but also contains some inadequate approaches which may contradict the theory of compressible fluid mechanics available today. This paper presents a complete analysis of steam conditions and its properties from power plant safety/relief valve inlet through its vent stack to the atmosphere. The analysis is based on the theory of compressible fluid flow under irreversible adiabatic process to establish a method and criterion for vent stack design. The method developed herein is applicable to both choking and nonchoking conditions at the valve exit and/or vent stack outlet, and greatly reduces complex trial-and-error solution. Furthermore, an accurate determination of fluid conditions will facilitate the calculation of reaction forces on safety/relief valve and its stack. This paper also presents the results of sensitivity analyses to verify the validity of applying perfect gas equations to steam.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):495-501. doi:10.1115/1.3446041.

Leakage tests have been run over a wide range of pressure ratios and clearances for several types of seals. The results of tests of labyrinth seals show some important differences compared to previous theory. The discharge coefficient of a single seal has been found to jump from 0.62 to 0.78 when a second seal is added downstream. This effect depends on the clearance, pitch, and the pressure ratio across the seal. This phenomena has not been considered in past theories which assumed fixed seal discharge coefficients independent of the seal position and its pressure ratio in the Labyrinth. The test results are presented in a form which is easier to use than those based on the more complicated previous theory.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):503-508. doi:10.1115/1.3446045.

This paper presents cooling tower theory and methods for analytical verification of manufacturers’ guaranteed performance curves for mechanical draft cooling towers. Both ASME PTC-23 and Cooling Tower Institute Bulletin ATP-105 are being revised and both test codes have historically used performance curves as a means of evaluating cooling tower capacity. Techniques and methods are given for calculating performance curves for both counterflow and crossflow type cooling towers. These procedures can be used during bid evaluation to assess and predict tower performance at various operating conditions other than the design point.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):509-514. doi:10.1115/1.3446046.

The effect of probe blockage on the free-stream pressure and Mach number has been studied for the two limiting cases of open free jets and closed tunnels. Cylinder probe calibrations carried out in subsonic free jets show that the blockage effect is much greater than previous analytical solutions predict. The blockage effect in free jets was found to be of approximately the same magnitude as in closed tunnels. Generalized blockage corrections are derived which indicate the importance of minimizing blockage effects both when calibrating a probe and when using it to make pressure measurements, especially in the transonic flow regime.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):516-520. doi:10.1115/1.3446049.

Six methods are given for converting to temperatures the measured values of emf generated by thermocouples. Two are based on the use of thermocouple reference tables alone. Two are based on the use of calibration data alone. And two are based on a combination of calibration data with reference table functions. It is shown that one method is preferred if graphical presentation is required, while another is clearly the best for computer conversions of thermocouple emf to temperatures.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):521-525. doi:10.1115/1.3446050.

Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures (100 atm (100 × 105 N/m2 )) where real-gas corrections are significant. Throat Reynolds number range extended up to 8 × 106 . Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 percent. Experimental coefficients for a long-radius ASME nozzle agreed to within 1/4 percent to an empirical equation representing the most probable subsonic discharge coefficient.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):527-530. doi:10.1115/1.3446054.

An evaluation of the effects caused by recirculation of hot final combustion products into unburned or partially burned fuel/air mixtures indicates that the thermal effect predominates the combustion activity. Dilution and the introduction of active radicals produce lesser results. Internal recirculation, such as produced by swirl or bluff body stabilization, differs from external recirculation by the temperature levels of the recirculant and its composition. The net effect of recirculation is to simulate a longer residence time and/or an effective higher inlet temperature. As a general result, the end products are closer to equilibrium, specifically the CO levels are lower and the NO levels higher.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):531-539. doi:10.1115/1.3446055.

A theoretical analysis of a gas turbine flowmeter in the measurement of pulsating flow is presented. The flow considered is periodic with repeatable but arbitrary wave shape. Both fluid drag and nonfluid drag on the rotor system are included in the analysis. Theoretical meter error due to pulsating flow is compared to test results from carefully controlled and instrumented laboratory tests. Results of this comparison and uses of the analysis are discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):540-547. doi:10.1115/1.3446056.

A review of the pertaining ASME literature shows that so far all ASME efforts to assign “uncalibrated” tolerances to ASME devices (orifice plates, ASME nozzles, PTC-6 throat tap nozzles) failed when tested against a newer set of calibration data. The paper shows that the cause of failure may have been the use of statistical methods and/or mathematical generalizations without physical scrutinization of the calibration data and the device under investigation. The purpose of the paper, therefore, is to help to map out the “physical road” to reliable “C” evaluation work. Another purpose of the paper is to uncover some hidden obstacles that have retarded progress in this area and would assure failure for future investigators, unless recognized and handled properly.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):549-558. doi:10.1115/1.3446059.

In recent years two general methods for flow analysis in turbomachinery have been developed, one generally called the Streamline Curvature Method, the other the Matrix Through-Flow Method. Both methods solve the same flow equations but the differences in technique introduce different operational constraints and difficulties. A comparative assessment of the relative merits of the two methods has been difficult because the various authors did not use similar cascade models to represent cascade loss and deviation, a necessary adjunct to each technique. This paper outlines the two methods, and a common cascade model for both, and compares two programs written to implement the two techniques for ease of use, computer time and storage requirements, flexibility and inherent limitations. The programs are used to compute the flow field in three axial flow compressor applications: an interconnecting duct, a transonic fan, and three stage axial compressor. The predicted performance for the above machines was fairly good, although no attempt was made to “tune” the cascade model for the specific type of machine, as the relative merits of each method were of interest. It is concluded that there is a small operational advantage to the matrix method.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):561-568. doi:10.1115/1.3446062.

Analysis and testing were performed to evaluate the potential for flow induced vibrations of the finned U-tubes of a sodium-to-air dump heat exchanger of the Fast Flux Test Facility (FFTF). The analysis showed that fluidelastic vibration of the U-bend sections, caused by a displacement-dependent mechanism, could be experienced. Consequently, model tests, with prototypic tubing and stagnant water simulating the sodium mass on the tubeside, were performed. The tests consisted of subjecting the overhanging U-bends of a bank of five U-tubes to a range of air flow velocities at room temperature. Test results showed that, for a given support and restraint condition, a critical flow velocity exists above which large vibration amplitudes are induced. Characterization of the critical flow velocity was investigated. Supplementary single tube experiments determined vortex shedding frequencies, U-tube natural frequencies, damping, and, separately, the effect of internal water flow.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):569-573. doi:10.1115/1.3446063.

The history of pipe wall tap nozzles and throat tap nozzles, as to performance characteristics, is briefly reviewed. A series of tests was conducted on pipe wall tap and throat tap nozzle installations at three independent calibration laboratories. These results are presented, analyzed, and compared with existing rational, empirical, and nominal performance characteristics in the form of discharge coefficient versus the throat Reynolds number. On the basis of these results, a recommendation is made that both pipe wall tap and throat tap nozzle installations be considered as equally accurate for use in precision fluid metering work.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):576-581. doi:10.1115/1.3446067.

The effect of inlet edge roundness on the discharge coefficient of an orifice plate is studied experimentally. Several methods for measuring edge roundness are discussed and applied. An optical method in particular is shown to provide reliable measurements of edge roundness. Flow results are summarized in terms of radius of curvature by the empirical equation ΔCD /CD = 0.85 ln (rk /d × 103 ) + 1.74.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):583-588. doi:10.1115/1.3446071.
Abstract
Topics: Fluids , Rankine cycle , Water
Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):589-593. doi:10.1115/1.3446072.

The two-phase flowmeter correlations of James, Marriott, and Murdock are evaluated using data for orifices and for venturi and nozzles previously reported. Further, a new correlation is proposed for the case where the phases may be treated as separated and this correlation is evaluated using the same data.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):596-602. doi:10.1115/1.3446075.

This paper reports the analytical results of the motions of current meters with low aspect ratio blades. Results obtained tell that calculation values of the lifting surface theory coincide with experimental results at apparent runaway speed of all runners. If the results of the lifting line theory are compensated, calculation results of each high pitch model nearly become equal to each experimental value. Moreover, constant pitch meters show better characters than variable pitch meters, concerning velocity fields around runner blades. From the foregoing results, the fundamental equations of the current meter runner designs are brought out.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):603-609. doi:10.1115/1.3446076.

Application of the potential theory to the full equations of two-dimensional compressible flow has yielded a method of calculation valid for isolated airfoils as well as for cascades situated on an arbitrary surface of revolution. Various computed subcritical and supercritical flows are presented and compared with exact solutions. Close relation between convergence interval and the existence of discontinuities in the solution was established, which makes it possible to recognize and develop transonic flow patterns having no or only weak shocks.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):610-618. doi:10.1115/1.3446077.

The pressure, temperature, and fuel-to-air ratio of a gas turbine combustor vary with ambient conditions, machine speed, and load. Only a few of these parameters are independent. An analysis has been developed which predicts the combustor operating parameters. The analysis includes low heating value fuel combustion, water injection, and three modes of steam injection. The analysis is used to predict the combustor operation for a simple-cycle gas turbine, but it is not restricted to this case. In addition, a simplified analysis is deduced and shown to be surprisingly accurate. Special solutions are presented which permit direct calculation of the firing temperatures, fuel heating value, or air extraction required to achieve a specified compressor pressure ratio. Finally, the analysis is compared with experimental results.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):619-627. doi:10.1115/1.3446078.

Many nuclear stations do not incorporate deaerators in their feedwater heating systems. To attain high turbine cycle performance without a deaerator, a drain pumping system is widely used for returning hot drains from the high-pressure heaters to the feedwater system. With a greatly increased feedwater flow for nuclear units, together with the drain pumping system being moved to a higher extraction point, the heater–drain tank system will be subject to a rapid pressure decay under turbine load rejections. In addition, the drain pump suction flow reduces considerably, thereby increasing the suction pipe resident time. It is these critical changes in operating conditions that should receive careful consideration in drain pumping system design. This paper presents an analytical approach for determining drain tank pressure decay, drain pump suction pressure decay, and transient behavior of the heater–drain tank system based on analysis of closed feedwater heater performance and the varying feedwater temperature entering the heater under turbine load rejections. The emphasis is placed on adequate and optimum design of a drain pumping system, including a discussion of some design criteria to be followed, as well as sizing of the pressure equalizer between heater and drain tank. All mathematical equations required for determining the design parameters are derived. Finally, some example calculations are given to illustrate the application of the developed analytical approach to system design.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):628-632. doi:10.1115/1.3446079.

Rigid plastic plate theory is used to determine the limit load for a pipe-supported flat plate loaded by uniform pressure. The solution is applied to design of condenser hotwell floors under hydrotest loading. A comparison is made with a formula for design of similar configurations suggested in Section VIII, Division 1 of the ASME Pressure Vessel Code, and in texts on elastic plate theory.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):633-639. doi:10.1115/1.3446080.

A procedure is presented by which the widely used MEL 21 program can be adapted to power plant applications. This is accomplished by writing a preliminary computer program which will require as input only those quantities which are pertinent to the description of piping sytems as encountered in power plants. The function of this preliminary program is to take the required input and generate the information required by the MEL 21 program but not pertinent to the power plant applications. Therefore this will allow the difficult to use but very general MEL 21 piping of flexibility program to be utilized by persons who have no computer background.

Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):640-644. doi:10.1115/1.3446081.
Abstract
Topics: Gas turbines , Storage
Commentary by Dr. Valentin Fuster
J. Eng. Power. 1975;97(4):645-654. doi:10.1115/1.3446082.

A theory is presented for predicting the transient behavior of bubbles in the downcomer and riser loop. It is found that a sudden drop in boiler pressure could seriously reduce the circulation velocity and this is attributed to steam formation in the downcomer tube. The reduction of the circulation velocity tends to prolong existence of individual bubbles in the water phase and therefore increases the water level swell. Transient behavior of circulation velocity in the riser, and water level responses in the steam drum were measured in a two-tube experimental boiler following a step increase in steam control-valve opening for various boiler pressures.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster

ERRATA

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