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At least 1,081 records · Page 60
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NASA NTRS2004

Effect of Random Thermal Spikes on Stirling Convertor Heater Head Reliability

Onboard radioisotope power systems being developed to support future NASA exploration missions require reliable design lifetimes of up to 14 yr and beyond. The structurally critical heater head of the high-efficiency developmental Stirling power convertor has undergone extensive computational analysis of operating temperatures (up to 650 C), stresses, and creep resistance of the thin-walled Inconel 718 bill of material. Additionally, assessment of the effect of uncertainties in the creep behavior of the thin-walled heater head, the variation in the manufactured thickness, variation in control temperature, and variation in pressure on the durability and reliability were performed. However, it is possible for the heater head to experience rare incidences of random temperature spikes (excursions) of short duration. These incidences could occur randomly with random magnitude and duration during the desired mission life. These rare incidences could affect the creep strain rate and therefore the life. The paper accounts for these uncertainties and includes the effect of such rare incidences, random in nature, on the reliability. The sensitivities of variables affecting the reliability are quantified and guidelines developed to improve the reliability are outlined. Furthermore, the quantified reliability is being verified with test data from the accelerated benchmark tests being conducted at the NASA Glenn Research Center.

Shah, Ashwin R.↗
NASA NTRS2004

Effect of Random Thermal Spikes on Stirling Convertor Heater Head Reliability

Onboard radioisotope power systems being developed to support future NASA exploration missions require reliable design lifetimes of up to 14 yr and beyond. The structurally critical heater head of the high-efficiency developmental Stirling power converter has undergone extensive computational analysis of operating temperatures (up to 650 C), stresses, and creep resistance of the thin-walled Inconel 718 bill of material. Additionally assessment of the effect of uncertainties in the creep behavior of the thin-walled heater head, the variation in the manufactured thickness, variation in control temperature, and variation in pressure on the durability and reliability were performed. However, it is possible for the heater head to experience rare incidences of random temperature spikes (excursions) of short duration. These incidences could occur randomly with random magnitude and duration during the desired mission life. These rare incidences could affect the creep strain rate and therefore the life. The paper accounts for these uncertainties and includes the effect of such rare incidences, random in nature, on the reliability. The sensitivities of variables affecting the reliability are quantified and guidelines developed to improve the reliability are outlined. Furthermore, the quantified reliability is being verified with test data from the accelerated benchmark tests being conducted at the NASA Glenn Research Center.

Shah, Ashwin R.↗
NASA NTRS2000

Development of a Battery-Free Solar Refrigerator

Recent technology developments and a systems engineering design approach have led to the development of a practical battery-free solar refrigerator as a spin-off of NASA's aerospace refrigeration research. Off-grid refrigeration is a good application of solar photovoltaic (PV) power if thermal storage is incorporated and a direct connection is made between the cooling system and the PV panel. This was accomplished by integrating water as a phase-change material into a well insulated refrigerator cabinet and by developing a microprocessor based control system that allows direct connection of a PV panel to a variable speed compressor. This second innovation also allowed peak power-point tracking from the PV panel and elimination of batteries from the system. First a laboratory unit was developed to prove the concept and then a commercial unit was produced and deployed in a field test. The laboratory unit was used to test many different configurations including thermoelectric, Stirling and vapor compression cooling systems. The final configuration used a vapor compression cooling cycle, vacuum insulation, a passive condenser, an integral evaporator/ thermal storage tank, two 77 watt PV panels and the novel controller mentioned above. The system's only moving part was the variable speed BD35 compressor made by Danfoss. The 365 liter cabinet stayed cold with as little as 274 watt-hours per day average PV power. Battery-free testing was conducted for several months with very good results. The amount of thermal storage, size of compressor and power of PV panels connected can all be adjusted to optimize the design for a given application and climate. In the commercial unit, the high cost of the vacuum insulated refrigerator cabinet and the stainless steel thermal storage tank were addressed in an effort to make the technology commercially viable. This unit started with a 142 liter, mass-produced chest freezer cabinet that had the evaporator integrated into its inner walls. Its compressor was replaced with a Danfoss DC compressor slightly larger than the one used in the laboratory unit. The control system was integrated onto a single electronics card and packaged with its starting capacitors. The water for thermal storage was placed behind a liner that was made to fit inside the original factory liner. The original condenser was also augmented with additional surface area to improve performance. PV panels with a total rated power of 180 watts were used. The unit was tested with very successful results in an outside ambient environment, demonstrating its potential for widespread use in many off-grid applications for solar refrigeration.

Ewert, Michael K.↗
NASA NTRS2011

Three-Fluid Magnetohydrodynamic Modeling of the Solar Wind in the Outer Heliosphere

We have developed a three-fluid, fully three-dimensional magnetohydrodynamic model of the solar wind plasma in the outer heliosphere as a co-moving system of solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Our approach takes into account the effects of electron heat conduction and dissipation of Alfvenic turbulence on the spatial evolution of the solar wind plasma and interplanetary magnetic fields. The turbulence transport model is based on the Reynolds decomposition of physical variables into mean and fluctuating components and uses the turbulent phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. We solve the coupled set of the three-fluid equations for the mean-field solar wind and the turbulence equations for the turbulence energy, cross helicity, and correlation length. The equations are written in the rotating frame of reference and include heating by turbulent dissipation, energy transfer from interstellar pickup protons to solar wind protons, and solar wind deceleration due to the interaction with the interstellar hydrogen. The numerical solution is constructed by the time relaxation method in the region from 0.3 to 100 AU. Initial results from the novel model are presented.

Usmanov, Arcadi V.↗
NASA NTRS2012

Simulation of Oxygen Disintegration and Mixing With Hydrogen or Helium at Supercritical Pressure

The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.

Bellan, Josette↗
NASA NTRSDate not supplied

Evaluating the Impact of Agricultural Soil NOx Emissions on Air Quality Using Advanced Satellite, Ground-based, and Model Data

Soil moisture can also influence the concentration of atmospheric trace gases by moderating the emission of nitrogen oxides (NOx = NO + NO2) from agricultural fields. Human activities can play an important role in controlling the available soil moisture depending on irrigation demand and agricultural management. To further complicate matters, nitrogen fertilizer use has also been found to be a significant source of NOx emissions in agricultural areas. In fact, some of the highest emissions have been reported from fertilized soils in high-temperature agricultural regions, such as the Imperial Valley of California. Since NO2 is an important precursor to ozone formation in the troposphere, which is a leading cause of premature death in humans, it is critical to understand how natural and anthropogenic factors contribute to NOx emissions in these areas. O3 pollution is also a growing threat to global food security due to its detrimental impacts on crop production. This work uses a suite of satellite, ground-based, and model data to investigate how agricultural soil NOx emissions from natural (rainfall) and anthropogenic factors (irrigation, nitrogen fertilizer) govern air quality over California. We evaluate the capabilities of using SMAP retrievals and SMAP Land Information System (LIS) output for monitoring irrigation activities over the major agricultural areas of California by conducting intensive analyses of soil moisture and precipitation data. High-resolution trace gas observations from the new generation TROPOspheric Monitoring Instrument (TROPOMI) sensor are used to characterize and monitor the variability of trace gases and air quality conditions associated with soil NOx emissions. We also synthesize satellite, ground-based, and agriculture data to estimate the separate contributions from rainfall, irrigation, and nitrogen fertilizer practices on soil NOx emissions and associated air quality conditions. Finally, unprecedented hourly trace gas retrievals from the NASA Tropospheric Emissions: Monitoring of Pollution (TEMPO) geostationary satellite sensor are used to monitor the diurnal evolution of NO2 and O3 concentrations from soil NOx emissions.

Aaron R Naeger↗
NASA NTRS1995

Probabilistic material strength degradation model for Inconel 718 components subjected to high temperature, high-cycle and low-cycle mechanical fatigue, creep and thermal fatigue effects

This report presents the results of both the fifth and sixth year effort of a research program conducted for NASA-LeRC by The University of Texas at San Antonio (UTSA). The research included on-going development of methodology for a probabilistic material strength degradation model. The probabilistic model, in the form of a postulated randomized multifactor equation, provides for quantification of uncertainty in the lifetime material strength of aerospace propulsion system components subjected to a number of diverse random effects. This model is embodied in the computer program entitled PROMISS, which can include up to eighteen different effects. Presently, the model includes five effects that typically reduce lifetime strength: high temperature, high-cycle mechanical fatigue, low-cycle mechanical fatigue, creep and thermal fatigue. Statistical analysis was conducted on experimental Inconel 718 data obtained from the open literature. This analysis provided regression parameters for use as the model's empirical material constants, thus calibrating the model specifically for Inconel 718. Model calibration was carried out for five variables, namely, high temperature, high-cycle and low-cycle mechanical fatigue, creep and thermal fatigue. Methodology to estimate standard deviations of these material constants for input into the probabilistic material strength model was developed. Using an updated version of PROMISS, entitled PROMISS93, a sensitivity study for the combined effects of high-cycle mechanical fatigue, creep and thermal fatigue was performed. Then using the current version of PROMISS, entitled PROMISS94, a second sensitivity study including the effect of low-cycle mechanical fatigue, as well as, the three previous effects was performed. Results, in the form of cumulative distribution functions, illustrated the sensitivity of lifetime strength to any current value of an effect. In addition, verification studies comparing a combination of high-cycle mechanical fatigue and high temperature effects by model to the combination by experiment were conducted. Thus, for Inconel 718, the basic model assumption of independence between effects was evaluated. Results from this limited verification study strongly supported this assumption.

Bast, Callie C.↗
NASA NTRS2021

Human Performance of Novice Schedulers for Complex Spaceflight Operations Timelines

Objective: Investigate the effects on human performance as a function of scheduling task complexity for novice schedulers creating spaceflight timelines. Background: Future astronauts will be expected to self-schedule, yet will not be experts in creating timelines that meet complex constraints inherent to spaceflight operations. Method: Conducted a within-subject experiment to measure scheduling efficiency, effectiveness, workload and situation awareness while varying scheduling task complexity factors, namely number of constraints and types of constraints. Results: Fifteen participants completed various scheduling problems. Performance differences were identified between the independent variables. There was a main effect due to the number of constraints and type of constraint for efficiency, effectiveness, and workload. Significant interactions were observed in situation awareness and workload for certain types of constraints. Results also suggest that a lower number of constraints may be manageable by novice schedulers when compared to scheduling activities without constraints. Conclusion: Results suggest that novice schedulers performance decreases with high number of constraints and future scheduling aids may have to be targeted to type of constraint. Application: Knowledge on the effect of scheduling task complexity will help design scheduling systems that will enable self-scheduling for future astronauts. It will also inform other domains that conduct complex scheduling, such as nursing and manufacturing.

scheduling↗
NASA NTRS1992

Leaf gas exchange of Andropogon gerardii Vitman, Panicum virgatum L., and Sorghastrum nutans (L.) Nash in a tallgrass prairie

Net CO2 assimilation as a function of internal CO2 and stomatal conductance to water vapor were measured on blades of the C4 grasses Andropogon gerardii Vitman, Panicum virgatrum L., and Sorghastrum nutans (L.) Nash in northeast Kansas over two growing seasons to determine the comparative physiological responses of these dominant grasses of the tallgrass prairie to environmental variables. The response of dark respiration to temperature and of net assimilation to CO2 concentration and absorbed quantum flux differed little among species. A. gerardii had lower potential photosynthetic rates at internal CO2 concentrations below saturation than P. virgatum and S. nutans, but net assimilation under ambient conditions was similar in the three species. Net assimilation and both the initial slope of assimilation versus internal CO2 curves and the maximum potential assimilation rate decreased as leaf water potential declined in blades of A. gerardii and S. nutans. Changes in assimilation capacity were paralleled by changes in stomatal conductance that were similar in all three species. The strong correlations among processes regulating leaf CO2 assimilation and transpiration in A. gerardii, P. virgatum, and S. nutans suggest that the processes are tightly and similarly coupled in these grasses over a wide range of environmental conditions encountered in the tallgrass prairie.

Polley, H. W.↗
NASA NTRS1997

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗
NASA NTRS2001

Sources of Variability in Chlorophyll Analysis by Fluorometry and by High Performance Liquid Chromatography

The need for accurate determination of chlorophyll a (chl a) is of interest for numerous reasons. From the need for ground-truth data for remote sensing to pigment detection for laboratory experimentation, it is essential to know the accuracy of the analyses and the factors potentially contributing to variability and error. Numerous methods and instrument techniques are currently employed in the analyses of chl a. These methods range from spectrophotometric quantification, to fluorometric analysis and determination by high performance liquid chromatography. Even within the application of HPLC techniques, methods vary. Here we provide the results of a comparison among methods and provide some guidance for improving the accuracy of these analyses. These results are based on a round-robin conducted among numerous investigators, including several in the Sensor Intercomparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) and HyCODE Programs. Our purpose here is not to present the full results of the laboratory intercalibration; those results will be presented elsewhere. Rather, here we highlight some of the major factors that may contribute to the variability observed. Specifically, we aim to assess the comparability of chl a analyses performed by fluorometry and HPLC, and we identify several factors in the analyses which may contribute disproportionately to this variability.

VanHeukelem, Laurie↗
NASA NTRS2010

Sources of Uncertainty in Predicting Land Surface Fluxes Using Diverse Data and Models

In the domain of predicting land surface fluxes, models are used to bring data from large observation networks and satellite remote sensing together to make predictions about present and future states of the Earth. Characterizing the uncertainty about such predictions is a complex process and one that is not yet fully understood. Uncertainty exists about initialization, measurement and interpolation of input variables; model parameters; model structure; and mixed spatial and temporal supports. Multiple models or structures often exist to describe the same processes. Uncertainty about structure is currently addressed by running an ensemble of different models and examining the distribution of model outputs. To illustrate structural uncertainty, a multi-model ensemble experiment we have been conducting using the Terrestrial Observation and Prediction System (TOPS) will be discussed. TOPS uses public versions of process-based ecosystem models that use satellite-derived inputs along with surface climate data and land surface characterization to produce predictions of ecosystem fluxes including gross and net primary production and net ecosystem exchange. Using the TOPS framework, we have explored the uncertainty arising from the application of models with different assumptions, structures, parameters, and variable definitions. With a small number of models, this only begins to capture the range of possible spatial fields of ecosystem fluxes. Few attempts have been made to systematically address the components of uncertainty in such a framework. We discuss the characterization of uncertainty for this approach including both quantifiable and poorly known aspects.

Dungan, Jennifer L.↗
NASA NTRS2012

Characterization of Hayabusa II Target Asteroid (162173) 1999 JU3

The Japanese Hayabusa II mission is planned to rendezvous with and return a sample from the near-Earth asteroid (162173) 1999 JU3. Previous mid-infrared studies have constrained the albedo and thermal properties of this object (Muller et al. 2011; Campins et al. 2011; Hasegawa et al. 2008). Visible wavelength spectra from 1999 and 2007 reveal a C-type asteroid that displays pronounced spectroscopic variability around 0.7 microns. Variability in the strength of a 0.7 micron band could be due to heterogeneous concentrations of iron-bearing phyllosilicates across its surface (Vilas 2008). We will present new observations from the favorable 2012 apparition to further characterize this object. In June of 2012 spectroscopic observations were conducted with the LDSS3 and FIRE instruments on the Magellan telescopes at Las Campanas Observatory in Chile. Between April and July of 2012 broadband visible-wavelength photometry was obtained with the Tenagra II telescope in Arizona and with the IMACS, Megacam and LDSS3 instruments on the Magellan telescopes. Our visible and near-infrared spectra confirm a C-type taxonomic classification, but do not show evidence for the presence of a 0.7 micron phyllosilicate band. Our time series of visible spectra cover approximately 60% of the rotational phases of 1999 JU3, but do not display any pronounced variability. We use our new optical light curves, combined with photometry from 2007, to refine a shape model of the asteroid. This shape model provides a means for mapping surface regions accessed by the spectroscopic observations from both 2007 and 2012, and thus to directly address the possibility of surface heterogeneity. This surface map, in conjunction with the newly measured photometric phase curve of the asteroid, will be used to make predictions regarding composition and surface properties that will ultimately be tested upon arrival of the Hayabusa II spacecraft.

Moskovitz, Abe↗
NASA NTRS1982

The dynamics of the Venus ionosphere. I - A simulation of the solar wind compression of the upper dayside ionosphere

One of the most exciting discoveries by the Pioneer Venus mission is the extreme variability in the structure of the Venus atmosphere. The solar wind plays a major, although as yet not well-defined, role in the dynamics of the ionosphere. An investigation is being conducted regarding the response of the dayside Venus ionosphere to changing solar wind conditions, in particular to the varying solar wind dynamic pressure. In the present study the dynamics of the upper (h equal to or greater than 200 km) ionosphere are simulated numerically using a one-dimensional, spherically symmetric, Lagrangian hydrodynamic code developed by Stein and Schwartz (1972). The ionosphere is assumed to be unmagnetized and is represented with a two-fluid model. The initial ionosphere is chosen to be in pressure equilibrium with the solar wind at the ionopause. It is shown how some of the time-dependent features of the Venus ionosphere may be simulated with the considered model.

Wolff, R. S.↗
NASA NTRS1982

High resolution analysis

The possibilities for the use of high spectral resolution analysis in the field of hydrology and water resources are examined. Critical gaps in scientific knowledge that must be filled before technology can be evaluated involve the spectral response of water, substances dissolved and suspended in water, and substances floating on water. The most complete mapping of oil slicks can be done in the ultraviolet region. A mean of measuring the ultraviolet reflection at the surface from satellite altitudes needs to be determined. The use of high spectral resolution sensors in a reasonable number of narrow bands may be able to sense the reflectance or emission characteristics of water and its contained materials that can be correlated with commonly used water quality variables. Technological alternative available to experiment with problems of sensing water quality are to use existing remote sensing instrumentation in an empirical mode and to develop instruments for either testing hypoteses or conducting empirical experiments.

Robinove, C. J.↗
NASA NTRS1983

KQ Mon and the nature of the UX Ursa Majoris Nova-like variables

The UX Ursa Majoris stars form a group of nova-like variables with common photometric and spectroscopic properties. These objects appear to be related to the cataclysmic variables. However, there is no information that they have undergone major outbursts. The present investigation is concerned with a new object, KQ Mon, which has been included in a program of study conducted with the IUE satellite. A description of observations of KQ Mon is presented, and the relationship of this star to other UX UMa stars is examined. Attention is given to the nature of the UX Ursa Majoris stars. It is argued that the accretion rates of the UX UMa stars are higher than, for example, the dwarf novae during quiescence and that the higher accretion rates of the UX UMa stars are responsible for their lack of major outbursts.

Sion, E. M.↗
NASA NTRS1985

Impact studies of a 1/3-scale model of an air cushion vehicle

An experimental investigation was conducted to determine the effects of various parameters of the impact performance of a 1/3-scale dynamic model of an air cushion vehicle. Impact response was determined by measuring the maximum values of variables, including sidelobe, front lobe, and cavity pressures, normal acceleration, pitch and roll angles, and vertical displacement during impact, for various combinations of drop height, initial pitch and roll angles, and forward speed. Increasing initial pitch angle increased the maximum values of the front lobe pressure, normal acceleration, nose down pitch angle, and to some extent, vertical displacement, but it inversely affected the maximum cavity pressure. Increasing the drop height of the model increased the potential energy of the system and generally produced larger responses over the entire range of variables measured, except for the roll angle after impact, which remained constant. Forward speed had no effect on the impact performance of the model, except for essentially doubling the maximum nose down pitch angle after impact at the maximum speed tested.

Daugherty, R. H.↗
NASA NTRS1986

Effect of an upstream wake on a pusher propeller

An analytical/computational study has been conducted to predict the effect of an upstream wake on an operating propeller. The upstream wing/pylon was modeled by a constant chord wing of NACA 0012 sections and was placed at a variable distance (0.1 - 0.3 chord) upstream of a scaled model propeller (SR-2). The wake model was a similarity formulation. The periodic behavior ofthe flow during the passage through the wake was formulated in terms of time-dependent variation of each blade section's angle of attack. It was found that the final expressions for the unsteady pressure distribution on each blade section are periodic and that the unsteady circulation and lift coefficieents exhibit a hysteresis loop.

Takallu, M. A.↗