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At least 361 records · Page 20

Liquid helium fluid dynamics studies. Final Technical Report

Future high energy physics accelerators depend on a number of advanced technologies to open the many doors of scientific discovery. Among these advanced technologies, superconducting magnets and superconducting radio frequency (SRF) cavities are the backbone of the accelerator and detector systems. But all these low temperature systems depend critically on successful and reliable operation of their supporting technologies, among which the liquid helium cooling system is of the utmost importance. To improve the quality of these systems both in terms of efficiency and reliability, a robust helium cryogenics research and development (R&D) effort is required. The proposed research to be conducted by the FSU cryogenics group aims to produce fundamental knowledge that meets this R&D need. The projects that we have completed over the past grant period at Florida State University consist of experimental research on liquid helium fluid dynamics and heat transfer problems relevant to the development of future superconducting particle physics accelerators. Liquid helium is the coolant used in all such facilities and in many of these facilities He II (the low temperature phase of liquid helium also known as superfluid helium) is preferred due to its outstanding heat transfer characteristics. The work consists of two main experimental studies that probe both fundamental as well as practical aspects of liquid helium cooling. The first is a broad and fundamental study of the heat and mass transfer processes that can occur during a sudden catastrophic loss of vacuum (SCLV) incident in a superconducting accelerator. SCLV refers to the remote but extremely critical accident scenario where atmospheric pressure air is allowed to flood into the insulating vacuum system and impinge on the liquid helium cooled surfaces in the accelerator. Safe performance and recovery from such accidents is essential to the reliable operation of superconducting accelerators. The dynamics of this process is quite complex and so our approach is to conduct a series of well-orchestrated experiments that probe the various physical phenomena that can occur during an SCLV event. The experiments are coupled with analytic and numerical analysis in an effort to develop a general understanding of the process and to assist with future accelerator design and development. The second activity is directed toward fundamental understanding of heat and mass transfer in He II, which is essential to the design of superconducting magnets and radio frequency cavities in accelerators. The work consists of flow visualization of the dynamics of He II using laser assisted techniques. Two complementary techniques are used to study the fundamentals of the turbulent state. The first technique uses neutrally buoyant solid hydrogen particles to probe the flow fields of the superfluid and normal fluid components. The other technique uses laser excited He2* molecules as tracers of the normal fluid motion within the He II. The activities also included an effort to use visualization techniques to locate transient hot spots in radio frequency superconducting cavities. Such work provides valuable information about the heat transfer process in He II and its impact on the performance of superconducting devices. The research effort at Florida State University is not directly in support of a specific high energy physics experiment or facility. Rather, the work is general and coordinated with HEP accelerator laboratories to provide valuable insight that can assist with future accelerator development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Studying Rate of Fire Spread Using Landscape Statistics and FIRETEC

Wildfires are multi-system and multi-scale processes that are influenced by the land and atmosphere. Here, we study the influence of land, in terms of topography and vegetation, on uphill and downhill fire spread using data of the state of California as a testbed. The California landscape is first quantified by reclassifying its dominant vegetation types into grass, trees, and shrubs. Next, statistics of slope, vegetation height, and live fuel moisture percentage for each dominant vegetation type are gathered to create ensembles of idealized computational fluid dynamics (CFD) model simulations representative of the landscape. Rate of spread values for each CFD simulation are recorded to observe the differences in perturbing slope and fuel moisture for each vegetation type. We have found that all vegetation types prefer slopes of less than 30 degrees. Trees in the California data are 10 to 40 meters high, whereas shrub heights are less than 3 meters and grass heights are less than 1 meter. The live fuel moisture percentage of both trees and shrubs fluctuates around approximately 100% over one year (2019-2020). Using these parameters as inputs into the CFD model, fire spread rate is found to be fastest in the grass ensemble (maximum 12 m s -1 ), followed by shrubs (maximum 10 m s -1 ) and lastly by trees (maximum 7 m s -1 ). Increasing slope increases the spread rate of the uphill fire but the downhill spread decreases for slopes greater than 15 degrees. Increasing fuel moisture decreases the spread rate both up and down the hill. This study highlights the impacts that topography and vegetation have on fire spread.

54 ENVIRONMENTAL SCIENCES↗

Inlet-Compressor Analysis using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. Isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (1-D) Euler inlet simulation showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition. To aid in this understanding and to help evaluate possible boundary conditions, an inlet-engine experiment was conducted at the University of Cincinnati. The interaction of acoustic pulses, generated in the inlet, with the engine were investigated. Because of the availability of experimental data for validation, it was decided to simulate the experiment using CFD. The philosophy here is that the inlet-engine system is best simulated by coupling (existing) specialized CFD component-codes. The objectives of this work were to aid in a better understanding of inlet-compressor interaction physics and the formulation of a more realistic compressor-face boundary condition for time-accurate CFD simulations of inlets. Previous simulations have used 1-D Euler engine simulations in conjunction with 1-D Euler and axisymmetric Euler inlet simulations. This effort is a first step toward CFD simulation of an entire engine by coupling multidimensional component codes.

Cole, Gary↗

Inlet-Compressor Analysis Using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (I-D) Euler inlet simulation (ref. 1) showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously, a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition.

Cole, Gary↗

Technology Development and Infusion by NASA's Entry Systems Modeling Project

This paper describes recent development of modeling and simulation technologies for entry systems and their infusion into NASA's exploration missions. Technology development is organized and prioritized using a system-level perspective, resulting in four broad technical areas of investment: (1) Thermal protection material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. The paper will highlight key contributions from each of these areas, their impacts from a spacecraft and mission design perspective, and discuss planned future investment. Aspects of each technical area are only briefly summarized here. Thermal protection material modeling is geared toward high-fidelity, predictive models capable of optimizing design performance, post-flight reconstruction, and quantifying thermal protection system reliability. New computational tools and experimental techniques have been applied to Orion, MSL/Mars 2020, Mars InSight, and Mars Sample Return missions. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. In both cases, substantial improvements in model uncertainty have directly impacted the development of mission margin policies, flight instrumentation design and analysis (Orion and Mars 2020), and have even revealed the importance of neglected phenomena like mid-wave infrared radiation of CO2. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics affecting Orion, Commercial Crew, and Mars programs; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate augmentation of aerothermal environments at Mars during dust storms; and studies of roughness-induced heating augmentation relevant to tiled (Orion, Mars 2020) and woven (Mars Sample Return) thermal protection systems. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent, with precision landing requirements driven by Mars human exploration goals.

Barnhardt, Michael D.↗

Prediction of prompt NO(x) in hydrocarbon air flames

The gas turbine industry is directing particular attention to very low NOx combustors, whether for aircraft or land based CCGT systems. These low NOx combustors frequently use liquid fuels or natural gas burning under very lean premixed conditions with air or under rich-lean conditions, although only the first case is studied here. In land based systems, diluted steam or nitrogen are sometimes injected into the combustion chambers to reduce flame temperature. The NOx emissions from such systems are the product of three chemical mechanisms which are interrelated: the hydrocarbon prompt NO, the thermal NO (extended Zeldovich mechanism), and the nitrous oxide route to NO. Formation of NO2 from NO also occurs, as well as emission of carbon monoxide and unburnt hydrocarbons. When the fuel-oxidant proportion decreases towards leaner conditions, flame temperatures are lowered, resulting in the total NO being reduced and the thermal-NO contribution greatly diminished to the benefit of the remaining two mechanisms of NO formation. While knowledge of the elementary reactions and their chemical kinetics concerning methane and simple hydrocarbons combustion has existed for a number of years, its use for computer modeling is limited to simple flow dynamics configurations. Nevertheless, understanding of such combusting flows under a wide range of experimental conditions allows for analogies or speculations with more complex actual systems. Such understanding can be achieved by means of one dimensional laminar premixed flame modeling, with a full chemical mechanism which incorporates the three routes of NO formation. Complementary to this understanding is the modeling of the actual combustion system using a full description of the fluid dynamics coupled with a reduced chemical scheme, which is then compared against the first model. The objective of this investigation is to evaluate the relative importance of the three mechanisms of NO formation in lean premixed methane-air combustion with increasing pressure using the one dimensional plug flow package PREMIX, and to test the validity of a three dimensional model with a global chemical mechanism against the one dimensional model in the atmospheric pressure case. Methane is chosen because it is the only mechanism which is reasonably well known and is a good guide to the behavior of other hydrocarbons. The mixture ratio chosen is richer than that in lean gas turbines, but the combustion of this mixture with the low preheat gives realistic gas turbine final flame temperatures. Conditions of NO2 formation are also analyzed in the one dimensional model and results extrapolated to the case of gas turbines.

Valerie Dupont↗

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no or some addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4 rocket engine fired on 1m2 area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon. The resulting computed values of plume impingement surface temperature, stagnation pressure, gas velocity, shear stress and heat flux were then matched as closely as possible in the Earth’s atmosphere in a sub-scale rocket engine GO2/CH4 test which was provided by Masten Space Systems in Mojave, California. The rocket engine was mounted on a test stand with vertical translation capabilities so that the landing operations of a lander could be simulated (Figure 1).The pad materials test coupons were placed at the surface of a large bin containing simulated lunar basalt regolith and subjected to a test firing as shown in Figure 2. The results of this testing will be presented with related findings, analysis and discussion.

Plume Surface Interaction↗

Completion of initial reduced-order model for flammable refrigerant dispersal in residential spaces

Environmental regulations aimed at reducing global warming impacts of HVAC&R refrigerants have resulted in the phase-out of chlorofluorocarbons (CFCs) in 2010 and hydrochlorofluorocarbons (HCFCs) by 2030 in developed countries with additional restrictions on the use of hydrofluorocarbons (HFCs) set to take effect in 2036. Many of the remaining alternative refrigerants that have lower global warming potential (GWP) and that are suitable for use in HVAC&R systems (e.g., propane, difluoromethane) are flammable to some degree. Flammable refrigerants introduce new challenges and hazards to property and personal safety related to potential deflagration during system maintenance or due to leakage of the refrigerant accumulating in the conditioned space. Standards have been developed to set maximum charge limits for flammable refrigerants in HVAC&R systems; however, existing safety standards and codes still restrict their use. The bodies that maintain and update these codes need publicly available, science-based information to enable credible guidelines for setting safe charge limits for different flammable refrigerants in different HVAC&R applications. In 2016, the Alliance for Responsible Atmospheric Policy, the Air-Conditioning Heating and Refrigeration Institute (AHRI), ASHRAE, the U.S. Department of Energy (DOE), and the State of California began efforts to develop such information. As part of this effort, Oak Ridge National Laboratory (ORNL) began the current, ongoing project to examine imposed charge limits for flammable refrigerants and identify reasonable adjustments to these limits when found appropriate. Past tasks under this project have included development of experimentally vetted, computational fluid dynamics (CFD) simulation approaches to study the results of leakage of flammable refrigerants from various HVAC&R systems into different types of commercial and residential spaces. In this report, we discuss recent efforts to develop a predictive model of the flammable volume fraction and accumulated refrigerant mass in a single-room residential space resulting from the leak of a flammable refrigerant from a small room air conditioning (RAC) unit. The eventual goal is development of a model suitable for public release which could simulate a range of scenarios. In discussions with the AHRTI Flammable Refrigerant Subcommittee (FRS) at the beginning of this effort, a total of 9 input parameters were chosen for consideration including room area, room/door opening area, ventilation fan flow rate, unit/leak height, leak area, leak rate, total refrigerant charge, refrigerant molecular weight, and state of the unit fan.

42 ENGINEERING↗

Space Science in the Twenty-First Century: Imperatives for the Decades 1995 to 2015

A unified program is outlined for studying the Earth, from its deep interior to its fluid envelopes. A system is proposed for measuring devices involving both space-based and in-situ observations that can accommodate simultaneously a large range of scientific needs. The scientific objectices served by this integrated infrastructure are cased into a framework of four grand themes. In summary these are: to determine the composition, structure, dynamics, and evolution of the Earth's crust and deeper interior; to establish and understand the structure, dynamics, and chemistry of the oceans, atmosphere, and cryosphere, and their interaction with the solid Earth; to characterize the history and dynamics of living organisms and their interaction with the environment; and to monitor and understand the interaction of human activities with the natural environment. A focus on these grand themes will help to understand the origin and fate of the planet, and to place it in the context of the solar system.

Source record↗

Stochastic Convection Parameterizations

computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts

atmospheric models↗

Atmospheric wind energization of ocean weather

Ocean weather comprises vortical and straining mesoscale motions, which play fundamentally different roles in the ocean circulation and climate system. Vorticity determines the movement of major ocean currents and gyres. Strain contributes to frontogenesis and the deformation of water masses, driving much of the mixing and vertical transport in the upper ocean. While recent studies have shown that interactions with the atmosphere damp the ocean’s mesoscale vortices O(100) km in size, the effect of winds on straining motions remains unexplored. Here, we derive a theory for wind work on the ocean’s vorticity and strain. Using satellite and model data, we discover that wind damps strain and vorticity at an equal rate globally, and unveil striking asymmetries based on their polarity. Subtropical winds damp oceanic cyclones and energize anticyclones outside strong current regions, while subpolar winds have the opposite effect. A similar pattern emerges for oceanic strain, where subtropical convergent flow is damped along the west-equatorward east-poleward direction and energized along the east-equatorward west-poleward direction. These findings reveal energy pathways through which the atmosphere shapes ocean weather.

54 ENVIRONMENTAL SCIENCES↗

Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method

Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.

42 ENGINEERING↗

A simulation of the atmospheric cloud physics laboratory to aid in its design and the design of the experiments within the laboratory

Using the finite difference method with overrelaxation, numerical solutions of the steady-state vorticity transport equation were obtained for a continuous flow diffusion chamber of the Hudson-Squires type. The calculation neglected the effects due to temperature, gravity, and saturation. The size and shape of the manifold used to inject the aerosol laden flow were varied to obtain a design which would improve the performance of the chamber from strictly low Reynolds number (less than 20) fluid dynamical considerations.

Winchester, L. W., Jr.↗

A survey of actuator shaft sealing techniques for extended space missions

Actuators for control and articulation aboard Mariner spacecraft have employed output shaft seals to maintain an internal gaseous atmosphere. On future missions, considerably greater expected lifetimes, temperature ranges, and radiation exposures have led to a need to determine the limitations of the present O-ring output shaft seal and to examine other candidate seals. Seals suited both to dynamic and static sealing were examined for potential use in three specific actuator applications and the following candidate seals were selected: (a) O-ring seal, (b) chevron seal, (c) bellows seal (linear actuator only), (d) magnetic fluid seal (rotary actuators only) and as a backup seal to any of the foregoing, (e) the labyrinth seal.

Hotz, G. M.↗

Rarefied-continuum gas dynamics transition for SUMS project

This program is to develop an analytic method for reducing SUMS data for the determination of the undisturbed atmosphere conditions ahead of the shuttle along its descending trajectory. It is divided into an internal flow problem, an external flow problem and their matching conditions. Since the existing method of Direct Simulation Monte Carlo (DSMC) failed completely for the internal flow problem, the emphasis is on the internal flow of a highly non-equilibrium, rarefied air through a short tube of a diameter much less than the gaseous mean free path. A two fluid model analysis of this internal flow problem has been developed and studied with typical results illustrated. A computer program for such an analysis and a technical paper published in Lecture Notes in Physics No. 323 (1989) are included as Appendices 3 and 4. A proposal for in situ determination of the surface accommodation coefficients sigma sub t and sigma e is included in Appendix 5 because of their importance in quantitative data reduction. A two fluid formulation for the external flow problem is included as Appendix 6 and a review article for AIAA on Hypersonic propulsion, much dependent on ambient atmospheric density, is also included as Appendix 7.

Cheng, Sin-I↗

Machine-learning identification of the variability of mean velocity and turbulence intensity for wakes generated by onshore wind turbines: Cluster analysis of wind LiDAR measurements

Light detection and ranging (LiDAR) measurements of isolated wakes generated by wind turbines installed at an onshore wind farm are leveraged to characterize the variability of the wake mean velocity and turbulence intensity during typical operations, which encompass a breadth of atmospheric stability regimes and rotor thrust coefficients. The LiDAR measurements are clustered through the k-means algorithm, which enables identifying the most representative realizations of wind turbine wakes while avoiding the imposition of thresholds for the various wind and turbine parameters. Considering the large number of LiDAR samples collected to probe the wake velocity field, the dimensionality of the experimental dataset is reduced by projecting the LiDAR data on an intelligently truncated basis obtained with the proper orthogonal decomposition (POD). The coefficients of only five physics-informed POD modes are then injected in the k-means algorithm for clustering the LiDAR dataset. The analysis of the clustered LiDAR data and the associated supervisory control and data acquisition and meteorological data enables the study of the variability of the wake velocity deficit, wake extent, and wake-added turbulence intensity for different thrust coefficients of the turbine rotor and regimes of atmospheric stability. Furthermore, the cluster analysis of the LiDAR data allows for the identification of systematic off-design operations with a certain yaw misalignment of the turbine rotor with the mean wind direction.

17 WIND ENERGY↗

Fuselage ventilation due to wind flow about a postcrash aircraft

Postcrash aircraft fuselage fire development, dependent on the internal and external fluid dynamics is discussed. The natural ventilation rate, a major factor in the internal flow patterns and fire development is reviewed. The flow about the fuselage as affected by the wind and external fire is studied. An analysis was performend which estimated the rates of ventilation produced by the wind for a limited idealized environmental configuration. The simulation utilizes the empirical pressure coefficient distribution of an infinite circular cylinder near a wall with its boundary later flow to represent the atmospheric boundary layer. The resulting maximum ventilation rate for two door size openings, with varying circumferential location in a common 10 mph wind was an order of magnitude greater than the forced ventilation specified in full scale fire testing. The parameter discussed are: (1) fuselage size and shape, (2) fuselage orientation and proximity to the ground, (3) fuselage-openings size and location, (4) wind speed and direction, and (5) induced flow of the external fire plume is recommended. The fire testing should be conducted to a maximum ventilation rate at least an order of magnitude greater than the inflight air conditioning rates.

Stuart, J. W.↗

Turbine blade tip and seal clearance excitation forces

Experimental and theoretical work done as Phase 3 of a program sponsored by MSFC to investigate the magnitude, origin, and parametric variations of destabilizing forces which arise in high power turbines due to blade-tip leakage effects are described. The two facilities which were built for this purpose are first described. The larger one is a closed, 2 atm pressurized Freon-12 flow loop in which is installed a 1:1 replica of the SSME first stage hydrogen turbine, which can be driven by the flow, and which generates about 14 KW of power into a load-absorbing DC generator. The smaller facility is used to measure the forces on labyrinth seals of the same type as those used in our turbine tests with a shrouded turbine. The seals can be kinematically whirled and spun (independently), and the inlet swirl can be set to a variety of values. Air is the working fluid (with atmospheric discharge) and the data are real-time pressure distributions in the seal glands. The five different unshrouded turbine configurations were tested with static offsets, plus one with a shroud band and a two-ridge seal. Theoretical models of various degrees of complexity were developed to help interpreting and extrapolating the data. The notion of partial work done by the fluid leaking through the tip gaps was put on a quantitative basis by examining the leakage vortex roll-up dynamics. This was used to obtain a theory of the work loss due to a uniform gap. Perturbation and multiple scale arguments were then used to extend this to the case of an eccentric turbine. This yields an unsteady, 3-D theory which can predict the distribution of the approach flow, and its effect on work defect, cross-forces, pressure patterns, and dynamic damping. The predictions agree qualitatively with the data and exhibit the correct trends, but the cross-forces are generally under-predicted.

Martinez-Sanchez, M.↗