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The Honeywell Uncertified Research Engine (HURE), a research version of a turbofan engine that never entered production, was tested in the NASA Propulsion Systems Laboratory (PSL), an altitude test facility at the NASA Glenn Research Center. The PSL is a facility that is equipped with water spray bars capable of producing an ice cloud consisting of ice particles, having a controlled particle diameter and concentration in the airflow. To develop the test matrix of the HURE, the numerical asw analysis of flow and ice particle thermodynamics was performed on the compression system of the turbofan engine to predict operating conditions that could potentially result in a risk of ice accretion due to ice crystal ingestion. The goal of the test matrix was to provide operating conditions such that ice would accrete either in the fan-stator through the inlet guide vane region of the compression system or within the first stator of the high-pressure compressor. The predictive analyses were performed with the mean-line compressor flow modeling code (comdes-melt) which includes an ice particle model. The HURE engine was tested in PSL with the ice cloud over the range of operating conditions of altitude, ambient temperature, simulated flight Mach number, and fan speed with guidance from the analytical predictions. The engine was fitted with video cameras at strategic locations within the engine compression system flow path where ice was predicted to accrete in order to visually confirm ice accretion when it occurred. In addition, traditional compressor instrumentation, such as total pressure and temperature probes, static pressure taps, and metal temperature thermocouples, were installed in targeted areas where the risk of ice accretion was expected. The current research focuses on the analysis of the data that were obtained after testing the HURE engine in PSL with ice crystal ingestion. The computational method (comdes-melt) was enhanced by computing key parameters through the fan-stator at multiple spanwise locations in order to increase the fidelity with the current mean-line method. The Icing Wedge static wet-bulb temperature thresholds were applied for determining the risk of ice accretion in the fan-stator, which is thought to be an adiabatic region. At some operating conditions near the splitter–lip region, other sources of heat (non-adiabatic walls) were suspected to be the cause of accretion, and the Icing Wedge was not applied to predict accretion at that location. A simple order-of-magnitude heat transfer model was implemented into the comdes-melt code to estimate the wall temperature minimum and maximum thresholds that support ice accretion, as observed by video confirmation. The results from this model spanned the range of wall temperatures measured on a previous engine that experienced ice accretion at certain operating conditions. The goal of this study is to show that the computational process developed on earlier engine icing tests can be used to provide an icing risk assessment in adiabatic regions for other engines.

The Honeywell Uncertified Research Engine (HURE), a research version of a turbofan engine that never entered production, was tested in the NASA Propulsion System Laboratory (PSL), an altitude test facility at the NASA Glenn Research Center. The PSL is a facility that is equipped with water spray bars capable of producing an ice cloud consisting of ice particles, having a controlled particle diameter and concentration in the air flow. To develop the test matrix of the HURE, numerical analysis of flow and ice particle thermodynamics was performed on the compression system of the turbofan engine to predict operating conditions that could potentially result in a risk of ice accretion due to ice crystal ingestion. The goal of the test matrix was to provide operating conditions such that ice would accrete in either the fan-stator through the inlet guide vane region of the compression system or within the first stator of the high pressure compressor. The predictive analyses were performed with the mean line compressor flow modeling code (COMDES-MELT) which includes an ice particle model. The HURE engine was tested in PSL with the ice cloud over the range of operating conditions of altitude, ambient temperature, simulated flight Mach number, and fan speed with guidance from the analytical predictions. The engine was fitted with video cameras at strategic locations within the engine compression system flow path where ice was predicted to accrete, in order to visually confirm ice accretion when it occurred. In addition, traditional compressor instrumentation such as total pressure and temperature probes, static pressure taps, and metal temperature thermocouples were installed in targeted areas where the risk of ice accretion was expected. The current research focuses on the analysis of the data that was obtained after testing the HURE engine in PSL with ice crystal ingestion. The computational method (COMDES-MELT) was enhanced by computing key parameters through the fan-stator at multiple span wise locations, in order to increase the fidelity with the current mean-line method. The Icing Wedge static wet bulb temperature thresholds were applicable for determining the risk of ice accretion in the fan-stator, which is thought to be an adiabatic region. At some operating conditions near the splitter-lip region, other sources of heat (non-adiabatic walls) were suspected to be the cause of accretion, and the Icing Wedge was not applicable to predict accretion at that location. A simple order-of-magnitude heat transfer model was implemented into the COMDES-MELT code to estimate the wall temperature minimum and maximum thresholds that support ice accretion, as observed by video confirmation. The results from this model spanned the range of wall temperatures measured on a previous engine that experienced ice accretion at certain operating conditions. The goal of this study is to show that the computational process developed on earlier engine icing tests can be used to provide an icing risk assessment in adiabatic regions for other engines.

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

A 24 foot diameter 3-stage axial compressor powered by variable-speed induction motors provides the airflow in the closed-return 11- by 11-Foot Transonic Wind Tunnel (11-Foot TWT) Facility at NASA Ames Research Center at Moffett Field, California. The facility is part of the Unitary Plan Wind Tunnel, which was completed in 1955. Since then, upgrades made to the 11-Foot TWT such as flow conditioning devices and instrumentation have increased blockage and pressure loss in the tunnel, somewhat reducing the peak Mach number capability of the test section. Due to erosion effects on the existing aluminum alloy rotor blades, fabrication of new steel rotor blades is planned. This presents an opportunity to increase the Mach number capability of the tunnel by redesigning the compressor for increased pressure ratio. Challenging design constraints exist for any proposed design, demanding the use of the existing driveline, rotor disks, stator vanes, and hub and casing flow paths, so as to minimize cost and installation time. The current effort was undertaken to characterize the performance of the existing compressor design using available design tools and computational fluid dynamics (CFD) codes and subsequently recommend a new compressor design to achieve higher pressure ratio, which directly correlates with increased test section Mach number. The constant cross-sectional area of the compressor leads to highly diffusion factors, which presents a challenge in simulating the existing design. The CFD code APNASA was used to simulate the aerodynamic performance of the existing compressor. The simulations were compared to performance predictions from the HT0300 turbomachinery design and analysis code, and to compressor performance data taken during a 1997 facility test. It was found that the CFD simulations were sensitive to endwall leakages associated with stator buttons, and to a lesser degree, under-stator-platform flow recirculation at the hub. When stator button leakages were modeled, pumping capability increased by over 20 of pressure rise at design point due to a large reduction in aerodynamic blockage at the hub. Incorporating the stator button leakages was crucial to matching test data. Under-stator-platform flow recirculation was thought to be large due to a lack of seals. The effect of this recirculation was assessed with APNASA simulations recirculating 0.5, 1, and 2 of inlet flow about stators 1 and 2, modeled as axisymmetric mass flux boundary conditions on the hub before and after the vanes. The injection of flow ahead of the stators tended to re-energize the boundary layer and reduce hub separations, resulting in about 3 increased stall margin per 1 of inlet flow recirculated. In order to assess the value of the flow recirculation, a mixing plane simulation of the compressor which gridded the under-stator cavities was generated using the ADPAC CFD code. This simulation indicated that about 0.65 of the inlet flow is recirculated around each shrouded stator. This collective information was applied during the redesign of the compressor. A potential design was identified using HT0300 which improved overall pressure ratio by removing pre-swirl into rotor 1, replacing existing NASA 65 series rotors with double circular arc sections, and re-staggering rotors and the existing stators. The performance of the new design predicted by APNASA and HT0300 is compared to the existing design.

The main focus of this study is to apply a computational tool for the flow analysis of the turbine engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) at NASA Glenn Research Center. The PSL has been used to test a highly instrumented Honeywell ALF502R-5A (LF11) turbofan engine at simulated altitude operating conditions. Test data analysis with an engine cycle code and a compressor flow code was conducted to determine the values of key icing parameters, that can indicate the risk of ice accretion, which can lead to engine rollback (un-commanded loss of engine thrust). The full engine aerothermodynamic performance was modeled with the Honeywell Customer Deck specifically created for the ALF502R-5A engine. The mean-line compressor flow analysis code, which includes a code that models the state of the ice crystal, was used to model the air flow through the fan-core and low pressure compressor. The results of the compressor flow analyses included calculations of the ice-water flow rate to air flow rate ratio (IWAR), the local static wet bulb temperature, and the particle melt ratio throughout the flow field. It was found that the assumed particle size had a large effect on the particle melt ratio, and on the local wet bulb temperature. In this study the particle size was varied parametrically to produce a non-zero calculated melt ratio in the exit guide vane (EGV) region of the low pressure compressor (LPC) for the data points that experienced a growth of blockage there, and a subsequent engine called rollback (CRB). At data points where the engine experienced a CRB having the lowest wet bulb temperature of 492 degrees Rankine at the EGV trailing edge, the smallest particle size that produced a non-zero melt ratio (between 3 percent - 4 percent) was on the order of 1 micron. This value of melt ratio was utilized as the target for all other subsequent data points analyzed, while the particle size was varied from 1 micron - 9.5 microns to achieve the target melt ratio. For data points that did not experience a CRB which had static wet bulb temperatures in the EGV region below 492 degrees Rankine, a non-zero melt ratio could not be achieved even with a 1 micron ice particle size. The highest value of static wet bulb temperature for data points that experienced engine CRB was 498 degrees Rankine with a particle size of 9.5 microns. Based on this study of the LF11 engine test data, the range of static wet bulb temperature at the EGV exit for engine CRB was in the narrow range of 492 degrees Rankine - 498 degrees Rankine , while the minimum value of IWAR was 0.002. The rate of blockage growth due to ice accretion and boundary layer growth was estimated by scaling from a known blockage growth rate that was determined in a previous study. These results obtained from the LF11 engine analysis formed the basis of a unique “icing wedge.”

We model vortex dynamics in a 2-dimensional Bose superfluid using the Thompson-Stamp (TS) equations of motion, which describes both the classical Hall-Vinen-Iordanskii (HVI) dynamical regime and the fully developed quantum regime, and the crossover between them. The TS equations can be written in the form of a quantum Langevin equation. Analytic solutions are given for all of these regimes for a single vortex in a 2-dimensional system. In the classical regime we include the vortex inertial and Langevin noise terms, which are dropped in the usual HVI analysis. In the quantum and crossover regimes the effect of memory terms is important, and leads to clear differences from the classical predictions., Comment: 14 pages, 8 figures

The Propulsion Systems Laboratory (PSL), an altitude test facility at NASA Glenn Research Center, has been used to test a highly instrumented turbine engine at simulated altitude operating conditions. This is a continuation of the PSL testing that successfully duplicated the icing events that were experienced in a previous engine (serial LF01) during flight through ice crystal clouds, which was the first turbofan engine tested in PSL. This second model of the ALF502R-5A serial number LF11 is a highly instrumented version of the previous engine. The PSL facility provides a continuous cloud of ice crystals with controlled characteristics of size and concentration, which are ingested by the engine during operation at simulated altitudes. Several of the previous operating points tested in the LF01 engine were duplicated to confirm repeatability in LF11. The instrumentation included video cameras to visually illustrate the accretion of ice in the low pressure compressor (LPC) exit guide vane region in order to confirm the ice accretion, which was suspected during the testing of the LF01. Traditional instrumentation included static pressure taps in the low pressure compressor inner and outer flow path walls, as well as total pressure and temperature rakes in the low pressure compressor region. The test data was utilized to determine the losses and blockages due to accretion in the exit guide vane region of the LPC. Multiple data points were analyzed with the Honeywell Customer Deck. A full engine roll back point was modeled with the Numerical Propulsion System Simulation (NPSS) code. The mean line compressor flow analysis code with ice crystal modeling was utilized to estimate the parameters that indicate the risk of accretion, as well as to estimate the degree of blockage and losses caused by accretion during a full engine roll back point. The analysis provided additional validation of the icing risk parameters within the LPC, as well as the creation of models for estimating the rates of blockage growth and losses.

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second-order-accurate in space and time and yields high resolution in the presence of discontinuities. In the basic Euler and Navier-Stokes upwind scheme, many concepts of high-order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However, even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called pathological behaviors (for example, the carbuncle, the expansion shock, etc.), which are mostly triggered due to some undesirable local numerical instability. A simple multidimensional dissipation model is used to systematically suppress such behaviors and stabilize the scheme for flows at high Mach numbers, whereas for flows at very low Mach number (for example, M = 0.02), it is found that computation can be directly carried out without invoking preconditioning. The modified, stabilized scheme is referred to as the enhanced time-accurate upwind scheme (Loh, C. Y., and Jorgenson, P. C. E., "A Time Accurate Upwind Unstructured Finite Volume Method for Compressible Flow with Cure of Pathological Behaviors," AIAA Paper 2007-4463, 2007.) in this paper. The unstructured grid capability renders flexibility for use in complex geometry, and the present enhanced time-accurate upwind Euler and Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both computational fluid dynamics and computational aeroacoustics. Numerous examples are included to demonstrate the robustness of the scheme.

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

The occurrence of ice accretion within commercial high bypass aircraft turbine engines has been reported under certain atmospheric conditions. Engine anomalies have taken place at high altitudes that have been attributed to ice crystal ingestion, partially melting, and ice accretion on the compression system components. The result was degraded engine performance, and one or more of the following: loss of thrust control (roll back), compressor surge or stall, and flameout of the combustor. As ice crystals are ingested into the fan and low pressure compression system, the increase in air temperature causes a portion of the ice crystals to melt. It is hypothesized that this allows the ice-water mixture to cover the metal surfaces of the compressor stationary components which leads to ice accretion through evaporative cooling. Ice accretion causes a blockage which subsequently results in the deterioration in performance of the compressor and engine. The focus of this research is to apply an engine icing computational tool to simulate the flow through a turbofan engine and assess the risk of ice accretion. The tool is comprised of an engine system thermodynamic cycle code, a compressor flow analysis code, and an ice particle melt code that has the capability of determining the rate of sublimation, melting, and evaporation through the compressor flow path, without modeling the actual ice accretion. A commercial turbofan engine which has previously experienced icing events during operation in a high altitude ice crystal environment has been tested in the Propulsion Systems Laboratory (PSL) altitude test facility at NASA Glenn Research Center. The PSL has the capability to produce a continuous ice cloud which is ingested by the engine during operation over a range of altitude conditions. The PSL test results confirmed that there was ice accretion in the engine due to ice crystal ingestion, at the same simulated altitude operating conditions as experienced previously in flight. The computational tool was utilized to help guide a portion of the PSL testing, and was used to predict ice accretion could also occur at significantly lower altitudes. The predictions were qualitatively verified by subsequent testing of the engine in the PSL. In a previous study, analysis of select PSL test data points helped to calibrate the engine icing computational tool to assess the risk of ice accretion. This current study is a continuation of that data analysis effort. The study focused on tracking the variations in wet bulb temperature and ice particle melt ratio through the engine core flow path. The results from this study have identified trends, while also identifying gaps in understanding as to how the local wet bulb temperature and melt ratio affects the risk of ice accretion and subsequent engine behavior.

The occurrence of ice accretion within commercial high bypass aircraft turbine engines has been reported under certain atmospheric conditions. Engine anomalies have taken place at high altitudes that have been attributed to ice crystal ingestion, partially melting, and ice accretion on the compression system components. The result was degraded engine performance, and one or more of the following: loss of thrust control (roll back), compressor surge or stall, and flameout of the combustor. As ice crystals are ingested into the fan and low pressure compression system, the increase in air temperature causes a portion of the ice crystals to melt. It is hypothesized that this allows the ice-water mixture to cover the metal surfaces of the compressor stationary components which leads to ice accretion through evaporative cooling. Ice accretion causes a blockage which subsequently results in the deterioration in performance of the compressor and engine. The focus of this research is to apply an engine icing computational tool to simulate the flow through a turbofan engine and assess the risk of ice accretion. The tool is comprised of an engine system thermodynamic cycle code, a compressor flow analysis code, and an ice particle melt code that has the capability of determining the rate of sublimation, melting, and evaporation through the compressor flow path, without modeling the actual ice accretion. A commercial turbofan engine which has previously experienced icing events during operation in a high altitude ice crystal environment has been tested in the Propulsion Systems Laboratory (PSL) altitude test facility at NASA Glenn Research Center. The PSL has the capability to produce a continuous ice cloud which are ingested by the engine during operation over a range of altitude conditions. The PSL test results confirmed that there was ice accretion in the engine due to ice crystal ingestion, at the same simulated altitude operating conditions as experienced previously in flight. The computational tool was utilized to help guide a portion of the PSL testing, and was used to predict ice accretion could also occur at significantly lower altitudes. The predictions were qualitatively verified by subsequent testing of the engine in the PSL. The PSL test has helped to calibrate the engine icing computational tool to assess the risk of ice accretion. The results from the computer simulation identified prevalent trends in wet bulb temperature, ice particle melt ratio, and engine inlet temperature as a function of altitude for predicting engine icing risk due to ice crystal ingestion.

The occurrence of ice accretion within commercial high bypass aircraft turbine engines has been reported under certain atmospheric conditions. Engine anomalies have taken place at high altitudes that were attributed to ice crystal ingestion, partially melting, and ice accretion on the compression system components. The result was one or more of the following anomalies: degraded engine performance, engine roll back, compressor surge and stall, and flameout of the combustor. The main focus of this research is the development of a computational tool that can estimate whether there is a risk of ice accretion by tracking key parameters through the compression system blade rows at all engine operating points within the flight trajectory. The tool has an engine system thermodynamic cycle code, coupled with a compressor flow analysis code, and an ice particle melt code that has the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Assumptions are made to predict the complex physics involved in engine icing. Specifically, the code does not directly estimate ice accretion and does not have models for particle breakup or erosion. Two key parameters have been suggested as conditions that must be met at the same location for ice accretion to occur: the local wet-bulb temperature to be near freezing or below and the local melt ratio must be above 10%. These parameters were deduced from analyzing laboratory icing test data and are the criteria used to predict the possibility of ice accretion within an engine including the specific blade row where it could occur. Once the possibility of accretion is determined from these parameters, the degree of blockage due to ice accretion on the local stator vane can be estimated from an empirical model of ice growth rate and time spent at that operating point in the flight trajectory. The computational tool can be used to assess specific turbine engines to their susceptibility to ice accretion in an ice crystal environment.

During the past two decades the occurrence of ice accretionwithin commercial high bypass aircraft turbine engines undercertain operating conditions has been reported. Numerousengine anomalies have taken place at high altitudes that wereattributed to ice crystal ingestion such as degraded engineperformance, engine roll back, compressor surge and stall,and even flameout of the combustor. As ice crystals areingested into the engine and low pressure compressionsystem, the air temperature increases and a portion of the icemelts allowing the ice-water mixture to stick to the metalsurfaces of the engine core. The focus of this paper is onestimating the effects of ice accretion on the low pressurecompressor, and quantifying its effects on the engine systemthroughout a notional flight trajectory. In this paper it wasnecessary to initially assume a temperature range in whichengine icing would occur. This provided a mechanism tolocate potential component icing sites and allow thecomputational tools to add blockages due to ice accretion in aparametric fashion. Ultimately the location and level ofblockage due to icing would be provided by an ice accretioncode. To proceed, an engine system modeling code and amean line compressor flow analysis code were utilized tocalculate the flow conditions in the fan-core and low pressurecompressor and to identify potential locations within thecompressor where ice may accrete. Note that there is abaseline value of aerodynamic blockage due to low velocityair near the compressor inner and outer walls and bladesurfaces (boundary layer blockage). There is also a blockagedue to the blade metal thickness. In this study, the “additionalblockage” refers to blockage due to the accretion of ice on themetal surfaces. Once the potential locations of ice accretionare identified, the levels of additional blockage due toaccretion were parametrically varied to estimate the effectson the low pressure compressor blade row performanceoperating within the engine system environment. This studyincludes detailed analysis of compressor and engineperformance during cruise and descent operating conditionsat several altitudes within the notional flight trajectory. Thepurpose of this effort is to develop the codes to provide apredictive capability to forecast the onset of engine icingevents, such that they could help in the avoidance of theseevents.It has been reported that ice crystal accretion in gas turbineengines is dependent on the amount of mixed phaseconditions (liquid and solid) that exist. In addition, theproblem of ice accretion is highly multi-disciplinary, since itinvolves heat transfer from the air to the compressor metalsurfaces. The first phase of this study focuses on addressingthe thermodynamic cycle through the engine system code andthe mean line flow analysis through the compressor through aflight trajectory. The second phase of this study focuses on

Ice buildup in the compressor section of a commercial aircraft gas turbine engine can cause a number of engine failures. One of these failure modes is known as engine rollback: an uncommanded decrease in thrust accompanied by a decrease in fan speed and an increase in turbine temperature. This paper describes the development of a model which simulates the system level impact of engine icing using the Commercial Modular Aero-Propulsion System Simulation 40k (C-MAPSS40k). When an ice blockage is added to C-MAPSS40k, the control system responds in a manner similar to that of an actual engine, and, in cases with severe blockage, an engine rollback is observed. Using this capability to simulate engine rollback, a proof-of-concept detection scheme is developed and tested using only typical engine sensors. This paper concludes that the engine control system s limit protection is the proximate cause of iced engine rollback and that the controller can detect the buildup of ice particles in the compressor section. This work serves as a feasibility study for continued research into the detection and mitigation of engine rollback using the propulsion control system.

We use central differences to solve the time dependent Euler equations. The schemes are all advanced using a Runge-Kutta formula in time. Near shocks, a second difference is added as an artificial viscosity. This reduces the scheme to a first order upwind scheme at shocks. The switch that is used guarantees that the scheme is locally total variation diminishing (TVD). For steady state problems it is usually advantageous to relax this condition. Then small oscillations do not activate the switches and the convergence to a steady state is improved. To sharpen the shocks, different coefficients are needed for different equations and so a matrix valued dissipation is introduced and compared with the scalar viscosity. The connection between this artificial viscosity and flux limiters is shown. Any flux limiter can be used as the basis of a shock detector for an artificial viscosity. We compare the use of the van Leer, van Albada, mimmod, superbee, and the 'average' flux limiters for this central difference scheme. For time dependent problems, we need to use a small enough time step so that the CFL was less than one even though the scheme was linearly stable for larger time steps. Using a total variation bounded (TVB) Runge-Kutta scheme yields minor improvements in the accuracy.

A capability for modeling ice crystals and mixed phase icing has been added to GlennICE. Modifications have been made to the particle trajectory algorithm and energy balance to model this behavior. This capability has been added as part of a larger effort to model ice crystal ingestion in aircraft engines. Comparisons have been made to four mixed phase ice accretions performed in the Cox icing tunnel in order to calibrate an ice erosion model. A sample ice ingestion case was performed using the Energy Efficient Engine (E3) model in order to illustrate current capabilities. Engine performance characteristics were supplied using the Numerical Propulsion System Simulation (NPSS) model for this test case.

In the authors previous studies [1], a time-accurate, upwind finite volume method (ETAU scheme) for computing compressible flows on unstructured grids was proposed. The scheme is second order accurate in space and time and yields high resolution in the presence of discontinuities. The scheme features a multidimensional limiter and multidimensional numerical dissipation. These help to stabilize the numerical process and to overcome the annoying pathological behaviors of upwind schemes. In the present paper, it will be further shown that such multidimensional treatments also lead to a nearly all-speed or Mach number insensitive upwind scheme. For flows at very high Mach number, e.g., 10, local numerical instabilities or the pathological behaviors are suppressed, while for flows at very low Mach number, e.g., 0.02, computation can be directly carried out without invoking preconditioning. For flows in different Mach number regimes, i.e., low, medium, and high Mach numbers, one only needs to adjust one or two parameters in the scheme. Several examples with low and high Mach numbers are demonstrated in this paper. Thus, the ETAU scheme is applicable to a broad spectrum of flow regimes ranging from high supersonic to low subsonic, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics).

In the context of the space-time conservation element and solution element method, a simple numerical procedure for solving hyperbolic conservation laws with stiff source terms is described. The accuracy of this non-upwinding procedure is verified using a problem involving ZND detonation waves.

A time-accurate, upwind, finite volume method for computing compressible flows on unstructured grids is presented. The method is second order accurate in space and time and yields high resolution in the presence of discontinuities. For efficiency, the Roe approximate Riemann solver with an entropy correction is employed. In the basic Euler/Navier-Stokes scheme, many concepts of high order upwind schemes are adopted: the surface flux integrals are carefully treated, a Cauchy-Kowalewski time-stepping scheme is used in the time-marching stage, and a multidimensional limiter is applied in the reconstruction stage. However even with these up-to-date improvements, the basic upwind scheme is still plagued by the so-called "pathological behaviors," e.g., the carbuncle phenomenon, the expansion shock, etc. A solution to these limitations is presented which uses a very simple dissipation model while still preserving second order accuracy. This scheme is referred to as the enhanced time-accurate upwind (ETAU) scheme in this paper. The unstructured grid capability renders flexibility for use in complex geometry; and the present ETAU Euler/Navier-Stokes scheme is capable of handling a broad spectrum of flow regimes from high supersonic to subsonic at very low Mach number, appropriate for both CFD (computational fluid dynamics) and CAA (computational aeroacoustics). Numerous examples are included to demonstrate the robustness of the methods.

A high-Reynolds-number, subsonic coannular jet is simulated, using a three-dimensional finite-volume LES method, with emphasis on the near field noise. The nozzle geometry used is the NASA Glenn 3BB baseline model. The numerical results are generally in good agreement with existing experimental findings.

The space-time conservation element and solution element method is employed to numerically study the acoustic feedback system in a high temperature, high speed wind tunnel mixer. The computation captures the self-sustained feedback loop between reflecting Mach waves and the shear layer. This feedback loop results in violent instabilities that are suspected of causing damage to some tunnel components. The computed frequency is in good agreement with the available experimental data. The physical phenomena are explained based on the numerical results.

An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.

The space-time conservation element and solution element (CE/SE) method is used to solve the conservation law form of the compressible axisymmetric Navier-Stokes equations. The equations are time marched to predict the unsteady flow and the near-field screech tone noise issuing from an underexpanded circular jet. The CE/SE method uses an unstructured grid based data structure. The unstructured grids for these calculations are generated based on the method of Delaunay triangulation. The purpose of this paper is to show that an acoustics solution with a feedback loop can be obtained using truly unstructured grid technology. Numerical results are presented for two different nozzle geometries. The first is considered to have a thin nozzle lip and the second has a thick nozzle lip. Comparisons with available experimental data are shown for flows corresponding to several different jet Mach numbers. Generally good agreement is obtained in terms of flow physics, screech tone frequency, and sound pressure level.

In the present paper, we report high-fidelity CFD simulation of plume dynamics of a pulse detonation engine (PDE) by using modern parallel computer architecture. The two-dimensional axisymmetric Euler equations for reacting flows are solved by the Space-Time CESE method. A one-step global reaction is employed to model chemical reactions of a propane/air mixture. Computational domain includes the interior of the detonation tube and the aft quadrants of the PDE up to 12 feet in the axial direction and 4.5 feet in the radial direction. Numerical results of averaged pressures oscillation and the wave speeds compare well with the experimental data. For the required numerical resolution, we used a Beowulf cluster with the channel bonding. Our experience in using the system is summarized in the present paper.

This paper reports preliminary numerical results of plume dynamics for a pulse detonation engine (PDE). The space-time CE/SE method was used to solve the two-dimensional and axisymmetric Euler equations in conjunction with one chemical species equation in a time-accurate manner. Chemical reactions are simulated by a one-step, irreversible, finite rate model. The stiff source term in the species equation is treated by a point-wise implicit method based on a space-time volumetric integration of the source term over each CE. Numerical results show complex vortex/shock interactions in the vicinity of the thruster exit. Away from the PDE tube, spherical expansion of sound waves is evident. Although a much finer mesh will be needed to further resolve the relevant flow physics, the present results provide an encouraging first step toward the analysis of this challenging computational aeroacoustics problem.

The space-time conservation element and solution element (CE/SE) method is employed to numerically study the near-field axisymmetric screech-tone noise of a typical underexpanded circular jet issuing from a sonic nozzle. For the computed cases, corresponding to fully expanded Mach numbers of 1.10, 1.15 and 1.19, the self-sustained feedback loop is automatically established. The computed shock-cell structure, acoustic wave length, screech tone frequencies, and sound pressure levels are in good agreement with experimental results.

Recently, an unstructured three-dimensional space-time conservation element and solution element (CE/SE) Euler solver was developed. Now it is also developed for parallel computation using METIS for domain decomposition and MPI (message passing interface). The method is employed here to numerically study the near-field of a typical 3-D rectangular under-expanded jet. For the computed case-a jet with Mach number Mj = 1.6. with a very modest grid of 1.7 million tetrahedrons, the flow features such as the shock-cell structures and the axis switching, are in good qualitative agreement with experimental results.

It is well known that due to vortex shedding in high speed flow over cutouts, cavities, and gaps, intense noise may be generated. Strong tonal oscillations occur in a feedback cycle in which the vortices shed from the upstream edge of the cavity convect downstream and impinge on the cavity lip, generating acoustic waves that propagate upstream to excite new vortices. Numerical simulation of such a complicated process requires a scheme that can: (1) resolve acoustic waves with low dispersion and numerical dissipation, (2) handle nonlinear and discontinuous waves (e.g. shocks), and (3) have an effective (near field) nonreflecting boundary condition (NRBC). The new space time conservation element and solution element method, or CE/SE for short, is a numerical method that meets the above requirements.

This paper describes the parallelization strategy and achieved parallel efficiency of an explicit time-marching algorithm for solving conservation laws. The Space- Time Conservation Element and Solution Element (CE/SE) algorithm for solving the 2D and 3D Euler equations is parallelized with the aid of domain decomposition. The parallel efficiency of the resultant algorithm on a Silicon Graphics Origin 2000 parallel computer is checked.

The space-time conservation element and solution element (CE/SE) method is used to solve an aeroacoustic benchmark problem regarding turbomachinery noise. It concerns the aeroacoustic field generated by the interaction of a convected gust with a 2D cascade of flat-plate airfoils with a downstream moving grid. This tests the accuracy of a numerical method and the ability to model the acoustic wave and the gust across a sliding interface typical of those used in rotor stator interaction problems. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. The comparison shows that the CE/SE method is capable of producing accurate solutions in a simple manner.

In this paper, the space-time conservation element solution element (CE/SE) method is tested in the classical axisymmetric jet instability problem, rendering good agreement with the linear theory. The CE/SE method is then applied to numerical simulations of several nearly fully expanded axisymmetric jet flows and their noise fields and qualitative agreement with available experimental and theoretical results is demonstrated.

The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.

In this paper, we report an extension of the Space-Time Conservation Element and Solution Element (CE/SE) Method for solving the Navier-Stokes equations. Numerical algorithms for both structured and unstructured meshes are developed. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, a new and unified boundary-condition treatment for solid wall is introduced. The Navier Stokes solvers retain all favorable features of the original CE/SE method for the Euler equations, including high fidelity resolution of unsteady flows, easy implementation of nonreflective boundary conditions, and simplicity of computational logic. In addition, numerical results show that the present Navier-Stokes solvers can be used for high-speed flows as well as low-Mach-number flows without preconditioning. The present Navier Stokes solvers are efficient, accurate, and very robust for flows at all speeds.

The benchmark problems in Category 1 (Internal Propagation) of the third Computational Aeroacoustics (CAA) Work-shop sponsored by NASA Glenn Research Center are solved using the space-time conservation element and solution element (CE/SE) method. The first problem addresses the propagation of sound waves through a nearly choked transonic nozzle. The second one concerns shock-sound interaction in a supersonic nozzle. A quasi one-dimension CE/SE Euler solver for a nonuniform mesh is developed and employed to solve both problems. Numerical solutions are compared with the analytical solution for both problems. It is demonstrated that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple way. Furthermore, the simple nonreflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well.

In this paper, we report a variation of Chang’s SpaceTime Conservation Element and Solution Element CE/SE Method for structured mesh. The algorithm of the present modified CE/SE method is even simpler than the original CE/SE method. Nevertheless, all advantageous features of the original CE/SE method have been retained, including a unified treatment of space and time, accurate calculation of the space-time flux, high-fidelity resolution of unsteady flow motions, and full compliance with the physics of initial valued problems. The present modified method is also extended to solve Navier Stokes equations. To calculate the viscous flux terms, a ‘midpoint rule’ is used. In the setting of space-time flux conservation, two boundary-condition treatments for solid wall are introduced. Numerical results show that the present Navier Stokes solver can be used for high-speed flows as well as low-Mach-number flows without preconditioning. Results of several standard flow problems show that the present method is efficient and accurate.

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.

The space-time conservation element solution element (CEASE) method is employed to numerically study several vortex dynamics problems in aeroacoustics. The scheme possesses low dispersion error and the implementation of non-reflecting boundary conditions is simple and effective. The scheme is advantageous for vorticity computation since the spatial derivatives of the flow variables are computed as an integral part of the solution, i.e. no further numerical differentiation with associated loss of accuracy is needed. The scheme is tested for several nonlinear vortex-shock and vortexblade problems to demonstrate its robustness. The method is found to be valuable for vortex simulation as well as computational aeroacaustics.

In the present paper, we report numerical calculations of stable and unstable ZND detonation waves by the method of Space-Time Conservation Element and Solution Element. Due to the finite-rate chemistry employed in the ZND model, a source term exists in the species equation, which is solved in conjunction with the continuity, momentum, and energy equations. In the context of the space-time method, a treatment for the stiff source term based on a volumetric integration over a space-time region is developed. As a contrast to the modern upwind schemes, no modulated Riemann solver or splitting method is used, thus the logic of the present scheme is much simpler. Nevertheless, unstable detonation waves can be accurately captured by using only five mesh nodes per half reaction length. Numerical accuracy of the present method is assessed by detailed comparisons between the theoretical solutions and the numerical results for both stable and unstable ZND waves.

An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.

In this paper, the algorithm for determining the stencil of a one-dimensional Essentially Nonoscillatory (ENO) reconstruction scheme on a uniform grid is reinterpreted as being based on extrapolation. This view leads to another extension of ENO reconstruction schemes to two-dimensional unstructured triangular meshes. The key idea here is to select several cells of the stencil in one step based on extrapolation rather than one cell at a time. Numerical experiments confirm that the new scheme yields sharp nonoscillatory reconstructions and that it is about five times faster than previous schemes.

A quasi-three-dimensional rotor/stator analysis has been developed for blade-to-blade flows in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant timestep. Results are shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Euler and Navier-Stokes results are compared on the scaled single- and multi-passage machine. The method is relatively fast and the quasi-three-dimensional formulation is applicable to a wide range of turbomachinery geometries.

A quasi-three dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.