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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Progress In Incompressible Pump Flow Calculations

Steady and unsteady flows for propulsion systems are efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard kappa - epsilon model equations. The resulting computer code is applied to the flow analysis inside an advanced rocket pump impeller in steadily rotating reference frames. Numerical results are compared with experimental measurements. The effects of exit and shroud cavities with the leak-age flow are investigated. Time-accurate incompressible Navier-Stokes formulation with the overlapped grid scheme capability was evaluated by using MIT flapping foil experiment. The grid dependency, turbulence model effects, and the effect of order of differencing were investigated. Numerical results were compared against experimental data. The resulting procedure were applied to unsteady flapping foil calculations. Two upstream NACA 0025 foils perform high frequency synchronized motion and generate unsteady flow conditions to the downstream larger stationary foil. Comparison between unsteady experimental data and numerical results from two different moving boundary procedures will be presented.

Kiris, Cetin↗
NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗
NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗
NASA NTRS1976

Structure of the atmosphere of Jupiter from Pioneer 10 and 11 radio occultation measurements

A technique for incorporating effects of the oblateness of Jupiter's atmosphere into the data analysis procedure for radio-occultation measurements is described which makes use of a spherical harmonic representation of the gravity field to compute the shape of the planet. With this technique, the center of refraction is located by the radius of curvature and the normal direction at the closest approach point of the ray. The present technique, a subsequent approximation involving the use of a constant center of refraction, and the Abel integral transform inversion method for spherical planets are applied to Pioneer 10 and 11 data. All the intermediate results obtained show a temperature inversion between 10 and 100 mb, with temperatures from 130 to 170 K at 10 mb and from 80 to 120 K at 100 mb. Comparison of the radio-occultation profiles with radiative-convective equilibrium models and the temperature profile based on Pioneer 10 IR radiometer data indicates good agreement between the models and the occultation results.

Kliore, A. J.↗
NASA NTRS1990

Trajectory optimization for an asymmetric launch vehicle

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Sullivan, Jeanne Marie↗
NASA NTRS1992

Experimental studies of characteristic combustion-driven flows for CFD validation

A series of rocket-related studies intended to develop a suitable data base for validation of Computational Fluid Dynamics (CFD) models of characteristic combustion-driven flows was undertaken at the Propulsion Engineering Research Center at Penn State. Included are studies of coaxial and impinging jet injectors as well as chamber wall heat transfer effects. The objective of these studies is to provide fundamental understanding and benchmark quality data for phenomena important to rocket combustion under well-characterized conditions. Diagnostic techniques utilized in these studies emphasize determinations of velocity, temperature, spray and droplet characteristics, and combustion zone distribution. Since laser diagnostic approaches are favored, the development of an optically accessible rocket chamber has been a high priority in the initial phase of the project. During the design phase for this chamber, the advice and input of the CFD modeling community were actively sought through presentations and written surveys. Based on this procedure, a suitable uni-element rocket chamber was fabricated and is presently under preliminary testing. Results of these tests, as well as the survey findings leading to the chamber design, were presented.

Santoro, R. J.↗
NASA NTRS1991

Efficient visual grasping alignment for cylinders

Monocular information from a gripper-mounted camera is used to servo the robot gripper to grasp a cylinder. The fundamental concept for rapid pose estimation is to reduce the amount of information that needs to be processed during each vision update interval. The grasping procedure is divided into four phases: learn, recognition, alignment, and approach. In the learn phase, a cylinder is placed in the gripper and the pose estimate is stored and later used as the servo target. This is performed once as a calibration step. The recognition phase verifies the presence of a cylinder in the camera field of view. An initial pose estimate is computed and uncluttered scan regions are selected. The radius of the cylinder is estimated by moving the robot a fixed distance toward the cylinder and observing the change in the image. The alignment phase processes only the scan regions obtained previously. Rapid pose estimates are used to align the robot with the cylinder at a fixed distance from it. The relative motion of the cylinder is used to generate an extrapolated pose-based trajectory for the robot controller. The approach phase guides the robot gripper to a grasping position. The cylinder can be grasped with a minimal reaction force and torque when only rough global pose information is initially available.

Nicewarner, Keith E.↗
NASA NTRS1992

Efficient visual grasping alignment for cylinders

Monocular information from a gripper-mounted camera is used to servo the robot gripper to grasp a cylinder. The fundamental concept for rapid pose estimation is to reduce the amount of information that needs to be processed during each vision update interval. The grasping procedure is divided into four phases: learn, recognition, alignment, and approach. In the learn phase, a cylinder is placed in the gripper and the pose estimate is stored and later used as the servo target. This is performed once as a calibration step. The recognition phase verifies the presence of a cylinder in the camera field of view. An initial pose estimate is computed and uncluttered scan regions are selected. The radius of the cylinder is estimated by moving the robot a fixed distance toward the cylinder and observing the change in the image. The alignment phase processes only the scan regions obtained previously. Rapid pose estimates are used to align the robot with the cylinder at a fixed distance from it. The relative motion of the cylinder is used to generate an extrapolated pose-based trajectory for the robot controller. The approach phase guides the robot gripper to a grasping position. The cylinder can be grasped with a minimal reaction force and torque when only rough global pose information is initially available.

Nicewarner, Keith E.↗
NASA NTRS1996

Observations Regarding Use of Advanced CFD Analysis, Sensitivity Analysis, and Design Codes in MDO

Observations regarding the use of advanced computational fluid dynamics (CFD) analysis, sensitivity analysis (SA), and design codes in gradient-based multidisciplinary design optimization (MDO) reflect our perception of the interactions required of CFD and our experience in recent aerodynamic design optimization studies using CFD. Sample results from these latter studies are summarized for conventional optimization (analysis - SA codes) and simultaneous analysis and design optimization (design code) using both Euler and Navier-Stokes flow approximations. The amount of computational resources required for aerodynamic design using CFD via analysis - SA codes is greater than that required for design codes. Thus, an MDO formulation that utilizes the more efficient design codes where possible is desired. However, in the aerovehicle MDO problem, the various disciplines that are involved have different design points in the flight envelope; therefore, CFD analysis - SA codes are required at the aerodynamic 'off design' points. The suggested MDO formulation is a hybrid multilevel optimization procedure that consists of both multipoint CFD analysis - SA codes and multipoint CFD design codes that perform suboptimizations.

Newman, Perry A.↗
NASA NTRS2000

ICEG2D: An Integrated Software Package for Automated Prediction of Flow Fields for Single-Element Airfoils with Ice Accretion

An integrated software package, ICEG2D, was developed to automate computational fluid dynamics (CFD) simulations for single-element airfoils with ice accretion. ICEG2D is designed to automatically perform three primary functions: (1) generating a grid-ready, surface definition based on the geometrical characteristics of the iced airfoil surface, (2) generating a high-quality grid using the generated surface point distribution, and (3) generating the input and restart files needed to run the general purpose CFD solver NPARC. ICEG2D can be executed in batch mode using a script file or in an interactive mode by entering directives from a command line. This report summarizes activities completed in the first year of a three-year research and development program to address issues related to CFD simulations for aircraft components with ice accretion. Specifically, this document describes the technology employed in the software, the installation procedure, and a description of the operation of the software package. Validation of the geometry and grid generation modules of ICEG2D is also discussed.

Thompson, David S.↗
NASA NTRS1988

Description of an oscillating flow pressure drop test rig

A test rig designed to generate heat exchanger pressure drop information under oscillating flow conditions is described. This oscillating flow rig is based on a variable stroke and variable frequency linear drive motor. A frequency capability of 120 hertz and a mean test pressure up to 15 mPA (2200 psi) allows for testing at flow conditions found in modern high specific power Stirling engines. An important design feature of this rig is that it utilizes a single close coupled dynamic pressure transducer to measure the pressure drop across the test sample. This eliminates instrumentation difficulties associated with the pressure sensing lines common to differential pressure transducers. Another feature of the rig is that it utilizes a single displacement piston. This allows for testing of different sample lengths and configurations without hardware modifications. All data acquisition and reduction for the rig is performed with a dedicated personal computer. Thus the overall system design efficiently integrates the testing and data reduction procedures. The design methodology and details of the test rig is described.

Wood, J. Gary↗
NASA NTRS1988

Description of an oscillating flow pressure drop test rig

A test rig designed to generate heat exchanger pressure drop information under oscillating flow conditions is described. This oscillating flow rig is based on a variable stroke and variable frequency linear drive motor. A frequency capability of 120 hertz and a mean test pressure up to 15 mPA (2200 psi) allows for testing at flow conditions found in modern high specific power Stirling engines. An important design feature of this rig is that it utilizes a single close coupled dynamic pressure transducer to measure the pressure drop across the test sample. This eliminates instrumentation difficulties associated with the pressure sensing lines common to differential pressure transducers. Another feature of the rig is that it utilizes a single displacement piston. This allows for testing of different sample lengths and configurations without hardware modifications. All data acquisition and reduction for the rig is performed with a dedicated personal computer. Thus the overall system design efficiently integrates the testing and data reduction procedures. The design methodology and details of the test rig are described.

Wood, J. Gary↗
NASA NTRS1996

Application of an Upwind High Resolution Finite-Differencing Scheme and Multigrid Method in Steady-State Incompressible Flow Simulations

The analysis and design of a submarine propulsor requires the ability to predict the characteristics of both laminar and turbulent flows to a higher degree of accuracy. This report presents results of certain benchmark computations based on an upwind, high-resolution, finite-differencing Navier-Stokes solver. The purpose of the computations is to evaluate the ability, the accuracy and the performance of the solver in the simulation of detailed features of viscous flows. Features of interest include flow separation and reattachment, surface pressure and skin friction distributions. Those features are particularly relevant to the propulsor analysis. Test cases with a wide range of Reynolds numbers are selected; therefore, the effects of the convective and the diffusive terms of the solver can be evaluated separately. Test cases include flows over bluff bodies, such as circular cylinders and spheres, at various low Reynolds numbers, flows over a flat plate with and without turbulence effects, and turbulent flows over axisymmetric bodies with and without propulsor effects. Finally, to enhance the iterative solution procedure, a full approximation scheme V-cycle multigrid method is implemented. Preliminary results indicate that the method significantly reduces the computational effort.

NAVIER STOKES EQUATIONS↗
NASA NTRS1985

Space motion sickness preflight adaptation training Preliminary studies with prototype trainers

Based on the otolith tilt-translation reinterpretation hypothesis (Parker et al., 1985), preflight adaptation procedures and several preflight adaptation trainers (PATs) have been developed. Two PAT prototypes, the Miami University Seesaw (MUS) and the Dynamic Environmental Simulator (DES), include a physical room that is moved relative to the restrained subject. Results from the MUS and DES PAT experiments indicate that exposure to the produced sensory rearrangement can change eye movement reflexes. The changes persisted for a period longer than the training exposure period, indicating similarity with the eye-movement reflexes observed immediately postflight in weightlessness-adapted astronauts. It is concluded that the apparatus and procedures to preadapt astronauts to the sensory rearrangement of weightless space flight can be developed on the basis of the reported PATs and procedures. The third PAT prototype tested, which employs a computer-generated scene, failed to produce changes similar to those recorded in the MUS and DES experiments.

Parker, D. E.↗
NASA NTRS1992

Grid generation and flow solution method for Euler equations on unstructured grids

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.

Anderson, W. Kyle↗
NASA NTRS1997

External Boundary Conditions for Three-Dimensional Problems of Computational Aerodynamics

We consider an unbounded steady-state flow of viscous fluid over a three-dimensional finite body or configuration of bodies. For the purpose of solving this flow problem numerically, we discretize the governing equations (Navier-Stokes) on a finite-difference grid. The grid obviously cannot stretch from the body up to infinity, because the number of the discrete variables in that case would not be finite. Therefore, prior to the discretization we truncate the original unbounded flow domain by introducing some artificial computational boundary at a finite distance of the body. Typically, the artificial boundary is introduced in a natural way as the external boundary of the domain covered by the grid. The flow problem formulated only on the finite computational domain rather than on the original infinite domain is clearly subdefinite unless some artificial boundary conditions (ABC's) are specified at the external computational boundary. Similarly, the discretized flow problem is subdefinite (i.e., lacks equations with respect to unknowns) unless a special closing procedure is implemented at this artificial boundary. The closing procedure in the discrete case is called the ABC's as well. In this paper, we present an innovative approach to constructing highly accurate ABC's for three-dimensional flow computations. The approach extends our previous technique developed for the two-dimensional case; it employs the finite-difference counterparts to Calderon's pseudodifferential boundary projections calculated in the framework of the difference potentials method (DPM) by Ryaben'kii. The resulting ABC's appear spatially nonlocal but particularly easy to implement along with the existing solvers. The new boundary conditions have been successfully combined with the NASA-developed production code TLNS3D and used for the analysis of wing-shaped configurations in subsonic (including incompressible limit) and transonic flow regimes. As demonstrated by the computational experiments and comparisons with the standard (local) methods, the DPM-based ABC's allow one to greatly reduce the size of the computational domain while still maintaining high accuracy of the numerical solution. Moreover, they may provide for a noticeable increase of the convergence rate of multigrid iterations.

Tsynkov, Semyon V.↗
NASA NTRS2001

On-Orbit Calibration of Redundant Spacecraft Gyros by Optimal Reduction to Three Axes

The Aqua spacecraft will carry four single-axis gyros configured with three orthogonal axes and one skew axis. This redundancy presents a challenge for batch methods of on-orbit gyro calibration that use a spacecraft rotation model deterministically related to gyro data, in that sensor data can respond to at most three angular velocity components. When the number of gyros, N, is greater than 3, the 3xN matrix, G, that reduces the N gyro measurements to three body-frame angular-velocity components cannot be fully determined by such methods; there are many such matrices that produce essentially the same angular velocity history. In such a case, spacecraft operators require information about the Nx3 gyro linear response matrix, R, that relates gyro outputs to the body-frame angular velocities causing them. This matrix provides sufficient information to determine multiple reduced-dimension G-matrices for use in case of failure or degradation of one or more gyros, as well as to determine an optimal 3xN G for the fully-functional configuration. A viable proposal is to apply a 3xN pre-filter matrix, F, to the N gyro outputs before carrying out a conventional gyro calibration procedure. The angular-velocity history emerging from conventional calibration may then be used as input data, together with the same gyro data that generated it, to fit the alignment, scale-factor, and bias parameters of each gyro axis in turn. A difficulty of such a proposal is the arbitrariness in the choice of F. Due to gyro noise, different pre-filter matrices produce different calibrations. This paper presents a method of choosing F that is based on optimizing gyro consistency in the limit of infinite weight on gyro data, as compared to sensor data. The choice of F is independent of a priori alignment and is based on the gyro data alone. The method is applicable to any N of three or more, but reduces to conventional batch-estimation methodologies when N = 3. Results of computational comparison among calibration simulations using various choices of F will be presented for the Aqua gyro configuration with N = 4.

Radomski, M. S.↗
NASA NTRS2012

Development and Applications of a Stage Stacking Procedure

The preliminary design of multistage axial compressors in gas turbine engines is typically accomplished with mean-line methods. These methods, which rely on empirical correlations, estimate compressor performance well near the design point, but may become less reliable off-design. For land-based applications of gas turbine engines, off-design performance estimates are becoming increasingly important, as turbine plant operators desire peaking or load-following capabilities and hot-day operability. The current work develops a one-dimensional stage stacking procedure, including a newly defined blockage term, which is used to estimate the off-design performance and operability range of a 13-stage axial compressor used in a power generating gas turbine engine. The new blockage term is defined to give mathematical closure on static pressure, and values of blockage are shown to collapse to curves as a function of stage inlet flow coefficient and corrected shaft speed. In addition to these blockage curves, the stage stacking procedure utilizes stage characteristics of ideal work coefficient and adiabatic efficiency. These curves are constructed using flow information extracted from computational fluid dynamics (CFD) simulations of groups of stages within the compressor. Performance estimates resulting from the stage stacking procedure are shown to match the results of CFD simulations of the entire compressor to within 1.6% in overall total pressure ratio and within 0.3 points in overall adiabatic efficiency. Utility of the stage stacking procedure is demonstrated by estimation of the minimum corrected speed which allows stable operation of the compressor. Further utility of the stage stacking procedure is demonstrated with a bleed sensitivity study, which estimates a bleed schedule to expand the compressors operating range.

Kulkarni, Sameer↗