Comparison of Two Methods for Sensitivity Analysis of Compressor Blades

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Robin Schmidt ◽  
Matthias Voigt ◽  
Konrad Vogeler ◽  
Marcus Meyer
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Polynomial Regression ◽  
Optical Measurement ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Sampling Strategy ◽  
Initial Flow ◽  
Efficient Sampling ◽  
The Impact

This paper will compare two approaches of sensitivity analysis, namely (i) the adjoint method which is used to obtain an initial estimate of the geometric sensitivity of the gas-washed surfaces to aerodynamic quantities of interest and (ii) a Monte Carlo type simulation with an efficient sampling strategy. For both approaches, the geometry is parameterized using a modified NACA parameterization. First, the sensitivity of those parameters is calculated using the linear (first-order) adjoint model. Since the effort of the adjoint computational fluid dynamics (CFD) solution is comparable to that of the initial flow CFD solution and the sensitivity calculation is simply a postprocessing step, this approach yields fast results. However, it relies on a linear model which may not be adequate to describe the relationship between relevant aerodynamic quantities and actual geometric shape variations for the derived amplitudes of shape variations. Second, in order to better capture nonlinear and interaction effects, a Monte Carlo type simulation with an efficient sampling strategy is used to carry out the sensitivity analysis. The sensitivities are expressed by means of the coefficient of importance (CoI), which is calculated based on modified polynomial regression and therefore able to describe relationships of higher order. The methods are applied to a typical high-pressure compressor (HPC) stage. The impact of a variable rotor geometry is calculated by three-dimensional (3D) CFD simulations using a steady Reynolds-averaged Navier–Stokes model. The geometric variability of the rotor is based on the analysis of a set of 400 blades which have been measured using high-precision 3D optical measurement techniques.

Comparison of Two Methods for Sensitivity Analysis of Compressor Blades

2016 ◽  
Author(s):  
Robin Schmidt ◽  
Matthias Voigt ◽  
Konrad Vogeler ◽  
Marcus Meyer
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Polynomial Regression ◽  
Optical Measurement ◽  
Measurement Techniques ◽  
Sampling Strategy ◽  
Compressor Blades ◽  
Initial Flow ◽  
Efficient Sampling ◽  
The Impact

This paper will compare two approaches of sensitivity analysis, namely (i) the adjoint method which is used to obtain an initial estimate of the geometric sensitivity of the gas-washed surfaces to aerodynamic quantities of interest and (ii) a Monte Carlo-type simulation with an efficient sampling strategy. For both approaches the geometry is parameterized using a modified NACA parameterization. First the sensitivity of those parameters is calculated using the linear (first order) adjoint model. Since the effort of the adjoint CFD solution is comparable to that of the initial flow CFD solution and the sensitivity calculation is simply a postprocessing step, this approach yields fast results. However, it relies on a linear model which may not be adequate to describe the relationship between relevant aerodynamic quantities and actual geometric shape variations for the derived amplitudes of shape variations. In order to better capture nonlinear and interaction effects, secondly a Monte Carlo-type simulation with an efficient sampling strategy is used to carry out the sensitivity analysis. The sensitivities are expressed by means of the Coefficient of Importance, which is calculated based on modified polynomial regression and therefore able to describe relationships of higher order. The methods are applied to a typical high pressure compressor stage. The impact of a variable rotor geometry is calculated by 3D CFD simulations using a steady RANS model. The geometric variability of the rotor is based on the analysis of a set of 400 blades which have been measured using high-precision 3D optical measurement techniques.

A quasi-Monte Carlo statistical three-dimensional tolerance analysis method of products based on edge sampling

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chuanyuan Zhou ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Jianrong Tan
Keyword(s):  
Monte Carlo ◽  
Three Dimensional ◽  
Sampling Strategy ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Content Type ◽  
Dimensional Tolerance ◽  
Quasi Monte Carlo ◽  
Edge Sampling ◽  
The Impact

Purpose The conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems. Design/methodology/approach With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements. Findings The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously. Research limitations/implications The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model. Practical implications The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection. Originality/value The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

Design of the Purdue Experimental Turbine Aerothermal Laboratory for Optical and Surface Aero-Thermal Measurements

2016 ◽  
Author(s):  
G. Paniagua ◽  
D. Cuadrado ◽  
J. Saavedra ◽  
V. Andreoli ◽  
T. Meyer ◽  
...  
Keyword(s):  
Test Section ◽  
Structural Engineering ◽  
Optical Measurement ◽  
Pressure Ratio ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Large Mass ◽  
Modern Technology ◽  
Computational Fluid Mechanics ◽  
Test Duration

Following three decades of research in short duration facilities, Purdue University has developed an alternative turbine facility in view of the modern technology in computational fluid mechanics, structural analysis, manufacturing, heating, control and electronics. The proposed turbine facility can perform both short transients and long duration tests, suited for precise heat flux, efficiency and optical measurement techniques to advance turbine aero-thermo-structural engineering. The facility has two different test sections, linear and annular, to service both fundamental and applied research. The linear test section is completely transparent for visible spectra, aimed at TRL 1 and 2. The annular test section was designed with optical access to perform proof of concepts as well as validation of turbine components at the relevant non-dimensional parameters in small engine cores, TRL 3 to 4. The large mass flow (28 kg/s) combined with a minimum hub radius to tip radius of 0.85 allows high spatial resolution. The Reynolds (Re) number extends from 60,000 to 3,000,000, based on the vane outlet flow with an axial chord of 0.06 m and a turning angle of 72 deg. The pressure ratio can be independently adjusted, allowing for testing from low subsonic to Mach 3.2. To ensure that the thermal boundary layer is fully developed the test duration can range from milliseconds to minutes. The manuscript provides a detailed description of the sequential design methodology from zero-dimensional to three-dimensional unsteady analysis as well as of the measurement techniques available in this turbine facility.

Vortex Tracking of Purge-Mainstream Interactions in a Rotating Turbine Stage

2021 ◽  
Author(s):  
Alex W. Mesny ◽  
Mark A. Glozier ◽  
Oliver J. Pountney ◽  
James A. Scobie ◽  
Yan Sheng Li ◽  
...  
Keyword(s):  
Secondary Flow ◽  
Gas Turbines ◽  
Optical Measurement ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Horseshoe Vortex ◽  
Suction Surface ◽  
Vortex Filaments ◽  
Passage Vortex ◽  
Purge Flow

Abstract The use of purge flow in gas turbines allows for high turbine entry temperatures, which are essential to produce high cycle efficiency. Purge air is bled from the compressor and reintroduced in the turbine to cool vulnerable components. Wheel-spaces are formed between adjacent rotating and stationary discs, with purge air supplied at low radius before exiting into the mainstream gas-path through a rim-seal at the disc periphery. An aerodynamic penalty is incurred as the purge flow egress interacts with the mainstream. This study presents unparalleled three-dimensional velocity data from a single-stage turbine test rig, specifically designed to investigate egress-mainstream interaction using optical measurement techniques. Volumetric Velocimetry is applied to the rotating environment with phase-locked measurements used to identify and track the vortical secondary flow features through the blade passage. A baseline case without purge flow is compared to experiments with a 1.7% purge mass fraction; the latter was chosen to ensure a fully sealed wheel-space. A non-localised vortex tracking function is applied to the data to identify the position of the core centroids. The strength of the secondary-flow vortices was determined by using a circulation criterion on rotated planes aligned to the vortex filaments. The pressure-side leg of the horseshoe vortex and a second vortex associated with the egress flow were identified by the experimental campaign. In the absence of purge flow the two vortices merged, forming the passage vortex. With the addition of purge flow, the two cores remained independent to 40% of the blade axial chord, while also demonstrating an increased radial migration and intensification of the passage vortex. The egress core was shown to remain closer to the suction-surface with purge flow. Importantly, where the vortex filaments demonstrated strong radial or tangential components of velocity, the circulation level calculated from axial planes underpredicted the true circulation by up to 50%.

Pathomechanics and gait analysis

2019 ◽  
pp. 227-248
Author(s):  
Graham Chapman ◽  
Philip Helliwell
Keyword(s):  
Gait Analysis ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Clinical History ◽  
Joint Disease ◽  
Core Knowledge ◽  
Analysis Techniques ◽  
Physical Treatments ◽  
And Function ◽  
The Impact

Gait analysis is the systematic study of human walking. This chapter summarizes currently available gait analysis techniques that are available to the clinician and researcher. Gait analysis can be used alongside clinical history and examination and other special investigations to gain a better understanding of the relationship between joint disease, impairment, and compensatory gait mechanisms. Abnormal pathology leads to abnormal biomechanics, and tools that demonstrate these changes can lead to insights into the effects of the disease on function, in disease progression, and the impact of physical treatments. Plantar pressure measurement techniques yield valuable information on structure and function and are probably the most likely tool to be used in clinical practice. Three-dimensional joint kinematic and kinetic analyses are more difficult to perform and interpret and are likely to remain largely research tools. Gait analysis techniques will drive experimental work to further advance core knowledge and inform future development of customized approaches to conservative therapies such as footwear and orthosis manufacture, as well as foot surgery.

Impact of Swirl Flow on the Penetration Behaviour and Cooling Performance of a Starter Cooling Film in Modern Lean Operating Combustion Chambers

2014 ◽  
Author(s):  
B. Wurm ◽  
A. Schulz ◽  
H.-J. Bauer ◽  
M. Gerendas
Keyword(s):  
Optical Measurement ◽  
Measurement Techniques ◽  
Swirl Flow ◽  
Main Flow ◽  
Heat Shield ◽  
Fuel Injector ◽  
Combustion Chambers ◽  
Cooling Performance ◽  
The Impact ◽  
Penetration Behaviour

An experimental and numerical study is presented that deals with the impact of the swirled hot gas main flow on the penetration behaviour and cooling performance of a starter cooling film. Within modern combustion chambers designed for lean combustion the whole fuel/air mixing process is done by the fuel injectors without any additional mixing ports. Typically swirl stabilization is used within this kind of combustion chambers. The swirl flow interacts in a particular way with near wall cooling flows like starter cooling films which assure a proper wall cooling near the fuel injector. Experiments without combustion show the impact of the swirled main flow on the stability of the starter cooling film. Thermal analyses reveal a reduced cooling performance of the starter film near the stagnation area of the swirl flow. Laser optical measurement techniques reveal a significant reduced penetration of the starter cooling film close to the stagnation area. Numerical simulations show the reason for the reduced starter film performance in areas which cannot be accessed by optical measurement techniques. Based on experimental and numerical data different adaptive hole geometries where tested in combination with heat shield ribs in order to improve the starter film cooling performance. Results show that the combined application of heat shield ribs and adaptive cooling holes stabilize the starter cooling film and lead to a homogenous cooling performance.

Monte Carlo Simulation of Radiative Heat Transfer in Rapid Thermal Processing (RTP) Systems

1994 ◽  
Vol 342 ◽  
Author(s):  
J. Vernon Cole ◽  
Karson L. Knutson ◽  
Klavs F. Jensen
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Thermal Processing ◽  
Measurement Techniques ◽  
Radiation Heat Transfer ◽  
Rapid Thermal Processing ◽  
Three Dimensional ◽  
General Purpose ◽  
Radiation Heat ◽  
Participating Media

ABSTRACTWe present a general purpose Monte Carlo method for the simulation of radiation heat transfer in rapid thermal processing (RTP) chambers. Three-dimensional mesh generation software is used to discretize the surfaces within the system, allowing the simulation of realistic chamber and reflector designs. An adaptive subdivision of the chamber geometry reduces the number of raysurface intersections which must be computed. The method models internal reflection, absorption, and transmission within participating media, and includes wavelength, temperature, and material dependent optical properties. Radiation heat transfer simulations are used to examine a reflector assembly, and to test the assumptions of optical wafer temperature measurement techniques.

Design of the Purdue Experimental Turbine Aerothermal Laboratory for Optical and Surface Aerothermal Measurements

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
G. Paniagua ◽  
D. Cuadrado ◽  
J. Saavedra ◽  
V. Andreoli ◽  
T. Meyer ◽  
...  
Keyword(s):  
Test Section ◽  
Structural Engineering ◽  
Optical Measurement ◽  
Pressure Ratio ◽  
Measurement Techniques ◽  
Three Dimensional ◽  
Large Mass ◽  
Modern Technology ◽  
Computational Fluid Mechanics ◽  
Imaging And Spectroscopy

Following three decades of research in short duration facilities, Purdue University has developed an alternative turbine facility in view of the modern technology in computational fluid mechanics, structural analysis, manufacturing, heating, control, and electronics. The proposed turbine facility can operate continuously and also perform transients, suited for precise heat flux, efficiency, and optical measurement techniques to advance turbine aerothermo-structural engineering. The facility has two different test sections, linear and annular, to service both fundamental and applied research. The linear test section is completely transparent for optical imaging and spectroscopy, aimed at technology readiness levels (TRLs) of 1–2. The annular test section was designed with optical access to perform proof of concepts as well as validation of turbine component performance for relevant nondimensional parameters at TRLs of 3–4. The large mass flow rate (28 kg/s) combined with a minimum hub to tip ratio of 0.85 allows high spatial resolution. The Reynolds number (Re) extends from 60,000 to 3,000,000, based on the vane outlet flow properties with an axial chord of 0.06 m and a turning angle of 72 deg. The pressure ratio can be independently adjusted, enabling testing from low subsonic to Mach 3.2. This paper provides a detailed description of the sequential design methodology from zero-dimensional to three-dimensional (3D) unsteady analysis as well as of the measurement techniques available in this turbine facility.

The Effect of Intrinsic Instabilities on Effective Flame Speeds in Under-Resolved Simulations of Lean Hydrogen–Air Flames

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Peter Katzy ◽  
Josef Hasslberger ◽  
Lorenz R. Boeck ◽  
Thomas Sattelmayer
Keyword(s):  
Flame Front ◽  
Optical Measurement ◽  
Initial Conditions ◽  
Measurement Techniques ◽  
Evaluation Methods ◽  
Line Of Sight ◽  
Flame Surface ◽  
Validation Data ◽  
Time Resolved ◽  
The Impact

The presented work aims to improve computational fluid dynamics (CFD) explosion modeling for lean hydrogen–air mixtures on under-resolved grids. Validation data are obtained from an entirely closed laboratory-scale explosion channel (GraVent facility). Investigated hydrogen–air concentrations range from 6 to 19 vol %. Initial conditions are p = 0.1 MPa and T = 293 K. Two highly time-resolved optical measurement techniques are applied simultaneously: (1) 10 kHz shadowgraphy captures line-of-sight integrated macroscopic flame propagation and (2) 20 kHz planar laser-induced fluorescence of the OH radical (OH-PLIF) resolves microscopic flame topology without line-of-sight integration. This paper presents the experiment, measurement techniques, data evaluation methods, and simulation results. The evaluation methods encompass the determination of flame tip velocity over distance and a detailed time-resolved quantification of the flame topology based on OH-PLIF images. One parameter is the length of wrinkled flame fronts in the OH-PLIF plane obtained through automated postprocessing. It reveals the expected enlargement of flame surface area by instabilities on a microscopic level. A strong effect of mixture composition is observed. Simulations based on the new model formulation, incorporating the microscopic enlargement of the flame front, show a promising behavior, where the impact of the augmented flame front on the observed flame front velocities can be detected.

Generalized Light Portals

2020 ◽  
Vol 3 (2) ◽  
pp. 1-19
Author(s):  
Shinji Ogaki
Keyword(s):  
Monte Carlo ◽  
Sampling Method ◽  
Sampling Strategy ◽  
Sampling Techniques ◽  
Two Dimensional ◽  
Multiple Importance Sampling ◽  
Path Tracing ◽  
Environment Map ◽  
Efficient Sampling ◽  
Polygon Meshes

Light portals are useful for accelerating the convergence of Monte Carlo path tracing when rendering interiors. However, they are generally limited to flat polygonal shapes. In this paper, we introduce a new concept that allows existing polygon meshes with arbitrary shaders in a scene to be used as generalized light portals. We also present an efficient sampling method that takes into account the pixel values of the environment map and ray guiding two-dimensional textures that are typically opacity or transparency maps. This novel sampling strategy can be combined with other sampling techniques by using multiple importance sampling.

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