Time-Harmonic 2D and 3D Gust-Airfoil Interactions: Comparison of Numerical Predictions with Analytical Models

AbstractA series of wave basin experiments is reported that investigates the flexural response of one or two floating thin elastic discs to monochromatic waves. The work is motivated by numerical model validation. Innovative techniques are used to ensure the experimental configuration is consistent with the model. This demands linear motions, time-harmonic conditions, homogeneity of the plate and the restriction of horizontal motions of the disc or discs. An optical remote sensing device is employed to record the deflection of the discs accurately. Tests involving a single disc and two discs are conducted for a range of disc thicknesses, incident wave steepnesses, frequencies and, in the case of two discs, geometrical arrangements. A data processing technique is used to decompose the raw data into its spectral harmonics and filter the higher-order components. Pointwise comparisons of the linear first-order component of the experimental deflection with numerical predictions are presented. Satisfying agreement is found, although the model consistently over predicts the deflection. Disc–disc interactions are observed in the two-disc tests. A brief discussion of the shortcomings of the pointwise analysis, with associated possible sources of discrepancy, provides a link to the study reported in Part 2 (Montiel et al. J. Fluid Mech., vol. 723, 2013, pp. 629–652).

Download Full-text

Comparison of Three Analytical Methods for the Precise Calculation of Cogging Torque and Torque Ripple in Axial Flux PM Machines

Mathematical Problems in Engineering ◽

10.1155/2016/2171547 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 6

Author(s):

Ahmed Hemeida ◽

Bert Hannon ◽

Hendrik Vansompel ◽

Peter Sergeant

Keyword(s):

Permanent Magnet ◽

Lateral Force ◽

Torque Ripple ◽

Analytical Models ◽

Permanent Magnet Synchronous Machines ◽

Axial Flux ◽

Cogging Torque ◽

Precise Calculation ◽

Analytical Tools ◽

2D And 3D

A comparison between different analytical and finite-element (FE) tools for the computation of cogging torque and torque ripple in axial flux permanent-magnet synchronous machines is made. 2D and 3D FE models are the most accurate for the computation of cogging torque and torque ripple. However, they are too time consuming to be used for optimization studies. Therefore, analytical tools are also used to obtain the cogging torque and torque ripple. In this paper, three types of analytical models are considered. They are all based on dividing the machine into many slices in the radial direction. One model computes the lateral force based on the magnetic field distribution in the air gap area. Another model is based on conformal mapping and uses complex Schwarz Christoffel (SC) transformations. The last model is based on the subdomain technique, which divides the studied geometry into a number of separate domains. The different types of models are compared for different slot openings and permanent-magnet widths. One of the main conclusions is that the subdomain model is best suited to compute the cogging torque and torque ripple with a much higher accuracy than the SC model.

Download Full-text

Evaluation of Localized Necking Models for Fracture Prediction in Punch-Loaded Steel Panels

Journal of Marine Science and Engineering ◽

10.3390/jmse9020117 ◽

2021 ◽

Vol 9 (2) ◽

pp. 117

Author(s):

Burak Can Cerik ◽

Kangsu Lee ◽

Joonmo Choung

Keyword(s):

Mesh Size ◽

Fracture Initiation ◽

Analytical Models ◽

Original Form ◽

Proportional Loading ◽

Stiffened Panels ◽

Shell Elements ◽

Localized Necking ◽

Numerical Predictions ◽

Steel Panels

This study compared the experimental test results on punch-loaded unstiffened and stiffened panels with numerical predictions using different localized necking modeling approaches with shell elements. The analytical models that were derived by Bressan–Williams–Hill (BWH) were used in their original form and extended version, which considers non-proportional loading paths while using the forming-severity concept and bending-induced suppression of through-thickness necking. The results suggest that the mesh size sensitivity depends on the punch geometry. Moreover, the inclusion of bending effects and the use of the forming-severity concept in the BWH criterion yielded improved estimations of fracture initiation with shell elements.

Download Full-text

The effects of heterogeneous mechanical properties on the response of a ductile material

Scientific Reports ◽

10.1038/s41598-021-97495-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Yichi Song ◽

Andreas Schiffer ◽

Vito L. Tagarielli

Keyword(s):

Mechanical Properties ◽

Scaling Law ◽

Heterogeneous Material ◽

Small Strain ◽

Analytical Models ◽

Elastic Response ◽

Ductile Material ◽

Numerical Predictions ◽

Yield Behaviour ◽

Computational Homogenisation

AbstractWe investigate numerically the small-strain, elastic–plastic response of statistically isotropic materials with non-uniform spatial distributions of mechanical properties. The numerical predictions are compared to simple bounds derived analytically. We explore systematically the effects of heterogeneity on the macroscopic stiffness, strength, asymmetry, stability and size dependence. Monte Carlo analyses of the response of statistical volume elements are conducted at different strain triaxiality using computational homogenisation, and allow exploring the macroscopic yield behaviour of the heterogeneous material. We illustrate quantitatively how the pressure-sensitivity of the yield surface of the solid increases with heterogeneity in the elastic response. We use the simple analytical models developed here to derive an approximate scaling law linking the fatigue endurance threshold of metallic alloys to their stiffness, yield strength and tensile strength.

Download Full-text

Integrally Bladed Rotor Mistuning Identification and Model Updating Using Geometric Mistuning Models

Volume 11: Structures and Dynamics: Structural Mechanics, Vibration, and Damping; Supercritical CO2 ◽

10.1115/gt2020-15539 ◽

2020 ◽

Author(s):

Joseph A. Beck ◽

Jeffrey M. Brown ◽

Daniel L. Gillaugh ◽

Emily B. Carper ◽

Alex A. Kaszynski

Keyword(s):

Elastic Modulus ◽

Model Updating ◽

Element Model ◽

Analytical Models ◽

Optical Scanners ◽

Reduced Order ◽

Optical Scanning ◽

Numerical Predictions ◽

Simulated Test ◽

Bladed Rotor

Abstract Non-uniform manufacturing variations and uneven usage wear and damage, referred to as mistuning, can drastically alter the dynamic response of Integrally Blade Rotors (IBR)s. Optical scanners, combined with Finite Element Model (FEM) mesh metamorphosis algorithms, have provided capabilities to create analytical models that reduce the effect of geometrical uncertainties in numerical predictions. However, deviations in material properties cannot be obtained via optical scanning, so additional approaches are needed. A geometric mistuning Reduced-Order Model (ROM) is developed and modified to solve for unknown IBR sector eigenvalues that are linearly proportional to Elastic modulus. The developed approach accounts for both proportional and non-proportional mistuning and allows updating of the Elastic modulus for each sector in the ROM. Different tuned and mistuned modal reduction procedures are employed to understand the implications of each for identifying mistuning. Simulated test data with known inputs indicate the efficiency and accuracy of the method and improvements over using a traditional, tuned mode approach. The developed methods are then extended to bench-level traveling wave excitation data to discern how sector frequencies vary due to geometry and modulus mistuning.

Download Full-text

An Analytic Model for PTH/PWB Stress Due to Three-Dimensional Forces Generated by Symmetric Compliant-Pins

Volume 5: Electronics and Photonics ◽

10.1115/imece2007-43491 ◽

2007 ◽

Author(s):

S. Roettele ◽

A. Dasgupta

Keyword(s):

Rapid Assessment ◽

Three Dimensional ◽

Design Guidelines ◽

Contact Forces ◽

Analytical Models ◽

Model Parameters ◽

Axial Forces ◽

Numerical Predictions ◽

Pin Geometry ◽

Insertion Process

Analytical models are presented, to address the deformations and stresses caused in PWBs by compliant-pins used for solder-less component-interconnection technologies. These models are proposed for rapid-assessment capabilities when designing such interconnect assemblies for reliability. This model is based on mechanistic understanding of the physics of the pin insertion process. Previous studies in the literature focused on analytic solutions for the in-plane (radial and tangential) forces generated in the PWB & PTH due to the compliant-pin. In this study, the approach is extended to three-dimensional solutions by approximately including the axial forces generated by friction during the compliant-pin insertion process. The solution is linear elastic and is based on Fourier series expansions of the contact forces generated by the compliant-pin. This approximate solution therefore is appropriate for rapid-assessment capabilities for parametric trade-off studies and design guidelines. Model parameters include PWB hole-diameter, PTH plating thickness, and the PTH and PWB material properties. The model can be used with any mirror-symmetric compliant-pin geometry and stiffness. The numerical predictions allow us to quantify the dependence of the stresses in the PWB on compliant-pin geometry and on the PTH construction.

Download Full-text

A fast bow shock location predictor‐estimator from 2D and 3D analytical models: Application to Mars and the MAVEN mission

Journal of Geophysical Research Space Physics ◽

10.1029/2021ja029942 ◽

2022 ◽

Author(s):

Cyril Simon Wedlund ◽

Martin Volwerk ◽

Arnaud Beth ◽

Christian Mazelle ◽

Christian Möstl ◽

...

Keyword(s):

Bow Shock ◽

Analytical Models ◽

Shock Location ◽

2D And 3D

Download Full-text

Numerical and Analytical Study of Reversed Flow and Heat Transfer in a Heated Vertical Duct

Journal of Heat Transfer ◽

10.1115/1.3109998 ◽

2009 ◽

Vol 131 (7) ◽

Cited By ~ 9

Author(s):

C. S. Yang ◽

D. Z. Jeng ◽

K. A. Yih ◽

C. Gau ◽

Win Aung

Keyword(s):

Heat Transfer ◽

Penetration Depth ◽

Analytical Models ◽

Reversed Flow ◽

Nusselt Numbers ◽

Flow And Heat Transfer ◽

Numerical Predictions ◽

Spacing Ratio ◽

Numerical Process ◽

Vertical Duct

Both analytical and numerical calculations are performed to study the buoyancy effect on the reversed flow structure and heat transfer processes in a finite vertical duct with a height to spacing ratio of 12. One of the walls is heated uniformly and the opposite wall is adiabatic. Uniform air flow is assumed to enter the duct. In the ranges of the buoyancy parameter of interest here for both assisted and opposed convection, a reversed flow, which can be observed to initiate in the downstream close to the exit, propagates upstream as Gr/Re2 increases. The increase in the Reynolds number has the effect of pushing the reversed flow downstream. Simple analytical models are developed to predict the penetration depth of the reversed flow for both assisted and opposed convection. The models can accurately predict the penetration depth when the transport process inside the channel is dominated by natural convection. Local and average Nusselt numbers at different buoyancy parameters are presented. Comparison with the experimental data published previously was also made and discussed. Good agreement confirms many of the numerical predictions despite simplifications of the numerical process made, such as two-dimensional and laminar flow assumptions.

Download Full-text

Experimental Evaluation of the Dynamic Air Gap of a Large-Volume Semi-Submersible Platform

Volume 1: Offshore Technology; Offshore Wind Energy; Ocean Research Technology; LNG Specialty Symposium ◽

10.1115/omae2006-92352 ◽

2006 ◽

Cited By ~ 3

Author(s):

Alexandre N. Simos ◽

Andre´ L. C. Fujarra ◽

Joa˜o V. Sparano ◽

Carlos H. Umeda ◽

Ronaldo R. Rossi

Keyword(s):

Large Volume ◽

Air Gap ◽

Analytical Models ◽

Scale Model ◽

Small Scale ◽

Design Storm ◽

Numerical Predictions ◽

Negative Effect ◽

Run Up ◽

Steep Waves

Definition of air gap is an extremely important issue in the design of floating offshore systems such as semi-submersible or TLP platforms. For these systems, any unnecessary increase in the static value of air gap generally demands the payload to be decreased or leads to a larger buoyant hull, which, in any case, has a negative effect on the project economics. Designers face a difficult challenge since there is no well-established methodology for predicting the air gap demand in the early stages of the design. This is a consequence of the inherent complexity involved in the problem of predicting the free-surface elevation around large structures in steep-waves, such as the largest wave expected during a design storm-sea spectrum. Non-linear diffraction models are usually called for a more consistent evaluation of the wave field under the deck and the wave run-up upon the columns, but even second-order analysis is not free of uncertainties. Therefore, air gap evaluation still relies heavily on experimental analysis. This paper presents some towing-tank results performed for the evaluation of the dynamic air gap of a large-volume semi-submersible platform. Regular wave tests were performed for the small-scale model in both restrained and moored configurations and results were confronted with numerical predictions. Air gap response at different locations of the hull was evaluated under three different sea states and results were compared to some semi-analytical models proposed in literature for preliminary air gap estimation. The role of dynamic coupling provided by a taut-leg mooring system on the air gap results is also discussed based on the experimental results.

Download Full-text

Measurement and Prediction of the Residual Stress Field in an Autogenously Welded Stainless Steel Plate

Volume 6: Materials and Fabrication, Parts A and B ◽

10.1115/pvp2008-61341 ◽

2008 ◽

Cited By ~ 1

Author(s):

Hassan Alizadeh ◽

Simon J. Lewis ◽

Christopher Gill ◽

S. Hossain ◽

David J. Smith ◽

...

Keyword(s):

Residual Stress ◽

Stainless Steel ◽

Residual Stresses ◽

Test Specimen ◽

Steel Plate ◽

Measurement Techniques ◽

Lessons Learned ◽

Analytical Models ◽

Stainless Steel Plate ◽

Numerical Predictions

There has been a concerted effort over recent years to develop and refine finite element models of welds in order to predict residual stresses. These residual stresses are required to ever improved accuracies in order to provide continued confidence in the safe operation of ageing plant. Not only have computing hardware and software developed at a rapid rate, but guidelines for weld modelling ‘best practice’ have started to be documented. In order to validate and verify weld modelling procedures, test specimens are required which may be subjected to a suite of residual stress measurement techniques in order to allow comparison and ‘benchmarking’ of the numerical predictions. An abundance of such test specimens have been developed over the last few years. These are typically studied via large multi-national ‘round robins’ and results used to fine tune methodologies. A specific example is the NeT ‘bead on plate’ specimen [1, 2] which considered a single weld bead on an austenitic stainless steel plate. Whilst the major thrust worldwide now is to fabricate and study test specimens more representative of real plant, by considering larger specimens, many weld passes, different materials (including ferritic steels and their associated phase change during welding), the research presented in this paper considers an even simpler test specimen. Thus, an autogenous (no filler material) weld on a stainless steel plate is considered. There were two principal motivations for this work. Firstly, numerical and experimental results were required to validate analytical models of welding induced residual stresses. These analytical models [3] are currently under development but, to date, have been formulated only for parent material. Secondly, the lessons learned on weld modelling from previous studies were desired to be tested on the simplest test specimen available.

Download Full-text