A reduced order model of the spine to study pediatric scoliosis

AbstractThe S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work we proposed a reduced order model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern showing that for rods deforming in a loop 1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the loop 2 shape the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves - Lenke 1 and Lenke 5. Our elastic rod model predicts deformations that are similar to those of a pediatric spine and it can differentiate between the clinically observed deformation patterns. This provides validation to the hypothesis that changes in the sagittal profile of the spine can be a mechanical factor in parthenogenesis of pediatric idiopathic scoliosis.

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A Reduced-Order Model for the Preliminary Design of Small-Scale Radial Inflow Turbines

10.1115/gt2021-59444 ◽

2021 ◽

Author(s):

Marco Manfredi ◽

Marco Alberio ◽

Marco Astolfi ◽

Andrea Spinelli

Keyword(s):

Heat Recovery ◽

Internal Combustion Engines ◽

Reduced Order Model ◽

Pollutant Emissions ◽

Small Scale ◽

Preliminary Design ◽

Order Model ◽

Reduced Order ◽

Wide Range ◽

Loss Models

Abstract Power production from waste heat recovery represents an attractive and viable solution to contribute to the reduction of pollutant emissions generated by industrial plants and automotive sector. For transport applications, a promising technology can be identified in bottoming mini-organic Rankine cycles (ORCs), devoted to heat recovery from internal combustion engines (ICE). While commercial ORCs exploiting turbo-expanders in the power range of hundreds kW to several MW are a mature technology, well-established design guidelines are not yet available for turbines targeting small power outputs (below 50 kW). The present work develops a reduced-order model for the preliminary design of mini-ORC radial inflow turbines (RITs) for high-pressure ratio applications, suitable to be integrated in a comprehensive cycle optimization. An exhaustive review of existing loss models, whose development pattern is retraced up to the original approaches, is proposed. This investigation is finalized in a loss models effectiveness analysis performed by testing several correlations over six existing geometries. These test case turbines, operating with different fluids and covering a wide range of target expansion ratio, size, and gross power output, are then employed to carry out the validation procedure, whose results prove the robustness and prediction capability of the proposed reduced-order model.

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A Reduced Order Model of Unsteady Flows in Turbomachinery

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; General ◽

10.1115/94-gt-291 ◽

1994 ◽

Cited By ~ 6

Author(s):

Kenneth C. Hall ◽

Răzvan Florea ◽

Paul J. Lanzkron

Keyword(s):

Fluid Motion ◽

Unsteady Flows ◽

Reduced Order Model ◽

Lanczos Algorithm ◽

Order Model ◽

Reduced Order ◽

Unsteady Aerodynamic ◽

Natural Modes ◽

Wide Range ◽

Modes Of Vibration

A novel technique for computing unsteady flows about turbomachinery cascades is presented. Starting with a frequency domain CFD description of unsteady aerodynamic flows, we form a large, sparse, generalized, non-Hermitian eigenvalue problem which describes the natural modes and frequencies of fluid motion about the cascade. We compute the dominant left and right eigenmodes and corresponding eigenfrequencies using a Lanczos algorithm. Then, using just a few of the resulting eigenmodes, we construct a reduced order model of the unsteady flow field. With this model, one can rapidly and accurately predict the unsteady aerodynamic loads acting on the cascade over a wide range of reduced frequencies and arbitrary modes of vibration. Moreover, the eigenmode information provides insights into the physics of unsteady flows. Finally we note that the form of the reduced order model is well suited for use in active control of aeroelastic and aeroacoustic phenomena.

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Statistics of Extreme Events in Fluid Flows and Waves

Annual Review of Fluid Mechanics ◽

10.1146/annurev-fluid-030420-032810 ◽

2021 ◽

Vol 53 (1) ◽

pp. 85-111 ◽

Cited By ~ 1

Author(s):

Themistoklis P. Sapsis

Keyword(s):

Nonlinear Dynamics ◽

Natural Disasters ◽

Extreme Events ◽

Fluid Flows ◽

Reduced Order Model ◽

Order Model ◽

Reduced Order ◽

Wide Range ◽

Expensive Model ◽

Statistics Of Extreme Events

Extreme events in fluid flows, waves, or structures interacting with them are critical for a wide range of areas, including reliability and design in engineering, as well as modeling risk of natural disasters. Such events are characterized by the coexistence of high intrinsic dimensionality, complex nonlinear dynamics, and stochasticity. These properties severely restrict the application of standard mathematical approaches, which have been successful in other areas. This review focuses on methods specifically formulated to deal with these properties and it is structured around two cases: ( a) problems where an accurate but expensive model exists and ( b) problems where a small amount of data and possibly an imperfect reduced-order model that encodes some physics about the extremes can be employed.

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Nonlinear Dynamics of Electrically Actuated Carbon Nanotube Resonators

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4000319 ◽

2009 ◽

Vol 5 (1) ◽

Cited By ~ 89

Author(s):

Hassen M. Ouakad ◽

Mohammad I. Younis

Keyword(s):

Nonlinear Dynamics ◽

Carbon Nanotube ◽

Natural Frequency ◽

Reduced Order Model ◽

Plane Boundary ◽

Beam Model ◽

Harmonic Load ◽

Order Model ◽

Reduced Order ◽

Wide Range

This work presents an investigation of the nonlinear dynamics of carbon nanotubes (CNTs) when actuated by a dc load superimposed to an ac harmonic load. Cantilevered and clamped-clamped CNTs are studied. The carbon nanotube is described by an Euler–Bernoulli beam model that accounts for the geometric nonlinearity and the nonlinear electrostatic force. A reduced-order model based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the carbon nanotube. The free-vibration problem is solved using both the reduced-order model and by solving directly the coupled in-plane and out-of-plane boundary-value problems governing the motion of the nanotube. Comparison of the results generated by these two methods to published data of a more complicated molecular dynamics model shows good agreement. Dynamic analysis is conducted to explore the nonlinear oscillation of the carbon nanotube near its fundamental natural frequency (primary-resonance) and near one-half, twice, and three times its natural frequency (secondary-resonances). The nonlinear analysis is carried out using a shooting technique to capture periodic orbits combined with the Floquet theory to analyze their stability. The nonlinear resonance frequency of the CNTs is calculated as a function of the ac load. Subharmonic-resonances are found to be activated over a wide range of frequencies, which is a unique property of CNTs. The results show that these resonances can lead to complex nonlinear dynamics phenomena, such as hysteresis, dynamic pull-in, hardening and softening behaviors, and frequency bands with an inevitable escape from a potential well.

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A Reduced-Order Model for Predicting the Performance of a Liquid-Ring Vacuum Pump

Volume 7: Fluids Engineering ◽

10.1115/imece2018-86710 ◽

2018 ◽

Author(s):

Irsha Pardeshi ◽

Ashutosh Pandey ◽

Tom I-P. Shih

Keyword(s):

Experimental Data ◽

Vacuum Pump ◽

Reduced Order Model ◽

Operating Parameters ◽

Order Model ◽

Impeller Blade ◽

Pump Design ◽

Reduced Order ◽

Wide Range ◽

Liquid Ring

Vacuum and low pressures are needed in many applications, and the liquid-ring vacuum pump, which does not have any solid-solid contacts between moving and stationary parts, is widely used because of its low operational cost and long service life. Though progress has been made in advancing this pump, industry still has aggressive goals on improving its efficiency and performance. In this study, a reduced-order model was developed to predict the ability of liquid-ring pumps to ingest air and thereby create lower pressure as a function of pump design and operating parameters. The model developed is semi-empirical — constructed by first analyzing available experimental data to extract features and trends and then encapsulating them into a model through appropriate dimensionless parameters. This model by being in closed form shows the functional relationship between the pump’s design and operating parameters and its ability to ingest air and create a vacuum. To make predictions, this model only requires the following inputs: suction pressure, impeller’s rotational speed, and a few dimensions of the pump. The model developed was assessed by using it to predict the ability of the pump to ingest air for a wide range of suction pressures (cavitation pressure to 760 torr), rotor speeds (up to 1,750 rpm), and dimensions of the pump (radius and span of the impeller blade, hub radius) and then comparing predictions with experimental data not used in the creation of the model. The model developed was found to be accurate within 11% of the experimental data.

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A Reduced Order Model of Unsteady Flows in Turbomachinery

Journal of Turbomachinery ◽

10.1115/1.2835672 ◽

1995 ◽

Vol 117 (3) ◽

pp. 375-383 ◽

Cited By ~ 28

Author(s):

K. C. Hall ◽

R. Florea ◽

P. J. Lanzkron

Keyword(s):

Fluid Motion ◽

Unsteady Flows ◽

Reduced Order Model ◽

Lanczos Algorithm ◽

Order Model ◽

Reduced Order ◽

Unsteady Aerodynamic ◽

Natural Modes ◽

Wide Range ◽

Modes Of Vibration

A novel technique for computing unsteady flows about turbomachinery cascades is presented. Starting with a frequency domain CFD description of unsteady aerodynamic flows, we form a large, sparse, generalized, non-Hermitian eigenvalue problem that describes the natural modes and frequencies of fluid motion about the cascade. We compute the dominant left and right eigenmodes and corresponding eigenfrequencies using a Lanczos algorithm. Then, using just a few of the resulting eigenmodes, we construct a reduced order model of the unsteady flow field. With this model, one can rapidly and accurately predict the unsteady aerodynamic loads acting on the cascade over a wide range of reduced frequencies and arbitrary modes of vibration. Moreover, the eigenmode information provides insights into the physics of unsteady flows. Finally we note that the form of the reduced order model is well suited for use in active control of aeroelastic and aeroacoustic phenomena.

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Eigenmode Analysis in Unsteady Aerodynamics: Reduced Order Models

Applied Mechanics Reviews ◽

10.1115/1.3101718 ◽

1997 ◽

Vol 50 (6) ◽

pp. 371-386 ◽

Cited By ~ 73

Author(s):

Earl H. Dowell ◽

Kenneth C. Hall ◽

Michael C. Romanowski

Keyword(s):

Unsteady Flow ◽

Unsteady Aerodynamics ◽

Reduced Order Modeling ◽

Reduced Order Model ◽

Full Potential ◽

Order Model ◽

Reduced Order ◽

Unsteady Aerodynamic ◽

Eigenmode Analysis ◽

Wide Range

In this article, we review the status of reduced order modeling of unsteady aerodynamic systems. Reduced order modeling is a conceptually novel and computationally efficient technique for computing unsteady flow about isolated airfoils, wings, and turbomachinery cascades. Starting with either a time domain or frequency domain computational fluid dynamics (CFD) analysis of unsteady aerodynamic or aeroacoustic flows, a large, sparse eigenvalue problem is solved using the Lanczos algorithm. Then, using just a few of the resulting eigenmodes, a Reduced Order Model of the unsteady flow is constructed. With this model, one can rapidly and accurately predict the unsteady aerodynamic response of the system over a wide range of reduced frequencies. Moreover, the eigenmode information provides important insights into the physics of unsteady flows. Finally, the method is particularly well suited for use in the active control of aeroelastic and aeroacoustic phenomena as well as in standard aeroelastic analysis for flutter or gust response. Numerical results presented include: 1) comparison of the reduced order model to classical unsteady incompressible aerodynamic theory, 2) reduced order calculations of compressible unsteady aerodynamics based on the full potential equation, 3) reduced order calculations of unsteady flow about an isolated airfoil based on the Euler equations, and 4) reduced order calculations of unsteady viscous flows associated with cascade stall flutter, 5) flutter analysis using the Reduced Order Model. This review article includes 25 references.

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