Dynamic Model of an Astronaut Equipped with a Manned Maneuvering Unit in Virtual Reality

A virtual reality simulation system for a manned maneuvering unit (MMU) and a training system for an astronaut space walk is introduced. The system can simulate an astronaut’s outer space walk by means of manipulating the MMU, and it also can be used as a training environment by taking advantage of virtual reality properties of imagination, interaction, and immersion. As in microgravity space, an astronaut’s moving limbs cause changes in the MMU posture; these changes result in great offsets to correct direction and have a great effect on the MMU’s manipulation performance. A multibody astronaut model is developed by using relative coordinates according to the motion characteristics of an astronaut equipped with MMU. Motion information on the user’s limbs are captured by means of a motion capture subsystem and are mapped to an astronaut in virtual environment to simulate the astronaut’s limb motions while the astronaut is navigating in outer space. It is an open-chain system for an astronaut multibody model. As an astronaut can control his limbs, the whole system dynamics is a hybrid forward and inverse dynamic problem. Recursive dynamic formulations of a previous method are introduced to solve the forward dynamic problem. For the inverse dynamic part, because the system can get motion characteristics of parts of the relative coordinates, unknown generalized driving forces are applied on these known relative coordinates. All the unknown generalized driving forces and unknown relative coordinates can be combined in a set of hybrid dynamic formulations based on a forward dynamic formulation. The motion characteristics of an astronaut multibody model can be obtained by solving the hybrid formulations. Finally, some simulation results for astronaut forward-flying mode with moving limbs are presented; these results show that the movement of an astronaut’s limbs has great effects on astronaut navigation and MMU manipulation performance. The multibody astronaut model has the capability of simulating real space walk with an MMU equipped astronaut.     

Applications of Genetic-Taguchi Algorithm in Flight Control Designs

A genetic algorithm (GA), a well-known numerical method, is widely applied in different areas of optimal studies. It is found that if the solution-search space is wide or if the selected fitness function is highly nonlinear, the GA’s solutions can strongly depend on the set parameters, which include population size, crossover rate, mutation rate, and the remaining size of the parent in the GA. This paper combines the Taguchi experimental method, which serves as a rough search tool, with the GA, which serves as a fine search tool, to find the best combination of the GA parameters for different flight-control problems. The purpose of such a combination is to make control more robust and closer to the optimal solution. To demonstrate this new idea, the writers consider its application to different flight-control problems for the F-16 fighter by using autostabilization, linear quadratic regulator (LQR) and H∞ design. The simulation results not only achieve the expected optimal design for flight-control problems but also justify the reliability and feasibility of the combination of the GA and the Taguchi method.     

Modeling the Temperature Dependence of Adsorption Equilibriums of VOC(s) onto Activated Carbons

In order to optimize the efficiency of the removal of volatile organic compounds (VOCs) by adsorption onto activated carbon beds, process simulations taking into account exothermicity effects are helpful. Significant temperature increases may arise in the bed during the VOC adsorption cycle, especially when high concentrations have to be treated. Consequently, reliable and easy-to-handle isotherms remain a key hurdle to build realistic models. In this study, adsorption models were tested to describe a set of experimental data obtained for three VOCs (acetone, ethyl formate, and dichloromethane) adsorbed onto five commercial activated carbons at four different temperatures (20, 40, 60, and 80°C). A new expression of the Freundlich equation [qe = (a1T+a2T2)Ce(1/nf)] was shown to be statistically the most efficient to describe the adsorption isotherms of VOCs, single or in mixtures. A second-order polynomial temperature-dependence was introduced in this expression. The so-adapted Freundlich relationship gave a mean coefficient of determination of 0.97 for single-component adsorption and a correlation coefficient of 0.98 for binary mixtures.     

Computer Modeling for the Complex Response Analysis of Nonstandard Structural Dynamics Problems

Over the past several decades, two intriguing classes of problems, having a wide range of applications in engineering, have been of interest to many researchers: (1) coupled dynamics of a distributed parameter system traversed by one or more moving oscillators; and (2) transient dynamic analysis of axially moving media (and associated phenomena of parametric resonances). Bridge vehicle interaction falls into the first class of problems, and the analysis of flexible appendages deployed from a satellite or a spacecraft is typical of the second class. Mathematically, these two problems are dual to each other, and they often are highly nonlinear in nature and typically involve large overall motion in space with complex effects of convective inertia terms in their governing equations of dynamic equilibrium. The “nonstandard” analytical nature of these problems stems from the fact that we are dealing with one or more of the following peculiarities: (1) variable problem domain; (2) varying spatial distribution of forces over the time duration of the analysis; and/or (3) changing location and type of constraints. Many researchers are trying to formulate the response of these problems, each having a different approach, but applicable only to certain specific details. Moreover, few researchers have concluded that these problems are beyond the scope of the present commercial finite-element (FE) software packages. However, we believe that if the nature and details of these problems are studied properly and carefully, it is immediately possible to simulate these problems in available commercial FE programs. An added advantage would also be the avoidance of many unrealistic simplifying assumptions that are often introduced to reduce the mathematical complexity; e.g., neglecting possible separation (after periods of prior contacts) in beam-moving vehicle problems, assuming linear behavior of suspension systems, and restriction to beam configuration only, among many others. For demonstration, we use ABAQUS in a large number of test cases to be presented. The results are compared with those presented in literatures.     

Distribution of Discharge Intensity along Small-Diameter Collector Well Laterals in a Model Riverbed Filtration

Experiments were performed to evaluate flow and head variations along perforated screens (10–30?mm in diameter) using sand tanks which were connected and a perforated screen extended through these tanks to form a model collector well lateral up to 2.6?m in length. Hydraulic heads and discharge along the lateral and production rates of the model collector well were measured as the water level in the well, the lateral length, and diameter, and the hydraulic conductivity of the filter sand were varied. A mathematical model was developed to predict the axial flow velocity distribution and the discharge intensity variation along the lateral using the head distribution. Results showed that the production rate increased as the lateral length and diameter and the drawdown at the well increased. However, the production rate increase was not linearly related to these factors. When larger-diameter laterals were used, the axial flow velocity in the laterals decreased. This caused the hydraulic heads along the lateral to become more flattened, resulting in a lateral of high efficiency in terms of water production. This condition is similar to the assumption of the uniform discharge intensity along the lateral that many researchers have used in the analysis of the horizontal wells. Under the conditions of this study, a critical axial flow velocity was determined to be 1?m/s. Hydraulic efficiency decreased drastically when the velocity exceeded 1?m/s. The roughness coefficient (the Manning’s n value) of the lateral varied as a function of factors such as axial velocity and discharge intensity, and it ranged from 0.010 to 0.015.     

Dimensional Analysis of the Earthquake Response of a Pounding Oscillator

In this paper, the dynamic response of a pounding oscillator subjected to pulse type excitations is revisited with dimensional analysis. The study adopts the concept of the energetic length scale which is a measure of the persistence of the distinguishable pulse of strong ground motions and subsequently presents the dimensionless Π products that govern the response of the pounding oscillator. The introduction of Buckingham’s Π theorem reduces the number of variables that govern the response of the system from 7 to 5. The proposed dimensionless Π products are liberated from the response of an oscillator without impact and most importantly reveal remarkable order in the response. It is shown that, regardless the acceleration level and duration of the pulse, all response spectra become self-similar and, when expressed in the dimensionless Π products, follow a single master curve. This is true despite the realization of contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachment) are captured via a linear complementarity approach. The proposed analysis stresses the appreciable differences in the response due to the directivity of the excitation (toward or away the stationary wall) and confirms the existence of three spectral regions where the response of the pounding oscillator amplifies, deamplifies, and equals the response of the oscillator without pounding.     

Adsorption of Carbon Disulfide (CS2) in Water by Different Types of Activated Carbon—Equilibrium, Dynamics, and Mathematical Modeling

Adsorption equilibrium and kinetics of carbon disulfide in water by granular activated carbon (GAC), powdered activated carbon (PAC), and activated carbon fiber (ACF) were investigated and compared in an effort to elucidate the fundamentals for optimizing the control process design. It has been shown that the BET expression can satisfactorily describe the adsorption equilibrium of carbon disulfide (CS2) on GAC, PAC, and ACF and the corresponding kinetic experimental data properly correlated with the second-order kinetic model, which indicates that the CS2 adsorption is the rate-limiting step. A two-phase mathematical model was developed to simulate CS2 transfer in fixed-bed operation filled with the GAC, PAC, and ACF, and the equilibrium and kinetics information is subsequently used in the model to characterize the dynamics of adsorption. The model includes mechanisms such as axial dispersion, advection, liquid-to-solid mass transport, and intraparticle mass transport by pore and surface diffusion. It is manifested that the model was able to predict the dynamic breakthrough curve of CS2 in a fixed-bed adsorption column filled with GAC, PAC, and ACF at varied conditions (standard deviations for 1.5?cm/min is 12.13% and for 2.2?cm/min is 16.12%), based on BET-3 equilibrium and second-order kinetics, which indicates that the methodology proposed by this work could be employed for adsorbents selection, adsorption design, and process optimization for CS2 waste-water emission control.     

Pilot-Scale Verification and Analysis of Iron Release Flux Model

An original model by Mutoti in 2003 was developed mathematically, and empirically, to predict the increase in total iron concentration in distribution systems. This model, referred to as a flux model, relates the increase in iron concentration in a reach of unlined or galvanized iron pipe to the surface area of the pipe in contact with the water. A flux term, defined with a dimension of mass per area per time was used. The effects of water chemistry, pipe material and hydraulic conditions were incorporated into the flux term. This paper describes the verification of the flux model using independent pilot data obtained with variable water quality under worst case, laminar flow conditions. The original model accurately predicted iron release for this independent verification data, with an overall R2 of 0.80. For laminar flow conditions, the increase in iron concentration is proportional to the flux and the hydraulic residence time, and is inversely proportional to the pipe diameter.     

Thermal Buckling Analysis of SMA Fiber-Reinforced Composite Plates Using Layerwise Model

Thermal buckling analysis of laminated smart composite plates subjected to uniform temperature distribution has been presented. Shape memory alloy (SMA) fibers whose material properties depend on temperature have been used as a smart material. A three-dimensional layerwise plate model has been employed in developing the system equations using variational approach. Finite-element method has been adopted for discretization of the laminate. Lagrangian interpolation functions have been used to approximate the displacement components along the thickness as well as in the in-plane direction. The actual variation of prebuckling stresses has been accounted for in the derivation of the geometric stiffness matrix of the laminates. An incremental load technique has been used in the analysis to take into account the nonlinearity in the material properties of the SMA arising due to their temperature dependence. The effects of thickness ratio, orthotropic ratio, fiber orientation, aspect ratio, stacking sequence and various boundary conditions on the critical buckling temperature have been examined in details. The results have been validated with those available in the literature.     

Numerical Analysis of Peristaltic Transport of a Tangent Hyperbolic Fluid in an Endoscope

This paper presents a tangent hyperbolic fluid in a cylindrical coordinate system. The governing equations are simplified using long-wavelength and low Reynolds number approximations. The solutions of the problem in simplified form are calculated with three methods: (1)?perturbation method, (2)?homotopy analysis method, and (3)?shooting method. Comparison of the three solutions shows very good agreement among them. Pressure rise and frictional force are calculated with the help of numerical integration. Graphical results for pressure rise and frictional forces are presented to show the physical behavior of the Weissenberg number We, amplitude ratio ?, tangent hyperbolic power law index n, and radius ratio ?.     

New Elastic Model of Pipe Flow for Stability Analysis of the Governor-Turbine-Hydraulic System

A higher-order elastic model of the flow in long pressurized pipelines is expected to be utilized for stability analysis of the governor-turbine-hydraulic system in hydropower stations. Because traditional elastic models are limited in lower order application because of their difficult decoupling in addition to the rigid model, a new linear elastic model of the flow in pressurized pipelines is derived on the basis of the equations of hydraulic vibration, in which each oscillatory flow with a different order has been obtained with ordinary differential equations in decoupling form. For water conveyance systems with branching pipes or parallel pipes in hydropower stations, the state equations to describe hydraulic characteristics of the governor-turbine-hydraulic system are established with the application of this new elastic model for diversion pipeline flow or tail tunnel flow. The influence of the elastic models with different order on a system’s stability are revealed in detail by two cases that illustrate that an elastic model with proper order should be used for the flow in pressurized pipelines of hydropower stations, according to their length, to improve the accuracy of stability analysis.     

Mathematical Model for the Sequestering of Chemical Contaminants by Magnetic Particles

A mathematical model is developed and implemented to characterize the pickup of various liquid chemical contaminants by polyethylene-coated magnetic particles. The model and its associated experimental and analytical protocols were applied to a wide range of liquid chemicals in order to gain insights into the physical basis for the pickup phenomenon. The characteristics of the pickup isotherms range between “ideal” and “nonideal” behaviors that are reflected in the mathematical model by a single parameter, α0, where α0 = 1 corresponds to ideal behavior and α0>1 corresponds to a departure from idealized behavior that is directly quantified by the magnitude of α0. The parameter α0 is also related to the efficiency of pickup, and since most isotherms observed in the study deviate from ideality, the high efficiency of pickup observed in these systems has been attributed in part to this deviation. The proposed model and its associated experimental and analytical protocols demonstrate great potential for the systematic evaluation of the uptake of chemical contaminants using magnetic particle technology.     

Case Study: Application of the HEC-6 Model for the Main Stem of the Kankakee River in Illinois

This case study paper presents results on the application of the HEC-6 model to the main stem of the Kankakee River in Illinois, a distance of about 39.3?km. Modeling was performed to develop comprehensive plans for enhancing the aquatic habitats and also to forecast future sedimentation problems if specific management practices are implemented. The paper concentrates on the modeling aspects of this research. The extent of the model was from the Stateline Bridge to Kankakee Dam in Kankakee. The HEC-6 model, originally developed by the Hydrologic Engineering Center (HEC) of the U.S. Army Corps of Engineers, was adapted for this application. The model was run, calibrated, and verified for both the hydraulic and sediment components. The hydraulic component was calibrated through comparison of measured yearly hydrographs with computed values for three gauging stations on the river. The hydrologic component was verified for the same three gauging stations for two yearly hydrographs for 2 additional water years. The sediment component was calibrated with river cross-sectional data collected by the Illinois State Water Survey in 1980 and 1999. The calibrated and verified hydraulic and calibrated sediment components then were used to predict future changes in water surface elevations and thalweg elevations for a 20-year period beginning in 1999, the last date for which river cross-sectional data are available.     

Analysis of the Friction Term in the One-Dimensional Shallow-Water Model

The numerical simulation of unsteady open channel flows is very commonly performed using the one-dimensional shallow-water model. Friction is one of the relevant forces included in the momentum equation. In this work, a generalization of the Gauckler-Manning friction model is proposed to improve the modeling approach in cases of dominant roughness, unsteady flow, and distorted cross-sectional shapes. The numerical stability conditions are revisited in cases of dominant friction terms and a new condition, complementary to the basic Courant-Friedrichs-Lewy condition, is proposed. Some test cases with measured data are used to validate the quality of the approaches.     

A Model of Coupled Heat and Moisture Transport in an Annular Clay Barrier

The design of repository seals for deeply buried high-level radioactive wastes incorporates densely compacted clayey barriers around metallic waste canisters. In this paper, a mathematical model that is based on conservation of thermal energy and mass is developed to describe the locations of moisture and temperature fronts within a barrier, around a cylindrical waste canister of 1 m radius, containing radionuclides with half-lives that range from 100 to 10,000 years. The solution developed is axisymmetric: the moisture fraction w and temperature T vary only with time t, and radial distance r from the axis of the cylindrical waste canister. The model produces parabolic partial differential equations. The spatial domain is discretized such that ordinary differential equations that result are solved. Computations using a uniform mesh of 0.1 m and a cooling coefficient of 6.7×10?2 with assumed but typical data on material properties, indicate that coupling of transport processes would be negligible in the case of radionuclides with long half-lives. Also, a quasisteady vaporization front can form and propagate outward over the course of several decades after waste emplacement. The evolution of the front is somewhat insensitive to the half-life used and the permeability of the clayey barrier material.     

Adjoint Sensitivity Analysis of Contaminant Concentrations in Water Distribution Systems

Sensitivity analysis is used to determine how a system state or a model output changes due to a change in the value of a system parameter or a model input. We present the adjoint approach for determining the sensitivity of the concentration of a contaminant in a water distribution system to a change in a system parameter such as the location of the source of contamination, the reaction rate of the contaminant, and others. With the adjoint method, the sensitivity of the model output to any number of parameters can be obtained with one simulation of the adjoint model. If the number of parameters of interest exceeds the number of model outputs for which the sensitivity is desired, the adjoint method is more efficient than traditional direct methods of calculating sensitivities. We develop the adjoint equations for water quality in a water distribution system, verify the adjoint-based sensitivity equation using an analytical example, and demonstrate the numerical calculation of adjoint sensitivities using EPANET.     

Assignment of Geometrical and Physical Parameters for the Confinement of Vibrations in Flexible Structures

A strategy for confinement of flexural vibrations in flexible structures by proper selection of their geometrical and physical parameters is proposed. We first show that the problem of vibration confinement can be formulated as an inverse eigenvalue problem (IEP) where the mode shapes and/or natural frequencies are assumed and the geometrical and physical properties are unknown functions of the space variables. It is required that the assumed modes form a complete and independent set of spatial functions that satisfy the boundary conditions and guarantee confinement within the desired spatial subdomain(s) of the structure. Using simple spatial functions, such as polynomials and exponentials, we determined approximate solutions of the geometrical and physical parameters by applying the orthogonality of the mode shapes with respect to the stiffness and mass density. The order of the selected polynomials or exponentials depends on the number of modes retained in the discretized model. Numerical simulations are presented on a beam and then on a plate to examine convergence of the solution to the IEP. We show that convergence is attained with few assumed mode shapes. The approximated parameters are finally substituted into the forward eigenvalue problem to confirm confinement at the desired locations.     

Stress Singularities in a Model of a Wood Disk under Sinusoidal Pressure

A thin, solid, circular wood disk, cut from the transverse plane of a tree stem, can be modeled as a cylindrically orthotropic elastic material. It is known that a stress singularity can occur at the center of a cylindrically orthotropic disk subjected to uniform pressure. If a solid cylindrically orthotropic disk is subjected to sinusoidal pressure distributions, then other stress singularities can also occur in the disk. The criterion for the existence of these singularities is based on a simple relationship between two dimensionless elastic constant parameters and the sinusoidal pressure loading mode number. For a given set of elastic constants, only a finite number of lower sinusoidal modes will produce stress singularities. In this paper, the mathematical relationships between these parameters are derived.     

User-Friendly Mathematical Model for the Design of Sulfate Reducing H2/CO2 Fed Bioreactors

This paper presents three steady-state mathematical models for the design of H2/CO2 fed gas-lift reactors aimed at biological sulfate reduction to remove sulfate from wastewater. Models 1A and 1B are based on heterotrophic sulfate reducing bacteria (HSRB), while Model 2 is based on autotrophic sulfate reducing bacteria (ASRB) as the dominant group of sulfate reducers in the gas-lift reactor. Once the influent wastewater characteristics are known and the desired sulfate removal efficiency is fixed, all models give explicit mathematical relationships to determine the bioreactor volume and the effluent concentrations of substrates and products. The derived explicit relationships make application of the models very easy, fast, and no iterative procedures are required. Model simulations show that the size of the H2/CO2 fed gas-lift reactors aimed at biological sulfate removal from wastewater highly depends on the number and type of trophic groups growing in the bioreactor. In particular, if the biological sulfate reduction is performed in a bioreactor where ASRB prevail, the required bioreactor volume is much smaller than that needed with HSRB. This is because ASRB can out-compete methanogenic archaea (MA) for H2 (assuming sulfate concentrations are not limiting), whereas HSRB do not necessarily out-compete MA due to their dependence on homoacetogenic bacteria (HB) for organic carbon. The reactor sizes to reach the same sulfate removal efficiency by HSRB and ASRB are only comparable when methanogenesis is inhibited. Moreover, model results indicate that acetate supply to the reactor influent does not affect the HSRB biomass required in the reactor, but favors the dominance of MA on HB as a consequence of a lower HB requirement for acetate supply.