Abstract: Treatment for the non-matching interface is an important computational issue. To handle this problem, the method of Lagrange multipliers including classical and localized versions are the most popular technique. It essentially imposes the interface compatibility conditions by introducing Lagrange multipliers. However, the numerical system becomes unstable and inefficient due to the Lagrange multipliers. The interface element-independent formulation that does not include the Lagrange multipliers can be obtained by modifying the independent variables mathematically. Through this modification, more efficient and stable system can be achieved while involving equivalent accuracy comparing with the conventional method. A numerical example is conducted to verify the validity of the presented method.
Abstract: The drying process is an important operation in the chemical industry and it is widely used in the food, grain industry and fertilizer industry. However, for demanding a considerable consumption of energy, such a process requires a deep energetic analysis in order to reduce operating costs. This paper deals with thermodynamic optimization applied to rotary dryers based on the entropy production minimization, aiming at to reduce the energy consumption. To do this, the mass, energy and entropy balance was used for developing a relationship that represents the rate of entropy production. The use of the Second Law of Thermodynamics is essential because it takes into account constraints of nature. Since the entropy production rate is minimized, optimals conditions of operations can be established and the process can obtain a substantial gain in energy saving. The minimization strategy had been led using classical methods such as Lagrange multipliers and implemented in the MATLAB platform. As expected, the preliminary results reveal a significant energy saving by the application of the optimal parameters found by the procedure of the entropy minimization It is important to say that this method has shown easy implementation and low cost.
Abstract: The polymer foil used for manufacturing of
laminated glass members behaves in a viscoelastic manner with
temperature dependance. This contribution aims at incorporating
the time/temperature-dependent behavior of interlayer to our earlier
elastic finite element model for laminated glass beams. The model
is based on a refined beam theory: each layer behaves according
to the finite-strain shear deformable formulation by Reissner and
the adjacent layers are connected via the Lagrange multipliers
ensuring the inter-layer compatibility of a laminated unit. The
time/temperature-dependent behavior of the interlayer is accounted
for by the generalized Maxwell model and by the time-temperature
superposition principle due to the Williams, Landel, and Ferry.
The resulting system is solved by the Newton method with
consistent linearization and the viscoelastic response is determined
incrementally by the exponential algorithm. By comparing the model
predictions against available experimental data, we demonstrate that
the proposed formulation is reliable and accurately reproduces the
behavior of the laminated glass units.
Abstract: The flexible follower response of a translating cam with
four different profiles for rise-dwell-fall-dwell (RDFD) motion is
investigated. The cycloidal displacement motion, the modified
sinusoidal acceleration motion, the modified trapezoidal acceleration
motion, and the 3-4-5 polynomial motion are employed to describe the
rise and the fall motions of the follower and the associated four kinds of
cam profiles are studied. Since the follower flexibility is considered,
the contact point of the roller and the cam is an unknown. Two
geometric constraints formulated to restrain the unknown position are
substituted into Hamilton-s principle with Lagrange multipliers.
Applying the assumed mode method, one can obtain the governing
equations of motion as non-linear differential-algebraic equations. The
equations are solved using Runge-Kutta method. Then, the responses of
the flexible follower undergoing the four different motions are
investigated in time domain and in frequency domain.
Abstract: This paper unifies power optimization approaches in
various energy converters, such as: thermal, solar, chemical, and
electrochemical engines, in particular fuel cells. Thermodynamics
leads to converter-s efficiency and limiting power. Efficiency
equations serve to solve problems of upgrading and downgrading of
resources. While optimization of steady systems applies the
differential calculus and Lagrange multipliers, dynamic optimization
involves variational calculus and dynamic programming. In reacting
systems chemical affinity constitutes a prevailing component of an
overall efficiency, thus the power is analyzed in terms of an active
part of chemical affinity. The main novelty of the present paper in the
energy yield context consists in showing that the generalized heat
flux Q (involving the traditional heat flux q plus the product of
temperature and the sum products of partial entropies and fluxes of
species) plays in complex cases (solar, chemical and electrochemical)
the same role as the traditional heat q in pure heat engines.
The presented methodology is also applied to power limits in fuel
cells as to systems which are electrochemical flow engines propelled
by chemical reactions. The performance of fuel cells is determined by
magnitudes and directions of participating streams and mechanism of
electric current generation. Voltage lowering below the reversible
voltage is a proper measure of cells imperfection. The voltage losses,
called polarization, include the contributions of three main sources:
activation, ohmic and concentration. Examples show power maxima
in fuel cells and prove the relevance of the extension of the thermal
machine theory to chemical and electrochemical systems. The main
novelty of the present paper in the FC context consists in introducing
an effective or reduced Gibbs free energy change between products p
and reactants s which take into account the decrease of voltage and
power caused by the incomplete conversion of the overall reaction.
Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.