Joule-Thomson coefficients of propane and n-butane

Experimental Joule-Thomson measurements were made on gaseous propane at temperatures from 100 to 280˚F and at pressures from 8 to 66 psia. Joule-Thomson measurements were also made on gaseous n-butane at temperatures from 100 to 280˚ and at pressures from 8 to 42 psia. For propane, the values of these measurements ranged from 0.07986˚F/psi at 280˚F and 8.01 psia to 0.19685˚F/psi at 100˚F and 66.15 psia. For n-butane, the values ranged from 0.11031˚F/psi at 280˚F and 9.36 psia to 0.30141˚F/psi at 100˚F and 41.02 psia. The experimental values have a maximum error of 1.5 percent.

For n-butane, the measurements of this study did not agree with previous Joule-Thomson measurements made in the Laboratory in 1935. The application of a thermal-transfer correction to the previous experimental measurements would cause the two sets of data to agree. Calculated values of the Joule-Thomson coefficient from other types of p-v-t data did agree with the present measurements for n-butane.

The apparatus used to measure the experimental Joule-Thomson coefficients had a radial-flow porous thimble and was operated at pressure changes between 2.3 and 8.6 psi. The major difference between this and other Joule-Thomson apparatus was its larger weight rates of flow (up to 6 pounds per hour) at atmospheric pressure. The flow rate was shown to have an appreciable effect on non-isenthalpic Joule-Thomson measurements.

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The instability of fluids with time dependent heating

The stability of a fluid having a non-uniform temperature stratification is examined analytically for the response of infinitesimal disturbances. The growth rates of disturbances have been established for a semi-infinite fluid for Rayleigh numbers of 10³, 10⁴, and 10⁵ and for Prandtl numbers of 7.0 and 0.7.

The critical Rayleigh number for a semi-infinite fluid, based on the effective fluid depth, is found to be 32, while it is shown that for a finite fluid layer the critical Rayleigh number depends on the rate of heating. The minimum critical Rayleigh number, based on the depth of a fluid layer, is found to be 1340.

The stability of a finite fluid layer is examined for two special forms of heating. The first is constant flux heating, while in the second, the temperature of the lower surface is increased uniformly in time. In both cases, it is shown that for moderate rates of heating the critical Rayleigh number is reduced, over the value for very slow heating, while for very rapid heating the critical Rayleigh number is greatly increased. These results agree with published experimental observations.

The question of steady, non-cellular convection is given qualitative consideration. It is concluded that, although the motion may originate from infinitesimal disturbances during non-uniform heating, the final flow field is intrinsically non-linear.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

Steady surface wave pattern in a shear flow

The subject under investigation concerns the steady surface wave patterns created by small concentrated disturbances acting on a non-uniform flow of a heavy fluid. The initial value problem of a point disturbance in a primary flow having an arbitrary velocity distribution (U(y), 0, 0) in a direction parallel to the undisturbed free surface is formulated. A geometric optics method and the classical integral transformation method are employed as two different methods of solution for this problem. Whenever necessary, the special case of linear shear (i.e. U(y) = 1+ϵy)) is chosen for the purpose of facilitating the final integration of the solution.

The asymptotic form of the solution obtained by the method of integral transforms agrees with the leading terms of the solution obtained by geometric optics when the latter is expanded in powers of small ϵ r.

The overall effect of the shear is to confine the wave field on the downstream side of the disturbance to a region which is smaller than the wave region in the case of uniform flows. If U(y) vanishes, and changes sign at a critical plane y = y_cr (e.g. ϵy_cr = -1 for the case of linear shear), then the boundary of this asymmetric wave field approaches this critical vertical plane. On this boundary the wave crests are all perpendicular to the x-axis, indicating that waves are reflected at this boundary.

Inside the wave field, as in the case of a point disturbance in a uniform primary flow, there exist two wave systems. The loci of constant phases (such as the crests or troughs) of these wave systems are not symmetric with respect to the x-axis. The geometric optics method and the integral transform method yield the same result of these loci for the special case of U(y) = U_o(1 + ϵy) and for large Kr (ϵr ˂˂ 1 ˂˂ Kr).

An expression for the variation of the amplitude of the waves in the wave field is obtained by the integral transform method. This is in the form of an expansion in small ϵr. The zeroth order is identical to the expression for the uniform stream case and is thus not applicable near the boundary of the wave region because it becomes infinite in that neighborhood. Throughout this investigation the viscous terms in the equations of motion are neglected, a reasonable assumption which can be justified when the wavelengths of the resulting waves are sufficiently large.

On the Cesari fixed point method in a Banach space

In a paper published in 1961, L. Cesari [1] introduces a method which extends certain earlier existence theorems of Cesari and Hale ([2] to [6]) for perturbation problems to strictly nonlinear problems. Various authors ([1], [7] to [15]) have now applied this method to nonlinear ordinary and partial differential equations. The basic idea of the method is to use the contraction principle to reduce an infinite-dimensional fixed point problem to a finite-dimensional problem which may be attacked using the methods of fixed point indexes.

The following is my formulation of the Cesari fixed point method:

Let B be a Banach space and let S be a finite-dimensional linear subspace of B. Let P be a projection of B onto S and suppose Г≤B such that pГ is compact and such that for every x in PГ, P^-1x∩Г is closed. Let W be a continuous mapping from Г into B. The Cesari method gives sufficient conditions for the existence of a fixed point of W in Г.

Let I denote the identity mapping in B. Clearly y = Wy for some y in Г if and only if both of the following conditions hold:

(i) Py = PWy.

(ii) y = (P + (I - P)W)y.

Definition. The Cesari fixed paint method applies to (Г, W, P) if and only if the following three conditions are satisfied:

(1) For each x in PГ, P + (I - P)W is a contraction from P^-1x∩Г into itself. Let y(x) be that element (uniqueness follows from the contraction principle) of P^-1x∩Г which satisfies the equation y(x) = Py(x) + (I-P)Wy(x).

(2) The function y just defined is continuous from PГ into B.

(3) There are no fixed points of PWy on the boundary of PГ, so that the (finite- dimensional) fixed point index i(PWy, int PГ) is defined.

Definition. If the Cesari fixed point method applies to (Г, W, P) then define i(Г, W, P) to be the index i(PWy, int PГ).

The three theorems of this thesis can now be easily stated.

Theorem 1 (Cesari). If i(Г, W, P) is defined and i(Г, W, P) ≠0, then there is a fixed point of W in Г.

Theorem 2. Let the Cesari fixed point method apply to both (Г, W, P₁) and (Г, W, P₂). Assume that P₂P₁=P₁P₂=P₁ and assume that either of the following two conditions holds:

(1) For every b in B and every z in the range of P₂, we have that ‖b=P₂b‖ ≤ ‖b-z‖

(2)P₂Г is convex.

Then i(Г, W, P₁) = i(Г, W, P₂).

Theorem 3. If Ω is a bounded open set and W is a compact operator defined on Ω so that the (infinite-dimensional) Leray-Schauder index i_LS(W, Ω) is defined, and if the Cesari fixed point method applies to (Ω, W, P), then i(Ω, W, P) = i_LS(W, Ω).

Theorems 2 and 3 are proved using mainly a homotopy theorem and a reduction theorem for the finite-dimensional and the Leray-Schauder indexes. These and other properties of indexes will be listed before the theorem in which they are used.

Estimativa de erros no cálculo de gradientes em malhas de Voronoi

O presente trabalho propõe analisar metodologias para o cálculo do gradiente em malhas não-estruturadas do tipo Voronoi que são utilizadas no método de Volumes Finitos. Quatro metodologias para o cálculo do gradiente são testadas e comparadas com soluções analíticas. As técnicas utilizadas são: Método do Balanço de Forças, Método do Mínimo Resíduo Quadrático, Método da Média dos Gradientes Projetos e Método da Média dos Gradientes Projetados Corrigidos. Uma análise por série de Taylor também foi feita, e as equações analíticas comparadas com resultados numéricos. Os testes são realizados em malhas cartesianas e malhas triangulares, que em um trabalho anterior apresentaram alguns resultados inconsistentes. A influência do ponto gerador e do ângulo de rotação é analisada. É verificado que a posição do ponto gerador e a metodologia utilizada em cada malha influencia no cálculo do gradiente. Dependendo da malha e da metodologia utilizada, as equações analíticas indicaram que existem erros associados, que prejudicam o cálculo do gradiente.

The analysis of the transient temperature distribution of double-slab Nd:YAG laser medium

A novel double-slab Nd:YAG laser, which uses face-pumped slab medium cooled by liquid with different temperatures on both sides, is proposed. The thermal distortion of wavefront caused by the non-uniform temperature distribution in the laser gain media can be self-compensated. According to the method of operation, the models of the temperature distribution and stress are presented, and the analytic solutions for the model are derived. Furthermore, the numerical simulations with pulse pumping energy of 10 J and repetition frequencies of 500 and 1000 Hz are calculated respectively for Nd:YAG laser medium. The simulation results show that the temperature gradient remains the approximative linearity, and the heat stress is within the extreme range. Then the absorption coefficient is also discussed. The result indicates that the doping concentration cannot be too large for the high repetition frequency laser. It has been proved that the high repetition frequency, high laser beam quality, and high average output power of the order of kilowatt of Nd: YAG slab laser can be achieved in this structure.

新型板条激光器的离轴混合腔模场计算

报道了一种新型双板条离轴混合腔激光器。这种激光器结构通过改变传统的冷却方式和采用特殊的谐振腔设计，将使从第一块介质板条高温一侧出射的激光对称地进入另一块板条的低温一侧，从而可对由于温度分布不均匀造成的波面畸变进行一定程度的自校正，减少热效应的影响，可望提高激光器的输出功率和光束质量。利用快速傅里叶变换（FFT）对这种激光器的近场、远场以及相位等模场特性进行了数值计算。分析了波面畸变对输出光束质量的影响，并与常规双板条激光器进行了比较，结果表明这种新型双板条离轴混合腔激光器可以实现一定程度的波面畸变自补偿，

硬边非稳腔平面波导激光器的光束特性

基于衍射理论和坐标变换,采用数值模拟的方法分析了硬边非稳腔平面波导激光器的光束特性,研究了存在非均匀抽运和增益饱和时,输出激光的光束质量.在端面抽运和边缘抽运时,比较了正支和负支非稳腔的输出光束特性.结果表明：利用优化的离轴硬边非稳腔可以得到近衍射极限的输出.在相同的抽运不均匀性情况下,对于边缘抽运和端面抽运,正支非稳腔的光束质量因子M^2分别为3.9和2.3,而相同条件下负支非稳腔的M^2因子为1.8和1.7.

Palaeoenvironmental analysis based on alluvial ostracod assemblages of the Cenicero section (lower Miocene, NW Ebro Basin)

In this work we perform for the first time a palaeoenvironmental and biostratigraphic analysis of the lower Miocene alluvial deposits of the Cenicero section (NW sector of the Ebro Basin; N Iberian Peninsula), based on the ostracod and micromammal assemblages. One of the main characteristics of this section is the unusual abundance on non-reworked ostracods present in the studied samples compared to other European sequences of similar age and sedimentary environment. This fact has allowed us to develop precise palaeoenvironmental reconstructions. The variations of the identified ostracod assemblages, defined by species such as Cyclocypris laevis, Ilyocypris bradyi, Ilyocypris gibba, Limnocythere sp. or Pseudocandona parallela, record the development of small, ephemeral and shallow ponds in a distal alluvial and/or floodplain environment. Towards the upper part of the section the ponds appear to be less ephemeral, being the aquatic systems more stable for ostracods development. Variations in the water temperature and salinity have been observed along the section, which are related to changes in the local pluviometric regime. On the other hand, the presence of micromammals in one of the studied samples has allowed the precise dating of this section. Thus, the presence of Armantomys daamsi dates the Cenicero section as Agenian (lower Miocene), local zone Y2 (MN2).

Qualidade das águas fluviais: estudo de caso da bacia hidrográfica de Jacarepaguá - RJ.

O processo de ocupação urbana da Baixada de Jacarepaguá a partir da década de 1970, promoveu inúmeros impactos ambientais que afetaram, de forma não uniforme, os diferentes grupos sociais, que habitam a região, e afetaram principalmente o meio ambiente, mais especificamente os recursos hídricos. A rápida e intensa ocupação urbana da região, impulsionada pela produção imobiliária, gerou inúmeros problemas ambientais, principalmente devido à precariedade nos serviços de saneamento. Diversos impactos se processam atualmente na rede de drenagem da Baixada de Jacarepaguá, os quais comprometem negativamente a qualidade de vida população que vive na região, assim como, do meio ambiente. Neste trabalho é avaliada a qualidade da água dos principais cursos dágua da bacia hidrográfica de Jacarepaguá, caracterizando o estado atual de degradação dos recursos hídricos da região a partir da análise dos dados referentes aos parâmetros de qualidade das águas, obtidos junto ao órgão ambiental estadual, no período compreendido entre os anos de 2003 e 2008. As variáveis estatísticas dos parâmetros foram determinadas, os resultados foram apresentados através dos gráficos boxplot e sua discussão foi realizada em consoante com a Resolução CONAMA 357/2005. Os cursos dágua da bacia de Jacarepaguá, em destaque aqueles avaliados neste trabalho expressam a degradação pela qual vem sofrendo em virtude das intervenções antrópicas que se projetam na bacia hidrográfica. Nota-se a partir, dos resultados para os parâmetros de qualidade de água avaliados que a poluição nos cursos dágua da baixada de Jacarepaguá que, possivelmente o principal aspecto da poluição hídrica é devido ao despejo de esgotos domésticos nos cursos dágua sem tratamento adequado.

A comparison of losses in small (<1 kW) drives using sine and space vector pulse width modulation schemes

this paper quantifies effects of using three different pulse width modulation (PWM) schemes on the losses in the inverter and induction motor of a 1 kW drive. Direct measurements of losses have been made with a calorimeter. Results show that for the inverter, discontinuous PWM excitation reduces losses by up to 15% compared to sine and symmetrical space vector PWM methods. However, at a low modulation index the greater harmonic content with discontinuous PWM increased motor losses by nearly 20%. This study demonstrates the importance of careful choice of modulation scheme to achieve high overall drive efficiency. © 2005 IEEE.

Modelling of long-term ground response to tunnelling under St James's Park, London

Following a tunnel excavation in low-permeability soil, it is commonly observed that the ground surface continues to settle and ground loading on the tunnel lining changes, as the pore pressures in the ground approach a new equilibrium condition. The monitored ground response following the tunnelling under St James's Park, London, shows that the mechanism of subsurface deformation is composed of three different zones: swelling, consolidation and rigid body movement. The swelling took place in a confined zone above the tunnel crown, extending vertically to approximately 5 m above it. On the sides of the tunnel, the consolidation of the soil occurred in the zone primarily within the tunnel horizon, from the shoulder to just beneath the invert, and extending laterally to a large offset from the tunnel centreline. Above these swelling and consolidation zones the soil moved downward as a rigid body. In this study, soil-fluid coupled three-dimensional finite element analyses were performed to simulate the mechanism of long-term ground response monitored at St James's Park. An advanced critical state soil model, which can simulate the behaviour of London Clay in both drained and undrained conditions, was adopted for the analyses. The analysis results are discussed and compared with the field monitoring data. It is found that the observed mechanism of long-term subsurface ground and tunnel lining response at St James's Park can be simulated accurately only when stiffness anisotropy, the variation of permeability between different units within the London Clay and non-uniform drainage conditions for the tunnel lining are considered. This has important implications for future prediction of the long-term behaviour of tunnels in clays.

Vortex deformation and breaking in superconductors: a microscopic description

Vortex breaking has traditionally been studied for non-uniform critical current densities, although it may also appear due to non-uniform pinning force distributions. In this article we study the case of a high-pinning/low-pinning/high-pinning layered structure. We have developed an elastic model for describing the deformation of a vortex in these systems in the presence of a uniform transport current density J for any arbitrary orientation of the transport current and the magnetic field. If J is above a certain critical value, J(c), the vortex breaks and a finite effective resistance appears. Our model can be applied to some experimental configurations where vortex breaking naturally exists. This is the case for YBa2Cu3O7-delta (YBCO) low-angle grain boundaries and films on vicinal substrates, where the breaking is experienced by Abrikosov-Josephson vortices (AJV) and Josephson string vortices (SV), respectively. With our model, we have experimentally extracted some intrinsic parameters of the AJV and SV, such as the line tension is an element of(l) and compared it to existing predictions based on the vortex structure.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.