Steady-state Experimental Data Research Articles

Modeling Growth Rate Dispersion in Industrial Crystallizers

AbstractThe phenomenon of healing appears to be a plausible explanation for the growth rate dispersion observed in many industrial crystallizers. In this paper a growth model is postulated, which describes the healing of plastically deformed attrition fragments. The rate of healing is assumed to be inversely proportional to the initial strain and to the rate of change of either the length, the area, or the volume of the crystal. The validity of the proposed model is verified by the simulation of growth of the smallest crystals (L0) in time in a growth experiment for specific combinations of the model parameters. In addition, the applicability of the proposed model is evaluated through simulations of steady state experimental data obtained in a 75‐liter Draft Tube (DT) crystallizer. It is concluded that the proposed model is able to fit reasonably well the experimental crystal size distribution. The model predicts the existence of a ‘dead time’ during which attrition fragments with large initial strain do not grow and which may last several residence times.

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.

TiO 2 photocatalytic oxidation of nitric oxide: transient behavior and reaction kinetics

Photocatalytic oxidation (PCO) of nitric oxide (NO) over TiO 2 catalyst was studied at source levels (5–60 ppm). The PCO process involves a series of oxidation steps by the OH radical: NO→HNO 2→NO 2→HNO 3. The product NO 2 can be collected in an adsorbent bed and either recycled back to the combustion chamber or recovered as nitric acid. The ratio of NO 2 − to NO 3 − from spent catalyst liquor drops with irradiation time until a steady state is reached. The reactions are limited by thermodynamic equilibrium after ∼12 s space time. The steady-state experimental data from space time and inlet concentration effects can be described with the Langmuir–Hinshelwood (L–H) kinetic model with R 2=0.9208.

Kinetics of cardiac RyR channel gating studied at high temporal resolution.

Measurements of ryanodine receptor (RyR) activity during dynamic changes of calcium concentration have suggested that RyR has at least four calcium binding sites, and that activation transpires as an increase in the activity within the high open probability H-mode. Binding of several Ca2+ ions within the H-mode should manifest itself in the steady-state RyR activity by the presence of multiple closed times. However, previously only two closed times were detected in the H-mode of RyR activity. Here we recorded steady-state activity of single cardiac RyRs with high temporal resolution and compared it to data simulated under the same conditions using our previously published model of RyR gating. At a 10 kHz resolution, the closed time histograms of both experimental and simulated data had three exponential components. The closed times of simulated data were not significantly different from those obtained experimentally. After filtering at 2 kHz, only two exponential closed time components with time constants not significantly different from those previously published could be detected in both experimental and simulated records. The conformity of the steady-state experimental data to the model derived from the dynamic data provides further support for the idea that RyRs need binding of multiple Ca2+ ions to open.

Kinetics of selective CO oxidation in excess of H 2 over the nanostructured Cu 0.1Ce 0.9O 2− y catalyst

The kinetics of CO oxidation in excess hydrogen over a nanostructured Cu 0.1Ce 0.9O 2− y catalyst prepared by a sol–gel method was studied under simulated preferential oxidation (PROX) reactor conditions. Reaction temperature was varied between 45 and 155 °C. The partial pressures of CO and O 2 in 0.5 bar excess of H 2 and He as a balance gas were varied between 0.001 and 0.025 and between 0.001 and 0.05 bar, respectively. The catalyst was found to be 100% selective in the temperature range from 45 to 90 °C. In this temperature range, the kinetics of the reaction was found to follow the redox mechanism represented by the Mars and van Krevelen type of rate equation. Kinetic parameters of the reaction calculated on the basis of this rate equation were found to be as follows: apparent activation energy for CO oxidation step, 57.2 kJ/mol, and for the catalyst reoxidation step, 60.2 kJ/mol. The observed reaction rate at the 0.01-bar CO partial pressure and stoichiometric O 2 partial pressure at 90 °C was 2.7×10 −6 mol/g cat s. The steady-state experimental data could be regressed almost equally well with the modified Langmuir–Hinshelwood model introduced by Liu et al. However, the transient experiments performed in our study reveal that lattice oxygen could be involved even at low reaction temperatures, thus favoring the use of a steady state Mars and van Krevelen kinetic model.

Characteristics of CF/PEI tape winding process with on-line consolidation

The effects of processing conditions on consolidation quality for the tape winding process of thermoplastic composites with on-line consolidation have been investigated. Composite rings were manufactured using carbon fibre (CF)/polyetherimide (PEI) tape for both cases with and without an insulated ring. Based on heat transfer and intimate contact/autohesion mechanisms, a steady-state finite element method (FEM) model was developed to analyze consolidation quality and overheating in composite tapes. The processing windows with the upper bound for good consolidation and the lower bound for overheating were established for winding speed as a function of processing temperature, when the compaction pressure was kept constant. Good correlation was obtained between the steady-state FEM model and experimental data.

Determination of diffusion and distribution coefficients in polymer membranes by unsteady-state dialysis and steady-state RO methods

A new method has been developed for determination and analysis of diffusion and distribution coefficients of salts in dialysis and RO membranes based on unsteady-state dialysis and steady-state RO experimental data. The method is based on a two-part model of heterogeneous RO membranes consisting of perfect or dense and imperfect or porous parts. Such a model can be described by differential equations accounting for all water and salt fluxes entering and leaving the membrane. The method was applied to various salt solution/polymer membrane systems. Thermodynamic and kinetic parameters of the system were found to be influenced by physico-chemical parameters of the penetrant reflecting its ionic properties, chemical composition of the polymer as well as structure the membranes.

A dynamic model of the type-2 inositol trisphosphate receptor.

The dynamic properties of the inositol (1,4,5)-trisphosphate (IP(3)) receptor are crucial for the control of intracellular Ca(2+), including the generation of Ca(2+) oscillations and waves. However, many models of this receptor do not agree with recent experimental data on the dynamic responses of the receptor. We construct a model of the IP(3) receptor and fit the model to dynamic and steady-state experimental data from type-2 IP(3) receptors. Our results indicate that, (i) Ca(2+) binds to the receptor using saturating, not mass-action, kinetics; (ii) Ca(2+) decreases the rate of IP(3) binding while simultaneously increasing the steady-state sensitivity of the receptor to IP(3); (iii) the rate of Ca(2+)-induced receptor activation increases with Ca(2+) and is faster than Ca(2+)-induced receptor inactivation; and (iv) IP(3) receptors are sequentially activated and inactivated by Ca(2+) even when IP(3) is bound. Our results emphasize that measurement of steady-state properties alone is insufficient to characterize the functional properties of the receptor.

Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion.

Magnetic resonance elastography (MRE) is an important new method used to measure the elasticity or stiffness of tissues in vivo. While there are many possible applications of MRE, breast cancer detection and classification is currently the most common. Several groups have been developing methods based on MR and ultrasound (US). MR or US is used to estimate the displacements produced by either quasi-static compression or dynamic vibration of the tissue. An important advantage of MRE is the possibility of measuring displacements accurately in all three directions. The central problem in most versions of MRE is recovering elasticity information from the measured displacements. In previous work, we have presented simulation results in two and three dimensions that were promising. In this article, accurate reconstructions of elasticity images from 3D, steady-state experimental data are reported. These results are significant because they demonstrate that the process is truly three-dimensional even for relatively simple geometries and phantoms. Further, they show that the integration of displacement data acquisition and elastic property reconstruction has been successfully achieved in the experimental setting. This process involves acquiring volumetric MR phase images with prescribed phase offsets between the induced mechanical motion and the motion-encoding gradients, converting this information into a corresponding 3D displacement field and estimating the concomitant 3D elastic property distribution through model-based image reconstruction. Fully 3D displacement fields and resulting elasticity images are presented for single and multiple inclusion gel phantoms.

Transport of methyl tert-butyl ether through alfalfa plants.

Concentrations measured in alfalfa plant stem segments indicated that plants grown in methyl tert-butyl ether (MTBE)-contaminated soil took up the chemical through their roots. Assuming a cylindrical shape for the plant stem, a mathematical model was developed to describe the transport of MTBE through the stems. Simulation results from uniform and nonuniform initial concentration distributions across the stem radius were compared with steady-state experimental data. With known values of plant stem radius, water usage, water content, and the distance over which the concentration decreased by 50%, the diffusion coefficient of MTBE radial transport across the plant stem was estimated with 95% confidence to be in the range of 8.43-16.2 x 10(-8) cm2/s with a mean of 1.23 x 10(-7) cm2/s. When the diffusion coefficient was calculated based on transient experimental data, the values with 95% confidence interval ranged from 4.14 x 10(-7) to 8.00 x 10(-7) cm2/s with a mean value of 6.07 x 10(-7) cm2/s. The difference between these two results can be reduced by more accurate estimation of the water flow velocity through plant stems. The model is applicable to other species including sunflowers and poplars upon substitution of appropriate parameters.

NADH-Regulated metabolic model for growth of Methylosinus trichosporium OB3b. Model presentation, parameter estimation, and model validation.

A biochemical model is presented that describes growth of Methylosinus trichosporium OB3b on methane. The model, which was developed to compare strategies to alleviate NADH limitation resulting from cometabolic contaminant conversion, includes (1) catabolism of methane via methanol, formaldehyde, and formate to carbon dioxide; (2) growth as formaldehyde assimilation; and (3) storage material (poly-beta-hydroxybutyric acid, PHB) metabolism. To integrate the three processes, the cofactor NADH is used as central intermediate and controlling factor-instead of the commonly applied energy carrier ATP. This way a stable and well-regulated growth model is obtained that gives a realistic description of a variety of steady-state and transient-state experimental data. An analysis of the cells' physiological properties is given to illustrate the applicability of the model. Steady-state model calculations showed that in strain OB3b flux control is located primarily at the first enzyme of the metabolic pathway. Since no adaptation in V(MAX) values is necessary to describe growth at different dilution rates, the organism seems to have a "rigid enzyme system", the activity of which is not regulated in response to continued growth at low rates. During transient periods of excess carbon and energy source availability, PHB is found to accumulate, serving as a sink for transiently available excess reducing power.

An Empirical Investigation of Polymer Flow in Porous Media

Steady-state flow experimental data have been analyzed for two commonly used polymers representing two generic classes, polysaccharides (Xanflood), and partially hydrolyzed polyacrylamides (Pusher-700), flowing inside bead packs and Berea sandstone. Oscillatory flow measurements have been used to compute the polymer solution's longest relaxation time (θf1), which is referred to as the characteristic relaxation time in this paper. Steady-state flow experimental data for the two polymers combined with measured polymer viscous properties have been converted to average shear stress−shear rate data inside porous media. An average power-law exponent (n) is therefore obtained for the polymer flow inside the porous medium. Using θf1, n, rock permeability (k), porosity (φ), and fluid flow velocity (u), a viscoelasticity number (Nv) is calculated and found to strongly correlate with the pressure gradient inside porous media. This correlation is the basis for defining a viscoelastic model for polymer flow, analogo...

Transient Response of a Cross-Flow Charge Air Intercooler and Its Influence on Engine Operation

To examine the influence of intercooler thermal inertia on transient engine operation, a 2D model of an air-to-air, cross-flow heat exchanger has been developed. Finned passages of heat exchanger core have been subdivided into separate channels of charge and cooling air, respectively. A two-step Lax-Wendroff differential method has been used to solve one-dimensional, nonhomentropic, unsteady, compressible fluid flow in each channel. Simultaneously, the Saul’yev explicit method has been applied to compute the 2D temperature distribution along the dividing plate. The Wieting correlation has been used to compute the local convection heat transfer coefficient and friction factor. The model has been verified against steady-state experimental data and then incorporated into an engine cycle simulation program based on “Filling-Emptying” method. Two engine transients have been simulated; the acceleration of the engine from idle to rated engine speed at constant load, and deceleration from rated power to rated torque by increasing the load torque. The first example shows the warming up of the intercooler, while in the second example intercooler temperatures are decreasing. The results have been compared with the predictions of an additional set of simulations, where the NTU-effectiveness method has been used to simulate the intercooler, and the thermal inertia of intercooler has been neglected. The results of both sets of simulations are discussed in the paper. [S0022-0434(00)02003-7]

A trickle-bed reactor model for hydrogenation of 2,4 dinitrotoluene: experimental verification

A trickle-bed reactor model has been developed for hydrogenation of 2,4 dinitrotoluene (DNT). This model incorporates the contributions of partial wetting and stagnant liquid hold-up effects in addition to external and intraparticle mass transfer resistances for a complex consecutive/parallel reaction scheme under consideration represented by L-H-type kinetics. As the reaction is highly exothermic, the heat effects have also been incorporated in the model. The reactor performance for complete wetting, partial wetting of catalyst particles and in the presence of stagnant liquid pockets has been compared and the significance of different parameters discussed. Experimental data were obtained for different particles sizes, different gas and liquid velocities in a temperature range 318–328 K. The model predictions were compared with experimental data and were found to agree very well for a wide range of operating conditions. The model proposed here also allowed prediction of maximum temperature rise in the catalyst bed and which was also found to agree well with the steady-state experimental data. Under certain conditions, hysteresis behaviour of the reactor performance has been observed.

Steady-State Investigation of Vapor Deposited Micro Heat Pipe Arrays

An experimental investigation of vapor deposited micro heat pipe arrays was conducted using arrays of 34 and 66 micro heat pipes occupying 0.75 and 1.45 percent of the cross-sectional area, respectively. The performance of wafers containing the arrays was compared with that of a plain silicon wafer. All of the wafers had 8 × 8 mm thermofoil heaters located on the bottom surface to simulate the active devices in an actual application. The temperature distributions across the wafers were obtained using a Hughes Probeye TVS Infrared Thermal Imaging System and a standard VHS video recorder. For wafers containing arrays of 34 vapor deposited micro heat pipes, the steady-state experimental data indicated a reduction in the maximum surface temperature and temperature gradients of 24.4 and 27.4 percent, respectively, coupled with an improvement in the effective thermal conductivity of 41.7 percent. For wafers containing arrays of 66 vapor deposited micro heat pipes, the corresponding reductions in the surface temperature and temperature gradients were 29.0 and 41.7 percent, respectively, and the effective thermal conductivity increased 47.1 percent, for input heat fluxes of 4.70 W/cm2. The experimental results were compared with the results of a previously developed numerical model, which was shown to predict the temperature distribution with a high degree of accuracy, for wafers both with and without the heat pipe arrays.

Thermal effects in the tilting pad journal bearings

This paper presents results from a study of thermal and elastic effects inthe tilting pad journal bearing. The analysis considers thermal and elastic distortions of the pad, thermal growth of the bearing components, and cross-filmvariations of lubricant viscosity. The computer model is verified against steady-state experimental data gathered from a five-shoe bearing. Calculations indicate that significant changes in bearing and pad clearances may occur as a result of pad, shaft and housing distortions. In some cases, this may lead to an operational preload which is substantially different from that called for in the initial design.

A Study of High-Temperature Heat Pipes With Multiple Heat Sources and Sinks: Part II—Analysis of Continuum Transient and Steady-State Experimental Data With Numerical Predictions

The experimental data presented in Part I were analyzed concerning the heat pipe performance characteristics and design. Postexperiment examination of the loosely wrapped screen wick revealed annular gaps both between the wick and the heat pipe wall and between adjacent screen layers, which greatly enhanced the maximum heat capacity of the heat pipe compared to the analytical capillary limit for a tightly wrapped screen wick. A numerical simulation for transient heat pipe performances including the vapor region, wick structure, and the heat pipe wall is given. Numerical results for continuum transient and steady-state operations with multiple heat sources were compared with experimental results and found to be in good agreement.

Modifications to transonic flow codes for unsteady perturbations around an experimental mean

The transonic small-disturbance equation is often used to compute unsteady transonic flow over a wing. However, as the equation assumes isentropic flow, it is inaccurate for strong shock waves. The inaccuracy is mostly seen as an incorrect time-averaged shock location, whereas the prediction of the time-accurate fluctuation about the mean is satisfactory. The time-averaged solution may be corrected using steady-state experimental data, but first the solution must be written in a strained coordinate system so that the shock movement, and thus the nonlinearities, are removed. This technique has been used in both twoand three-dimensional calculations, and has been shown to correct satisfactorily the time-accurate shock locations. Slight errors in the corrected pressure distributions may be attributed to scatter in the experimental data and to the interpolation between sparse data points.

Analytical solution for the transient thermal response of volumetrically heated fixed porous nuclear debris beds

An analytical solution is presented for the problem of the transient distribution of fluid and solid temperatures in a volumetrically heated fixed porous nuclear debris bed through which a single-phase fluid, either subcooled liquid or superheated vapor, is flowing. The one-dimensional, time-dependent Modified Dispersion-Concentric Model (D-C Model) is used in the analysis of this problem. The method of solution is based on transformations that reduce the equations and then the application of Green's function in a straightforward manner. The mathematical solution characteristics for the transient fluid and solid temperature distributions are analyzed for subcooled liquid flow and for superheated vapor flow. Also, the transient fluid and solid phase temperature distributions for infinite time are compared with steady-state experimental data.

THE DYNAMIC BEHAVIOR OF A FIXED-BED STEAM-OXYGEN COAL GASIFIER DISTURBED BY WATER INFLUX II. MODEL DEVELOPMENT AND VERIFICATION

A one-dimensional transient model has been developed to simulate the unsteady-state behavior of a fixed-bed coal gasifier disturbed by water injection. The resulting set of differential equations was solved numerically using a finite difference method. The validity of the model was first tested against the steady-state experimental data on the product gas composition and the gas production rate for different feed conditions, and the model has been further extended to include transient operation of the gasifier. The dynamic analysis includes the quantitative validation of the system response to changes in the feed condition—either a step change or a rectangular-pulse type change. The simulation results show that the dynamic behavior has a quite different trend in the product gas composition than equilibrium models predict. Such a discrepancy occurs because dynamic behavior is controlled by the changes in the gasification reaction rate rather than a shift in equilibrium The controlling mechanism can be elucidated in terms of the relative contribution by each gasification reaction.