Log Mean Temperature Correction Factor: An Alternative Representation

2002 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Correction Factor ◽  
Functional Dependence ◽  
Cross Flow ◽  
Practical Interest ◽  
Temperature Correction ◽  
Operating Conditions ◽  
Alternative Representation ◽  
Mean Temperature ◽  
Wide Range ◽  
Variable Function

The Log Mean Temperature Difference (LMTD) correction factor, F, is traditionally expressed in terms of two non-dimensional parameters P=t2−t1T1−t1, and R=T1−T2t2−t1 in form of charts as the underlying equations are complicated. F shows strong functional dependence on both P and R, reducing the accuracy of reading the charts particularly in the steep regions. In this study it is shown that the LMTD correction factor F, can be expressed in terms of two new variables, φ=(T1−T2)2+(t2−t1)22[(T1+T2)−(t1+t2)] and ρ=T1−t2T2−t1. Expressed in terms of these variables, F correlations and charts are much better behaved. Furthermore, it is shown that for the shell and tube and cross flow of heat exchangers, over a wide range of operating conditions of practical interest (0.5 ≤ ρ ≤ 1.0), F can be approximated as a function of a single variable function φ, to within 4% accuracy.

scholarly journals Systematic derivation of a surface polarisation model for planar perovskite solar cells

2018 ◽  
Vol 30 (3) ◽  
pp. 427-457 ◽  
Author(s):  
N. E. COURTIER ◽  
J. M. FOSTER ◽  
S. E. J. O'KANE ◽  
A. B. WALKER ◽  
G. RICHARDSON
Keyword(s):  
Solar Cells ◽  
Numerical Solutions ◽  
Perovskite Solar Cells ◽  
Practical Interest ◽  
Operating Conditions ◽  
Asymptotic Approach ◽  
Perovskite Layer ◽  
Current Voltage ◽  
Wide Range ◽  
Vacancy Density

Increasing evidence suggests that the presence of mobile ions in perovskite solar cells (PSCs) can cause a current–voltage curve hysteresis. Steady state and transient current–voltage characteristics of a planar metal halide CH3NH3PbI3PSC are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width ~2 nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer (~600 nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplifiedsurface polarisationmodel in which the slow ion dynamics are replaced by interfacial (non-linear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.

A General Expression for the Determination of the Log Mean Temperature Correction Factor for Shell and Tube Heat Exchangers

2003 ◽  
Vol 125 (3) ◽  
pp. 527-530 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Exchanger ◽  
Correction Factor ◽  
Heat Exchangers ◽  
Direct Determination ◽  
Temperature Correction ◽  
Tube Heat Exchanger ◽  
Mean Temperature ◽  
Shell And Tube ◽  
Graphical Presentation

This paper presents a single closed form algebraic equation for the determination of the Log Mean Temperature Difference correction factor F for shell and tube heat exchangers having N shell passes and 2M tube passes per shell. The equation and its graphical presentation generalize the traditional equations and charts used for the determination of F. The equation presented is also useful in design, analysis and optimization of multi shell and tube heat exchanger, particularly for direct determination of the number of shells.

A Tubular Cross-Flow Filtration Module Based on Chaotic Advection

2015 ◽  
Author(s):  
T. G. Kang ◽  
K. T. Park ◽  
S. U. Kim
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Cross Flow ◽  
Operating Conditions ◽  
Membrane Module ◽  
Chaotic Advection ◽  
Thin Plates ◽  
Tubular Membrane ◽  
Cross Flow Filtration ◽  
Wide Range

We propose a tubular membrane module with embedded three-dimensional structures which is efficient in a wide range of operating conditions (covering both laminar and turbulent flows). Thin plates with barriers are inserted periodically in the circular channel geometry, leading to chaotic advection in a spatially periodic channel flow. Using a numerical scheme combining a particle-tracking and the finite element method, the insert geometry is optimized. The performance of the newly proposed membrane module is assessed by experiments. The membrane module with embedded inserts is found to be better in performance than an ordinary tubular membrane module.

Free Convective Flow Patterns in Cylindrical Annuli

1969 ◽  
Vol 91 (3) ◽  
pp. 310-314 ◽  
Author(s):  
R. E. Powe ◽  
C. T. Carley ◽  
E. H. Bishop
Keyword(s):  
Unsteady Flow ◽  
Convective Flow ◽  
Cross Flow ◽  
Flow Patterns ◽  
Operating Conditions ◽  
Experimental Investigations ◽  
Free Convective Flow ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Written Descriptions

The results of all available experimental investigations into the characteristics of free convective flow of air between horizontal isothermal concentric cylinders are reviewed and several discrepancies are pointed out. An experimental study is described which was directed at resolving these discrepancies and categorizing the several flow patterns which have been observed. Using six different cylinder sets and varying both the annulus pressure and temperature difference between the cylinder surfaces, a range of Grashof numbers (based on annulus width) from 300 to 3.4 × 106 was achieved. The resulting air flow patterns were made visible with the use of tobacco smoke and are documented by written descriptions, photographs, motion pictures, and quantitative data. One steady and three unsteady flow patterns were observed and comparison with the results of other investigators is presented. A chart is presented which allows prediction of the type of unsteady flow that will occur for a wide range of cylinder combinations and annulus operating conditions. A comparison with cylinders in forced cross-flow is used to satisfactorily predict the onset of one of the unsteady flow patterns. Also, the flow patterns observed experimentally are compared to those predicted by an available analytical solution.

The Influence of Channel Orientation and Flow Rates on the Bubble Formation in a Liquid Cross-Flow

2010 ◽  
Author(s):  
Kamran Siddiqui ◽  
Wajid A. Chishty
Keyword(s):  
Flow Rate ◽  
Liquid Flow ◽  
Gas Turbines ◽  
Alternative Fuels ◽  
Bubble Formation ◽  
Cross Flow ◽  
Operating Conditions ◽  
Flow Rates ◽  
Bubble Detachment ◽  
Wide Range

For gas turbines burning liquid fuels, improving fuel spray and combustion characteristics are of paramount importance to reduce emission of pollutants, improve combustor efficiency and adapt to a range of alternative fuels. Effervescent atomization technique, which involves the bubbling of an atomizing gas through aerator holes into the liquid fuel stream, has the potential to give the required spray quality for gas turbine combustion. Bubbling of the liquid stream is presently used in a wide range of other applications as well such as spray drying, waste-water treatment, chemical plants, food processing and bio- and nuclear-reactors. In order to optimize control of the required aeration quality and thus the resulting spray quality over a wide range of operating conditions, it is important that the dynamics of bubble formation, detachment and downstream transport are well understood under these circumstances. The paper reports on an experimental study conducted to investigate the dynamics of gas bubbles in terms of bubble detachment frequency when injected from an orifice that is subjected to a liquid cross-flow. The experiments were conducted over a range of gas and liquid flow rates and at various orientations of the liquid channel. Analyses presented here are based on shadowgraph images of two-phase flow, acquired using a high speed camera and a low intensity light source. An image processing algorithm was developed for the detection and characterization of the bubble dynamics. Results show that bubble detachment frequency is a function of both liquid cross-flow rate and the gas-to-liquid flow rate ratio.

On the Sensitivity of the Asperity Pressures and Temperatures to the Fluid Pressure Distribution in Mixed-Film Lubrication

1999 ◽  
Vol 122 (1) ◽  
pp. 77-85 ◽  
Author(s):  
L. Chang ◽  
Yongwu Zhao
Keyword(s):  
Pressure Distribution ◽  
Fluid Pressure ◽  
Practical Interest ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Time Duration ◽  
Time Step ◽  
Wide Range ◽  
Mixed Film ◽  
Film Lubrication

This paper studies the sensitivities of the asperity pressures and temperatures to the fluid pressure distribution in concentrated contacts operating in the regime of mixed-film lubrication. Two fluid pressure distributions are used in the study. One is a Hertz-like distribution that neglects micro-EHL responses of the lubricant, and the other models the micro-EHL effects with significant pressure rippling. The asperity pressures and temperatures are deterministically calculated in time by numerically solving the asperity-contact and the transient energy equations as the two surfaces move relative to each other. The contact is simulated for sufficient time duration until the samples of the calculated asperity variables reach a statistical equilibrium that reflects the random-process nature of the problem. Parametric analyses are carried out that cover a wide range of operating conditions of practical interest. The results obtained consistently suggest that the asperity pressures and temperatures are not sensitively related to the fluid pressure. This insensitivity supports the use of any fluid pressure distribution consistent with the underlying mixed-film problem, rather than determining it by numerically solving the Reynolds equation at every time step of the simulation process. The study lays a foundation on which to advance modeling of the mixed-film contacts with a proper balance among model robustness, computational efficiency and solution accuracy. [S0742-4787(00)01101-2]

Comparison of Deterministic and Linear Cosine Spatial Filtering of Transmission Electron Micrographs

1972 ◽  
Vol 30 ◽  
pp. 596-597
Author(s):  
David A. Ansley
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Spatial Filter ◽  
Operating Conditions ◽  
Objective Lens ◽  
List Type ◽  
Spatial Filters ◽  
Transmission Electron ◽  
Wide Range

The coherence of the electron flux of a transmission electron microscope (TEM) limits the direct application of deconvolution techniques which have been used successfully on unmanned spacecraft programs. The theory assumes noncoherent illumination. Deconvolution of a TEM micrograph will, therefore, in general produce spurious detail rather than improved resolution.A primary goal of our research is to study the performance of several types of linear spatial filters as a function of specimen contrast, phase, and coherence. We have, therefore, developed a one-dimensional analysis and plotting program to simulate a wide 'range of operating conditions of the TEM, including adjustment of the:(1) Specimen amplitude, phase, and separation(2) Illumination wavelength, half-angle, and tilt(3) Objective lens focal length and aperture width(4) Spherical aberration, defocus, and chromatic aberration focus shift(5) Detector gamma, additive, and multiplicative noise constants(6) Type of spatial filter: linear cosine, linear sine, or deterministic

Evaluation of the accuracy indicators in determination of the coating thickness by crater grinding method

2020 ◽  
Vol 86 (7) ◽  
pp. 39-44
Author(s):  
K. V. Gogolinsky ◽  
A. E. Ivkin ◽  
V. V. Alekhnovich ◽  
A. Yu. Vasiliev ◽  
A. E. Tyurnina ◽  
...  
Keyword(s):  
Coating Thickness ◽  
Functional Dependence ◽  
Measurement Procedure ◽  
Metrological Certification ◽  
Measuring Instruments ◽  
Properties Of Coatings ◽  
Special Equipment ◽  
Grinding Method ◽  
Accuracy Of Measurements ◽  
Wide Range

Thickness is one of the key indicators characterizing the quality and functional properties of coatings. Various indirect methods (electromagnetic, radiation, optical) most often used in practice to measure thickness are based on the functional dependence of a particular physical parameter of the system «base – coating» on the coating thickness. The sensitivity of these procedures to the certain properties of coatings imposes the main restriction to the accuracy of measurements. Therefore, the development and implementation of the approaches based on direct measurements of geometric parameters of the coating appears expedient. These methods often belong to the class of «destructive» and, in addition to measuring instruments, require the use of special equipment. To ensure the uniformity of measurements in the laboratory or technological control, these methods are isolated as a separate procedure (method) and must undergo metrological certification in accordance with GOST R 8.563–2009. We present implementation, metrological certification and practical application of the method for measuring thickness of coatings by crater-grinding method. The principles of technical implementation of test equipment, measurement procedure and calculation formulas are described. The results of evaluating the accuracy indicators of the proposed procedure by calculation and experimental methods are presented. In both cases, the relative error did not exceed 6%. The applicability of the developed technique is shown for a wide range of coating materials (from soft metals to superhard ceramics) of different thickness (with from units to hundreds of micrometers). Apart from the goals of process control and outgoing inspection, the method can be recommended as a reference measurement procedure for calibration of measures and adjusting samples for various types of thickness gauges.

Structure and properties of compact articles from high-alloyed iron powder with adding of boron nitride

2020 ◽  
pp. 39-48
Author(s):  
B. O. Bolshakov ◽  
◽  
R. F. Galiakbarov ◽  
A. M. Smyslov ◽  
◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Boron Nitride ◽  
Grain Boundary ◽  
Bending Strength ◽  
Physical And Mechanical Properties ◽  
Operating Conditions ◽  
Structure And Properties ◽  
Steam Turbines ◽  
Friction Forces ◽  
Wide Range

The results of the research of structure and properties of a composite compact from 13 Cr – 2 Мо and BN powders depending on the concentration of boron nitride are provided. It is shown that adding boron nitride in an amount of more than 2% by weight of the charge mixture leads to the formation of extended grain boundary porosity and finely dispersed BN layers in the structure, which provides a high level of wearing properties of the material. The effect of boron nitride concentration on physical and mechanical properties is determined. It was found that the introduction of a small amount of BN (up to 2 % by weight) into the compacts leads to an increase in plasticity, bending strength, and toughness by reducing the friction forces between the metal powder particles during pressing and a more complete grain boundary diffusion process during sintering. The formation of a regulated structure-phase composition of powder compacts of 13 Cr – 2 Mо – BN when the content of boron nitride changes in them allows us to provide the specified physical and mechanical properties in a wide range. The obtained results of studies of the physical and mechanical characteristics of the developed material allow us to reasonably choose the necessary composition of the powder compact for sealing structures of the flow part of steam turbines, depending on their operating conditions.

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