Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

scholarly journals Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

2020 ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

Strategies for solving inverse problems in thermal processes and systems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yogesh Jaluria
Keyword(s):  
Experimental Data ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Temperature Variation ◽  
Small Region ◽  
Optimization Techniques ◽  
Thermal Processes ◽  
Thermal Systems ◽  
Content Type ◽  
Final Design

Purpose This paper aims to discuss inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches that may be used to obtain results that lie within a small region of uncertainty. Therefore, the non-uniqueness of the solution is reduced so that the final design and boundary conditions may be determined. Optimization methods that may be used to reduce the uncertainty and to select locations for experimental data and for minimizing the error are presented. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. Design/methodology/approach In most analytical and numerical solutions, the basic equations that describe the process, as well as the relevant and appropriate boundary conditions, are known. The interest lies in obtaining a unique solution that satisfies the equations and boundary conditions. This may be termed as a direct or forward solution. However, there are many problems, particularly in practical systems, where the desired result is known but the conditions needed for achieving it are not known. These are generally known as inverse problems. In manufacturing, for instance, the temperature variation to which a component must be subjected to obtain desired characteristics is prescribed, but the means to achieve this variation are not known. An example of this circumstance is the annealing, tempering or hardening of steel. In such cases, the boundary and initial conditions are not known and must be determined by solving the inverse problem to obtain the desired temperature variation in the component. The solutions, thus, obtained are generally not unique. This is a review paper, which discusses inverse problems that arise in a variety of practical thermal processes and systems. It presents some of the approaches or strategies that may be used to obtain results that lie within a small region of uncertainty. It is important to realize that the solution is not unique, and this non-uniqueness must be reduced so that the final design and boundary conditions may be determined with acceptable accuracy and repeatability. Optimization techniques are often used for minimizing the error. This review presents several methods that may be applied to reduce the uncertainty and to select locations for experimental data for the best results. A few examples of thermal systems are given to illustrate the applicability of these methods and the challenges that must be addressed in solving inverse problems. By considering a variety of systems, the paper also shows the importance of solving inverse problems to obtain results that may be used to model and design thermal processes and systems. Findings The solution of inverse problems, which frequently arise in thermal processes, is discussed. Different strategies to obtain the conditions that lead to the desired result are given. The goal of these approaches is to reduce uncertainty and obtain essentially unique solutions for different circumstances. The error of the method can be checked against known conditions to see if it is acceptable for the given problem. Several examples are given to illustrate the use of these methods. Originality/value The basic strategies presented here for solving inverse problems that arise in thermal processes and systems, as well as the optimization techniques used to reduce the domain of uncertainty, are fairly original. They are used for certain challenging problems that have not been considered in detail earlier. Several methods are outlined for considering different types of problems.

scholarly journals Experimental Determination of the Buckling Loads of Floating Ice Sheets

1983 ◽  
Vol 4 ◽  
pp. 260-265 ◽  
Author(s):  
D. S. Sodhi ◽  
F. D. Haynes ◽  
K. Kato ◽  
K. Hirayama
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Experimental Determination ◽  
Characteristic Length ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Experimental Results ◽  
Buckling Loads ◽  
Data Points

Experiments were performed to determine the forces required to buckle a floating ice sheet pushing against structures of different widths. The characteristic length of each ice sheet was determined to enable a comparison to be made between the theoretical and experimental results.Most of the experimental data points are within the range of the theoretical values of normalized buckling loads for frictionless and hinged boundary conditions, which represent the extreme situations for ice-structure contact. Thus, the agreement between the theoretical and experimental buckling loads is considered to be good. Photographs of the buckled ice sheets show a resemblance to the theoretical mode of buckling.

Utilization of Experimental Data as Boundary Conditions for the Solidification Model Tempsimu-3D

2020 ◽  
Vol 165 (5) ◽  
pp. 237-242
Author(s):  
Lukas Preuler ◽  
Seppo Louhenkilpi ◽  
Christian Bernhard ◽  
Sergiu Ilie ◽  
Matthias Taferner
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Solidification Model

scholarly journals Experimental Determination of the Buckling Loads of Floating Ice Sheets

1983 ◽  
Vol 4 ◽  
pp. 260-265 ◽  
Author(s):  
D. S. Sodhi ◽  
F. D. Haynes ◽  
K. Kato ◽  
K. Hirayama
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Experimental Determination ◽  
Characteristic Length ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Experimental Results ◽  
Buckling Loads ◽  
Data Points

Experiments were performed to determine the forces required to buckle a floating ice sheet pushing against structures of different widths. The characteristic length of each ice sheet was determined to enable a comparison to be made between the theoretical and experimental results. Most of the experimental data points are within the range of the theoretical values of normalized buckling loads for frictionless and hinged boundary conditions, which represent the extreme situations for ice-structure contact. Thus, the agreement between the theoretical and experimental buckling loads is considered to be good. Photographs of the buckled ice sheets show a resemblance to the theoretical mode of buckling.

Energy Approach for Determine Frequency and Amplitude of Vibration of Piping With Closed Side Branches

2015 ◽  
Author(s):  
Igor Orynyak ◽  
Iaroslav Dubyk ◽  
Anatolii Batura
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Calculation Method ◽  
Acoustic Vibration ◽  
Energy Functional ◽  
Energy Approach ◽  
Calculation Algorithm ◽  
Local Excitation ◽  
Resonance Frequencies ◽  
System Energy

This article suggests calculation method for frequency and amplitude of acoustic vibration in piping with closed side branches, caused by gaseous running flow. The calculation algorithm consists of following steps: i) local excitation system is defined; ii) different combinations of boundary conditions are formed; iii) for fixed pair of boundary conditions ratio of stored in system energy and radiated from boundaries energy is written; iv) for every frequency energy functional is maximized to find boundary conditions; v) resonance frequencies are determined from plotting a curve of maximal energy ratio vs. frequency. Energy approach was further developed to analyze amplitude of vibration. For amplitude determine balance between injected energy (which depends on the Strouhal number and is defined from experimental data for laboratory geometries), and radiated from boundaries energy is written.

CFD Analysis of Effects of Damage Due to Bird Strike on Fan Performance

2010 ◽  
Author(s):  
Baizura Bohari ◽  
Abdulnaser Sayma
Keyword(s):  
Experimental Data ◽  
Boundary Conditions ◽  
Structural Integrity ◽  
Operating Point ◽  
Computational Techniques ◽  
Test Case ◽  
Base Line ◽  
Bird Strike ◽  
Stall Margin ◽  
Speed Characteristic

Bird ingestion has been a hazard that affects the structural integrity and survivability of turbofan engines. It can result in deformation of one or more fan blades, in which case, the engine is likely to surge and not recover. Numerical studies and simulations of bird strikes have become essential to optimize the design of engine components simultaneously to increase the engine capabilities for acceptable damage tolerance. Good understanding of these phenomena and the implications on the behaviour of the flow field with respect to the damage affecting the fan blades are usually investigated using computational techniques and/or experimental methods. The purpose of this paper is to present a Computational Fluid Dynamics (CFD) method for the analysis of the aerodynamic behaviour of an aero-engine fan affected by a bird strike. NASA rotor 67 was used as a test case because of the availability of experimental data that can be used to calibrate the model for the undamaged fan. The undamaged fan characteristic was mapped using a modification to the methodology developed by Sayma (2007). In this method a downstream variable throttle is added which allows changing the operating point on the speed characteristic without having to change downstream boundary conditions. This approach allows for changes in fan operating point to come out of the calculation as opposed to those dictated by the downstream static pressure boundary conditions used in typical computations. The methodology is automated allowing for a sweep along a speed characteristic or along a working line in one calculation in the same way as a rig test is conducted. Agreement with experimental data when available was excellent. This provided the base line for the undamaged blades. A damaged blade was inserted among undamaged blades in the fan assembly and the fan characteristic was mapped for a range of rotational speeds. Two different degrees of damage were analysed in an attempt to establish a correlation between the extent of the damage and the locus of the stall boundary. It was found that small increments on the damage lead to significant reduction in stall margin particularly at higher rotational speeds.

scholarly journals The Computation of Adjacent Blade-Row Effects in a 1.5 Stage Axial Flow Turbine

1997 ◽  
Author(s):  
Rolf Emunds ◽  
Ian K. Jennions ◽  
Dieter Bohn ◽  
Jochen Gier
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Boundary Conditions ◽  
Axial Flow ◽  
The Other ◽  
Navier Stokes ◽  
Blade Row ◽  
Flow Through ◽  
The University

This paper deals with the numerical simulation of flow through a 1.5 stage axial flow turbine. The 3-row configuration has been experimentally investigated at the University of Aachen where measurements behind the first vane, the first stage and the full configuration were taken. These measurements allow single blade row computations, to the measured boundary conditions taken from complete engine experiments, or full multistage simulations. The results are openly available inside the framework of ERCOFTAC 1996. There are two separate but interrelated parts to the paper. Firstly, two significantly different Navier-Stokes codes are used to predict the flow around the first vane and the first rotor, both running in isolation. This is used to engender confidence in the code that is subsequently used to model the multiple bladerow tests, the other code is currently only suitable for a single blade row. Secondly, the 1.5 stage results are compared to the experimental data and promote discussion of surrounding blade row effects on multistage solutions.

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