Effect of Nozzle Junction and Equipment Stiffness on Absorption of Pipe Thermal Loads

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kedar A. Damle ◽  
Pratik S. Gharat ◽  
Rudolf Neufeld ◽  
Wilhelm Peters
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Pressure Range ◽  
Nozzle Diameter ◽  
Combined Effects ◽  
Thermal Loads ◽  
Actual System ◽  
Foundation Design ◽  
Local Loads ◽  
The Given

As an industry norm, the nozzle local loads are considered to be local and are not considered in foundation design. Presently, this norm is under debate. One opinion is some percent of these loads are to be considered to be transferred to the foundation. The horizontal forces on the foundation are more critical than vertical forces. Attempt has been made to understand the system and create a model which will represent the system to a good approximation. A mathematical model is developed to demonstrate the actual system. It is a stiffness system consisting of equipment, nozzle junction, and connected piping. The connected pipes are heated sequentially to generate nozzle loads in axial and out plane directions. Steady-state thermal loads are calculated for the given system stiffness. Governing parameters are identified and altered to note the effect. The governing parameters identified are equipment diameter (D), nozzle location on equipment (x), and nozzle diameter (d). The effect is studied for pressure range (20–120 bar) and temperature (100–400 °C). The results of percentage loads transferred with respect to the governing parameters are plotted. It is observed that nozzle loads in axial directions are transferred to the foundation almost 100%, whereas out plane loads are absorbed by the system to a greater extent. Further study is required to investigate combined effects of all such nozzle loads for single equipment. The results may be refined for different materials and effect of nozzle reinforcement.

scholarly journals Experimental and Theoretical Study of Microturbine-Based BCHP System

2001 ◽  
Author(s):  
P. D. Fairchild ◽  
S. D. Labinov ◽  
A. Zaltash ◽  
D. T. Rizy
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Air Temperature ◽  
Flow Rate ◽  
Waste Heat ◽  
Actual Data ◽  
Thermal Loads ◽  
Power Demand ◽  
Gas Temperature ◽  
Power Setting

Abstract On-site and near-site distributed power generation (DG), as part of a Buildings Cooling, Heating and Power (BCHP) system, brings both electricity and waste heat from the DG sources closer to the end user’s electric and thermal loads. Consequently, the waste heat can be used as input power for heat-activated air conditioners, chillers, and desiccant dehumidification systems; to generate steam for space heating; or to provide hot water for laundry, kitchen, cleaning services and/or restrooms. By making use of what is normally waste heat, BCHP systems meet a building’s electrical and thermal loads with a lower input of fossil fuel, yielding resource efficiencies of 40 to 70% or more. To ensure the success of BCHP systems, interactions of a DG system — such as a microturbine and thermal heat recovery units under steady-state modes of operation with various exhaust backpressures — must be considered. This article studies the performance and emissions of a 30-kW microturbine over a range of design and off-design conditions in steady-state operating mode with various backpressures. In parallel with the experimental part of the project, a BCHP mathematical model was developed describing basic thermodynamic and hydraulic processes in the system, heat and material balances, and the relationship of the balances to the system configuration. The model can determine the efficiency of energy conversion both for an individual microturbine unit and for the entire BCHP system for various system configurations and external loads. Based on actual data from a 30-kW microturbine, linear analysis was used to obtain an analytical relationship between the changes in the thermodynamic and hydraulic parameters of the system. The actual data show that, when the backpressure at the microturbine exhaust outlet is increased to the maximum of 7 in. wc (0.017 atm), the microturbine’s useful power output decreases by from 3.5% at a full power setting of 30 kW to 5.5% at a one-third power setting (10 kW), while the efficiency of the unit decreases from 2.5 to 4.0%, accordingly. Tests on the microturbine were conducted at the Cooling, Heating, and Power Laboratory set up at the Oak Ridge National Laboratory’s Buildings Technology Center. Data were collected from the microturbine at power demand settings of 30 kW (full load) to 10 kW in 5-kW increments. For each power demand setting, data measurements were taken over an entire range of microturbine exhaust backpressures. The parameters measured were engine speed, ambient air temperature, air temperature at the microturbine inlet, gas temperature at the turbine outlet, exhaust gas temperature, throttle pressure loss, flow rate of natural gas, and composition of combustion products. The mathematical model provided gas temperature before the turbine, compression rate, and air flow rate, which were determined based on the measured data. The results of these early tests and the computer-based simulation model are in very close agreement.

Tip-Tilt Motion Control of Fast Steering Mirror in the Giant Magellan Telescope (GMT)

2011 ◽  
Author(s):  
Taekyung Lee ◽  
Hyo-Sung Ahn ◽  
Young-Soo Kim ◽  
Kwijong Park
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Motion Control ◽  
Actuator Saturation ◽  
Adaptive Controller ◽  
Motion Controller ◽  
Modeling Error ◽  
Actual System ◽  
Model Stability ◽  
Motion System

This paper develops a tip-tilt motion controller of fast steering mirror (FSM) in the Giant Magellan telescope (GMT). A mathematical model of tip-tilt motion system of FSM is derived, and then based on this model, stability analysis is carried out. A heuristic adaptive controller is designed for the tip-tilt motion control with modeling error. The heuristic controller consists of two different adaptations such as initial adaptive control and adaptation at steady state errors. Through numerical simulations, the validity of the controller is illustrated. After that this paper addresses several practical issues like disturbance from wind, actuator saturation and resonance frequency from mechanical structure in implementing the controller to the actual system.

scholarly journals Computer Modeling of Aerosol Emissions Spread in the Atmosphere

2019 ◽  
Vol 97 ◽  
pp. 05023 ◽  
Author(s):  
Daler Sharipov ◽  
Sharofiddin Aynakulov ◽  
Otabek Khafizov
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Atmospheric Boundary Layer ◽  
Computer Modeling ◽  
Numerical Experiments ◽  
Climatic Factors ◽  
Numerical Algorithms ◽  
Aerosol Emissions ◽  
The Given ◽  
And Diffusion

The paper deals with the development of mathematical model and numerical algorithms for solving the problem of transfer and diffusion of aerosol emissions in the atmospheric boundary layer. The model takes into account several significant parameters such as terrain relief, characteristics of underlying surface and weather-climatic factors. A series of numerical experiments were conducted based on the given model. The obtained results presented here show how these factors affect aerosol emissions spread in the atmosphere.

Pressure dependent ultrasonic properties of hcp hafnium metal

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ramanshu P. Singh ◽  
Shakti Yadav ◽  
Giridhar Mishra ◽  
Devraj Singh
Keyword(s):  
Elastic Constants ◽  
Pressure Range ◽  
Room Temperature ◽  
Ultrasonic Attenuation ◽  
Coupling Constants ◽  
Ultrasonic Properties ◽  
Acoustic Coupling ◽  
Third Order Elastic Constants ◽  
The Stability ◽  
The Given

Abstract The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.

Approximating the stationary distribution of an infinite stochastic matrix

1991 ◽  
Vol 28 (1) ◽  
pp. 96-103 ◽  
Author(s):  
Daniel P. Heyman
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Stationary Distribution ◽  
Numerical Approximation ◽  
Stochastic Matrix ◽  
Sufficient Conditions ◽  
Finite System ◽  
Balance Equations ◽  
The Given ◽  
Steady State Balance

We are given a Markov chain with states 0, 1, 2, ···. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.

Preliminary Investigations of Machine Frame Vibration Damping Using Eddy Current Principle

2016 ◽  
Vol 821 ◽  
pp. 288-294 ◽  
Author(s):  
George Juraj Stein ◽  
Peter Tobolka ◽  
Rudolf Chmúrny
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Eddy Current ◽  
Asynchronous Motor ◽  
Oscillatory System ◽  
Vibration Damping ◽  
Combined Effects ◽  
Magnetic Forces ◽  
Novel Approach ◽  
Vibration Attenuation

A novel approach to vibration attenuation, based on the eddy current principle, is described. The combined effects of all magnetic forces acting in the oscillatory system attenuate frame vibrations and, concurrently, decrease the damped natural frequency. A mathematical model of the forces balance in the oscillatory system was derived before. Some experimental results from a mock-up machine frame excited by an asynchronous motor are presented.

Study of Temperature Effect on Servovalve-Controlled Fuel Metering Unit

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Bin Wang ◽  
Haocen Zhao ◽  
Ling Yu ◽  
Zhifeng Ye
Keyword(s):  
Steady State ◽  
Temperature Variation ◽  
Dynamic Characteristics ◽  
Numerical Study ◽  
Step Response ◽  
Fuel Temperature ◽  
Wide Range ◽  
Fuel Rate ◽  
Testing Condition ◽  
The Given

It is usual that fuel system of an aero-engine operates within a wide range of temperatures. As a result, this can have effect on both the characteristics and precision of fuel metering unit (FMU), even on the performance and safety of the whole engine. This paper provides theoretical analysis of the effect that fluctuation of fuel temperature has on the controllability of FMU and clarifies the drawbacks of the pure mathematical models considering fuel temperature variation for FMU. Taking the electrohydraulic servovalve-controlled FMU as the numerical study, simulation in AMESim is carried out by thermal hydraulic model under the temperatures ranged from −10 to 60 °C to confirm the effectiveness and precision of the model on the basis of steady-state and dynamic characteristics of FMU. Meanwhile, the FMU testing workbench with temperature adjustment device employing the fuel cooler and heater is established to conduct an experiment of the fuel temperature characteristics. Results show that the experiment matches well with the simulation with a relative error no more than 5% and that 0–50 °C fuel temperature variation produces up to 5.2% decrease in fuel rate. In addition, step response increases with the fuel temperature. Fuel temperature has no virtual impact on the steady-state and dynamic characteristics of FMU under the testing condition in this paper, implying that FMU can operate normally in the given temperature range.

Signal Synthesis Model Reference Adaptive Controller with Artificial Intelligent Technique for a Control of Continuous Stirred Tank Reactor

2018 ◽  
Vol 17 (2) ◽  
Author(s):  
Harsh Goud ◽  
Pankaj Swarnkar
Keyword(s):  
Steady State ◽  
Stirred Tank ◽  
Continuous Stirred Tank Reactor ◽  
Stirred Tank Reactor ◽  
Tank Reactor ◽  
Design And Implementation ◽  
Control Scheme ◽  
Signal Synthesis ◽  
Continuous Stirred Tank ◽  
The Given

AbstractModelling and controlling of Continuous stirred tank reactor (CSTR) is one of the major problems in the process industry. The nonlinear characteristic of CSTR may change the variation of temperature in either direction from the given set value. Chemical reactions within the CSTR depends on the given reference temperature. Such variation from reference values may result in degrading the variety of biomass. Design and implementation of the precise control device in such system are difficult for researchers. This paper proposes the MIT based control scheme as a solution to control problem of CSTR. An improvement of signal synthesis MIT system has been proposed in this study to enhance the steady-state and transient performance of CSTR. Artificial Bee Colony (ABC) based controller parameter tuning technique is applied to get the optimal performance of the controller. This paper shows the design and implementation of conventional PID tuned with the Z-N method, adaptive PID tune with ABC, MIT and ABC-MIT for CSTR. Detailed comparison based on simulation studies is presented which shows that ABC-MIT based control scheme improves the transient and steady state response.

scholarly journals Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
M. V. Barbarossa ◽  
M. Polner ◽  
G. Röst
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Temporal Evolution ◽  
Disease Outbreaks ◽  
Population Level ◽  
Coupled System ◽  
Disease Outbreak ◽  
Periodic Disease ◽  
Evolution Of Immunity

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

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