Lumped Parameter Approach Research Articles

Assessment of zero-dimensional, hybrid and multidimensional simulations for transient air flow through a cylinder-duct assembly

The pressure-time characteristics for the charging process of a cylinder with a piston-controlled port through a connecting duct is studied with the objective of assessing the accuracy of various methods such as the lumped parameter or zero-dimensional approach, an intermediate hybrid approach and a full three-dimensional computational fluid dynamics (CFD) calculation. The predictions from all the approaches are compared with experimental data. It is observed that, for a particular cup-shaped geometry of the piston, both the zero-dimensional and hybrid approach overpredict the pressure recovery rate in comparison with the three-dimensional CFD calculation, which is in good agreement with the experimental pressure-time variation. On the other hand, the agreement between the lumped parameter approach and the detailed CFD calculation is better for a flat piston, indicating the importance of the piston geometry.

Compact model based on a lumped parameter approach for the prediction of solid propellant micro-rocket performance

Abstract The development of a lumped parameter model is described for the performances prediction of a solid propellant micro-scale rocket. A micro-scale rocket consists of a combustion chamber containing the propellant, a converging and a diverging part to accelerate the gas generated by the propellant combustion. The input modelling parameters are the geometrical features of the rockets, the propellant characteristics and the ambient conditions. The output results are the temperature, the pressure, the volumic mass of the gas in the combustion chamber and the resulting thrust as a function of time. To illustrate the computational results, the performances of one micro-rocket investigated at LAAS for micro-propulsion application have been evaluated. The micro-rocket has a throat diameter of 108 μm, a chamber diameter of 850 μm, a chamber length of 1500 mm, a convergent length of 500 μm and a diverging length of 500 μm. The computational results give a chamber pressure of ∼5 bar and a thrust value of ∼3 mN at steady state. To illustrate the capabilities of the model, Section 3.3 discussed two points: • The influence of the heat loss on the thrust force; • The influence of the diverging part design on the thrust force. Results show that the divergent length has an interest and must be optimised when the external pressure is closed to vacuum, whereas the diverging part length has no effect on the thrust results when the external pressure is atmospheric.

Lumped parameters analysis of coupled kinetics and thermal-hydraulics for small reactors

A useful model is presented that permits to predict with simple means the dynamic response of a small research reactor core. The model uses a lumped parameters approach for the coupled kinetics (point reactor) and thermal-hydraulics, with continuous reactivity feedback due to coolant and fuel temperature effects. The model predictions are qualified by comparing with results from detailed simulations of reactivity insertion transients reported in the literature. Satisfactory results have been obtained for various reactivity insertion rates, up to insertions as high as $1.5. A simple criterion on the applicability range of the model is suggested, namely, the model can provide reasonably accurate predictions as long as the exit coolant temperature remains below saturation, i.e. no bulk boiling occurs in the core.

Effect of process parameters on the kerf width during the laser cutting process

One of the deficiencies in laser cutting quality is the large size of striation formed at the cut edges. Striation formation is related to the slow drifts and disturbances in various parameters during the laser cutting process. In the present study, the effects of laser power, cutting speed and energy coupling factor on the kerf size are investigated. A simplified formulation based on the lumped parameter approach is considered for the kerf width analysis. An experiment is carried out to verify the present predictions. In addition, a kerf width formulation developed in a previous study is used to compare the predictions of the present analysis and the previous results. It is found that increasing laser power and energy coupling factor increase the kerf width size. Slight variations in laser power, cutting speed and energy coupling factor modify the kerf width size considerably, in which case the striation size increases or the striation initiates during the cutting process.

Effects of spatial detail of soil information on watershed modeling

The impacts of detailed and spatially continuous soil information on hydro-ecological modeling over watersheds of mesoscale size are investigated. The impacts were assessed by comparing the simulated hydro-ecological responses based on the detailed soil spatial information derived from a fuzzy logic-based inference approach with those based on the soil information derived from a conventional soil map. This study reveals that the detailed soil spatial information has impacts on the simulated hydro-ecological responses under a lumped parameter approach. Peak runoff was reduced, yielding more realistic hydrographs for forested watersheds in the area. The detailed soil spatial information strongly impacted the simulation of net photosynthesis over the period when there is a moisture stress, but negligible impacts when there is sufficient water recharge to soil profiles. Simulation of hydro-ecological responses using a distributed parameter approach is less impacted by the detailed soil spatial information. The difference in simulated net photosynthesis under the distributed approach is smaller and also only occurred during the period of moisture stress. The impacts on spatial distribution of simulated transpiration occurred mainly over south facing slopes during the period of moisture stress.

Improved lumped parameter formulation for simplified LWR thermohydraulic analysis

Transient heat transfer in a nuclear fuel rod is modelled by an improved lumped parameter approach. Hermite approximation for integration is used to obtain the average fuel and cladding temperatures in the radial direction. Thermohydraulic behaviour of a pressurized water reactor (PWR) during reactivity insertion and partial loss-of-flow is simulated by using a simplified mathematical model of reactor core and primary coolant. Transient temperature response of fuel, cladding and coolant is analysed.

Determination of Thermoacoustic Response in a Demonstrator Gas Turbine Engine

This paper describes an analytical and experimental investigation to obtain the thermoacoustic response of a demonstrator gas turbine engine combustor. The combustor acoustic response for two different fuel injector design configurations was measured. It was found that the combustor maximum peak to peak pressure fluctuations were 0.6 psi to 2 psi for configuration A and B, respectively. Based on the measured acoustic response, another experimental investigation was conducted to identify the design features in configuration B that caused the increase in the acoustic response. The data showed that by changing the fuel injector swirler’s vane to inner passage discharge area ratio, the engine acoustic response could be lowered to an acceptable level. A simplified analytical model based on the lumped-parameter approach was then developed to investigate the effect of geometrical changes upon the engine response. The analytical model predicted the fuel injector/swirlers acoustic response as a function of the swirlers inner passage discharge area ratio and frequency. The predictions were consistent with the experimental observations, in particular, it was predicted that as the area ratio was increased, the system reactance was decreased and as a result the system changed from a damping to an amplifying system.

Venting of deflagrations: hydrocarbon–air and hydrogen–air systems

Abstract A set of 34 experiments on vented hydrocarbon–air and hydrogen–air deflagrations in unobstructed enclosures of volume up to 4000 m 3 was processed with use of the advanced lumped parameter approach. Reasonable compliance between calculated pressure–time curves and experimental pressure traces is demonstrated for different explosion conditions, including high, moderate, low and extremely low reduced overpressures in enclosures of different shape ( L max : L min up to 6:1) with different type and position of the ignition source relative to the vent, for near-stoichiometric air mixtures of acetone, methane, natural gas and propane, as well as for lean and stoichiometric hydrogen–air mixtures. New data were obtained on flame stretch for vented deflagrations. The fundamental Le Chatelier–Brown principle analog for vented deflagrations has been considered in detail and its universality has been confirmed. The importance of this principle for explosion safety engineering has been emphasized and proved by examples. A correlation for prediction of the deflagration–outflow interaction number, χ / μ , on enclosure scale, Bradley number and vent release pressure is suggested for unobstructed enclosures and a wide range of explosion conditions. Fractal theory has been employed to verify the universality of the dependence revealed of the deflagration–outflow interaction number on enclosure scale. In spite of differences between the thermodynamic and kinetic parameters of hydrocarbon–air and hydrogen–air systems, they both obey the same general regularities for vented deflagrations, including the Le Chatelier–Brown principle analog and the correlation for deflagration–outflow interaction number.

Improved lumped analysis of transient heat conduction in a nuclear fuel rod

Transient heat conduction in a nuclear fuel rod is analysed by an improved lumped parameter approach. The circunferential symmetry is assumed with the heat transfer through the gap modelled by a heat transfer coefficient. Hermite approximation for integration is used to obtain the average temperature and heat flux in the radial direction. Significant improvement over the classical lumped parameter formulation has been achieved. The proposed fuel rod heat conduction model can be used in stability analysis of BWR, simplified model of PWR or real-time simulator of nuclear power plants.

An Innovative Device for Passive Control of Surge in Industrial Compression Systems

The present paper reports a numerical–experimental study on the dynamic behavior of a compression system based on a multistage centrifugal blower and fitted with an innovative device for the dynamic suppression of surge instability. The control device is of passive type and is based on the aeroelastic coupling of the basic compression system with a hydraulic oscillator. The controlled system is modeled at first by using a nonlinear lumped parameter approach. The simulated system dynamics within a wide range of operating conditions allows a parametric analysis to be performed and the optimal values of the control parameters to be singled out. Such optimal values are then used to design the hydraulic oscillator, which results in a technically feasible and very simple configuration. Finally, experimental tests are carried out on the compression plant with and without the passive control device, which demonstrate the effectiveness of the proposed control system in suppressing surge instabilities, at least within the limits predicted by the numerical simulation.

Dynamic simulator for the miniature neutron source reactor

A dynamic simulator for the Syrian Miniature Neutron Source Reactor was developed and implemented on a desktop computer using C++ Builder. Mathematical models for the main physical phenomena of reactor such as heat transfer and neutronics were developed on the basis of the lumped parameter approach and real experimental data fitting. Point model equations of reactor kinetics was employed and solved using fourth order Runge-Kutta integration procedure. Simulation for training purposes of both real and accelerated time for normal and abnormal conditions can be accomplished with the model. The simulator is user friendly with operator.

Risk Assessment for Polycyclic Aromatic Hydrocarbon NAPLs Using Component Fractions

Polycyclic aromatic hydrocarbons (PAHs) are important environmental contaminants because of their suspected carcinogenicity. PAH contamination is often found in the form of nonaqueous phase liquids (NAPLs), such as coal tar. These materials are very complex mixtures with the constituent compounds exhibiting a wide range of chemical, physical, and toxicological properties. This makes it difficult to characterize a PAH NAPL and predict its behavior. Lumped metrics, such as total petroleum hydrocarbons (TPH), are often used to specify remediation goals at PAH NAPL sites, but these metrics do not capture the variation in NAPL composition over time and as such do not consider changes in risk over time. This paper presents an alternative method for characterizing PAH NAPLs that is based on the fraction approach developed by the Total Petroleum Hydrocarbon Criteria Working Group (TPHCWG). The fraction approach characterizes the PAH NAPL as a collection of U.S. EPA Priority Pollutants plus hydrocarbon fractions. This approach allows prediction of the NAPL compositional dynamics while retaining some of the simplified analysis of a lumped parameter approach. The fractions and priority pollutants are modeled as NAPL components for performing risks assessments and assessing the potential of remediation strategies. This makes the fraction approach amenable for use in a Risk-Based Corrective Action (RBCA) framework. In this work, the TPHCWG fraction approach was modified for description of NAPL constituents that are solids in their pure states. This was accomplished by assigning an equivalent solid−liquid reference fugacity ratio for each fraction. Thirty-year simulations with two model coal tars are presented, comparing the risk calculations for the fraction approach to those accounting for the complete NAPL composition. These simulations show that the model using the fraction approach predicts similar NAPL compositional dynamics and PAH carcinogenic risk as the model describing all the compounds. Use of the fraction approach at PAH NAPL sites will allow a more accurate accounting of the risk variation than the TPH approach. Additionally, it will emphasize development and use of remediation methods that address risk reduction, not just the reduction in total contaminant mass.

Thermal sensitivity analysis of a 22 N bipropellant thruster in a spacecraft

Transient thermal sensitivities of a 22 N bipropellant thruster in a spacecraft environment are studied in the on-orbit non-firing, firing and soak-back modes. The system has conductive and radiative modes of heat transfer and also for some time heat dissipation on valves. Temperatures of valves of the thruster assembly are analysed for their sensitivities to some of the design parameters, such as conductance between the thruster flange/mounting bracket, thruster flange/combustion chamber and thruster flange/ valve and conductance of the multilayer insulation blanket. Similarly, the influence of optical properties such as absorptance and emittance of the combustion chamber and heat shield are investigated. Studies relating to the heater power on the valves are also conducted. The lumped parameter approach is adopted and the governing equations are solved using a numerical technique. It was demonstrated that flange/ bracket conductance is the controlling parameter of the valve temperature during the sunlit period of the non-firing mode. In the soak-back condition, conductance across the flange and the valve dictates the valve temperature.

Investigation of Factors Influencing the StructuralVibration in Ball Bearings

Hertzian equation for elastic contact is utilized along with lumped parameter approach to obtain the equations that govern the structural vibration of ball bearings. The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates.Effects of preload, ball rotational speed, and damping are studied using the formulation. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 1 to 10 N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

Heavy-Duty Gas Turbine Plant Aerothermodynamic Simulation Using Simulink

This paper presents a physical simulator for predicting the off-design and dynamic behavior of a single shaft heavy-duty gas turbine plant, suitable for gas-steam combined cycles. The mathematical model, which is nonlinear and based on the lumped parameter approach, is described by a set of first-order differential and algebraic equations. The plant components are described adding to their steady-state characteristics the dynamic equations of mass, momentum, and energy balances. The state variables are mass flow rates, static pressures, static temperatures of the fluid, wall temperatures, and shaft rotational speed. The analysis has been applied to a 65 MW heavy-duty gas turbine plant with two off-board, silo-type combustion chambers. To model the compressor, equipped with variable inlet guide vanes, a subdivision into five partial compressors is adopted, in serial arrangement, separated by dynamic blocks. The turbine is described using a one-dimensional, row-by-row mathematical model, that takes into account both the air bleed cooling effect and the mass storage among the stages. The simulation model considers also the air bleed transformations from the compressor down to the turbine. Both combustion chambers have been modeled utilizing a sequence of several sub-volumes, to simulate primary and secondary zones in presence of three hybrid burners. A code has been created in Simulink environment. Some dynamic responses of the simulated plant, equipped with a proportional-integral speed regulator, are presented.

A modified approach to overfluxing analysis of transformers

A flux-linkage model for transformers is presented which can be used for studying the behaviour of transformers under overfluxing conditions. In this lumped parameter approach, all the flux fringing to tank and clamping structures is combined into one parameter: air flux. Thus, air flux is taken as a parameter for studying core saturation as an indirect method. A simple modification to account for saturation in the limb portion is suggested here. This may be achieved by representing the flux between the core outer diameter and the winding inner diameter with an extra path parallel to the limb. In addition, study of the inrush current for the transformer is taken as test case to check the extension of the model. The variation of excitation current with overvoltage and the respective harmonic contents have been reported. The results are presented and discussed.

THERMAL MODEL FOR A SWITCHED RELUCTANCE MOTOR OF TEFC DESIGN DURING STEADY AND TRANSIENT OPERATION

A lumped-parameter approach is adapted for the prediction of the steady-state and transient thermal behaviour of a prototype multiple teeth per stator pole switched reluctance motor (SRM), of TEFC (Totally Enclosed fan-cooled) design as an illustrative example. The merit of the method has been demonstrated by its application to the induction motor and experimental verification. The SRM is subdivided into simple geometries and the equivalent circuits and the proper connection of these equivalent circuits are presented. The combination of these circuits forms the full model which is used for prediction of the temperature rise of different parts of the motor.

Analysis of chaotic instabilities in boiling systems

An analytic model for the investigation of non-linear dynamics in boiling systems has been developed. This model is comprised of a nodal formulation that uses one-dimensional homogeneous equilibrium assumptions for diabatic two-phase flow, a lumped parameter approach for heated wall dynamics, and point neutron kinetics for the consideration of nuclear feedback in a boiling water reactor (BWR) loop. This model indicates that a boiling channel coupled with a riser may experience chaotic oscillations. In contrast, a boiling channel without a riser that is subjected to a constant pressure drop (i.e. a parallel channel) may undergo a supercritical bifurcation (i.e. may experience a limit cycle), but chaos was not found. Flow instabilities in a two-phase natural circulation loop have been verified using the model presented in this paper. The predictions of the effects of the channel inlet resistance, outlet resistance and liquid level in the downcomer agree with the data of Kyung and Lee. Finally, an analysis of nuclear-coupled density-wave instabilities in a simplified BWR (SBWR) was performed. Significantly, even for low pressure conditions, a simplified SBWR appears to be stable during start-up and normal operations; however, a limit cycle may occur for abnormal operating conditions.

Finite element analysis of steady state behavior of squirrel cage induction motors compared with measurements

The paper describes the steady-state analysis of squirrel cage induction motors using a two-dimensional finite element solution. Saturation is included using an iterative process combining both static and time-harmonic solutions. The motor end-effects are calculated using 2D and 3D finite elements including a lumped parameter approach during the solution of the time-harmonic problem. Both motors types, with closed and open rotor slots, are analysed. Different operating points for load, no-load and locked rotor situations are analysed and compared. The influence of the different end-effect parameters is analysed by including or neglecting them in the calculations. Good agreement with measurements are found for all operating conditions. The calculations are performed using a commercial FEA package.

Influence of Gas-Phase Reactions on the Product Yields Obtained in the Pyrolysis of Polyethylene

The characterization of the product fractions obtained from the pyrolysis of polyethylene (PE) in a laboratory-scale fixed bed reactor was performed. The experimental system allowed quantitative information to be obtained on the global tar, char, and gas yields. Pyrolysis runs were performed using reactor temperatures ranging between 500 and 800 °C. The influence of the residence times in the reactor of the primary volatiles generated by the pyrolysis process was also discussed. The secondary reactivity of the tar originated from PE pyrolysis was examined. A lumped-parameters approach was used in order to evaluate the global kinetic parameters for the gas-phase tar-cracking process. PE tars resulted to be more refractory to thermal decomposition than those obtained in the pyrolysis of biomass and lignocellulosic materials, but more reactive than tars obtained in the pyrolysis of coal.