The Dissipation Function-Based Efficiency for Turbomachinery—Part I: The Efficiency of a Cooled Turbine Row1

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Chong M. Cha
Keyword(s):  
Mass Transfer ◽  
Dissipation Function ◽  
One Dimensional ◽  
Specific Heats ◽  
Gas Streams ◽  
Blade Row ◽  
The One ◽  
Turbine Airfoils ◽  
The Impact ◽  
Mixing Problem

The effect of coolant addition or “mixing loss” on aerodynamic performance is formulated for the turbine, where mixing takes place between gas streams of different compositions as well as static temperatures. To do this, a second-law efficiency measure is applied to a generalization of the one-dimensional mixing problem between a main gas stream and a single coolant feed, first introduced and studied by Hartsel (1972, “Prediction of Effects of Mass-Transfer Cooling on the Blade-Row Efficiency of Turbine Airfoils,” AIAA Paper No. 1972-11) for the turbine application. Hartsel's 1972 model for mass transfer cooling loss still remains the standard for estimating mixing loss in today's turbines. The present generalization includes losses due to the additional contributions of “compositional mixing” (mixing between unlike compositions of the main and coolant streams) as well as the effect of chemical reaction between the two streams. Scaling of the present dissipation function-based loss model to the mainstream Mach number and relative cooling massflow and static temperature is given. Limitations of the constant specific heats assumptions and the impact of fuel-to-air ratio are also quantified.

The Dissipation Function-Based Efficiency for Turbomachinery: Part 1 — The Efficiency of a Cooled Turbine Row

2014 ◽  
Author(s):  
Chong M. Cha
Keyword(s):  
Aerodynamic Performance ◽  
Dissipation Function ◽  
Second Law ◽  
Efficiency Measure ◽  
One Dimensional ◽  
Specific Heats ◽  
Gas Streams ◽  
The One ◽  
The Impact ◽  
Mixing Problem

The effect of coolant addition or “mixing loss” on aerodynamic performance is formulated for the turbine, where mixing takes place between gas streams of different compositions as well as static temperatures. To do this, a second law efficiency measure is applied to a generalization of the one-dimensional mixing problem between a main gas stream and a single coolant feed, first introduced and studied by Hartsel [1] for the turbine application. Hartsel’s 1972 model for mass-transfer cooling loss still remains the standard for estimating mixing loss in today’s turbines. The present generalization includes losses due to the additional contributions of “compositional mixing” (mixing between unlike compositions of the main and coolant streams) as well as the effect of chemical reaction between the two streams. Scaling of the present dissipation function-based loss model to the mainstream Mach number and relative cooling massflow and static temperature is given. Limitations of the constant specific heats assumptions and the impact of fuel-to-air ratio are also quantified.

A Simple One-Dimensional Model for Primary Turbine Blade Erosion Prediction

1983 ◽  
Author(s):  
J. L. Dussourd
Keyword(s):  
Turbine Blades ◽  
Predictive Ability ◽  
Bluff Bodies ◽  
One Dimensional ◽  
Erosion Prediction ◽  
Blade Cascade ◽  
Blade Row ◽  
Quantitative Manner ◽  
First Order Method ◽  
The Impact

Sophisticated models to predict the erosion process in turbine blades exposed to dust laden gas stream quickly become complex and tedious for use for everyday engineering applications. A simpler model for primary erosion can be formulated by assimilating the blade row to a device having a certain size and deflecting the stream through a given angle and at a given rate. The technology which exists for particle impacts physics with bluff bodies can be adapted to cascades. Thus, basically the model is derived from first principles. This approach is formulated in a quantitative manner in terms of cascade parameters, gas properties, and particulate parameters. The result is a simple equation which is easy to use and the physics of which are logical and intuitively reasonable. Its predictive ability, however, is limited to the frequency of impacts and the strength of the impacts. It does not address the mechanics of the impact process or the properties of the material being impacted. These variables are introduced through an experimental coefficient which, as it turns out, is the only experimental input in the analysis. The method is tested against quite a few experimental cases with a degree of predictive ability which is acceptable in a simple, first order method. The agreement is thought to be at least as good as the credibility or accuracy of the test data. The method is finally applied to study the effects of various blade cascade parameters on erosion resistance, the results of which are presented in the form of general curves.

scholarly journals Analytical Model to Compare and Select Creep Constitutive Equation for Stress Relief Investigation during Heat Treatment in Ferritic Welded Structure

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 688
Author(s):  
Mengjia Hu ◽  
Kejian Li ◽  
Shanlin Li ◽  
Zhipeng Cai ◽  
Jiluan Pan
Keyword(s):  
Heat Treatment ◽  
Constitutive Equation ◽  
Analytical Model ◽  
Stress Relief ◽  
Treatment Temperature ◽  
Hole Drilling ◽  
One Dimensional ◽  
Welded Structure ◽  
The One ◽  
The Impact

The one-dimensional analytical model was promoted to help select the creep constitutive equation and predict heat treatment temperature in a ferritic welded structure, along with neglecting the impact of structural constraint and deformation compatibility. The analytical solutions were compared with simulation results, which were validated with experimental measurements in a ferritic welded rotor. The as-welded and post weld heat treatment (PWHT) residual stresses on the inner and outer cylindrical surfaces were measured with the hole-drilling method (HDM) for validation. Based on the one-dimensional analytical model, different effects of Norton and Norton-Bailey creep constitutive equation on stress relief during heat treatment in a ferritic welded rotor were investigated.

scholarly journals A one-dimensional modeling study on the effect of advanced insulation coatings on internal combustion engine efficiency

2020 ◽  
pp. 146808742092158
Author(s):  
Alberto Broatch ◽  
Pablo Olmeda ◽  
Xandra Margot ◽  
Josep Gomez-Soriano
Keyword(s):  
Heat Transfer ◽  
Combustion Engine ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Insulation Material ◽  
One Dimensional ◽  
Engine Efficiency ◽  
Dimensional Modeling ◽  
The One ◽  
The Impact

This article presents a study of the impact on engine efficiency of the heat loss reduction due to in-cylinder coating insulation. A numerical methodology based on one-dimensional heat transfer model is developed. Since there is no analytic solution for engines, the one-dimensional model was validated with the results of a simple “equivalent” problem, and then applied to different engine boundary conditions. Later on, the analysis of the effect of different coating properties on the heat transfer using the simplified one-dimensional heat transfer model is performed. After that, the model is coupled with a complete virtual engine that includes both thermodynamic and thermal modeling. Next, the thermal flows across the cylinder parts coated with the insulation material (piston and cylinder head) are predicted and the effect of the coating on engine indicated efficiency is analyzed in detail. The results show the gain limits, in terms of engine efficiency, that may be obtained with advanced coating solutions.

Influence of the combustion chamber geometry on the scavenging of a four-stroke internal-combustion engine during the valve overlap period

2016 ◽  
Vol 230 (14) ◽  
pp. 1873-1890
Author(s):  
Nicolas-Ivan Hatat ◽  
David Chalet ◽  
François Lormier ◽  
Pascal Chessé
Keyword(s):  
Internal Combustion Engine ◽  
Combustion Engine ◽  
Internal Combustion ◽  
One Dimensional ◽  
Digital Testing ◽  
The One ◽  
Small Engines ◽  
Variable Valve ◽  
Valve Overlap ◽  
The Impact

The performance of an internal-combustion engine is directly related to the fuel quantity that can react with the oxygen in the air during the exothermic oxidation step, also called combustion. Thus, the amount of fuel introduced is intrinsically linked to the air volume that can be admitted into the cylinder (air filling of the cylinder). Hence keeping the air in the cylinder is one of the most important concepts to predict in simulations. Nevertheless, the phenomenon of air filling depends on many parameters. Also, the discharge coefficients, and the impact of the piston presence near the valves on the flow, during valve overlap are investigated. For this, a digital flow bench is constructed to reproduce a series of tests carried out on a flow test bench functioning as a result of the reduction in the pressure. In this paper, the engine studied is a 125 cm3 single-cylinder four-stroke atmospheric type with two valves. Thus, the idea of this paper is to treat the case of engines with large valve overlaps as small engines or engines with variable valve timing. First, traditional tests through a single valve are performed. The forward and reverse directions are systematically tested to ensure proper operation of the digital testing, and to determine the differences between tests and simulations in the case of conventional configurations. Then, the flow through the entire cylinder head, i.e. the intake valve–cylinder with piston–exhaust valve system, is tested and studied. The aim is to compare the results obtained by the tests and the simulations during the valve overlap period. Significant differences were highlighted between the rates measured in one-dimensional simulations and in the tests. It was noteworthy that the one-dimensional code overestimated the mass passing through the system during valve overlap by about one fifth of the estimated mass passing through the system from the results obtained with the test rig.

Numerical Solution for Two-Dimensional Elastic Wave Propagation in Finite Bars

1967 ◽  
Vol 34 (3) ◽  
pp. 725-734 ◽  
Author(s):  
L. D. Bertholf
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Numerical Solutions ◽  
Step Change ◽  
Two Dimensional ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
The Impact

Numerical solutions of the exact equations for axisymmetric wave propagation are obtained with continuous and discontinuous loadings at the impact end of an elastic bar. The solution for a step change in stress agrees with experimental data near the end of the bar and exhibits a region that agrees with the one-dimensional strain approximation. The solution for an applied harmonic displacement closely approaches the Pochhammer-Chree solution at distances removed from the point of application. Reflections from free and rigid-lubricated ends are studied. The solutions after reflection are compared with the elementary one-dimensional stress approximation.

Longitudinal Impact of Semi-Infinite Elastic Bars: Plane Any Time Solution

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
M. A. Malkov
Keyword(s):  
Analytical Solution ◽  
Exact Analytical Solution ◽  
The Other ◽  
Longitudinal Impact ◽  
Infinite Plane ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Contact Surfaces ◽  
The One ◽  
The Impact

Using the Sobolev–Smirnov method, we have found the exact analytical solution of a longitudinal impact of semi-infinite plane elastic bars for any time after the impact. After collision, there are loading waves from contact surfaces of bars and unloading waves from lateral surfaces. Then the unloading waves reach the opposite surface of the bars and create the reflected loading waves. These loading waves reach the other surface of the bars and generate new unloading waves. The number of waves grows exponentially. The sum of waves tends to the wave of the one-dimensional approximation.

The Dissipation Function-Based Efficiency for Turbomachinery: Part 2 — The Power of a Cooled Turbine

2015 ◽  
Author(s):  
Chong M. Cha
Keyword(s):  
Control Volume ◽  
Dissipation Function ◽  
Dimensional Control ◽  
One Dimensional ◽  
Cooling Flow ◽  
Volume Model ◽  
Efficiency Measures ◽  
The Impact

Euler’s turbine equation is generalized to include cooling flow addition. Euler’s turbine equation for the uncooled case is still used for the design and analysis of today’s cooled turbines. A simple, one-dimensional control volume model is developed to illustrate the impact of cooling flow addition on the turbine power and efficiency. The efficiency measures include the familiar isentropic turbine efficiencies and the dissipation function-based measure, introduced in Part 1 [1] of this work.

scholarly journals The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 44
Author(s):  
Kaushik Y. Bhagat ◽  
Baibhab Bose ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Rathindra N. Das ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Quantum Statistical Mechanics ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Potential Well ◽  
One Dimensional ◽  
Quantum Randomness ◽  
The One ◽  
The Impact

The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both micro-canonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional Potential Well problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

Jet Breakup and Mixing Throat Lengths for the Liquid Jet Gas Pump

1974 ◽  
Vol 96 (3) ◽  
pp. 216-226 ◽  
Author(s):  
R. G. Cunningham ◽  
R. J. Dopkin
Keyword(s):  
Work Performance ◽  
Velocity Ratio ◽  
Area Ratio ◽  
Liquid Jet ◽  
Pump Efficiency ◽  
One Dimensional ◽  
Jet Breakup ◽  
Nozzle Contour ◽  
The One ◽  
The Impact

Gas compression with a liquid jet occurs isothermally and hence with minimum work. Performance characteristics of the liquid jet gas pump (efficiency and compression ratio versus inlet volumetric flow ratio) are predicted accurately by a one-dimensional analysis providing the mixing zone remains in the throat. Jet breakup was investigated to enable prediction of required throat length and to improve efficiency. Effects of throat length, nozzle contour and spacing, nozzle-throat area ratio (0.15 to 0.45), jet velocity and suction pressure were investigated. Optimum throat lengths were found; corresponding efficiencies exceed 40 percent. Two jet breakup flow regimes were found: impact and jet disintegration. For the impact regime, jet breakup length-depends on inlet velocity ratio, jet Reynolds number and nozzle-to-throat area ratio. Optimum throat lengths were found to be an empirical function of nozzle-to-throat area ratio and ranged from 12 to 32 throat dia. These results, coupled with the one-dimensional model, permit design of efficient liquid jet gas pumps.

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