Novel Closed-Form Equation for Critical Pressure and Optimum Pressure Ratio for Turbojet Engines

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Foroozan Zare ◽  
Árpád Veress
Keyword(s):  
Closed Form ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Reduction Rate ◽  
Pressure Recovery ◽  
Algebraic Equations ◽  
Unknown Parameters ◽  
Optimum Pressure ◽  
Recovery Rates ◽  
Plausibility Check

Abstract Advanced mathematical model has been developed for design and analysis of turbojet engines. It includes closed form algebraic equation for critical pressure and optimum pressure ratio at maximum thrust. The model and the algebraic equations consider efficiencies, pressure recovery rates meanwhile the gas parameters are the function of the fuel to air ratio and the temperature. РД-9Б and АЛ-21Ф3 engines are applied for demonstrating the capabilities of the calculation process. The unknown parameters as efficiencies, pressure recovery rates, power reduction rate of the auxiliary systems, bleed air ratio, air income ratio due to blade cooling and total temperature in the afterburner were identified by constrained optimization. The effect of i. T04/T02 ratio for the thrust and TSFC in the function of compressor pressure ratio, ii. the real (viscous) flow conditions and iii. the temperature and fuel to air ratio on gas parameters were also investigated for verification and plausibility check.

scholarly journals Effect of Thrust on the Structural Vibrations of a Nonuniform Slender Rocket

2020 ◽  
Vol 25 (2) ◽  
pp. 29
Author(s):  
Desmond Adair ◽  
Aigul Nagimova ◽  
Martin Jaeger
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Structural Vibrations ◽  
Unknown Parameters ◽  
One Dimensional ◽  
Vibration Problems ◽  
Nonuniform Beam

The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-free boundary conditions. The equations of motion are derived by applying the extended Hamilton’s principle for non-conservative systems. Natural frequencies and associated mode shapes of the rocket are determined using the relatively efficient and accurate Adomian modified decomposition method (AMDM) with the solutions obtained by solving a set of algebraic equations with only three unknown parameters. The method can easily be extended to obtain approximate solutions to vibration problems for any type of nonuniform beam.

scholarly journals A new method for calculating the sonic conductance of airflow through a short-tube orifice

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401668726 ◽  
Author(s):  
Fan Yang ◽  
Gangyan Li ◽  
Dawei Hu ◽  
Toshiharu Kagawa
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Pressure Ratio ◽  
Momentum Equation ◽  
Diameter Ratio ◽  
Test Method ◽  
Theoretical Formula ◽  
Engineering Applications ◽  
Short Tube ◽  
Length To Diameter Ratio

In this study, we proposed a method for calculating the sonic conductance of a short-tube orifice. First, we derived a formula for calculating the sonic conductance based on a continuity equation, a momentum equation and the definition of flow-rate characteristics. The flow-rate characteristics of different orifices were then measured using the upstream constant-pressure test method in ISO 6358. Based on these test data, the theoretical formula was simplified using the least squares fitting method, the accuracy of which was verified experimentally. Finally, the effects of the diameter ratio, the length-to-diameter ratio and the critical pressure ratio were analysed with reference to engineering applications, and a simplified formula was derived. We conclude that the influence of the diameter ratio is greater than that of the length-to-diameter ratio. When the length-to-diameter ratio is <5, its effect can be neglected. The critical pressure ratio has little effect on the sonic conductance of a short-tube orifice, and it can be set to 0.5 when calculating the sonic conductance in engineering applications. The formula proposed in this study is highly accurate with a mean error of <3%.

scholarly journals Methanol Dissociative Intercooling in Gas Turbines

1982 ◽  
Author(s):  
M. F. Bardon ◽  
J. A. C. Fortin
Keyword(s):  
Carbon Monoxide ◽  
Theoretical Analysis ◽  
Gas Turbine ◽  
Gas Turbines ◽  
Pressure Ratio ◽  
Unit Mass ◽  
Cycle Model ◽  
Optimum Pressure ◽  
Heating Value ◽  
Compressor Work

This paper examines the possibility of injecting methanol into the compressor of a gas turbine, then dissociating it to carbon monoxide and hydrogen so as to cool the air and reduce the work of compression, while simultaneously increasing the fuel’s heating value. A theoretical analysis shows that there is a net reduction in compressor work resulting from this dissociative intercooling effect. Furthermore, by means of a computer cycle model, the effects of dissociation on efficiency and work per unit mass of airflow are predicted for both regenerated and unregenerated gas turbines. The effect on optimum pressure ratio is examined and practical difficulties likely to be encountered with such a system are discussed.

Optimum Performance of a Regenerative Gas Turbine Power Plant Operating With/Without a Solid Oxide Fuel Cell

2011 ◽  
Vol 8 (5) ◽  
Author(s):  
Y. Haseli
Keyword(s):  
Fuel Cell ◽  
Pressure Drop ◽  
Solid Oxide Fuel Cell ◽  
Hybrid System ◽  
Thermal Efficiency ◽  
Pressure Ratio ◽  
Solid Oxide ◽  
Work Output ◽  
Oxide Fuel ◽  
Optimum Pressure

Optimum pressure ratios of a regenerative gas turbine (RGT) power plant with and without a solid oxide fuel cell are investigated. It is shown that assuming a constant specific heat ratio throughout the RGT plant, explicit expressions can be derived for the optimum pressure ratios leading to maximum thermal efficiency and maximum net work output. It would be analytically complicated to apply the same method for the hybrid system due to the dependence of electrochemical parameters such as cell voltage on thermodynamic parameters like pressure and temperature. So, the thermodynamic optimization of this system is numerically studied using models of RGT plant and solid oxide fuel cell. Irreversibilities in terms of component efficiencies and total pressure drop within each configuration are taken into account. The main results for the RGT plant include maximization of the work output at the expenses of 2–4% lower thermal efficiency and higher capital costs of turbo-compressor compared to a design based on maximum thermal efficiency. On the other hand, the hybrid system is studied for a turbine inlet temperature (TIT) of 1 250–1 450 K and 10–20% total pressure drop in the system. The maximum thermal efficiency is found to be at a pressure ratio of 3–4, which is consistent with past studies. A higher TIT leads to a higher pressure ratio; however, no significant effect of pressure drop on the optimum pressure ratio is observed. The maximum work output of the hybrid system may take place at a pressure ratio at which the compressor outlet temperature is equal to the turbine downstream temperature. The work output increases with increasing the pressure ratio up to a point after which it starts to vary slightly. The pressure ratio at this point is suggested to be the optimal because the work output is very close to its maximum and the thermal efficiency is as high as a littler less than 60%.

Some Studies on Low Solidity Vaned Diffusers of a Centrifugal Compressor Stage

2005 ◽  
Author(s):  
T. Ch. Siva Reddy ◽  
G. V. Ramana Murty ◽  
Prasad Mukkavilli ◽  
D. N. Reddy
Keyword(s):  
Centrifugal Compressor ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Pressure Recovery ◽  
Compressor Stage ◽  
Recovery Coefficient ◽  
Vaned Diffuser ◽  
Flow Angle ◽  
Centrifugal Compressor Stage ◽  
Pressure Recovery Coefficient

Numerical simulation of impeller and low solidity vaned diffuser (LSD) of a centrifugal compressor stage is performed individually using CFX- BladeGen and BladeGenPlus codes. The tip mach number for the chosen study was 0.35. The same configuration was used for experimental investigation for a comparative study. The LSD vane is formed using standard NACA profile with marginal modification at trailing edge. The performance parameters obtained form numerical studies at the exit of impeller and the diffuser have been compared with the corresponding experimental data. These parameters are pressure ratio, polytropic efficiency and flow angle at the impeller exit where as the parameters those have been compared at the exit of diffuser are the static pressure recovery coefficient and the exit flow angle. In addition, the numerical prediction of the blade loading in terms of blade surface pressure distribution on LSD vane has been compared with the corresponding experimental results. Static pressure recovery coefficient and flow angle at diffuser exit is seen to match closely at higher flows. The difference at lower flows could be due to the effect of interaction between impeller and diffuser combinations, as the numerical analysis was done separately for impeller and diffuser and the effect of impeller diffuser interaction was not considered.

Effect of Non-Condensible Gas on the Subcooled Water Critical Flow in a Safety Valve

2002 ◽  
Author(s):  
Se Won Kim ◽  
Sang Kyoon Lee ◽  
Hee Cheon No
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Safety Valve ◽  
Pressure Ratio ◽  
Water Flow Rate ◽  
Critical Flow ◽  
Inlet Temperature ◽  
Nitrogen Gas ◽  
Critical Flow Rate ◽  
Subcooled Water

The effect of non-condensable gas on the subcooled water critical flow in a safety valve is investigated experimentally at various subcoolings with 3 different disk lifts. To evaluate its effect on the critical pressure ratio and critical flow rate, three parameters are considered: the ratios of outlet pressure to inlet pressure, the subcooling to inlet temperature, and the gas volumetric flow to water volumetric flow are 0.15–0.23, 0.07–0.12, and 0–0.8, respectively. It turns out that the critical pressure ratio is mainly dependent on the subcooling, and its dependency on the gas fraction and the pressure drop is relatively small. When the ratio of nitrogen gas volumetric flow to water volumetric flow becomes lower than 20%, the subcooled water critical flow rate is decreased about 10% compare to the water flow rate of without non-condensable gas. However, it maintains a constant value after the ratio of gas volumetric flow to water volumetric flow becomes higher than 20%. The subcooled water critical flow correlation, which considers subcooling, disc lift, backpressure, and non-condensable gas, shows good agreement with the total present experimental data with the root mean square error 8.17%.

Identification of Nonlinear Systems by Haar Wavelet

2004 ◽  
Author(s):  
Shy-Leh Chen ◽  
Keng-Chu Ho
Keyword(s):  
Nonlinear Systems ◽  
Least Square Method ◽  
Haar Wavelet ◽  
State Equation ◽  
Least Square ◽  
Algebraic Equations ◽  
Function Form ◽  
Unknown Parameters ◽  
Complete Orthogonal Basis ◽  
Unknown System

This study addresses the identification of autonomous nonlinear systems. It is assumed that the function form in the nonlinear system is known, leaving some unknown parameters to be estimated. It is also assumed that the free responses of the system can be measured. Since Haar wavelets can form a complete orthogonal basis for the appropriate function space, they are used to expand all signals. In doing so, the state equation can be transformed into a set of algebraic equations in unknown parameters. The technique of Kronecker product is utilized to simplify the expressions of the associated algebraic equations. Together with the least square method, the unknown system parameters are estimated. Several simulation examples verify the analysis.

A Discretization Approach to Modeling Capacitive MEMS Filters

2007 ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab Abdel-Rahman
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Wide Range

We present a reduced-order model and closed-form expressions describing the response of a micromechanical filter made up of two clamped-clamped microbeam capacitive resonators coupled by a weak microbeam. The model accounts for geometrical and electrical nonlinearities as well as the coupling between them. It is obtained by discretizing the distributed-parameter system using the Galerkin procedure. The basis functions are the linear undamped global mode shapes of the unactuated filter. Closed-form expressions for these mode shapes and the coressponding natural frequencies are obtained by formulating a boundary-value problem (BVP) that is composed of five equations and twenty boundary conditions. This problem is transformed into solving a system of twenty linear homogeneous algebraic equations for twenty constants and the natural frequencies. We predict the deflection and the voltage at which the static pull-in occurs by solving another boundary-value problem (BVP). We also solve an eigenvalue problem (EVP) to determine the two natural frequencies delineating the bandwidth of the actuated filter. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We found a good agreement between the results obtained using our model and the published experimental results. We found that the filter can be tuned to operate linearly for a wide range of input signal strengths by choosing a DC voltage that makes the effective nonlinearities vanish.

scholarly journals Performance Analysis With Different Means of Cooling in a Combined Cycle

1995 ◽  
Author(s):  
Onkar Singh ◽  
R. Yadav
Keyword(s):  
Gas Turbine ◽  
Power Plants ◽  
Pressure Ratio ◽  
Combined Cycle ◽  
Inlet Temperature ◽  
Optimum Pressure ◽  
Cooling Medium ◽  
Cooling Technology ◽  
Improved Performance ◽  
Topping Cycle

Combined cycle based power plants and their development and application for energy efficient base load power generation necessitates enforced cooling to maintain the topping cycle gas turbine blade temperature at permissible levels, attributed to the increased turbine inlet temperature and compressor pressure ratio, for the improved performance and reliability of combined cycle. The mathematical model based on expansion path inside gas turbine considering dilution of mainstream and aerodynamic mixing losses for a range of cooling medium has been developed based on internal, film, transpiration cooling technologies and a combination of these. It is found that the appreciation of a cycle configuration as well as the optimum pressure ratio and peak temperature vary significantly with types of cooling technology adopted. Steam cooling for rotor appears to be a very potential cooling medium, when employed with an appropriate cooling technology. This paper deals with the thermodynamic analysis of turbine cooling using, different means of cooling i.e. air, water and steam.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

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