Minimum Cross Section Research Articles

Effect of shock structure on stabilization and blow-off of hydrogen jet flames

Under-expanded hydrogen jet has characteristic shock structure immediately downstream of the nozzle exit. The shock structure depends on the ratio pEX/pA, i.e. the ratio of nozzle exit to ambient pressure, and the distributions of velocity and concentration in an under-expanded hydrogen jet depend on characteristics of the shock structure. Therefore, the shock structure should affect the blow-off behaviour of under-expanded hydrogen jet flame. Since this issue has not been investigated in detail, this study aims to close this knowledge gap. The effect of changes in shock structure on lift-off length and blow-off conditions for non-premixed turbulent hydrogen free jet flame has been experimentally investigated. The shock structure was varied by using three types of nozzles: convergent, straight and divergent nozzles. Inlet diameters of nozzles change from 0.31 to 1.04 mm and outlet diameters from 0.34 to 1.7 mm. The static pressure and the ratio of cross-section area at the nozzle inlet to that at the outlet were varying parameters in this study. Hydrogen was horizontally spouted through a nozzle to atmosphere. The maximum static pressure in a nozzle was 13.2 MPa. The experiments revealed that when the hydrogen jet had sequential shock cell structures, which occurred in the range of pEX/pA smaller than 2.45, a higher mass flow rate of hydrogen was needed for the stabilization of a jet flame than that for pEX/pA larger than 2.45 and that when closed to the ideal expansion (pEX/pA = 1), the mass flow rate for stable flame became maximum. In addition, it was observed that the lift-off length of stable flames followed with sequential shock cell structures were almost the same when the minimum cross-section area of used nozzles was constant. However, when hydrogen jet had a shock structure with single Mach disk, the lift-off lengths and the minimum mass flow rate required for the stable jet flame were decreasing with the decrease of the cross-sectional area ratio of the nozzle exit to inlet.

Adsorptive Separation of Geometric Isomers of 2-Butene on Gallate-Based Metal-Organic Frameworks.

The separation of mixed C4 olefins is a highly energy-intensive operation in the chemical industry due to the close boiling points of the unsaturated C4 isomers. In particular, the separation of trans/cis-2-butene is among the most challenging separation processes for geometric isomers and is of prime importance to increase the added value of C4 olefins. In this work, we report a series of isostructural gallate-based metal-organic frameworks (MOFs), namely, M-gallate (M = Ni, Mg, Co), featuring oval-shaped pores, that are ideally suitable for shape-selective separation of trans/cis-2-butene through their differentiation in minimum molecular cross-section size. Significantly, Mg-gallate displays a record high trans/cis-2-butene uptake selectivity of 3.19 at 298 K, 1.0 bar in single-component adsorption isotherms. These gallate-based MOFs not only exhibit the highest selectivity for trans/cis-2-butene separation but also accomplish a highly efficient separation of 1,3-butadiene, 1-butene, and iso-butene. DFT-D study shows that Mg-gallate interacts strongly with trans-2-butene and 1,3-butadiene along with short distances of C···H-O cooperative supramolecular interaction of 2.57-2.83 and 2.45-2.79 Å, respectively. In breakthrough experiments, Mg-gallate not only displays prominent separation performance for trans/cis-2-butene but also realizes the clean separation of a ternary mixture of 1,3-butadiene/1-butene/iso-butene and a binary mixture of 1-butene/iso-butene. This work indicates that M-gallate are industrially promising materials for adsorption separation of geometric isomers of C4 hydrocarbons.

High-brightness source of energetic He atoms

In atom beam lithography, a beam of kilo-electron-volt helium atoms illuminates a stencil mask and transmitted beamlets transfer the mask pattern to resist on a substrate. It shares the advantages of masked ion beam lithography but is immune to charging artifacts that limit resolution and pattern fidelity. This paper describes a high-brightness source of energetic He atoms, where He+ ions are extracted from a multicusp ion source, focused by two-stage accelerating optics, and neutralized by charge-transfer scattering in a differentially pumped, He-filled cell. Since scattering angles are extremely small, the straight line trajectories of scattered atoms are essentially tangent to the (possibly curved) trajectories of the parent ions. Space-charge repulsion prevents the ion beam crossing over; instead, it converges to a waist of minimum cross section before diverging further downstream. Atom trajectories produced by a cell placed in the region of intense space charge near the waist are strongly affected by the curvature of ion trajectories within the cell. The flaring of the ion beam due to space charge can be used to increase the width of the atom beam, although to the detriment of resolution. In this paper, the authors study a configuration where the cell is placed in the converging ion beam as far as practicable from the ion-beam waist. The atom beam then converges to a crossover, which becomes the virtual source seen by the mask. The source diameter and angular flux density initially increase with increasing cell pressure but saturate at higher pressures; the respective saturation values at 50 keV are 125 μm (2σ) and 8.7 × 1017 particles/s sr. Under these conditions, the beam diameter is ∼2.5 cm, 7 m from the source. A practical system for subnanometer printing is discussed with 0.2 nm (2σ) penumbral blur and 1.25 × 1013 particles/s cm2 flux density over a 1 cm circular field.

Water Vapor Near‐UV Absorption: Laboratory Spectrum, Field Evidence, and Atmospheric Impacts

AbstractAbsorption of solar radiation by water vapor in the near‐UV region is a poorly understood but important issue in atmospheric science. To better understand water vapor near‐UV absorption, we constructed a cavity ring‐down spectrometer with bandwidth of 5 cm−1 (~0.05 nm) and obtained water vapor absorption cross sections at 1‐nm increments in the 290‐ to 350‐nm region. Water vapor displays structured absorption over this range with maximum and minimum cross sections of 8.4 × 10−25 and 1.6 × 10−25 cm2/molecule. Major water vapor absorption bands were observed at 293–295, 307–313, 319, 321–322, and 325 nm, with cross‐section values higher than 4.0 × 10−25 cm2/molecule. To obtain further insight into major water vapor absorption bands, we measured water vapor absorption cross sections at 0.05‐nm intervals in the 292‐ to 296‐nm, 306‐ to 314‐nm, and 317‐ to 326‐nm region. Field UV residual spectra not only exhibited increased attenuation at higher atmospheric water vapor loadings but also showed structures suggested by the laboratory water vapor absorption spectrum. Spaceborne UV radiance spectra have spectral structures resembling the differential cross‐section spectrum constructed from the laboratory wavelength‐dependent water vapor absorption cross sections presented here. Incorporating water vapor absorption cross‐section data into a radiative transfer model yielded an estimated energy budget of 0.26 W/m2 for the standard U.S. atmosphere and 0.76 W/m2 for the tropics. This shows that water vapor near‐UV absorption is an important contributor for climate simulation and ozone retrievals.

Numerical modeling of heat transfer during spark plasma sintering of titanium carbide

Spark plasma sintering (SPS) is an efficient manufacturing method especially for ultra-high temperature ceramics (UHTCs) such as titanium carbides. Heating mechanism in SPS is a result of high electric current in the device including die, punch, and sample powder. Because the temperature distribution in the sintering process has considerable effect on the microstructure of the final sintered sample, in the present work, SPS of a cylindrical sample consist of a titanium carbide was investigated numerically. The governing equations of heat diffusion and electricity distribution in the whole device was solved using finite element method. In the heat diffusion equation, heat generation per volume was considered as a result of electric current in the device. Boundary conditions including radiation heat transfer and convective cooling by water flow were modelled by Stefan-boltzman and Newton cooling laws, respectively. The maximum temperature was observed at the center of the TiC sample. The radial temperature distribution in the sample showed considerable gradient as the minimum and maximum temperatures were 2000 °C and 1920 °C, respectively. Despite the radial direction, vertical temperature gradient was negligible in TiC sintering. Although the highest current density and consequent heat generation were observed at the die/punch interface with the minimum cross section, the maximum temperature of the whole apparatus was at the punch location.

Application of the Ford-Falkerson algorithm to detect excess information

The object of the article is the network maximum flow algorithm, mainly the Ford-Fulkerson algorithm. The algorithm began to be developed by two scientists: Ford and Fulkerson. This algorithm was proposed in order to find the maximum flow in the network. They began to be actively studied by scientists from the middle of the last century. The first report of "Maximum Network Flow" dates back to 1954. The authors of the report, Ford and Fulkerson had proved the theorem on the maximum flow and the minimum cross section for non-oriented graphs: the value of the maximum flow in the network is equal to the minimum throughput capacity of the section. The interest in the solution of these tasks was primarily due to practical needs, for that time construction of routes for the transportation of raw materials was not optimal and transported more raw materials than can transfer the connection between points. Such problems often arise when constructing connections that transport oil through pipes or transport coal through special excavators. The subject of the article is the problem of finding the maximum flow in the network. In graph theory, the transport network is an indicative graph in which each arc has no negative throughput and flow. Two peaks are distinguished: source and drain - such that any other vertex in the network lies on the way from source to drain. The article consists of two sections. In the first section we consider the mathematical formulation of the problem and concrete examples of problems. The second section examines the classic Ford-Fulkerson algorithm, the modified Ford-Fulkerson algorithm to find excess information on the network, and the work of a modified algorithm on a specific example from the first section. The considered problems are relevant both from a theoretical and a practical point of view.

Highly compact nanosecond laser for space debris tracking

This study demonstrated the use of a highly compact nanosecond laser system operating at 532 nm and producing a maximum output power of 70 W with a pulse width of 5 ns at 0.5 kHz, for space debris tracking. To improve the ranging accuracy while minimizing the influence of the pulse noise, a bidirectional Q-switch was adopted in the oscillator to generate a short pulse width with less tailing. The laser was applied for low-Earth-orbit space debris tracking, and space debris with the farthest distance of 1701.9 km at the minimum radar cross-section of 1 m2 could be detected with a ranging precision of up to 26.90 cm.

Dynamic optimization of the rail-crown geometry in the rigid frog area by controlling the position of the wheel-load transition

To improve the stability of a train and reduce its influence on the nose rail when passing a rigid frog, the optimization of the rail-crown geometry in the rigid frog area is proposed in this study by controlling the transition range of the wheel load on the nose-rail head and evaluating it by a wheel–rail dynamic coupling model. The method was verified by studying a Chinese CN60-350-1:12 turnout. Results show that if the wing-rail heightening and nose-rail reduction are small, then the transition section of the wheel load on the nose rail may be close to or smaller than the minimum load-bearing cross section, which will cause damage to the weaker section of the front of the nose rail due to excessive load. If the wing-rail heightening and nose-rail reduction are large, the wheel-load transition section of the nose rail may exceed the extreme transition cross section, which will cause the wheel to hit the nose-rail head or make it difficult to climb the wing rail when the wheel passes through the rigid frog. During the optimization process of the rail-crown geometry in the rigid frog, the reasonable transition range of the nose-rail head can be determined by adjusting the wing-rail heightening and nose-rail reduction, and combined with the wheel–rail dynamics evaluation method, the optimal scheme can be selected to protect the nose rail and improve the running stability of the train.

Rate dependent behaviour and dynamic strain localisation of three novel impact resilient titanium alloys: Experiments and modelling

The tensile behaviour of three ductile titanium alloys, Ti0.7Al4V, Ti1Al4V and Ti3Al2.5V, conceived for impact containment applications, is characterised at quasi-static, intermediate and high strain rates. Tests have been performed using a screw driven mechanical system and a bespoke in-house developed split Hopkinson tension bar equipped with ultra-high speed photographic equipment. The three alloys present noticeable strain rate sensitivity. Ti1Al4V is characterised by the lowest flow stress and highest ductility of the three alloys. Ti3Al2.5V higher flow stress but lowest strain to failure while Ti0.7Al4V has similar flow stress but larger engineering failure strain compared to Ti3Al2.5V. The dynamic true strain rate, determined by measuring the time history of the minimum cross-section diameter during necking, reaches values up to one order of magnitude higher than the nominal strain rate. This phenomenon, occurring during dynamic strain localisation, is of fundamental importance for understanding and modelling the dynamic behaviour of ductile alloys designed to withstand impact loading. The experimental results are used to determine the material parameters of the Johnson-Cook (JC) and Khan–Huang–Liang (KHL) models, which are incorporated in the ABAQUS/explicit code for finite element simulations of the dynamic tensile tests. It is found that the KHL model predicts the experimentally measured strain field, deformed geometry, effective strain rate and macroscopic force-displacement response during the high strain rate experiments with significantly better agreement than the JC model.

A general and rapid method for performance evaluation of enhanced heat transfer techniques

Evaluation of the comprehensive performance of different heat transfer technologies and selection the best enhanced surface to meet the requirements are of great significance for efficient energy recovery. In this paper, based on the previous research results from our group, a rapid multi-criterion comprehensive evaluation method of enhanced heat transfer surfaces was first proposed; it realizes the rapid evaluation of heat transfer performance under the condition of equal flow rate, equal pressure drop and equal pump power constraints. Three baselines divide evaluation plot into six zones, namely zone 1 (non-energy-saving zone), zone 2 (relative energy-saving zone), zone 3 (value-added energy-saving zone), zone 4 (ideal energy-saving zone), zone 5 (pure energy-saving zone), and zone 6 (simple energy-saving zone). A simplified evaluation plot was then developed to overcome the dependence on the correlations of the reference surface. Next, the prediction results of the evaluation plot under the condition of variable minimum flow cross-section area, variable total heat transfer area, variable equivalent diameter, and variable tube bundle arrangement were compared with the traditional method to verify the applicability and accuracy of the evaluation plot. Finally, numerical simulations and engineering application of typical heat transfer surfaces were conducted to compare the energy-saving effectiveness of different enhanced surfaces and to analyze the effect of geometry and operation parameters on comprehensive performance. The results showed that the evaluation chart established in this paper can be successfully applied to the comprehensive comparison of multiple evaluation criteria and has a high prediction accuracy. Compared with the common evaluation methods, this method has excellent practicability and visualization, and contributes to the rapid development of new enhanced surfaces and efficient utilization of energy.

METHODS MODELING SYSTEMS FOR THE IMPROVEMENT OF THEIR RELIABILITY


 
 
 
 The method of Markov’s processes for the analysis of systems with constant bounce and recovery intensities considered. The article presents calculations of the failure probability of the system for describing the various cases of redundancy of its components using Markov’s models. Expressions obtained for calculating the approximate value of the failure probability of the system and analyzed of failures to improve the reliability of the system. The Markov’s graph of transitions in the reservation of the system, which reflects its behavior, described. Analysis of the results of numerical solution of systems shows that when loaded with redundancy, the probability of failure is higher than with partially loaded, and with partially loaded - higher than with unloaded backup. A tree of errors for the system of cooling and clearing of flue gas at the reservation made by replacing "2 of 3", which has seven minimum bounce cross sections. Calculated the probability of system failure. The obtained calculations allow to analyze failures of technical systems in order to increase the reliability of their functioning.
 
 
 

Analytical Solution to the Boundary Value Problem of Steady Creep of a Nonaxisymmetric Thick-Walled Tube under the Action of Internal Pressure

The boundary value problem of the steady-state creep of a nonaxisymmetric thick-walled tube under the action of internal pressure is considered under the assumption that the material is incompressible for creep deformations. An approximate analytical solution of the problem by the small parameter method up to the third order of approximation, inclusively, for a plane deformed state is presented. The small parameter in the problem is the displacement of the centers of the inner and outer radii of the tube. The error in solving the problem is estimated by comparing the approximate analytical solution with a numerical solution obtained by the finite element method for some special cases. The analytical and numerical solutions for stresses are analyzed by dependence on the small parameter and the stress exponent of the steady-state creep. The error of the approximate analytical solution for the stress tensor components in the minimum cross section is analyzed in accordance with the industrial standards for the permissible deviation of the wall thickness in the industrial production of tubes.

AUTOMATION CONTROL SYSTEM OF TECHNICAL CONDITION OF GAS TURBINE ENGINE COMPRESSOR

The article is devoted to one of the approaches to the construction of an automated system for solving the problems of diagnostics and monitoring of the flow duct of aircraft gas turbine engines and gas turbine plants. Timely detection of faults and subsequent monitoring of their development in operation are possible thanks to automated systems for assessing the technical condition of engines. This is particularly relevant in operating conditions as the knowledge of the technical condition of the engine is necessary in any engine maintenance system allows to choose the content and timing of maintenance, repair of the flow duct of gas turbine engines and gas turbine plants, as well as commissioning. The engineering technique, which can be applied at performance of maintenance and at stages of tests and debugging of aircraft engines, is considered. The automated system implements a method of measuring the air flow through the compressor and a technique for assessing the technical condition of the compressor by the relative change in air flow. To determine the air flow rate through the gas turbine engine, it is sufficient to measure only static pressure values in the flow part. The static pressure receivers are not located in the flow part and do not obscure it, and thus do not affect the compressor gas dynamic stability margin. The inspection area is selected for measuring in the flow duct of the air intake. Static pressure in the maximum and minimum cross sections of the chosen area is measured; the maximum cross-section area of the flow duct, the total temperature of the air flow is measured outside the air intake. To determine the air flow rate, the functional dependence of the air flow rate on the static pressure is used. The algorithm for monitoring and diagnosing the operating condition of the engine is based on a comparison of the actual values of air flow rate with the air flow rate determined during the control tests or when using a mathematical model adapted for this gas turbine engine. The positive effect of the using of the proposed automated control system of technical condition is that the air flow rate measured under operating conditions will significantly increase the objectivity of the control of the operation and technical condition of the gas turbine engine.

Numerical simulation of sulfuric acid vapor condensation characteristics on an external three-dimensional finned tube surface

Three-dimensional external finned tube heat exchanger has been widely applied in waste heat recovery system. However, the current researches mainly focus on its fluid flow and heat transfer characteristics. The condensation of sulfuric acid and water vapors on heat exchanger surface, which can cause severe low temperature corrosion and reduce equipment efficiency, has rarely been reported. In this study, a heat and mass transfer model for flue gas on finned tube surface was developed to investigate the sulfuric acid and water vapor condensation characteristics and their distributions. The effects of flue gas velocity and temperature, acid and water vapor concentrations, and surface temperature were examined. The results show that the distribution of acid solution concentration on finned tube surface mostly depends on the distribution of fin surface temperature. At the windward side (especially near the minimum flow cross section region), both fin surface temperature and condensed acid solution concentration reaches the maximum value. Increasing velocity leads to vapors condensation rate and acid solution concentration increasing. The acid solution concentration decreases with flue gas temperature or tube wall temperature increasing. The present work could provide effective theoretical guidance for anti-corrosion design of finned tube heat exchanger.

Influence of Cold Plastic Deformation on the Structure and Physicomechanical Properties of the Biocompatible Low-Modulus Zr51Ti31Nb18 Alloy

The influence of the degree of compression in the range of 46–84% upon cold rolling of rods of a biocompatible low-modulus Zr51Ti31Nb18 (IMP BAZALM) alloy preliminarily quenched from the β field on the formation of its structure, phase composition, and physicomechanical properties (hardness, elastic modulus) has been studied by the methods of optical microscopy, transmission electron microscopy, X-ray diffraction analysis, back-scattering electron diffraction, and microindentation. It has been established that with an increase in the degree of compression, a reorientation and elongation of the initially equilibrium β grains occur along the direction of rolling with the formation of a perfect filamentary structure in the rods with a minimum cross-section. The values of microhardness are stabilized in the range of 320–325 HV due to the development of dynamic recovery processes in the deformed structure, and the elastic modulus decreases from 68 to 55 GPa in the rolling plane of rods owing to the improvement of the {001}RP〈110〉RD-type texture, which leads to the appearance of the predominantly “low-modulus” 〈110〉 orientation in the direction of measurement.

Probabilistic model of the minimum effective cross-section area of non-uniform corroded steel bars

Abstract In general, the corroded reinforced concrete members is induced by the natural environment in existing buildings or by the two artificial accelerated corrosion such as electrochemical method and artificial simulated environment. The deterioration of yield strength of corroded steel bars is mainly caused by the decrease of the effective cross-section area, the randomness and the variability of the corrosion. The position of the yield point occurs at the minimum effective cross-section area. Through the statistical analysis of 1706 groups of experimental data on yield strength of corroded steel bars, the relationship between the minimum effective cross-section area of non-uniform corroded steel bars and the average corrosion ratio under three corrosion conditions has been established. After that, a probabilistic model of minimum effective cross-section area of corroded steel bars has been proposed and, meanwhile, a correction coefficient is suggested to adjust the deviation of the yield strength between the average corrosion ratios of artificial accelerated corrosion and natural environment corrosion. Based on the presented probabilistic model, a reinforced concrete beam member under natural environment was analyzed. It is found that the flexure-shear competition happened during its service life, that is, the failure mode may change because of the non-uniform corrosion. Therefore, the non-uniform corrosion of the corroded RC members should be taken into account seriously in structural design.

3D Airway changes using cone beam computed tomography in patients following mandibular advancement surgery with and without constriction

The aim of this study was to compare three-dimensional airway changes resulting from mandibular advancement surgery and mandibular advancement surgery with constriction. The University of Michigan School of Dentistry and Medical Center. A total of 42 patients undergoing mandibular advancement with or without simultaneous constriction. A retrospective airway evaluation of patients undergoing mandibular advancement with or without simultaneous mandibular constriction was performed. Cross-sectional evaluation at standardized locations, minimum cross section and volumetric analysis were performed using Dolphin Imaging TM Version 11.7. Patients undergoing mandibular advancement with or without constriction experienced significant airway increases (P<0.05). Patients who underwent mandibular advancement only gained nearly twice as much airway volume as mandibular advancement with simultaneous constriction (8.69mm3 vs 4.3mm3 ). The largest increase for both groups was observed in the minimum axial area in the oropharynx segment (119.5mm2 ) and the axial area of the retroglossal region (137.2mm2 ). The findings demonstrate mandibular advancement with constriction results in airway enlargement following surgery.

3D Airway changes using CBCT in patients following mandibular setback surgery ± maxillary advancement.

The aim of this study was to determine the 3D airway changes that occur following mandibular setback surgery alone vs bimaxillary surgery in patients with similar skeletal start forms. The University of Michigan School of Dentistry and Medical Center. A total of 85 patients undergoing mandibular setback with or without simultaneous maxillary advancement. A retrospective evaluation of pre- and post-surgical CBCT scans for patients undergoing mandibular setback surgery alone (14) vs bimaxillary surgery (71) was performed. Cross-sectional evaluation at standardized locations, minimum cross section and volumetric analysis were performed (Dolphin Imaging & Management Solutions). Patients who underwent mandibular setback surgery alone showed a statistically significant average increase of 47.5mm2 in minimum axial area. Patients who underwent bimaxillary surgery showed a statistically significant increase in airway volume, minimum axial area, location of minimum axial area, and axial area at the retropalatal and retroglossal regions. The results demonstrate that the mandible can be setback safely without decreasing airway dimensions. In borderline OSA patients, bimaxillary surgery remains the preferred approach due to the larger airway increases observed. Long-term follow-up with polysomnography must be conducted to determine the full functional implications of both procedures.

Flow Field Influence Analysis of Combination Intake Port to Port and In-Cylinder for a Four-Valve Diesel Engine

Intake port structure directly affects the flow characteristics and combustion process of diesel engine, and then affects the comprehensive performance of diesel engine. To the intake ports of a four-valve direct injection diesel engine, the flow characteristics are analyzed on the four combined intake ports : (1) helical (left) and tangential (right), (2) tangential (left) and helical (right); (3) helical (left) and helical (right); and (4) tangential (left) and tangential (right).And the influence of air flow in four combined intake ports to in-cylinder gas flow is also analyzed. Results show that the helical and tangential combination intake ports flow velocity increases with the valve lift increases, and small turbulence arises at the valve guide lug, and the intake flow velocity of the minimum cross-section of the junction of the guiding section and the helical section is the maximum. The air flow in- cylinder moves from top cylinder head bottom to the cylinder bottom, the air flow is enlarged gradually by the small-scale irregular swirl, which eventually converges to a single swirl. The turbulence kinetic energy is very big when the air is just entering the cylinder, the flow space expands rapidly, and the dissipation of turbulent kinetic energy is very significant with the gas moves to the bottom of the cylinder.

A Comprehensive Optimization Design Method of Aerodynamic, Acoustic, and Stealth of Helicopter Rotor Blades Based on Genetic Algorithm

In this paper, a comprehensive optimization approach is presented to analyze the aerodynamic, acoustic, and stealth characteristics of helicopter rotor blades in hover flight based on the genetic algorithm (GA). The aerodynamic characteristics are simulated by the blade element momentum theory. And the acoustics are computed by the Farassat theory. The stealth performances are calculated through the combination of physical optics (PO) and equivalent currents (MEC). Furthermore, an advanced geometry representation algorithm which applies the class function/shape function transformation (CST) is introduced to generate the airfoil coordinates. This method is utilized to discuss the airfoil shape in terms of server design variables. The aerodynamic, acoustic, and stealth integrated design aims to achieve the minimum radar cross section (RCS) under the constraint of aerodynamic and acoustic requirement through the adjustment of airfoil shape design variables. Two types of rotor are used to illustrate the optimization method. The results obtained in this work show that the proposed technique is effective and acceptable.