An analytical theory of heated duct flows in supersonic combustors

One-dimensional analytical theory is developed for supersonic duct flow with variation of cross section, wall friction, heat addition, and relations between the inlet and outlet flow parameters are obtained. By introducing a self- similar parameter, effects of heat releasing, wall friction, and change in cross section area on the flow can be normalized and a self-similar solution of the flow equations can be found. Based on the result of self-similar solution, the sufficient and necessary condition for the occurrence of thermal choking is derived. A re- lation of the maximum heat addition leading to thermal choking of the duct flow is derived as functions of area ratio, wall friction, and mass addition, which is an extension of the classic Rayleigh flow theory, where the effects of wall friction and mass addition are not considered. The present work is expected to provide fundamentals for developing an integral analytical theory for ramjets and scramjets.

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.

A MULTI-SCALE APPROACH FOR THE ANALYSIS OF PROPER SAMPLED DATA SCALE IN HOT-WIRE EXPERIMENT OF SQUARE DUCT FLOW

Without rational criteria to determine the Proper Sampled Data Scale （PSDS）, it would result in the expense of the too much unnecessary processing time and storage space in turbulent experiments. A novel approach for PSDS was established herein on the basis of turbulence theory and statistics. The specific procedure was given by using wavelet tools. A case study to prove the reliability and rationality of this approach was reported, where the sampled hot-wire data were from the experiment of square duct flow and turbulence kinetic energy was selected as the concerned turbulence parameter. It is shown that 2^20 quantities of the sampled data are enough to analyze turbulence kinetic energy in the present experiment. The PSDSs of three turbulence parameters at different Reynolds numbers （Re = 4.60×10^4, 7.68×10^4 and 1.23×10^5） were studied. The results illustrate that the PSDSs increase with the increment of the Reynolds number and the order of concerned turbulence parameter.

Numerical analysis of a magnetohydrodynamic duct flow with flow channel insert under a non-uniform magnetic field

This study performs a numerical analysis of three-dimensional liquid metal(LM) magnetohydrodynamic(MHD) flows in a square duct with an FCI in a non-uniform magnetic field. The current study predicts detailed information on flow velocity, Lorentz force, pressure, current and electric potential of MHD duct flows for different Hartmann numbers. Also, the effect of the electric conductivity of FCI on the pressure drop along the main flow direction in a non-uniform magnetic field is examined. The present study investigates the features of LM MHD flows in consideration of the interdependency among the flow variables.

Three Dimensional Separation with Spiral-Focus in a Decelerating Duct Flow (Effect of Asymmetric Inlet Boundary Layer Thickness)

An experimental apparatus was developed to study the three dimensional separated flow with spiral-foci. The internal decelerating flow was generated by the air suction from a side wall to produce the separation on an opposite-side wall. The relation between the upstream boundary layer and the generation of spiral-foci in the separation region was observed by a tuft method. As a result, it was clarified that the spiral-focus type separation could be produced on the side wall and its behavior was closely related to the vortices supplied into the separation region from the boundary layer developing along top wall or bottom one.

Numerical Investigation of Electrohydrodynamic (EHD) Flow Control in an S-Shaped Duct

An electrohydrodynamic （EHD） method, which is based on glow discharge plasma, is presented for flow control in an S-shaped duct. The research subject is an expanding channel with a constant width and a rectangular cross section. An equivalent divergence angle and basic function are introduced to build the three-dimensional model. Subsequently, the plasma physical models are simplified as the effects of electrical body force and work （done by the force） on the fluid near the wall. With the aid of FLUENT software, the source terms of momentum and energy are added to the Navier-Stokes equation. Finally, the original performance of three models （A, B and C） is studied, in which model A demonstrates better performance. Then EHD control based on model A is discussed. The results show that the EHD method is an effective way of reducing flow loss and improving uniformity at the duct exit. The innovation in this study is the assessment of the EHD control effect on the flow in an S-shaped duct. Both the parametric modeling of the S-shaped duct and the simplified models of plasma provide valuable information for future research on aircraft inlet ducts.

Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method.The stability of this finite difference scheme method is discussed.The distributions of the velocity and phase difference are given numerically and graphically.The effects of the Reynolds number,relaxation time,and aspect ratio of the cross section on the oscillatory flow are investigated.The results show that when the relaxation time of the Maxwell model and the Reynolds number increase,the resonance phenomena for the distributions of the velocity and phase difference enhance.

Time-Dependent Flow with Convective Heat Transfer through a Curved Square Duct with Large Pressure Gradient

A numerical study is presented for the fully developed two-dimensional laminar flow of viscous incompressible fluid through a curved square duct for the constant curvature δ = 0.1. In this paper, a spectral-based computational algorithm is employed as the principal tool for the simulations, while a Chebyshev polynomial and collocation method as secondary tools. Numerical calculations are carried out over a wide range of the pressure gradient parameter, the Dean number, 100 ≤ Dn ≤ 3000 for the Grashof number, Gr, ranging from 100 to 2000. The outer wall of the duct is treated heated while the inner wall cooled, the top and bottom walls being adiabatic. The main concern of the present study is to find out the unsteady flow behavior i.e. whether the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if Dn or Gr is increased. It is found that the unsteady flow is periodic for Dn = 1000 at Gr = 100 and 500 and at Dn = 2000, Gr = 2000 but steady-state otherwise. It is also found that for large values of Dn, for example Dn = 3000, the unsteady flow undergoes in the scenario “periodic→chaotic→periodic”, if Gr is increased. Typical contours of secondary flow patterns and temperature profiles are also obtained, and it is found that the unsteady flow consists of single-, two-, three- and four-vortex solutions. The present study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal force in a curved square passage that stimulates fluid mixing and consequently enhance heat transfer in the fluid.

A Study on the Half-Ducted Axial Flow Fan Designed by a Diagonal Flow Fan Design Method

A study on the half-ducted axial flow fan designed by a diagonal flow fan design method was conducted. The rotor which has NACA65 blades was designed, calculated numerically, manufactured and tested experimentally. As a result of the design and CFD, the meridional streamline and three distributions of the meridional, tangential and radial velocity at inlet and outlet go well as designed values of the half ducted fan. On the other hand, the values of the meridional velocity and the tangential velocity are little smaller than the design values at the hub side of the radial distribution. The improvement of the design is prospected for this point, that is, the approach between the design value and the actual flow is prospected if the tangential velocity is assigned small at hub and is assigned large at the tip so as to accord the actual flow in the vortex design of the rotor blade. Then the designed half-ducted rotor with four NACA65 blades was fabricated by a three-dimensional printer and tested in the wind tunnel in order to validate the half-ducted design method. For the comparison between the design values and the experimental values at the design flow rate coefficient of φ = 0.264, the experimental values of the pressure rise coefficient ψ and the efficiency η are rather small than the design values, while the experimental value of the torque coefficient τ is almost the same as the design value. However, the experimental value of approximately 0.45 of the maximum efficiency is comparably large value considering for the limitation of the situation of half-ducted. For the comparison between the experimental values and the CFD values at φ = 0.264, the CFD values are almost the same values as the experimental values for all the values of ψ, τ and η. In addition, the tendencies of the CFD values when the flow rate coefficient changes are almost similar as the experimental tendencies, though the flow rate coefficient for the CFD values when ψ or η takes the peak value shifts toward larger flow rate. For the case at rotor outlet at φ = 0.264, two values of the meridional velocity and the tangential velocity are larger than the design values at the tip side of the radial distribution.

Design of Half-Ducted Axial Flow Fan Considering Radial Inflow and Outflow

Half-ducted fan and ducted fan have been designed and numerically analyzed for investigating the radial flow effect on the overall performance and the three dimensional flow field in design. Based on quasi-three dimensional flow theory, the meridional flow was calculated by adopting the radial balance equations, while the calculation of the blade to blade flow was obtained by 2D cascade data with the correction by a potential flow theory. Two types of axial flow fan were designed. One is the full ducted case as if it was in the straight pipe and another is the half-ducted case with the radial inflow and outflow. The previous experimental results of authors were used to decide the inclinations of both the inflow and outflow. And the circular arc blade with equal thickness was adopted. The numerical results indicate that both of the designed fans can reach the specified efficiency and also the efficiency surpasses more than 11%. Furthermore, the static pressure characteristic of half-ducted fan is much better than that of ducted fan. In comparison of the three dimensional internal flow of these two fans, the improvement of the flow angle at inlet and outlet, the distributions of velocity in the flow field and the pressure distributions on the blade surfaces can be achieved more successfully in accordance with the design intension on consideration of flow angle in design. The conclusion that half-ducted design with considering radial inflow and outflow is feasible and valid in comparison with ducted design for axial flow fans has been obtained at the end of the paper.

TIME-PERIODIC ISENTROPIC SUPERSONIC EULER FLOWS IN ONE-DIMENSIONAL DUCTS DRIVING BY PERIODIC BOUNDARY CONDITIONS

We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.

Slip flow in an annular sector duct using radial eigenfunctions

The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.

Combined Effects of Centrifugal and Coriolis Instability of the Flow through a Rotating Curved Duct with Rectangular Cross Section

Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number ?for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three-and multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic?→ multi-periodic?→ periodic?→ steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

In this paper,to simulate the three dimensional turbulent flow in suddenly expanded rectangular duct numerically,the SIMPLEC algorithm is employed to solve the incompressible Navier-Stckes equation with k-εturbulence model.The numerical resulis show well the three dimensional turbulent flow field in the rectangular duct behind the sudden expansion cross-section. and agree.fairly well with the experimental result of the length of the main circumfluence.The numerical method of this paper can be applied to numerical analysis of this kind of turbulent flow.

SIMULATION OF BLEED AIR BEHAVIOR DURING AIRCRAFT IN FLIGHT BASED ON FLOWMASTER

Bleed air system is one of the most important components of air management system(AMS).It acts as transfer pipes responsible for air supply at high temperature and pressure.The thermal and flow performance of the bleed air system is a key issue for the design of AMS since the characteristics of air source have a great influence on the anti-ice system,the environmental control system and other downstream system in need of high temperature pressurized air.Based on the one-dimensional lumped parameter technology,a computer analysis model of bleed air system is developed in order to analyze the thermal and flow behaviors of the nodal points in the pipeline network.The simulation are performed with a given flight assignment using the analysis model,and the results verify that the system meets the design requirements.

CFD analysis of performance improvement of the Savonius water turbine by using an impinging jet duct design

The majority of research on water turbines focuses on design improvement of large-scale hydrokinetic turbines for power generation, which may have delayed the utilization of kinetic energy contained in rivers and canals. The aim of this paper is to improve the efficiency of a two bladed Savonius type cross-flow hydrokinetic turbine, which can be used as an energy converter to harness free-stream kinetic energy of water. An impinging jet duct design is presented for improving performance of the Savonius turbine in wind application as seen from literature. The performance of the modified turbine is evaluated using CFD software Fluent, and is compared with that of a simple two bladed Savonius water turbine and some of the prominent literature designs of the Savonius turbine. It is shown that the present design exhibits improved performance compared to the selected designs of the Savonius turbine.Further an insight of the improved performance of the modified turbine is also obtained from flow physics study.

The Solely Use of the “Hydraulic-Diameter” Concept Is Not Sufficient to Describe Correctly Non-Symmetric Flow in Conduits

A well-known cornerstone in fluid mechanics is the equations that relate the friction factor to the Reynolds number obtained from the measurements in cylindrical cross-sectional tubes. The extension of these equations to different geometries failed to give reliable results. The introduction of the Hydraulic Diameter has fixed this issue particularly for the square ducts. However, for non-symmetric flows, as in concentric annuli, the discrepancies were unacceptable. Several attempts have been made to fix these problems with finally the introduction of a new concept like, “Laminar Equivalent Hydraulic Diameter” or “Efficient Hydraulic Diameter” provided satisfactory results. This approach seems to have fixed the problem and hence has been widely accepted. Nevertheless, it is based on a non-robust theoretical argument. In the present paper, it has been demonstrated that the solely use of the “Hydraulic Diameter” concept is insufficient to describe non-symmetric flows as in concentric annuli. It appears the need to use the Z axis component of the skew driving force for the laminar flow and the parameter λ for the turbulent one. At the same time, instead, it has been shown that in the case of flow in square and rectangular ducts, the “Hydraulic Diameter” is sufficient to describe it. In this case, the flow is practically symmetric. Moreover, several new straightforward equations are provided, which simplify a lot dealing with non-cylindrical cross-sectional conduits. In doing so, the concept of “Eigenvectors-Eigenvalues” has been implemented. This theoretical approach could help to simplify other non-symmetric cases in fluid dynamics. To mention, “Flow past immersed non-symmetric bodies”, “Flow in curved conduits” etc.

喷水推进器进水流道在来流含气条件下的内部流动特性分析

为了研究喷水推进器进水流道在来流含气条件下的内部流动特性,以轴流式喷水推进器为研究对象,对喷水推进器在不同来流含气条件下进行全流域定常数值仿真,得到了不同来流含气条件下进水流道各截面气相体积分数分布特征和不均匀度变化规律.计算结果表明:在低航速区间时,进水流道内流量小、流速低,受管道几何结构影响,下部弯管处流体堆积现象明显,随着航速的升高,流量增大、流速提高,流体在上部弯管处产生流动分离,导致堆积区向上部弯管转移;在来流含气条件下,进口含气率和气泡直径的增大,会导致气液两相干涉作用变强,造成气体堆积现象加剧,影响流面的不均匀度.

汽轮发电机带有交替径向风道的转子流体与传热耦合分析

针对汽轮发电机带有交替径向通风道的转子发热冷却问题,以一台350 MW水氢氢冷汽轮发电机为研究对象,依据流体力学和传热学的基本理论,首先建立计及旋转的电机全域通风网络模型,采用逐次迭代法计算得到各支路流量和节点压力。其次,建立了带有交替径向风道的发电机转子流体-传热三维物理模型和数学模型,给出了基本假设和相应的边界条件,同时将通风网络计算得到的风速和压力作为转子求解域的耦合边界,采用有限体积法进行求解,计算结果与实测值吻合。然后分析了交替径向风道内流量分配和氢气流动情况,研究了转子内部氢气温度分布和槽楔出风口风温变化规律,探明了转子绕组和铁心轴向温度分布特性,讨论了副槽入口流量和槽楔出口直径对转子流体和温度的影响。得出副槽入口流量应控制在0.1~0.16 m^(3)/s范围内,且选择较小的槽楔出口直径,可以提高通风系统的效率与风量分配均匀性,降低转子轴向热不平衡。