60中英文雙語外文文獻(xiàn)翻譯成品； 二維進(jìn)氣歧管流模擬

1、<p>　　外文標(biāo)題：A Two-dimensional Intake Manifold Flow Simulation</p><p>　　外文作者： Peter Li </p><p>　　文獻(xiàn)出處: 《Mathematical Modelling》 , 1987 , 8 (6) :437-442 </p>&l

2、t;p>　　英文3089單詞， 16963字符，中文4508漢字。</p><p>　　此文檔是外文翻譯成品，無需調(diào)整復(fù)雜的格式哦！下載之后直接可用，方便快捷！只需二十多元。</p><p>　　原文：A Two-dimensional Intake Manifold Flow Simulation</p><p><b>　　Peter Li<

3、;/b></p><p>　　Scientific Research Laboratory, Ford Motor Company 20000 Rotunda, Dearborn, Michigan 48121</p><p><b>　　ABSTRACT</b></p><p>　　A computer flow model of an

4、 intake manifold of a four cylinder engine has been developed using a computational fluid dynamic code. This code is based on the Conchas -Spray code developed at the Los Alamos National Laboratory. The flow inside the i

5、ntake manifold is assumed to be two-dimensional, unsteady, compressible, and turbulent. A simple subgrid scale (SGS) turbulence model and hypothetical boundary conditions are employed, in the simulation. Atmospheric pres

6、sure is specified at the inlet an</p><p>　　Keywords: Computational Fluid Dynamics; Intake Manifold; Flow stimulacion; Engine induction; Turbulence flow. </p><p>　　INTRODUCTION</p><p&g

7、t;　　The Performance of an internal combustion engine, be it power, fuel economy or emissions, is strongly influenced by the combustion of the air and fuel inside an engine cylinder. This combustion process is strongly a

8、ffected by the in-cylinder 'support flow1 that results from the transport of the air and fuel through the induction system. The understanding of the effect of the induction geometry on the support flow is therefore e

9、ssential for internal combustion engine development.</p><p>　　The Cask of describing and understanding the fluid flows inside the complex induction geometries is difficult. This is due to the multi-dimensio

10、na- lity of the flow geometry, and the highly transient operation of the automotive engine. There are many research studies, experimental and theo- ;retical, trying to understand this difficult problem . Most theoretic

11、al work includes mostly zerodimensional (Sullivan, 1978; Wu, 1983) or onedimensional (Benson, 1971; Low, 1981; Chapman, 1982) approach</p><p>　　Among these codes, an in-house modified version of the CONCHA

12、S-SPRAY code (Cloutman, 1982) from Los Alamos National Laboratories is used in this study. The purpose of this report is to discuss our extended development of this code as applied Co induction flow research, and a parti

13、cular application to the simulation of air flow inside a 1.6 liter intake manifold.</p><p>　　INTAKE MANIFOLD,FLOW MODEL </p><p>　　The Flow Geometry</p><p>　　The manifold (Figure 1)

14、is idealized to be twodimensional (Figure 2). The flow in the manifold is unsteady, compressible and turbulent. The governing equations together with the boundary and initial conditions that form the mathematical proble

15、m are given below. The computational code is then used to numerically solve this problem.</p><p>　　Governing Equations</p><p>　　Direct solution of the Navier-Stokes equations to resolve all scal

16、e of turbulence is yet to be realized. Thus, approximate "mean" equations have to be used to describe the flow. There are various ways of averaging that have been reported in the literature (Schlichting, 1968;

17、Deardorff, 1971; Launder, 1972). The resulting "mean" governing equations for the two dimensional turbulent, compressible, unsteady flow in the Cartesian coordinates are given below:</p><p>　　Con

18、tinuity equation,</p><p>　　Momentum equations,</p><p>　　The internal energy equation，</p><p><b>　　where</b></p><p>　　Ideal gas is assumed and</p><

19、;p><b>　　Where,</b></p><p>　　X- horizontal coordinate</p><p>　　Y- vertical coordinate</p><p>　　U- velocity component in X direction</p><p>　　V- veloci

20、ty component in Y direction</p><p>　　?- fluid density</p><p><b>　　t- time</b></p><p>　　µ- mean" viscosity </p><p><b>　　Pressure</b>

21、</p><p>　　GX,GY- body forces</p><p>　　specific internal energy </p><p>　　internal heat generation</p><p>　　T- temperature</p><p>　　K- means thermal condu

22、ctivity</p><p>　　Ø-viscous dissipation function </p><p>　　Rg- universal gas constant</p><p>　　The "mean" equations given above retain Che form of the Navier-Stokes eq

23、uations. The difference only lies in the expression of the transport coefficients (i.e. viscosity, thermal conductivicy). For the exact Navier-Stokes equations, these coefficients are properties of the fluid only, whil

24、e for the "mean" equations, these coefficients also depend on the "mean" flow field.</p><p><b>　　where</b></p><p>　　Note that physically, turbulence flow is three

25、dimensional . An inherent consequence of the twodimensional flow assumption with this simple turbulence model is that only the smaller scale (cell size) three-dimensional turbulence is accounted for by the model, whil

26、e larger scale turbulence is assumed two-dimensional and resolved numerical-</p><p>　　The Boundary Conditions</p><p>　　Figure 2. shows the discretized flow geometry and the corresponding boundar

27、y conditions used in the simulation. At the runner outlets, the induction process is simulated by specifying a hypothetical outlet flow velocity. For convenience, the flow velocity is assumed to be spatially uniformed an

28、d a half sinusoid in time. The engine firing order is 1-3-4-2. The outlet boundary conditions for one complete engine cycle or two engine revolutions are given as:</p><p>　　At the manifold inlet, wide open

29、throttle is simulated by letting the inlet pressure be atmospheric ,neglecting the effects of air ducts upstream of the air cleaner, or</p><p>　　The law of the wall is used on the solid boundaries (Schlic

30、hting, 1968). For a turbulent boundary layer this is</p><p>　　The wall shear speed is defined in term of the wall shear stress tw as</p><p>　　Replacing the U* on the right hand side of the equa

31、tion (10) with the 1/7-law (Schlichting, 1968) approximation U*, which is</p><p>　　eliminates the transcendental nature of the equation with respect to U*. For smooth wall (B-5.5) equation (8) becomes,</

32、p><p>　　Equation (13) is used for ywu/v >130 . 3 . However, for ywu/v<1Z0.3, equation (13) is replaced by the laminar sublayer formula:</p><p>　　For simplicity, the thermal boundary layer is

33、approximated using che Reynolds analogy. Thus for turbulent flow, the heat flux is given as</p><p>　　This is the same formula used by Cloutman (1982). Again for the laminar sublayer, equation (15) is replace

34、d by</p><p>　　which is a simple difference approximation to the laminar heat flux with Prandtl number equaling 0.89. For simplicity, tw is assumed to be constant along the wall boundary and equal to 343 K.&

35、lt;/p><p>　　The Initial Conditions</p><p>　　The air inside the manifold is assumed to be quiescent in che beginning. The initial pressure is assumed adnospheric. The initial temperature is assumed

36、to be 343 degrees kelvin.</p><p>　　The Computer Code</p><p>　　A computer code called Flody is used to numerically solve the flow simulation problem given above. It is a modified version of the

37、Conchas - Spray code (Cloutman, 1982). Extensive modification is made to include inflow and outflow boundary condi- tions. For this study, combustion and spray are excluded. A preprocessor and a postprocessor allowing ea

38、sy specification of the flow problem and expedient output presentation are added. A brief description of the numerical scheme is given here.</p><p>　　Flody is a time marching procedure that solves the finite

39、 difference approximation of the governing equations given above. The transient solution is semi-implicit. It uses spatial differences in the generalized quadrilateral cells. The corners of che cells, called vertices, ar

40、e allowed to arbitrarily move in time. These allow a Lagrangian and/or Eulerian description. This type of mesh, known as the arbitrary Lagrangian-Eulerian (ALE) mesh (Hire, 1971; Arasden,1973; Pracht, 1976), is particul

41、arl</p><p>　　RESULTS AND DISCUSSIONS</p><p>　　The flow inside the idealized intake manifold is calculated for a duration of two complete engine cycles (or four engine revolutions). The Flody cod

42、e on the Dec 20 computer is used. Total cpu time for the simulation is approximately 50 hours. The computational grid and boundary conditions used are shown in Figure 2. Some numerical results are presented below. Figur

43、e 3 is a sequence of pictures that show the development of the flow field during che induction of runner . #1. The plots presented </p><p>　　Figure 4 shows in a sequence of three pictures the variation of t

44、he pressure field during the indue - tion of runner #1. The first picture corresponds to the beginning of the induction when the flow is accelerating. The second picture corresponds</p><p>　　to the midpart o

45、f the induction when the flow is maximum, and the last picture corresponds co the later part of the induction when the flow is decelerating. During acceleration and deceleration the pressure appears constant throughout

46、the cross section of the runner, varying only along the flow direction. These show the dominance of the acceleration forces during these periods. The pressure decreases along the runner during acceleration and increases

47、 during deceleration. This</p><p>　　shows that perhaps one-dimensional flow simulation during these two periods may be adequate. On the other hand, the second picture in figure 4 shows that during peak fl&l

48、t;5w, when the flow is neither accelerating nor decelerating, the pressure field is two-dimensional. Larger concentration of pressure lines is observed near corners and cross section changes, indicating where a large p

49、ortion of the manifold losses occur. Figures 5 and 6 plot the density and the temperature distributions during </p><p>　　Figure 7 shows the temporal variation of the pressure at each of the four runner out

50、lets. The first 15 milliseconds correspond to the induction of runner #1. The line plot clearly shows the pressure dip during acceleration of the flow, the crossover during peakflow, and the surge during flow decelerati

51、on. This definitely is different from the quasi- steady assumption, where temporal variation of the pressure would have been symmetrical during acceleration and deceleration. Subsequent fluctua</p><p>　　du

52、ring the induction of other runners are due to the air compressibility. Comparison of the pressure fluctuations of all four runners shows the pressure fluctuations of runners #1 and #4 are quite similar when shifted tem

53、porally. The same is true with runners #2 and #3. But, the fluctuations of #1 and #4 are both larger than those of #2 and #3. This is associated with the difference in the runners' length. This demonstrates the cap

54、ability of the two-dimensional fluid code in simulating such c</p><p>　　The manifold efficiency (?) is used to measure Che performance of the intake manifold. In this study, ? is calculated for each of the n

55、ers and is defined as</p><p>　　Ma is the time integral of the volume flow rate multiplied by the fluid density at the runner's outlet, while Mitot is time integral of the volume flow rate multiplied by t

56、he manifold inlet density (i.e. , atmospheric). The efficiency for the 1.6 liter manifold is calculated based on the numerical data for the two engine cycles simulated. The results are tabulated in table 1 below.</p&

57、gt;<p>　　The Loop Manifold</p><p>　　An attractive feature of "Flody" is the ease with which the geometry can be changed. As an example, the flow inside a concept loop-manifold (Figure 8) is

58、simulated by simply changing the geometry outline in the code. The initial and boundary conditions used are those of the 1.61 intake manifold. Results are summarized by the temporal pressure variations in Figure 9 and t

59、he manifold efficiency tabulated in table 1. Comparison is Chen made with the 1.61 manifold. Table 1 clearly</p><p>　　shows the efficiency of the loop-manifold to be higher. This is reflected by the 3.6 % lo

60、ss in the loop-manifold versus the 5.2 % loss in the 1.61 manifold. And there is no deterioration in the distribution of mass flow between each runner. The magnitude of the pressure fluctuations are smaller in figure 9

61、than those shown in figure 7. In addition, the pressure fluctuation between each runner are more similar for the loop manifold . This clearly demonstrates the use of "Flody" code in simulati</p><p&g

62、t;　　CONCLUSION</p><p>　　A computer simulation model of air flow inside an intake manifold for a 1.6 liter four cylinder engine has been developed using a fluid code. The code, called Flody, is based on the C

63、onchas-Spray code developed at the Los Alamos</p><p>　　National Laboratory. The flow is assumed to be two-dimensional, unsteady, compressible, and turbulent . A simplified subgrid scale (SGS) turbulence mo

64、del is used. Hypothetical initial and boundary conditions are specified. Atmospheric pressure is assumed at the manifold inlet. The velocities at all che outlets are specified. The law of the wall boundary condition is u

65、sed for the solid walls. Numerical results have been presented. The flow in a concept "loop manifold" is also simulated. Results</p><p>　　REFERENCES</p><p>　　Amsden, A.A., and Hirt, C.

66、W., "YAQUI: An Arbitrary Lagrangian-Eulerian Computer Program for Fluid Flow at All Speeds", Los Alamos Scientific Laboratory report LA- 5100, March, 1973*.</p><p>　　Arasden, A.A., Ruppel, H.M., an

67、d Hirt, C.W., "SALE: A Simplified ALE Computer Program for Fluid Flow at All Speeds”， Los Alamos Scientific Laboratory report LA-8095, June, 1980.</p><p>　　Anderson, R.C., and Sandford II, M.T., "Y

68、OKXFER： A Two-Dimensional Hydrodynamics and Radiation Transporc Program", Los Alamos Scientific Laboratory report LA*5704-MS, January, 1975.</p><p>　　Benson, R.S. "A Comprehensive Digital Computer

69、 Pro - gram Co Simulate Compression Ignition Engine Including Intake and Exhaust Systems", SAE</p><p>　　paper no. 710173, 1S71.</p><p>　　Butler, T.D., Cloutman, L.D., Dukowicz, J.K., and Ra

70、mshaw, J.D., "CONCHAS: An Arbitrary Lagrangian-Eulerian Computer Code for Multi- componepc Chemically ReacCive Fluid Flow at All Speeds", Los Alamos Scientific Laboratory report LA-8129-MS, November, 1979.</

71、p><p>　　Patankar, S.V. Numerical Heac Transfer and Fluid Flow, McGraw Hill 1980.</p><p>　　Pracht, W.E., and Brackbill, J.U., "BAAL: A Code</p><p>　　for Calculating Three- Dimensio

72、nal Fluid Flows at All Speeds with an Eulerian-Lagrangian Computing Mesh", Los Alamos Scientific Labo- ratorv report LA-6342, August, 1976.</p><p>　　Schlichting, H., Boundary Layer Theory, McGraw Hill.

73、6th Edition, 1968.</p><p>　　Shimamoto, Y., et. al. "A Research on Inertia Charging Effect of Intake System in Multi-Cylinder Engines", JSME Bulletin p.502-510. vol.21,</p><p><b>

74、;　　1978.</b></p><p>　　Stein, L.R.， Gentry, R.A., and Hirt, C.W., CompManifold Flow in a Four Cylinder Internal Combustion Engine", SAE paper no.790244,</p><p><b>　　1979.</b&

75、gt;</p><p>　　Chapman, M., Novak, J.M., Stein, R.A. "Numerical</p><p>　　Modeling of Inlet and Exhaust Flows tn Multi- cylinder Internal Combustion Engines", ASHE Winter Meeting Presenta

76、tion. Phoenix, Arizona,</p><p>　　Nov. 1982.</p><p>　　Cloutman, L.D., Dukowicz, J.K., Ramshaw, J.D.,</p><p>　　Amsden, A.A., " CONCHAS -SPRAY : A Computer Code for Reactive Flows

77、 with Fuel Sprays", Los Alamos Report No. LA-9294-HS, 1982.</p><p>　　Deardorfff J.W., Journal of Computational Phvsics. no. 7， pl20, 1971.</p><p>　　Gosman, A.D., Khalil, E,E. and Whitelaw,

78、J.H., "The Calculation of Two- Dimensional Turbulent Recirculating Flows", Proc. Symposium on Turbulent Shear Flows. Pennsylvania, 1977.</p><p>　　Hirt, C.W., "An Arbitrary Lagrangian- Euleri

79、an Com puting Technique*1, Proc. Intern. Cor>f. Numerip350， Springer-Verlag, 1971.</p><p>　　Launder, B.E., Spalding, D..B., "Mathematical Models of Turbulence”，Academic Press. 1972.</p><p

80、>　　Low, S.C., Baruah, P.C., "A Generalized Computer Aided Design Package for I.C. Engine Manifold System", SAE paper no. 810498, 1981.Meth. AppI. Mech. Eng, no. 11, p57, 1977.</p><p>　　Sullivan,

81、 D.A. "Historical Review of Real-Fluid</p><p>　　Isentropic Flow Models", Transaction of ASME. pp.258-267, Vol. 103, June 1981.</p><p>　　Taylor, C.F., Livengood, J,C., Tsai, D.H. "

82、Dynamics In The Inlet System of a Four-Stroke SingleCylinder Engine", Transaction of ASHE, p.1133-1145, vol.77, 1955.</p><p>　　Tunstall, J.N., "On the Derivation of Conservative Finite-Difference

83、Expressions for the Navier-Stokes Equations", Union Carbide Corporation. Nuclear Division report K/CSD-5, Oak Ridge, Term., April, 1977.</p><p>　　Wu, H., Aquino, C.F., Chou, G.L. "A 1.6 Liter Engin

84、e and Intake Manifold Dynamic Model", ASME paper no. 83-WA/DSC-39, 1983.</p><p>　　譯文 二維進(jìn)氣流形模擬</p><p><b>　　彼得李</b></p><p>　　科學(xué)研究實驗室，福特汽車公司20000 Rotunda，迪

85、爾伯恩，密執(zhí)安48121</p><p><b>　　摘要：</b></p><p>　　已經(jīng)使用計算流體動力學(xué)代碼開發(fā)了四缸發(fā)動機(jī)的進(jìn)氣歧管的計算機(jī)流量模型。該代碼基于Los Alamos國家實驗室開發(fā)的Conch as-Sp射線代碼。 進(jìn)氣歧管內(nèi)的氣流被假定為二維的，不穩(wěn)定的，可壓縮的以及湍流。 在模擬中采用簡單的子網(wǎng)格尺度（SGS）湍流模型和假設(shè)的邊界條件。 在

86、入口處指定大氣壓力，并且在歧管的出口處指定速度以及在所有壁邊界處的壁的定律。 模擬的數(shù)值結(jié)果以速度，壓力，密度和溫度場的形式給出。 該模型的設(shè)計方式可以輕松模擬不同的流形幾何形狀。 還提出了一個概念流形“環(huán) - 馬尼褶11的模擬。</p><p>　　關(guān)鍵詞：計算流體動力學(xué); 進(jìn)氣歧管; 流動模擬; 引擎; 湍流流動。</p><p><b>　　介紹</b><

87、/p><p>　　內(nèi)燃機(jī)的性能，無論是耗油量，燃油經(jīng)濟(jì)性還是排放量，都受發(fā)動機(jī)氣缸內(nèi)空氣和燃油燃燒的強(qiáng)烈影響。 這種燃燒過程受到空氣和燃料通過感應(yīng)系統(tǒng)輸送的缸內(nèi)“支撐流”的強(qiáng)烈影響。 因此，理解誘導(dǎo)幾何結(jié)構(gòu)對支撐流動的影響對于內(nèi)燃機(jī)開發(fā)是必不可少的。</p><p>　　描述和理解復(fù)雜感應(yīng)幾何體內(nèi)的流體流動的任務(wù)是困難的。 這是由于流動幾何的多維度以及汽車發(fā)動機(jī)的高度瞬態(tài)操作。 有許多研究，實

88、驗和理論; 想要了解這個難題。 大多數(shù)理論工作主要包括零維（Sullivan，1978; Wu，1983）或一（Benson，1971; Low，1981; Chapman，1982）。直到最近才有報道：關(guān)于這個問題的維度研究（Chapman，1979）。 這項研究提出了一個攝入mani褶皺內(nèi)部流動的二維模型。 假定流動不穩(wěn)定，可以湍流。 描述該流動問題的一組偏微分方程包括連續(xù)性方程，兩個摩爾矩陣方程和簡單的SGS湍流模型（Deard

89、orff，1971）。 這些方程是耦合的，非線性的，具有非常復(fù)雜的幾何形狀。 解決這種內(nèi)部再循環(huán)湍流問題是非常困難的。 對這些問題的純粹分析處理當(dāng)然是不可能的。然而，在過去的幾十年中，計算機(jī)技術(shù)，數(shù)值技術(shù)和流量測量技術(shù)的進(jìn)步，滿足了行業(yè)巨大的需求，促成了這一領(lǐng)域的許多集中研究活動。 這是大量的反映</p><p>　　允許用近似的一組橢圓偏微分方程來對這種湍流流動進(jìn)行數(shù)學(xué)描述。 這些導(dǎo)致了許多計算公式的發(fā)展，其

90、中可能有多維流動模擬（Hirt，1971; Amsden，1973; P racht，1976;Gosman，1977; Cloutman，1982）。</p><p>　　在這些代碼中，本研究使用來自Los Alamos國家實驗室的CONCHAS-SPRAY代碼（Cloutman，198 2）的內(nèi)部修改版本。 本報告的目的是討論我們將該規(guī)范的擴(kuò)展開發(fā)應(yīng)用于指示流量研究，以及特定應(yīng)用于模擬1.6升進(jìn)氣歧管內(nèi)的氣

91、流。</p><p>　　進(jìn)氣歧管，D流量模型</p><p><b>　　流動幾何</b></p><p>　　歧管（圖1）理想化為二維（圖2）。 歧管中的流動是不穩(wěn)定的，可壓縮的和湍流的。 下面給出了控制方程以及形成數(shù)學(xué)問題的邊界條件和初始條件。 計算代碼然后用于數(shù)值解決這個問題。</p><p><b>

92、　　治理方程式</b></p><p>　　直接求解Navier-Stokes方程來解決所有尺度的湍流尚未實現(xiàn)。因此，必須使用近似的“均值”方程來描述流量。有文獻(xiàn)報道過的各種平均方法（Schlichting，1968; Deardorff，1971; Launder，1972）。 下面給出笛卡爾坐標(biāo)系下二維湍流，可壓縮，非定常流動的“平均”控制方程：</p><p><

93、;b>　　連續(xù)性相等</b></p><p><b>　　動量方程,</b></p><p><b>　　內(nèi)部能量方程，</b></p><p><b>　　其中</b></p><p><b>　　理想的氣體是假設(shè)的</b></p

94、><p><b>　　其中,</b></p><p><b>　　X-水平坐標(biāo)</b></p><p><b>　　Y-垂直坐標(biāo)</b></p><p>　　V- Y方向流體密度的速度分量</p><p><b>　　?- 流量濃度</b&

95、gt;</p><p><b>　　t- 時間</b></p><p>　　µ- 意思是“粘度</p><p><b>　　壓力</b></p><p>　　GX，GY-身體部隊</p><p><b>　　F特定的內(nèi)部能量</b></

96、p><p><b>　　S內(nèi)部發(fā)熱</b></p><p><b>　　T-溫度</b></p><p><b>　　K-意味著導(dǎo)熱性</b></p><p><b>　　Ø-粘性耗散功能</b></p><p><b&

97、gt;　　Rg-通用氣體常數(shù)</b></p><p>　　上面給出的“均值”方程保留了Navier-Stokes方程的Che形式。 區(qū)別僅在于傳輸系數(shù)的表達(dá)（即粘度，導(dǎo)熱系數(shù)）。 對于精確的Navier-Stokes方程，這些系數(shù)只是流體的性質(zhì)，而對于“平均”方程，這些系數(shù)也取決于“平均”流場。</p><p><b>　　其中</b></p>

98、<p>　　請注意，物理上，湍流是三維的。 這個簡單的湍流模型的二維流動假設(shè)的一個固有結(jié)果是模型只考慮了較小尺度（單元尺寸）的三維湍流，而較大尺度湍流假設(shè)為二維并且數(shù)值解析。</p><p><b>　　邊界條件</b></p><p>　　圖2顯示了離散化的流動幾何形狀和相應(yīng)的邊界條件</p><p>　　模擬。 在轉(zhuǎn)輪出口處，

99、通過指定假設(shè)的出口流速模擬感應(yīng)過程。 為了方便起見，假定流速在空間上均勻并且在時間上是半正弦波。 發(fā)動機(jī)點(diǎn)火順序為1-3-4-。 一個完整發(fā)動機(jī)循環(huán)或兩個發(fā)動機(jī)轉(zhuǎn)速的出口邊界條件給出如下：</p><p>　　在歧管入口處，通過使入口壓力為大氣，忽略空氣濾清器上游的空氣管道的影響來刺激大開度節(jié)流閥，或者</p><p>　　墻的規(guī)律被用于固定邊界（Schlichting，1968）。 這是

100、一個動蕩的邊界層</p><p>　　壁剪切速度根據(jù)壁剪切應(yīng)力tw 定義</p><p>　　用公式（10）右邊的U *代替1/7-law（Schlichting，1968）近似U *，即</p><p>　　消除了關(guān)于U *的等式的超越特性。 對于平滑墻（B-5.5）方程（8）變成，</p><p>　　方程（13）用于ywu / v>

101、; 130。 3。 然而，對于ywu / v <1Z0.3，方程（13）由層流子層公式代替：</p><p>　　為了簡單起見，熱邊界層使用切雷諾類比近似。 因此，對于湍流，熱通量給出為</p><p>　　這與Cloutman（1982）使用的公式相同。 再次對于層狀子層，等式（15）被替換為</p><p>　　這是普朗特數(shù)等于0.89的層流熱流的簡單差分

102、近似。為了簡單起見，假定tw沿壁面邊界是有利的，并等于343K。</p><p><b>　　初始條件</b></p><p>　　假設(shè)歧管內(nèi)的空氣靜止。初始壓力假定為穹頂。初始溫度假定為343開爾文。</p><p><b>　　計算機(jī)代碼</b></p><p>　　一個名為Flody的計算機(jī)代

103、碼用于數(shù)值地解決上面給出的流動模擬問題。它是Conchas - Spray代碼的修改版本（Cloutman，1982）。對流入和流出邊界條件進(jìn)行了大量修改。對于這項研究，不包括燃燒和噴霧。預(yù)處理器和后處理器可以輕松指定流量問題和便捷的輸出顯示。這里給出數(shù)值方案的簡要描述。</p><p>　　Flody是一個時間推進(jìn)過程，它解決了上面給出的控制方程的有限差分近似。瞬態(tài)解是半隱式的。它使用廣義四邊形單元格中的空間差

104、異。 che cells的角落，被稱為頂點(diǎn)，可以隨時隨地移動。這些允許拉格朗日和/或歐拉描述。被稱為任意拉格朗日 - 歐拉（ALE）網(wǎng)格（Hire，1971; Arasden，1973; Pracht，1976）的這種類型的網(wǎng)格在表示彎曲和/或移動邊界表面時特別有用。只要有可能，空間差異保守。所使用的程序以整體形式區(qū)分基本方程式。發(fā)散項被轉(zhuǎn)化為局部單元邊界上的表面（線）積分。該方法被稱為ICED方法（Stein，1977; Tunsta

105、ll，1977）。這種ICED-ALE方法也在諸如YAQUI（Amsden，1973），BAAL（Pracht，1976），YOKIPER（Anderson，1975），SALE（Amsden，1980）和CONCHAS（Butler，1979）等其他編碼中找到。更多細(xì)節(jié)。關(guān)于數(shù)值方案的信息參見參考文獻(xiàn)（Cloutman，1982）。</p><p><b>　　結(jié)果與討論</b></

106、p><p>　　理想化進(jìn)氣歧管內(nèi)的流量計算持續(xù)兩個完整的發(fā)動機(jī)循環(huán)（或四個發(fā)動機(jī)轉(zhuǎn)速）。使用Dec 20計算機(jī)上的Flody代碼。模擬的CPU總時間大約為50小時。所用的計算網(wǎng)格和邊界條件如圖2所示。一些數(shù)值結(jié)果如下所示。圖3是一張照片，顯示了轉(zhuǎn)輪咀嚼時流場的發(fā)展情況。 ＃1。所呈現(xiàn)的圖表是針對第二發(fā)動機(jī)循環(huán)的。流場由velo？city矢量表示，顯示它們的方向和大小。這些圖顯示了高度瞬態(tài)誘導(dǎo)過程的復(fù)雜性質(zhì)。例如，請注

107、意歧管腔中兩個大的殘余渦流如何影響后續(xù)流場的發(fā)展。這在誘導(dǎo)開始期間很明顯，其中che流繞過兩個渦流。但是，當(dāng)流量增加到峰值時，它對流量歷史的依賴性就會降低，并且更多地取決于上游和邊界條件。這可以通過流過che主流道的主速度大的空氣流來觀察。注意在這個柱子兩側(cè)產(chǎn)生的兩個漩渦如何在誘導(dǎo)的后期階段增長并進(jìn)入全會，從而影響下一名參賽者的感應(yīng)。由于歧管流動歷史（初始條件）和復(fù)雜流形幾何（邊界條件）以及可壓縮性效應(yīng)的相互作用，歧管內(nèi)部的不穩(wěn)定流動變