清华大学2007级期中考试A卷试题(含答案)

清华大学热能工程系2007级“燃烧学”期中考试试卷（A卷）

Middle Term Examination of Combustion (A)

考试时间(Date)： 2010年4月26日 学号(Student No.)：

Instructions(提示):

1 请将你的学生证放在桌子的右上角（Please put your Photo student ID on the

desk）

2 考试为开卷考试，允许带教科书，作业，课件，笔记本和另外的参考书各一

样，但不能互借，答题必须独立完成。（The examination is OPEN BOOKS. Calculators, textbook, homework and notebook are allowed, but they can not be lent to others. You should answer the questions independently and help is not allowed）

3 试卷共有8题，你要在120分钟内完成这次考试，先检查一下你的卷子，题目

是否对，共有5页。答案必须写在答题卷上，试题卷上回答无效。答题必须明确，清晰，计算题应给出单位。（There are 8 questions on this exam with 5 pages. You have up to 120 minutes to work on this exam. Please be sure that you have a complete exam package. Please work exam problems on the pages provided. Show your work neatly and write your answers. Give units for all answers requiring them.） 4 如果试卷不对，请立即与监考教师说明。（If a page is missing, take the exam to

a proctor immediately.）

5 强烈推荐你先读一下所有的问题，并对回答问题的时间进行按排。答卷完成

后请再仔细检查一下。（Budget your time for each question and be sure to first answer those questions that you know how to work. Check your work after completing the exam.）

6 请你现在就在答卷纸和试卷纸上写上你的名字与学号，并在你的答卷纸首页

（PRINT your name NOW in the spaces at the 上标明你的试卷的类型（A或B卷）

top of your pages. Mark the exam type A or B）

7 答卷可以用中文或英文，如果是双语的，以中文为准。试卷有英译的，也以

中文为准。(The answers can be in English or Chinese. If two languages are used in one answer, I will take Chinese as the selection. Some of the problems have

been translated in English. If there are any difference between Chinese and English, Chinese is for your choice.)

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班级(Class)：

姓名(Name)：

试 题

1. 己烷(C6H14)在干空气中燃烧，对于燃烧产物分析各组分干基组成的体积百分比为CO2为8.5%、 CO为5.2%、O2为3%，其余为氮气，试确定上述燃烧过程的空燃比A/F和当量比Φ？[13分]

Considering hexane combustion in dry air, the dry-basis compositions of the species in product are CO2 with 8.5%, CO with 5.2%, O2 with 3%, and the rest are N2. Please determine the air-fuel ratio A/F and the equivalence ratio Φ. [13 points]

2. 液态的丙烷在25℃下，用25℃的空气进行燃烧，假设燃烧完全，反应物和燃烧产物为理想气体，试求下述两种情况下理想燃烧温度：[14分] (1) 当丙烷在当量比条件下燃烧； (2) 当量比Φ=0.4的条件下燃烧。

The liquid Propane burns with air at 25℃. Assuming complete combustion and ideal gas, please determine adiabatic flame temperature under conditions below, [14 points]

(1) with equivalence ratio Φ=1.0 (2) with equivalence ratio Φ=0.4

3. 计算以下三个反应的化学反应速率，并对各反应速率的大小进行比较，假设反应温度1800K，压力101325Pa：[16分]

CO + OH → CO2 + H (1) H + H + M → H2 + M (2) O2 + M → O + O + M (3) 其中反应(1)和(2)的正反应速率常数为

k1f4.76107T1.23exp(70/T) cm3/mol-s k2f11018T1 cm6/mol2-s

而反应(3)的逆反应速率常数为：

k3r1.21017T1 cm6/mol2-s

混合物中具体摩尔分数为 χOH=4.0×10-3; χCO=2.0×10-2

χH=7.0×10-4; χH2=2.0×10-7;

χO2=3.0×10-2; χO=1.0×10-7; χN2=0.70; χCO2=0.10;

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χH2O=0.145;

Calculate the values of reaction rate of three elementary reactions below, and compare them. The temperature is 1800K, and pressure is 101325Pa：[16分] CO + OH → CO2 + H (1) H + H + M → H2 + M (2) O2 + M → O + O + M (3) The rate coefficients of forward reactions of (1), (2) are given as,

k1f4.76107T1.23exp(70/T) cm3/mol-s

k2f11018T1 cm6/mol2-s

Meanwhile, the rate coefficient of reverse reaction (3) are given,

k3r1.21017T1 cm6/mol2-s

The molar fraction of the mixture in product are given as below, χOH=4.0×10-3; χCO=2.0×10-2

χH=7.0×10-4; χH2=2.0×10-7; χO2=3.0×10-2; χO=1.0×10-7; χN2=0.70; χCO2=0.10;

χH2O=0.145;

4. 如下图一个柱锥型的敞口杯中，液面始终维持不变，即x=0处半径r0=1cm，开口高度L=5cm，倾斜角度45o, 液体为苯(性质ρl=879kg/m3; MW=78.10kg/kmol; hfg=393kJ/kg；Tboil=353K)，空气在管口掠过，系统的环境温度310K，质量扩散系数DC6O6-air为0.93×10-5 m2/s, 假设系统密度取液面处和开口端的平均，试确定： (1) 苯的质量蒸发速率；[9分]

(2) 与半径r0=1cm的等直径量筒相比，二者蒸发速率的比较。[6分]

Air, 310K x x=L r0 x=0 In a broad-opening cylindrical/conical jar like a figure above, the interface of liquid

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benzene is kept at a position of x=0, where the radius at the interface are held at r0=1cm. The height from the interface to the top of jar are L=5cm，and the inclination is 45o. The properties of benzene include ρl=879kg/m3, MW=78.10kg/kmol, hfg=393kJ/kg and Tboil=353K. The air flows across the jar with a system temperature of 310K, the mass diffusivity (DC6O6-air) is 0.93×10-5 m2/s. The mean density of system is obtained by averaging the value at the interface and that at jar top surface. (1) determine the mass evoration rate (kg/s) of benzene [9分]

(2) compare the evaporation rate with a 1-cm-radius (r0=1cm) tube [6分]

5．假设一个微型燃气轮机为理想的全混流反应器，进行的是甲烷-空气混和物在当量比Φ=0.8条件下的燃烧，假设反应器系统内温度为1573K，如果系统压力为5atm(即5个大气压)，反应器体积为268cm3, 甲烷的流率为0.005kg/s, 试计算全混流反应器内混合物的停留时间。[10分]

Assuming a micro-scale gas turbine as a well-stirred reactor, methane burns with air at Φ=0.8. The system temperature is 1573K, and the pressure are 5atm (i.e., 0.5066Mpa). The volume of the well-stirred reactor is 268cm3. The flow rate of methane is 0.005kg/s. Please determine the residence time of mixture in this well-stirred reactor. [10分]

6. 对于多组分扩散，其物理基础来自组分i的动量变化率的方程，

NDvpiZijmij(vj,diffvi,diff)Yifi YiDtj1(1) 试说明方程中每项的表达物理意义，并解释所有符号的含义。[7分]

(2) 表征浓度扩散的Stefan-Maxwell公式

iijvj,diff,vidiff,Dj1ij

N,  i 1,2,N......,

就是从上述组分动量变化方程中推导而来的，请问Stefan-Maxwell公式中Dij物理意义上是二元扩散系数，还是多元扩散系数？[3分]

As for the multi-component diffusion, its physical bass are built on the momentum changing rate of species i as below,

NDv YipiZijmij(vj,diffvi,diff)Yifi

Dtj1(1) please explain the physical meaning of each term or symbol in the above

equation [7 points]

(2) the Stefan-Maxwell equation representing the diffusion due to concentration

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difference (as below)

iijvj,diff,vi,diff, i1,2,......,Nj1Dij

Nare just derived from the momentum equation in (1), please clarify what does Dij

in the Stefan-Maxwell represent among binary diffusivity or multi-component diffusivity. [3 points]

7. 根据燃烧理论课程所学知识，尝试搭建一个标准的柱塞流(Plug-flow)反应器系

统，假设某一关键组分的质量扩散系数为8×10-5 m2/s, 同时假定反应主要发生在2mm的狭窄区内，尝试分析该反应器的气流流速在什么样的条件下，才能保证系统满足柱塞流反应器的假设。[10分]

提示：反应器内最大的浓度梯度发生主要产生在反应区。

The knowledge during combustion study is helpful to build a standard plug-flow reactor. Assuming the mass diffusivity of the key species is 8×10-5 m2/s. It is assumed that the reaction mainly occurs within a narrow zone with a length of 2mm. Please determine the proper condition for mixture velocity to ensure the basic assumption of plug flow reactor. [10 points]

Clue：the maximum gradient of the species concentration exists in thin reaction zone

8. 在火箭燃烧室产物中含有H原子和OH游基, 其浓度均为4×10-6mol/cm3，温度为3000K，总气体浓度为4×10-4mol/cm3。若这些气体是在1000K的温度下从燃烧室排出(此时H2O基本上不再离解), 此时气体密度是燃烧室内气体密度的1/20，若排气以3000m/s的速度流动,试计算在下游中多远的地方能测出H和OH已有99.9%再化合。假设除H+OH+MH2O+M外(k=1016cm6/mol2s, 且与温度无关), 不考虑其他任何的再化合反应。[12分]

(There are H radicals and OH radicals in the combustor of rocket. The concentrations of H and OH are same as 4×10-6mol/cm3. The temperature of the combustor is 3000K. The total gas concentration is 4×10-4mol/cm3. The gas exits the combustor at the temperature of 1000K, where the formed H2O does not dissociate. The density of the exit gas is about 1/20 of the density of the gas in combustor. Please determine the distance of the gas flow from the exit to the point of the downstream where H and OH recombined to 99.9%. The velocity of exit gas is about 3000m/s. Assume that only the recombine reaction takes place: H+OH+MH2O+M and k=1016cm6/mol2s and k is independent of temperature.) [12分]

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