EML 5131 EXAM_2

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EML 4930/5131: Combustion Exam 2 Due Wednesday, Dec 8 at 11:59 PM, on Canvas 'ljhis exam is open book and open notes. Discussing this exam with anyone prior to turning it in will be considered cheating. Show all of your work. Do not use Cantera, use the supplied tables, tables in Turns, or appendices in Turns for data such as the enthalpies of formation. Show all of your work. students. You do not have to interpolate tabular entries. Question 1: /5 Question 2: /10 Question 3: /5 Question s - telsvs. iz o ifh Question 5: = /b Question 6: /5 Question T: cizii]b Question 8: _ - st sim/10 Question 9: /10 Question 10: .5 Question 11 #20sedit 7720 Question 12: © 15 decin 15 Total: .. a0

Nam 1. 5 points Sketch the ZND structure of a Chapman-Jouguet detonation. In addition, sketch the thermodynamic process of the ZND detonation structure on Rankine-Hugoniot curves. Label the ZND point, CJ point, and other notable features of a detonation on both sketches. State how the reactants are heated. NP il P A ZNP Spike = ’*\ : R 2 & = ,,,,f Roactor 2 1 Hugonsot 9) : = v="'{2 5 ShOpb\WUVE 7“"1‘ ;wcl: Hre (('a(‘,'u,% o ;\){,(’(;aw}c :[(‘FIJS. [Pevence Jred shrts o chemical " reachon. e ,nr,Jnf‘}} ﬂ"e &%V‘GHO/‘ cavses a ; Wen -{W,\{ 56"' rawfvtzfies;, fhrere s a Pyesswe o 3 and Hhe tempevatve o ! vefea“c‘; il N Dl)"‘“§ Hnic ?rmeSS, [hewn(al erergy sﬂjfb .lmjvtcu’ . Page 2

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3. 5 points Write the equation for conservation of species mass in a one-dimensional variable-area he significance of each term. PS 223 -22¢ : TURNS — b /01' 7 duct. Label and state tk /4 = sy ) - Base d on Lechove 26 & pév o ‘/ & 4 { A AL - NI M b b=l at e AL i I’_\)J‘“ A l ASA 20, M ageh _ o5 e = BAE Vet o T s of s d¢ A ) R A T ot S & We aPP\\[ Fhese (qua%ma for one )173“5 i § W d } Al da heevieled - Dy o s 58 . W Al 1. = ol av b= — 4y ((,.—/,)f'lwr,fi [ b 4 Ly é(v Wid¥ =W ¥ - W AR T AN W - cons. of 3pecies Page 4

4. 5 points 1\{0 Write the expression for the diffusion heat flux vector in vector form. Label and state M the significance of each term. s Q" ! oT S Lon \:S\/ 5 La) A % 2 rV';,m"i Hent Mlux CondueRon . fPusion veetor oy SpeoeslDe = contitbrivon bl hon Bt s atdendl BlUn of the ik species Ls ;g ! o R i L Page 5

Nameg— 5. 5 points An engineer unfamiliar with combustion proposes to increase the operating pressure of a pipe flowing flammable gases to increase throughput. The pipe uses a flame arrestor that has been highly optimized for original design condition. What safety concerns should the engineer raise about the proposed new operating condition? Explain. Assume the pipe system can easily withstand the increase in pressure and that the temperature and flammable gas mixture are unchanged. K thed arises iF Pe engiveer i nereages the nevenscd over hime, ox h e Flome to Tiore. 15 ok 18sue safe pressove. Faclier, 71 s pbseved that as pressuve = 4 A ecold i ovduw dO guUEnE ; ) O dearease., As o resoby ; ‘ g B Plame speed o 1 CF i 5 ol i 7”(”514‘,'3 distance most inereae, A iy convol, T 3 . - S pwing o1 oF ¢ s R Thor Ke "+ o & ) s R eshor wos 0pT7 4 e 3 | that e avees : i ks o gy P A Q) e Was { encine i o ; Howeves +re 5 e I g cavenoet 2 S50 { s Jﬂl .t b . LY L eal ™ o * ot . 7l - 2 vt r[l-’/u(‘ S de =X 3’\ cont Jare cgnviot 2 vacveased @ ov f); ~al distanice Page 6

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\ Name:g_, ?—(oo Sketch the temperature and heat release profile of a premixed laminar flame. Label the % pleheat and reaction zones and what is the 51gn1ficance of these zones. State how the 6. 5 points ,T\)(J\S Preheat Zone Recchon 2une 2 -y o — [ nmd—:-n‘{“fi, Xa 75 L v/("\f'l"“'l"“: Y y {eheedvic heod e | R Y1 P o The P’?/‘f\fi.’/" gone ; “lime next 20N 1-_ ve lease ¢ < T LGS e K of cromical &Y ﬂ,\e rw:%a" Tone ) Ko E e i e TR te arder of spheric Pfgce)/(; the Flome Hrudkness 1= HC g on aroecsa ! = of ox sdvl 1o dmde the reaction e Arther ”\’lo a fhin ”3“'\ ¥ g ,ﬂ‘,\l'lw}e"- T is usd? e yougkrt Sraduv«\t\') 3 speces concontradon . yse his 2 fask Jremisiey. e \IV/‘{ radents st Y Page 7

7. Answer True or False. Correct the answer with a short statement if it is false. 5 points a) The equilibrium constant, K, is a function of only temperature. gl b) A detonation is a supersonic combustion wave that consists of a shock leading a flame. N Py ez | e ¢) The chemical reaction rate has a relatively little effect on the height of a laminar diffusion flame. ¥ o ds = The “rxr.«;\‘f‘i oF o larivar diffusion Pame APP(W = rabe. ! ! : . ) L .,'M\L‘l"‘ CHM . Pre :iausvu:fi for on aw Lor d) The velocity of a Chapman-Jouguet combustion wave is dependent on the chemical reaction rate. = = ) rue e) Turbulence increases mass consumption rate of premixed fuel-oxidizer mixture only by increasing the surface area of a locally laminar flame if the turbulent length scales are smaller than the thickness of a laminar flame. ( L3¢ i Jrue Page 8

8. 10 points A experiment was performed to determine the length of a non-premixed flame as a function of fuel flow rate using a circular tube. The images for each test case from this experimental series are shown below. Each test was performed with a different fuel flow rate. a) Which case (test number labeled in the figure) has the highest flow rate? b) Many of the experimental tests show roughly the same flame height. Is it likely that the diameter of the fuel tube varied from test-to-test? Explain. c) Explain the increasing flame height for Tests 1 - 3. What is the dominant parameter that controls the flame height for these cases? Figure 1: Problem 10 s Aovete e ‘r'\rvf“:ﬂ(‘, fo this ,OJ;L' s 1S q\ Vest coces B —1S hove stemlor Aarme JMXHAS. et ca%). . Ny constan). poe Rovee \V‘Sws o VW\O'(" fg?fi"*‘?{’ jo was neveased Harsughoot gl o X o i (st Aow rote Lassiming has #e NS s ?oss\\o‘t ot the Jess Fhan O- 122 1, for dont- Fl + : hei IS vely e o Floweate. 03 i o I5L+' M(le |r,e, iﬂw@ L\e‘-S\r\'}. "Ut\OJ(eV\ce also bfsms o allven i 4. Howanr, the ke dhamedovs most \ave g vavie ; be diometers vart e essentially 0 b) I frg Alame lengths Ae Floweate Incveose,

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- T teliee that ¥ne —Hr\'lLV-u\eé Flave 2pp Smolate S ,Y\os'm«\. o D Explosion simulation codes for industrial safety often cannot resolve flames (deflagra- tions) to due to the very large length scales of a chemical processing plant, mine, oil rig, ote. relative to the length scale of the flame (~ 1 to 10 mm). Resolving the flame in a chemical processing facility (around 100 m or more) would require more them 10%° grid points using supercomputers that won’t exist for the foreseeable future. However, safety engineers often want to simulate how an unwanted flame would propagate through an en- tire processing plant using relatively modest (around 1000 processors or less) computing Tesources. Tt is of utmost importance to preserve the flame speed and overall fluid dynamics in order to simulate the feedback between the flame propagation and fluid flow when simulating an explosion. Heat transfer to walls and structures is a minor (sometime non-existent) concern. In these applications a so-called thickened flame model is sometimes applied make simulations more practical. The thickened flame model is designed to increase the laminar flame thickness without influencing the laminar flame speed. 9. 10 points An explosion safety analyst performing a simulation wants to increase the flame thickness by a factor of 10, but leave the laminar flame speed alone. By what factors should they change the thermal diffusivity and pre-factor for the chemical reaction? Would the thickened flame approach be viable if heat transfer to the surrounding structures was a primary output for these simulation codes? Explain. Assume that the model used by explosion simulation has constant thermophysical properties, a Lewis number of unity, and a single-step global irreversible Arrhenius reaction. 14 5§ = ot Ovv Plame Hae Kness s egua’ 4o 2 O = sy '. ) 4 2 . . . . Fom e velahons'rip, we Wwnow Fhed ovr fueymal dvflosividy T f{:recH\l On tre ofher hawg, oor flawme Hhickness P we want o Lactor of 1O withoof '1"0(_)(/"1;-/\5 Aame szcu], we aced o 9vopw+‘mm>\ Yo oor FAeme Haichoness, ; TS ;n\/else‘\, Frapuf‘h'wnp.\ Jo por Plowe g.f‘(‘(d_ As a /tsu]‘)" Voevease Higkness by oa nevease. didusivity Ve Gickor oF = (Of s, well Avirenos ealuorHewf A exp (&5 50 /RuT\ : we have "o Jake tato account ¥ 0| orfiamal ;“LPREC.}QO,\ soke wost Yo decreast ouw Flome s?eu\ anouched. e Foedbaidlt Beteesnt Fhe ROt popagetion Page 10 oach s neble, I+ 15 g goost Plac‘“(ﬂl Wy end Aud Aoy oot §\Mol&ﬂf\5 Yol our Flawme 5(zccl k) ‘T addihon : e - Ao gRel 5 Ak AND o roachon cate. Thevebove, 51, to ouvr (JIH\J.,x ‘\‘l 'N‘Ll ‘b{wa RAC‘,D( op ¥ " weep +o

b) The oenbushon uavt is }M’F"S“HAS % The \/tsime of Mo combo @) Jn derms o Ronkine Name:! The image below shows the surface of a premixed combustion wave propagating in a duct produced from a numerical simulation. 10. 5 points a) In terms of Rankine-Hugoniot analysis, what type of combustion wave is this? b) What type of flow the combustion wave is propagating through (i.e., laminar, tur- bulent, supersonic, etc.)? ¢) If the type of the combustion wave can be divided into multiple regimes, what is the regime of the combustion wave? (If the combustion wave is traditionally not broken into multiple regime, then simply state. ”This combustion wave is not divided into multiple regimes.”) Tere = 1.147 . time chice Gtion = 0413 e Cycle = 308 Figure 2: Problem 10 - Hugoni >4 onalysis, T believe #hod s 2 a Sronsy Agﬂo\sm%or\ com ushon wave . ﬂmwsh subolonil How. h wavt PPN "’\'\5"\ "a{ifLL' Jovioolemd «CS“Me. shown Page 11

(5o *5Cste 5.5(0as 37402) B> 2B 2 a0 <2 CHy + Catly * T(0. #376 N} qcaa # 6H.O % 3 Nam 11. 20 points A non-premixed flame burner with 30% primary aeration burns fuel that is’coﬂ)riﬂlof aix_tgzg of methane and propane. The burner uses 40 square ports that are 3 mm in width. TR T a) Compute the lower heating value (per kg) of the fuel blend. b) Compute the total volumetric flow rate in the fuel stream if the burner produces 2.8 kW. ¢) Compute the flame length. Show all of your work by dividing the reaction into primary and external air and using fundamental definitions to compute S or fs Z“fi 9.62 depending on which is needed. Note: Python, Matlab, Wolfram Alpha, graphing calculators, etc. all have access to any necessary special function(s) that you may need. i) e LT T v W ] a DA, = H[LQM f’fivau fl;c/ ks .,(U " o v ) \"{,1,“7‘ [() £ 2o F,He0(5) — s L Mgl s Foni b / e = =241, 191 kT Jumel Wiong = T, 831 ST e ,g R i RE LR s Tl «3 [ kenol \:7.‘:”{: - 103, BT w3kl < Mo = 2 70,508+ e i ” w096 Y JEmet = 50 2 246 583 «I MW g f‘"i\/‘!{:.;“ * fJxVJL:»\: Z jb.od> «5“("‘ s 0, 3 bjlym\ SRR g CggestMWt A isiqg 07 wls 3 - ApsiGe @ o BeEy Bl gt Seatea Bl L o e oy, ot °'3(%> iyl (£ < Mo MMaie ()N85, 9904 Nl Stoie L, F )srac i 1A (;$30.06‘$ : :(o,z)(15.7ﬂ(5.qnuo'3\ = 200 <19 Wl i e e R FRlgutel = e ToT [3 A, P ) “ MR Bl e Sty e £ °0:09094 Wi = = 04091 G (R M, = 0.90m(24.5)+ 0.0409(b0. 139 < a \*Qw 22w 20 7- P = 01328 = 1208 [ 5 oo ( MN..,S T (ii;—n)kg L C) oN Sc AT cH o ¥ Page 12 PAPESL

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I o = s (Pﬂi 5 Wi = 0.30 P+ (1] 5pee) 67"“’ = | x+yly : 7(’0,_ =ph i 0,20 S s D Ko 4¢ L3t (Y33.42) S = 3331 S . 2.021 5 e - Lf = 10965 Q, (To/Tz Qe = Grer . 2.4 70 _ 66610 Ciaverk (01 +3Y" %) ; ¥ 4o Ly (Hs)"s = 0.5kb WoaveFlae) = < ,LF = 0.022m = 22.)9 am /

12. 15 points For the following association reaction: P A+Bemc L d \ 2 C+M 2B M, use Lindemann theory to derive an expression for the apparent rate constant, kapp, for the molar rate of production of C (i.e., d[C]/dt = kypp[A][B]). Evaluate kqpp at the low and high-pressure limits and sketch kqp, as a function of p at fixed T. » - ) [0106] - 6] - wer][n] - o dt dLd Lk [e][m] dt & . [A10871 7 b el = kae[s1Le} afe} ke [1)) kohile] % kg + w M7 di kg ¢ ko[l b dlc] Ks Ke [] i — [»1la} H Ky + ¥ 0] e \‘/\/\/ = K KD Kagp = ¥ KnTM) ky « w5 (1 Low P: A P=o0 ,[M)> 0 [m)~_P Page 13