Mechanical Engineering 2022 Paper II 50 marks Solve

Q7

(a) (i) Briefly discuss HC, CO and NOₓ emission formation in SI engine. Explain the dependence of these emissions on equivalence ratio with a neat diagram. (10 marks) (ii) An IC engine working on an ideal Otto cycle has AFR of 15 : 1 and compression ratio of 9 : 1. The pressure and temperature at the start of compression are 1 bar and 27 °C, respectively. Find the maximum temperature and pressure of the cycle. Assume that compression process follows the law pV¹·³³ = C, the calorific value of fuel is 43000 kJ/kg and Cᵥ of working fluid is 0·717 kJ/kg-K. (10 marks) (b) A food processing room has a very high latent heat load and is required to be air conditioned as per the following data: Room design conditions : 20 °C DBT, 60% RH Outside conditions : 45 °C DBT, 30 °C WBT Room sensible heat : 35 kW Room latent heat : 20 kW The ventilation air requirement is 90 cmm Determine the (i) ventilation load, (ii) room and effective sensible heat factors and (iii) ADP and amount of reheat for economical design. Assume bypass factor of the coil as 0·05. [Psychrometric chart is given at the end of this Paper] (20 marks) (c) Prove mathematically that for maximum discharge through a chimney of a certain height and cross-section, the absolute temperature of gases bears a certain ratio to the absolute temperature of the outside atmosphere, in case of natural draught of a boiler. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) (i) एस० आइ० इंजन में HC, CO तथा NOₓ उत्सर्जन के गठन की संक्षेप में विवेचना कीजिये। इन उत्सर्जकों की समतुल्य अनुपात पर निर्भरता को एक स्वच्छ चित्र की सहायता से समझाइये। (10 अंक) (ii) एक आइ० सी० इंजन, जिसका वायु-ईंधन अनुपात (ए० एफ० आर०) 15 : 1 तथा संपीडन अनुपात 9 : 1 है, एक आदर्श ऑटो चक्र पर कार्यरत है। संपीडन के आरम्भ में दाब तथा तापमान क्रमशः 1 बार तथा 27 °C है। चक्र के अधिकतम तापमान तथा दाब ज्ञात कीजिये। ऐसा मानिये कि संपीडन प्रक्रिया pV¹·³³ = C नियम का पालन करती है, ईंधन का कैलोरी मान 43000 kJ/kg तथा कार्यकारी द्रव का Cᵥ = 0·717 kJ/kg-K है। (10 अंक) (b) एक खाद्य प्रसंस्करण कक्ष का गुप्त उष्मा भार बहुत ज्यादा है तथा निम्न आँकड़ों वाला वातानुकूलन अपेक्षित है : कक्ष अभिकल्प अवस्था : 20 °C DBT, 60% RH बाह्य अवस्था : 45 °C DBT, 30 °C WBT कक्ष संवेग उष्मा : 35 kW कक्ष गुप्त उष्मा : 20 kW अपेक्षित संवातन वायु 90 cmm है गणना कीजिये (i) संवातन भार, (ii) कक्ष तथा प्रभावी संवेग उष्मा गुणांक और (iii) ए० डी० पी० तथा मितव्ययी अभिकल्प के लिये पुनःतापन की मात्रा। कुडली का बाइपास गुणांक 0·05 मानिये। [इस पत्र के अंत में साइक्रोमैट्रिक चार्ट दिया हुआ है] (20 अंक) (c) एक वाष्पीय (बॉयलर) में, प्राकृतिक प्रवाह की अवस्था के लिये, गणितीय रूप से सिद्ध कीजिये कि एक निश्चित ऊँचाई तथा अनुप्रस्थ काट की चिमनी में, अधिकतम निस्सरण के लिये, गैसों के निरपेक्ष तापमान का बाह्य वातावरण के निरपेक्ष तापमान से एक निश्चित अनुपात वाला सम्बन्ध होता है। (10 अंक)

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Approach

Solve this multi-part question by allocating time proportionally to marks: ~20 minutes for (a)(i) emissions discussion with diagram, ~20 minutes for (a)(ii) Otto cycle numerical, ~40 minutes for (b) air conditioning psychrometric calculations, and ~20 minutes for (c) chimney draught derivation. Begin each part with clear identification of given data, apply appropriate thermodynamic principles, and conclude with physically meaningful results.

Key points expected

  • (a)(i) HC formation via flame quenching and crevice volumes; CO from incomplete combustion in rich mixtures; NOx via thermal (Zeldovich) mechanism at high temperatures; emissions vs equivalence ratio diagram showing HC/CO peak rich, NOx peak slightly lean
  • (a)(ii) State 1: p1=1 bar, T1=300K; polytropic compression to state 2: p2=p1*(r)^1.33, T2=T1*(r)^0.33; heat addition using Q=m*Cv*(T3-T2) with fuel energy release; solve for T3 (max temp) and p3=p2*T3/T2 (max pressure)
  • (b) Plot room condition (20°C DBT, 60% RH) and outside condition (45°C DBT, 30°C WBT) on psychrometric chart; calculate ventilation sensible and latent loads; determine RSHF=RSH/(RSH+RLH) and ESHF accounting for bypass factor; find ADP from coil process line and reheat needed
  • (b) Ventilation load: mass flow rate from 90 cmm, enthalpy difference between outside and room air; split into sensible and latent components
  • (c) Derive draught pressure Δp = H*g*(ρa-ρg) = H*g*ρa*(1-Ta/Tg); discharge ṁ ∝ √(Δp/Tg); maximize ṁ w.r.t. Tg to obtain Tg/Ta = 2 for maximum discharge
  • (c) Alternative derivation using chimney height equation and differentiating discharge equation with respect to gas temperature, showing optimal temperature ratio is 2:1

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies thermal NOx mechanism (Zeldovich), flame quenching for HC, and rich mixture CO formation in (a)(i); applies polytropic process correctly with n=1.33 in (a)(ii); uses psychrometric relationships properly including bypass factor in (b); establishes correct optimization condition for chimney discharge in (c).Identifies basic emission sources but confuses NOx formation mechanism; uses polytropic relations but may apply ideal gas incorrectly in heat addition; understands psychrometric chart but makes errors in bypass factor application; derives chimney equation but misses optimization step.Confuses emission formation mechanisms (e.g., treats NOx as fuel NOx); applies isentropic relations instead of polytropic; fails to understand bypass factor concept; cannot set up basic chimney draught equation.
Numerical accuracy20%10(a)(ii) T2 ≈ 300×9^0.33 ≈ 625K, p2 ≈ 1×9^1.33 ≈ 20.8 bar; heat added per kg air = CV/(AFR+1) ≈ 2687 kJ/kg; T3 ≈ 625+2687/0.717 ≈ 4372K, p3 ≈ 20.8×4372/625 ≈ 145 bar; (b) ventilation mass flow ≈ 1.08 kg/s, loads calculated to 2 significant figures; (c) correctly proves Tg/Ta=2.Correct method but arithmetic slips in exponent calculations or unit conversions (e.g., °C vs K); psychrometric enthalpy readings slightly off; reaches Tg/Ta=2 but with algebraic errors in derivation.Major calculation errors (e.g., uses r instead of r^(n-1) for temperature); confuses specific heat values; order-of-magnitude errors in final answers; no numerical verification in (c).
Diagram quality20%10(a)(i) Clear emissions vs equivalence ratio plot with three curves: HC and CO rising in rich region (φ>1), NOx peaking at φ≈0.9-1.0; axes labelled (equivalence ratio 0.6-1.4, emissions g/kWh or relative); (b) Psychrometric chart sketch showing room point R, outside point O, mixed air M, apparatus dew point ADP, and supply air S with coil process line and reheat shown.Emissions diagram shows correct trends but poorly labelled axes or missing units; psychrometric process shown but ADP location approximate or bypass factor not illustrated.No emissions diagram or completely wrong trends (e.g., NOx increasing with φ); no psychrometric representation; diagrams drawn without any labels or values.
Step-by-step derivation20%10(a)(ii) Explicitly writes pV^n=C, derives T2/T1=(V1/V2)^(n-1)=r^(n-1), calculates p2 from p2/p1=r^n; sets up energy balance mf×CV=(ma+mf)×Cv×(T3-T2) with mf/ma=1/AFR; (b) Shows RSHF and ESHF formulas with derivation from bypass factor; (c) Full derivation: ṁ=Cd×A×√(2ρgΔp), substitutes Δp, expresses in terms of Tg, differentiates dṁ/dTg=0.Shows key formulas but skips some algebraic steps; states ESHF formula without deriving from BPF; sets up chimney discharge equation but differentiation step unclear.Jumps to final answers without showing working; no derivation of ESHF from first principles; states Tg/Ta=2 without any proof.
Practical interpretation20%10(a)(i) Links emission trends to catalytic converter design (three-way catalyst window at φ≈1); (a)(ii) Comments on unrealistically high T3 indicating ideal cycle limitations, suggests actual engines use lower compression or richer mixtures; (b) Explains why high latent load needs low ADP and reheat for comfort control, mentions Indian climate challenges; (c) Discusses why actual chimneys operate below optimum for material temperature limits.Brief mention of catalytic converters or real engine deviations; states reheat purpose without explaining energy penalty; notes chimney height practical constraints without temperature discussion.No practical context provided; treats all problems as purely academic exercises; no mention of why results may differ from reality.

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