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ME 400 Energy Conversion Systems Lecture 6. Emad Jassim & Ty Newell Department of Mechanical Science and Engineering University of Illinois at Urbana-Champaign. © 2009 University of Illinois Board of Trustees. All Rights Reserved. Project 1 Thermodynamics of a Potato Gun.

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me 400 energy conversion systems lecture 6

ME 400Energy Conversion SystemsLecture 6

Emad Jassim & Ty NewellDepartment of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaign

© 2009 University of Illinois Board of Trustees. All Rights Reserved.

project 1 thermodynamics of a potato gun
Project 1 Thermodynamics of a Potato Gun
  • The process involved in launching a potato is similar to that of common internal combustion engines….except the piston does not return (hopefully) to complete a cycle
  • We want to determine:
    • how to predict the performance of the potato gun
    • how optimize the system
    • have an excuse for shooting some potatoes
project 1 potato gun
Project 1 - Potato Gun
  • What should the optimal potato gun look like?
  • This???
slide5

Potato Gun Experiments

PRESSURE

TRANSDUCER

POTATO GUN

HP 3562A DSA

Note Professor Miller in background

COMPUTER

slide6

Pressure versus Time

  • Similar pressure trace
  • Mass of potato/peak pressure correlation
  • Resonant frequency
slide7

Pressure/Mass Correlation

  • Larger mass, higher peak pressure
  • Vertical shots: smallest mass and lowest pressure
  • Due to mass, potato “stiction”, or other (coincidental) effects?

(9.9s)

Note: would be nice to have calibrated control of fuel mass....fuel of choice is “AquaNet”

(7.2s)

project 1 potato gun analysis

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Project 1 - Potato Gun - Analysis
  • We will consider 2 process paths for describing the firing of the potato:
    • First, a constant volume “heating” of the chamber gas that results in pressurizing the chamber
    • Second, a reversible (Sgen = 0), adiabatic expansion process of the chamber gas that adds kinetic energy to the potato and performs work on the atmosphere and gun barrel (friction)
  • “Closed” or “open” system viewpoints may be taken for the analyses.
project 1 potato gun closed system analysis

1Q2

2W3

Project 1 - Potato Gun - Closed System Analysis

Closed system analysis

-No mass crosses boundaries

-Heat and work transfers of energy allowed

Process 1-2: constant volume heating of chamber gas

Process 2-3: reversible, adiabatic expansion of chamber gas…increases potato KE and performs work on atmosphere and barrel (friction)

project 1 potato gun closed system analysis1

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Project 1 - Potato Gun - Closed System Analysis

Process 1-2; constant volume heating

Mass Conservation

1stLaw

2ndLaw

project 1 potato gun closed system analysis2
Project 1 - Potato Gun - Closed System Analysis
  • No change of system mass
  • If ideal gas assumed, for a given heat input, substitute specific heat relation for internal energy terms to determine temperature change
  • Ideal gas equation of state can be used to find pressure changes
  • Alternatively, assume pressures and work backwards to find temperature and heat input
  • 2nd Law allows entropy generation to be determined … must assume boundary temperature … use Tds relation for system entropy change

Process 1-2; constant volume heating

Mass Conservation

1stLaw

2ndLaw

And remember,

project 1 potato gun closed system analysis3

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Project 1 - Potato Gun - Closed System Analysis

Process 2-3; reversible, adiabatic expansion

Mass Conservation

1stLaw

reversible

adiabatic

2ndLaw

project 1 potato gun closed system analysis4
Project 1 - Potato Gun - Closed System Analysis
  • No change of system mass
  • Reversible process assumed, therefore, use 2nd Law first
  • Ideal gas Tds relations give relations between temperature, pressure and volume
  • Use specific heat relation for internal energy changes in 1st Law
  • Work transfer is constant pressure work on atmosphere and potato friction … calculated directly
  • Find potato KE from 1st Law

Process 2-3; reversible, adiabatic expansion

Mass Conservation

1stLaw

2ndLaw

(V3 - V2)=barrel volume

X = barrel length

And,

summary project 1 potato gun

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Summary, Project 1 - Potato Gun
  • Putting it together:
    • When potato KE is determined for a set of conditions, mechanics of the potato flight can be determined
    • What will the chamber-barrel pressure be at the optimal (highest potato KE) condition?
      • Higher or lower than Patm?
    • How does the chamber gas temperature change?
    • Is work on the atmosphere significant?
    • Is barrel friction significant?
    • And, and, ?????
project 1 potato gun alternative open system analysis
Project 1 - Potato Gun Alternative open system analysis
  • Major assumptions remain unchanged, but viewpoint used to define system is altered
  • End result should not be changed by viewpoint
  • For this problem, only process 2-3 analysis is changed by the altered viewpoint
project 1 potato gun open system analysis

1Q2

2W3

Project 1 - Potato Gun - Open System Analysis

Open system analysis

-Mass crosses boundaries

-Heat and work transfers of energy allowed

Process 1-2: constant volume heating of chamber gas

Process 2-3: reversible, adiabatic expansion of chamber gas…increases potato KE and performs work on barrel (friction)

-Barrel gas flows out of system

project 1 potato gun open system analysis1

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Project 1 - Potato Gun - Open System Analysis

As before … Process 2-3; reversible, adiabatic expansion

Mass Conservation

1stLaw

reversible

adiabatic

2ndLaw

project 1 potato gun closed system analysis5
Project 1 - Potato Gun - Closed System Analysis

Process 2-3; reversible, adiabatic expansion

  • The analysis boils down to same relation as the closed system viewpoint … atmospheric work of closed system is included in the “flow work” of the exiting enthalpy of the barrel volume

Mass Conservation

1stLaw

2ndLaw

Part of m(t2) is chamber gas and part is barrel gas … equivalent to closed view

And,

Only friction … no volume change work