Schmidt Analysis of Solar Stirling Power SystemsDavid WillyMS Mechanical Engineering EGR 501 Topics in Sustainable SystemsProject Advisor: Dr. Okey Onyejekwe

Presentation OutlineIntroduction to Solar ConcentrationStirling Engine TypesScientific PrinciplesOptics ThermodynamicsSchmidt Results using MatlabAnalytical vs. NumericalFuture Steps to Take if this was a Thesis

Introduction to Solar ConcentrationParabolic Trough Designs2-dimensional ParabolaSingle Axis TrackingTypically Rankine CyclePossibility of Stirling Cycle use

Introduction to Solar ConcentrationFresnel Lens DesignsFresnel vs. Standard Convex LensCurrently used in PhotovoltaicsDouble Axis TrackingMaterial Costs tradeoff? (Silicon $$ vs. Aluminum $$)

Introduction to Solar ConcentrationPower Tower DesignsArray of HeliostatsDouble Axis Tracking

Introduction to Solar ConcentrationParabolic Bowl (Dish) Collector3-dimensional ParabolaArray of ReflectorsDouble Axis Tracking Stirling CycleAir cooled(No Water Required)Air Lubricated (No Oil Required)

Stirling Engine Types Alpha, Beta, & GammaStirling Engines are External Combustion engines that can run on any fuel (heat source).Alpha Type Configuration Dual Piston Type

Example Engine STM 4-120 engine by Stirling Thermal Motors

Stirling Engine Types Alpha, Beta, & GammaBeta Type Configuration Piston/Displacer

http://www.keveney.com/Stirling.html

Stirling Engine Types Alpha, Beta, & GammaGamma Type Engine Piston/Displacer in different cylinders. MM-7

Scientific Principles - OpticsEquation of Parabola

Rim Angle

Local Mirror Radius

Scientific Principles - OpticsPerfect ParabolaDiameter of Receiver

Imperfect Parabola Diameter of Receiver (w/ dispersion angledue to slope error)

Scientific Principles - OpticsPerfect Concentration Ratios

Imperfect Concentration RatiosTrough Slope errorTrough w/ Cylindrical Receiver

Bowl w/ Flat Receiver

Scientific Principles - Thermodynamics1-2: Heat is transferred to the working fluid (isothermal Expansion).2-3: Forces the fluid into the cold cylinder.3-4: The right piston compressing the fluid(Isothermal Compression).4-1: Forces the fluid back into the left cylinder.

**Regeneration: The heat stored in process 2-3 is ideally picked back up by process 4-1.

Scientific Principles - ThermodynamicsIdeal Case with Dead Volume

Schmidt Analysis: Ideal Case with Dead Volume and Sinusoidal Motion

Schmidt Results using MatlabThe Schmidt Cycle was named from Gustav Schmidt (1871)who first published the solution. It is defines as a Stirling Cycle in which Sinusoidal motion of the pistons. It is the most complicated case of a Stirling Engine that can be solved analytically. All other cases have had to be solved numerically.

Schmidt Results using MatlabIn order to get Power per Engine Cycle, a Schmidt analysis has to be performed. Before this happens, the following assumptions have to be made:Sinusoidal motion of all parts.Known and constant gas temperatures in all parts of the engine.No gas leakage.Working fluid obeys perfect gas law.At each instant in the cycle, the gas pressure is the same throughout the working gas.

Schmidt Results using MatlabDual Piston (Alpha type engine)Unit of Energy:Joule=Watt*Second

Schmidt Results using MatlabNomenclature

Schmidt Results using MatlabPlots of 30 and 1 degree Increments. As Degree Increments approaches zero, the true work per cycle can be found.

Schmidt Results using MatlabPlots of pressure and volume at 0.25 degree Increments.

Analytical vs. NumericalSome Special Case Numerical Work EquationsMort Mayer Work Equation

J. R. Senft Work Equation

Cooke-Yarborough Work EquationWalker Work EquationFinkelstein Work Equation

Analytical vs. NumericalNumerical: Mort Mayer Work Equation=329.2018 JAnalytical: Schmidt

Future Steps to Take if this was a ThesisPerform the Finkelstein Adiabatic (no heat transferred in fluid) Analysis of Stirling Engines. Similar to the Otto cycle gasoline engine. The next closest analysis to reality in Stirling Engines. Combine Optics into full analysis with some physical imperfections.Include Alternator and transmission efficiencies.Include 2-axis tracking errors.

Questions??

CitationTwidell, John; Weir, Tony. Renewable Energy Resources (2nd Ed.). New York, NY: Taylor and Francis. 2007.

Martini, William R. Stirling Engine Design Manual (2nd ed.). NASA. US Department of Energy. 1983.

Engel, Thomas; Reid, Philip. Thermodynamics, Statistical Thermodynamics, and Kinetics. San Francisco, CA: Pearson Education Inc. 2006.

Duffie, John; Williams Beckman. Solar Engineering of Thermal Processes (Third Edition ed.). New York: John Wiley & Sons, Inc. 2006.

United States Department of Energy (DOE). http://www.nrel.gov/solar/parabolic_ trough.html. Sept 19, 2008.

Stirling Energy Systems (SES). http://www.stirlingenergy.com/. Oct 22, 2008. http://www.stirlingenergy.com/technology/suncatcher.asp

Solar Paces. Spain SP10. http://www.solarpaces.org/Tasks/Task1/PS10.HTM. Oct 20, 2008.

Wormser, Paul. Concentrated Photovoltaics (CPV). http://solar.nau.edu. Jan 11, 2008. http://solar.nau.edu/csp/docs/presentations/Paul%20Wormser.pdf. Oct 27, 2008.

Urieli, Izzy. Stirling Cycle Machine Analysis. http://www.ent.ohiou.edu. 2007. http://www.ent.ohiou.edu/~urieli/stirling/me422.html. Nov 6, 2008.

engal, Yunus A.; Boles, Michael A. Thermodynamics: An Engineering Approach (Fourth Ed.). New York, NY: McGraw-Hill Companies Inc. 2002.