Basic hermal Engineering Steady state energy balance ME 47 Design of Alternative Energy Systems Sample Equation Sheet: Quiz Work Devices: W in m (h h (v v / g(z z eat Devices: Q in m (h h (v v / g(z z eat Exchanges: m (h h (v v / g(z z Ideal Performance Work Devices: s 0 eat Devices: P 0 Device Efficiencies Qin W Work Consuming Devices: W ideal act s Work Producing Devices: W act sw ideal Property Evaluation Ideal Gas: h c P, s c P ln( / -Rln(P /P Incompressible iquid: h c P + vp, s c P ln( / Compressible Substance: Must use property tables/ ime Value of Money Functions Definitions A: Annual Cost or Value P: Present Cost or Value F: Future Cost or Value : number of compound periods i: interest rate in decimal form. Conversion Factors F/P, i, (+i F P(F/P,i, ( + i F A(F/A,i, F/A,i, i P/F, i, ( + i P F(P/F,i, (+ i - P A(P/A,i, P/A, i, i(+ i i A F(A/F,i, A/F,i, ( + i - -
ME 47 Design of Alternative Energy Systems A P(A/P,i, A/P,i, i(+ i (+ i - Ocean Energy Calculations Wave Energy Conversion Assuming that the energy of a is in its potential energy, we can write the power as W W sw g( z V : power of the sw : density of the sea water g: acceleration due to gravity (z : height of V : volume of f : frequency of Assuimng the is sinusoidal, and approximating the sine function as a triangle, we could write V ( z t : thickness of the w : width of the t w f Oscillating Water Column We consider that we have an initial state of air in the chamber (state, a final state of the air in the chamber (state, the state of the air entering the turbine (state 3, and the turbine exit state (state 4. We assume that the following are specified in the problem P, V,, V, and P 4 and the following properties of air are known c P, c V, and k he polytropic coefficient for the compression of the air column can be taken to be.. he power produced a two chamber OWC is given by W W f OWC turb he turbine work is given by W turb m 3 C p ( 3-4 with 4 3 m m - 3 m m P V /(R P4 (P P / k- k
ME 47 Design of Alternative Energy Systems n V P P V All of these calculations require a value of, which is given by - b b a - 4ac a (m C p / b [P V C v /R - m C v + m C p / P V C p /(R + (P V -P V /(-n] c P V C p /(R ydraulic Pump Float System he power of a float system can be calculated by W float float mfloat g( z f in W float : conversion efficiency of the float WEC system m float : mass of the float ide Energy Conversion (EC Assuming that water only flows through the turbine of a tidal energy system from low tide to neutral tide (the point the water level in the reservoir is equal to the ocean level, the power output of a EC system can then be calculated with sw(zht - znt Aresturbw ideal W EC z ht : height of high tide z nt : height of neutral tide A res : surface area of the reservoir : tide period turb : efficiency of the hydraulic turbine w ideal : specific ideal work of the tide It can be shown that 3 w ideal gz 4 Current Energy Power System he current power density is defined by 3 W current sw v current he power output of a marine turbine would be given by W mturb mturb AW current mturb : marine turbine efficiency 3
ME 47 Design of Alternative Energy Systems A: current flow area that is captured by the marine turbine. For a marine turbine with rotor diameter, D A D /4 Ocean hermal Energy Conversion (OEC he maximum efficiency or work output that can be achieved by using the Carnot cycle efficiency is given by max he minimum amount of hot water consumed by an OEC system would be given by m W max W c OEC p, ( OEC: required power output of the OEC system c P, : specific heat of the hot sea water ( : allowed temperature change for the hot sea water For a Rankine cycle based system, the condenser and boiler temperatures are given by boiler,in ( B ( C cond C,in C is the heat exchanger effectiveness of the boiler or condenser. Geothermal Calculations ot Geothermal Sources Modeling as a heat engine, we have igh emperature eat Reservoir at Q eat Engine W net Q ow emperature eat Reservoir at 4
ME 47 Design of Alternative Energy Systems he high temperature reservoir is the hot geothermal source and the low temperature heat reservoir is typically the ambient air. Our appropriate equations are: Q W net + Q W th net Q - Carnot An energy on the geothermal source would give Q m GS in out m GS is the mass flow rate of the hot water or steam from the geothermal source. For a hot water source, we can write Q m GS c P,hw ( in - out Cold Geothermal Source For most locations in the U.S. we may take the ground temperature 0 feet below the surface to be 4ºC. For heating purposes we may use a heat pump system. An interaction diagram is shown below. igh emperature eat Reservoir at Q eat Pump W net he high temperature reservoir is the building being heated and the low temperature heat reservoir is the earth. Our appropriate equations are: Q W net + Q Q COP P Wnet COPCarnot - he plant used for the heat pump is typically based on the vapor compression system shown below. Q ow emperature eat Reservoir at 5
ME 47 Design of Alternative Energy Systems Ground Q Evaporator Valve Compressor Condenser Q ouse o calculate the performance of the various devices, we can use Q Q W m m ref ref m in out out in cond evap net ref out in comp o estimate the earth required for either underground heating of cooling we can use the following equation. m c ( Q earth P,earth earth E 6