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For a given duty cycle, or percentage of time spent at some level of exhaust power, it is possible to calculate the average amount of electrical power generated by a TE system. Assuming a fixed conversion efficiency, ηTE sys, and maximum power rating, Pmax, TE sys, the average electrical power generated by the TE system is P=f⋅max(P ,η P)+(1−f)⋅η P, elec v max,TE sys TE sys exh v TE sys exh,0 where fv is the percentage of time spent at exhaust waste heat Pexh, and Pexh,0 is the exhaust waste heat produced by idling the engine. For a Class 8 truck with ηTE sys = 10%, Figure 9 graphically depicts the equation above with contours of Pelec (kW) versus fv. The maximum power rating, Pmax, TE sys, appears on the left y-axis; consequently, contours of Pelec are unobtainable if they occur above a horizontal line drawn to intersect a chosen value of Pmax, TE sys. For reference, limits on TE system power output during constant-speed driving are given on the right y-axis. Figure 9. Contour lines showing average electrical power, Pelec, avg. (kW), generated by a TE system with conversion efficiency, ηTE sys., = 10% for a Class 8 truck. Duty cycle (x-axis) is the fraction of time spent driving at a constant speed (100%) versus idling (0%). Left y-axis gives limits on Pelec, avg. as a result of the maximum power rating of the TE system, Pmax, TE sys. Right y-axis gives limits on Pelec, avg. for constant-speed driving. Statistics from Figure 8 are overlaid to estimate Pelec, avg. for different driving cycles. As an example, consider a Class 8 truck traveling at a 40-mph constant speed and producing roughly 55 kW of exhaust power. As long as the 10% efficient TE system is sized sufficiently to capture this amount of power (i.e., Pmax, TE sys ≥ 5.5 kW), the TE system will produce Pelec = 5.5 kW. If the Class 8 truck is driven half the time at 40 mph and is idled half the time at zero speed (i.e., fv = 50% duty cycle), the TE system will produce, on average, approximately Pelec = 2.8 kW. 11PDF Image | Feasibility of Thermoelectrics for Waste Heat Recovery in Conventional Vehicles
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