Bizarro João P S, Rodrigues Paulo
Associação Euratom-IST, Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 Lisboa, Portugal.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051109. doi: 10.1103/PhysRevE.86.051109. Epub 2012 Nov 7.
For work-producing heat engines, or work-consuming refrigerators and heat pumps, the percentage decrease caused by friction in their efficiencies, or coefficients of performance (COP's), is approximately given by the ratio W(fric)/W between the work spent against friction forces and the work performed by, or delivered to, the working fluid. This universal scaling, which applies in the limit of small friction (W(fric)/W </~ 20%) and when the engine's figures of merit (FOM's, either efficiencies or COP's) do not come too close to unity (no higher than, say, 0.5 in the case of heat-engine efficiencies), allows a simple and quick estimate of the impact that friction losses can have on the FOM's of thermal engines and plants, or of the level of those losses from the observed and predicted FOM's. In the case of refrigerators and heat pumps, if W(fric)/W </~ 20% is not ensured (actually a condition that can be largely relaxed for heat engines), the COP percentage decrease due to friction approaches asymptotically (W(fric)/W)/(1+W(fric)/W) instead of W(fric)/W. Estimates for the level of frictional losses using the Carnot (or, for heat engines and power plants only, the Curzon-Ahlborn) predictions and observed FOM's of real power plants, heat engines, refrigerators, and heat pumps show that they usually operate in domains where these behaviors are valid.
对于产生功的热机，或消耗功的冰箱和热泵，摩擦力导致其效率或性能系数（COP）降低的百分比，大约由克服摩擦力所消耗的功与工作流体所做的功或传递给工作流体的功之比W(fric)/W给出。这种通用的标度关系适用于小摩擦力的极限情况（W(fric)/W </~ 20%），并且当发动机的品质因数（FOM，即效率或COP）不太接近1时（例如，热机效率不高于0.5），它能对摩擦损失对热机和装置的FOM产生的影响，或者从观测和预测的FOM来估算这些损失的水平，进行简单快速的估计。对于冰箱和热泵，如果不能确保W(fric)/W </~ 20%（实际上对于热机来说这个条件可以大大放宽），由于摩擦导致的COP降低百分比渐近地趋近于(W(fric)/W)/(1 + W(fric)/W)，而不是W(fric)/W。利用卡诺（或者仅对于热机和发电厂而言的柯曾 - 艾尔伯恩）预测以及实际发电厂、热机、冰箱和热泵的观测FOM来估计摩擦损失水平，结果表明它们通常在这些行为有效的范围内运行。
