OCR Text |
Show following equation, Here, Is is the representative scale of the concentration eddy, £ is the dissipation rate of the turbulent energy. In the range of high Reynolds number, £ is balanced with the energy transfer rate from low wave number eddies to high wave number eddies . 13) Namely, where A is constant near 1.0, 1 is the velocity eddy scale and u' is the turbulent fluctuation velocity. Furthermore, if the following assumptions are satisfied, l)Factor of A in Eq.(3) is constant irrespective of Re number 2)The turbulent velocity u' is proportional to mean velocity U u' =CtU 3)The velocity eddy scale is proportional to combustor scale L 1=C2L 4 )The veloci ty eddy scale is nearly equal to the concentration eddy scale l=ls Eq.(3) is substituted into Eq.(2). Hence, the scaling law for keeping micro-mixing time ~ constant m can be expressed as L/V=constant (4) because 1=C2L and u'=C1V f~om above assumptions. This means that ~ can be kept constant II 1f the residence time can be kept constant in the scaling. Next, the scale effect on macro-mixing time ~ M which expresses the diffusion of fuel in the combustor is discussed. When turbulent diffusion coefficient is £ and combustor scale c is L, 't M is expressed as ~ =L2/£ (5) H c 5 |