tailieunhanh - Computational Fluid Dynamics 2011 Part 11

Tham khảo tài liệu 'computational fluid dynamics 2011 part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 294 Computational Fluid Dynamics developments in computer hardware in the meantime engineers need to work on computational procedures which can supply adequate information about the turbulent flow processes but which can avoid the need to predict the effects of each and every eddy in the flow. We examine the effects of the appearance of turbulent fluctuations on the mean flow properties. Reynolds equations First we define the mean r of a flow property Ọ as follows 1 rAt . r T- t dt AtJ0 In theory we should take the limit of time interval At approaching infinity but At is large enough to hold the largest eddies if it exceeds the time scales of the slowest variations of the property general equations of the fluid flow with all kinds of considerations are represented by the Navier stokes equations along with the continuity equation. The time average of the fluctuations r is given as r -L tp t dt The following rules govern the time averaging of the fluctuating properties used to derive the governing equations of the turbulent fluid flow. __ __ dip 0 p - - - - OS OS Lies J rds Ợ v r - - and The root mean square of the fluctuations is given by the equation The kinetic energy associated with the turbulence is k - v 2 w 2 To demonstrate the influence of the turbulent fluctuations on the mean flow we have to consider the instantaneous continuity and N-S equations. div 11 0 1 p div uu dp 77- V div grad u ox dv 7 4- div va dp 77- V div grad V dy dw 1 dp div wu ----------- V div grad w st 7 Modeling of Turbulent Flows and Boundary Layer 295 The flow variables u and p are to be replaced by their sum of the mean and fluctuating components. u u u u u ur V V v w w 4- w1 p p p Continuity equation is div u 0 I The time averages of the individual terms in the equation are as under du _ du dt dt div uu div UV r iv w u 1 dp _ 1 dP p dx pdx V div grad u V div grad u Substitution of the average values in the basic derived equation would yield the following .

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