8.1.2 Classifications of turbulence simulation methodsDNSDirectnumerical simulationN-SLarge eddy simulationLESequationSecond momentclosureRANSNumericalAlgebraic stress modelturbulenceReynoldsAveragedmodelTurbulentviscositymodelN-S eqs.BoltzmannMixing length theoryequationOne-equation modelTwo-equation modelNon-linear model.etc.6/82
6/82 N-S equation Boltzmann equation DNS LES RANS Second moment closure Algebraic stress model Turbulent viscosity model Mixing length theory One-equation model Non-linear model. etc. Two-equation model Numerical turbulence model Direct numerical simulation Large eddy simulation Reynolds Averaged N-S eqs. 8.1.2 Classifications of turbulence simulation methods
1.DNSIn DNS very small time step and space stepare needed to reveal the evolutions (演化)of eddies withdifferent scales. Required computer resource is veryhigh. Often high-performance computers (HPC) are neededFor a fully developed mixedconvectioninasquareduct(L=6.4H), when Re=6400,Gr= 104 ～ 107 DNS is绝热conducted with 4.194x106Thnodes(=256x128x128),and8 ×105 time steps are needed绝热for statistical average7/82
7/82 In DNS very small time step and space step are needed to reveal the evolutions (演化) of eddies with different scales. Required computer resource is very high. Often high-performance computers (HPC) are needed. 1.DNS L H H x z v u w h T 绝 热 绝 热 For a fully developed mixed convection in a square duct (L=6.4H), when Re=6400, Gr= DNS is conducted with 4.194 106 nodes(=256 128 128), and time steps are needed for statistical average. 4 7 10 ~ 10 5 8 10
2. LESBasic idea:Turbulent fluctuations are mainly generated bylargescaleeddies,whicharenon-isotropic(各向异性）andvarywithflowsituation;Small scaleeddiesdissipate(耗散)kineticenergy(from mechanic to thermal energy),and are almost isotropic (各向同性). The N-S eqs. are used to simulate the large scale eddies and thebehavior of small scale eddies is simulated by simplified modelLES requires less computer resource than that of DNS, eventhough still quite high, and has been used for some engineeringproblemsFor the above problem when simulated by LES only 128×80x80=819200 grids are needed (compared with 4.194 × 106)8/82
8/82 Basic idea：Turbulent fluctuations are mainly generated by large scale eddies, which are non-isotropic(各向异性) and vary with flow situation；Small scale eddies dissipate(耗散) kinetic energy (from mechanic to thermal energy), and are almost isotropic (各向同 性). The N-S eqs. are used to simulate the large scale eddies and the behavior of small scale eddies is simulated by simplified model. 2. LES LES requires less computer resource than that of DNS, even though still quite high, and has been used for some engineering problems For the above problem when simulated by LES only 128 80 80=819200 grids are needed (compared with 4.194 106 ).
3.ReynoldstimeaverageN-SEqs.methodsExpressing a transient term as the sum of average term andfluctuation(脉动) term. Time average is conducted for thetransient N-S equations, and the time average terms of thefluctuations isexpressedvia somefunctionoftheaverageterms8.1.3Reynoldstimeaveragesandtheir characteristicst+A元 「 (t)dtΦ=+pN1At is the time step, which should be large enough relative to thefluctuation but small enough with respect to the variation period ofthetime averaged quantity9/82
9/82 3. Reynolds time average N-S Eqs. methods Expressing a transient term as the sum of average term and fluctuation(脉动) term. Time average is conducted for the transient N-S equations, and the time average terms of the fluctuations is expressed via some function of the average terms. 8.1.3 Reynolds time averages and their characteristics ' = + 1 ( ) t t t t dt t + = t is the time step, which should be large enough relative to the fluctuation but small enough with respect to the variation period of the time averaged quantity
准稳态端流非稳态湍流7AAA(a)Quasi-steadyUnsteadyCharacteristics of time average operations4. Φ==01. Φ=0; 2.Φ=Φ; 3.Φ+Φ=§adad65.f=(@+Φ)f+f)=f+Φaxxada(pf)apfasa(Φf)8.=07axaxaxaxax10/82
10/82 Characteristics of time average operations ' 1. 0; 2. = ; 3. ' + = ; 4. ' ' = = 0 5. ' ' ' ' f f f f f = + + = + ( )( ) 6. ; x x = ' ' 0 x x = = 7. 8. ' ' ( ) ( ) ( ) f f f x x x = + 非 稳 态 湍 流 Unsteady 准 稳 态 湍 流 Quasi-steady