COMPUTATIONAL FLUID DYNAMICS ME G515

Transcription

1 BITS Plan Duba Campus COMPUTATIONAL FLUID DYNAMICS ME G515

2 BASICS OF COMPUTATIONAL FLUID DYNAMICS ANALYSIS BITS Plan, Duba Campus

3 Overvew Introducton Hstory of CFD Basc concepts CFD Process Dervaton of Naver-Stokes Duhem Equaton Example Problem Applcatons BITS Plan, Duba Campus

4 BASIC CONCEPTS Flud Mechancs Flud Statcs Flud Dynamcs Lamnar Turbulent Newtonan Flud Non-Newtonan Flud Ideal Fluds Vscous Fluds Rheology Compressble Flow Incompressble Flow CFD Solutons for specfc Regmes Components of Flud Mechancs BITS Plan, Duba Campus

5 Flud (gas and lqud) flows are governed by partal dfferental equatons whch represent conservaton laws for the mass, momentum, and energy. Computatonal Flud Dynamcs (CFD) s the art of replacng such PDE systems by a set of algebrac equatons whch can be solved usng dgtal computers. BITS Plan, Duba Campus

6 What s flud flow? Flud flows encountered n everyday lfe nclude Meteorologcal phenomena (ran, wnd, hurrcanes, floods, fres) Envronmental hazards (ar polluton, transport of contamnants) Heatng, ventlaton and ar condtonng of buldngs, cars etc. Combuston n automoble engnes and other propulson systems Interacton of varous objects wth the surroundng ar/water Complex flows n furnaces, heat exchangers, chemcal reactors etc. Processes n human body (blood flow, breathng, drnkng... ) and so on and so forth BITS Plan, Duba Campus

7 Introducton What s CFD? Predcton flud flow wth the complcatons of smultaneous flow of heat, mass transfer, phase change, chemcal reacton, etc usng computers. BITS Plan, Duba Campus

8 What s CFD/FD? CFD s a branch of Flud dynamcs So what really s Engneerng Flud Dynamcs n the frst place? Lets look at some examples: We are nterested n the forces (pressure, vscous stress etc.) actng on surfaces (Example: In an arplane, we are nterested n the lft, drag, power, pressure dstrbuton etc) We would lke to determne the velocty feld (Example: In a race car, we are nterested n the local flow streamlnes, so that we can desgn for less drag) We are nterested n knowng the temperature dstrbuton (Example: Heat transfer n the vcnty of a computer chp) BITS Plan, Duba Campus

9 What s CFD/FD? Roughly put, n Engneerng flud dynamcs, we would lke to determne certan flow propertes n a certan regon of nterest, so that the nformaton can be used to predct the behavour of systems, to desgn more effcent systems etc..

10 Hstory of CFD Snce 1940s analytcal soluton to most flud dynamcs problems was avalable for dealzed solutons. Methods for soluton of PDEs were conceved only on paper due to absence of personal computer. Damler Chrysler was the frst company to use CFD n Automotve sector. Speedo was the frst swmwear company to use CFD. There are number of companes and software's n CFD feld n the world. Some software's by Amercan companes are FLUENT, TIDAL, C-MOLD, GASP, FLOTRAN, SPLASH, Tetrex, VGPLOT, VGRID, etc. BITS Plan, Duba Campus

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31 Compressble and Incompressble flow A flud flow s sad to be compressble when the pressure varaton n the flow feld s large enough to cause substantal changes n the densty of flud. dq 1 ~ f p, q, jj dt Vscous and Invscd Flow In a vscous flow the flud frcton has sgnfcant effects on the soluton where the vscous forces are more sgnfcant than nertal forces ( u) ( v) 0 x y BITS Plan, Duba Campus

32 Steady and Unsteady Flow Whether a problem s steady or unsteady depends on the frame of reference Lamnar and Turbulent Flow Newtonan Fluds and Non-Newtonan Fluds In Newtonan Fluds such as water, ethanol, benzene and ar, the plot of shear stress versus shear rate at a gven temperature s a straght lne BITS Plan, Duba Campus

33 Intal or Boundary Condtons Intal condton nvolves knowng the state of pressure (p) and ntal velocty (u) at all ponts n the flow. Boundary condtons such as walls, nlets and outlets largely specfy what the soluton wll be. BITS Plan, Duba Campus

34 Dscretzaton Methods Fnte volume method t Qdv FdA 0 Fnte Element method R W Qdv e Where Q - vector of conserved varables F - vector of fluxes V - cell volume A Cell surface area R=Equaton resdual at an element vertex Q- Conservaton equaton expressed on element bass W= Weght Factor BITS Plan, Duba Campus

35 Fnte dfference method Q t F x G y H z 0 Q Vector of conserved varables F,G,H Fluxes n the x,y, z drectons Boundary element method The boundary occuped by the flud s dvded nto surface mesh BITS Plan, Duba Campus

36 CFD PROCESS Geometry of problem s defned. Volume occuped by flud s dvded nto dscrete cells. BITS Plan, Duba Campus

37 CFD PROCESS cont.. Physcal modelng s defned. Boundary condtons are defned whch nvolves specfyng of flud behavor and propertes at the boundares. Equatons are solved teratvely as steady state or transent state. Analyss and vsualzaton of resultng soluton. post processng BITS Plan, Duba Campus

38 Flud = Lqud + Gas Densty ρ const varable Vscosty μ: resstance to flow of a flud Physcs of Flud ncompressble compressble Ns ( Pose) 3 m Substance Ar(18ºC) Water(20ºC) Honey(20ºC) Densty(kg/m 3 ) Vscosty(P) 1.82e e-2 190

39 n m n M m out out dm dt m n m out m n m out dm dt 0 Mass Momentum Energy Conservaton Law

40 Mass ConservatonContnuty Equaton D U Dt x 0 D const, 0 Dt Compressble U x 0 Incompressble Naver-Stokes Equaton I

41 Naver-Stokes Equaton II Momentum ConservatonMomentum Equaton V j IV j III j II j I j g x x P x U U t U k k j j j j x U x U x U 3 2 I : Local change wth tme II : Momentum convecton III: Surface force IV: Molecular-dependent momentum exchange(dffuson) V: Mass force

42 Naver-Stokes Equaton III Momentum Equaton for Incompressble Flud j j j j j g x U x P x U U t U 2 2 k k j j j j x U x x U x U x x x U j j j j x U x U x x U x

43 Energy ConservatonEnergy Equaton T c t I T cu x II 2 U T U j P j x x x 2 I : Local energy change wth tme II: Convectve term III: Pressure work IV: Heat flux(dffuson) V: Irreversble transfer of mechancal energy nto heat III IV V Naver-Stokes Equaton IV

44 Analytcal Equatons Dscretzaton Dscretzed Equatons Dscretzaton Methods Fnte Dfference Straghtforward to apply, smple, sturctured grds Fnte Element Any geometres Fnte Volume Conservaton, any geometres Dscretzaton

45 General Form of Naver-Stokes Equaton t x U x Local change wth tme Flux Source q 1,U j,t Integrate over the Control Volume(CV) V x dv S n ds Integral Form of Naver-Stokes Equaton V t dv Local change wth tme n CV S U nds x Flux Over the CV Surface V q dv Source n CV Fnte Volume I

46 Fnte Volume II Conservaton of Fnte Volume Method V S V dv q n ds x U dv t A B A B

47 U P U E Approxmaton of Volume Integrals m dv V; V p mu u dv u V P P V U e Approxmaton of Surface Integrals ( Mdpont Rule) V P dv S P ds k P k S k k n, s, e, w Interpolaton Upwnd U e U U P E f f ( U n) ( U n) e e 0 0 Central U e U E U (1 ) e P e e x x e E x x P P Fnte Volume III

48 DERIVATION OF NAVIER-STOKES-DUHEM EQUATION The Naver-Stokes equatons are the fundamental partal dfferentals equatons that descrbe the flow of ncompressble fluds. Two of the alternatve forms of equatons of moton, usng the Euleran descrpton, were gven as Equaton (1) and Equaton (2) respectvely: ( q dq dt t ) q t q q j f j, j q j q, j f 1, j j, j. (1) (2) BITS Plan, Duba Campus

49 DERIVATION (Cont d) If we assume that the flud s sotropc, homogeneous, and Newtonan, then : ~ ( ) 2 ~ j p kk j j. (3) Substtutng Equ(3) nto Equ(2), and utlzng the Euleran relatonshp for lnear stress tensor we get : dq dt f 1 p, ~ ~ q j, j ~ q, jj, (4) ( for compressble fluds ) BITS Plan, Duba Campus

50 DERIVATION (Cont d) For ncompressble flud flow the Naver-Stokes- Duhem equaton s: dq dt f 1 p, ~ q, jj If the flud medum s a monatomc deal gas, then : ~ 2 ~ 3 BITS Plan, Duba Campus

51 DERIVATION (Cont d) Naver stokes equaton for compressble flow of monatomc deal gas s : dq dt f 1 p, 1 3 ~ q j, j ~ q, jj, BITS Plan, Duba Campus

52 EXAMPLE PROBLEM Neglectng the gravty feld, descrbe the steady two- dmensonal flow of an sotropc, homogeneous, Newtonan flud due to a constant pressure gradent between two nfnte, flat, parallel, plates. State the necessary assumptons. Assume that the flud has a unform densty. BITS Plan, Duba Campus

53 SOLUTION (Cont d) The Naver stokes equatons for ncompressble flow s: dq dt q j q, j f 1 p, ~ q, jj Snce the flow s steady and the body forces are neglected, the Naver-stokes equaton becomes: 1 ~ q jq, j p, q, jj BITS Plan, Duba Campus

54 SOLUTION (Cont d) The no slp boundary condtons for vscous flow are: q 0 at y a 2 Usng the boundary condtons ( q 2= 0 at y 2 =+/- a ) Thus, the frst Naver-stokes equatons becomes d q dy dp dy 1 BITS Plan, Duba Campus

55 SOLUTION (Cont d) Integratng twce, we obtan q dp dy 1 y 2 2 a 2 The results, assumptons and boundary condtons of ths problem n terms of, mathematcal symbols are as follows: Constant f 0 t 0 y 3 0 q dp dy 1 y 2 2 a 2 BITS Plan, Duba Campus

56 HOMEWORK PROBLEM Usng the Naver-Stokes equatons nvestgate the flow (q ) between two statonary, nfnte, parallel plates a dstance h apart. Assumng that you have lamnar flow of a constant-densty, Newtonan flud and the pressure gradent s constant (partal dervatve of P wth respect to 1). BITS Plan, Duba Campus

57 Types of Errors and Problems Types of Errors: Modelng Error. Dscretzaton Error. Convergence Error. Reasons due to whch Errors occur: Stablty. Consstency. Conservedness and Boundedness. BITS Plan, Duba Campus

58 Applcatons of CFD 1. Industral Applcatons: CFD s used n wde varety of dscplnes and ndustres, ncludng aerospace, automotve, power generaton, chemcal manufacturng, polymer processng, petroleum exploraton, pulp and paper operaton, medcal research, meteorology, and astrophyscs. Example: Analyss of Arplane CFD allows one to smulate the reactor wthout makng any assumptons about the macroscopc flow pattern and thus to desgn the vessel properly the frst tme. BITS Plan, Duba Campus

59 Applcaton (Contd..) 2. Two Dmensonal Transfer Chute Analyses Usng a Contnuum Method: Fluent s used n chute desgnng tasks lke predctng flow shape, stream velocty, wear ndex and locaton of flow recrculaton zones. 3. Bo-Medcal Engneerng: The followng fgure shows pressure contours and a cutaway vew that reveals velocty vectors n a blood pump that assumes the role of heart n open-heart surgery. Pressure Contours n Blood Pump BITS Plan, Duba Campus

60 Applcaton (Contd..) 4. Blast Interacton wth a Generc Shp Hull The fgure shows the nteracton of an exploson wth a generc shp hull. The structure was modeled wth quadrlateral shell elements and the flud as a mxture of hgh explosves and ar. The structural elements were assumed to fal once the average stran n an element exceeded 60 percent Results n a cut plane for the nteracton of an exploson wth a generc shp hull: (a) Surface at 20msec (b) Pressure at 20msec (c) Surface at 50msec and (d) Pressure at 50msec BITS Plan, Duba Campus

61 Applcaton (Contd..) 5. Automotve Applcatons: Streamlnes n a vehcle wthout (left) and wth rear center and B-pllar ventlaton (rght) In above fgure, nfluence of the rear center and B-pllar ventlaton on the rear passenger comfort s assessed. The streamlnes markng the rear center and B-pllar ventlaton jets are colored n red. Wth the rear center and B-pllar ventlaton, the rear passengers are passed by more cool ar. In the system wthout rear center and B-pllar ventlaton, the upper part of the body, n partcular chest and belly s too warm. BITS Plan, Duba Campus

62 The followng are the detals of conductng practcals Fve experments are to be conducted n the CAD lab usng ANSYS fluent software 1. Lamnar flow through a crcular ppe wth constant radus 2. Turbulent flow though a crcular ppe wth constant radus 3. Compressble flow through a CD Nozzle 4. Steady flow over a rotatng cylnder 5. Unsteady flow over rotatng cylnder. Four experental are to be conducted usng Vapor Refrgeraton test rg, Wnd tunnel and Smoke analyzer. BITS Plan, Duba Campus