CFD-Simulation thermoakustischer Resonanzeffekte zur Bestimmung der Flammentransferfunktion

Transcription

1 CFD-Simlation thermoakstischer Resonanzeffekte zr Bestimmng der Flammentransferfnktion Ator: Dennis Paschke Technische Universität Berlin Institt für Strömngsmechanik nd Technische Akstik FG Experimentelle Strömngsmechanik Co-Ator: Andreas Spille-Kohoff CFX Berlin Software GmbH Karl-Marx-Allee 90 A Berlin

2 Master Thesis Master Thesis at Technische Universität Berlin Spervision by the Fachgebiet für Experimentelle Strömngsmechanik Investigation of thermoacostics in combstion systems by Jn.-Prof. Dr. J. P. Moeck Determine Flame Transfer Fnctions (FTF) amongst other things Content of the Master Thesis Determination of Heat Transfer Fnctions with 3D CFD and their application on 1D CFD Simlation of thermoacostics in a Rijke Tbe with ANSYS CFX Finding a model to represent the effects of heated wires in a flctating flow Determination of a simple mathematical model Simlate a Transfer Fnction for the heated wires, from the idea of FTFs Thesis was written in cooperation with CFX Berlin Slide 2

3 The Rijke Tbe Singing Tbe (19 th centry) Pipe with a compact heat sorce in it which generates an adible sond Heat sorce indcts convective flow followed by an acostic distrbance Reflection at the pipe ends leads to an acostic oscillation Acostics distrbs heat sorce, flctating heat sorce distrbs acostics again Feedback loop Standing wave at the pipes resonance freqency self excites 0.4 m long pipe ~ 500 Hz Thermoacostic resonator Slide 3

4 Motivation Redction of the simlation time of thermoacostics Simlation of thermoacostic effects cold replace cost intensive experiments Redce complex 3D physical problem into 1D mathematical model Modeling the heat release rate in a flctating stream No wires needed to be simlated Lesser mesh elements needed Less comptational power needed Slide 4

5 Rijke Tbe in ANSYS CFX Geometry A section of 6 of a vertical pipe Length: 0.4 m, Diameter: m Ambient volmes at the top and bottom with a radis of 0.1 m 5 heated wires at ¼ of the pipe length with a diam. of 1.5 mm Flid domain setp Compressible air from ANSYS CFX database Heat transfer model: Total energy Trblence model: (none) laminar Boyancy model Boyant Gravity Y Dirn.: -g Ref. density: ρ ref = P ref M air R T ref Slide 5

6 Rijke Tbe ANSYS CFX Bondary conditions Pipe wall: Defalt no slip Wall Symmetry planes: Symmetry condition Ambient volmes srfaces: Opening condition At ambient pressre: 1 atm Opening temperatre: 300 K Wires srfaces No slip Wall Fixed temperatre: 1300 K, 1800K and 2300 K m ot m in Solver setp Defalt settings MAX residal < 10 4 Q v abv, p abv v blw, p blw Slide 6

7 Simlating the Rijke Tbe Steady-state simlation with 1300 K wire temperatre Velocity: v blw 0.5 m/s, v abv 0.75 m/s Temperatre: T blw = 300 K, T abv 464 K Mass flow rate: m kg/s Slide 7

8 Transient Setp in ANSYS CFX Solver Setp Defalt settings Coefficient Loops: min. 2, max.15 Max Residal: 10 3 Calclation of the time step size Resonance freqency f 1 was calclated considering the temperatre jmp throgh the heat sorce beforehand t = 1 f t = 38 µs for all simlations Parameter Vale Unit T K f Hz t µs Slide 8

9 Transient Simlation of the Rijke Tbe Start from Ambient Conditions with 1300 K wire temperatre Slide 9

10 Transient Simlation of the Rijke Tbe Start from steady-state soltion Wire temperatre of 1300 K Oscillation starts immediately Limit cycle is reached 1 s earlier ANSYS CFX can represent thermoacostic oscillations 3 s simlated time 3 day real time at 4 CPU Cores Start from ambient conditions Start with steady-state soltion Slide 10

11 Transient Simlation of the Rijke Tbe Also instable at higher temperatres Higher mean flow velocities and heat release rates Higher amplitdes Limit cycle is formed faster Enogh energy inpt to stimlate more freqencies Temp. 1 st harm K 482 Hz 1500 K 501 Hz 2300 K 516 Hz 1800 K wire temperatre 2300 K wire temperatre Slide 11

12 A Simple Heat Transfer Approximation Redce a complex 3D instability effect to an approximated 1D mathematical context Context: Q t ~ v t Q (t) is the heat release rate over the wires v t is the velocity straight before the wires in pipe-axis direction Decomposition of Q : Q t = Q t + Q t Decomposition of v: v t = v t + v t 1300 K τ Q t ~ v t Q t ~ v t τ τ time delay between Q and v Model: Q (t) = F1 v(t) + F2 v t τ F1 = Q v F2 = Q v Slide 12

13 F1, F2 and τ Determination 1300 K Time development was observed Stable mean at the beginning (low amplitdes of v and Q ) Small change when flctation amplitdes grow bigger, de to a mean shift of Q Stable mean at the limit cycle F1 and F2 are calclated by taking the mean at limit cycle part τ is calclated via phase angle between v and Q 1300 K 1800 K 2300 K τ = 244 µs τ = 229 µs τ = 221 µs Slide 13

14 ANSYS CFX Model withot Wires Wires are replaced by Sbdomain Isotropic Loss Model with K Loss set (flow resistance throgh wires) Total heat sorce term activated Sorce: Q (t) = F1 v blw (t) + F2 v blw t τ v blw - area average at plane below the wires Sorce defined via User Fortran rotine User Fortran Rotine Rotine stores v blw for 20 periods Calclates v blw, v blw, Q and Q Retrns: Q t = Q + Q Q (t) = F1 v blw (t) + F2 v blw t τ Sbdomain Heat Inpt: Q (t) areaave(v blw (t)) Slide 14

15 Simlation with Approximated Q Model for 2300 K wire temperatre works in the expected range Oscillation amplitdes are slightly weaker (1. mode) Resonance freqency is slightly higher Time ntil limit cycle has formed is longer (different start soltions) Phase delay slightly lower (no distance between v blw and Q in Sbdomain) model original f 1 = 527 Hz τ = 173 µs f 1 = 516 Hz τ = 173 µs Slide 15

16 Simlation with Approximated Q Models for 1300 K and 1800 K don t work properly Don t self excite No limit cycle Variation of different flow/script parameters doesn t change the problem Model only works for one specific setp The simple model is too simple A change in the mathematical model is needed Slide 16

17 Change in the Mathematical Model Unregarded properties of thermoacostic systems Delay between Q and v is freqency dependent: τ(ω) Flames or heated wires have a low pass behavior Can be represented by a Transfer Fnction f 0 v(t) New model New fnction f 0 v(t) = α + β v(t) for Q Model for a Heat Transfer Fnction HTF(v ω ) for Q Q t = f 0 v(t) + HTF(v ω ) Restriction of Transfer Fnctions Valid for linear time-invariant systems Only for low amplitdes Transfer fnctions have no satration mechanism linear nonlinear Slide 17

18 HTF Model Simlating a Transfer Fnction for the wires Freqency dependent simlations Called Heat Transfer Fnction (HTF) HTF iω = Q (ω) (ω) e iφ Q Calclation of a State Space model (SSM) Representation of the HTF in time domain 6 dimensional state vectors x (t) = Ax(t) + B (t) q (t) q = Cx(t) Implicit model via User Fortran rotine Expansion to Advanced SSM (ASSM) Amplitde dependent simlations Leads to an additional nonlinear fnction N (t) = 1 + γ 1 (t) + γ 2 (t) 2 x n+1 = x n + t A x n+1 + B n+1 Q t Q t Q n+1 Q = C x n+1 x (t) = Ax(t) + B t = Cx(t) 1 + γ 1 t + γ 2 t 2 Slide 18

19 Simlating the Self Exciting case with ASSM System self excites as expected Amplitdes are slightly higher Limit cycle not completely stable Resonance Freqency (1. mode): Model 527 Hz (p to 550 Hz) Original 527 Hz FFT after 1.52 s 1300 K 3rd mode gets amplified strongly after 0.26 s Cold be a model problem of the ASSM: x = Ax + B y = Cx + γ 1 Cx + γ 2 Cx 2 ~ sin ω Integrating sin³(ω) leaves a cos 3ω term 3 rd harmonic Slide 19

20 Smmary and Otlook Simple model only works for specific flow parameters Easy to determine Doesn t cover freqency dependencies of thermoacostic effects ASSM model covers more thermoacostic characteristics More complex to determine 30 simlations for the final HTF and non linear fnction each New problems appear (3 rd harmonic) Saving comptational power leads to lower simlation times Mesh with wires elements 3 days on 4 CPU Cores Mesh withot wires elements 2 days on 2 CPU Cores Otlook Implementation into 1D CFD wold redce simlation time even more Usage of simplified models to replace experiments less time and cost Slide 20

21 Qestions? Thank yo for yor attention For any frther qestions feel free to contact me: Slide 21

22 HTF Model Determination Simlating a Transfer Fnction for the wires Freqency dependent simlations Different wire temperatres investigated Called Heat Transfer Fnction (HTF) HTF iω = Q (ω) (ω) e iφ Q Calclation of a State Space model (SSM) for the Transfer Fnction Model transformation into time domain State Space Model x (t) = Ax(t) + B (t) q (t) q = Cx(t) Feeding Vector Fit with discrete freqency dependent data leads to 6 dimensional state vectors ( Implicit model via User Fortran rotine x n+1 = x n + t A x n+1 + B n+1 Q n+1 Q = C x n+1 Slide 22

23 Determination of and Simlation with the HTF Determined HTF compared to Lighthills theory Amplitde redction Q ω /v blw ω Q ω 0 /v blw ω 0 Reslts show same trend 24 simlations needed for the presented data only The Nonlinear Fnction (satration) Amplitde dependent simlations One fnction for all temperatres: N (t) = 1 + γ (t) 1 + γ (t) 2 Implemented via User Fortran rotine 2 Q a /v blw a Q a 0 /v blw a 0 ASSM(t, a) Q t Q t x (t) = Ax(t) + B t = Cx(t) 1 + γ 1 t + γ 2 t 2 Slide 23

24 ASSM at 1800 K and 2300 K System self excites as expected Amplitdes are slightly higher Temperatre increase too strong At 1300K it s still high bt doesn t explode Temperatre explodes at higher wire temperatres 1800 K 2300 K Slide 24

25 Forier Analysis of the Rijke Tbe Resonance freqencies are excited Clean spectrm of the velocity flctation straight below the wires Q also oscillates at the 2nd harmonic (and at very low freqencies) Calclated freqencies are slightly higher End correction was neglected in the calclation Parameter Vale Unit T K f 1,calc Hz f 1,sim Hz Slide 25

26 Determination of τ Calclating phase angle difference Using FFT data of v and Q Calclate phase delay φ τ = φ ω = φ 2π f K Parameter Vale Unit τ T K f 1,sim Hz φ τ µs Slide 26

27 Determination of the HTF Problem with compressible air model At 250 and 750 Hz the oscillation amplitde gets amplified Maybe a problem with the systems acostics Bypassing by sing incompressible air Simlations with incompressible air show expected behavior Density can still change when the temperatre changes (Table Generation) Heat Transfer Model: Thermal Energy Compressible (1300 K) Incompressible (1300K) Dennis Paschke, Slide 27

28 Final Heat Transfer Model Derivation Q t = Q t + Q t Q t = f 0 t + AHTF(ω, a) with f 0 t = α + β (t) Q t = f 0 t + HTF(ω) N a with N a = N (t) = 1 + γ 1 (t) + γ 2 (t) 2 HTF(ω) SSM(t) x (t) = Ax(t) + B (t) Q (t) Q (t) = Cx(t) AHTF(ω, a) ASSM(t, a) Q t Q t x (t) = Ax(t) + B t = Cx(t) 1 + γ 1 t + γ 2 t 2 Dennis Paschke, Slide 28