DINAMICA FLUIDELOR COMPUTATIONALA APLICATA LA VEHICULE: DE LA TEORIE LA PRACTICA

Transcription

1 Valorile RTR DINAMICA FLUIDELOR COMPUTATIONALA APLICATA LA VEHICULE: DE LA TEORIE LA PRACTICA Profesionalism şi exemplaritate Respect şi solidaritate Dezvoltare personală Satisfacţia clientului

2 Overview INTRODUCTION FROM THEORY TO NUMERICS AERODYNAMICS THERMODYNAMICS 2

3 01 INTRODUCTION

4 CUSTOMER SPECIFICATIONS: Activities Numerical simulations NVH Performance and fuel consumption CFD: aero/heat transfer Vehicle dynamics Measurements NVH Thermal Customer usage analysis Statistics of the usage of our/competitor car Subjective evaluations/bench NVH noise levels Driving pleasure Competition benchmark

5 02 FROM THEORY TO NUMERICS

6 Modelling a phenomenon REAL PHENOMENON ERROR MATHEMATICAL MODEL DOMAIN BORDER INFORMATION ANALYTICAL SOLUTION ERROR NUMERICAL MODEL MESH BOUNDARY CONDITIONS SOLVER NUMERICAL SOLUTION

7 BACKGROUND (1) Initial Conditions (IC) Boundary Conditions (BC) u t u u u p u f convection 0 stress extra forces IC are important in order to have good starting points (according to the physical modeled phenomena) IC are very useful to speed up the numerical convergence BC are the most important data to be added BC need to add NEW information to the model

8 BACKGROUND (2) Meshes/Grids Types of grids: structured unstructured Elements: triangles, rectangles, hexagons in 2D prisms/tetrahedra, parallelepipeds, etc in 3D Different grids have different impact on the numerical solution We will talk later about!

9 BACKGROUND: NUMERICAL SCHEMES (1) Quality Properties of all numerical schemes: Consistency: means that the discretized version of the equation must fit the analytical one if one goes with the grid size to zero and the truncation error (i.e. the difference between the exact and numerical (discrete) equation) must be small and bounded Stability: assures that the errors made at each time step/iteration will not grow in time Convergence: numerical solution tends to the exact one as the grid size tends to zero LAX equivalence theorem: consistency + stability convergence

10 BACKGROUND: NUMERICAL SCHEMES (2) Diversity Based on FEM method Try to approximate the solution Remark: Not often used for NS equations because forces the div-free condition only globally! Based on FV method Try to approximate the NS system and NOT the solution My opinion: the most used in CFD computations! Codes: FLUENT Based on FD method Try to approximate the NS system and NOT the solution The most ancient and simple method! Based on LBM method Based on Boltzmann equation approach Relatively new on the market Based on Spectral approximation (based on Fourier transform)

11 NUMERICAL SCHEMES (2) Dummy Unsteady Approach Integrating in time T fin u( T ) u(0) u u dt ( p u fin 0 T fin 0 f ) dt Final time = T fin T fin 0 u dt 0 The above integration is exact! There is not explicit integration of the remaining integrals! To completely get the exact u we need to integrate exact in space too! First concept of global error is needed!!!

12 NUMERICAL SCHEMES (3) Sources of errors To define in a rigorous general way the concept of error it is an impossible task! etime eround e e space - round-off errors accum - temporal errors - accumulation error - spatial errors Total error e tot e round e time e space e accum In software engineering (and not only) numerical error bears all (d)effects which may disturb the final solution/result In the numerical error is included first of all the incapability of the computer to store an rational/irrational number

13 SPATIAL ERRORS Definition: The function u has a derivative at the point x 0 if the following limit exists: lim x x 0 u( x) x u( x x 0 0 ) not ' u ( x 0 ) What is happening in numerical case? Here begins the crowd world of numerical definitions, and let researchers to write many papers in this field Each numerical definition is strictly connected/adapted to the problem to be solved

14 SPATIAL ERRORS Consider the following 2D example: y Δx mesh size u u( x x y t u x y t x y t ) 0, 0, ) ( 0, 0, 0, 0, x x lim x0 u( x 0 could be an approximation (forward) of the exact derivative x, y 0, t) u( x0, y 0, t) x y 0 y 0 -Δy x 0 Dummy grid x 0 +Δx Δy x The error between the exact and approximate derivative is called truncation error How this error can be evaluated?

15 TEMPORAL ERRORS When is necessary to numerically integrate a function? Answer: f (x) when an analytical result is unavailable when the function is too complicated only few values of the function is given b a f dx 0 a b x Looking geometrically at the right picture, first idea to approximate an integral would be to approximated as good as we can the hashed area! Split big area in a sum of small areas! b a f n ( x) dx a f ( x ) index i counts the nodes number between i0 i i a and b.

16 NUMERICAL SCHEMES From theory to numerics u t u u u p u f convection 0 stress extra forces Discretization procedure In this case we treat only this way, and not other nonlinear approaches based on Newton iterations!!! Linear system (LS) Ax b A = matrix (SPARSE) coefficients x = unknown variables (u,v,w,p,etc) b = known data (data at previous time, BC, IC, f)

17 SOLVING LS Behind linear systems Direct Methods Ax b + Preconditioning Multigrid x A 1 b Iterative Methods Generalities: if x has N entries then A has the dimension N 2! # of arithmetic operations needed to obtain the solution x is proportional usually with N 3! How to decrease the computational time? Computational demand today: Solve the linear system within N iterations!!!

18 NUMERICAL SCHEMES FACTS Overview: Usually in CFD the matrix A is sparse (e.g. more zero entries than non-zero)! A is always quadratic. For a grid points the dimension of A is ( ) 2! The non-zero entries are only the coefficients of the unknown values and the connections to their neighbors! So, A is never stored as a full matrix. A is stored as a three vectors: 1st vector: position in x dir in A 2 nd vector: position in y dir in A 3 th vector: non-zero value of A Important to have symmetric matrices easier to solve the LS The type of discretization operators, or in the grid elements together with the overall numerical scheme chosen have direct impact to the coefficients of the A matrix more tuning needed to solve LS! That s why Do not use angles too small Discretization lengths in all directions in the same range, and smooth transition of the layers!

19 FINAL REMARKS Numerical scheme For our purposes use ALWAYS a second-order scheme both in time and space A first-order scheme is producing in excess numerical diffusion which will spoil the solution A higher-order scheme will produce more accurate results, but the price paid is that needs more computational time and finer tuning of the start-up! It is also a must when dealing with turbulence. Each turbulence model is producing a turbulent viscosity ~ O(h 2 )!!! Indeed, if using a first-order scheme, it does not mater which turbulence model is taken the effect on the final solution will be ~0! WHY? 1 st -order scheme 2 nd -order scheme higher-order schemes Accuracy RAM demand CPU time ~ mesh size / time step ~ with O(mesh size 2, timestep 2 ) third-order or higher exponentially exponentially exponentially exponentially

20 MODELLING: Turbulence? Turbulence modelling Definition : a turbulent flow is characterized by a non regular/chaotic movement! Models (just few ) No model: DNS usually for small Re numbers Zero-order models (algebraic): ex. Baldwin-Lomax Model 1 equation models: Spalart-Allmaras model (implemented FLUENT) 2 equations models: k-ε and variants (well accepted in industry) Reynolds Stress Models (RSM) LES, VLES DES to treat near boundaries in a RANS view and in other parts as LES. etc Turbulent solutions give you only mean values instead of point wise There are NO exact turbulence models, only approximations Always playing/changing the overall viscosity Need a lot of coefficients to be tuned LES/VLES/DES new on the market

21 03 AERODYNAMICS

22 Basic Aerodynamics (1) L : Roll Fx : Drag force M : Pitch Fy : Lateral force N : Lace Fz : Lift force

23 Basic Aerodynamics (2) Fx : Drag Global design Cooling Mirror Fx = ½ S.C x V² Fuel Consumption Under body 6 SC x SC xi i1 Wheel covers Tires Disque : Cx = 1,17 Cube : Cx = 1,05 Sphère : Cx = 0,47 Aile : Cx = 0,04 Clio 3 : Cx = 0,34 F1 : Cx = 1.0 Cz=-3

24 Basic Aerodynamics (3) Cx represents the aero performance, and do not take into account the frontal surface Some superstructures are more suitable to be aerodynamic 0,25 0,30 0,35 0,4 Cx A2 Prius Xsara Break K J C220 B L

25 Aerodynamic results: Different visualizations

26 Aerodynamic result: SCx improvement Initial car S*Cx wake = 0,105 Car with a little rear spoiler S*Cx wake = 0,073

27 04 HEAT TRANSFER

28 WHAT DOES MEAN VEHICLE HEAT TRANSFER? Validation of the cooling systems Water Oil Heat exchangers Underbody/underhood validation Material choice Component position Thermal shields Thermal comfort Air diffusion Heat and AC system Defrost windshield

29 Coupling PWF-PWT-AmeSim (1) airflow ( DES as turbulence model ) PowerFlow (PF) T_conv T_diff PowerTherm (PT) Amesim T_cond T_rad T (Heat exchangers backflow) FINAL STRATEGY: Coupling between PF - PT - Ame!

30 Coupling PWF-PWT-AmeSim (2) PF mesh PT mesh T HTC, T

31 Unsteady coupling PF-PT strategy Numerical Strategy Period PF run Δt PF time t=0 t=t_fin PT run Δt PT Exchange/Update BC Δt PF Δt PT coupling time time step size PF time step size PT

32 Duster Condensation analysis Airflow is taken from the engine compartment The suction side to the beam implies recirculation of hot air on the COND Recirculation zone zones Temperature [degc]

33 Megane: Underhood/Underbody thermal simulation Aero and thermal analysis Temperature field and airflow at 165km/h Temperature field and airflow for hill

34 Megane: Underhood/Underbody part positioning Aero and thermal analysis Surface temperature field at 165 km/h Stagnation zone behind EGR

35 Megane: Tests/simulations V165km/h correlation 160 mm Sens de l écoulement Thermocouples 1 Calcul H2S Trap Thermocouples Test ( o C) Simulation ( o C)

36 Megane: Tests/simulations Hill correlation 160 mm Sens de l écoulement Thermocouples 1 Calcul H2S Trap Thermocouples Test( o C) Simulation ( o C)

37 Duster: Defrosting

38 Conclusions Scientific computation is used with success within Renault Nowadays experiments and theory are supplemented in many cases by numerical computation that is an equally important component Within scientific computing one can treat more complex and less simplified problems through massive amounts of numerical calculations and thanks to the increased computer facilities in short time

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