Wall film model - Introduction

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1 WALL FILM MODEL

2 Wall film model - Introduction To comply with the requirement of the industry a constant improvement of the accuracy of the physical model used in CFD is necessary. To predict the correct mixture formation and pollutant evolution a model for the wall film is required. The basic physics of the wall film formation and evolution is widely treated in literature. Our model is based on the one proposed by Foucart et al. (SAE Paper ) with the evaporation sub-model based on the work of O Rourke et al. (SAE Paper ) We have chosen to focus our work on the accuracy of the implementation of the model and on the resolution of the numerical issue that could arise.

3 WALL FILM THE PHYSICAL ISSUE WALL INTERACTION SPRAY GAS Two-dimensional flux over three-dimensional surfaces Impinging i i Spray Heat transfer with wall and gas Fuel evaporation Gravity and other body forces Shear forces at the interface with gas and wall

4 WALL FILM NUMERICAL MODEL HYPOTHESIS Boundary-layer approximation Laminar Flow Incompressible Flow Newtonian Fluid The equations of mass, momentum and energy are written and integrated q gy g following a finite volume approach. Because of the variation of mass inside a control volume these equations resemble a virtual compressibility.

5 INTEGRAL CONTINUITY EQUATION Nside Δ δ 1 ˆ S + ( V r ) d f n δili = Δt A i ρ A w i In order to underline the variable film height htused in the numerical solution, the equation is divided by ρa w The time derivative of film height in a control volume is related to the convective fluxes and to the interaction with gas and spray through the source terms S d w S d S s d S t d Spray-film interaction Film evaporation

6 SPRAY-WALL INTERACTION The impingement regime is a function of the Weber number (According to Stanton et. al SAE ) We = We 5 ρ du d σ 2 nd 5< We ρ < We 18.0 d d ν f σ ρ d d ν f < We σ The wall film model does not distinguish between different impact regimes. The droplets are supposed to adhere to the wall.

7 Δ ( δv f ) INTEGRAL MOMENTUM EQUATION r 1 Nside r r ˆ 1 Nside 1 1 Nedge r r r + Vf Vf n δil i = pn δil i+ δg + M tan + τia i t A i ρa ρa ρa ( ) ( ˆ ) ( ) Δ w i w i w w i z y Imposed the condition of film adhesion to the wall Different influences of the normal component of the impinging i i droplet velocity from the tangential ti one x A relative system of coordinates has been created

8 Δ r FILM PRESSURE DEFINITION ( δvδ V ) 1 Nside ( ) 1 Nside ( ) 1 1 Nedge f r r r r r + V ˆ ˆ f Vf n δili = pnδili+ δg+ Mtan + ( τiai) Δt A ρa ρa ρa i w i w i w w i p= p + p g d Pressure of the surrounding gas Dynamic pressure due the impinging droplets p d n = 4πρ A 1 ru ini t 3 i w i= Δ 1 The time-step used in calculations could be 3 longer or shorter than the duration of the droplet impingement. We choose to consider that the duration of the impact is equal to the computational timestep Δt

9 PRESSURE GRADIENT TERM ( δv Nside Nside Nedge f ) + 1 V ( ˆ) 1 ( ˆ) 1 1 f Vf n δili = pnδili+ δg r r + Mtan + ( τiai) Δ r r r r Δt A ρa ρa ρa i w i w i w w i p g p p The pressure gradient contribution to momentum of the j-th cell involves the valuation of pressure at the boundary faces. The different film heights between neighbour cells must be taken into account by appling the film pressure only over the common contact area, while the gas pressure is applied over the remaining boundary area

10 INTEGRAL ENERGY EQUATION ( ) Nside Δ δt 1 J i ˆ g Jw SH + T ( V r ) f n δi li = + Δt A ρca ρca ρca The film exchange: w i i p w p w p w Convective heat transfer with the gas (J g ) Conductive heat transfer with the wall (J w ) Energy with the spray (S h ) Fuel vaporization alters the structure of the turbulent boundary layer above the film because of the gas velocity normal to the wall induced by the vaporization. The wall film energy equation is integrated over the control volume with the hypothesis of parabolic temperature profile across the film height M difi d ll f ti i d t l l t th ll fil i ti t Modified wall functions are use in order to calculate the wall film vaporization rate (Stanton et al. SAE )

11 INTEGRATION METHOD - ALE The discretized equations are solved with an Arbitrary Lagrangian Eulerian (ALE) methodology with a fully explicit approach The diffusive terms in direction tangential to the wall are neglegible compared to convective terms. The high Peclet number justifies the use a first order upwind differencing scheme LAGRANGIAN PHASE δ φ = δ φ + S Δt L L n n L φ During the Lagrangian phase the computational cell moves with fluid and source terms are accounted for uur δ φ δ φ t φ V n δ l Nside n+ 1 n + 1 L L L L = +Δ ( ˆ f ) EULERIAN PHASE i= 1 i f i i i In the Eulerian phase the flow is frozen and remapped onto the computational In the Eulerian phase the flow is frozen and remapped onto the computational grid

12 FILM-GAS INTERFACE AT BOUNDARY EDGE The main limits of a continuous finite volume approach of the film models are at the boundary edges of the liquid phase: the approximation of constant film height over the control volume does not permit to reconstruct the characteristics of the interface. Real gas-film interface of boundary edge Computed gas-film interface of boundary edge This scattering of liquid film causes high numerical diffusion and an overextimation of evaporation, which is proportional to the area of contact with gas.

13 FILM-GAS INTERFACE AT BOUNDARY EDGE In order to reproduce the effect of surface tension a fitting minimum threshold value is used to impose a minimum film height into a control volume Real interface Computed with threshold Yes No Min Height The convective fluxes are inhibited according to a double control on the minimum film height of two neighbour cells The area at the interface with gas is calculated by supposing that all the fluid inside the control volume has the minimum film height, avoiding the overextimation of wall film evaporation.

14 KIVA3 The wall film model has been implemented in our customized version of the KIVA3 code. The code has been updated regarding the combustion sub-models: Shell ignition model (Kong et al.) Characteristic-time combustion model (Abraham et al.), modified with the correction proposed by Bianchi et al. And the spray break-up and evaporation sub-models: Liquid jet and atomization model Hybrid model (Bianchi et al.) CLE coupling between gas and liquid phase (Beard et al.)

15 VALIDATION The wall film model has been tested against two cases that are representative of different wall film formation and dynamics : Diesel Engine (Single injection DI Engine) Pipe with pulsed injection (PFI-like condition) Both cases are choosen because the impact regime is prevalently sticky

16 VALIDATION DIESEL ENGINE SIMULATION Stanton et al. (SAE ) Two-Stroke DI Diesel Engine Simulation between IVC and EVO Injection and Combustion simulation Bore 150 mm Stroke 225 mm Number of cylinders 8 Engine speed 750 rpm Compression ratio 14 Fuel Diesel Wall temperature 673 K Inlet air pressure 2.94 bar Injected mass 12.3 mg/cycle Start of injection -19 ATDC Duration of injection 19 C.A. Injection pressure 174 bar Small angle between spray direction and bowl wall Prevalent impinging regime is Stick

17 VALIDATION DIESEL ENGINE SIMULATION Sensors position Sensor 1 Sensor 5 Sensor 3

18 VALIDATION PFI GASOLINE ENGINE Le Coz et al. (7th Int. Symp. on Application of Laser Techniques to Fluid Mechanics) Sauter Mean Diameter Droplet Velocity 90μm 16m/s Spray Cone Angle 30 Injection Duration 6.7ms Angle injector/tube 45 Injection frequency 40Hz Injected quantity per shot 21.5mm 3 Air flow rate 0.42m 3 /min Reproduces injection and liquid-film conditions similar to those occuring in PFI gasoline engines Pulsed injection with 8 injection events Characterized by low Weber number Prevalent impinging regime is Stick The experimental ldata has been compared with iththe result obtained dby Foucart et al. (SAE ) and by our model

19 VALIDATION PFI GASOLINE ENGINE Sensor 1 View Sensor 2

20 Wall film model comparison Evaluation of wall film models of other commercial CFD codes FLUENT v6.2 Lagrangian model with discrete particles transportation Model of interaction between particles and wall Equation of Mass, Momentum and Energy solved FIRE v8.4 Semi-implicit eulerian model Dynamic Mass and Energy equation Momentum equation with quasi stationary hupothesis

21 Comparision of wall film models of different commercial cfd code The wall film model in FLUENT intensifies the dynamic effect of spray impact on the momentum of wall film The evolution of the film far away from the impact zone is good The quasi stationary model of FIRE underextimate the dynamics of the film. The analysis of the equation of the model allows us identifying the cause in th elack of source terms of the momentum equation and to the quasi stationary HP of the velocity profiles imposed. The fully explicit model implemented in KIVA is y accurate in the prediction of film heigth and also well predicts the dynamics of the film

22 KIVA FIRE

23 Momentum equation in FIRE Quasi stationaty profiles Momentum equation

24 Wall Film - Conclusion A wall film model that also accounts for the spray-wall interaction has been implemented on our version of the KIVA3 code Particular attention has been given to the physics of the phenomenon and to the numerical and implementation issue that arise from its modelling The model resolves the film dynamic using an explicit integration method The model has been validated d against a PFI-like an Diesel engine case, giving good result both for the predicted film height and evaporation rate The model has been implemeted in FIRE (beta version)

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