Acta Polytechnica doi:10.14311/AP.2019.59.0162 Acta Polytechnica 59(2):162–169, 2019 © Czech Technical University in Prague, 2019 available online at http://ojs.cvut.cz/ojs/index.php/ap DETERMINATION OF DETONABLE GAS MIXTURE HEAT FLUXES AT THERMAL DEBURRING Sergey Plankovskyya, Andrzei Teodorczykb, Olga Shypula, Oleg Tryfonova, Dmytro Bregaa,∗ a National Aerospace University “Kharkiv aviation institute”, Aircraft Manufacturing Department, Kharkiv, Ukraine b Warsaw University of Technology, Institute of Heat Engineering, Warsaw, Poland ∗ corresponding author: brega10.04@gmail.com Abstract. Modern technology requires a multitude of precise parts that are a necessity in reliable methods of surface finishing. Energy of detonable gas mixture combustion has been used in manufac- turing as a processing source for a long time. One of the most underappreciated methods is thermal deburring; this is caused by certain difficulties in modelling and simulation of this process due to a complex and poorly predictable nature of the combustion. A theoretical approach towards thermal deburring process using the conception of an equivalent chamber is described. Processing of combined experimental and computational data results in a simplified model of thermal deburring in the case with deflagration and combustion with a shock waves formation. The proposed mathematical model was verified by an experimental investigation of the combustion in a shock tube, the difference of compared parameters did not exceed 3%. The heat fluxes at thermal deburring by combustible gas mixtures and their distribution on part surfaces according to the direction of the shock waves propagation were calculated. A relation between the value of the heat flux and shock waves propagation was found with a convincing repeating trend. Keywords: Thermal deburring, edge finishing, heat flux, shock waves, detonable gas mixtures. 1. Introduction Thermal deburring, also known as Thermal Energy Method (TEM), is a process of removing burrs that are caused by different procedures (i.e. drilling, milling etc.) during the surface formation in machinery and related areas. It was ranked among the top of the most convenient and effective methods of deburring, due to a low performing time, simple automation, absence of abrasive inclusions after the processing and removing both internal and external located burrs [1? , 2]. The heat source varies according to instrument: edge finishing laser [3–5], electron beam melting (EBM) [6], electric and plasma arc [7], high frequency currents heating [8]; nevertheless, the main common drawback of these methods is still the necessity for a high accuracy of positioning to the processed detail, heating intensity and performance time of aforemen- tioned heat sources. All of these treatment methods show satisfactory results in external surface finishing, but in terms of internal defects processing treatment of processed part with combustion gases have numerous advantages in performance, accuracy and reliability [1, 9, 10]. In addition, the TEM is used in an automatic mode us- ing a CNC (computer numerical control) deburring machine. The main settings of this machine are a composition of the gas mixture, its initial pressure and exposure time. The specified parameters should provide the values of heat fluxes required for process- ing and their uniform interaction with the surfaces of the part. Nowadays, the developing of operation settings of thermal treatment for the CNC deburring machine could be represented by two different approaches. The experimental path utilizes the data from previous experiments, but obtained empirical equations cannot provide accurate results and ensure the quality of the ultimate product. Another way is a full numerical simulation of the deburring process using combustion gases. In this case, a careful consideration of all particular processes (i.e. combustion of initial gas mixture, shock waves formation, and heat distribution) should be included, making this method excessively costly for complicated and precise parts. In current work, we propose an alternative way for the thermal deburring process simulation based on a simplified model, with some corrections from empiri- cal data. The model was built with the assumption of the possibility to replace a real chamber with a com- plex shape part on the chamber with an equivalent volume. The result of the theoretical and experimen- tal study of heat fluxes, shock waves propagation in combustion chamber in the presence of processed part is represented below. 2. Mathematical model The simulation of deburring by combustion gases was performed with transient analysis. 162 http://dx.doi.org/10.14311/AP.2019.59.0162 http://ojs.cvut.cz/ojs/index.php/ap vol. 59 no. 2/2019 Determination of detonable gas mixture heat fluxes at thermal deburring Taking into account the complicated nature of the modelled system, some assumptions were used: • A premixed flame is used. • 2D axisymmetric case is considered. • Reynolds decomposition is used to simplify Navier- Stokes equations. A commercial code ANSYS Fluent was used for numerical simulations [12]. The geometry as well as the mesh was created via Workbench platform, a model was created according to the dimensions of the experimental tube. The mesh size was chosen according to the expected velocities magnitude. Several simulations were done to check the case sensitivity on a mesh size and to obtain a discretization error using a grid convergence index. It was found out that the difference in heat flux value between one and 10 million of elements is less than 1%. Initially, a mesh with half a million of elements was used, so after the mesh dependence check, we found out that 1 million of cells is enough to obtain an accurate solution with a minimal computational time. The combustion of gases is governed by a set of equations describing the conservation of mass, mo- mentum, energy, and species. Excluding the mass forces, baro – and thermal diffusion, the equations are given by: ∂ρ ∂t +∇ · (ρ · u) = 0 (1) ∂(ρ · u) ∂t +∇ · (ρ · u · u) = −∇P +∇ · τeff (2) ∂(ρh) ∂t +∇ · (uρh) = ∂P ∂t + u · ∇P+ +∇ ( λeff∇T − ∑ i hiJi + τeff · u ) + + N∑ i=1 Qi −Qrad (3) ∂(ρYi) ∂t +∇ · (ρuYi) = = ∇ · (( ρDi + µt Sct ) ∇Yi ) +Ri (4) where ρ is the density, [kg/m3]; u is the velocity vector; t is the time, [s]; P is the pressure, [Pa]; τeff = (µ + µt)(∇u + (∇u)T − 2/3I · (∇ · u)) is the effective stress tensor (i.e., the sum of the viscous and turbulent stresses); µ is the viscosity, [Pa·s]; µt is the turbulent viscosity; I is the unit tensor; h is the enthalpy of the mixture, [J]; λeff = λ+ λt is the effective thermal conductivity; λ is the laminar heat conductivity [J/(m·s·K]; λt = CpµtPr −1 t is the turbu- lent heat conductivity; Cp is the specific heat, [J/K]; Prt is turbulent Prandtl number; T is the tempera- ture, [K]; , where Tref is 298.15 K, is the enthalpy of species i, [J]; Ji is the diffusion rate vector of species i; Qi = h0 iRi/Mi is the heat of the chemical reactions that the species i participate in, [J]; Qrad is the radia- tion heat, [J]; Yi is the mass fraction of species i; Di is the diffusion coefficient of species i in the mixture, [m2/s]; Sct is the turbulent Schmidt number; Ri is the rate of the production of species i by the chemical reaction. For the current study, the SST turbulence model was used, which shows good results simulating the wall surface flows. According to this model, the turbulent viscosity is calculated as [11]: µT = 0.31 ρk max(0.31ω; ΩF2) (5) where F2 = tanh(arg2 2); arg2 = max ( 2 √ k 0.09ωy ; 500ν y2ω ) - function equals one for the boundary layer, and it equals zero for the free layer; Ω = (∂u/∂n) - is the derivative of the flow rate on the normal to the wall; k and ω are the turbulence kinetic energy and the specific dissipation rate, respectively. Parameters k and ω were obtained from the follow- ing transport equations: ∂ρk ∂t + ∂ ∂xi (ρvik) = τij ∂vi ∂xj − β∗ρωk+ + ∂ ∂xi ( (µ+ σkµt) ∂k ∂xi ) , (6) ∂ρω ∂t + ∂ ∂xi (ρviω) = γ ντ τij ∂vi ∂xj − βρω2+ + ∂ ∂xi ( (µ+ σωµt) ∂ω ∂xi ) + + 2ρ(1− F1)σω2 1 ω ∂k ∂xj ∂ω ∂xj , (7) where ντ = a1k max(a1ω; ∂u/∂yF2) ; model constant φSST (γ, σk, σω, β, β∗) associated with k − ω model con- stants φkω and transformed k − ε model φkε as: ΦSST = ΦkωF1 + (1 − F1) Φkε; F1 = tanh ( arg4 1 ) ; arg1 = min [ max ( √ k 0.09ωy ; 500ν y2ω ) ; 4ρσω2k CDkωy2 ] ; y - distance to the nearest wall, [m]; CDkω = max ( 2ρσω2 1 ω ∂k ∂xj ∂ω ∂xj , 10−20 ) . The net source of chemical species i, due to the fact that the reaction is computed as the sum of the Arrhenius reaction sources over the NR reactions that the species participate in: Ri = Mi NR∑ r=1 R̂i,r, (8) where Mi is the molecular weight of species i, [kg/mol] and R̂i,r is the Arrhenius molar rate of cre- ation/destruction of species i in reaction r, [mol/s]. 163 S. Plankovskyy, A. Teodorczyk, O. Shypul et al. Acta Polytechnica For a reversible reaction, the molar rate of cre- ation/destruction of species i in the reaction r is given by [12]: R̂i,r = J ( ν ′′ i,r − ν ′ i,r ) ( kf,r ∏N j=1 [Cj,r]η ′ j,r − kb,r ∏N j=1 [Cj,r]η ′′ j,r ) , (9) where N is the number of chemical species in the system; ν′ i,r is the stoichiometric coefficient for the reactant i in the reaction r; ν′′ i,r is the stoichiometric coefficient for the product i in the reaction r; kf,r is the forward rate constant for the reaction r; kb,r is the backward rate constant for the reaction r; J represents the net effect of third bodies on the reaction rate; Ci,r is the molar concentration of each reactant and product species j in reaction r (kg mol/m3); η′ j,r , η ′′ j,r - forward and backward rate exponent for each reactant and product species j in reaction r respectively. To determine the constants of direct and backward reactions, the Arrhenius equals have been used [13]: kf,r = Ar1T βr1 exp ( − Er RT ) , (10) kb,r = Ar2T βr2 exp ( − Er RT ) , (11) where Ar, βr – are the pre-exponential factor and the temperature exponent; Er is the activation energy for the reaction, [J/mol]; R is the universal gas constant, [J/(mol·K)]. In the presented paper, the combustion simulation was carried for the commonly used fuel gases: hydro- gen, methane and propane, and oxidants: oxygen and air. Methane-air combustion mechanism consists of 17 species and 37 reactions, propane-air mechanism – 35 species and 108 reactions and hydrogen-air mechanism – 8 species and 40 reactions. For the convective heat flux calculation, the formulation of Kader has been applied [14, 15]: T+ = Pr · ỹ+ exp(−Γ)+ + [ 2.12 ln(1 + ỹ+) + β ] exp(−1/Γ), (12) where β = ( 3.85Pr1/3 − 1.3 )2 + 2.12 ln(Pr); Γ = 0.01(Pr·ỹ+)4 1+5Pr·ỹ+ . In expression (12) dimensionless temperature was used: T+ = ρcpũτ (Tw − Tf ) qw , (13) where Tw - wall temperature, [K]; Tf - temperature of combustion products in the flow core, [K]; qw - the wall heat flux, [W/m2]; ũτ = [ (ũvisτ )4 + (ũlog τ )4]0.25 - the velocity profile in the boundary layer; ũvisτ = U1 ỹ+ - the velocity in the viscous sublayer; ũlog τ = U1 (1/k) ln(ỹ+)+C - the velocity in logarithmic sublayer; y+ - dimensionless distance from the first grid node to the wall; ỹ+ = max(y+, 11.067), the limiting value of y+ = 11.067 marks the intersection between the logarithmic and the linear profile; U1 - the flow rate in the node, which is the nearest to the wall. The calculation grid near the wall was built accord- ing to the recommendations for y+ grid spacing for SST model. In order to cope with high gradients of pressure and velocity a time step of 1e-6s was used for the pressure based solver. The value of the heat flux was calculated with use Eq. (13): qw = ρcpũτ T+ (Tw − Tf ). (14) The radiation is calculated by P1 radiation model [16]. 3. Numerical simulation and experimental analysis To evaluate the accuracy of the proposed model, a set of experiments was performed. An experimental investigation of deflagration-to-detonation transition in a tube with obstacles was carried out [17]. An experimental setup for the detonation study is shown in Figure 1. The main part of the installation is a cir- cular cross-section detonation tube, made of stainless steel 1X18H9T. The general scheme of the installation is shown on Figure 2. The tube (1) has a total length L = 6m and an internal diameter D = 0.14m consists of four sections (2, 2, 1 and 1m) connected together. Thin ring-shape obstacles (2) with an axial hole di- ameter d = 0.108m are installed inside the tube. The considered pipe locking ratio is equal to 0.4. The number of obstacles is 35 rings, which are arranged in increments equal to S = 0.14m (equal to the diameter of the tube) and connected with each other by 0.015m diameter rods to ensure the constancy of the interval. Figure 3 shows the scheme of the obstacles location. To ensure the tightness of the detonation tube, its ends are closed with metal flanges. Diameter of the flanges is equal to 0.26m and they are made from a material similar to the pipe. PCB Piezotronics pressure sensors (10), which are located along the tube at a distance of 1.25, ,750; 2.75; 3.25; 3.75; 4,625 and 5,125m from the entrance end, were used to monitor the pressure. The experimental results were obtained and processed using an auto- matic data collection system and a personal computer (3). Before filling the tube, the fuel mixture was pre- viously prepared in a cylinder (5), the air from the detonation tube was pumped out with a vacuum pump (6) to a vacuum at pressure 10Pa. Ignition of the mixture was carried out using an automobile spark plug (8) and a time sequence gen- erating device (4). The spark plug is connected to the ignition device (7) and is mounted on the flange, which closes the inlet end of the pipe. The release 164 vol. 59 no. 2/2019 Determination of detonable gas mixture heat fluxes at thermal deburring Figure 1. Experimental setup for the detonation study. Figure 2. The scheme of the installation: 1 – detona- tion tube; 2 – obstacle; 3 – automatic data collection system and a personal computer; 4 – time sequence generating device ; 5 – cylinder filled with air-hydrogen mixture; 6 – vacuum pump; 7 – ignition device; 8 – spark plug; 9 – exhaust valve; 10 – pressure censor. Figure 3. Scheme of the obstacles location. 165 S. Plankovskyy, A. Teodorczyk, O. Shypul et al. Acta Polytechnica Figure 4. Calculated (top) and experimental (bot- tom) pressure profiles. of combustion products was carried out through the exhaust valve (9). Obtained experimental and simulations results are shown in the Figure 4 and 5, demonstrating the con- vergence of pressure and detonation velocity values in both cases (difference between pressure and time peak values do not exceed 3% and 5% respectively). The same accuracy results were obtained in measurements of shock waves damping and the in-chamber heat ex- change for the acetylene-oxygen and methane-oxygen mixtures combustion, showing the applicability of the proposed model in further investigations. Further work was carried out to study the ther- mal deburring of parts with complex shapes by com- bustible gas mixtures. As the main hypothesis, it was assumed that, to determine the required heat flux and damping time of the shock waves in the chamber for treatment parts with a complex shape, it is possible to use calculation results from the simplified model with an equivalent chamber. As an equivalent chamber, two cases have been considered. The first case is an empty chamber, the volume of which is defined as Veqvcham = Vcham − Vparts (Figure 6a), where Veqvcham, Vcham, Vparts - the volume of the equivalent chamber, the volume of the real chamber and the volume of treatment parts, respectively. The second case is the chamber with simple geometric shaped parts located inside, for which Veqvpart = Vparts (Figure 6b), where Veqvpart - the volume of the equivalent part. At least three different modes can be distinguished for the combustion process inside a closed chamber - deflagration, detonative and knocking combustion. The heat transfer between the processed part and heat fluxes significantly differs for all cases, requiring a careful consideration of process conditions for a uniform distribution of heat along the part. The lowest values of heat fluxes are achieved for deflagration. The main drawback of this approach is a high heterogeneity of temperature inside the cham- ber – the difference can reach more than 500K; this phenomenon is known as the Mache effect. The so- lution of this problem lies in a modification of the ignition source( i.e. corona discharge [18] or laser radiation [19]). In our previous work we describe the pre-chamber torch ignition, which results in ho- mogeneous temperature in chamber with a standard deviation that does not exceed 1% [20]. The dependence of the heat fluxes on pressure can be estimated from the following considerations. The heat transfer coefficient in the thermal boundary layer can be described: α(Tmixture − Twall) = λ ∂T ∂n ≈ ≈ λ (Tmixture − Twall) δ , where δ - the thickness of the thermal boundary layer, which is inversely proportional to the square root of the Reynolds number for laminar flow δ ∼ 1/ √ Re. Assuming that the viscosity, temperature and veloc- ity of the combustion products are weakly dependent on the initial state of the mixture: δ ∼ 1/√ρ, and con- sidering that ρ = p/RT , finally we have α ∼ √ p/T . For arbitrary initial pressure and temperature of the mixture, the equation for the heat flux determination will be: qp = qp0 √ pT0mixture/p0Tmixture, (15) where – qp0 heat flux, defined for the mixture with the initial pressure p0 and temperature T0. The cyclic mode of a deburring machine work im- poses more restrictions on the proposed model – peri- odic contact of combustion gases with chamber walls causes a rise of their temperature; additional heating of starting gas mixture affects the internal pressure, re- sulting in a fuel dosage error and an incorrect work of the deburring machine. To counterbalance this effect in our model, the simulations of additional heating impact on gas mixture dosage were performed using the mathematical model presented above, excluding the equations that describe chemical reactions. It was found out that temperature increase from 293K to 423K reduces the mass of the fuel by 12% at stable pressure conditions. It should be noted that mass con- trol of the introduced fuel cannot be the solution of the aforementioned problem due to unknown starting temperature of the fuel mixture, and, as a result – unknown final temperature. The most accurate way of the fuel dosage is a combined mass and pressure control. Using the latter values, it is possible to clearly determine the density and temperature of the starting 166 vol. 59 no. 2/2019 Determination of detonable gas mixture heat fluxes at thermal deburring Figure 5. Simulation of flame propagation and deflagration-to-detonation transition in the pipe with obstacles. Figure 6. Variants of the transition to an equivalent chamber. gas mixture: ρmix = mmix/(Vcham − V parts) Tmix = pmix/