Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler*

Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler* Jie Yao 1, Zhao-Xiang Deng 1,2, Pei-Ran Li 1, and Liang Yang 2 1 State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China 2 State Key Laboratory of Vehicle NVH and Safety Technology, Chongqing 401120, China yaojie5@gmail.com Abstract. This paper presents a CFD model of reverse-flow extended-tube muffler which is analyzed by a set of experimental tests, in order to acquire the relations between the structure and its corresponding pressure loss; a lot of research have been done through the numeric simulation. For the specific model, the distance from inlet pipe s rear to the end cap has a large impact on the pressure loss, furthermore, a critical value about the distance has been found: If the distance is less than the critical value, the pressure loss will sharply rise; If the distance is larger than it, the pressure loss will change little. In the end, to calculate the critical value about the distance, evaluation formulary is displayed, which possesses great importance to the design of muffler and its pressure loss prediction. Keywords: reverse-flow extended-tube, pressure loss, the critical distance, CFD. 1 Introduction Pressure loss is a ey factor to evaluate the aerodynamic performance of vehicle muffler. Pressure loss could badly affect the engine efficiency. High pressure loss can lead to increase of bac-pressure which is corresponding to the power loss of the internal combustion engines, so with high pressure loss, the engine will consume more fuel[1].therefore, during the process of muffler design, the consideration of structure effect on the pressure loss has become a hot topic nowadays [2][3].Semiempirical formula method is generally applied to reactive muffler design, and the fact is this method can t promise necessary precision, while the application of highprecision experimental method always require a large amount of investment, which is not suitable for the beginning of product design. Taing these factors into account, m 1 any scholars turn to the CFD technology for help. Many researchers have used the CFD technology to carry out the simulation of pressure loss. Middelberg.JM [4] The earliest user of CFD technology to study the internal pressure loss for muffler; Hu Xiaodong [5][6] has done lots of pressure loss * Key Research Program of Chongqing :CSTC2008AB6108. H. Deng et al. (Eds.): AICI 2011, Part I, LNAI 7002, pp. 475 483, 2011. Springer-Verlag Berlin Heidelberg 2011

476 J. Yao et al. study on a single and dual-chamber resistance muffler via this method. Liu Cheng, Ji Zhenlin [7] also calculated the three inds of mufflers pressure loss with the help of GT-POWER software. Shao [8] used CFD methods to calculate the accuracy of HVAC piping pressure loss problems. Kim [9] using the finite element software on a expansion chamber muffler complex flow field simulation. Fang Jianhua [10] used CFD to calculate the structure of the excavator muffler with complex flow field simulation, analysis of the causes of pressure loss. But now research on pressure loss of the muffler is for most of the situation downstream. (the significance of reflux into the tube) this paper, computational fluid dynamics (CFD) method was used to study pressure loss of the reverse-flow extended-tube muffler. We had analyzed the situation in the upstream uniform flow into the muffler pressure loss variation. The reverse-flow extended-tube muffler pressure loss prediction method was got. 2 Basic Theory of Fluid Dynamics for Muffler Many fluid mechanics research and numerical simulation results show that can be used in engineering on realistic turbulent simulation method is still based on solving Reynolds time-averaged equation and associated transport equation turbulent quantity simulation method, i.e. turbulent orthodoxy simulation method. In orthodoxy model, using the longest, accumulate the most experienced is mixed length model and the ε model. ε model was established by Spalding and Launder in 1972 proposed two equation turbulent model, from the experimental phenomena of a half empirical formulas [11]. Two equations model in lower computational cost is based on guarantee good calculation accuracy, and therefore the most widely was used in engineering. This paper also adopts the model for calculating model. ε model is mainly by solving two additional equation, the equation and the ε equation ( equation is expressed as turbulent inetic equation, ε equation is expressed as turbulent dissipative equation) to determine turbulence viscosity coefficient, thus solving turbulent stress. The model of the control equations for: Turbulent inetic energy ( ) equations: ( ρ) ( ρ u j ) μ t u j u i u j + = ( μ + ) + μt ρε σ + (1) t x i x j x j xi x j xi Turbulent inetic energy dissipation rate (ε ) equations: _ 2 ( ρε ) ( ρ u j ε ) μt ε ε u i u j ε + = ( μ + ) + C1 μi C2 t xi x j σ ε x j + (2) x j xi Turbulence viscosity coefficient: 2 μt = ρc (3) μ ε

Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler 477 Type: μ for turbulence viscosity, ρ coordinates component, u i u j For fluid average density ; x i x j for For fluid along x i and x j direction of velocity component average; i= 1, 2, 3, representing the three coordinate direction; C 1 C 2, σ σ ε C μ is the experience constant, the current widespread use of launder and Spalding recommended values for 1.11, 1.92, 1.00, 1.30, 0.09. 3 Model and Boundary Conditions 3.1 Physical Model As a classical resistance unit, mufflers with extended pipes possess well acoustic performance, and among these mufflers, reverse-flow ones could not only allow the diversion of flow, but also prolong the effective extended length, so they have been widely used. This ind of muffler is displayed as Fig. 1.a, based on this structure, this paper provides much research on the potential rules between the structure feature and its pressure loss. (a) (b) Fig. 1. a Reverse-flow extended tube b. Reverse-flow extended tube muffler muffler meshedrawing This article utilizes CATIA to establish the 3-D model, and then the model is meshed by hexahedron elements under the ANSA bacground. Besides, for model s inlet, outlet and shell surface, we set different element Id. After all the wor above, the finite element models are then attained as Fig.1.b shows. In order to simplify the issues, the following assumptions are listed: (1) performance parameters for the muffler and the flow field are constants, (2) the flow is turbulent among the steady flows; (3) ignore the influence of gravity (4) inlet velocity of flow is stable and without pulse influence. 3.2 Boundary Condition Settings Setting boundary conditions is a crucial step for numerical analysis, for it is directly related to the accuracy of the calculated results. This paper chooses ANSYS-CFX to

478 J. Yao et al. calculate the ε model. In order to assure the same comparisons standards, the field status of the entry surface is simplified to be stable. The CFD model s internal fluid flow field is turbulence and consists of incompressible air. The velocity near the wall is regarded as 0. The average velocity of floe in the entry is between 10~60 m/s, and at the end of outlet the average static pressure is 0Pa. For the abstract calculation, the time pace is adaptive type and the convergence value is the difference of two neighboring results root mean square, which is below 1 10-4. 4 Verify the Accuracy of Calculation In order to ensure the validity of the numerical results, in this paper, a test model was used to measure the pressure loss. Fig. 2. shows the test device by the fan, motor, inverter, pitot tube, pressure meter, muffler test pieces, taing pressure tube and other accessories. Test cases are the inlet and outlet total pressure value, the difference between the inlet and outlet is the pressure loss is the test pieces, and compared with calculation results of ANSYS CFX software, the results shown in Fig. 3. Comparative results show that ANSYS CFX software to calculate high agreement with the experimental results, due to the loss and partial loss along the way and the Fig. 2. Reverse-flow extended tube muffler pressure loss test sets physical map Fig. 3. Reverse-flow extended tube muffler comparison of pressure loss

Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler 479 flow measurement error caused in an acceptable range, so can use the CFD software can be used for muffler Calculation of pressure loss. 5 Analysis on Computation Results ANSYS CFX was used to every model in two-equation turbulence model equations, change L1 and L2 of the distance from 10mm to 300mm. A series of data was made of three-dimensional map diagram, as shown in Fig. 4. Fig. 4 shows that the L1 of the distance within a certain range when the pressure loss while the effect of the outlet control within the relatively large impact on pressure loss. Keep L2 distance constant, change L1, when L1 less than some length, reverseflow extended tube muffler pressure loss with a sharp increase and decrease of L1, When L1 greater than this range, with the increase of L1, the pressure loss will eep constant. When is less than this distance range, the length of inlet tube increase,pressure loss will be amplified, at the same time, when is more than this distance range, the length of outlet tube increase, pressure loss will be amplified. Fig. 4. Three-dimensional graph of the reverse-flow extended-tube muffler pressure loss 5.1 Reverse-Flow Extended-Tube Muffler Various Parameters on the Impact of Pressure Loss Earlier in reverse-flow extended tube muffler pressure loss into the rule is in a particular state of the inlet and outlet diameter and gaseous state, the following discussion of inlet and outlet of pipe diameter, temperature, and air speed parameters on the pressure loss. Fig. 5. a can be seen that the main factors of influence critical distance is the inlets pipe diameters, in order to consider outlet tube of influence to this distance, change the outlet of pipe diameter 40mm, 60mm and 80mm, calculation of different L1; the influence of pressure loss from Fig. 5. a, we can see that the outlet tube diameter of that distance of the impact is not big, but with the increases of outlet tube, the muffler pressure loss greatly reduces.

480 J. Yao et al. (a) (b) (c) (d) Fig. 5. a. different inlet and outlet pipe diameter (b. different temperature,c. different velocity,d. different pipe diameter)reverse-flow extended-tube muffler pressure loss with L1 changes When the inlet tube from the end after a certain distance to the range, the pressure loss is essentially the same, mainly due to the air inlet tube at this time can be fully expanded greatly reduced by the resistance, and in the outlet tube from the end unchanged Under the inlet tube at this time the pressure loss along the main loss of this part of the losses are small, so the critical distance, the pressure loss is expressed as a horizontal line. Description After more than critical distance, the length of the inlet tube on the pressure loss was less affected. The pressure loss of the resistance muffler was concerned by the internal air density and viscosity of air, and the physical properties of air was affected by the environment temperature. In the calculation of the pressure loss process should be considered in gas temperature. The CFD method to calculate the pressure loss, research reverseflow extended tube muffler under different temperature conditions, pressure loss of changing trends for L1 changing. Fig. 5. b can see as L1 increases, the pressure loss gradually decrease, when L1 reach a certain value, then the pressure loss basically unchanged. And with the increase of temperature, pressure loss gradually decrease, but as L1 increased, pressure loss variation trend is changeless, just change the amplitude decreases. The distance that L1 scope is not related to temperature, and under the same boundary conditions, with the increase of temperature, pressure loss will decrease.

Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler 481 Fig. 5. c shows that the curve, with different speed for inlet pipe, that as L1 changed, how pressure loss changed; it can be seen from the graph with figure 4 the same trend that this distance is not related to velocity, in the same boundary conditions, the higher the velocity, the higher pressure loss. From the above analysis, we can see, apparently L1 that reverse-flow extended tube muffler inlet pipes the distance from the rear wall exists a critical range, and the scope for reverse-flow extended tube muffler is the inherent parameters. For this distance range, through the statistics obtained a estimate formula, such as type (4). This estimate formula can be used to estimate and analyze the pressure loss of reverse-flow extended tube muffler. L C =S/d (4) Type (4) : S for inlet pipes circulation areaâ d for inlet pipes circulation diameter; L C for the critical distance. 5.2 Prediction and Verification of Critical Distance From estimating formula observation, the ey factor that influences critical distance is the inlet tube diameter. We changed the inlet of pipe diameter for different diameter. It is calculated to verify the correctness of the estimation formulae. Table 1 for through the formulas for calculating the muffler critical distance. Table 1. Extended tube muffler critical distance prediction tube diameter 40mm 60mm 80mm thicness 2mm 2mm 2mm LC 28.27433mm 43.9823mm 59.69026mm Fig. 5. shows that the curve that pressure loss with the L1 changing under different diameters for inlet and outlet. We can see from the graph, as distance of L1 increases, the pressure loss gradually decrease, when L1 get to the critical distance, pressure loss will basically unchanged. Moreover, the critical distance and forecast is consistent, illustration, critical distance estimation formulae are effectively. It can be used to predict pressure loss of reverse-flow extended tube muffler. 6 Engineering Application Example Fig. 6. for a project with internal combustion engine exhaust three Chambers muffler of geometric model, expansion chamber of cross-sectional is circular. Between one cavity and other cavity it connected through extended tube. Based on the CFD, the muffler is optimized.it get the table 3 simulation data. According to the above conclusions, not changing the muffler acoustics characteristics, we made two inds of projects, project one for the third cavity exchange inlet pipes 2 and 3 of outlet tube length, project two for second cavity exchange inlet pipes 3 and 4 outlet tube length. By critical distance estimation formulae (4) we can now, critical distance estimation for 36.1 mm. According the above conclusions, Improvement of the third cavity can cause pressure loss increases.

482 J. Yao et al. In table 3, it displayed on the inlet speed 100m/s pressure loss of different structures. Pressure loss of project one, for 44171.91 Pa, and the original model in the same boundary conditions, the pressure loss for 41516.22 Pa, improved the pressure loss increases, and the predictions expected. Improvement of the second cavity can cause pressure loss reduce. In the table 2, pressure loss of project two for 41161.24 Pa, and the original model in the same boundary conditions, the pressure loss for 41516.22 Pa, the pressure loss is reduced, and the predictions corresponding. So we can get the conclusion, critical distance for the reverse-flow extended-tube muffler in pressure loss of prediction and design is credible, has a great practical value. Table 2. Pressure loss simulation data of the muffler original model Project1 Project2 Velocity(m/s) PL(Pa) PL(Pa) PL(Pa) 30 3772.816 4003.544 3738.253 40 6690.2 7104.27 6629.517 50 10432.73 11088.14 10341.22 60 15000.63 15936.47 14868.61 70 20392.9 21672.81 20214.41 80 26612.44 28309.63 26380.07 90 33653.93 35802.59 33358.93 100 41516.22 44171.91 41161.24 Fig. 6. A muffler geometric model and its three cavity size 7 Conclusion Through computing and simulating the reverse-flow extended-tube muffler, the muffler pressure loss at a certain boundary condition is analyzed.the pressure loss law of the reverse-flow extended-tube muffler is got. So some specific conclusions are obtained, as follows: (1) Critical distance of the inlet pipe plays an important role in the pressure loss for the reverse-flow extended-tube muffler. If distance that inlet pipe end to the posterior wall is less than the critical distance, the pressure loss will cause a sharp rise. On the contrary, the distance more than the critical distance, the pressure loss will be little change. Critical distance is closely related with the inlet tube diameter, with temperature, flow rate, outlet pipe diameter changes, it is not changes. Critical distance is the intrinsic parameters of the reverse-flow extended-tube muffler.

Research on Pressure Loss for the Reverse-Flow Extended-Tube Muffler 483 (2) Distance in the inlet and outlet of pipe to the posterior wall greater than the critical distance, the inlet tube extended length has little effect to the muffler of pressure loss, the extended length of exit pipe has great impact on the pressure loss; (3) A critical distance of estimation formulae was got in Research, and the formula was verified validity; (4) Through design an application example to illustrate the critical distance on reverse-flow extended-tube muffler design and the pressure loss of prediction is credible, and it has a great practical value (5) The more temperature increases, the less the pressure loss of the reverse-flow extended-tube muffler changes. With the increase of flow rate, the pressure loss of the reverse-flow extended-tube muffler will increase. The diameter of outlet-pipe has little effect on the critical distance, but the increase of the diameter can greatly reduce the pressure Loss of muffler; References 1. He, Y., Deng, Z.: Noise Control In Automobile. China Machine Press, Bengjing (1999) 2. Jiang, P., Fu, X., Wu, B.: Optimization Design and Overall Evaluation Indices of Automotive Exhaust Muffler. Automotive Engineering 30(3), 230 247 (2008) 3. Hu, X.D., Zhou, Y.Q., Fang, J.H., et al.: Computational Fluid Dynamics Research on Pressure Loss of Cross-Flow Perforated Muffler. Chinese Journal of Mechanical Engineering 20(2), 88 93 (2007) 4. Middelberg, J.M., Barber, T.J.: CFD analysis of the acoustic and mean flow performance of simple expansion chamber mufflers. In: 2004 ASME International Mechanical Engineering Congress and Exposition (Conference code: 64903), pp. 151 156. ASME, Anaheim (2004) 5. Hu, X.-d., Zhou, Y.-q., Fang, J.-h.: CFD computation of pressure loss of single and dualchamber resistance mufflers. China Mechanical Engineering 17(24), 567 572 (2006) 6. Hu, X.-d., Zhou, Y.-q., Fang, J.-h., et al.: Muffler structure optimization research of digging machine based on CFD. Journal of System Simulation 19 (2007) 7. Liu, C., Ji, Z.-l., Guo, X.-l., Xu, H.-s.: Effects of Configurations on Pressure Losses in Automotive Exhaust Muffler. Automotive Engineering 30(12), 1113 1116 (2008) 8. Shao, L., Riffat, S.B.: Accuracy of CFD for predicting pressure loss in HVAC duct fittings. Applied Energy 51(3), 233 248 (1995) 9. Kim, M.H.: Three 2 dimensional numerical study on the pulsating flow inside automotive muffler with complicated flow path. In: SAE 2001 World Congress. SAE Paper, M.I (2001) 10. Fang, J.-h., Zhou, Y.-q., Hu, X.-d., et al.: CFD simulation of exhaust muffler with complicated structures for an excavator. Transactions of CSICE 27(1), 6873 (2009) 11. Launder, B.E., Spalding, D.B.: Lectures in mathematical models of turbulence. Academic Press, London (1972)