TURBULENTT FUEL FLOW ANALYSIS TO IDENTIFY FLOW NATURE

International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 5, May 2017, pp.386 394, Article ID: IJCIET_08_05_045 Available online at http://www.ia aeme.com/ijciet/issues.asp?jtype=ijciet&vtyp pe=8&itype=5 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 IAEME Publication Scopus Indexed COMPARATIVE STUDY OF CFD SOLVERS FOR TURBULENTT FUEL FLOW ANALYSIS TO IDENTIFY FLOW NATURE K. Shiva Shankar Assistant Professor, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, India. Dr. M. Satya Narayana Gupta Professor, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, India. G. Parthasarathy Associate Professor, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, India. ABSTRACT This project is a comparative analysis of various explicit solving methods in computational fluid dynamics to evaluate pressure losses in turbulent flows. All explicit solution methods currently available in the field of computational fluid dynamics apply some arbitrary mathematical equation to meshed surface as there are no governing equations available for turbulent flows. Analyzing a CFD problem (turbulent flow in a annular duct) by using various solvers in a CFD application and validating these results with available empirical formulae such as Darcy friction factor formula or Swamee Jain equation, Thus best solver for particular type of problem considered can be suggested. This project mainly emphasizes on flows with Reynold s number varying typically from 1 million to 9.7 millions. Possibility of obtaining exact or near exact solution for chosen problem with possible error and deviation and suggestions accordingly were made based on the resultss obtained from the analysis and interpolation. Keywords: Turbulent flow, Pipe, Mathematical models, Comparison. Cite this Article: K. Shiva Shankar, Dr. M. Satya Narayana Gupta and G. Parthasarathy Comparative Study of CFD Solvers for Turbulent Fuel Flow Analysis to Identify flow Nature. International Journal of Civil Engineering and Technology, 8(5), 2017, pp. 386 394. http://www.iaeme.com/ijci IET/issues.asp?JType=IJCIET&VType=8&ITy ype=5 http://www.iaeme.com/ijciet/index.asp 386 editor@iaeme.com

Comparative Study of CFD Solvers for Turbulent Fuel Flow Analysis to Identify flow Nature 1. INTRODUCTION There are lot of turbulence models available to evaluate or simulate turbulent flows. It is not possible to solve numerically Navier Stokes by DNS on a large enough scale with a high enough resolution to be sure that the computed numbers converge to a solution of N-S. A well known example of this inability is weather forecast the scale is too large, the resolution is too low and the accuracy of the computed solution decays extremely fast. This doesn t prevent establishing empirical formulas valid for certain fluids in a certain range of parameter sat low space scales (e.g meters) - typically air or water at very high Reynolds numbers. These formulas allow to design water pumping systems but are far from explaining anything about Navier Stokes and chaotic regimes in general. We can create multi-particle computer models such as lattice gas automate that generate turbulence at large length and time scales. We can write down the equations that govern turbulence. These are the Navier-Stokes equations. So there is an argument among fluid dynamists whether the existing physical phenomena such as Navier-Stokes equation is sufficient enough to describe the turbulence or not? At the same time lack of mathematical governing equation makes it difficult to understand, analyze or evaluate with numerical methods or CFD accurately. 1.1. Purpose of the Study 1. For a particular type of turbulent fluid flow what can be the best possible numerical methods out of all existing models. 2. In other words, to identify numerical model that can give near exact values for a particular problem in reference to the empirical solutions. 3. At the same time to identify the deviation and percentile of possible error generation. 4. To identify non-linear form of governing equation for a particular type of turbulent problem. 2. APPROACH & ASSUMPTIONS 2.1 Approach 1. A system with turbulent flow is considered such that there are empirical formulae available in existing literature 2. This system is modelled in CFD software such as ANSYS Fluent. 3. Appropriate solver is opted Here opting a solver is based on literature survey. 4. Various iterations are for same model for various assumptions such as: a) Varying interpolation methods b) Varying numerical algorithms 5. These results are compared with empirical formulae to identify which solver give more acceptable solutions for certain chosen algorithms and interpolation methods Basically, empirical formulae are obtained based on experimental data. Therefore, comparing a solution from numerical method with empirical formulae is almost comparing it with experimental data. 1. Identifying the range of error and deviation of the solutions. http://www.iaeme.com/ijciet/index.asp 387 editor@iaeme.com

K. Shiva Shankar, Dr. M. Satya Narayana Gupta and G. Parthasarathy 2. Once comparison is done the solver with best interpolation methods and algorithm is identified. 3. Interference to the deviation and error percentile observed and calculated the probable induced error of the results are predicted for solvers under the subject of study. 4. At the same time, if necessary mathematical statement of the turbulent can be verified and correction factors may be suggested. 2.2. Assumptions 1. The well-known method to study a turbulent flow in a aerospace industry is wind tunnel experiments. However, Navier-Stokes equations are considered to explain flow characteristics at this regime by most of the aerodynamists. As it would be really expensive to construct and operate a wind tunnel for this purpose and even such expensive tunnels do require idealization. 2. Thus, a simple flow in duct is considered as problem for CFD solver. However, this system is replica ofthe fuel pipes in aircraft. 3. A typical pipe facilitating Jet A-1 fuel with velocity around 1 to 7 m/s at 40.(Pipe is duct with circularcross-section). 4. Flow is considered incompressible. Though the fuel is at its flash point and vaporization occurs. Therate of displacement is very high than rate of vaporization. 5. Boundary layer theory is considered by means of Reynolds decomposition This study majorly emphasizes on energy equation as the empirical formulae and solvers are widely available for this type of models. 2.3. Shaping and Sizing Moreover investigation is mostly concerned on two-dimensional turbulent flows which can be solved using Navier-Stokes equation. Thus dimensions of assumed model will be developed on standard guidelines laid by Federal Aviation Authority. (1) Figure 1 Illustration of pipe in an aircraft fuel system. A pipe is a duct used to convey water, gas, oil, or other fluid substances which has commonly with tubular cylindrical cross-section. Here, D is diameter of pipe, l is length of pipe considered, is surface roughness. Therefore, from above standard data from FAA guidelines and Manufacturing Engineering and Technology following design specifications shown in Table 1 are considered for the study of the problem in CFD. http://www.iaeme.com/ijciet/index.asp 388 editor@iaeme.com

Comparative Study of CFD Solvers for Turbulent Fuel Flow Analysis to Identify flow Nature 3. ANALYSIS Table 1 Design specifications of the model S.No Parameter Dimension 1 Diameter (D) 175 mm 2 length (l) 10 D = 1750 mm 3 Roughness (Rg) 10 µm 3.1. Analytical Method This analysis carried out based on Darcy Weisbachequation. =.. Fuel properties are taken from SAE Handbook on Aviation Fuel properties. Properties of Jet-A1 are shown in Table 2 Table 2 Fluid Properties S. No Parameter 1 Density (ρ) 820 Kg/cm3 2 Dynamic Viscosity (v) 1.25 Cs 3 Specific Heat (C p ) 2.25 KJ/Kg K 4 Thermal Conductivity (Λ) 0.0112w/m k As per FAA guidelines velocity should not increase more7 m/s at any section of pipe. Table 3. RE and Corresponding F d For Various Velocities in the Pipe S.No V(m/s) Re f D 1 1 140000 0.013 2 2 280000 0.013 3 3 420000 0.013 4 4 560000 0.0125 5 5 700000 0.01 6 6 840000 0.01 Therefore, for considered dimensions which are stated in Table 1. Re for various velocities of fuel for same geometry are calculated and tabulated in Table 3 for diameter 0.175mm and surface roughness 10mm. fistaken from Moody chart. Using equation 2 pressure losses are calculated for unit length. According to FAA guidelines maximum refueling pressure should not exceed 3.45 bar. There fore, if the pressure loss equals to 3.45 then fluid momentum will bezero. It means energy lost by fluid is equal to work done in terms of heat generated or load applied on structure. Energy losses for the above model is illustrated in Table 4 and Table 5 for the corresponding velocity and Re. (2) http://www.iaeme.com/ijciet/index.asp 389 editor@iaeme.com

K. Shiva Shankar, Dr. M. Satya Narayana Gupta and G. Parthasarathy Table 4 Energy Losses in Pipe per Unit Length V(m/s) Re P(Pa) 1 140000 23.43 2 280000 93.70 3 420000 210.86 4 560000 374.86 5 700000 585.70 6 840000 843.43 Table 5 Energy Losses in Pipe for Entire Characteristic length V(m/s) Re P(Pa) 1 140000 41.0025 2 280000 163.975 3 420000 369.005 4 560000 656.005 5 700000 1024.975 6 840000 1476.0025 The results illustrated in table 4.4 are loss in fuel energy along length of 1.75 m when g, acceleration due to gravity is 9.81 m/s 2 and flow is assumed to incompressible with a boundary layer. 3.2. CFD Analysis Same model is generated and simulated using various computational models and solvers in ANSYS Fluent and then compared with empirical results. Based on literature survey three models are considered for investigation: 3.2.1. Spalart-Almaras The model is analyzed for inlet velocity of 1m/s and Green-Guass cell based discretization for second order momentum equation. Results obtained from this model of analysis are illustrated in the following figure 2. Spalart-Almaras model could not illustrate any change in dynamic pressure of the flow. When boundary layer is considered there will be change in velocity and correspondingly dynamic pressure along its length. Spalart-Almaras model fails to show this phenomenon and thus any further analysis on this model is ignored. 3.2.2. k-epsilon model This model consists of some adjustable constants σ k σ k, σ ε σ ε, C 1ε C 1ε C 2ε C2εThe values of these constants for a wide range of turbulent flows areas follows: Cµ= 0.09 σ k = 1.00 σ ε = 1.30 http://www.iaeme.com/ijciet/index.asp 390 editor@iaeme.com

Comparative Study of CFD Solvers for Turbulent Fuel Flow Analysis to Identify flow Nature σ ε = 1.30 C 1ε = 1.44 C 2ε = 1.92 Analysis is done for the above model for velocity from 1 m/s to 6 m/s. Results as shown in Figure 3 for Velocity 1 m/s. k- ε model gives linear pressure loss but fails to give eddy losses and turbulence accurately when compared to empirical solutions. 3.2.3. DES (Direct Eddy Simulation) Direct eddy simulation (DES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents. DES gives dynamic pressure and velocity magnitude quite convincingly when eddies and vortex formation are considered but just like k- ε model fails to give near exact results. Figure 4 gives pressure, velocity, and turbulent energy for both models with velocity for 1 m/s. However, these results don t compare with empirical solutions along the characteristic length of pipe. (a) Convergence History (b) Contours of Absolute Pressure (c) Contours of Dynamic Pressure (d) Contours of Total Pressure Figure 2 Contours of Spalart-Almaras model. http://www.iaeme.com/ijciet/index.asp 391 editor@iaeme.com

K. Shiva Shankar, Dr. M. Satya Narayana Gupta and G. Parthasarathy (a) Convergence History (b) Contours of Absolute Pressure (c) Contours of Dynamic Pressure (d) Contours of Total Pressure (e) Contours of Turbulent Energy (k) (f) Contours of Velocity magnitude Figure 3 Contours of k-e model for velocity of 1 m/s. http://www.iaeme.com/ijciet/index.asp 392 editor@iaeme.com

Comparative Study of CFD Solvers for Turbulent Fuel Flow Analysis to Identify flow Nature (a) Convergence History (b) Contours of Absolute Pressure (c) Contours of Dynamic Pressure (d) Contours of Total Pressure (e) Contours of Turbulent Energy (k) (f) Contours of Velocity magnitude Figure 4 Contours of DES model. http://www.iaeme.com/ijciet/index.asp 393 editor@iaeme.com

K. Shiva Shankar, Dr. M. Satya Narayana Gupta and G. Parthasarathy 4. CONCLUSIONS From the above analysis, it seen that Navier-Stoke s equation won t give accurate results in turbulent flows especially when Re is considerably high. However, it is observed that k-ε model gives more linear solutions for pressure losses along the length of pipe. DES illustrates good flow visualization for velocity magnitude and its changes due to creation of eddies. However, magnitude of these results are not in accordance with empirical values. A attempt is made to identify correction factors, deviation for empirical solution as the velocity increased. Nonetheless it proved to be disappointing. Thus, from the study a nonlinear equation or exponential correction factor based on Re and surface roughness has to determined. For this further study has to be conducted using experimental methods. From the analysis, it is observed that a second order up wind equation based on Prandtl-Meyer equations can be more promising than Navier-Stokes equations. Further emphasis can be done to mathematical model based on above recommendations to analyze a turbulent model. REFERENCES [1] Spalart, P. R. and Allmaras, S. R. A One-Equation Turbulence Model for Aerodynamic Flows 1992. AIAA Paper 92-0439. [2] H. Versteeg, W. MalalasekeraAn Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition) 1973: Pearson Education Limited; 2007; ISBN 0131274988. [3] Wilcox C. D. Turbulence Modeling for CFD 2nd Ed. DCW Industries; 1998 ; ISBN 096360510. [4] Bradshaw, P. An introduction to turbulence and its measurement; 1971; Pergamon Press; ISBN 0080166210. [5] Randall J. Leveque. Numerical Methods for Conservation Laws (2 nd ed.). (1992) Birkh auser Basel. ISBN 978-3-7643-2723-1. [6] Ghosal, S. An analysis of numerical errors in large-eddy simulations of turbulence. (April 1996); Journal of Computational Physics. 125 (1): 187 206. [7] Darcy, H.; Les FontainesPubliques de la Ville de Dijon (1856), Dalmont, Paris. [8] Manning, Francis S.; Thompson, Richard E., Oilfield Processing of Petroleum. Vol. 1: Natural Gas, (1991), PennWell Books, p. 420, ISBN 0-87814-343-2 See page 293. [9] Brown, Glenn. The Darcy-Weisbach Equation. Oklahoma State University Stillwater. [10] Afzal, Noor; Friction Factor Directly from Transitional Roughness in a Turbulent Pipe Flow. (2007), Journal of Fluids Engineering. ASME. 129 (10): 1255 1267. [11] Colebrook, C. F. Turbulent flow in pipes, with particular reference to the transition region between smooth and rough pipe laws. ;(February 1939). Journal of the Institution of Civil Engineers. London. [12] Shockling, M.A.; Allen, J.J.; Smits, A.J. Roughness effects in turbulent pipe flow.;(2006). Journal of Fluid Mechanics. [13] Langelandsvik, L. I.; Kunkel, G. J.; Smits, A. J. Flow in a commercial steel pipe ;(2008). Journal of Fluid Mechanics. Cambridge University Press. 595: 323 339. [14] P. Batten, M. A. Leschziner, and U. C. Goldberg; Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows; JOURNAL OF COMPUTATIONAL PHYSICS;137, 38 78 (1997);ARTICLE NO.CP975793. [15] Douvi C. Eleni, Tsavalos I. Athanasios and Margaris P. Dionissios;Evaluation of the turbulence models for the simulation of the flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil;journal of Mechanical Engineering Research Vol. 4(3), pp. 100-111, March 2012;ISSN 2141-2383c 2012 Academic Journals. http://www.iaeme.com/ijciet/index.asp 394 editor@iaeme.com