Effects of body force on the statistical behaviour and modelling of scalar variance in turbulent premixed flames |
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| Institution: | 1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China;2. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China;3. Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615–8540, Japan;4. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China;1. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, China;2. Dalian National Laboratory for Clean Energy, Dalian 116023, China;1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China;2. Institute for Aero Engine, Tsinghua University, Beijing 100084, China;1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China;2. College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, China;1. Division of Mechanical and Aerospace Engineering, Hokkaido University, N13 W8, Kita-ku, Sapporo, Hokkaido 060-8628, Japan;2. University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8654, Japan |
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| Abstract: | The effects of body force/external pressure gradient on the statistical behaviours of the reaction progress variable variance and the terms of its transport equation have been investigated for different turbulence intensities using DNS data of statistically planar flames. Since the extent of flame wrinkling increases with the strengthening of body force promoting unstable stratification, the scalar variance has been found to decrease under strong body force promoting stability. This trend is particularly strong for low turbulence intensities where the probability density function of the reaction progress variable cannot be approximated by a bimodal distribution. Therefore, an algebraic relation for the reaction progress variable variance, derived based on a presumed bimodal probability density function of reaction progress variable, cannot be used for general flow conditions. The contributions of chemical reaction and scalar dissipation rates in the scalar variance transport equation remain leading order source and sink, respectively for all cases irrespective of the strength and direction of the body force. The counter-gradient type transport is found to weaken with increasing body force magnitude when the body force is directed from the heavier unburned gas to the lighter burned gas side of the flame brush, and vice versa. Although a scalar dissipation rate-based reaction rate closure can be utilised to model the reaction rate contribution to the scalar variance transport accurately, the dissipation rate contribution due to the gradient of the Favre-averaged reaction progress variable cannot be ignored and it plays a key role for large magnitudes of body force promoting stable stratification. An algebraic closure of the scalar dissipation rate, originally proposed for high Damköhler number combustion, has been modified for the thin reaction zones regime combustion by incorporating the effects of Froude number. This model has been shown to predict the scalar dissipation rate accurately for all cases considered here. |
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