顆粒對氣相紊流場所造成之調制效應(modulation effect)，一直是兩相紊流主要的研究課題之一，楊進成(2000)為探討此一效應，以張克勤等人(1997)與楊進成(2000)推導出之Lagrangian型式的顆粒紊流動能方程式及紊流調制項方程式為基礎，藉由數值模擬與黃登淵(1995)所提出之實驗結果作比較，發現黃登淵(1995)所提出之紊流調制量在剪力層區有明顯高估之情況，故本文基於以上之疑慮，重新整理黃登淵(1995)之量測數據，試圖釐清此疑點。
由於紊流調制量無法直接量測而得，故本文使用多項式外插及由圖形觀察而得之指數經驗式求得其值。經與黃登淵(1995)結果比較，得知在入口處其結果與本文所得結果尚屬相近;但隨著越往下游，二者差距則越來越大。為確定本文結果與黃登淵結果間何者較為正確，藉由理論推導出之調制量範圍以及黃登淵提出之與紊流調制量相關之參數來觀察，由調制量範圍及紊流調制量相關之參數分析之結果得知黃登淵(1995)所得結果在下游處剪力層的確有明顯高估之情況，故確定黃登淵(1995)下游截面之結果的確存在高估之情形。最後由誤差因素分析發現「圖形對稱」之假設在分析較大顆粒時，會造成求解紊流調制量產生錯誤，尤其是在剪力層區域。

Modification of carrier-fluid turbulence due to existence of particles is one of the major issue in the study of two-phase turbulence up to now. In order to analyze this effect, Yang (2000) performed numerical simulations using the Lagrangian and transport equations derived by Chang et al. (1997) and Yang (2000) and compared his predictions with the experimental data of Huang (1995). It was found that Huang's result might be overestimated the turbulent modulation quantity ( ) in shear layer region. In order to clarify this doubt, the turbulent modulation quantity is re-determined from the raw data of Huang (1995) in this thesis.
Because the turbulent modulation quantity cannot be measured directly, its value is then extracted from the profiles of using two approaches. One is to determine a polynomial extrapolation from available experimental data, while the other is to interpolate with an exponential function which curve-fits the data of best. From the comparison between the present results and Huangs results (1995), it was found that the results obtained from the two present approaches are in chose agreement with the Huang’s data in the upstream region. But, the derivations become more and more pronounced as the location moves downstream. To insure that the present approaches can determine the turbulent modulation quantity accurately, two conditions are imposed here. One condition is to set the upper and lower bounds of through the mathematical constraint. The other condition is to justify the correctness of the calculated value of through the guidelines suggested by Huang (1995). With the aid of the above two conditions, it is sure that Huang did overestimated the turbulent modulation quantity in the shear layer in the downstream regions. In addition, It is found that the symmetric assumption for about is invalid for large particles, particularly in the shear layer region.

Adeniji-Fashola, A., and Chen, C.P., “Modeling of confined turbulent fluid-particle flows using Eulerian and Lagrangian schemes,” Int. J. Heat Mass Transfer, Vol. 33, No. 4, pp.691-701. (1990)

Berlement, A., Desjonqueres, P., and Gouesbet, G., “Particle Lagrangian Simulation in Turbulent Flows,” Int. J. Multiphase Flow, Vol.16, No. 1, pp. 19-34. (1990)

Best, J.L., ”The influence of particle rotation on wake stability at particle Reynolds number, Rep < 300-implications for turbulence modulation in two-phase flows,” Int. J. of Multiphase Flow, Vol.24, pp.693-720. (1998)

Burry, D., and Bergeles, G., ”Dispersion of particle in anisotropic Turbulent flows,” Int. J. Multiphase Flow, pp. 651-664. (1993)

Calabrese, R. V., and Middleman, S., “The Dispersion of Discrete Particles in a Turbulent Fluid Field,” AIChE J., Vol. 25, No. 6, pp.1025-1035. (1979)

Chang, K.-C., Wang, M.-R., Wu, W.-J., Liu, Y.-C., “Theoretical and Experimental Study on Two-Phase Structure of Planar Mixing Layer,” AIAA J., Vol. 31, No. 1, pp. 68-74. (1993)

Chen, X.-Q., and Pereira, J.C.F. “Computation of Particle-Laden Turbulent Gas Flows Using Two Dispersion Models,” AIAA J., Vol. 36, No. 4 (1998)

Chen, X.-Q., and Pereira, J.C.F., “Computation of turbulent evaporating sprays with well-specified measurements: a sensitivity study on droplet properties,” Int. J. Heat Mass Transfer, Vol. 39, No. 3, pp. 441-454. (1996)

Chen, X.-Q., and Pereira, J.C.F., “Efficient computation of particle dispersion in turbulent flows with a stochastic-probabilistic model,” Int. J. Heat Mass Transfer, Vol. 40, No. 8, pp. 1727-1741. (1997)
Chen, X.-Q., and Pereira, J.C.F., “Prediction of evaporating spray in anisotropic turbulent gas flow,” Numerical Heat Transfer, Part A, 27, pp. 143-162. (1995)

Crowe, Clayton, T., “On models for turbulence modulation in fluid-particle Flows,” Int. J. of Multiphase Flow, Vol.26, pp.719-727. (2000)

Durst, F., Milojevic, D., Schönung, B., “Eulerian and Lagrangian predictions of particulate two-phase flows: a numerical study,” Appl. Math. Modeling, Vol. 8, pp. 101-115. (1984)

Elghobashi, S., “On Predicting Particle-Laden Turbulent Flows,” Applied Scientific Research, 52, pp. 309-329. (1994)

Elghobashi, S., and Truesdell, G.G., ”Direct simulation of particle dispersion in a decaying isotropic turbulence,” J. Fluid Mech., Vol. 242, pp. 655-700. (1992)

Gouesbet, G., and Berlemont, A., “Eulerian and Lagrangian approaches for predicting the behaviour of discrete particles in turbulent flows,” Progress in Energy and Combustion science, 25, pp.133-159. (1999)

Kenning, V. M., and Crowe, C.T., ”On the effect of particles on carrier phase turbulence in gas-particle flows,” Int. J. of Multiphase Flow, Vol.23, No.2, pp.403-408. (1997)

Litchford, R.J., and Jeng S.-M., “Efficient Statistical Transport Model for Turbulent Particle Dispersion in Sprays,” AIAA J., 29, pp. 1443-1451. (1991)

Litchford, R.J., and Jeng, S.-M., “Probability Density Function Shape Sensitivity in the Statistical Modeling of Turbulent Particle Dispersion,” AIAA J., Vol. 30, No. 10, pp. 2546-2549. (1992)

Lu, Q.Q., Fontanine, J. R., and Aubertin, G., “Particle Dispersion in Shear Turbulent Flows,” Aerosol Science and Technology, Vol. 18, pp. 85-99. (1993)
Lun, C. K. K., ”Numerical simulation of dilute turbulent gas-solid flows”, Int. J. of Multiphase Flow, Vol. 26, pp.1707-1736. (2000)

Parthasarathy, R. N., and Faeth, G. M., ”Turbulence modulation in homogeneous dilute particle-laden flows,” J. Fluid Mech., Vol.220, pp.485-514. (1990)

Picart, a., Berlemont, A., and Gouesbet, G., “Modeling and Prediction Turbulence Fields and the Dispersion of Discrete Particles Transported by Turbulent Flows,” Int. J. Multiphase Flow, Vol. 12, No. 2, pp. 237-261. (1986)

Rizk, M. A., and Elghobashi, S.E., “A Two-Equation Turbulence Model for Dispersed Dilute Confined Two-Phase Flows,” Int. J. of Multiphase Flow, 15, pp. 119-133. (1989)

Sakakibara, J., Wicker, R.B. and Eaton, J.K., ”Measurement of the particle-fluid velocity correlation and the extra dissipation in a round jet,”
Int. J. of Multiphase Flow, Vol.22, No.5, pp. 863-881. (1996)

Shirolkar, J. S., Coimbra, C. F. M., and McQuay, M. Q., “Fundamental aspects of modeling turbulent particle dispersion in dilute flows,” Progress. Energy Combustion Science, Vol. 22, pp. 363-399. (1996)

Wang, L.P., and Stock, D. E., “Stochastic trajectory models for turbulent diffusion: Monte Carlo process versus Markov chains,” Atmospheric Environment, Vol. 26A, No. 9, pp. 1599-1607. (1992)

Wang, M.R., and Huang, D. Y., “Measurements of in Mixing-Layer Flow with Droplet Loading,” Atomization and Sprays, Vol. 5, pp. 305-328. (1995)

黃登淵, ”雙相紊流場中氣液兩相在邊界層流與混合層流交互作用之研究,”國立成功大學航空太空工程研究所博士論文, 1996.

楊進成, ”兩相紊流場隨機Eulerian-Lagrangian計算法之檢視,”國立成功大學航空太空工程研究所博士論文, 1999.

黃士軒, ”兩相相關性及紊流調制量之研究,” 國立成功大學航空太空工程研究所碩士論文, 2002.