1、第一篇文獻(xiàn)

Improvement of k-epsilon turbulence model for CFD simulation of atmospheric boundary layer around a high-rise building using stochastic optimization and Monte Carlo Sampling technique

盡管經(jīng)過(guò)多年研究，建筑物周圍湍流的CFD數(shù)值模擬仍然是一個(gè)具有挑戰(zhàn)性的問(wèn)題(Lateb等人，2016)。即使對(duì)于一個(gè)簡(jiǎn)單的立方體形式的獨(dú)立建筑，實(shí)驗(yàn)結(jié)果和CFD預(yù)測(cè)之間也存在明顯的差異。

相關(guān)的研究發(fā)現(xiàn)，標(biāo)準(zhǔn)k-e模型不能在建筑的頂部產(chǎn)生逆流，改善后的模型如LK k-e(kato,1993)，RNG k-e (Yakhot and Orzag,1986)，MMK k-e(Tsuchiya,1997)可以更準(zhǔn)確地預(yù)測(cè)流動(dòng)形態(tài)，但標(biāo)準(zhǔn)k-e和改善的k-e模型都高估了建筑后面的再附著距離。

Yoshie et al. (2007), Tominaga and Stathopoulos (2010), Vardoulakis et al. (2011)，Gousseau et al.(2011)等人的研究也發(fā)現(xiàn)(RANS)湍流模型在再現(xiàn)建筑物后面的弱風(fēng)區(qū)和高估建筑物后面的再附著長(zhǎng)度方面的不準(zhǔn)確性。

Tominaga (2015),研究了孤立建筑的非定常雷諾平均湍流模型（unsteady Reynolds-averaged Navier– Stokes (URANS) turbulence modeling）的精度，發(fā)現(xiàn) SST k-o能夠模擬建筑后方的非定常波動(dòng)，能夠較好的再現(xiàn)建筑后面的速度場(chǎng)，但是該模型高估了拐角處的分離。

先前的研究表明，相比較于LES模型和URANS模型，RANS 湍流模型在預(yù)測(cè)孤立建筑周圍的氣流提供了較差的結(jié)果。但是LES模型和URANS模型在具體精確的邊界條件，合適的網(wǎng)格和時(shí)間尺度方面的高度復(fù)雜性，以及他們固有的高計(jì)算成本，使得它們作為許多實(shí)際工程問(wèn)題的可靠和快速解決方案的潛在應(yīng)用非常有限。

參考文獻(xiàn)

Lateb M, Meroney R N, Yataghene M, et al. On the use of numerical modelling for near-field pollutant dispersion in urban environments? A review[J]. Environmental Pollution, 2016, 208: 271-283.

Kato M. The modelling of turbulent flow around stationary and vibrating square cylinders[J]. Turbulent Shear Flow, 1993, 1: 10.4. 1-10.4. 6.

Yakhot V, Orszag S A. Renormalization group Analysis of turbulence. I. Basic theory[J]. Journal of scientific computing, 1986, 1(1): 3-51.

Tsuchiya M, Murakami S, Mochida A, et al. Development of a new k? ε model for flow and pressure fields around bluff body[J]. Journal of Wind Engineering and Industrial Aerodynamics, 1997, 67: 169-182.

Yoshie R, Mochida A, Tominaga Y, et al. Cooperative project for CFD prediction of pedestrian wind environment in the Architectural Institute of Japan[J]. Journal of wind engineering and industrial aerodynamics, 2007, 95(9-11): 1551-1578

Tominaga Y, Stathopoulos T. Numerical simulation of dispersion around an isolated cubic building: model evaluation of RANS and LES[J]. Building and Environment, 2010, 45(10): 2231-2239.

Vardoulakis S, Dimitrova R, Richards K, et al. Numerical model inter-comparison for wind flow and turbulence around single-block buildings[J]. Environmental Modeling & Assessment, 2011, 16(2): 169-181.

Gousseau P, Blocken B, Van Heijst G J F. CFD simulation of pollutant dispersion around isolated buildings: On the role of convective and turbulent mass fluxes in the prediction accuracy[J]. Journal of Hazardous Materials, 2011, 194: 422-434.

Tominaga Y. Flow around a high-rise building using steady and unsteady RANS CFD: Effect of large-scale fluctuations on the velocity statistics[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 142: 93-103.

2、第二篇文獻(xiàn)

RANS model calibration using stochastic optimization for accuracy improvement of urban airflow CFD modeling

一般來(lái)說(shuō)，與LES相比，RANS模型的計(jì)算成本要低一個(gè)數(shù)量級(jí)。這使得它們更適合作為設(shè)計(jì)和分析工具[37]（which makes them more suitable tools for design and Analysis purposes.）

城市建筑氣流研究中最常用的是兩方程模型，包括標(biāo)準(zhǔn)k-e [38]、RNG k-e[39]、可實(shí)現(xiàn)k-e[40]和k-o SST[41]，針對(duì)這些模型，已經(jīng)有應(yīng)用指南[42,43]。

RANS模型的一個(gè)缺點(diǎn)是，在預(yù)測(cè)建筑物周圍和后面弱風(fēng)區(qū)域的平均流量時(shí)，兩方程湍流模型的精確度較低[45–48]?？偟膩?lái)說(shuō)，兩方程湍流模型的不準(zhǔn)確性部分，是由于湍流粘度假設(shè)的簡(jiǎn)化和湍流動(dòng)能(TKE)耗散率(ε)的導(dǎo)出方程[49]造成的。湍流粘性假設(shè)是在雷諾應(yīng)力各向異性和平均速度梯度之間存在直接關(guān)系的假設(shè)下發(fā)展起來(lái)的，該平均速度梯度類似于牛頓流體中的分子粘性應(yīng)力。然而，正如參考文獻(xiàn)中所討論的[49]，湍流的物理學(xué)完全不同于分子過(guò)程，分子過(guò)程被用來(lái)達(dá)到牛頓粘性應(yīng)力定律。另一方面，不可能解決ε的精確傳輸方程，因?yàn)樗枰M(jìn)一步建模和開發(fā)經(jīng)驗(yàn)方程[50]。

RANS家族模型中的閉合方程主要被假設(shè)為完全的經(jīng)驗(yàn)方程，由幾個(gè)未知系數(shù)組成，這些未知系數(shù)通過(guò)觀察少量基本流來(lái)近似，包括均勻各向同性衰減湍流、充分發(fā)展的渠道流和簡(jiǎn)單剪切流[49]。盡管如此，這些基本氣流和大氣邊界層中建筑物周圍的氣流之間還是有一定的相似性。因此，這導(dǎo)致了一系列研究，以校準(zhǔn)平坦地形[51]和復(fù)雜地形[10]上的大氣邊界層流動(dòng)、高層建筑周圍的流動(dòng)[5，53–55]以及街道峽谷內(nèi)的流動(dòng)[56，57]的k-ε模型的閉合系數(shù)。還考慮了其他湍流模型閉合系數(shù)的校準(zhǔn)，用于使用Spalart–Allmaras和RNG k-ε模型預(yù)測(cè)低層建筑上的風(fēng)壓[58]，以及使用k-ω SST模型預(yù)測(cè)建筑塊周圍的污染擴(kuò)散[59]。

參考文獻(xiàn)

[5] Q.M.Z. Iqbal, A.L.S. Chan, Pedestrian level wind environment assessment around group of high-rise cross-shaped buildings: effect of building shape, separation and orientation, Build. Environ. 101 (2016) 45–63.

[10] H.W. Detering, D. Etling, application of the E-ε turbulence model to the atmospheric boundary layer, Boundary-Layer Meteorol. 33 (1985) 113–133.

[37] B. Blocken, LES over RANS in building simulation for outdoor and indoor applications: a foregone conclusion? Build. Simulat. 11 (2018) 821–870.

[38] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flows, Comput. Methods appl. Mech. Eng. 3 (1974) 269–289.

[39] V. Yakhot, S.A. Orszag, Renormalization-group Analysis of turbulence, Phys. Rev. Lett. 57 (1986) 1722.

[40] T.-H. Shih, W.W. Liou, A. Shabbir, Z. Yang, J. Zhu, A new k-ε eddy viscosity model for high Reynolds number turbulent flows, Comput. Fluids 24 (1995) 227–238.

[41] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605.

[42] J. Franke, A. Hellsten, H. Schlünzen, B. Carissimo, Best Practice Guideline for the CFD Simulation of Flows in the Urban Environment. COST Action 732: Quality Assurance and Improvement of Microscale Meteorological Models. Hamburg, Ger, 2007.

[43] Y. Tominaga, A. Mochida, R. Yoshie, H. Kataoka, T. Nozu, M. Yoshikawa, T. Shirasawa, AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings, J. Wind Eng. Ind. Aerod. 96 (2008) 1749–1761.

[45] A. Mochida, Y. Tominaga, S. Murakami, R. Yoshie, T. Ishihara, R. Ooka, Comparison of various ke models and DSM applied to flow around a high-rise building, Wind Struct. 5 (2002) 227–244.

[46] S. Murakami, R. Ooka, S. Kato, S. Iizuka, A. Mochida, Numerical prediction of flow around a building with various turbulence models: comparison of {kappa}-{var_epsilon} EVM, ASM, DSM, and LES wind tunnel tests, in: American Society of Heating, Refrigerating and Air-Conditioning Engineers, 1996.

[47] T. Shirasawa, A. Mochida, Y. Tominaga, H. Yoshino, Evaluation of turbulent time scale of linear revised κ-ε models based on LES data, Jpn. Wind Eng. Res. J. (JWE) (2006) 125–128.

[48] Y. Tominaga, Flow around a high-rise building using steady and unsteady RANS CFD: effect of large-scale fluctuations on the velocity statistics, J. Wind Eng. Ind. Aerod. 142 (2015) 93–103.

[49] S.B. Pope, Turbulent Flows, 2001.

[50] D.C. Wilcox, Turbulence Modeling for CFD, DCW Industries. Inc 5354, La Canada, California, 1998, pp. 124–128.

[51] P.G. Duynkerke, application of the E-ε turbulence closure model to the neutral and stable atmospheric boundary layer, J. Atmos. Sci. 45 (1988) 865–880.

[53] H. Mittal, A. Sharma, A. Gairola, Numerical simulation of pedestrian level wind conditions: effect of building shape and orientation, Environ. Fluid Mech. (2019) 1–26.

[54] H. Mittal, A. Sharma, A. Gairola, Numerical simulation of pedestrian level wind flow around buildings: effect of corner modification and orientation, J. Build. Eng. 22 (2019) 314–326,

[55] M. Shirzadi, P.A. Mirzaei, M. Naghashzadegan, Improvement of k-epsilon turbulence model for CFD simulation of atmospheric boundary layer around a high-rise building using stochastic optimization and Monte Carlo Sampling technique, J. Wind Eng. Ind. Aerod. 171 (2017),

[56] N. Glover, S. Guillas, L. Malki-Epshtein, Statistical calibration of CFD modelling for street canyon flows, in: Proceedings of Building Simulation 2011: 12th Conference of International Building Performance Simulation Association, International Building Performance Simulation Association (IBSPA), 2011, pp. 1513–1520.

[57] S. Guillas, N. Glover, L. Malki-Epshtein, Bayesian calibration of the constants of the k–ε turbulence model for a CFD model of street canyon flow, Comput. Methods appl. Mech. Eng. 279 (2014) 536–553.

[58] J.M. Gimenez, F. Bre, Optimization of RANS turbulence models using genetic algorithms to improve the prediction of wind pressure coefficients on low-rise buildings, J. Wind Eng. Ind. Aerod. 193 (2019) 103978,

[59] H. Yu, J. Th′e, Validation and optimization of SST k-ω turbulence model for pollutant dispersion within a building array, Atmos. Environ. 145 (2016) 225–238,?

3、第三篇文獻(xiàn)

Validation and optimization of SST k-u turbulence model for pollutant dispersion within a building array

CFD模擬通常需要高水平的計(jì)算資源，并且在驗(yàn)證之前不被認(rèn)為是準(zhǔn)確的(Blocken et al., 2013)。

通過(guò)發(fā)布綜合實(shí)踐指南支持城市環(huán)境中污染物擴(kuò)散的CFD模擬(Franke et al., 2007; Schatzmann et al., 2010; Tominaga et al., 2008)。

對(duì)于復(fù)雜建筑環(huán)境中污染物擴(kuò)散的CFD模擬已經(jīng)有了大量的研究。數(shù)值技術(shù)主要包括雷諾平均納維爾-斯托克斯(RANS)方法、大渦模擬(LES)和分離渦模擬(DES)?；趉-ε的RANS模型仍然是模擬復(fù)雜城市環(huán)境中污染物擴(kuò)散最常用的模型，因?yàn)樗骖櫫藴?zhǔn)確性和計(jì)算成本(Lateb et al., 2016; Pontiggia et al., 2010)。

雷諾應(yīng)力模型(RSM)是另一種用于復(fù)雜室外環(huán)境的RANS技術(shù)(Buccolieri et al., 201 1)。然而，與基于k-ε的模型相比，RSM方法經(jīng)常產(chǎn)生較差的結(jié)果，盡管它花費(fèi)更多的計(jì)算時(shí)間(Koutsourakis et al., 2012; Tominaga and Stathopoulos, 2013)。

更多數(shù)值參數(shù)的優(yōu)化被認(rèn)為是性能不佳的原因。The optimization of more numerical parameters was deemed responsible for the inferior performance (Tominaga and Stathopoulos, 2013).

LES本質(zhì)上比RANS模型更精確，因?yàn)樗梢圆蹲礁嗟奈锢硖卣?，包括流?dòng)不穩(wěn)定性和標(biāo)量的各向異性(Buccolieri et al., 2011)。然而，據(jù)報(bào)道LES的計(jì)算工作量高10-100倍(Cheng et al., 2003)。此外，LES對(duì)網(wǎng)格質(zhì)量和流入條件非常敏感(Xie and Castro, 2009)。

DES是一種混合方法，在靠近墻的區(qū)域使用RANS，在自由流中使用LES (Strelets, 2001)。

Kakosimos和Assael (2013年)采用基于SpalarteAllmaras湍流的DES方法模擬建筑陣列的濃度場(chǎng)，并獲得了可接受的驗(yàn)證指標(biāo)。這可能是現(xiàn)有方法的一種有前途的替代方法，但需要進(jìn)一步的探索。

基于k-ε的湍流模型的大多數(shù)缺點(diǎn)是顯而易見的。標(biāo)準(zhǔn)的k-ε模型不能一直積分到壁面，并且很難預(yù)測(cè)湍流產(chǎn)生遠(yuǎn)大于其耗散的流動(dòng)。這些類型流動(dòng)區(qū)域包括分離和沖擊(Li et al., 2006; Moukalled et al., 2015)。修正的k-ε模型不能捕捉尾流體積和升高位置的信息（the wake volume, and elevated positions）(Lateb et al., 2013; Tominaga and Stathopoulos, 2013)。

盡管近壁處理更好，但據(jù)作者所知，k-o閉合模型從未被報(bào)道用于污染物擴(kuò)散，這可能是由于其對(duì)自由流的敏感性。Menter提出的剪切應(yīng)力輸運(yùn)(SST) k-u模型綜合了k-ε和k-o模型的優(yōu)點(diǎn)(Menter, 1993, 1994)。因此，它可能是k-e家族的一個(gè)極好的替代品。然而，SST k-o模型方法很少用于模擬城市環(huán)境下的污染物遷移(Yu and The, 2016)。更重要的是，各種RANS模式之間的具體比較表明了SST k-o優(yōu)于同類產(chǎn)品。Daroczy et al. (2015)聲明SST k-o和可實(shí)現(xiàn)的k-ε模型是模擬H-Darrieus轉(zhuǎn)子的兩種合適的RANS模型。Ramponi and Blocken (2012) 明確指出SST k-o模型在建筑物的橫向通風(fēng)的流動(dòng)模擬中優(yōu)于其基于k-ε的競(jìng)爭(zhēng)對(duì)手。關(guān)于交叉通風(fēng)模擬的類似結(jié)論也被報(bào)道by Peren et al. (2015)。

非定常SST k-o模型能夠再現(xiàn)高層建筑后面和周圍的流動(dòng)不穩(wěn)定性，盡管它高估了建筑拐角處的流動(dòng)分離(Tominaga, 2015)。

SST k-o提供了與更為計(jì)算機(jī)密集型的DES模擬幾乎相同的結(jié)果(Yu and The, 2016)。

參考文獻(xiàn)

Blocken, B., Tominaga, Y., Stathopoulos, T., 2013. CFD simulation of micro-scale pollutant dispersion in the built environment. Build. Environ. 64, 225e230.

Franke, J., Hellsten, A., Schlünzen, H., Carissimo, B., 2007. Best Practice Guideline for the Cfd Simulation of Flows in the Urban Environment. Brussels, Belgium.

Schatzmann, M., Olesen, H., Frank, J., 2010. COST 732 Model Evaluation Case Studies: approach and Results. University of Hamburg, Hamburg, Germany, p. 122.

Tominaga, Y., Mochida, A., Yoshie, R., Kataoka, H., Nozu, T., Yoshikawa, M., Shirasawa, T., 2008. AIJ guidelines for practical applications of CFD to pedestrian wind environment around buildings. J. Wind Eng. Ind. Aerodyn. 96, 1749e1761.

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Pontiggia, M., Derudi, M., Alba, M., Scaioni, M., Rota, R., 2010. Hazardous gas releases in urban areas: assessment of consequences through CFD modelling. J. Hazard. Mater 176, 589e596.

Buccolieri, R., Salim, S.M., Leo, L.S., Di Sabatino, S., Chan, A., Ielpo, P., de Gennaro, G., Gromke, C., 2011. Analysis of local scale treeeatmosphere interaction on pollutant concentration in idealized street canyons and application to a real urban junction. Atmos. Environ. 45, 1702e1713.

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Tominaga, Y., Stathopoulos, T., 2013. CFD simulation of near-field pollutant dispersion in the urban environment: a review of current modeling techniques.? Atmos. Environ. 79, 716e730.

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Moukalled, F., Mangani, L., Darwish, M., 2015. The Finite Volume Method in Computational Fluid Dynamics: an Advanced Introduction with OpenFOAM and Matlab. Springer International Publishing.

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Yu, H.S., The, J., 2016. Simulation of gaseous pollutant dispersion around an isolated building using the k-u SST turbulence model. J. Air Waste Manag. Assoc. Accepted.

?Daroczy, L., Janiga, G., Petrasch, K., Webner, M., Thevenin, D., 2015. Comparative Analysis of turbulence models for the aerodynamic simulation of H-Darrieus rotors. Energy 90, 680e690. Part 1.

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?Tominaga, Y., 2015. Flow around a high-rise building using steady and unsteady RANS CFD: effect of large-scale fluctuations on the velocity statistics. J. Wind Eng. Ind. Aerodyn. 142, 93e103.

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