﻿ 长时间流固耦合传热过程的快速算法<sup>*</sup>
 文章快速检索 高级检索

A fast algorithm for long-term fluid-solid conjugate heat transfer process
MENG Fanchao, DONG Sujun, JIANG Hongsheng, WANG Jun
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-05-24; Accepted: 2016-10-14; Published online: 2016-11-16 10:10
Corresponding author. DONG Sujun, E-mail:dsj@buaa.edu.cn
Abstract: Concerning the specific demands for solving problems of the long-term conjugate heat transfer (CHT) problem at the kilosecond level, a new loosely coupled algorithm of the global tightly transient coupled heat transfer based on the quasi-steady flow field is put forward. The flow field is updated alone by steady algorithm and the transient temperature field of the fluid and solid regions are solved by transient heat transfer algorithm alternately. Compared to the traditional loosely coupled algorithm, the computational efficiency is further improved with the greatly reduced update frequency of the flow field. Taking a tube heated by inner forced air flow heating process for 300 s as an example, the results by Fluent software show that, compared to the tightly transient coupled calculation, the maximum wall temperature rise deviation is 5% while the computing time is reduced to 14.8%.
Key words: fluid-solid conjugate heat transfe     loosely coupled     quasi-steady     computational fluid dynamics (CFD)     forced convection

1 总体算法

 T—温度; Pf—流体压力; Vf—流体速度; Δtf—稳态流场更新步长; Δtc—瞬态时间步长; n—瞬态迭代步数; Tw—壁面温度 图 1 新型松耦合算法流程示意图 Fig. 1 Flow diagram of new loosely coupled algorithm

1) t0时刻：初始化流体和固体区域温度场。

2) 更新流场：单独对流体区域稳态流场进行求解，即将流固耦合壁面设为固定温度边界，联立求解流体区域稳态动量、湍流及能量方程，获得稳态流场。

3) 瞬态温度场计算：同时对流体区域和固体区域进行瞬态传热计算，即将流固耦合壁面设为传热耦合边界，联立求解流体及固体区域瞬态能量方程，获得每时刻温度场分布情况，直至下一个流场更新时刻。

4) 重复2)、3) 两步，交替进行流场更新和瞬态温度场计算，直至计算终止时刻t

 (1)

 (2)

2 控制方程及数值算法

2.1 准稳态流场

 (3)

1) 假定一个速度分布，记为V0，以此计算动量离散方程中的系数和常数项。

2) 假定一个压力场p*，依次求解各方向上的动量方程，得到新的速度分布，记为V*

3) 求解压力修正方程，得p′

4) 据p′改进速度值V′。

6) 利用改进后的速度场V求解那些通过源项、物性等与速度场耦合的变量，如果变量并不影响流场，则应在速度场收敛后再求解。

7) 利用改进后的速度场重新计算动量离散方程的系数，并用改进后的压力场作为下一层迭代的初值，重复上述步骤，直到获得收敛解。

2.2 流固耦合瞬态温度场

 (4)

 (5)

 (6)
 (7)

1) 假定耦合边界上的温度分布，作为流体区域的边界条件。

2) 对其中流体区域进行稳态求解，得出耦合边界上的局部热流密度和温度梯度，作为固体区域的边界条件。

3) 求解固体区域，得出耦合边界上新的温度分布，作为流体区域的边界条件。

4) 重复2)、3) 两步计算，直到收敛。

3 定来流强制对流加热问题分析

 图 2 空气内加热管几何模型 Fig. 2 Geometric model of inner-air-heated tube

3.1 准稳态流场假设的合理性分析

Fluent软件瞬态紧耦合算法获得位置6~位置10处管内流体静压值随时间变化曲线如图 3所示。从中可以看出：计算初期，各位置处流体静压均有一定波动，且距入口越远波动越不明显，约0.5 s后各位置处流体静压均基本达到稳定。

 图 3 管内不同位置处空气静压变化曲线 Fig. 3 Changing curves of inner air staticpressure at different locations

3.2 管体结构瞬态温度场对比分析

 图 4 2种算法所得不同位置管体温升、温升绝对偏差及温升相对偏差变化曲线 Fig. 4 Changing curves of wall temperature rise, absolutedeviation of wall temperature rise and relative deviation ofwall temperature rise at different locations by two algorithms

1) 如图 4(a)所示，与紧耦合算法相比，松耦合计算的温升总体在入口处偏低，出口处偏高，且由于出口处总体温升值较小，导致其在温升绝对偏差近似的情况下温升的相对偏差值略高。

2) 如图 4(b)所示，两者绝对偏差随着时间呈现一定波动，离入口越远波动周期越长，且入口处波动幅度最大，在42.5 s时达到最大值1.4 K左右。

3) 如图 4(c)所示，两者各位置相对偏差均在初始时刻最大，并逐渐趋近于0。如管体三处温升相对偏差25 s时均已下降到4%以内，100 s时下降到1%以内。

 图 5 2种算法所得不同时刻管体温升分布对比曲线 Fig. 5 Contrast curves of wall temperature rise distribution at different moments by two algorithms

 K 时刻/s 位置1 位置2 位置3 位置4 位置5 紧耦合 松耦合 偏差 紧耦合 松耦合 偏差 紧耦合 松耦合 偏差 紧耦合 松耦合 偏差 紧耦合 松耦合 偏差 100 71.79 71.24 -0.55 49.43 49.38 -0.05 36.43 36.53 0.10 26.72 26.84 0.12 20.09 20.37 0.28 200 90.41 90.78 0.37 77.80 77.46 -0.34 65.10 64.89 -0.21 53.68 53.61 -0.07 44.95 45.08 0.13 300 96.45 96.79 0.34 90.62 90.57 -0.05 82.36 82.20 -0.16 73.44 73.28 -0.16 65.93 65.80 -0.13

3.3 计算效率对比分析

 图 6 定来流工况下，管内壁热流随时间变化曲线 Fig. 6 Curve of inner wall heat flux variation with time under constant flow rate condition

4 结论

1) 本文算法避免了传统松耦合算法需要不断调用流场计算以更新流固耦合壁面上热流密度值问题，只要流场不变就不需要更新流场，进而大大减小流场更新频率，进一步提高计算效率。

2) 针对该类管内定来流速度强制对流耦合传热问题，采用本文算法可以在保证瞬态温度场计算精度的情况下，将计算效率提高近一个量级，进而满足工程上对长时间流固耦合传热过程的求解需求。

3) 该管内强迫对流算例中，由边界流动参数的变化引起管内流场不稳定时间大约只有0.5 s。这与不可压流场的快速传播特性是相符的，同时也说明本文算法中基于准稳态流场的假设是具有一定适应性的，如类似不可压流体长时间耦合传热问题，只要边界流动参数阶跃变化间隔远大于0.5 s这个量级，都可以考虑采用本文算法在保证计算精度的同时提高计算效率。

 [1] STOKOS K, VRAHLIOTIS S, PAPPOU T, et al. Development and validation of an incompressible Navier-Stokes solver including convective heat transfer[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2015, 25(4): 861–886. [2] HOOPER R W, SMITH T M, OBER C C.Enabling fluid-structural strong thermal coupling within a multi-physics environment[C]//44th AIAA Aerospace Sciences Meeting and Exhibit.Reston:AIAA, 2006:1-10. [3] KAZEMI-KAMYAB V, VAN ZUIJLEN A H, BIJL H. Analysis and application of high order implicit Runge-Kutta schemes for unsteady conjugate heat transfer:A strongly-coupled approach[J]. Journal of Computational Physics, 2014, 272: 471–486. DOI:10.1016/j.jcp.2014.04.016 [4] 曾大文, 黄开金. 非交错网格下三维准稳态激光重熔熔池数值模拟[J]. 计算物理, 1999, 16(6): 616–623. ZENG D W, HUANG K J. Numerical simulation of three dimensional quasi-steady state laser melted pools on the non-staggered grids[J]. Chinese Journal of Computational Physics, 1999, 16(6): 616–623. (in Chinese) [5] 殷鹏飞, 张蓉, 熊江涛, 等. 搅拌摩擦焊准稳态温度场数值模拟[J]. 西北工业大学学报, 2012, 30(4): 622–627. YIN P F, ZHANG R, XIONG J T, et al. An effective numerical simulation of temperature distribution of friction stir welding in quasi-steady-state[J]. Journal of Northwestern Polytechnical University, 2012, 30(4): 622–627. (in Chinese) [6] BAUMAN P T, STOGNER R, CAREY G F, et al. Loose-coupling algorithm for simulating hypersonic flows with radiation and ablation[J]. Journal of Spacecraft and Rockets, 2011, 48(1): 72–80. DOI:10.2514/1.50588 [7] KAZEMI-KAMYAB V, VAN ZUIJLEN A H, BIJL H. A high order time-accurate loosely-coupled solution algorithm for unsteady conjugate heat transfer problems[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 264: 205–217. DOI:10.1016/j.cma.2013.05.021 [8] KAZEMI-KAMYAB V, VAN ZUIJLEN A H, BIJL H. Accuracy and stability analysis of a second-order time-accurate loosely coupled partitioned algorithm for transient conjugate heat transfer problems[J]. International Journal for Numerical Methods in Fluids, 2014, 74(2): 113–133. DOI:10.1002/fld.v74.2 [9] LOHNER R, YANG C, CEBRAL J, et al.Fluid-structure-thermal interaction using a loose coupling algorithm and adaptive unstructured grids[C]//Proceedings of 29th AIAA Fluid Dynamics Conference.Reston:AIAA, 1998:1-16. [10] LI Q, LIU P, HE G. Fluid-solid coupled simulation of the ignition transient of solid rocket motor[J]. Acta Astronautica, 2015, 110: 180–190. DOI:10.1016/j.actaastro.2015.01.017 [11] MILLER B A, CROWELL A R, MCNAMARA J J.Loosely coupled time-marching of fluid-thermal-structural interactions:AIAA-2013-1666[R].Reston:AIAA, 2013. [12] KONTINOS D. Coupled thermal analysis method with application to metallic thermal protection panels[J]. Journal of Thermophysics and Heat Transfer, 1997, 11(2): 173–181. DOI:10.2514/2.6249 [13] CHEN Y K, MILOS F S, GOKCEN T. Loosely coupled simulation for two-dimensional ablation and shape change[J]. Journal of Spacecraft & Rockets, 2010, 47(5): 775–785. [14] ZHANG S, CHEN F, LIU H. Time-adaptive, loosely coupled strategy for conjugate heat transfer problems in hypersonic flows[J]. Journal of Thermophysics and Heat Transfer, 2014, 28(4): 1–12. [15] AMES W F. Numerical methods for partial differential equations[M].2nd edNew York: Academic Press, 1977: 114-151.

#### 文章信息

MENG Fanchao, DONG Sujun, JIANG Hongsheng, WANG Jun

A fast algorithm for long-term fluid-solid conjugate heat transfer process

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(6): 1224-1230
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0447