换热管及内外流体多场耦合数值分析方法研究
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摘要
管壳式换热器是过程工业中广泛应用的换热设备,换热效率分析、设备安全评价一直是换热器设计、运行维护中的关键技术问题。本文将管壳程流体与换热管结构相结合,开展流体域流场及温度场、结构域位移场及温度场的多场耦合数值分析方法研究,具有重要的学术价值和良好的工程应用前景。管壳式换热器多场耦合分析是一个涉及多物理场计算、多界面耦合和多参数迭代收敛的数值模拟,本着从简单到复杂的原则,开展如下研究工作。
首先,选择套管式换热器为研究对象,流体域多物理场分析采用有限体积法、结构域多物理场分析采用有限单元法,建立了小变形条件下轴对称结构与流体的多场耦合模型,推导了轴对称耦合界面温度与热量双向传递、界面载荷单向传递的插值计算公式和迭代格式,建立了耦合界面完全匹配网格的直接传递法、非匹配网格的最小距离法和函数插值矩阵法。算例表明：界面非匹配网格与匹配网格的数值模拟结果基本相同,验证了耦合界面非匹配网格插值算法的正确性；多场耦合数值模拟得到的套管式换热器光管管型总传热系数,与解析式计算结果的最大误差小于10.2%,为复杂管型换热系数计算提供了数值模型和计算方法。
其次,建立了径向大变形条件下轴对称结构与管程流体的多场耦合模型,推导了轴对称耦合界面位移和载荷双向传递的插值计算公式和迭代格式。算例表明：在低速层流作用下,随着径向位移的增大,流体进口压力减小,进出口温差减小,壁面传热系数下降,但流道中的主流速度和温度并没有出现扩展现象,换热性能降低。
其三,建立了横向振动条件下三维管壳结构与流体的多场耦合瞬态动力学模型,综合考虑拉格朗日和欧拉描述的优缺点,建立了套管式换热器任意拉格朗日欧拉动网格法,解决了流体域流动和结构域大变形、振动引起的网格变化问题；依据界面位移协调、载荷平衡,以及温度连续和热量守恒条件,推导了随时间变化的三维界面温度与热量、位移与载荷的多场耦合迭代格式,给出了收敛判断准则；根据流固耦合理论,建立了套管式换热器多场耦合充分算法,实现界面物理量的时间同步推进。算例表明：无阻尼振动换热管在壳程流体介质中作周期性衰减运动,衰减频率为80.1Hz,比固有频率101.5Hz下降了21%；还得到了激振力大小、激振力频率、壳程介质流速、密度、粘度、壳程外边界尺寸对套管式换热器多场耦合瞬态响应计算结果的影响规律。
其四,建立了旋转运动条件下细长管与管内外流体的流固耦合动力学模型,将细长管离散成梁单元,依据梁单元与流体域体积元关系,推导了三维柱面耦合边界时的位移和载荷插值计算公式,给出了收敛判断准则。算例表明：旋转细长管各处的横向运动轨迹不同,发生公转和自转现象,细长管与管内外流体耦合效应明显。
最后,建立了横向振动条件下多管束与流体的多场耦合瞬态动力学模型,推导了多管束耦合界面条件下的多场耦合迭代格式,给出了收敛判断准则,解决了换热管与换热管之间界面物理量相互影响与迭代收敛问题；运用分布式PC机求解技术,实现了PC机求解多界面多场耦合问题。算例表明：位于刚性换热管之中的弹性换热管瞬态响应呈现周期性发散状态,得到了正三角形和转角三角形排列弹性管束之间的瞬态响应规律,多管束与流体多场耦合呈现复杂的瞬态响应现象。
本文研究成果也可为热采井、海洋钻井隔水管束等石油钻采工程中的多场耦合分析提供理论基础和数值计算方法。
Shell-and-tube heat exchanger is widely used in the process industry. Heat transfer efficiency analysis, and equipment safety evaluation is the key technical issues in heat exchanger design, operation and maintenance. In this paper, tube-side and shell-side fluid is combined with the structure of heat exchange tube, numerical simulation method of multi-physics couping with flow and temperature field in fluid domain, and displacement and temperature field in structure domain, is carried out. It has important academic value and good prospects for engineering applications. Multi-field coupling analysis of shell-and-tube heat exchanger is numerical simulation, involving multi-field calculation, multi-interface coupling and multi-parameter iterative. At the point of gradual research principle from the simple to complex issues, the research work are as follows.
First, select casing heat exchanger as the research object, use finite volume method to analysis multi-physics of fluid domain, use finite element method to analysis multi-physics of solid domain. Under the condition of small deformation, the multi-field coupled model of axisymmetric fluid and solid is established. For two-way transfer of temperature and heat flux and one-way transfer of force at the two-dimensional coupling interface, the interpolation formula and iterative is derived. Direct transfer method of exactly match grid, the minimum distance method and interpolation function matrix method of non-matching grid is established. The example shows that non-matching grid interfaces with the matching grid interfaces have the same numerical results. The accuracy of non-matching grid interpolation algorithm is verified. Compared the numerical result of multi-field coupling with analytical formula, the maximum error of the overall heat transfer coefficient is 10.2%. It provides numerical model and method for the heat transfer coefficient calculation of complex heat exchange tube.
Second, under the condition of large radial deformation, the multi-field coupled model of the symmetry structure and tube-side fluid is established. For two-way coupling of displacement and force at the coupling interface, the interpolation formula and iterative scheme is derived. The example shows that, under the low speed laminar flow, with the increase of radial displacement, inlet pressure decreases, temperature difference between the inlet and outlet increases, wall heat transfer coefficient decreases, but the mainstream flow velocity and temperature has no expansion, the heat transfer performance is decreases.
Third, under the condition of lateral vibration, the multi-field coupled transient dynamic model of three-dimensional shell-and-tube structure and fluid is established. Considering the advantages and disadvantages of Lagrangian and Eulerian description, ALE moving grid method is established to solve the flow of fluid domain, and the problems of large deformation and transient problems of solid domain. Basis on the conditione of the interface displacement compatibility, load balance, temperature continuity and energy conservation, iterative scheme of temperature and heat flux, displacement and force for multi-field coupling is derived, and convergence criterion is given. According to theory of fluid-structure interaction, the full algorithm of multi-physics couping to promote physical value with synchronization time. The example shows that tube without damping vibration has periodic motion attenuation, attenuation frequency is 80.1 Hz, it decreases by 21% from natural frequency. The inflence of the exciting force, the exciting force frequency, shell-side fluid velocity, density, viscosity, size of the outer boundary of the shell side on transient response of casing heat exchanger, is also received.
Fourth, under the condition of rotate movement, the dynamics model of fluid-structure interaction for slender tube with its inner pipe fluid and outer annular fluid is established. The slender tube discretes into beam elements, based on the relationship of beam element and volume element, interpolation formula of displacement and force is derived, and the convergence criterion is given. The example shows that horizontal trajectory of rotating slender tube is diferent at different parts, and the phenomenon of revolution and rotation occures. Slender tube with its fluids has a strong coupled phenomenon.
Finally, under the condition of transverse vibration, the multi-field coupled transient dynamic model of multi-tube bundles and fluid is established. Iterative scheme of multi-interface and multi-field is derived, and the convergence criterion is given. The problem of physical interaction and iterative convergence between tubes is solved. Using distributed technology, the caculation of large-scale multi-bundle and multi-field coupling numerical simulation is realized. The example shows that the flexibe tube in rigid tubes has cyclical divergence transient state. The inflence of flexibe multi-bundles on transient response is received. Multi-bundles and fluid presents complex multi-field coupling phenomena.
This research also provides the theoretical basis and numerical methods for thermal recovery wells, offshore drilling riser tubes and other oil drilling enginering in the multi-field coupling analysis.
首先,选择套管式换热器为研究对象,流体域多物理场分析采用有限体积法、结构域多物理场分析采用有限单元法,建立了小变形条件下轴对称结构与流体的多场耦合模型,推导了轴对称耦合界面温度与热量双向传递、界面载荷单向传递的插值计算公式和迭代格式,建立了耦合界面完全匹配网格的直接传递法、非匹配网格的最小距离法和函数插值矩阵法。算例表明：界面非匹配网格与匹配网格的数值模拟结果基本相同,验证了耦合界面非匹配网格插值算法的正确性；多场耦合数值模拟得到的套管式换热器光管管型总传热系数,与解析式计算结果的最大误差小于10.2%,为复杂管型换热系数计算提供了数值模型和计算方法。
其次,建立了径向大变形条件下轴对称结构与管程流体的多场耦合模型,推导了轴对称耦合界面位移和载荷双向传递的插值计算公式和迭代格式。算例表明：在低速层流作用下,随着径向位移的增大,流体进口压力减小,进出口温差减小,壁面传热系数下降,但流道中的主流速度和温度并没有出现扩展现象,换热性能降低。
其三,建立了横向振动条件下三维管壳结构与流体的多场耦合瞬态动力学模型,综合考虑拉格朗日和欧拉描述的优缺点,建立了套管式换热器任意拉格朗日欧拉动网格法,解决了流体域流动和结构域大变形、振动引起的网格变化问题；依据界面位移协调、载荷平衡,以及温度连续和热量守恒条件,推导了随时间变化的三维界面温度与热量、位移与载荷的多场耦合迭代格式,给出了收敛判断准则；根据流固耦合理论,建立了套管式换热器多场耦合充分算法,实现界面物理量的时间同步推进。算例表明：无阻尼振动换热管在壳程流体介质中作周期性衰减运动,衰减频率为80.1Hz,比固有频率101.5Hz下降了21%；还得到了激振力大小、激振力频率、壳程介质流速、密度、粘度、壳程外边界尺寸对套管式换热器多场耦合瞬态响应计算结果的影响规律。
其四,建立了旋转运动条件下细长管与管内外流体的流固耦合动力学模型,将细长管离散成梁单元,依据梁单元与流体域体积元关系,推导了三维柱面耦合边界时的位移和载荷插值计算公式,给出了收敛判断准则。算例表明：旋转细长管各处的横向运动轨迹不同,发生公转和自转现象,细长管与管内外流体耦合效应明显。
最后,建立了横向振动条件下多管束与流体的多场耦合瞬态动力学模型,推导了多管束耦合界面条件下的多场耦合迭代格式,给出了收敛判断准则,解决了换热管与换热管之间界面物理量相互影响与迭代收敛问题；运用分布式PC机求解技术,实现了PC机求解多界面多场耦合问题。算例表明：位于刚性换热管之中的弹性换热管瞬态响应呈现周期性发散状态,得到了正三角形和转角三角形排列弹性管束之间的瞬态响应规律,多管束与流体多场耦合呈现复杂的瞬态响应现象。
本文研究成果也可为热采井、海洋钻井隔水管束等石油钻采工程中的多场耦合分析提供理论基础和数值计算方法。
Shell-and-tube heat exchanger is widely used in the process industry. Heat transfer efficiency analysis, and equipment safety evaluation is the key technical issues in heat exchanger design, operation and maintenance. In this paper, tube-side and shell-side fluid is combined with the structure of heat exchange tube, numerical simulation method of multi-physics couping with flow and temperature field in fluid domain, and displacement and temperature field in structure domain, is carried out. It has important academic value and good prospects for engineering applications. Multi-field coupling analysis of shell-and-tube heat exchanger is numerical simulation, involving multi-field calculation, multi-interface coupling and multi-parameter iterative. At the point of gradual research principle from the simple to complex issues, the research work are as follows.
First, select casing heat exchanger as the research object, use finite volume method to analysis multi-physics of fluid domain, use finite element method to analysis multi-physics of solid domain. Under the condition of small deformation, the multi-field coupled model of axisymmetric fluid and solid is established. For two-way transfer of temperature and heat flux and one-way transfer of force at the two-dimensional coupling interface, the interpolation formula and iterative is derived. Direct transfer method of exactly match grid, the minimum distance method and interpolation function matrix method of non-matching grid is established. The example shows that non-matching grid interfaces with the matching grid interfaces have the same numerical results. The accuracy of non-matching grid interpolation algorithm is verified. Compared the numerical result of multi-field coupling with analytical formula, the maximum error of the overall heat transfer coefficient is 10.2%. It provides numerical model and method for the heat transfer coefficient calculation of complex heat exchange tube.
Second, under the condition of large radial deformation, the multi-field coupled model of the symmetry structure and tube-side fluid is established. For two-way coupling of displacement and force at the coupling interface, the interpolation formula and iterative scheme is derived. The example shows that, under the low speed laminar flow, with the increase of radial displacement, inlet pressure decreases, temperature difference between the inlet and outlet increases, wall heat transfer coefficient decreases, but the mainstream flow velocity and temperature has no expansion, the heat transfer performance is decreases.
Third, under the condition of lateral vibration, the multi-field coupled transient dynamic model of three-dimensional shell-and-tube structure and fluid is established. Considering the advantages and disadvantages of Lagrangian and Eulerian description, ALE moving grid method is established to solve the flow of fluid domain, and the problems of large deformation and transient problems of solid domain. Basis on the conditione of the interface displacement compatibility, load balance, temperature continuity and energy conservation, iterative scheme of temperature and heat flux, displacement and force for multi-field coupling is derived, and convergence criterion is given. According to theory of fluid-structure interaction, the full algorithm of multi-physics couping to promote physical value with synchronization time. The example shows that tube without damping vibration has periodic motion attenuation, attenuation frequency is 80.1 Hz, it decreases by 21% from natural frequency. The inflence of the exciting force, the exciting force frequency, shell-side fluid velocity, density, viscosity, size of the outer boundary of the shell side on transient response of casing heat exchanger, is also received.
Fourth, under the condition of rotate movement, the dynamics model of fluid-structure interaction for slender tube with its inner pipe fluid and outer annular fluid is established. The slender tube discretes into beam elements, based on the relationship of beam element and volume element, interpolation formula of displacement and force is derived, and the convergence criterion is given. The example shows that horizontal trajectory of rotating slender tube is diferent at different parts, and the phenomenon of revolution and rotation occures. Slender tube with its fluids has a strong coupled phenomenon.
Finally, under the condition of transverse vibration, the multi-field coupled transient dynamic model of multi-tube bundles and fluid is established. Iterative scheme of multi-interface and multi-field is derived, and the convergence criterion is given. The problem of physical interaction and iterative convergence between tubes is solved. Using distributed technology, the caculation of large-scale multi-bundle and multi-field coupling numerical simulation is realized. The example shows that the flexibe tube in rigid tubes has cyclical divergence transient state. The inflence of flexibe multi-bundles on transient response is received. Multi-bundles and fluid presents complex multi-field coupling phenomena.
This research also provides the theoretical basis and numerical methods for thermal recovery wells, offshore drilling riser tubes and other oil drilling enginering in the multi-field coupling analysis.
引文
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