基于化學勢的多相流晶格Boltzmann方法的研究
發(fā)布時間：2019-03-14 09:29
【摘要】：自然界普遍存在的多相流現(xiàn)象在工農(nóng)業(yè)生產(chǎn)、科學研究和日常生活中具有廣泛的應用,它的相間涉及表面現(xiàn)象、熱力學與流體力學的平衡問題,存在傳熱、傳質(zhì)和化學反應等復雜的物理化學過程,這些效應使得多相流問題的研究變得極為復雜,也正因此,關于多相流現(xiàn)象的研究一直是流體力學領域的熱點。計算流體動力學(Computational Fluid Dynamics,CFD)是人們在借助數(shù)值與離散的方研究流體運動的長期實踐中不斷發(fā)展形成的一門學科,它在研究包括多相流在內(nèi)的復雜流體運動方面取得了巨大的成功。然而,由于多相流常常呈現(xiàn)十分復雜的幾何界面,且伴隨著劇烈的界面拓撲形變(如液滴的聚合與分裂等),傳統(tǒng)的CFD方法對多相流的進一步研究將遭遇瓶頸,即復雜幾何邊界下的Navier-Stokes方程不易求解,對發(fā)生劇烈拓撲形變的界面追蹤也非常困難。晶格Boltzmann方法(Lattice Boltzmann method,LBM)以分子動力學為基礎,是連續(xù)Boltzmann方程的一種特殊離散格式,屬于新興的介觀方法,兼有連續(xù)理論和微觀方法的優(yōu)勢,在研究復雜流體運動方面取得了顯著成功,尤其是在多相流研究方面具有突出的表現(xiàn),已經(jīng)得到了人們的高度認同。與傳統(tǒng)的CFD方法相比至少具有如下優(yōu)勢:1.算法簡單,無需直接求解復雜的Navier-Stokes方程而僅需求解簡單的晶格Boltzmann方程;2.易于處理復雜的幾何邊界條件,也無需顯式地追蹤界面,界面的變化自然地蘊含于簡單的演化過程;3.LBM的演化具有局域性,非常適合于高性能并行計算等。經(jīng)過近30年的發(fā)展和完善,LBM已經(jīng)成為了一種新的、不可替代的計算流體動力學方法,在研究多相流方面占據(jù)了重要地位,成為了主流的研究方法之一。迄今為止,已經(jīng)得到人們共同認可、并得到廣泛流行與成功應用的LBM多相流模型主要有偽勢模型和自由能模型,然而,這兩個模型及其后續(xù)的改進均不能同時滿足伽利略不變性和熱力學一致性——偽勢模型不具有熱力學一致性,而自由能模型則不能滿足伽利略不變性。不具有熱力學一致性的模型將難以準確地刻畫系統(tǒng)的熱力學行為,而不滿足伽利略不變性的模型則無法精確地描述運動系統(tǒng)的特性。本人參加的課題小組圍繞這一問題深入分析了這兩個模型的原理,在借助自由能和壓力張量計算非理想力的基礎上,提出了一種基于壓力張量的晶格Boltzmann多相流模型(簡稱:壓力張量模型,EPL,112(2015)44002),并從理論和數(shù)值實驗的角度驗證了新模型既具有熱力學一致性又滿足伽利略不變性,其算法簡單易于實現(xiàn),且模擬一級相變所得的兩相共存曲線與理論吻合更好,有望獲得進一步地推廣和應用。盡管壓力張量模型無論在理論上,還是數(shù)值上都有明顯優(yōu)勢,也有很好的推廣應用前景,然而,本文在深入地研究中發(fā)現(xiàn)該模型尚有進一步改進與提升的空間。首先通過壓力張量或許并非最佳、更非唯一計算非理想力的有效途徑,系統(tǒng)的自由能、化學勢和熵等均是能很好描述系統(tǒng)熱力學行為的宏觀量,尤其是化學勢在描述相平衡和化學平衡時具有獨特的優(yōu)勢;另一方面,受限多相流系統(tǒng)的流固潤濕邊界條件采用壓力張量難以直接表述,采用有效密度表達也具有一定復雜性,采用化學勢描述潤濕中固相與液相的相互作用可能更方便。于是,本文從化學勢入手對原壓力張量模型進行了探索與改進,通過推導獲得的基于化學勢的非理想力計算公式,構建了基于化學勢的晶格Boltzmann多相流模型(簡稱:化學勢模型),同樣由化學勢出發(fā),發(fā)展了一套基于化學勢的流固潤濕邊界條件(簡稱:化學勢潤濕邊界條件)。經(jīng)理論和數(shù)值實驗檢驗,本文提出的新模型與潤濕邊界條件主要具有如下優(yōu)勢與特色:1.由于是對原壓力張量模型的改進與完善,化學勢模型仍然既具有熱力學一致性同時又滿足伽利略不變性,且化學勢模型與潤濕邊界條件通過化學勢在理論上達到了統(tǒng)一與自洽,在數(shù)值計算上達到了相互協(xié)調(diào)與共享。2.化學勢模型與潤濕邊界條件較之壓力張量模型算法更簡潔,通過典型的van der waals流體一級相變模擬實驗表明:新的化學勢模型在計算精度、計算效率和穩(wěn)定性上均有不同程度地提升,充分說明其在數(shù)值方面也具有系統(tǒng)的、全面的優(yōu)勢。3.幾種常用非理想流體(包括:van der waals,Peng-Robinson,Redlich-Kwong Soave和Carnahan-Starling流體)一級相變和具有不同速度的van der Waals液滴變形模擬表明,化學勢模型數(shù)值上能很好地描述非理想流體的兩相共存現(xiàn)象,也準確地滿足伽利略不變性。4.初步應用于固壁表面van der Waals液滴潤濕現(xiàn)象的實例充分說明,化學勢模型與潤濕邊界條件的實現(xiàn)與應用方便、可行。數(shù)值實驗中發(fā)現(xiàn)潤濕接觸角隨指定的固壁表面化學勢變化幾乎是線性的,使得實際應用中通過調(diào)整表面化學勢以獲得所需要的接觸角變得十分簡單,因此化學勢模型與潤濕邊界條件應用于表面潤濕現(xiàn)象的研究具有足夠的優(yōu)勢。5.由于化學勢是描述熱力學系統(tǒng)的一個重要而又普適的宏觀量,因此化學勢模型及潤濕邊界條件能夠直接推廣應用于具有電磁場環(huán)境或存在化學反應的多相流系統(tǒng)的研究。以上優(yōu)勢與特色展現(xiàn)了化學勢模型與潤濕邊界條件具有較堅實的理論基礎和出色的數(shù)值性能,有望在多相流領域中得到普遍地推廣與應用。
[Abstract]:The phenomenon of multi-phase flow in nature has a wide application in industrial and agricultural production, scientific research and daily life, and its phases involve surface phenomena, thermodynamic and fluid mechanics balance problems, and there are complex physical and chemical processes such as heat transfer, mass transfer and chemical reaction. These effects make the study of the multi-phase flow problem very complex, and therefore, the research on the multi-phase flow phenomenon has been a hot spot in the field of fluid mechanics. Computational Fluid Dynamics (CFD) is a subject of constant development in the long-term practice of fluid movement by means of numerical and discrete research, which has made great success in the study of complex fluid movement, including multi-phase flow. However, because the multi-phase flow often presents a very complex geometric interface, and with the severe interface topology deformation (such as the polymerization and splitting of the droplets, etc.), the conventional CFD method will encounter the bottleneck of the further study of the multi-phase flow, that is, the Navier-Stokes equations under the complex geometric boundary are not easy to solve, It is also very difficult to trace the interface with violent topological deformation. Lattice Boltzmann method (LBM), based on the molecular dynamics, is a special discrete form of the continuous Boltzmann equation, and belongs to the new mesoscopic method. In particular, it has outstanding performance in the research of multi-phase flow, and has been highly accepted by people. Compared with the traditional CFD method, at least the following advantages are:1. The algorithm is simple, and the complex Navier-Stokes equations need not be solved directly, but only a simple lattice Boltzmann equation is needed. It is easy to handle complex geometric boundary conditions, and does not need to track the interface explicitly, and the change of the interface is naturally contained in the simple evolution process;3. The evolution of the LBM is local, and is very suitable for high-performance parallel computing and the like. After nearly 30 years of development and improvement, the LBM has become a new and irreplaceable computational fluid dynamic method, which has taken an important position in the research of multi-phase flow and has become one of the main research methods. So far, the LBM multi-phase flow model, which has been widely accepted and widely popular and successfully applied, has a pseudo-potential model and a free-energy model, however, The two models and their subsequent improvements can not meet the Galileo invariance and the thermodynamic consistency. The pseudo-potential model does not have the thermodynamic consistency, and the free energy model can not satisfy the Galileo invariance. The model that does not have the thermodynamic consistency will not be able to accurately describe the thermodynamic behavior of the system, and the model that does not meet the Galileo invariance can not accurately describe the characteristics of the moving system. On the basis of calculating the non-ideal force with the aid of the free energy and the pressure tensor, a lattice Boltzmann multi-phase flow model based on the pressure tensor is proposed, which is called the pressure tensor model, EPL,112 (2015)44002). From the theoretical and numerical experiments, the new model is proved to have both thermodynamic consistency and Galileo invariance. The algorithm is simple and easy to realize, and the two-phase co-existence curve obtained by the simulation of one-stage phase change is better with the theory, and is expected to be further promoted and applied. Although the pressure tensor model has obvious advantages in both the theory and the numerical value, it has a good application prospect. However, this paper has found that the model has further improved and improved space in the in-depth study. First, through the pressure tensor may not be the best, more than the only effective way to calculate the non-ideal force, the free energy, chemical potential and entropy of the system can describe the macroscopic quantity of the thermodynamic behavior of the system, especially the chemical potential has a unique advantage when describing the phase equilibrium and the chemical balance; On the other hand, the fluid-solid wetting boundary condition of the constrained multi-phase flow system is difficult to express directly by the pressure tensor, and the effective density expression also has a certain complexity, and the chemical potential is used to describe the interaction between the solid phase and the liquid phase in the wetting. In this paper, the original pressure tensor model is explored and improved from the chemical potential, and a chemical potential-based lattice Boltzmann multi-phase flow model (the chemical potential model) is constructed by the derivation of a chemical potential-based non-ideal force calculation formula, which is also based on the chemical potential. A set of flow-solid wetting boundary conditions based on chemical potential is developed (for short, chemical potential wetting boundary conditions). Based on the theoretical and numerical experiments, the new model and the wetting boundary condition have the following advantages and characteristics:1. because of the improvement and perfection of the original pressure tensor model, the chemical potential model still has both the thermodynamic consistency and the Galileo invariance, and the chemical potential model and the wetting boundary condition are in a unified and self-consistent theory through the chemical potential, In that numerical calculation, the mutual coordination and share are achieved. The chemical potential model and the wetting boundary condition are more concise than the pressure tensor model algorithm, and through a typical van der waals fluid-level phase change simulation experiment, the new chemical potential model has different degrees of improvement in the calculation accuracy, the calculation efficiency and the stability, It fully shows that it also has a systematic and comprehensive advantage in the field of numerical value. Several commonly used non-ideal fluids (including van der waals, Peng-Robinson, Redlich-Kwang Soave and Carnahan-Starling fluid) and van der Waals droplet deformation simulation with different speeds show that the chemical potential model can well describe the two-phase co-existence of the non-ideal fluid, Galileo invariance is also exactly satisfied. The examples of the wetting phenomenon of the van der Waals droplet on the surface of the solid wall show that the realization and application of the chemical potential model and the wetting boundary condition are convenient and feasible. in that numerical experiment, it is found that the wetting contact angle is almost linear with the change of the chemical potential of the specified solid wall surface, so that the required contact angle is very simple by adjusting the surface chemical potential in the practical application, Therefore, the application of the chemical potential model and the wetting boundary condition to the surface wetting phenomenon has a sufficient advantage. Since the chemical potential is an important and universal macroscopic quantity for describing the thermodynamic system, the chemical potential model and the wetting boundary condition can be directly applied to the research of a multi-phase flow system with an electromagnetic field environment or a chemical reaction. The above advantages and characteristics show that the chemical potential model and the wetting boundary condition have a solid theoretical foundation and excellent numerical performance, and are expected to be widely promoted and applied in the field of multi-phase flow.
【學位授予單位】：廣西師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O641
本文編號：2439861
[Abstract]:The phenomenon of multi-phase flow in nature has a wide application in industrial and agricultural production, scientific research and daily life, and its phases involve surface phenomena, thermodynamic and fluid mechanics balance problems, and there are complex physical and chemical processes such as heat transfer, mass transfer and chemical reaction. These effects make the study of the multi-phase flow problem very complex, and therefore, the research on the multi-phase flow phenomenon has been a hot spot in the field of fluid mechanics. Computational Fluid Dynamics (CFD) is a subject of constant development in the long-term practice of fluid movement by means of numerical and discrete research, which has made great success in the study of complex fluid movement, including multi-phase flow. However, because the multi-phase flow often presents a very complex geometric interface, and with the severe interface topology deformation (such as the polymerization and splitting of the droplets, etc.), the conventional CFD method will encounter the bottleneck of the further study of the multi-phase flow, that is, the Navier-Stokes equations under the complex geometric boundary are not easy to solve, It is also very difficult to trace the interface with violent topological deformation. Lattice Boltzmann method (LBM), based on the molecular dynamics, is a special discrete form of the continuous Boltzmann equation, and belongs to the new mesoscopic method. In particular, it has outstanding performance in the research of multi-phase flow, and has been highly accepted by people. Compared with the traditional CFD method, at least the following advantages are:1. The algorithm is simple, and the complex Navier-Stokes equations need not be solved directly, but only a simple lattice Boltzmann equation is needed. It is easy to handle complex geometric boundary conditions, and does not need to track the interface explicitly, and the change of the interface is naturally contained in the simple evolution process;3. The evolution of the LBM is local, and is very suitable for high-performance parallel computing and the like. After nearly 30 years of development and improvement, the LBM has become a new and irreplaceable computational fluid dynamic method, which has taken an important position in the research of multi-phase flow and has become one of the main research methods. So far, the LBM multi-phase flow model, which has been widely accepted and widely popular and successfully applied, has a pseudo-potential model and a free-energy model, however, The two models and their subsequent improvements can not meet the Galileo invariance and the thermodynamic consistency. The pseudo-potential model does not have the thermodynamic consistency, and the free energy model can not satisfy the Galileo invariance. The model that does not have the thermodynamic consistency will not be able to accurately describe the thermodynamic behavior of the system, and the model that does not meet the Galileo invariance can not accurately describe the characteristics of the moving system. On the basis of calculating the non-ideal force with the aid of the free energy and the pressure tensor, a lattice Boltzmann multi-phase flow model based on the pressure tensor is proposed, which is called the pressure tensor model, EPL,112 (2015)44002). From the theoretical and numerical experiments, the new model is proved to have both thermodynamic consistency and Galileo invariance. The algorithm is simple and easy to realize, and the two-phase co-existence curve obtained by the simulation of one-stage phase change is better with the theory, and is expected to be further promoted and applied. Although the pressure tensor model has obvious advantages in both the theory and the numerical value, it has a good application prospect. However, this paper has found that the model has further improved and improved space in the in-depth study. First, through the pressure tensor may not be the best, more than the only effective way to calculate the non-ideal force, the free energy, chemical potential and entropy of the system can describe the macroscopic quantity of the thermodynamic behavior of the system, especially the chemical potential has a unique advantage when describing the phase equilibrium and the chemical balance; On the other hand, the fluid-solid wetting boundary condition of the constrained multi-phase flow system is difficult to express directly by the pressure tensor, and the effective density expression also has a certain complexity, and the chemical potential is used to describe the interaction between the solid phase and the liquid phase in the wetting. In this paper, the original pressure tensor model is explored and improved from the chemical potential, and a chemical potential-based lattice Boltzmann multi-phase flow model (the chemical potential model) is constructed by the derivation of a chemical potential-based non-ideal force calculation formula, which is also based on the chemical potential. A set of flow-solid wetting boundary conditions based on chemical potential is developed (for short, chemical potential wetting boundary conditions). Based on the theoretical and numerical experiments, the new model and the wetting boundary condition have the following advantages and characteristics:1. because of the improvement and perfection of the original pressure tensor model, the chemical potential model still has both the thermodynamic consistency and the Galileo invariance, and the chemical potential model and the wetting boundary condition are in a unified and self-consistent theory through the chemical potential, In that numerical calculation, the mutual coordination and share are achieved. The chemical potential model and the wetting boundary condition are more concise than the pressure tensor model algorithm, and through a typical van der waals fluid-level phase change simulation experiment, the new chemical potential model has different degrees of improvement in the calculation accuracy, the calculation efficiency and the stability, It fully shows that it also has a systematic and comprehensive advantage in the field of numerical value. Several commonly used non-ideal fluids (including van der waals, Peng-Robinson, Redlich-Kwang Soave and Carnahan-Starling fluid) and van der Waals droplet deformation simulation with different speeds show that the chemical potential model can well describe the two-phase co-existence of the non-ideal fluid, Galileo invariance is also exactly satisfied. The examples of the wetting phenomenon of the van der Waals droplet on the surface of the solid wall show that the realization and application of the chemical potential model and the wetting boundary condition are convenient and feasible. in that numerical experiment, it is found that the wetting contact angle is almost linear with the change of the chemical potential of the specified solid wall surface, so that the required contact angle is very simple by adjusting the surface chemical potential in the practical application, Therefore, the application of the chemical potential model and the wetting boundary condition to the surface wetting phenomenon has a sufficient advantage. Since the chemical potential is an important and universal macroscopic quantity for describing the thermodynamic system, the chemical potential model and the wetting boundary condition can be directly applied to the research of a multi-phase flow system with an electromagnetic field environment or a chemical reaction. The above advantages and characteristics show that the chemical potential model and the wetting boundary condition have a solid theoretical foundation and excellent numerical performance, and are expected to be widely promoted and applied in the field of multi-phase flow.
【學位授予單位】：廣西師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O641
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