Momentum Source Terms Research Articles

Hovering Helicopter Rotors Modeling Using the Actuator Line Method

An implementation of the actuator line method (ALM) is applied to a hovering helicopter rotor. This method, which is widely used for wind turbine simulations, replaces the rotor blades by momentum source terms in the unsteady Reynolds-averaged Navier–Stokes equations. The removal of the blade mesh significantly reduces the computational mesh size, thus lowering the computational cost. The ALM is presented along with some improvements, notably the choice and treatment of the projection kernel. A parameter sweep is performed showcasing the importance of proper selection of the Gaussian smearing coefficient for accurate rotor performance predictions with a value of scaled around a quarter chord in size. With this value, a new set of simulations on a refined mesh is performed and analyzed covering global rotor performance coefficients, sectional blade loading, tip vortex characteristics in terms of positions, circulation, and core radius. The ALM is benchmarked against an equivalent blade resolved case on the well-known S-76 rotor. Results confirm the appropriateness of the ALM model for a hovering rotor for main flow features and performance metrics, although there was a small loss of accuracy on the tip blade loading in the presence of a blade–vortex interaction. Finally, computational performances indicate an elapsed-time speed-up between 3 and 4× in addition to a greater parallel efficiency in favor of the ALM.

Refined hydro-environmental modelling for tidal energy generation: West Somerset Lagoon case study

An accurate assessment of the hydro-environmental impacts of tidal range energy schemes, where the performance of the scheme has an impact on the marine environment and ecology, is crucial in optimising the design and development of such schemes. A proposal for a new coastally-attached impoundment, namely West Somerset Lagoon, has been investigated in this research and the numerical model TELEMAC-2D has been refined to model theimpacts of this scheme on the Bristol Channel and Severn Estuary. Domain decomposition was applied and full momentum conservation between the subdomains was included in the model by implementing momentum source terms at the turbine locations. The results have confirmed the importance of including full momentum conservation in modelling the effects of turbo-machinery in tidal lagoons. It was found that the operation of the scheme decreased the high water level slightly in the Bristol Channel and Severn Estuary, while there was a decrease in the low intertidal areas. The maximum velocity and bed shear stress were predicted to increase in the inner Bristol Channel, while they decreased noticeably across most of the interior of the lagoon, away from the turbine wakes. Furthermore, the operation of the lagoon significantly improved the water renewal in the region.

Study on convection and dispersion characteristics of dense gases in urban environment considering trees

Although several studies on the dispersion of heavy toxic gas released from ruptured tanks on vehicles during transportation have considered complex terrain such as urban buildings, the influence of trees on the flow field in urban areas during gas dispersion tends to be ignored. In this study, a Computational Fluid Dynamics (CFD) model was proposed to investigate the characteristics of gas release and dispersion from loaded vehicle in the urban environment. In this model, the tree crown was treated as a porous medium, and the influence of drag due to the crown was incorporated into the model by a momentum source term through a user-defined function. In this study, the dynamic characteristics of chlorine (Cl2) dispersion under the conditions of building distribution, tree species and porosities were comprehensively analysed, to cover the influence of urban complexity, leaf density, and tree planting configuration. The results show that compared with flat terrain, the presence of urban buildings will prolong the dense gas retention time and increase the dangerous distance. It is found that the horizontal dispersion distance can increase by 63% and the isosurface of 25 ppm hazardous gas can increase by 130% with the introduction of buildings. Compared with the terrain with only buildings, the introduction of arbors or shrubs can result in a 147% or 359% increase in the maximum concentration. Also, trees will prolong the dispersion duration. It is also found that the higher the porosity, the less the wind blocking effect, and the weaker the ability of capturing gas. The wind field affected by arbores and shrubs are different in height, and arbores capture more Cl2. Planting short shrubs around buildings can effectively reduce the spread of harmful gases.

An Implicit Finite Volume Scheme to Solve the Time-dependent Radiation Transport Equation Based on Discrete Ordinates

Abstract We describe a new algorithm to implicitly solve the time-dependent, frequency-integrated radiation transport (RT) equation, which is coupled to an explicit solver for equations of magnetohydrodynamics (MHD) using Athena++. The radiation field is represented by specific intensities along discrete rays, which are evolved using a conservative finite volume approach for both Cartesian and curvilinear coordinate systems. All terms for spatial transport of photons and interactions between gas and radiation are calculated implicitly together. An efficient Jacobi-like iteration scheme is used to solve the implicit equations. This removes any time-step constraint due to the speed of light in RT. We evolve the specific intensities in the lab frame to simplify the transport step. The lab frame specific intensities are transformed to the comoving frame via Lorentz transformation when the source term is calculated. Therefore, the scheme does not need any expansion in terms of v/c. The radiation energy and momentum source terms for the gas are calculated via direct quadrature in the angular space. The time step for the whole scheme is determined by the normal Courant–Friedrichs–Lewy condition in the MHD module. We provide a variety of test problems for this algorithm, including both optically thick and thin regimes, and for both gas and radiation pressure-dominated flows to demonstrate its accuracy and efficiency.

Energy-saving optimization for spacing configurations of a pair of self-propelled AUV based on hull form uncertainty design

This paper presents a spacing configuration-based energy-saving optimization approach for a pair of AUVs to achieve minimum resistance through the hull forms and propeller interactions. The traveling resistance is relevant to hull lines optimization design, which uncertainties exist in design variables need to be considered seriously. A reliability analysis based on the first-order reliability method demonstrates that the engineering quality is not acceptable; thus, the design for six sigma was performed with uncertainty optimization to improve the design levels. Two body force models, RANS-UT and RANS-HO, were used to represent the propeller as an axial and a tangential momentum source term. The results highlight that the radial thrust distribution has a significant impact of the propeller performance. For a pair of AUVs, the energy consumption of the fleet is classified into six zones depending on the spacing configurations with a longitudinal offset and transverse separation. This study details and categorizes the relevant sources of the drag reduction and provides the most effective fleet configuration for the optimal energy profits to validate previous experimental results. Based on energy considerations, the optimal fleet configuration is determined to show excellent adaptability and reliability to provide insights for decision makers.

Reactive LES-Euler/Lagrange modelling of bubble columns considering effects of bubble dynamics

Bubble columns are complex multiphase reactors producing large contact areas for mass transfer and subsequent chemical reactions. For allowing a deeper insight into this complexity and providing strategies for process optimisation, CFD (computational fluid dynamics) has become a standard tool. However, accurate models are needed to reproduce correctly such dynamic systems. Numerical computations of reactive bubble columns are conducted based on a LES-Euler/Lagrange approach. For extending this approach beyond the point-mass assumption for the dispersed elements, a bubble oscillation model based on stochastic generation of eccentricity and motion angle is proposed. The effects of bubble dynamics are modelled in the interfacial forces accounting for instantaneous eccentricity. A dynamic Sherwood number is used to consider bubble dynamics in the mass transfer. The influence of chemical reactions in species consumption within the liquid phase was modelled through the enhancement factor. Large Eddy Simulation (LES) was used for calculating the fluid flow with momentum source terms for bubbles and modelling sub-grid-scale (SGS) turbulence in the continuous phase through a transport equation for the turbulent kinetic energy. The effect of sub-grid-scale (SGS) turbulence on bubble motion, and also SGS turbulence modification by bubbles (BIT) is considered, introducing an extra source term in a kSGS equation. This source term automatically accounts for turbulence dissipation as well as enhancement (i.e. BIT). Numerical simulations of the chemisorption process for CO2 bubbles rising in highly concentrated NaOH solutions were compared with data presented in the literature. A very good agreement was only found when applying the full bubble dynamics model.

Detached helium plasma simulation by a one-dimensional fluid code with detailed collisional-radiative model

To increase the accuracy of a particle, momentum, and energy source terms in the detached helium plasma simulation, rate coefficients with the collisional-radiative model were introduced into the fluid code LINear Divertor Analysis (LINDA). Obtained effective rate coefficients and related source terms were compared with those from the conventional empirical databases. It is shown that a high-density condition in future fusion devices causes larger deviation between the effective and the empirical source terms. One-dimensional detached plasma simulation indicated that the peak amplitude of the plasma density during the rollover is sensitive to the source term difference related to the recombination. This study additionally revealed that the heating effect in the three-body recombination process strongly affects the detached plasma formation and downstream plasma parameters.

Numerical investigation on the flow and heat transfer characteristics of waxy crude oil during the tubular heating

In industrial practice, tubular heating is known as an effective technology to ensure the security storage of waxy crude oil in the tank. Insights of the thermal and flow behaviors during the tubular heating is a key aspect to optimize the strategy of this heating technology, in order to reduce the cost. In this study the physical and mathematical models representing the heat transfer and flow of waxy crude oil during tubular heating are established. The additional specific heat capacity and momentum source terms methods are employed to address the changing physical properties related to the paraffin crystallization and dissolution. The FVM, PISO and fully implicit first order temporal differentiation algorithms are used to perform the numerical simulation. Our outcomes show that the thermal process during tubular heating can be divided into four phases: ①Local thermal response phase, ②Thermal diffusion phase, ③Global thermal response phase, ④Elimination of gelled oil phase. The initial thermal influence range is inhibited by the thermal condition and solid-like gelled waxy crude oil formed after cooling. The plume flow takes great effects of transferring the heat from the tubes to crude oil and accelerating the phase transition, and finally facilitates the oil temperature uniform increasing in most parts of the tank. Whereas the gelled crude oils in the corner between the sidewall and base wall have the strongest solid-like character and lowest temperature. A low temperature layer keeps covering the base wall. At the top wall, the center region between the sidewall and center of the tank is long time occupied by gelled oil. The proportion of solid-like gelled crude oil keeps decreasing with a small slope value following a linear relationship with heating time. A pronounced phase change of waxy crude oil from the transition state into the pure liquid is observed. The minimum temperature value decreases in the initial heating period, and then steeply increases to an approximate plateau value. The fluctuations of the heating powers are observed indicating the transient thermal convections around the tubes. The heat loss power is lowest at the base wall and nearly unchanged. The heat loss power at top wall and sidewall are significantly influenced by heating tubes and depend on the wall temperature.

The effect of physical properties on the gelation behavior of waxy crude oil during shutdown

In this paper, the effect of different viscosity and specific heat capacity on the gelation behavior of waxy crude oil was studied. The additional specific heat capacity method and the momentum source term method are used for numerical simulation. Grey correlation analysis method was used to quantitatively express the correlation degree of viscosity and specific heat capacity on average flow velocity, temperature drop rate and the ratio of gelled oil area to total area. The results show that the influence of viscosity on the gelation behavior of waxy crude oil is greater than that of specific heat capacity. When the viscosity of crude oil is large, natural convection is weaker and the temperature drop rate is smaller, which retards the development of the gelation behavior of crude oil. For crude oil with larger heat capacity, the temperature drop rate is smaller and the natural convection is slightly stronger, but the temperature drop rate has a great influence on the gelation behavior of crude oil, making it develop slowly. The influence of both viscosity and specific heat capacity on gelation behavior is limited.

A robust two-dimensional model for highly sediment-laden unsteady flows of variable density over movable beds

AbstractIn this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes.

Sneezing and asymptomatic virus transmission.

The novel coronavirus disease (COVID-19) spread pattern continues to show that geographical barriers alone cannot contain a virus. Asymptomatic carriers play a critical role in the nature of this virus quickly escalating into a global pandemic. Asymptomatic carriers may transmit the virus unintentionally through sporadic sneezing. A novel Computational Fluid Dynamics (CFD) approach has been proposed with a realistic modeling of a human sneeze achieved by the combination of state-of-the-art experimental and numerical methods. This modeling approach may be suitable for future engineering analyses aimed at reshaping public spaces and common areas, with the main objective to accurately predict the spread of aerosol and droplets that may contain pathogens. This study shows that the biomechanics of a human sneeze, including complex muscle contractions and relaxations, can be accurately modeled by the angular head motion and the dynamic pressure response during sneezing. These have been considered as the human factors and were implemented in the CFD simulation by imposing a momentum source term to the coupled Eulerian–Lagrangian momentum equations. The momentum source was modeled by the measured dynamic pressure response in conjunction with the angular head motion. This approach eliminated the need to create an ad hoc set of inlet boundary conditions. With this proposed technique, it is easier to add multiple fixed and/or moving sources of sneezes in complex computational domains. Additionally, extensive sensitivity analyses based on different environmental conditions were performed, and their impact was described in terms of potential virus spread.

Numerical Solution of Single and Two Bubbles Moving in Quiescent Liquid Using Euler-Lagrange Approach

It is known that the bubbles dynamics are very important and dominant property in multiphase airlift systems. The major benefit came from understanding visually and numerically these dynamics that lead to improvement of bubbles distribution and a well-mixed mixture inside reactors. Hence, Euler-Lagrange approach has been used to study bubbles dynamics. By using the two-dimensional Reynolds-averaged Navier–Stokes equations that reinforces turbulence model the continuous phase velocity is calculated. The coupling between the phases was take into consideration through source terms of momentum and the source terms in the equations (ε and k), which include the effect of wake-generated turbulence by means consistent Lagrangian-similar terms. by utilizing the motion equations taking into account added mass, drag, pressure, gravity, wall, and the transverse lift force the Bubble motion was calculated. So as to determine the importance relative for the different physical phenomena’s included in the model., a modified particle source in cell (PIC) is introduced, where the effect of bubble is accounted not only where the center of bubble is located but also to all the cells that containing bubble.

Numerical Analysis and Experimental Validation of Heat Transfer During Solidification of Phase Change Material in a Large Domain

Abstract Transient solidification of phase change material (PCM) dominated by natural convection is studied in this work. Water is solidified inside an insulated tank while local temperature and liquid/solid phase distributions are studied numerically and experimentally until a steady-state is reached. During the analysis, it is noted that water solidification dominated by heat transfer mechanism of natural convection is a demanding numerical procedure due to specific properties of the water that is enhancing local heat transfer. The water solidification is studied via an interactive combination of transient three-dimensional computational fluid dynamics analysis incorporating phase change modeling and the results are validated with experimentally obtained data. Existing literature recommendations suggest that large-scale and long-term solidification processes cannot be accurately modeled with large time-steps, while the objective of this work was to develop such a model. The model is based on using temperature-dependent water properties for studying the cooling of the water and the magnitude of velocities inside the tank are derived in this manner upon reaching steady-state. Consequently, the mixing effect induced by natural convection is incorporated into the solidification and melting model with constant water properties via momentum source terms to enhance the heat transfer during the transient solidification simulations and the simulation results are compared with experimentally obtained data. Before implementing the developed method, after 100 minutes from the initiation of the cooling, the results were in disagreement by ca. 15°C, while after implementing the method the difference was reduced to ca. 1-2°C for most of the observed points, significantly improving the accuracy of the solidification model.

A Fast Modeling Approach for the Numerical Prediction of Urea Deposit Formation

<div class="section abstract"><div class="htmlview paragraph">The permanently tightening emission regulations for NOx pollutants force further development of automotive exhaust aftertreatment systems with selective catalytic reduction (SCR). Of particular interest is the long-term reliability of SCR systems with regard to unfavorable operating conditions, such as high injection rates of urea water solution (UWS) or a low exhaust gas temperature. Both of them may lead to formation of solid deposits which increase backpressure and impair ammonia uniformity.</div><div class="htmlview paragraph">A fast modeling approach for numerical prediction of deposit formation in urea SCR systems is desired for optimization of system design. This paper presents a modified methodology for the modeling of deposit formation risk. A new determination of the initial footprint of the spray, where the deposit formation is inhibited, is proposed. The threshold values for the evaluation of the film transport were validated based on experimental results. To achieve a more realistic simulation in terms of wall wetting and cooling, the impingement heat transfer as well as the impingement model were modified based on optical investigations.</div><div class="htmlview paragraph">In order to accomplish the modeling of deposit formation with typical time ranges of several minutes, a recently developed injection source approach was applied. The substitution of the Lagrange-particles with source terms of mass, momentum and energy allowed to reduce simulation time by a factor of 30. The presented modeling approach was validated against both, the experimental data from an optical box and an exhaust aftertreatment system. The comparison of measured and simulated results shows the capability of the presented modeling approach to predict the position and the severity of solid deposits.</div></div>

An Investigation of Real-Gas and Multiphase Effects on Multicomponent Diesel Sprays

<div class="section abstract"><div class="htmlview paragraph">Lagrangian spray modeling represents a critical boundary condition for multidimensional simulations of in-cylinder flow structure, mixture formation and combustion in internal combustion engines. Segregated models for injection, breakup, collision and vaporization are usually employed to pass appropriate momentum, mass, and energy source terms to the gas-phase solver. Careful calibration of each sub-model generally produces appropriate results. Yet, the predictiveness of this modeling approach has been questioned by recent experimental observations, which showed that at trans- and super-critical conditions relevant to diesel injection, classical atomization and vaporization behavior is replaced by a mixing-controlled phase transition process of a dense fluid. In this work, we assessed the shortcomings of classical spray modeling with respect to real-gas and phase-change behavior, employing a multicomponent phase equilibrium solver and liquid-jet theory. A Peng-Robinson Equation of State (PR-EoS) model was implemented, and EoS-neutral thermodynamics derivatives were introduced in the FRESCO CFD platform turbulent NS solver. A phase equilibrium solver based on Gibbs free energy minimization was implemented to test phase stability and to compute phase equilibrium. Zero-dimensional flash calculations were employed to validate the solver with single- and multi-component fuels, at conditions relevant to diesel injection. The validation showed that 2-phase mixture temperature in the jet core can deviate up to 40K from the single-phase solution. Surface equilibrium with Raoult’s law employed for drop vaporization calculation was observed to deviate up to 100% from the actual multiphase real-gas behavior. Liquid-jet spray structure in high pressure fuel injection CFD calculations was modeled using an equilibrium-phase (EP) Lagrangian injection model, where liquid fuel mass is released to the Eulerian liquid phase, assuming phase-equilibrium in every cell. Comparison to state-of-the-art modeling featuring KH-RT breakup and multicomponent fuel vaporization highlighted the superior predictive capabilities of the EP model in capturing liquid spray structure at several conditions with limited calibration efforts.</div></div>

CFD Simulation of Aeration and Mixing Processes in a Full-Scale Oxidation Ditch

This study aims to build a computational fluid dynamics (CFD) model that can be used to predict fluid flow pattern and to analyse the mixing process in a full-scale OD. CFD is a widely used numerical tool for analysing, modelling and simulating fluid flow patterns in wastewater treatment processes. In this study, a three-dimensional (3D) computational geometry was used, and the Eulerian-Eulerian multiphase flow model was built. Pure water was considered as the continuous phase, whereas air was modelled as the dispersed phase. The Shear Stress Transport (SST) turbulence model was specified which predicts turbulence eddies in free stream and wall-bounded region with high accuracy. The momentum source term approach and the transient rotor-stator approach were implemented for the modelling of the submersible agitators. The hydrodynamic analysis was successfully performed for four different scenarios. In order to prevent the incorrect positioning of the submerged agitators, thrust analysis was also done. The results show that the minimum required water velocity was reached to maintain the solid particles suspended in the liquid media and adequate mixing was determined.

Effect of pipe diameter on heat transfer characteristics of waxy crude oil pipeline during shutdown

Additional specific heat capacity method and momentum source term method are used to establish the mathematical model of the heat transfer process in different diameter waxy crude oil pipeline, and the finite volume method is used to solve the mathematical model. The average temperature of the crude oil in the pipeline with smaller pipe diameter decreases faster. At the initial stage of shutdown, there is a layer of low-temperature crude oil near the pipe wall. The smaller the pipe diameter is, the bigger the thickness of this layer of low-temperature crude oil is. When crude oil is shut down in the pipeline with small diameter, the flow speed of crude oil is limited, and the flow of crude oil is stable and slow. When crude oil is shut down in the pipeline with large diameter, there will be a flow structure of two eddies, the flow speed is relatively large. With the same average temperature of crude oil, the larger the diameter of the pipe, the more difficult it is to form a complete gel structure in the center of the pipeline.

Numerical study on porosity distribution and hydrodynamics of packed bed in narrow square channels

Recently square-channel packed bed reactors with micro to milli dimensions are often found in the literature on process intensification. However, its porosity profiles and resultant flow behaviors have been overlooked. Therefore, this study proposes two new CFD approaches to model such reactors relying on the accurate local porosity profiles in the square bed. Discrete element method was employed to model random packed beds of monodisperse spherical particles in square channels with channel-to-particle size ratio of 3 to 10. The obtained lateral porosity profiles were axially averaged and expressed as a function of distance from the wall in three defined zones. Momentum source term to be added in the momentum conservation equation was calculated based on the local porosity profile functions in Correlations-based Continuum (CC) approach, while on the axially-averaged porosity profiles in Pseudo-Particle Resolved (PPR) approach. The square beds’ hydrodynamic behaviors were investigated using CC and PPR approaches, which were validated with Particle Resolved approach in terms of velocity profile, and with empirical correlations for pressure drop.

On the force competition in bubble columns: A numerical study

Computational Fluid Dynamics (CFD) is nowadays fully accepted in engineering practice as a potential tool for the prediction of flows, conversion rates and process efficiency. The Euler/Lagrange is one of the available approaches for describing dispersed multiphase systems, for example in bubble columns. Hence, the flow field within the bubble column is computed using large eddy simulations (LES) considering full coupling with the bubble phase through momentum source terms as well as sub-grid-scale (SGS) turbulence modification by modelling bubble induced turbulence (BIT). Despite the required point-particle approximation, necessary for computing large-scale technical and industrial systems, bubble dynamics was included in the numerical modelling, through shape (eccentricity) and trajectory oscillations. The performance of the proposed bubble dynamics model is analysed in detail and it is shown that without a bubble dynamics model the bubble fluctuating velocities cannot be predicted correctly. In order to predict the bubble motion accurately it is necessary to account for all relevant acting forces in the calculations, namely, gravity/buoyancy, drag, transverse lift, added (virtual) mass, fluid inertia (part of the pressure term), Basset (history term) force and possibly modifications of these forces due to the presence of walls. Based on the state-of-the-art, instantaneous resistance coefficients for all these forces were elaborated and extended for allowing consideration of the bubble dynamic behaviour and deformation through the eccentricity. The proposed resistance coefficients do not consider any swarm effects and are therefore only applicable to bubbly systems with volume fractions of less than 5%. For the beginning clean systems with mobile bubbles are considered only which are moving in low-viscous systems such as a water-air two phase flows with small bubble Morton numbers. Most important, a lift force coefficient which is valid for such low viscous systems is applied based on recent studies. Consequently, a comprehensive and complete model is introduced for describing bubble motion in a point-particle approximation including bubble dynamics (eccentricity) and therefore using composite formulations especially for drag and transverse lift, and in addition accounting for added mass with bubble deformation and wall effects as well as the Basset force. For the regime of deformable bubbles, the resulting instantaneous resistance coefficients are extracted from bubble column simulations and compared with the mean resistance coefficients. Moreover, the local importance of all considered forces on the motion of bubbles within the bubble column was evaluated in detail in terms of bubble size, column height, radial position and Stokes number without and with bubble dynamics model. The importance of these forces and the correspondent effects on the velocity and volume fraction profiles are explored for a laboratory-scale bubble column. The influence of the bubble dynamics model and the considered interfacial forces on the predicted hydrodynamics of the laboratory bubble column is analysed for validation considering two cases with different bubble size distributions with sizes smaller than about 5 mm. Furthermore, the effect of Basset term on particle dispersion is highlighted in a turbulent pipe flow test case.

Quantitative effects of different factors on the thermal characteristics of waxy crude oil pipeline during its shutdown

By means of momentum source term method and additional specific heat capacity method, the thermal characteristics of waxy crude oil pipeline during its shutdown are investigated by the numerical simulation. The quantitative effects of crude oil viscosity, specific heat capacity, pipeline diameter and insulation thickness on the thermal characteristics of waxy crude oil pipeline during shutdown are studied. The results show that pipe diameter has a great influence on the average temperature drop rate, and the average temperature drop rate decreases significantly with the increase of pipe diameter. The thickness of insulation and the viscosity of crude oil have a great influence on the oil temperature variance. As the thickness of insulation layer increases or the viscosity of crude oil increases, the oil temperature variance increases significantly. The viscosity of crude oil has a great influence on the average velocity, and the average velocity decreases significantly with the increase of the viscosity of crude oil.