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Now, long flexible deepwater riser vortex-induced models can be divided into: empirical models, mixed models and CFD models.
The development of computer provides favorable conditions for the research and application of CFD, and makes the numerical method be widely used [3,4].
Table 1 Parameters of model riser riser length 1500[m] Elastic Modulus 207G[pa] outer diameter 0.3239[m] shear modulus 79000[pa] inner diameter 0.285[m] Material Density 7850[kg/m*3] Table 2 VIV response parameters uniform current velocity[m/s] 0.2/0.4 1.0 1.0 0.9 0.05 According to Fig.2, the relation curves of reduced amplitude and reduced speed，TTR cross-flow vibration lock-in range is：4<<6.3，thus in this paper, velocity 0.2m/s,which in lock-in range, and velocity 0.4m/s which is outside lock-in range are selected as simulation speeds .

Analysis Two-dimensional computational fluid dynamics (CFD) analysis [6] showed that no SiC grows at Ts ≥ 1863 K and that C-to-Si ratio is larger than unity at growth position when Ts was 1813−1853 K (Fig. 2).
To make a comparison with the reported observation under P of 18 kPa [5], additional CFD analysis was carried out at Ts of 1843 K (i.e., Tpyrometer = 1923 K [5]).
Topography simulation [7] was carried out, in a manner similar to the way in the previous section, using CSiH2e(∞) and CSiH20 (in the absence of HCl) or CSiCle(∞) and CSiCl0 (in the presence of HCl).
Symbols: experiments; lines: simulation using γ of (a) 0.04, (b) 0.05, and (c) 0.06 J/m2.

aoka18usmmech@gmail.com, bmezul@usm.my Keywords: Thermal Simulation, Convergence Study, Thermal Resistance, Mass Equation, Momentum Equation, Energy Equation.
Few approaches were used to ensure the accuracy of the thermal simulation method, ranging from the minimum number of simulation iterations required in the finite element analysis, to the residuals target in terms of the momentum, continuity and energy equations, the objective is to ensure the simulations are converged and provide the reasonable results, which is also an indication of how the partial equations have successfully been solved with analytic method.
The analysis of CPU with variable heat sink base plate thickness using CFD addressed the convergence issue with the simulation data, the study converged at 10-4 and 10-8 for flow and energy equations respectively［3］.
Thermal Simulation A full 3D thermal model has been developed in the Ansys software [10], which consists of a fan to act as the forced air cooling device, together with a heat sink which is attached with an IC Package, the simulation was performed with the different heat source and the corresponding monitor point is measured to represent the response of the junction temperature.
Govindarajan, Thermal Analysis of CPU with variable Heat Sink Base Plate Thickness using CFD, 2010 [4] Darwin Edwards, Semiconductor and IC Package Thermal Metrics [5] Pelham, Simplified Method for Estimating Heat Sink Thermal Resistance, Forced Convection [6] VA.

This paper mainly focuses on the numerical simulation of temperature field in the cyclone separation.
Therefore the simulation only focuses on the single cylinder.
Meshing is the premise process of numerical simulation and also the discrete process of calculating region.
The number of the grid has nothing to do with the final result according to the theory of CFD, and when the intensity of the grid reaches a certain value, it has little effect on the simulation result by continuing encryption [1].
Fig. 5 Total temperature field Numerical simulation analysis Temperature distribution at various locations in CLT/A type cyclone can be intuitively obtained through numerical simulation shown in the Fig. 5.

Numerical simulations have been conducted by using the FIRE v2008 code.
(1) cylinder set (2) piston (3) cylinder cover (4) main combustion chamber (5) conical-spray nozzle (6) oriented surface (7) passage (8) central pedestal (9) swirl chamber Fig. 1 The diagram of combustion chamber Numerical Simulation The simulation of processes of spray and combustion is based on a single cylinder diesel engine, the combustion system is axial symmetry.
Pariotis, Investigation of piston bowl geometry and speed effects in a motored HSDI diesel engine using a CFD against a quasi-dimensional model, J.
Mattarelli, CFD parametric analysis of the combustion chamber shape in a small HSDI diesel engine, SAE paper 32 (2005) 1-13
Xin, Numerical simulation on effects of spray angle in a swirl chamber combustion system of DI diesel engines, J.

Numerical Simulations In total 3 designs of the air fin where used to perform 2D numerical simulation using the commercial software Autodesk Simulation CFD 360.
Fig 4 Simulation domain: a) no straight section; b) 2.5 [mm] straight section; c) 7.5 straight section Fig 4 shows the domain boundary conditions used.
Data given by the simulation software isn’t in a form that permits us to extract directly the convection coefficient and the friction coefficient.
Here the problem arises from the fact that the simulations are 2D and not 3D.
Nagi, “Numerical Study of Corrugation Amplitude Influence of a Wavy Fin in Overall Performance of a Compact Heat Exchanger,” in ACME 2014, (2014) [9] Autodesk Simulation CFD 2014, “Help: SST K-Omega Turbulence Models.”

Another method is the use of CFD (Computational Fluid Dynamics) simulation software.
A mathematical model and a CFD method are used to analyze the effects of different tube shapes on the radiant system performance.
The utilization of a large number of control volumes used in the simulation will have a proportional effect on the simulation time.
The file has 8760 time steps corresponding to each time step of the simulation.
A greater number of nodes have been tried in some simulations but the simulation time of the model increases proportionally with the complexity of the model.

Yang Institute of Hydraulic Engineering ,Xi’an University of Technology,Xi’an, China wei_wenli@126.com Keywords: characteristics; CFD simulation; Water drop falling Abstract: In this paper, a numerical two-phase flow model combining with the Realizable k–ε turbulent model for compressible viscous fluid is presented for the computation of water drop falling characteristics; and the equations are solved with the finite volume method.
The results of this simulation are presented in Figs.3.

Computational fluid dynamics (CFD) simulations using ANSYS Fluent demonstrated that most designs achieved a flow rate of 14.56 nL/s, closely matching theoretical values and meeting the physiological requirements of islets.
The generated models were seamlessly integrated into ANSYS Fluent, renowned for its precision in computational fluid dynamics (CFD) simulations.
By leveraging these tools, detailed models were developed, and advanced fluid simulations were conducted to analyze flow behavior within the irrigation channels.
Computational Simulation The geometries were imported into ANSYS Workbench 2021 R1.
The obtained Re values remained below 2300 in all simulations, confirming a consistent laminar flow [27].

But their results are without the simulation of air core.
The numerical solutions were carried out using commercial CFD code FLUENT 6.1.
The simulation was realized using a large eddy simulation (LES) for turbulent modeling and discrete phase model (DPM) for particle trahectories calculation.
This study drop 1470 particles at inlet at simulation time 1.9 s.
Fig. 2 shows the particle movement simulation from 1.98 s to 2.50 s.