Types Of Turbulence Models Research Articles

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier–Stokes (RANS) equations are solved using turbulence modelling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been performed for similar performance with two-equation models of the k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}-ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically refined mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the model itself. Additionally, in this paper analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Numerical Investigation on the Distribution of Pressure Coefficients of Modified Building Shapes

The construction of tall buildings in urban areas has grown in number in recent years. However, architects and engineers face a variety of design challenges due to the variety of heights and shapes of new building designs. This study evaluates the impact of shape mitigation on tall buildings by applying corner modifications, such as chamfered, corner cut, plan changes with height, tapered, and setback, and combining a single modification model. The numerical simulations were carried out using Computational Fluid Dynamic (CFD) simulation with the RNG k-ε type of turbulence model. All single modifications reduced the maximum +C<i><sub>p</sub></i> and -C<i><sub>p</sub></i> better than the basic model. The corner-cut model was the most effective method for reducing the suction effect. Combining the setback, chamfering the corner, and twisting the building model at 45° modification was the most effective approach to reduce the maximum +C<i><sub>p</sub></i> in the 25–42.10% range in Face 1. Modifying a square model with the combination of setback, chamfer, and 45° rotation reduced the maximum -C<i><sub>p</sub></i>, ranging from 36.9–50%. The composite 1 model and composite 2 model reduced the suction effect in the range of 15.38–33.33% in Face 3. The adoption of composite modification was insignificant in reducing the suction effect on the sidewall, where the maximum -C<i><sub>p</sub></i> was recorded to be between 3.62–5.43%.

Zonal Turbulence Modeling Approach for Simulating Compartment Fire for Initial Hazard Assessment

The flow field driven by a compartment fire usually contains several flow zones with different physical structures. As each type of turbulence model has its own predominant application area, it is logical to apply two or more simple turbulence models to the same fire-induced flow field at different locations according to their predominant features to yield a comparatively simple, accurate, and stable zonal turbulence model. A zonal turbulence model, which is a hybrid of the standard k-ε model and its modification, is developed in this paper. The model is tested and compared with the experimental data. A promising improvement is observed when comparing it with the base turbulence model, i.e., the standard k-ε model, especially in the recirculating region near the corners of the compartment. This approach in having different zones in the plume region will be useful for handling more scenarios at the initial stage of fire hazard assessments.

Моделювання течії в надзвуковій компресорній решітці

The design of modern aircraft engines cannot be imagined without numerical simulation methods. The advantages of numerical simulation at the first stages of creating engines are obvious: the ability to explore different geometric models in a fairly short time, while the accuracy of calculations reaches 5 ... 15%. An integral part of the numerical experiment is conducting test problems, because of which it is necessary to identify the necessary topology of the computational grid and the turbulent viscosity model. The current study conducts a test problem of flow simulation in a supersonic compressor cascade-based on the STFF rotor to select the topology of the computational grid and the turbulent viscosity model for closing the system of Navier-Stokes equations. In this work, four variants of the computational grid and four models of turbulent viscosity were studied. The time step was automatically changed. The maximum time over time was 0.00005…0.001 s. Control points were set in front of the grating and behind it, where the value of the Mach number was displayed. When calculating, the value of the Mach number in front of the grating was selected by changing the value of the velocity at the input. The calculation was terminated when the values of the Mach numbers at the input and output of the cascade were reached, as well as constant values of the residuals, which did not change during subsequent iterations. 4 variants of the structured type computational grid were built. Grid No. 3 was chosen for further calculations since it provides sufficient similarity with the test results, and it also has a smaller size, which makes it possible to speed up the calculation. Next, calculations are performed for different types of turbulence models. The turbulence models SST, SST GTT, k-ω and RNG k-ε were considered. For all turbulence models, the boundary layer height was chosen based on the condition Y+ < 1. An analysis of the calculation results showed that the smallest error was obtained in calculations with the SST GTT turbulence model. This paper presents a comparison of the density distribution in the cross-section of the cascade with a schlieren photograph obtained from a field experiment. A qualitative analysis of the obtained results shows that the flow patterns around the STFF-based compressor grate are of a similar nature, in particular, in the interblade channel and edge wakes behind the cascade. Thus, for further research to study the flow in the fan, the topology of the Mesh3 computational grid and the turbulent viscosity model SST GTT were chosen.

Average-based mesh adaptation for hybrid RANS/LES simulation of complex flows

Generating meshes with the right resolution is crucial for hybrid RANS/LES simulations of high Reynolds number flow with complex physical phenomena and geometries. This makes automatic mesh generation through adaptive refinement an interesting option. However, since the behavior of these turbulence models depends on the local grid size, mesh changes in time as a result of adaptive refinement may affect the production and destruction of turbulence. Therefore, grid adaptation with refinement criteria based on time-averaged quantities is proposed here to produce meshes that do not evolve rapidly in time and that are suitable for capturing the unsteady flow at each instant. Two averaging approaches, averaging over the instantaneous flow field, and averaging over the refinement criterion, are tested to simulate a turbulent flow behind a backward-facing step with a Detached Eddy Simulation type turbulence model. Compared to grid adaption based on instantaneous solutions, the computational cost is reduced, the accuracy of the solutions improves and an adapted mesh which has a generally static topology based on the main flow features is obtained. The investigation of this refinement process for two realistic test cases, a ship and a hybrid delta wing, confirms the reliability of the average-based adaptation and shows that automatic meshing for hybrid RANS/LES simulations of complex flows is possible.

Numerical studies of the effects of design parameters on flow fields in spiral concentrators

ABSTRACT Spiral concentrators are widely used for the concentration of coal and heavy minerals. The design for the spiral concentrator is full of challenge because of the sensitivity of design parameters to water flow field. The study aims to reveal the rule of the design parameters on water flow field in spiral concentrators. The pitch, the transverse angle, and the flow rate were taken as the variables. A suggested simulation method based on grid independence investigation, four types of turbulence models, and Volume of Fluid (VOF) approach was proposed. The water flow field on spirals with different design parameters was determined by the validated model. The predicted water flow depth show agreement with the measured results. The Reynolds-Stress Model (RSM) turbulence model is superior to other turbulence models. The water depth and the primary velocity in spiral concentrators increase smoothly outward. The secondary velocity is relatively small compared with the primary velocity. No obvious secondary flow exists in the inner trough. The reversal position of the secondary flow is approximate at the fractional depth of 0.2 ~ 0.5. The reduction of the pitch and the flow rate, together with the increase of the transverse angle, can strengthen the secondary flow in spiral concentrators.

Computational Simulation of Wind Microclimate in Complex Urban Models and Mitigation Using Trees

Due to a rapid increase in urbanisation, accurate wind microclimate assessment is of crucial importance. Evaluating wind flows around buildings is part of the planning application process in the design of new developments. In this study, computational fluid dynamics (CFD) simulations are carried out for a case study, representing the East Village in the London Olympic Park. Following a validation test against experimental data for a simpler urban configuration, the key input parameters, including appropriate boundary conditions, mesh setting and type of turbulence model, are selected for the Olympic Park model. All the simulations are conducted using the commercial code STARCCM+ under steady-state conditions with the Reynolds-averaged Navier–Stokes (RANS) method. The turbulence is modelled using different common variants of eddy-viscosity models (EVMs) including standard k-ε, realizable k-ε and standard and shear stress transport (SST) k-ω. The results demonstrate that standard and realisable k-ε models correlate very well with the experimental data, while some discrepancies are found with standard and SST k-ω. Following the determination of areas of high velocity, appropriate tree planting is proposed to overcome the effect of corner and downwash acceleration. With the optimised arrangement of trees and using specific types of tree (e.g., birch), wind speeds at the pedestrian level are reduced by 3.5, 25 and 66% in three main regions of interest. Moreover, we investigate the effects of tree heights. The obtained results illustrate that the wind velocity reduces when the crowns of the trees are located closer to the buildings and the ground. Our high-resolution CFD simulation and results offer a quantitative tool for wind microclimate assessment and optimised design and arrangement of trees around buildings to improve pedestrian comfort.

ACAT1 Benchmark of RANS-Informed Analytical Methods for Fan Broadband Noise Prediction—Part I—Influence of the RANS Simulation

A benchmark of Reynolds-Averaged Navier-Stokes (RANS)-informed analytical methods, which are attractive for predicting fan broadband noise, was conducted within the framework of the European project TurboNoiseBB. This paper discusses the first part of the benchmark, which investigates the influence of the RANS inputs. Its companion paper focuses on the influence of the applied acoustic models on predicted fan broadband noise levels. While similar benchmarking activities were conducted in the past, this benchmark is unique due to its large and diverse data set involving members from more than ten institutions. In this work, the authors analyze RANS solutions performed at approach conditions for the ACAT1 fan. The RANS solutions were obtained using different CFD codes, mesh resolutions, and computational settings. The flow, turbulence, and resulting fan broadband noise predictions are analyzed to pinpoint critical influencing parameters related to the RANS inputs. Experimental data are used for comparison. It is shown that when turbomachinery experts perform RANS simulations using the same geometry and the same operating conditions, the most crucial choices in terms of predicted fan broadband noise are the type of turbulence model and applied turbulence model extensions. Chosen mesh resolutions, CFD solvers, and other computational settings are less critical.

The Effect of Turbulence Model and Nanofluid on Fluid Flow and Heat Transfer in a Narrow Rectangular Duct

The effect of turbulence model and nanofluid on the heat transfer and fluid flow in a horizontal narrow rectangular duct is numerically studied under constant wall heat flux boundary condition. Numerical study is carried out using ANSYS Fluent 17.0 software. Examined parameters are the type of turbulence model, the type of nanofluid, the volume fraction of nanofluid, and the Reynolds number. Three different k-e and four different k-w turbulence models are employed. Aluminum oxide Al2O3-water and copper oxide CuO-water are used as nanofluids. Volume fractions of nanoparticles used are 0%, 0.1%, 0.5%, 1%, 2% and 4%. Reynolds number changes from 3×103 to 50×103. Results showed that k-ω standard turbulence model with low Reynolds number correction gives better result. It is seen that both the type and volume fraction of nanofluid affect heat transfer and pressure drop. Using Al2O3 and CuO nanoparticles in water increases thermal performance. It is found that the performance of CuO-water nanofluid is better than that of Al2O3-water nanofluid. It is seen that using turbulent fully developed correlations derived for circular ducts may end up with incorrect results for the flow in a two dimensional rectangular duct.

Intensification of liquid steel active flow volume in one-strand tundish using a modified ladle shroud

This work presents the numerical and physical simulation results of the liquid steel flow in the one-strand tundish. The results obtained during the numerical simulations and the water modeling results were compared to each other. Six types of turbulence models were tested. Among tested turbulence models the BSL k-ω was turned out the best correlating with the results from the laboratory experiments. Besides, the ladle shroud modification was proposed by the authors and the influence of the modified ladle shroud immersion depth in the liquid steel on the hydrodynamic structure in the tundish was checked. The ladle shroud modification depended on the expansion, narrowing, and re-expansion of the liquid steel feed stream. The four tundish variants with the four different ladle shroud immersion depths (at 0.1, 0.2, 0.3 and 0.4 m) in the liquid steel were tested. The liquid steel flow volumes were calculated and according to the generated active flow volume, the most beneficial research case was indicated. The tundish variant with the ladle shroud immersion depth of 0.3 m in the liquid steel was characterized by the lowest stagnant flow volume. The numerical simulations were performed by using the Ansys-Fluent computer program.

Comparative Study on Several Type of Turbulence Model Available in ANSYS-Fluent Software for ONERA M6 Wing Aerodynamic Analysis

ONERA M6 wing model is definitive computational fluid dynamic (CFD) validation case for aerodynamic investigations. Therefore, such investigation on aerodynamic characteristics is conducted with commercial CFD software known as ANSYS-Fluent software. The advantages of this software beside offer various flow solvers, this software also provides a various type of Turbulence Models can be implemented. In the present works, an investigation on capabilities of turbulence models available in the ANSYS-Fluent software based on Boussinesq hypothesis had been studied. The investigation had used five ty pe Turbulence Models for evaluating the aerodynamic characteristics of the ONERA M6 wing model. These five turbulent models are: (1) Spalart-Allmaras, (2) k-ε Standard, (3) k-ε Realizable, (4) k-ω Standard and (5) k-ω SST turbulence models. The flow analysis are carried at two different angle of attacks namely at α = 3.060 and α = 6.060. These two angle of attacks correspond with Mach number 𝑀𝑀∞= 0.84 and the Reynolds number Re = 11.76×106. The comparison between ANSYS software with the experimental result as provided by AGARD AR-138 in term pressure coefficient distribution at several wing span location and overall aerodynamics characteristics in term lift coefficients shows that among those five turbulence models had been found that Spalart-Allmaras and k-ω SST turbulence model gives result close to the experimental results and the smallest number of iteration for getting a converge solution.

A New simplified calculation model of geometric thermal features of a vertical propane jet fire based on experimental and computational studies

Jet fires and their consequences are one of the significant factors responsible for catastrophic events in industrial process units. In this research, various types of turbulence models were investigated to simulate a vertical propane jet fire using computational fluid dynamics (CFD). CFD was applied to evaluate the following turbulence models of k-ε, SST, BSL, BSL RS and the Realizable k-epsilon (RNG k-ε), the Eddy Dissipation Concept (EDC) for combustion, and the Monte Carlo model for radiation. All the above-mentioned turbulence models are used for a temperature range of 1500–1700K. The results showed that the SST turbulence model is the best option, with average error of 4.7 % for a jet fire simulation, with a lower computational time. The simulation of the jet fire shape at surface temperature of 800K was also compared with the experimental data obtained under the same conditions. By taking into account the time parameter in the simulation, the predicted ratio of flame length and equivalent flame diameter results are in good agreement with the experimental jet fire data.

CFD simulations of single-phase flow in settling tanks: comparison of turbulence models

ABSTRACT In the present work, single-phase CFD simulations are performed to study flows in the rectangular and circular settling tank. The three-dimensional flow was studied for the predictions of the velocity profiles in the settling tank. The performance of seven different types of turbulence models, standard k-ε model, low Re k-ε models such as AKN model, CHC model and Abid Model, k-ω model, low Re k-ω model and RSM model has been evaluated for the prediction of flow fields. The CFD model is validated with previously published experimental data. The comparison of velocity profiles, turbulent kinetic energy, turbulent Reynolds number and vorticity are presented. The predictive ability of Abid model is better than other models for prediction of the flow field for both rectangular and circular settling tank. The absolute error for the velocity predictions in the case of the low Re k-ε model is around 30% less as compared to the other models. The better prediction using the low Re k-ε models is attributed to the damping functions used in the model.

Evaluation of the Impact of Horizontal Grid Spacing in Terra Incognita on Coupled Mesoscale–Microscale Simulations Using the WRF Framework

Abstract Coupled mesoscale–microscale simulations are required to provide time-varying weather-dependent inflow and forcing for large-eddy simulations under general flow conditions. Such coupling necessarily spans a wide range of spatial scales (i.e., ~10 m to ~10 km). Herein, we use simulations that involve multiple nested domains with horizontal grid spacings in the terra incognita (i.e., km) that may affect simulated conditions in both the outer and inner domains. We examine the impact on simulated wind speed and turbulence associated with forcing provided by a terrain with grid spacing in the terra incognita. We perform a suite of simulations that use combinations of varying horizontal grid spacings and turbulence parameterization/modeling using the Weather Research and Forecasting (WRF) Model using a combination of planetary boundary layer (PBL) and large-eddy simulation subgrid-scale (LES-SGS) models. The results are analyzed in terms of spectral energy, turbulence kinetic energy, and proper orthogonal decomposition (POD) energy. The results show that the output from the microscale domain depends on the type of turbulence model (e.g., PBL or LES-SGS model) used for a given horizontal grid spacing but is independent of the horizontal grid spacing and turbulence modeling of the parent domain. Simulation using a single domain produced less POD energy in the first few modes compared to a coupled simulation (one-way nesting) for similar horizontal grid spacing, which highlights that coupled simulations are required to accurately pass the mesoscale features into the microscale domain.

An actuator line - immersed boundary method for simulation of multiple tidal turbines

This work proposes an efficient actuator line – immersed boundary (AL-IB) method to predict the wake of multiple horizontal-axis tidal turbines (HATTs). A sharp IB method with a simple adaptive mesh refinement strategy is used to improve the computational efficiency. The velocity and other scalar fields adjacent to the solid surface are reconstructed by a moving least square (MLS) interpolation. A computationally efficient AL model is applied to represent the rotors by adding source term to the governing equation rather than resolving the fully geometry of the blade. To predict the turbulent wake, the AL-IB method is implemented with an unsteady Reynolds-averaged Navier–Stokes (URANS) solver. Performance of three types of turbulence models, k−ω−SST model, standard and corrected k−ω model are evaluated. An efficient wall function model is proposed for the MLS-IB approach. The accuracy of the present AL-IB method is validated by numerical tests of a single rotor and multiple tandem arranged IFREMER rotors [1,2]. Wake interference of Manchester rotors [3] with side by side arrangement is also investigated numerically. The predicted wake velocity and turbulence intensity (TI) are in reasonably good agreement with the experimental results.

Evaluation of three turbulence models in predicting the steady state hydrodynamics of a secondary sedimentation tank

The secondary sedimentation tank (SST) is a sensitive and complicated process in an activated sludge process. Due to the importance of its performance, computational fluid dynamics (CFD) methods have been employed to study the underflow hydrodynamics and solids distribution. Unlike most of the previous numerical studies, in the present investigation, the performance of three different types of turbulence models, standard k-ε, RNG k-ε and Realizable k-ε, are evaluated. Firstly, two-dimensional axisymmetric CFD models of two circular SSTs are validated with the field observations. Next, comprehensive comparisons are presented of the model predictions of the key physical quantities, such as the concentration of effluent suspended solids (ESS), and returned activated sludge (RAS), sludge blanket height (SBH), turbulent properties and flow and concentration patterns.A surprising result shows that the prediction of the ESS concentration is not sensitive to the change of turbulence models; while remarkable prediction difference can be observed in the inlet zone and near-field of sludge hopper and SBH. The results suggest that more observations inside the inlet zone are needed to achieve better model calibration and correct application of the turbulence model, which can be crucial to optimizing the geometry of inlet structure and sludge hopper as well as changing return solids concentration for the operation.

Investigation of geometry and dimensionless parameters effects on the flow field and heat transfer of impingement synthetic jets

In order to improve the cooling process in impingement synthetic jets, it is necessary to evaluate the influence of dimensionless parameters and the geometry of the flow field and heat transfer. In this paper, the effects of geometry (confined and unconfined impingement synthetic jets), and jet-to-surface spacings, Reynolds number and dimensionless stroke length on a three-dimensional unsteady impingement synthetic jet are studied. For this purpose, two types of turbulence models, namely the v2−f and SST/k−ω, have been employed. The simulation results have been indicated that the v2−f model comparing to the SST/k−ω model has a close agreement with the available experimental data. The results show that the flow field and the corresponding heat transfer distribution of the impingement synthetic jet are affected by geometry such that an unconfined impingement synthetic jet is more efficient in a cooling process relative to the confined case. Also, increasing jet-to-surface spacing affects the vortex structure and consequently the heat transfer. The stagnation heat transfer rate reaches to the maximum value at an optimum impingement distance as a result of the appropriate ventilation and the coherence vortex structures. The stagnation heat transfer rate experiences several extrema as a result of the increasing stroke length and under the higher stroke length, the impingement synthetic jet acts similar to the impingement continuous jet.

Numerical investigation on cavitation flow of hydrofoil and its flow noise with emphasis on turbulence models

In this study, cavitation flow of hydrofoils is numerically investigated to characterize the effects of turbulence models on cavitation-flow patterns and the corresponding radiated sound waves. The two distinct flow conditions are considered by varying the mean flow velocity and angle of attack, which are categorized under the experimentally observed unstable or stable cavitation flows. To consider the phase interchanges between the vapor and the liquid, the flow fields around the hydrofoil are analyzed by solving the unsteady compressible Reynolds-averaged Navier–Stokes equations coupled with a mass-transfer model, also referred to as the cavitation model. In the numerical solver, a preconditioning algorithm with dual-time stepping techniques is employed in generalized curvilinear coordinates. The following three types of turbulence models are employed: the laminar-flow model, standard k − ε turbulent model, and filter-based model. Hydro-acoustic field formed by the cavitation flow of the hydrofoil is predicted by applying the Ffowcs Williams and Hawkings equation to the predicted flow field. From the predicted results, the effects of the turbulences on the cavitation flow pattern and radiated flow noise are quantitatively assessed in terms of the void fraction, sound-pressure-propagation directivities, and spectrum.

The effect of turbulence modeling on hydrogen jet dispersion inside a compartment space using the HYDRAGON code

ABSTRACTThe mitigation of hydrogen in the containment of nuclear reactor after the Loss of Coolant Accident is essential to preserve the structural reliability of the containment. This paper presents the results of the systematic work done by using the HYDRAGON code to investigate the effect of turbulence models on the concentration distribution of hydrogen and to determine the HYDRAGON code thermal-hydraulic simulation capability during a severe accident at the nuclear power plant. The HYDRAGON code is developed by the Department of Engineering Physics, Tsinghua University, which is an independent research program. The influence of various types of turbulence models, i.e. a standard k − ϵ model, a re-normalized group (RNG) k − ϵ model, and a realizable k − ϵ model were analyzed and the simulation results were compared with the experimental data. When simulation results were compared to experimental data, it was found that, in most compartments, the standard k − ϵ model generally yielded reasonable agreement with the experimental results as compared to RNG k − ϵ and realizable k − ϵ models; however, for probes P7 and P12, better trend was captured by RNG k − ϵ and realizable k − ϵ models, respectively.

Grid independence in the study of boundary layer and its application in Hypergolic Propellants

Numerical simulation and experimental validation of a hypersonic flat plate and isothermal turning wall flow were conducted in the current study. The investigation was based on three kinds of grids (Grid1, Grid2, and Grid3) with laminar flow and three types of turbulence models (BL, SA, and SST). Under the same initiation and different turbulence models, the convergence process of the friction drag coefficient CP and the Stanton number St of a hypersonic flat plate flow revealed four results. First, the flow turbulence effect in the BL model simulation was responsive to CP and St. Second, the SA and SST model simulations both reflected the development process of flow turbulence. Third, the flow turbulence effect in the SST model simulation did not gradually emerge until the laminar flow simulation was sufficient. Moreover, the SA model simulation did not exist on such obvious hysteresis. Fourth, by comparing CP and St of a hypersonic flat-plate laminar simulation under the three grids, the errors of the calculation results of Grid2 and Grid3 were small.