Menter Shear Stress Transport Model Research Articles

SIMULATION OF AIR HEAT TRANSFER IN CIRCULAR PIPES WITH TRIANGULAR AND SQUARE TURBULENCE STIMULATORS FOR HIGH REYNOLDS CRITERIA UP TO ONE MILLION

Objective . Conduct mathematical modeling of tornado zone structure systems between cyclic flow turbulence stimulators with the surface arrangement of triangular and square cross-sections based on multiblock computational techniques, based on solutions of the factorialized finite- volume procedure of the Reynolds equations (closed through the Menter shear stress transport model) and energy equations (on a multiscale intersecting structured grid) at high Reynolds criteria Re=10 6 with an exhaustive analysis of the relevant current lines. Methods. The calculations were carried out on a mathematical foundation based on the solution of the factorized finite-volume procedure of the Reynolds equations, which are closed using the low-Reynolds Menter shear stress transport model, and the energy equations on a multiscale intersecting structured grid (factorized finite-volume procedure). Results . Mathematical simulations of the heat exchange process in straight and round horizontal pipes with turbulence stimulators with d/D=0.95...0.90 and t/D=0.25...1.00 of triangular and square transverse profiles with large Reynolds numbers (Re=10 6 ) on a foundation with multiblock computing technologies, which are based on solutions of factorized and finite-volume Reynolds equations and energy equations, were conducted. It was found that the relative intensification of heat transfer [(Nu/Nu GL )| Re=106 ]/[(Nu/Nu GL )| Re=105 ] in round pipes with square air turbulence stimulators for large Reynolds numbers (Re=10 6 ), which may be relevant in the channels used in heat exchangers, could be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re=10 5 ), for relatively high flow turbulence stimulators d/D=0.90 for the entire range under consideration for the parameter of the relative step between them t/D=0.25...1.00 a little more than 3%; for triangular turbulence stimulators, the crosssection profiles have similar values. For lower square turbulence stimulators with d/D=0.95, this increase in relative heat transfer for large Reynolds numbers (Re=10 6 ) compared to smaller numbers (Re=10 5 ) does not exceed 6%; for triangular cross-section turbulence stimulators, similar indicators are slightly more than 4%. Conclusion. The calculated results based on the developed model can optimize the intensification by turbulence stimulators and control the processes of heat transfer intensification. It is shown that for higher square turbulence stimulators and higher Reynolds numbers, a limited increase in the relative Nusselt criterion Nu/Nu GL is accompanied by a significant increase in the relative hydro resistance due to the very significant influence of return currents, which can flow directly on the turbulence stimulator to the greater extent, the higher the Reynolds number; for triangular turbulence stimulators, the above trend persists and even deepens.

Computational Analysis of Unstart in Variable-Geometry Inlet

Computational fluid dynamics was used to study the flow through a scaled, mixed-compression, high-speed inlet with a rotating cowl at Mach 4.0 conditions. First, steady Reynolds-averaged Navier–Stokes computations were undertaken with a range of popular turbulence models including the Spalart–Allmaras model, the realizable model, the cubic model, and the Menter shear stress transport (SST) model to assess the impact on the inlet operating state. It was found that two models, the Spalart–Allmaras model and the Menter SST model, predicted the inlet to become unstarted at a cowl angle where the experimental data indicated the inlet remained started. Next, steady-state flow structures were studied at three discrete cowl positions, identifying highly three-dimensional flow features including regions of separated flow and spanwise gradients that became stronger as the cowl opened. Finally, the study culminated with the development of the new transient model, which allowed for time-accurate investigation into the unstart, restart, and hysteresis. The evolution of the separation bubbles was shown to be a major factor in the hysteresis, causing the inlet to restart at an angle different from where it unstarted. The utility of unsteady Reynolds-averaged Navier–Stokes computations to capture the complex time-dependent details of such flows was demonstrated.

MODELING HEAT EXCHANGE DEPENDING ON THE PRANDTL NUMBER FOR VARIOUS GEOMETRIC AND REGIME PARAMETERS

Objectives. The aim is to study the dependency of the distribution of integral heat transfer during turbulent convective heat transfer in a pipe with a sequence of periodic protrusions of semicircular geometry on the Prandtl number using the calculation method based on a numerical solution of the system of Reynolds equations closed using the Menter’s shear stress transport model and the energy equation on different-sized intersecting structured grids.Method. A calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations by factored finite-volume method closed with the help of the Menter shear stress transport model, as well as the energy equation on different-scaled intersecting structured grids (fast composite mesh method (FCOM)).Results. The calculations performed in the work showed that with an increase in the Prandtl number at small Reynolds numbers, there is an initial noticeable increase in the relative heat transfer. With additional increase in the Prandtl number, the relative heat transfer changes less: for small steps, it increases; for median steps it is almost stabilised, while for large steps it declines insignificantly. At large Reynolds numbers, the relative heat transfer decreases with an increase in the Prandtl number followed by its further stabilisation.Conclusion. The study analyses the calculated dependencies of the relative heat transfer on the Pr Prandtl number for various values of the relative h/D height of the turbulator, the relative t/D pitch between the turbulators and for various values of the Re Reynolds number. Qualitative and quantitative changes in calculated parameters are described all other things being equal. The analytical substantiation of the obtained calculation laws is that the height of the turbuliser is less for small Reynolds numbers, while for large Reynolds numbers, it is less than the height of the wall layer. Consequently, only the core of the flow is turbulised, which results in an increase in hydroresistance and a decrease in heat transfer. In the work on the basis of limited calculation material, a tangible decrease in the level of heat transfer intensification for small Prandtl numbers is theoretically confirmed. The obtained results of intensified heat transfer in the region of low Prandtl numbers substantiate the promising development of research in this direction. The theoretical data obtained in the work have determined the laws of relative heat transfer across a wide range of Prandtl numbers, including in those areas where experimental material does not currently exist.

Enhanced Delayed Detached Eddy Simulation for Cavities and Labyrinth Seals

Abstract A range of popular hybrid Reynolds-averaged Navier–Stokes -large eddy simulation (RANS-LES) methods are tested for a cavity and two labyrinth seal geometries using an in-house high-order computational fluid dynamics (CFD) code and a commercial CFD code. The models include the standard Spalart–Allmaras (SA) and Menter shear stress transport (SST) versions of delayed detached eddy simulation (DDES) and the Menter scale adaptive simulation (SAS) model. A recently formulated, enhanced, variant of SA-DDES presented in the literature and a new variant using the Menter SST model are also investigated. The latter modify the original definition of the subgrid length scale used in standard DDES based on local vorticity and strain. For all geometries, the meshes are considered to be hybrid RANS-LES adequate. Very low levels of resolved turbulence and quasi-two-dimensional flow fields are observed for the standard DDES and SAS models even for the test cases here that contain obstacles, sharp edges, and swirling flow. Similar findings are observed for both the commercial and in-house high-order CFD codes. For the cavity simulations, when using standard DDES and SAS, there is a significant under prediction of turbulent statistics compared with experimental measurements. The enhanced versions of DDES, on the other hand, show a significant improvement and resolve turbulent content over a wide range of scales. Improved agreement with experimental measurements is also observed for profiles of the vertical velocity component. For the first labyrinth seal geometry swirl velocities are more accurately captured by the enhanced DDES versions. For the second labyrinth seal geometry, the mass flow coefficient prediction using the enhanced models is significantly improved (up to 30%). Standard, industrially available hybrid RANS-LES models, when applied to the present canonical cases can produce little to no resolved turbulent content. The standard SA- and Menter-based DDES models can yield lower levels of eddy viscosity when compared to equivilent steady RANS simulations which means that they are not operating as RANS or LES. It is recommended that hybrid RANS-LES models should be extensively tested for specific flow configurations and that special care is exercised by CFD practitioners when using many of the popular hybrid RANS-LES models that are currently available in commercial CFD packages.

Estimation of the Possibility to Equalize the Fluid Temperature in a Hydrolevelling System by Mixing

Measurement systems that are based on the hydrostatic leveling method under ideal conditions allow one to determine vertical displacements with accuracy on the order of a micron. Heterogeneous and time-varying environmental conditions have a significant effect on the measurement error. One method to increase the accuracy of results is to equalize the temperature of the fluid in the hydrostatic level by mixing the liquid inside it before taking measurements. In this paper, the possibility to perform this operation by forced circulation of the fluid is estimated. For this purpose, a model problem of the circulation flow created by a pump in a simplified analog of the hydrostatic level with allowance for the heat transfer through the hose wall is solved. The fluid dynamics is described by the Reynolds averaged Navier-Stokes equations which are closed by the Menter shear stress transport model. The analytically obtained estimates of heat transfer coefficients on the lateral surface of the hose are refined based on experiments at two values of the flow rate of water flowing through the pipe. The evolution of the temperature field is found from the numerical solution of the coupled heat transfer problem by the finite volume method. In a test example, in which two parts of the hydrostatic level are located in areas with markedly different temperature, the spatial inhomogeneity of the temperature field at different times is calculated. The mixing time sufficient to achieve a temperature distribution close to the homogeneous distribution of the flowing fluid in the hose at different volumes of the mixer joint with the hydrostatic level is determined. The proposed approach can be used under real external conditions for the selection of optimal operation parameters: the pump flow rate, mixing time, and mixing tank volume. The temperature field obtained in the calculation can serve as a basis for estimating the achievable accuracy of the measurement system.

Turbulence Model Assessment in Compressible Flows around Complex Geometries with Unstructured Grids

One of the key factors in simulating realistic wall-bounded flows at high Reynolds numbers is the selection of an appropriate turbulence model for the steady Reynolds Averaged Navier–Stokes equations (RANS) equations. In this investigation, the performance of several turbulence models was explored for the simulation of steady, compressible, turbulent flow on complex geometries (concave and convex surface curvatures) and unstructured grids. The turbulence models considered were the Spalart–Allmaras model, the Wilcox k- ω model and the Menter shear stress transport (SST) model. The FLITE3D flow solver was employed, which utilizes a stabilized finite volume method with discontinuity capturing. A numerical benchmarking of the different models was performed for classical Computational Fluid Dynamic (CFD) cases, such as supersonic flow over an isothermal flat plate, transonic flow over the RAE2822 airfoil, the ONERA M6 wing and a generic F15 aircraft configuration. Validation was performed by means of available experimental data from the literature as well as high spatial/temporal resolution Direct Numerical Simulation (DNS). For attached or mildly separated flows, the performance of all turbulence models was consistent. However, the contrary was observed in separated flows with recirculation zones. Particularly, the Menter SST model showed the best compromise between accurately describing the physics of the flow and numerical stability.

MATHEMATICAL LOW-REYNOLDS MODELING OF HEAT EXCHANGE IIN TURBULENT FLOW IN FLAT CHANNELS WITH TURBULATORS SYMMETRICALLY LOCATED ON BOTH SIDES

ObjectivesThe aim of the study was to simulate the heat transfer in flat channel with turbulators, symmetrically located on its both sides, depending on the channel's geometric parameters and the coolant flow modes followed by the verification of the obtained calculated data by the existing experiment.MethodsThe calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations, closed with the help of the Menter shear stress transport model, by factored finite-volume method, as well as the energy equation on multiscale intersecting structured grids (Fast COmposite Mesh method, FCOM).ResultsA theoretical mathematical calculation model for intensified heat exchange in turbulent flow for a flat channel with turbulators, symmetrically located on both sides, depending on the channel's geometric parameters and coolant flow modes was generated. The calculation results of the intensified heat exchange in flat channels with double turbulators, depending on the determining parameters, are in very good agreement with the existing experimental material and have an undeniable advantage over the latter, since the assumptions made in their derivation cover a much wider range of determining parameters than the limitations of the experiments (Pr = 0.7 ч 100; Re = 103ч 106; h / dЭ= 0.005 ч 0.2; t / h= 1 ч 200). ConclusionAccording to the calculation results based on the developed model, it is possible to optimise the heat exchange intensification in flat channels with double turbulators, as well as to control the process of heat exchange intensification. The comparative calculations of the intensified hydraulic resistance and heat exchange for flat channels with two-sided symmetrical flow turbulators with corresponding data for round channels with turbulators were carried out and analysed. From the point of view of heat exchange intensification, all other conditions being equal, the reduction of a flat channel with two-sided symmetrical turbulators with respect to a round tube with turbulators takes place because a smaller increase in heat exchange is achieved with a greater increase in hydraulic resistance. It was established by calculation that the relative hydraulic resistance ξП/ ξT for channels with turbulators is always higher than for smooth channels; however, the relative heat exchange NuП/ NuT for channels with turbulators can be higher than for smooth channels. Therefore, there is an enhanced redistribution of the temperature drop over the channel section with an intensified heat exchanger. The developed theoretical method based on the solution of the Reynolds equations by the factored finite-volume method, combined with the energy equation on multiscale intersecting structured grids and closed by means of the Menter shear stress transport model, makes it possible, with reasonable accuracy, to calculate heat exchange coefficients and hydraulic resistance in flat channels of practically any forms of double symmetrically located flow turbulators.

High-Order Simulation of Aeronautical Separated Flows with a Reynold Stress Model

Based on the symmetrical conservative metric method, the high-order weighted compact nonlinear schemes with the Speziale–Sarkar–Gatski/Launder–Reece–Rodi- Reynolds stress model are applied to a series of separated flow cases in aeronautics. The relevant cases include the NASA CW-22 transonic turbine cascade, the NASA Common Research Model wing–body configuration, and the wingtip vortex on a NACA 0012 half-span wing. To assess the Reynolds stress model’s predictive capabilities, simulation results are compared with predictions by weighted compact nonlinear schemes with the Menter shear-stress transport model. Moreover, to demonstrate the advantage of high-order methods for separated flow simulations, the second-order method MUSCL is also adopted for comparisons.

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work is to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to uncertainty in the values of closure coefficients for transonic wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients is performed for transonic flow over an axisymmetric bump and the RAE 2822 transonic airfoil. Three turbulence models are considered: the Spalart–Allmaras model, Wilcox (2006) model, and Menter shear-stress transport model. The FUN3D code developed by NASA Langley Research Center is used as the flow solver. The uncertainty quantification analysis employs stochastic expansions based on non-intrusive polynomial chaos for efficient uncertainty propagation. Several integrated and point quantities are considered as uncertain outputs for both computational fluid dynamics problems. Closure coefficients are treated as epistemic uncertain variables represented with intervals. Sobol indices are used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identifies a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic wall-bounded flows.

Simulation of reducing the drag of a Soyuz-type missile’s reentry vehicle with a coaxial disk placed in front of it

The effect of a considerable reduction in the drag of the reentry vehicle of a Soyuz-type missile with a small-sized disk placed in front of it is grounded on the solution by a factorized finite-volume approach of the Navier-Stokes and Reynolds equations, closed in the latter case by a modified Menter shear-stress transport model considering the curvature of the streamlines.

Uncertainty Assessments of Hypersonic Shock Wave-Turbulent Boundary-Layer Interactions at Compression Corners

Simulations of a shock emanating from a compression corner and interacting with a fully developed turbulent boundary layer are evaluated herein. Mission-relevant conditions at Mach 7 and Mach 14 are defined for a precompression ramp of a scramjet-powered vehicle. Two compression angles are defined: the smallest to avoid separation losses and the largest to force higher temperature flow physics. The Baldwin–Lomax and the Cebeci– Smith algebraic models, the one-equation Spalart–Allmaras model with the Catrix–Aupoix compressibility modification, and two-equation models, including the Menter shear stress transport model and the Wilcox k-! 98 and k-! 06 turbulence models, are evaluated. Comparisons are made to existing experimental data and Van Driest theory to provide preliminary assessment of model-form uncertainty. A set of coarse-grained uncertainty metrics are defined to capture essential differences among turbulence models. There is no clearly superior model as judged by these metrics. A preliminary metric for the numerical component of uncertainty in shock– turbulent-boundary-layer interactions at compression corners sufficiently steep to cause separation is defined as 55%. This value is a median of differences with experimental data averaged for peak pressure and heating and for extent of separation captured in new grid-converged solutions presented here.

Drag Prediction on DLR-F6 Wing-Body Configuration

This paper mainly investigate the accuracy of the computed drag on the DLR-F6 Wing-Body configuration, and analyze effect of grid and the turbulence models including the Spalart-Allmaras model, Wilcox’s k-ω model and Menter shear-stress transport model on aerodynamic forces for wing-body configuration. The computed results show that grid refinement has little effect on the pressure distributions, significant effect on drag. The turbulence models have certain effects on the pressure distributions, especially positions of the shock wave. They have obvious effects on drag, particularly friction drag. This study shows that performing the CFD calculation at the same angle-of-attack as experiment resulted in good comparisons with wing surface pressures.

Numerical Simulations of a Wingtip Vortex in the Near Field

We investigate the accuracy of current state-of-the-art turbulence models and a compressible Reynolds-averaged Navier-Stokes solver in computing the formation of a wingtip vortex in the near field. The Reynolds-averaged Navier-Stokes solvers used in this investigation are the NPARC WIND 5.0 and Wind-US 1.0 codes. The turbulence models explored are the standard Spalart-Allmaras model, the Spalart-Allmaras model with correction for system rotation and streamline curvature, the Menter shear stress transport model, and the Rumsey-Gatski explicit algebraic stress model. Additionally, we study how solution accuracy is affected by using higher-order numerical schemes as opposed to more grid points. Accuracy is assessed by comparing the results of the wingtip-vortex computations with the data of a reliable, thorough experiment. The solutions obtained using a fifth-order-accurate numerical scheme show that the Spalart-Allmaras turbulence model with corrections for rotation and streamline curvature predicts the mean flow most accurately. However, we find that within the vortex, none of the turbulence models explored accurately captures the magnitudes of the turbulence quantities or the lag of the Reynolds stress components behind the corresponding strain-rate components.