Menter's Shear Stress Transport Research Articles

Effect of the wing trailing-edge flaps and spoilers position on the jet-vortex wake behind an aircraft during takeoff and landing run

The large-scale vortex structure of flow in the near wake behind an aircraft during its run on a runway is investigated numerically. The geometrical aircraft configuration was taken close to a mid-range commercial aircraft like Boeing 737-300. It included all essential elements: a body (fuselage), wings with winglets, horizontal and vertical stabilizers, engine nacelles, nacelle pylons, inboard flap track fairings, leading-edge and trailing-edge flaps, and spoilers. The position of flaps and spoilers corresponded to the takeoff and landing run conditions. Computational simulation was based on solving the Reynolds averaged Navier–Stokes equations closed with the Menter Shear Stress Transport turbulence model. Patterns of streamlines, fields of the axial vorticity and the turbulent intensity, vertical and horizontal velocity profiles in the wake are compared and discussed for both run regimes. The flow model was preliminary tested for validity by comparison of the calculated velocity profiles behind a reduced-scale aircraft model with those obtained in special wind tunnel experiments.

Effect of Turbulence Model Uncertainty on Scramjet Isolator Flowfield Analysis

The goal of this work was to quantify the uncertainty in the solution of a scramjet isolator flowfield due to the uncertainty in the closure coefficients of commonly used turbulence models in Reynolds-averaged Navier–Stokes simulations. The Menter baseline, Menter shear stress transport, Spalart–Allmaras, and Wilcox-2006 turbulence models were examined; and simulations were carried out using the VULCAN flow solver. Nonintrusive polynomial chaos theory was used for efficient uncertainty propagation, and Sobol indices were employed to establish relative sensitivities of the flow solution to closure coefficients. The results obtained were compared to experimental data as well as to previous work focusing on relevant flow problems. Sets of closure coefficients that contribute most to solution uncertainty for each turbulence model were identified, which warrant further investigation because more knowledge about the effects of these coefficients is expected to reduce the uncertainty in the numerical design of scramjet isolators.

Thermofluid Characteristics of Czochralski Melt Convection Using 3D URANS Computations

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

Reynolds-averaged Navier–Stokes modelling in transonic S-ducts with passive flow control

S-duct diffusers are used in aircraft with embedded engines to route ambient air to the fan face. Sizing and stealth considerations drive a need for high curvature ducts, but the curvature causes complex secondary flows that lead to total pressure distortion and swirl velocities at the engine face. These must be controlled for stable engine operation. In this paper, tubercles, a novel bio-inspired passive flow control method, are analysed numerically in a duct with transonic flow. The results are compared to experimental data obtained as part of a campaign at the Royal Military College, Canada to investigate the effects of S-duct geometry and novel passive flow control devices on the performance of transonic S-ducts. The performance of Reynolds-averaged Navier–Stokes turbulence models in the S-ducts is assessed – Menter's shear stress transport model predicts excessive losses due to the overactivity of its stress limiter. The realisable k–ɛ model gives a significant improvement in the prediction of static pressure distributions, but losses and distortion characteristics are predicted poorly due to the model's inability to resolve the effects of unsteadiness in separated regions. Large tubercle geometries are found to trigger earlier separation in the centre of the duct by concentrating low momentum fluid in valleys, but they also act as boundary layer fences away from the duct centre. Smaller geometries are found to generate vortices that re-energise the boundary layer, delaying flow separation. Methods are recommended for future computational analyses of S-ducts and new designs of tubercles.

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.

Determination of pitch angles and wind speeds ranges to improve wind turbine performance when using blade tip plates

In this article a wind turbine performance enhancement is studied numerically using two type of tip plates. A three dimensional finite volume code is developed to simulate the wind turbine flow field periodically at different wind speeds and pitch angles. The well-known Menter's Shear Stress Transport (kω−SST) turbulence modelling is incorporated into the code to investigate the turbulent flow field that occurs in wind turbines. Here we show that using tip plates for wind turbines performance improvement can only occur if the turbine blade pitch angle is set at the maximum output power based on the given wind speed. Otherwise, using the tip plates play negative role and reduce the wind turbine output power. This physical effect is related to the wind turbine working condition at which both the blade span-wise flow as well as the tip blade trailing vortices stay at their minimum amount.

Uncertainty and sensitivity analysis of SST turbulence model on hypersonic flow heat transfer

Due to the lacking of knowledge and incomplete information about the closure coefficients in Menter Shear Stress Transport (SST) turbulence model, numerical predictions of hypersonic flow heat transfer possess some uncertainties. The objective of this work is to investigate the uncertainty and identify the key parameters contributing most to the uncertainty in hypersonic aeroheating predictions. In the current study, the nine closure coefficients in SST turbulence model are treated as uncertainty variables represented with intervals, meanwhile stochastic expansion based on non-intrusive polynomial chaos (NIPC) expansion is utilized to represent and propagate the uncertainties, afterwards the Sobol indices evaluated by the polynomial chaos expansion coefficients are used to rank the relative contribution of each closure coefficient. Totally, 110 CFD evaluations are adopted to quantify the uncertainty and sensitivity in hypersonic flow heat transfer. Specifically, uncertainty and sensitivity analysis are performed for hypersonic flow over the double-ellipsoid model and the X-33 flight vehicle. The numerical results show that heat flux is more sensitive to uncertainty of closure coefficients compared to pressure. For the SST model, the coefficients which contribute most to uncertainty in hypersonic flow heat are σω1, κ and a1. While a1 is one of the dominant source of heat flux and pressure in the shock region near the wall.

Numerical investigation of the supersonic stabilizing parachute's heating loads

In the design of the scale reduced model of the new generation reusable re-entry capsule, the supersonic stabilizing parachute should be applied to avoid the failure of the main parachute due to the uncertainty of the space capsule's attitude. Compared with the inflation technology during the subsonic process, special attention should be paid to the aerodynamic heating loads during the inflation process at supersonic speeds. In this manuscript, the inflation process of the supersonic stabilizing parachute is numerically studied by adopting the fluid–structure coupling method. The three-dimensional compressible Reynolds Averaged Navier–Stokes (RANS) equations are simulated and Menter's shear stress transport (SST) turbulence model is applied. Also, we study the aerodynamic heating loads of the stabilizing parachute by conducting numerical simulations at a typical reentry trajectory point. Results suggest that the wake of the capsule increases the temperature of the flow field remarkably. Also, the inner faces of the parachute encounter severer heating loads than the outer faces, and the severest heating load appears at the first horizontal parachute belt.

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.

The effect of coolant injection from the tip of spike on aerodynamic heating of nose cone at supersonic flow

Aerodynamic heating is the main challenge for increasing the speed of hypervelocity vehicles. In this work, three-dimensional numerical simulations have been performed to investigate the influence of the cooling injection from the tip of the spike mounted on the nose cone. This work comprehensively focused on the effect of different types of gas injections (Air, He and CO2) on the flow feature and mechanism of cooling through three-dimensional simulations. Comprehensive parametric studies are performed to reveal the main effective parameters on the cooling performance along the nose cone. In order to perform numerical simulations, Reynolds-averaged Navier–Stokes equations with Menter's Shear Stress Transport (SST) turbulence model are applied. Our findings show that the injection of the CO2 jet from the tip of a spike is more efficient on the cooling of the nose cone due to the formation of larger circulation in the vicinity of the spike. In addition, the mass distribution of these two jets confirms that helium jets penetrate more in the upstream. Our results clearly show that the effect of the helium in low jet pressure is more significant on the cooling performance of the nose cone.

Numerical study on the internal flow characteristics of an axial-flow pump under stall conditions

When an axial-flow pump works in low flow rate conditions, rotating stall phenomena will probably occur, and the pump will enter hydraulic unsteady conditions. The rotating stall can lead to violent vibration, noise, turbulent flow, and a sharp drop in efficiency. This affects the safety and stability of the pump unit. To study the rotating stall flow characteristics of an axial-flow pump, the steady and unsteady internal flow field in a large vertical axial-flow pump was investigated using 3D computational fluid dynamic (CFD) technology. Numerical calculations were carried out using the Reynolds-averaged Navier–Stokes (RANS) solver and Menter's shear stress transport (SST) k-ω turbulence model. Steady flow characteristics including streamline, velocity vector, pressure and turbulent kinetic energy are presented and analyzed. Unsteady flow characteristics are described using post-processing signals for pressure monitoring points in the time and frequency domains. Using Q-criterion, the locations and evolution rules of the core region of the vortex structure in guide vanes under deep stall conditions were investigated. The reliability of the numerical simulation results was verified using the experimental prototype pressure fluctuation test. In this way, typical flow structure and pressure fluctuation characteristics in an axial-flow pump were analyzed, with contrastive analysis in design condition and stall conditions. Finally, the mechanism of low-frequency pressure fluctuation in a pump unit under the stall condition was revealed.

Numerical investigation of blunt body’s heating load reduction with combination of spike and opposing jet

In the design of the new generation reusable re-entry space vehicle, how to effectively reduce the heating load is important. In this paper, the thermal protection system combining the spike technology with the opposing jet technology is investigated. The three-dimensional compressible Reynolds Averaged Navier–Stokes (RANS) equations are simulated and Menter's shear stress transport (SST) turbulence model is applied. Also, the all-speed flux scheme called E-AUSMPWAS is adopted. The grid study is done and the numerical procedure is validated. Models with spikes of different lengths and opposing jets of different pressures are compared. Results show that the total pressure of the jet and the length of the spike have significant influences on the peak heating load of the vehicle. Also, the total heating load can reduce almost 95% compared to the base model. The findings suggest that the thermal protection system, which combines the spike technology with the opposing jet technology, is promising to be widely used in the design of the new generation reusable re-entry space vehicle.

Numerical study on lateral jet interaction in supersonic crossflows

This paper presents numerical analyses of lateral jets in supersonic cross flows on a flat plate and on a generic missile. The freestream Mach number is 4 for the flat plate and 3 for the missile, and the jets are sonic for both cases. The numerical results are validated with wind tunnel data such as Schlieren images and surface pressure distributions. The flow structure due to the jet interaction with the supersonic free-stream is examined in terms of the vortex structure. A 3-dimensional compressible RANS solver is used for the study. To describe the effects of high temperature, a thermally perfect gas is assumed. When high temperature is applied, the shock structure changes, which affects the separation region and recirculation zone. Next, the effects of turbulence models on the jet interaction flow are investigated. The Spalart–Allmaras, Menter's shear-stress transport k–ω, Huang and Coakley's k–ε, and Coakley's q–ω models are used to analyze the flows. The differences in pressure distribution among the turbulence models are larger in the case of the flat plate than the missile. In addition, several numerical flux functions are compared to investigate their effects on the jet interaction: the Roe scheme with Sanders's H-correction, RoeM scheme, and the HLLE scheme. Although the HLLE scheme shows a little difference at the indent of the barrel shock, the three numerical flux schemes give similar CP distributions on the wall.

An improved SST [formula omitted] model for pollutant dispersion simulations within an isothermal boundary layer

The selection of turbulence models has always been one of the important aspects of computational fluid dynamics model simulations of wind flow and pollutant dispersion problems. The commonly industrially adopted steady Reynolds-averaged Navier–Stokes turbulence models are the realizable k−ε model and Menter's shear stress transport k−ω model.In this study, we demonstrated that the realizable k−ε model and Menter's SST k−ω model produced non-satisfactory correlation results with the experimental data, in terms of the normalized pollutant concentration for a cuboid obstacle.Here, an improved formulation of Menter's SST k−ω turbulence model, particularly for the wind flow and pollutant dispersion simulations, is applied. The modifications have been added in a systematic manner which include the addition of damping functions in the closure equations, the inclusion of the turbulent cross-diffusion term in the omega equation, and the re-establishment of model constants and parameter profiles. Considerable improvement in the correlation between the prediction and the experimental data up to a value of 0.78 with matching wind and turbulent kinetic energy profiles was obtained by the proposed model. Significant reduction of more than 80% in NSME and a satisfactory FAC2 value of 0.54 are also achieved with the improved model.

Quantification and Analysis of the Irreversible Flow Loss in a Linear Compressor Cascade.

A local loss model and an integral loss model are proposed to study the irreversible flow loss mechanism in a linear compressor cascade. The detached eddy simulation model based on the Menter shear stress transport turbulence model (SSTDES) was used to perform the high-fidelity simulations. The flow losses in the cascade with an incidence angle of 2°, 4° and 7° were analyzed. The contours of local loss coefficient can be explained well by the three-dimensional flow structures. The trend of flow loss varying with incidence angle predicted by integral loss is the same as that calculated by total pressure loss coefficient. The integral loss model was used to evaluate the irreversible loss generated in different regions and its varying trend with the flow condition. It as found that the boundary layer shear losses generated near the endwall, the pressure surface and the suction surface are almost identical for the three incidence angles. The secondary flow loss in the wake-flow and blade-passage regions changes dramatically with the flow condition due to the occurrence of corner stall. For this cascade, the secondary flow loss accounts for 26.1%, 48.3% and 64.3% of the total loss for the flow when the incidence angles are 2°, 4° and 7°, respectively. Lastly, the underlying reason for the variation of the secondary flow loss with the incidence angle is explained using the Lc iso-surface method.

The influence of coolant jet direction on heat reduction on the nose cone with Aerodome at supersonic flow

Reduction of aerodynamic heating is a critical issue for the development of the hypersonic vehicles. In this study, a computational fluid dynamic is applied to study the effect of location of coolant jet in the vicinity of the aerodome on the heat reduction of the nose cone at M = 5. In addition, the influence of the gas types (Air, He and CO2) on the cooling performance is investigated. This research mainly focused the flow feature and mass distributions of various coolant jets. In order to study these effects, a two-dimensional model with spike is chosen to simulate the various shocks in the vicinity of the nose cone. The effect of significant parameters is studied by using the Reynolds-averaged Navier–Stokes equations with Menter's Shear Stress Transport (SST) turbulence model. Results show that the injection of the coolant gas from the top of aerodome significantly decreases the heat load on the nose cone. In addition, injection of the coolant jet from the top is more efficient on the recirculation region on the top of spike. The obtained results reveal that the injection of coolant from the front of the aerodome does not reduce the heat load substantially. In addition, the cooling performance of helium jet as the lateral jet is 15% more than other gases.

Grid Influence on Turbulence Model Coefficient Uncertainties in Transonic Wall-Bounded Flows

The goal of this work is to determine the effect of grid topology and flow solver discretization on the uncertainty quantification and sensitivity analysis of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to uncertainty in the values of turbulence model coefficients as well as to rank the contribution of each coefficient to uncertainty in various output quantities of interest for transonic flow over an RAE 2822 airfoil. Three turbulence models were considered: Spalart–Allmaras, 2006 Wilcox , and Menter shear-stress transport. Several structured and unstructured grid topologies were employed in the analysis. The Fun3D code of NASA Langley Research Center and the BCFD code of the Boeing Company were used as the flow solvers. The uncertainty analysis employed stochastic expansions based on nonintrusive polynomial chaos for efficient uncertainty propagation. Sobol indices were used to rank the relative contributions of each coefficient to the total uncertainty in the output quantities of interest. The solutions obtained with all grids and computational-fluid-dynamics codes identified a common set of coefficients for each turbulence model that influence the output uncertainty significantly for transonic wall-bounded flows.

Effect of dual micro fuel jets on mixing performance of hydrogen in cavity flameholder at supersonic flow

In this article, numerical simulations were done to study the influence of the various hydrogen injections on the mixing rate in the cavity flameholder of the scramjet. This study tried to present the main effective parameters on the flow feature and distribution of the hydrogen jet within a cavity in supersonic free stream domain. In order to simulate the cavity flameholder with micro air/fuel jets, a three-dimensional model is chosen and computational fluid dynamic approach is used for the simulations. The effect of significant parameters is studied by using the Reynolds-averaged Navier–Stokes equations with Menter's Shear Stress Transport (SST) turbulence model. The effect of horizontal and vertical fuel injection is comprehensively studied. Moreover, the characteristics of the mixing in various free stream velocities (M = 1.2, 2.2 and 3.2) are examined and the effects of micro air jet on the size of ignition domain for preserving flame holder are investigated. Results show that the increase of free stream Mach number significantly enhances the mixing of horizontal fuel injection in the cavity. The obtained results reveal that the injection of micro air jets enhances the mixing rate in low Mach number (M = 1.2). Our findings also show that vertical hydrogen injection considerably increases the mixing zone within the cavity and the mixing rate significantly improves by rising free stream velocity.

The influence of micro air jets on mixing augmentation of fuel in cavity flameholder at supersonic flow

In this study, numerical simulations are performed to study the effect of micro air jets on the mixing of fuel in the cavity flameholder of the scramjet. This research mainly focused the optimum position of fuel (C2H4) injection on the mixing rate inside the cavity. In order to simulate the cavity flameholder with micro air/fuel jets, a three-dimensional model is chosen and computational fluid dynamic approach is used for the simulations. The effect of significant parameters is studied by using the Reynolds-averaged Navier–Stokes equations with Menter's Shear Stress Transport (SST) turbulence model. In this work, the transient study is also performed to reveal the flow feature and mass distribution inside the cavity in the supersonic free stream (M=2.2). Results show that the injection of the fuel in the middle of the vertical wall significantly enhances the mixing of fuel in the cavity. The obtained results reveal that the injection of micro air jets distributes the fuel uniformly inside the cavity. Therefore, an enhanced mixing zone occurs in the downstream of the injection slots which lead to flame-holding.

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.