Reynolds-Averaged Navier-Stokes Code Research Articles

Calibration of the Transitional Turbulence Model

In the present paper, the turbulent transition model from Langtry and Menter (“Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes,” AIAA Journal, Vol. 47, No. 12, 2009, pp. 2894–2906) is implemented in the structured finite volume Reynolds-averaged Navier–Stokes code FANSC and coupled with the shear-stress transport turbulence model. The model is modified and recalibrated to better match experimental results. The local turbulent intensity is replaced with a more consistent turbulent fluctuation representation to avoid nonphysical solutions at the stagnation point that would contaminate the downstream boundary-layer predictions. A calibration is devised by customizing several constants involved in the equation for the intermittency and the destruction term for the turbulent kinetic energy . An optimization algorithm is thus employed to facilitate the calibration on well-known two-dimensional test cases, such as the flat plates of the T3 series and of Schubauer and Klebanoff (“Contributions on the Mechanics of Boundary-Layer Transition,” NACA TN 3489, 1955), as well as the NACA 0012 airfoil. The calibrated model is then validated on the NLF-0416 and S809 airfoil cases that have not been involved in the optimization process.

Analysis and comparison of turbulence model coefficient uncertainty for canonical flow problems

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-Averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for a set of turbulence model validation cases that represent the structure of several canonical flow problems. The study focuses on the analysis of a 2D Zero Pressure Gradient Flat Plate, a 2D NASA Wall Mounted Hump, and an Axisymmetric Shock Wave Boundary Layer Interaction, all of which are well documented on the NASA Langley Research Center Turbulence Modeling Resource website. The Spalart–Allmaras (SA), the Wilcox (2006) κ−ω (W2006), and the Menter Shear-Stress Transport (SST) turbulence models are considered in the stochastic analyses of these flow problems, and the FUN3D code was utilized as the flow solver. The uncertainty quantification approach involves stochastic expansions based on non-intrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results generalize a set of closure coefficients which have been identified as contributing most to the uncertainty in various output quantities of interest for the set of canonical flow problems considered in this study. Mainly, the SA turbulence model is most sensitive to the uncertainties in the diffusion constant (σ), the log layer calibration constant (κ), and the turbulent destruction constant (cw2). The predictive capability of the W2006 model is most sensitive to the uncertainties in a dissipation rate constant (σw), the shear stress limiter (Clim), and a turbulence-kinetic energy constant (β*). Likewise, the SST turbulence model was found to be most sensitive to the diffusion constants (σw1 and σw2), the log layer calibration constant (κ), and the shear stress limiter (a1).

A simplified model for transition prediction applicable to wind-turbine rotors

Abstract. This work aims to develop a simple framework for transition prediction over wind-turbine blades, including effects of the blade rotation and spanwise velocity without requiring fully three-dimensional simulations. The framework is based on a set of boundary-layer equations (BLEs) and parabolized stability equations (PSEs), including rotation effects. An important element of the developed BL method is the modeling of the spanwise velocity at the boundary-layer edge. The two analyzed wind-turbine geometries correspond to a constant airfoil and the DTU 10-MW Reference Wind Turbine blades. The BL model allows an accurate prediction of the chordwise velocity profiles. Further, for regions not too close to the stagnation point and root of the blade, profiles of the spanwise velocity agree with those from Reynolds-averaged Navier–Stokes (RANS) simulations. The model also allows predicting inflectional velocity profiles for lower radial positions, which may allow crossflow transition. Transition prediction is performed at several radial positions through an “envelope-of-envelopes” methodology. The results are compared with the eN method of Drela and Giles, implemented in the EllipSys3D RANS code. The RANS transition locations closely agree with those from the PSE analysis of a 2D mean flow without rotation. These results also agree with those from the developed model for cases with low 3D and rotation effects, such as at higher radial positions and geometries with strong adverse pressure gradients where 2D Tollmien–Schlichting (TS) waves are dominant. However, the RANS and PSE 2D models predict a later transition in the regions where 3D and rotation effects are non-negligible. The developed method, which accounts for these effects, predicted earlier transition onsets in this region (e.g., 19 % earlier than RANS at 26 % of the radius for the constant-airfoil geometry) and shows that transition may occur via highly oblique modes. These modes differ from 2D TS waves and appear in locations with inflectional spanwise velocity. However, except close to the root of the blade, crossflow transition is unlikely since the crossflow velocity is too low. At higher radial positions, where 3D and rotation effects are weaker and the adverse pressure gradient is more significant, modes with small wave angles (close to 2D) are found to be dominant. Finally, it is observed that an increase in the rotation speed modifies the spanwise velocity and increases the Coriolis and centrifugal forces, shifting the transition location closer to the leading edge. This work highlights the importance of considering the blade rotation and the three-dimensional flow generated by that in transition prediction, especially in the inner part of the blade.

Coarse grained simulations of shock-driven turbulent material mixing

We revisit coarse-grained simulation strategies for turbulent material mixing applications involving shock-driven turbulence in the context of the Radiation Adaptive Grid Eulerian (xRAGE) hydrodynamics and Besnard–Harlow–Rauenzahn (BHR) Reynolds-averaged Navier–Stokes codes, using newly available Low-Mach-Corrected (LMC) xRAGE hydrodynamics. Impact assessments are based on comparisons with a relevant shock-tube experiment for which turbulent mixing and velocity data are available. xRAGE Implicit Large-Eddy Simulation (ILES) and a recently proposed xRAGE-BHR bridging paradigm are tested. Bridging models turbulent stresses dynamically, based on decomposing the full stress into modeled and resolved components, using a differential filter as a secondary filtering operation to define the resolved part, and additionally requiring the resolved stress to approach the full stress with grid resolution refinement to ensure realizability of the bridging-based large-eddy simulation. Much improved scale-resolving with LMC-xRAGE ILES and with dynamic LMC-xRAGE/BHR bridging enables higher simulated mixing and turbulence levels on coarser grids. For the tested planar shock-tube case, the more-accurate models can achieve the same level of accuracy with less resolution than required with the highest-fidelity turbulence simulation models typically used at scale with default xRAGE hydrodynamics; two-levels of grid-coarsening savings can be thus achieved for the mixing prediction in these comparisons: one associated with the more-accurate LMC xRAGE hydrodynamics and an additional one from using the dynamic xRAGE-BHR bridging.

Analysis of Turbulence Model Uncertainty for Shock-Wave/Boundary-Layer Interaction Simulations

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for shock-wave/turbulent boundary-layer interaction simulations. The study focuses on the analysis of an axisymmetric shock-wave/boundary-layer interaction (ASWBLI) turbulence model validation case including an axisymmetric cylindrical body with a trailing-edge flare of 20 deg at an upstream Mach number of 7.11. The Spalart–Allmaras, the Wilcox 2006 , and the Menter shear-stress transport turbulence models are considered in the stochastic analyses of the ASWBLI, which used the FUN3D flow solver. The uncertainty quantification approach involves stochastic expansions based on nonintrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results of the current study identify a set of closure coefficients that contribute most to the uncertainty in various output quantities of interest, which are also consistent with the similar shock-induced separation studies.

On the Influence of High Turbulence on the Convective Heat Flux on the High-Pressure Turbine Vane LS89

High-pressure turbine vanes and blades are subjected to a turbulent combustor flow affecting the heat transfer and boundary layer transition, hence, the temperature distribution. The accurate prediction of the temperature distribution is crucial for a reliable design and cooling implementation. Engine-representative measurements are hence mandatory for improving design tools. Recently, convective heat transfer measurements were conducted on a high-pressure turbine inlet guide vane (VKI LS89 airfoil) in the Isentropic Compression Tube (CT-2) facility at the von Karman Institute. This contribution focuses on the effect of high freestream turbulence generated by a new turbulence grid allowing a range of turbulence intensities in excess of 10% with representative length scales of the order of 1–2 cm. Three cases with varying turbulence levels are discussed in this paper. The different flow conditions are exit isentropic Mach numbers of 0.70–0.97, Reynolds numbers of 0.53∙× 106 and 1.15∙× 106 and a constant temperature ratio equal to 1.36. The heat transfer distributions along the vane suction side indicate a clear link between boundary layer transition and the stream-wise pressure gradients even at high levels of freestream turbulence intensity. Differences are put in evidence in the dynamics of the transition development. Future developments will focus also on the contribution of the other flow parameters under high turbulence. Heat transfer predictions from the boundary layer code TEXSTAN and Reynolds-Averaged Navier–Stokes code elsA (ensemble logiciel pour la simulation en Aérodynamique) are additionally compared to the experiments. Inherent difficulties associated with high turbulence modelling are clear from this early numerical work.

Starting flow in an impulse wind tunnel with a throttled prechamber

The unsteady axisymmetric flow forming in the process of starting an impulse wind tunnel equipped with a throttled prechamber was numerically simulated. A regime with the operating flow Mach number M = 8 was under consideration. Numerical simulation on the basis of Reynolds-averaged Navier–Stokes code and the k-ω SST turbulence model was performed. The starting process was simulated as a sudden rupture of a diaphragm separating the prechamber volume with high pressure and temperature from low pressure part of the facility including a nozzle, an operating section and an exhaust vacuum tank.. The diaphragm rupture initiates a gasdynamic process associated with the Riemann problem when the primary shock wave arises which moves through the nozzle to the operating section. Computed data show another “inverse” shock wave emerging in the nozzle. A starting “shock-wave package” forms between these shock waves, it includes a flow portion of high temperature and pressure. The specificity is discussed of identified the characteristics and flow patterns forming during the process of moving the shock-wave package.

Vortex-Sheet Representation of Leading-Edge Vortex Shedding from Finite Wings

A characteristic feature of flows past many oscillating airfoils and wings is the leading-edge vortex (LEV). Although considerable progress has been made in the low-order modeling of LEV formation over airfoils, the prediction of LEV formation on finite wings remains a challenge. A low-order method is presented for modeling the formation of the LEV on finite wings. An unsteady vortex-lattice method has been augmented to model the effect of the LEV, which is modeled as a vortex sheet. The criticality of leading-edge suction is used to modulate the formation of the LEV at different spanwise locations of the wing. This feature enables prediction of the spanwise location of the LEV onset and the subsequent nonuniform growth of the LEV on the wing. A good comparison of the predicted flow features is seen with results from a higher-order Reynolds-averaged Navier–Stokes code. The predicted forces are also in reasonable agreement. The LEV sheet model has the potential to be used in a variety of low-order methods for rapid prediction of unsteady finite-wing aerodynamics.

Low-Order Model for Prediction of Trailing-Edge Separation in Unsteady Flow

Computational and experimental results for pitching and plunging airfoils were used to study the time lag associated with boundary-layer convection and to develop a model that can be used to augment inviscid theoretical methods for unsteady airfoil flows to include the effects of trailing-edge separation and unsteady stall. Computations using an unsteady Reynolds-averaged Navier–Stokes code were used to obtain results for airfoils in steady flow and for several pitch and plunge motions. The motions were selected such that stall occurred only due to trailing-edge separation without leading-edge vortex formation. Viscous corrections to inviscid airfoil theory are first calculated in steady flow by implementing a nonlinear decambering flap to model the effect of the separated boundary layer. A leading-edge suction parameter, from earlier research, is used to connect the aerodynamic state in unsteady motion with a steady-state condition. Computational results showed that the differences in aerodynamic loads between steady and unsteady flows can be attributed to the boundary-layer convection lag, which can be modeled by choosing an appropriate value of a time-lag parameter . To provide appropriate viscous corrections to inviscid unsteady calculations, the nonlinear decambering flap is applied with a time lag determined by the value, which was found to be essentially independent of motion kinematics for a given airfoil and Reynolds number. The predictions of the aerodynamic loads, unsteady stall, hysteresis loops, and flow reattachment from the low-order model agree well with computational fluid dynamics and experimental results, both for individual cases and for trends between motions. The model was also found to perform as well as existing semi-empirical models while using only a single empirically defined parameter.

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.

Numerical investigation of the vortex-induced vibration of an elastically mounted circular cylinder at high Reynolds number (Re = 104) and low mass ratio using the RANS code.

This study numerically investigates the vortex-induced vibration (VIV) of an elastically mounted rigid cylinder by using Reynolds-averaged Navier–Stokes (RANS) equations with computational fluid dynamic (CFD) tools. CFD analysis is performed for a fixed-cylinder case with Reynolds number (Re) = 104 and for a cylinder that is free to oscillate in the transverse direction and possesses a low mass-damping ratio and Re = 104. Previously, similar studies have been performed with 3-dimensional and comparatively expensive turbulent models. In the current study, the capability and accuracy of the RANS model are validated, and the results of this model are compared with those of detached eddy simulation, direct numerical simulation, and large eddy simulation models. All three response branches and the maximum amplitude are well captured. The 2-dimensional case with the RANS shear–stress transport k-w model, which involves minimal computational cost, is reliable and appropriate for analyzing the characteristics of VIV.

Dynamic overset rans simulation of a wave-driven device for the oxygenation of deep layers

The most common methods of counteracting hypoxic events at the bottom sea layers are indirect measures aimed to reduce organic load introduced in the environment. No direct approach has been investigated except the WEBAP and OXYFLUX devices. The estimation of the surface water pumped from such devices is still largely based on physical or empirical methods. The present work adopts the CFD approach to the estimation of the pumped surface water as well as the analysis of the dynamic response of the OXYFLUX device. By means of a Reynolds-averaged Navier-Stokes code, through overset grid method, the 1:16 OXYFLUX model's dynamic response and pumping performance are evaluated under the action of 13 regular wave states. A grid sensitivity analysis is performed in order to define the best configuration able to describe the function of the device. The model is validated by comparing numerical and physical results of heave decay test, while systematic studies on the heave response and pumping performance under the action of regular waves are completed through the paper. The results demonstrate the importance of nonlinear effects, including viscous drag, wave overtopping and the interaction between heave and pitch modes. Moreover, the study shows also that nonlinear effects significantly decrease the dynamic response of the device and generate a second harmonic for pitch response, increasing the capacity of the OXYFLUX to be overtopped by small waves caused by the summer breeze typical of the hypoxic events.

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.

Study of the Liquid Breakup Process in Solid Rocket Motor

In a solid rocket motor, when the aluminum based propellant combusts, the fuel is oxidized into alumina (). It tends to agglomerate into molten droplets, impinge on the chamber walls, and then flow along the nozzle wall. Such agglomerates cause erosive damage. The focus of the current research is to characterize the agglomerate flow within the nozzle section by studying the breakup process of the liquid film that flows along the wall of a straight test channel while a relatively higher-speed gas moves over it. We have used an unsteady-flow Reynolds-averaged Navier–Stokes code to investigate the interaction of the liquid film flow with the gas flow. The rate of the wave breakup was characterized by introducing breakup length, Ohnesorge number, and Weber number for various flow conditions. Based on the volume fraction of the liquid, these three numbers are indicators of the level of liquid breakup. We summarize that a larger breakup length relates to a high breakup state of the liquid because the appearance of droplets contributes to a larger total boundary length during calculation.

Parabolized Stability Equations Code with Automatic Inflow for Swept Wing Transition Analysis

This paper aims at developing a parabolized stability equation transition analysis code coupled to the industrial in-house accurate Reynolds-averaged Navier–Stokes code developed at Israel Aerospace Industries for stability analysis of three-dimensional boundary layers over swept wings. In the first step, the parabolized stability equation derivation in a body-fitted coordinate system is exposed, as well as its classical initialization, using the solution procedure of the global Chebyshev eigenvalue problem for the linear stability equations. This initialization procedure demands large user interactions, and it prevents the parabolized stability equation method to be of practical use in an industrial environment. Therefore, one exposes in the second step a new way to automatically generate the inflow solution of the linear stability equations needed by the parabolized stability equations. This new robust approach paves the way for innovative automatic industrial use of the parabolized stability equation technology without the need to involve the user. This approach supplies the inflow conditions required for the parabolized stability equation marching procedure without the need to solve the standalone linear stability global eigenvalue problem. The solution of the linear stability equations at initialization is now obtained by iteratively converging the local linear stability solver starting from the new inflow empirical approximation obtained in two special coordinate systems for crossflow and Tollmien–Schlichting, respectively. These formulas represent some invariant functions of the stability characteristics of the exact Navier–Stokes laminar boundary-layer profiles instead of self-similar boundary-layer profiles like the Falkner–Skan–Cooke. Standard academic validation test cases and industrial results of the parabolized stability equation/Reynolds-average Navier-Stokes codes on a generic unmanned aerial vehicle swept wing are exposed.

Predicting wind farm wake interaction with RANS: an investigation of the Coriolis force

A Reynolds-averaged Navier-Stokes code is used to simulate the interaction of two neighboring wind farms. The influence of the Coriolis force is investigated by modeling the atmospheric surface/boundary layer with three different methodologies. The results show that the Coriolis force is negligible for a single wind turbine, small for a single wind farm, but important for simulations of wind farm wake interaction.

Grid-Adapted FUN3D Computations for the Second High-Lift Prediction Workshop

Contributions of the unstructured Reynolds-averaged Navier–Stokes code FUN3D to the 2nd AIAA Computational Fluid Dynamics High-Lift Prediction Workshop are described, and detailed comparisons are made with experimental data. Using workshop-supplied grids, FUN3D results for the simplified high-lift configuration are compared with results from the structured code CFL3D. Using the same turbulence model, both codes compare reasonably well in terms of total forces and moment, and the maximum lift is similarly over-predicted for both codes compared to experiment. By including more representative geometry features such as slat and flap support brackets and slat pressure tube bundles, FUN3D captures the general effects of the Reynolds number variation, but under-predicts maximum lift on workshop-supplied grids in comparison with the experimental data due to excessive separation. However, when output-based, off-body grid adaptation in FUN3D is employed, results improve considerably. In particular, when the geometry includes both brackets and the pressure tube bundles, grid adaptation results in a more accurate prediction of lift near stall in comparison with the wind-tunnel data. Furthermore, a rotation-corrected turbulence model shows improved pressure predictions on the outboard span when using adapted grids.

Uncertainty Analysis of Heat Transfer Predictions Using Statistically Modeled Data From a Cooled 1-1/2 Stage High-Pressure Transonic Turbine

This paper compares predictions from a 3D Reynolds-averaged Navier–Stokes code and a statistical representation of measurements from a cooled 1-1/2 stage high-pressure transonic turbine to quantify predictive process sensitivity. A multivariable regression technique was applied to both the inlet temperature measurements obtained at the inlet rake, the wall temperature, and heat transfer measurements obtained via heat-flux gauges on the blade airfoil surfaces. By using the statistically modeled temperature profiles to generate the inlet boundary conditions for the computational fluid dynamics analysis, the sensitivity of blade heat transfer predictions due to the variation in the inlet temperature profile and uncertainty in wall temperature measurements and surface roughness is calculated. All predictions are performed with and without cooling. Heat transfer predictions match reasonably well with the statistical representation of the data, both with and without cooling. Predictive precision for this study is driven primarily by inlet profile uncertainty followed by surface roughness and gauge position uncertainty.

Unsteady Effects in Axial Compressors: A Multistage Simulation

This work presents a numerical simulation of a four-stage axial compressor with cantilevered stators and repeating stages. Two simulations have been accomplished, namely, unsteady with sliding plane and steady with mixing plane, over a wide range of operating conditions. The solver is an unsteady Reynolds-averaged Navier–Stokes code with the Spalart–Allmaras turbulent model. It has been found that the greatest effect of unsteadiness is near the end walls. The stall point for the unsteady simulation is 40% closer to the experimental data when compared with the steady one with mixing planes. This is due to the recovery and segregation of the rotor tip vortex near the casing, which has a stabilizing effect in terms of stall limit. The unsteady simulation is able to reproduce total pressure loss experimentally observed near the hub at the stator exit but not found in the steady simulation. A previous experimental campaign suggested this loss was generated by the wakes of upstream inlet guide vanes propagating through the machine. However, this work found that it is generated by the migration of hub leakage flow induced by the incoming rotor wakes. The unsteady simulation shows higher performance at midspan. This has been found to be related to the rotor wake rectification with a 70% inviscid recovery of wake.

Simulations of a low-boom, axisymmetric, external compression inlet

AbstractComputational simulations have been used to study a new low-boom, axisymmetric, external compression supersonic inlet with an on-design Mach number of 1·7. The inlet incorporates a relaxed compression surface with a near-zero cowl angle to help reduce external oblique shock waves due to spillage and cowl geometry. To reduce mechanical complexity the inlet is designed with zero-bleed. To understand the impact on performance and shock overpressure caused by the inlet itself, several throat and diffuser designs were simulated. The computations utilised a Reynolds-averaged Navier-Stokes code. Inflow properties were held consistent with the operational characteristics of the NASA GRC 8′ × 6′ Supersonic Wind Tunnel (SWT) for experimental testing of the inlet of Mach 1·67 at a Reynolds number of 5·4 × 106. Stagnation pressure recovery performance for the baseline condition exceeded 94% at design mass flow rates, and reduced only slightly with increases in Mach number (consistent with theoretical predictions) and extension of cowl position. The simulations also showed that the relaxed compression surface combined with the near-zero cowl angle helps to significantly reduce external oblique shocks This is partly due to the reduced inlet spillage in combination with a reduced overall turning angle placed on the free-stream flow relative to the cowl shape.