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Assessment of Two-Equation Turbulence Models for Transonic Flows
Abstract
Four two-equation eddy-viscosity turbulence models are tested against a number of transonic airfoil and wing flows. All models are based on a kappa-omega formulation that serves as a flexible platform with regard to the models. The models have been tested previously against low Mach number flows and have shown distinctive differences in their performance. In addition to standard test cases, the paper includes some newer flow. One of the computed airfoil experiments was conducted in a wind tunnel with a closed test section. The inclusion of the wind tunnel walls in the computation of slotted wall wind tunnel experiments.
... The first is to provide benchmark LES data that can be used to guide the development of RANS models for predicting flow and heat transfer in U-ducts that include results for the mean flow and the Reynolds stresses as well as the pressure-strain rate, turbulent diffusion, turbulent transport, and velocity-temperature correlations. Second, use the data generated to assess the performance of the following three widely used RANS models: (1) the realizable k-ε model [41]; (2) the shear-stress transport model (SST) [15,[42][43][44]; and (3) the stress-omega Reynolds stress model (RSM) [15]. ...
... In this study, three RANS models were examined. Two are eddy-viscosity models: the realizable k-ε model [41] and the shear-stress transport (SST) [15,[42][43][44]. The third model is the stress-omega Reynolds stress model (RSM) [15]. ...
... The switch between these two equations is carried out by a smooth interpolation [9]. For the SST model, in Equation (4) is modeled by the following [15,[42][43][44]: ...
Large-eddy simulation (LES) and Reynolds-Averaged Navier–Stokes (RANS) equations were used to study incompressible flow and heat transfer in a U-duct with a high-aspect-ratio trapezoidal cross section. For the LES, the WALE subgrid-scale model was employed, and its inflow boundary condition was provided by a concurrent LES of incompressible fully-developed flow in a straight duct with the same cross section and flow conditions as the U-duct. LES results are presented for turbulent kinetic energy, Reynolds stresses, pressure–strain rate, turbulent diffusion, turbulent transport, and velocity–temperature correlations, with a focus on how they are affected by the U-turn region of the U-duct. The LES results were also used to assess three commonly used RANS models: the realizable k-ε with the two-layer model in the near-wall region, the two-equation shear-stress transport model, and the seven-equation stress-omega Reynolds stress model. Results obtained show steady and unsteady RANS to incorrectly predict the effects of unsteady flow separation. The results obtained also identified the terms in the RANS models that need to be modified and suggested how turbulent diffusion should be modeled when there is unsteady flow separation.
... It has been shown that the magnitude of the eddy-viscosity can change by more than 100% by changing the free stream values of ω. The shear-stress transport (SST) model [88] reduces this problem by using a zonal approach that switches between k −ω and k −ε where they perform the best. ...
... The von-karman lengthscale is used in a source term Q S AS in the ω−equation of the k-ω SST model [88] (see Appendix 8.2): ...
... In this study, HTLES is based on the k − ω SST model [88], as proposed by Tran et al. [129]. ...
Internal aerodynamics is a key element for improving the combustion efficiency in Spark-Ignition (SI) engines. Within this context, CFD tools are increasingly used to investigate in-cylinder flows and to support the design of fuel-efficient engines. The present research aimed at extending and validating a non-zonal hybrid Reynolds-Averaged Navier-Stokes / Temporal Large-Eddy Simulation (HTLES) approach, initially formulated for stationary flows, to cyclic SI engine flows with moving walls. The aim was to model the near-wall regions and coarse mesh regions in RANS, while solving the turbulent scales in core regions with sufficient mesh resolution using temporal LES, in a seamless approach with no a priori user input. HTLES was retained as it proposed a consistent hybridization combining time-averaging in RANS regions with temporal filtering in TLES.A first development consisted in implementing a smooth shielding function that enforces the RANS mode in near-wall regions, regardless of the local temporal and spatial resolution. The extension of HTLES to cyclic flows was then achieved via the formulation of a method allowing approximating the phase averages of resolved flow quantities based on an Exponentially Weighted Average (EWA). A dynamic expression for the width of the weighted average was proposed, in order to ensure that the high frequency turbulent fluctuations be filtered out from the resolved quantities, while keeping the low frequency cyclic components of the flow variables. The resulting EWA-HTLES model was implemented in the commercial CONVERGE CFD code. The developed EWA-HTLES model was first applied to the simulation of two steady flow configurations: a minimal turbulent channel and a steady flow rig. Predictions were confronted with reference data, as well as with those from RANS and LES. All simulations relied on the use of standard wall laws and coarse grids at walls. Imposing the RANS mode at walls yielded EWA-HTLES predictions of pressure losses much closer to DNS and experimental findings than with LES. At the same time, it allowed yielding results in terms of mean and RMS velocities s in the core regions of the same quality than LES, and superior to RANS.Finally, EWA-HTLES was applied to the simulation of two cyclic flows representative of SI engines: the compressed tumble and the Darmstadt single-cylinder pentroof 4valve engine. For each configuration, a total number of 40 consecutive cycles were simulated. The results were confronted to PIV data, and to RANS and LES predictions obtained using the same numerical set-up. It was shown that EWA-HTLES successfully drives the RANS-to-LES transition in such complex configurations exhibiting unsteady flow features and important cyclic geometrical deformations. It switched from the RANS mode at the walls to LES in the core region of the cylinder, allowing a better prediction of unsteady phenomena including the evolution of the overall tumble characteristics and phenomena associated to cyclic variability. The EWA-HTLES results were shown to be comparable to those predicted by LES, and superior to RANS.The performed developments and obtained results open encouraging perspectives for the application of this hybrid RANS/LES method in industrial configurations involving non-stationary conditions and in particular moving boundaries.
... The SST − (SST for shear-stress transport) model in the present CFD simulation, which is available inside the ISIS-CFD solver code, where is the turbulent kinetic energy and is the particular dissipation rate. The SST − model, according to Menter and Rumsey [15], incorporates several desirable characteristics of existing two-equation models. The SST − model is used to improve the predictions achieved with algebraic mixing-length models, construct a local model for complex flows, and provide a simpler alternative for two-equation turbulence models, according to Spalart and Allmaras [16]. ...
... where the cross-diffusion term appears in the transformed -equation from the originalequation, and the last source term of Eq. (6) represents it. The production term of is sometimes approximated as proportionate to the absolute value vorticity, according to Menter and Rumsey [15]. ...
The axe-bow ship design has been primarily introduced to minimize ship's slamming condition during sailing, which inherently deals with sufficient of her total ship's resistance. The presence of nonlinear-hydrodynamic flow behaviours around the ship will forcefully impose pressure and viscous resistances on her hull. This complex phenomenon is so intricate that a reliable approach leading into more feasible prediction of her total ship’s resistance (RT) is necessarily required, while explaining the rationale behind the analysis results. This paper presents a computational investigation into prediction total ship's resistance of an axe-bow hull in the calm water condition. Here, the Computational Fluid Dynamic (CFD) software called Numeca Fine Marine was accordingly used. Several parameters such as various Froude numbers (Fr) and trim's angles, have been taken into account in the computational simulations. The results showed that the viscous ship’s resistance has more relatively significant influence on the axe-bow ship than the pressure ship’s resistance especially at Fr ≥ 0.568. It is noteworthy that this causes the pressure resistance coefficient (CP) decrease indicated with moderately diminished high-pressures acting on the axe-bow ship’s hull. The increase of the trim’s angle demonstrates that the existence of the higher turbulent viscosity extends over the entire submerged hull surfaces and causes reduction of the viscous coefficient (CV). In general, the subsequent increase of Froude number and the trim’s angle were proportionally to the total ship’s resistance. It can be concluded that the current computational results are useful as preliminary prediction of the total ship’s resistance towards determining the effective power.
... SST k-ω model is a combination of k-ω and k-ε models, and k-ω model is used in the boundary layer region and k-ε model is used in the region outside the boundary layer. the model equation is shown in the following equation, and the values of the coefficients in the equation are taken from the literature [27]. ...
The tail-sitter VTOL UAV boasts not only high-speed cruising and air hovering capabilities, but also its unique tail-sitting vertical takeoff and landing and hovering attitude enable aerial operations with an exceptionally small cross-sectional area. This feature effectively broadens the scope of application for the UAV in intelligent agriculture, encompassing tasks such as agricultural inspection, production monitoring, and topographic mapping. Given the necessity for frequent modal transitions, this paper is grounded in a thorough examination of the typical structural characteristics of the tail-sitter VTOL UAV. A comprehensive technical solution for tail-sitter VTOL UAVs, based on the free-tail configuration, is proposed in this paper. The free-tail structure is utilized to address the limitations of traditional tailless layout and fixed landing gear in terms of flight stability and takeoff/landing performance of tail-sitter VTOL UAVs. However, the implementation of this solution necessitates the addition of a new maneuvering unit. Consequently, this paper delves into the aerodynamic coupling characteristics and laws between the layout parameters such as tail number, tail length, and tail area and the tail-sitter VTOL UAV fuselage. To optimize the free-tail configuration, a multi-objective optimization is performed by integrating the overall UAV dynamics, landing dynamics, and modal transition trajectory constraints. The results of stability modeling simulations and flight tests demonstrate that the tail-sitter VTOL UAV equipped with this technical solution exhibits enhanced maneuverability and flight efficiency compared to the conventional tailless layout.
... The detailed descriptions of S-A and SST turbulence models are presented in references [43,44]. ...
To further develop a more effective turbulence model and to improve the calculation accuracy of the flow around airfoil, a new PAFV turbulence model has here been constructed by using a deformation rate tensor and the grouping of an average fluctuation velocity. To evaluate the applicability of the PAFV turbulence model, the numerical calculations of flow around the airfoil have here been implemented, which was based on the OpenFOAM calculation platform. On the basis of grid independence research, the model was used to calculate the low-speed flow-around problem for the plano-convex airfoil NACA4412 and the symmetric airfoil NACA0012. It was also compared with the S-A (Spalart-Allmaras) and SST (Shear Stress Transport) k-ω turbulence models. Firstly, the maximum lift angle-of-attack case of the NACA4412 airfoil was calculated. Thereafter, numerical calculations were performed for the flow around the airfoil in the multi-angle-of-attack case of NACA0012 airfoil. The results showed that the NACA4412 airfoil had an obviously separated vortex at the trailing edge of the airfoil at the maximum lift angle of attack. Also, there was a certain velocity loss downstream of the trailing edge, as was calculated by all three models. However, the results of the PAFV turbulence model were found to be better than those of the S-A and SST turbulence models. The three turbulence models showed comparable accuracies for the calculations of the surface pressure coefficients of the NACA0012 airfoil. However, the S-A and SST k-ω turbulence models were slightly better for the calculations of the mean velocity profiles of the NACA0012 airfoil. Also, the PAFV turbulence model was more accurate for the calculations of the lift and drag coefficients. In conclusion, the PAFV model can make effective predictions for the airfoil low-speed flow around the problem at hand, which in turn preliminarily verifies the applicability of this turbulence model for the low-speed flow around airfoil problems.
... Menter's Shear Stress Transport (SST) model was adopted to approximately simulate the turbulence. The model was first proposed by Menter in 1994 [11,12], which combines advantages of both k-ε and k-ω models. It acts equivalent to k-ω model near the wall, while gradually shifts to k-ε model away from the wall, showing high accuracy in general turbulent flow calculations. ...
Two or more planes can fly in close formation similar to migratory birds, making use of the wing-tip vortex of the leader plane to increase lift and reduce drag, thereby effectively improving the flying range. By conducting wind tunnel tests and numerical simulations, the aerodynamic performance of formation flight at different relative positions can be obtained, the optimal formation position can thereby be solved. However, significant nonlinear and unsteady aerodynamic characteristics, induced by the interference between the follower plane and the wing-tip vortices of the leader plane, will affect the flight safety of the whole formation. At present, there is no effective prediction methods. Numerical simulations adopting adaptive grid refinement and dynamic overset grid were conducted for the dynamic entering process of the formation flight containing two Ty-154 planes. The aerodynamic characteristics and vortex interferences were analysed considering the effects of approaching direction and speed. The results indicate that there is deterioration of stability at the position where maximum lift gain is reached; Compared to the entering speed, the impact of directions on dynamic aerodynamic characteristics is more significant.
... To compute the entire flow passage field, the Reynolds averaged Navier-Stokes (RANS) equations are utilized [26]. In order to accurately predict the onset and extent of flow separation under adverse pressure gradients, and to account for the transport of turbulent shear stress, the SST k-ω model is adopted in this study [27]. ...
The bolt has been widely used in many kinds of machines, and it shows complex dynamic behavior. This paper analyzed a failure case of pumped storage unit bolt based on the multibody dynamic theory and the fluid-structure interaction theory. The results show that the non-axisymmetric in the circumferential direction of the head-cover and stay ring results in the different of the tensile force and relative stiffness and results significant bending stress on the bolts. In addition, the plastic deformation has occurred in the local area of the thread and there are significant differences in the contact pressure distribution among different cycles, with the contact pressure increasing closer to the inner cycle. The conclusions in this paper provide an in-depth understanding on the dynamic behavior of the bolt, which could be helpful for preventing the failure of the bolt and improving the safety of the pumped storage unit.
... where the last source term of Eq. (5) represents the cross-diffusion term that appears in the transformed ω-equation from the original ε-equation. Menter et al., [26] noted that the production term of ω is sometimes approximated as proportional to the absolute value of vorticity: ...
The presence of incident divergent waves between two demi-hulls on catamaran ship will attempt to generate a non-linear hydrodynamic behaviour, which inherently induced an accuracy of predicting her total resistance (RT). Correspondingly, this becomes an attractive factor to propose a more reliable prediction of the total ship’s resistance through quantifying both of pressure and viscous resistances components. This paper presents computational investigation into predicting the viscous (CV) and pressure coefficients (CP) in calm water condition; whilst the rationale behind the analysis results explained. Several parameters have been taken into accounts in the computational simulation such as the effect of lateral separation (S/L) and longitudinal staggered (R/L) ratios at various Froude numbers. The preliminary validation shows that the total ship’s resistance at various S/L and R/L ratios constitute a fairly good agreement as compared to the experimental results. In addition, the CFD simulations revealed that the highest CV and CP occurred at the Fr= 0.47. The comparison in various lateral separation ratio showed that the symmetrical catamaran produced highest CV and CP at S/L=0.2 and S/L=0.4, respectively. Meanwhile, the staggered catamaran with S/L=0.2 produces highest the values of CV and CP at R/L=0.4 and R/L = 0.2, respectively. It is merely concluded that the current computational prediction provides useful outcomes particularly to estimate the effective power at preliminary design stage.
... In Equation (5), the coefficient β is taken from 0.1 to 0.6. To avoid redundancy, the relevant equations and detailed descriptions of the Spalart-Allmaras turbulence model, the SST k-ω turbulence model, and the k-ε turbulence model are described in detail in references [21][22][23]. On the k-ε model, the standard k-ε model [23] was used in the far field and the Wolfshtein model [24] was used in the near-wall region. ...
One of the most commonly used techniques in aerospace engineering is the RANS (Reynolds average Navier–Stokes) approach for calculating the transonic compressor flow field, where the accuracy of the computation is significantly affected by the turbulence model used. In this work, we use SA, SST, k-ɛ, and the PAFV turbulence model developed based on the side-biased mean fluctuations velocity and the mean strain rate tensor to numerically simulate the transonic compressor NASA Rotor 67 to evaluate the accuracy of turbulence modeling in numerical calculations of transonic compressors. The simulation results demonstrate that the four turbulence models are generally superior in the numerical computation of NASA Rotor 67, which essentially satisfies the requirements of the accuracy of engineering calculations; by comparing and analyzing the ability of the four turbulence models to predict the aerodynamic performance of transonic compressors and to capture the details of the flow inside the rotor. The errors of the Rotor 67 clogging flow rate calculated by the SA, SST, k-ɛ, and PAFV turbulence models with the experimental data are 0.9%, 0.8%, 0.7%, and 0.6%, respectively. The errors of the calculated peak efficiencies are 2.2%, 1.6%, 0.9%, and 4.9%. The SA and SST turbulence models were developed for the computational characteristics of the aerospace industry. Their computational stability is better and their outputs for Rotor 67 are comparable. The k-ɛ turbulence model calculates the pressure ratio and efficiency that are closest to the experimental data, but the computation of its details of the flow field near the wall surface is not ideal because the k-ɛ turbulence model cannot accurately capture the flow characteristics of the region of high shear stresses. The PAFV turbulence model has a better prediction of complex phenomena such as rotor internal shock wave location, shock–boundary layer interaction, etc., due to the use of a turbulent velocity scale in vector form, but the calculated rotor efficiency is small.
... This solver adopts internal implicit iteration within a time step iteration to ensure a strong and accurate flow/motion coupling. And the Menter's k-ω shear-stress transport turbulent model was used (Menter and Rumsey, 1994). ...
As a promising form of oscillating hydrofoil propulsion, self-pitching flapping foil (SPFF) has been widely used in ocean engineering applications such as ships, underwater vehicles and ocean energy devices. Due to the complexity of its mass spring system, it is still a lack of comprehensive parametric analysis to conclude the theoretical maximum efficiency of SPFF up to now. Particular interest of this work is centered on the influence of frequency ratio (r), spring stiffness ratio (K′), advance coefficient (J) and pitch axis (c0/c) on the propulsive performance of self-pitching flapping foil (SPFF), including induced propulsion force, propulsive efficiency and related wake structure. The analysis covers the range of full advance coefficient, which starts around 0 and ends at a thrust drop of 0. The influence of stiffness ratio (K') on the SPFF performance was discussed in the large range of 0.1-100. Special attention is also paid to the impact of system resonance on performance. By employing an appropriate combination of various parameters, the highest efficiency of SPFF could reach 87.6%, which shows it could perform a satisfactory propulsion performance as a marine propulsion. This study is expected to provide guidance on both academics and industries in relevant fields.
... Specifically, the Reynolds averaged Navier-Stokes (RANS) equations were utilized for calculating the entire flow passage field [29]. To account for the transport of the turbulent shear stress and accurately predict the onset and amount of flow separation under adverse pressure gradients [30], this paper adopted the SST k-ω model. ...
... We evaluate the drag reduction resulting from the simulations against a reference clean bluff body depicted in Fig. 2. It is nearly the same as the presented bluff body, with the only difference that it has neither jets nor curved edge on the back, so the back is totally plain. The fluid motion is modeled by the URANS equations [42,3] and the k − ω SST model for the closure [32,33]. The numerical schemes configurations and the set of constants used for k − ω SST are reported in Appendix A. Figure 3: Geometry of the computational domain. ...
We present a deep reinforcement learning approach to a classical problem in fluid dynamics, i.e., the reduction of the drag of a bluff body. We cast the problem as a discrete-time control with continuous action space: at each time step, an autonomous agent can set the flow rate of two jets of fluid, positioned at the back of the body. The agent, trained with Proximal Policy Optimization, learns an effective strategy to make the jets interact with the vortexes of the wake, thus reducing the drag. To tackle the computational complexity of the fluid dynamics simulations, which would make the training procedure prohibitively expensive, we train the agent on a coarse discretization of the domain. We provide numerical evidence that a policy trained in this approximate environment still retains good performance when carried over to a denser mesh. Our simulations show a considerable drag reduction with a consequent saving of total power, defined as the sum of the power spent by the control system and of the power of the drag force, amounting to 40% when compared to simulations with the reference bluff body without any jet. Finally, we qualitatively investigate the control policy learnt by the neural network. We can observe that it achieves the drag reduction by learning the frequency of formation of the vortexes and activating the jets accordingly, thus blowing them away off the rear body surface.
... The k-ω shear stress transport (SST) turbulence model was used, which was first proposed by Menter in 1994 [14,15], combining the advantages of the k-ε model away from the wall and k-ω model near the wall. The SST model is widely used in turbulent flow simulations due to its accuracy and efficiency. ...
Cryogenic wind tunnels provide the for possibility aerodynamic tests to take place over high Reynolds numbers by operating at a low gas temperature to meet the real flight simulation requirements, especially for state-of-the-art large transport aircrafts. However, undesirable temperature gradients between the test model and the surroundings will be caused by the thermal non-equilibrium, changing the boundary layer characteristics and resulting in test errors. To study the nonadiabatic wall effects on the aerodynamic characteristics of the model in cryogenic wind tunnels, a numerical study was carried out for the CHN-T1 standard model under different wall temperature gradients. A code with a finite volume method and γ-Reθt transition model were used. The analysis concluded that the change in wall temperature significantly affects the surface pressure distribution, transition position and skin-friction coefficient of the model, thus varying the lift and drag coefficients of the aircraft. The influences on the flow characteristics of both laminar and turbulent boundary layers by the wall temperature gradient were also investigated.
... The mean SGS stress and heat flux are constrained by Reynolds stress and heat flux approximately by RANS models through the following relations: can be modeled from different models for the specific flow geometry, such as k − ǫ model, k − ω model [36], Baldwin-Lomax (B-L) model [37], SST model [38], etc. In the present work, the turbulent viscosity µ t is calculated from the one equation Spalart-Allmaras (S-A) model [39]. ...
An improved approach for constrained large-eddy simulations (CLES) of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor. The improved model is tested and validated with compressible channel flows at various Mach numbers and Reynolds numbers that are transitioning from laminar to turbulent states. The improved model is compared against traditional dynamic Smagorinsky model (DSM) and Direct Numerical Simulations (DNS), where the improved model is in better agreement with DNS results than traditional DSM model, in terms of mean velocity profiles, total Reynolds stress and total heat flux. Therefore, the proposed method can be used to accurately predict the temporal laminar-turbulent transition process of compressible wall-bounded flows.
... An in-house parallel computation program is employed as the flow solver, in which the central scheme finite volume method (FVM), Runge-Kutta time-marching method, multi-grid acceleration technique, etc. are included. In the study, the Menter's shear stress turbulence (SST) model [47] is used and the γ − Re θt transition model equations [48] are solved to model the flow transition in boundary layer. ...
... Lastly, the closure coefficients are summarized in Table 3.1. It should be noted that the closure coefficients in TAU follow a publication by Menter and Rumsey (1994). ...
The present thesis aims to provide a validation database of existing RANS models for high Reynolds number flows with history effects due to streamwise changing mild pressure gradients, and to assess the predictive accuracy and its uncertainty of each RANS model. For this purpose, two recent wind tunnel experiments with mild pressure gradients were selected, and the two-dimensional computational setups for RANS simulations were defined. The first test case is the Virginia Tech wind tunnel experiment conducted in the framework of the North Atlantic Treaty Organization (NATO) Science & Technology Organization (STO) Air Vehicles Technology (AVT) 349 project (Fritsch et al. (2022)). The second test case considered is the Laboratoire de Mécanique de Lille (LML) wind tunnel experiment by Cuvier et al. (2017). Both flow cases encompass streamwise changing mild pressure gradients, which result in the non-equilibrium effects and history effects. For both test cases, the influence of changes in the computational setup and their sensitivities were investigated. The RANS simulations were carried out using three turbulence models, the SA-neg, the Menter SST, and the SSG/LRR-omega models and the results were compared with the experimental data. The experimental and RANS results are in good agreement in regions where the flow is in near equilibrium. Some appreciable discrepancies are observed in the region where the flow is at APG and in non-equilibrium. However, the deviations are relatively small due to mild pressure gradients, which is a further reason to demand highly accurate measurement data. The largest deviations of the RANS predictions from the experimental data are found in the regions of the largest non-equilibrium, i.e., in the regions of the largest streamwise changes in the local pressure gradient. Also, the greater discrepancy is observed in the LML test case than the Virginia Tech test case, which is most likely due to the larger pressure gradient coefficient. These observations might suggest that the existing RANS models, that are calibrated for equilibrium boundary layer flows, fail to capture all details of non-equilibrium effects. Comparisons of different RANS models reveal a fairly less model dependency on both test cases than might be expected. This could be explained by the fact that the SSG/LRR-omega model uses the same length-scale equation as the Menter SST model, and all models are mainly calibrated for equilibrium turbulent boundary layer flows. Also, comparisons of different numerical set-ups demonstrate the difficulty of reproducing a 3D experimental set-up in 2D computations.
... To improve convergence, local time stepping and implicit residual smoothing algorithms are applied. The turbulence is modelled using the 2-layer k-ε model [32]. Turbulent mass diffusion fluxes and enthalpy fluxes are modelled via the turbulent Schmidt and Prandtl numbers with constant values of Sc tr = 0.7 and Pr tr = 0.9, respectively. ...
Methane (CH4) is a promising rocket fuel for various future space mission scenarios. It has advantages in terms of cost, performance, and environmental friendliness. Currently, there is no clear definition on standards and specifications for liquefied methane or similar liquids such as liquefied natural gas (LNG) for their use as rocket fuel. However, those regulations are necessary for the commercial, safe, and proper operation of methane rocket engines. Composition and impurities of liquefied methane gas mixtures obtained from natural gas or biogenic sources depend on location of the natural gas source (Europe, Asia, or America), its extraction method and treatment, used cleaning methods or conditions of the gasification process, and biomass sources. In the present work, effects of impurities (N2, CO2, C2H6) within liquid natural gas/liquid methane on the methalox rocket engine operation behavior are analyzed. Regarding the cold cryogenic side, phase diagrams are discussed and critical temperatures for the fuel side are outlined. Carbon dioxide is identified as a rather problematic pollutant. The combustion processes are investigated with several numerical simulations (1D and 2D CFD). The results indicate a minor influence on the overall combustion temperature and a minor but potentially relevant influence on the pressure within the combustion chamber. Additionally, the results indicate that with respect to temperature and pressure, no complex NOx nitrogen chemistry is required.
... The Reynolds averaged Navier-Stokes (RANS) equations were used to calculate the entire flow passage field in the prototype bulb turbine [24]. The SST k − ω model which gives very accurate predictions of the onset and the amount of flow separation under adverse pressure gradients to account for the transport of the turbulent shear stress [25] was adopted in this paper. ...
The control mechanism of the Kaplan turbine is quite complex, and many of the failure cases of the control mechanism have been reported. The present work analyzed a failure case of the blade lever based on the multibody mechanics and fluid-structure interaction method. The flow characteristics in 49 operating conditions are simulated, and the pressure on the runner surface is applied on the FEM model. A dynamic stress isoline is proposed to carry out an in-depth analysis of the failure reason of the blade lever in full operating conditions. The fracture of the blade lever could be attributed to long time operation in high dynamic stress region, which leads to the accelerated fatigue damage. Results in this paper could be helpful for the design, operation and maintenance of the Kaplan turbine.
... In order to solve the incompressible Reynolds averaged Navier-Stokes equations, the commercial computational fluid dynamics (CFD) software ANSYS CFX 18.0 (based on the finite volume method) was adopted [29]. The SST k − ω model show good performance on predicting the onset and the amount of flow separation under adverse pressure gradients [30], and it was adopted to account for the transport of the turbulent shear stress. ...
Bulb turbine is widely used on the utilization of the hydraulic resources with relatively low head and the tidal energy, and it is troubled by fatigue problems. Thus, it is significant to investigate the influence of the crack on the dynamic response of the rotor to enlarge the service life of the bulb turbine. This paper investigates the modal characteristics and the dynamic response characteristics of a bulb turbine rotor, considering the crack at the flange root. A CFD model and seven FEM models are established, and the boundary conditions for flow and FEM analysis are determined. Firstly, the flow characteristics of the bulb turbine are calculated, and the transient pressure loads on the runner are obtained. Then the effect of added mass, gravity and crack size on the modal characteristics and the dynamic response characteristics of the rotor are discussed. The results show that the crack has little effect on the modal characteristics of the rotor and the frequency spectra of the dynamic stress, but will result in the increase of the mean value and the amplitude of the dynamic stress. In addition, the gravity has a greater effect on the dynamic stress than the added mass of the surrounding water. Results of this study helps to understand the dynamic behavior of the cracked rotor, the proposed method could be used for accurate calculation of the dynamic behavior of the rotor, and possible resonance and fatigue failure problems in future designs of bulb turbine units could be avoided.
... where the last source term of Eq. (6) represents the cross-diffusion term that appears in the transformedequation from the original -equation. Florian Menter and Rumsey (1994) noted that the production term of is sometimes approximated as proportional to the absolute value vorticity: ...
Prediction of ship’s total resistance of a pusher-barge system has become enormous complexity involving nonlinear-hydrodynamic flows behaviour along their hull forms. Both of empirical and simplified numerical solutions may still lead into inaccurate results due to presence of nonlinear characteristics of the pressure and viscous resistances. The use of a more sophisticated method would obviously necessitate to solve the above problem. This paper presents a Computational Fluid Dynamics (CFD) approach to predict the total ship’s resistance of a pusher-barge system at various barge’s configurations. To achieve such objective, four different configurations of the barge models incorporated with various Froude numbers have been taken into account in the computational simulation. In general, the results revealed that the increase of Froude number (Fr = 0.182 to 0.312) was proportional to the magnitude of RT, RP and RV. Regardless of the various Froude number, the pusher-barge system with a 13BP configuration provides the highest resistance compared to the 12BP and 11BP. In addition, the arrangement of barges in the longitudinal (12BP) and lateral (21BP) configurations produced a significant effect with increases in RT, RP and RV values of 110%, 167.5% and 77.6%, respectively. The possible reason for this is that the increase of the total wetted surface area for 21BP has produced to a proportionally higher amount of the pressure and viscous resistance. Overall study, the numerical results were presented and analysed based on few aspects involved the total resistance and resistance coefficient in terms of pressure and viscous resistance of the pusher-barge system. This analysis provides very valuable information on choosing the most reliable arrangement of pusher-barge system. This analysis provides very valuable information on choosing the most reliable arrangement of pusher-barge system
... The CFD simulations performed here to assess the flow performance of the EGR pump are 3-D transient simulations performed using commercial software Ansys CFX 17.1, in which the working fluid is air (which has been modeled using the ideal gas law to account for compressibility effects). The turbulent flow in the pump is captured using the SST turbulence model, which has been shown to perform well for flows in the presence of an adverse pressure gradient (Menter and Rumsey, 1994). The model uses a blending function to take advantage of both the near-wall modeling capability of the k-omega model and the boundary layer edge (free shear layer) modeling capability of the k-epsilon model (Menter, 1993). ...
Upcoming global emission regulations include considerable reduction in emission of nitrogen oxides (NOx) and greenhouse gases (GHGs) for vehicles with heavy-duty (HD) diesel application. These regulations will phase between 2024 and 2030 in the United States and the European Union. CARB Regulations include up to 90% reduction in NOx levels along with ∼25% reduction in CO2. One of the primary technologies used to reduce engine out NOx emission is the use of cooled exhaust gas recirculation (EGR). Research studies carried out across multiple domains by engine/vehicle original equipment manufacturers (OEMs) and others have identified air handling as one of the technologies to help meet next-generation regulations ( Joshi, 2020 ; Dreisbach et al. 2021 ). This includes more efficient turbomachinery which helps improve engine efficiency and thus reduce GHGs. This has an adverse effect on driving EGR which affects engine out NOx. In this study, the development and performance impact of the EGR pump is investigated, which allows improved engine fuel efficiency without the corresponding penalty to engine out NOx. Computational fluid dynamics (CFD) is used to optimize the EGR pump design, which leads to reduction in fluid-borne noise of the pump, which is then evaluated for fuel benefits using a calibrated GT-POWER engine model.
... where ε is the turbulent energy dissipation; additionally, ω represents the rate at which turbulence kinetic energy is converted into thermal internal energy per unit volume and time. According to the previous research [31,32], β 1 β 2 , and β 3 , are 0.075, 0.09, and 0.0828, respectively. Besides, γ 2 and κ are 0.44 and 0.41; σ k and σ ω are 1 and 0.857. ...
To obtain high gas turbine efficiency, a film cooling hole is introduced to prevent the destruction of thermal barrier coating systems (TBCs) due to hot gases. Furthermore, environmental calcium-magnesium-aluminum-silicate (CMAS) particulates plug the film cooling hole and infiltrate the TBCs to form a CMAS-rich layer, which results in phase transformations and significant modifications in the thermomechanical properties that impact the TBCs during cooling. This study aimed to establish a three-dimensional thermo-fluid-solid coupling TBCs model with film cooling holes and CMAS infiltration to analyze the temperature and residual stress distribution via simulations. For the interfacial stress around the cooling hole at the TC/BC interface, the film cooling holes alleviated the interfacial residual stress by 60% due to the reduction in temperature by 40%. In addition, CMAS infiltration intensified the interfacial residual stress via phase transformation. As a result of the influence of larger penetration depths and expansion rates of phase transformation, a significant increase in residual stress was observed. At the beginning of CMAS infiltration, the interfacial stress would be more dominated by the effect of infiltration depth. In addition, the failure due to interfacial normal and tangential stresses was more likely to be found at the infiltration zone near the cooling hole.
... To improve convergence, local time stepping and implicit residual smoothing algorithms are applied. The turbulence is modelled using the 2-layer k-ε model [22]. Turbulent mass diffusion fluxes and enthalpy fluxes are modelled via the turbulent Schmidt and Prandtl numbers with constant values of = 0.7 and = 0.9, respectively. ...
... Therefore, Reynolds-averaged Navier-Stokes (RANS) simulation is still the dominant tool for industrial problems in the near future. Traditional RANS models, especially based on the eddy viscosity models [Spalart-Allmaras (SA) model, 2 k-e/k-x model, [3][4][5] Menter's Shear Stress Transport (SST) model 6,7 ] have been widely used to solve turbulence problems in engineering. These models can generally predict reliable aerodynamic coefficients for attached flows around complex configurations. ...
Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in posterior iterations. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in posterior iterations; while the mutual coupling mode can maintain good convergence and stability in the process of iterations. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in posterior iterations.
... Compared with the standard k-ε and RNG k-ε models, this model considers the viscosity of the inner wall of the model and has better turbulent shear stress transmission. The algorithm is more stable and has a better simulation performance for flow in a narrow space [23]. The corresponding turbulent kinetic energy and frequency equations are as follows [24]: ...
To study the effect of tip clearance on unsteady flow in a tubular turbine, a full-channel numerical calculation was carried out based on the SST k–ω turbulence model using a power-plant prototype as the research object. Tip leakage flow characteristics of three clearance δ schemes were compared. The results show that the clearance value is directly proportional to the axial velocity, momentum, and flow sum of the leakage flow but inversely proportional to turbulent kinetic energy. At approximately 35–50% of the flow direction, velocity and turbulent kinetic energy of the leakage flow show the trough and peak variation law, respectively. The leakage vortex includes a primary tip leakage vortex (PTLV) and a secondary tip leakage vortex (STLV). Increasing clearance increases the vortex strength of both parts, as the STLV vortex core overlaps Core A of PTLV, and Core B of PTLV becomes the main part of the tip leakage vortex. A “right angle effect” causes flow separation on the pressure side of the tip, and a local low-pressure area subsequently generates a separation vortex. Increasing the gap strengthens the separation vortex, intensifying the flow instability. Tip clearance should therefore be maximally reduced in tubular turbines, barring other considerations.
... The final mesh size selected in this paper is proven to be applicable, which can clearly resolve the vortex in the flow field. The two-dimensional viscous flow is simulated which used Menter's k-ω shear-stress transport turbulent model [27], and the governing equations can be written as follows: ...
This paper researched into the harmonic and anharmonic underwater flapping foil propulsion systems to improve the efficiency of these bioinspired propulsors. The angle of attack, the pitching angle, the heaving amplitude, and the phase difference are parametrically investigated in this paper. A rigid two-dimensional NACA (National Advisory Committee for Aeronautics) 0012 airfoil is modeled with the aid of a commercial computational fluid dynamics software, FINE™/Marine. Unsteady Reynolds Average Navier-Stokes (URANS) equation is solved together with dynamic mesh to simulate the foil motion. The investigation first verifies the reliability of the developed modeling method against the benchmark data. Then, the systematic investigation is conducted and identifies that the heaving amplitude is most influential factor for the propulsion efficiency. Secondly, phase difference also has a significant influence on efficiency, but this effect is related to the reference working condition, which needs further study. Then, the pitching amplitude has little effect on the maximum efficiency value of flapping foil, while it will affect its optimal speed range. When the heaving amplitude ratio reaches 3 and the corresponding maximum angle of attack is about 9°, the maximum efficiency can reach 87%. The effect of anharmonic motion on the efficiency is very small and varies with the St number, but in summary, it can maintain the peak efficiency over a wider range of operations. In addition, the force and flow field characteristics of different efficiency points are compared and analyzed to distinguish their corresponding relationship with the propulsion efficiency.
... The validation process compares corner flow measurements against simulations using the Spalart-Allmaras [14,15], Menter SST [22,23], and Wilcox - [24,25] turbulence models. It is important to ensure that any observed differences in the corner regions are not due to any turbulence-model sensitivity of the global flow computation. ...
Model validation studies are becoming increasingly relevant when investigating complex flow problems in high-speed aerodynamics. This paper presents the lessons learned from the practical aspects of a joint experimental–computational investigation, aimed at validating the quadratic constitutive relation in Mach 2.5 corner flows. Several instructive insights were gained from the careful, additional quantitative tests performed to obtain high-quality experimental data and to eliminate any systematic errors. In particular, the importance of identifying implicit assumptions in the methodology is demonstrated, quantitative evaluation of computations in the overall flowfield is shown to be crucial, and the benefits of a closely integrated experimental–computational approach are highlighted. For instance, this type of close collaboration enabled a better understanding of measurement techniques, helped to improve the infrastructure of the facility, and resulted in the discoveries of bulk secondary flows and streamwise vortices within the sidewall boundary layers.
... In particular, traditional two-equation turbulence models (k À x and k À e) solve two partial differential equations to obtain two independent scales. Similar to classical turbulence models (k À x and k À e), the GEKO model is capable of accurately predicting flows with the adverse pressure gradients, commencement and intensity of flow separations [45]. However, the coefficients of traditional models cannot be changed casually, because they are interconnected and must satisfy certain conditions. ...
Vortex-induced vibration (VIV) is a fluid structure interaction phenomena that can lead to the fatigue failure of high-rise structures. To study the basic principles and method of VIV suppression for a cylinder structure, a two-dimensional simulation model using a cylinder with two degrees of freedom in-line and cross-flow directions is presented herewith. A nonlinear energy sink is added to cylinder structures to assess its impact on vibration suppression. As a result, this study aims to investigate the VIV of cylinder under the action of the NES at low Reynolds numbers. The accuracy of the simulation model is verified by the comparison with the experimental results. Particularly, the VIV response is investigated with different mass ratio \(\beta\) between the NES and cylinder (namely \(\beta\) of 0.15, 0.2 and 0.3) at Re = 100 in air environment by analyzing the vibration response, phase diagram, time–frequency and vorticity contours of cylinder and NES oscillator. Three distinct function modes of NES for selected mass ratio \(\beta\) are also observed. The results indicate that the NES can change between resonance capture states, from weak to strong, when the mass ratio \(\beta\) increases to a defined value. In this case, the main vibration frequency of the cylinder varies over time, and the motion is in the chaotic state. The NES can also effectively reduce the vibration amplitude in both the in-flow and cross-flow directions.
... To define the turbulence closure, the shearstress transport (SST) k − ω model was adopted in the FLUENT commercial code. e k − ω SST model embraces the best of the two turbulent models developed by Menter and Rumsey [10]: the k − ε in the free-stream region and the k − ω at the near-wall in the boundary layer. e compressible equations of kinetic turbulent energy and specific dissipation rate conservation can be written as equations (2) and (3): ...
This paper is presented on the tandem two-dimensional hydrofoils with profiles NACA4412 in single-phase and two-phase flow domains for different submergence depths and different distances in a various angle of attack (AoA). Also, supercavitation is studied at σ=0.34 by the Zwart cavitation model. Reynolds-averaged Navier–Stokes (RANS) with the shear stress transport (SST) K-ω is employed as a turbulence model in transient analysis of Ansys FLUENT software. The numerical results show that, by increasing depth, the drag coefficient increases for both hydrofoils 1 and 2 as well as the lift coefficient. The drag coefficient of hydrofoil 2 is bigger than hydrofoil 1 for all depths; moreover, it was found that the flow pressure behind the hydrofoil 1 had affected the upper and the lower surface of the hydrofoil 2 at each distance or AoA. These effects are observed in the hydrofoil 2 lift coefficient as well as the flow separation. However, the maximum lift-to-drag ratio is observed at AoA = 8° and 3.5c distance. Also, single-phase results reveal that the value of pressure and the hydrodynamic coefficient are very different from the two-phase flow results, due to the elimination of the free surface. So, a two-phase flow domain is recommended for increasing the accuracy of results. In addition, the investigation of supercavitation shows a growth in cavity occurrence on the surface by raising AoA.
... Centre-span floor boundary-layer profiles using Spalart-Allmaras [18,19], Menter SST [20,21], and Wilcox :-l [22,23] turbulence models were compared (Fig. 4a). The di erences between these profiles are minimal, as expected for an attached boundary layer, which suggests that computations of this relatively simple flow appear to be insensitive to the turbulence model used. ...
Streamwise-coherent structures were observed in schlieren images of a Mach 2.5 flow in an empty supersonic wind tunnel with a rectangular cross section. These features are studied using Reynolds-averaged Navier–Stokes computations in combination with wind-tunnel experiments. The structures are identified as regions of streamwise vorticity embedded in the sidewall boundary layers. These vortices locally perturb the sidewall boundary layers, and they can increase their thickness by as much as 37%. The vortices are caused by a region of separation upstream of the nozzle where there is a sharp geometry change, which is typical in supersonic wind tunnels with interchangeable nozzle blocks. Despite originating in the corners, the vortices are transported by secondary flows in the sidewall boundary layers so they end up near the tunnel center height, well away from any corners. The successful elimination of these sidewall vortices from the flow is achieved by replacing the sharp corner with a more rounded geometry so that the flow here remains attached.
... The k-ω shear stress transport turbulence (SST) model (Menter, 1994;Menter & Rumsey, 1994) combines a high Reynolds number version of the k-ε model with a k-ω model (Wilcox, 1988(Wilcox, , 1993, providing the benefits of both models. Under the SST model, the k-ω model is applied to sublayers near any walls because it does not require a dampening function. ...
Over 3.7 billion years of Earth history, life has evolved complex adaptations to help navigate and interact with the fluid environment. Consequently, fluid dynamics has become a powerful tool for studying ancient fossils, providing insights into the palaeobiology and palaeoecology of extinct organisms from across the tree of life. In recent years, this approach has been extended to the Ediacara biota, an enigmatic assemblage of Neoproterozoic soft-bodied organisms that represent the first major radiation of macroscopic eukaryotes. Reconstructing the ways in which Ediacaran organisms interacted with the fluids provides new insights into how these organisms fed, moved, and interacted within communities. Here, we provide an in-depth review of fluid physics aimed at palaeobiologists, in which we dispel misconceptions related to the Reynolds number and associated flow conditions, and specify the governing equations of fluid dynamics. We then review recent advances in Ediacaran palaeobiology resulting from the application of computational fluid dynamics (CFD). We provide a worked example and account of best practice in CFD analyses of fossils, including the first large eddy simulation (LES) experiment performed on extinct organisms. Lastly, we identify key questions, barriers, and emerging techniques in fluid dynamics, which will not only allow us to understand the earliest animal ecosystems better, but will also help to develop new palaeobiological tools for studying ancient life.
... The convergence criterion for the simulations consisted of converging the density residual by six orders of magnitude, as is best practice in prior investigations of this case. 43,44 We outline this case as a test against the false positive. In locations where RANS model discrepancy is significant, the uncertainty bounds should indicate this. ...
Computational strategies that explicitly quantify uncertainties are becoming increasingly used in aerospace applications to improve the consistency in reliability, robustness, and performance of designs. A major source of uncertainty in simulations is due to the structural assumptions invoked in the formulation of turbulence models. Accounting for the turbulence model-form uncertainty has been described as “the greatest challenge” in simulation-based engineering design. Despite its importance, design exploration and optimization under turbulence model-form uncertainty is an avenue that has not been investigated in depth in prior literature. In this investigation, we outline methodologies for the design analysis, exploration, and robust optimization under model-form uncertainty due to Reynolds averaged Navier–Stokes models. We exhibit how interval uncertainty estimates enable the use of alternative criteria for decision making under uncertainty in engineering design. It is shown that such criteria can lead to different design choices in design exploration. Finally, we carry out design optimization under mixed uncertainties by using the perturbation framework in conjunction with polynomial chaos expansions. We introduce an approach for engineering design optimization under uncertainty that utilizes physics-based uncertainty estimation along with decision theory criteria under uncertainty to produce designs that are more robust to turbulence model uncertainties. These methodologies are illustrated via their application to complex turbulent flow cases, pertinent to aerospace design applications.
In this paper the description of the internal flow in a Francis turbine is addressed from a numerical point of view. The simulation methodology depends on the objectives. On the one hand, steady simulations are able to provide the hill chart of the turbine and energetic losses in its components. On the other hand, unsteady simulations are required to investigate the fluctuating pressure dynamics and the rotor-stator interaction. Both strategies are applied in this paper to a working Francis turbine in Colombia. The employed CFD package is ANSYS-CFX v. 11. The obtained results are in good agreement with the in site experiments, especially for the characteristic curve.
Aiming at the wing-mounted and hose-drogue refueling platform of tanker, the disturbance of the wake flow field of tanker on the aerodynamic characteristics of the receiver is studied. Based on the patched mesh technology, the mesh of the tanker, the hose-drogue and the receiver are generated respectively and then patched together to reduce the difficulty of mesh generation. By solving the Reynold Averaged Navier-Stokes (RANS) equation, the numerical simulation of the entire flow field of refueling is carried out on the receiver under the influence of the wake flow field of tanker and its engine jet, and the increments of the aerodynamic force and moment coefficient along the flow wise, span wise and height direction of the receiver is obtained. The influence of the wake of tanker on the trim control of the receiver is studied. The finite element method (FEM) is adopted to analyze the aerodynamic loading of the hose-drogue assembly, and the stress and deformation of each element are obtained. Based on the numerical simulation technology of the coupling solution of CFD and FEM, the equilibrium position of the hose-drogue assembly under the influence of the wake field of the tanker is calculated.
In the present study, the mixing characteristics of the Mach 1.86 jet from a convergent-divergent nozzle of square cross-section from inlet to exit were investigated numerically. The jet studied were uncontrolled and controlled with limiting tab of rectangular and circular cross-sections. The nozzle pressure ratio is varied from 4 to 6 with a step size of one, leading to the confinement of the present study for the over-expansion and near correct expansion levels of the jet. It is observed that the core length, which is a direct indication of the extent of jet mixing, reduced significantly for the jet controlled with limiting tab as compared to that with the uncontrolled counterpart. Also, among the circular and rectangular limiting tabs, the tab with rectangular cross-section caused maximum core length reduction. The jet spread and the waves prevailing in the jet field were studied and visualized using pressure profiles and Mach contours, respectively. The present work may be used in understanding and solving complex phenomena occurring in the fields of aeroacoustics noise suppression, reduction of base heating of launch vehicles, supersonic combustion, mitigation of infrared radiations due to chimney smoke, etc., where jet mixing is highly desirable.
Results of investigation of the turbulent mixing of liquid flows in a static mixer are presented. It was established that, in the case where liquids inflow into such a mixer with equal velocities, their movement in the radial direction in the mixer is absent. In this case, the main mechanism providing the mixing of liquid flows in a static mixer is their molecular diffusion, and, therefore, the intensity of mixing of the liquid flows is low. An increase in the difference between the velocities of the liquid flows at the inlet of a static mixer leads to their turbulization, with the result that the mixing of the liquids is substantially intensified, and a homogenous distribution of their mass fractions in the mixture is attained at a smaller distance from the inlet cross section of the mixer. When the difference between the velocities of the liquid flows at the inlet of a static mixer is large, at the center of the mixer channel there arises a recirculation flow zone in which the liquids are mixed intensively.
Bleed is often used to alleviate the detrimental effects of shock-wave/boundary-layer interactions in high-speed vehicles. Simulations play a crucial role in successfully implementing this control methodology; however, high-fidelity approaches are prohibitively expensive for parametric design studies. Thus, simplified models are typically employed. The errors introduced by these models are difficult to quantify, especially under off-design conditions, which results in compounding uncertainties in realistic configurations. To address this knowledge gap, a three-dimensional Reynolds-averaged Navier–Stokes simulation with discrete bleed holes is compared to a two-dimensional simulation with a bleed boundary condition. Notable differences in boundary-layer shape and turbulence parameters are observed, which are then used to perform sensitivity analyses on an impinging shock response. The response quantity of interest is the shock-reflection angle, for which a variation of more than 3 deg is observed. The most sensitive input uncertainties are found to be the inflow shape factor and the eddy viscosity magnitude, which have not been directly explored in existing models. Therefore, this work assimilates the simulation results to account for the observed disagreement between existing experimental and numerical campaigns. Additionally, the identified sensitive parameters inform future model development efforts, thus aiding in improving the design capabilities of high-speed inlets.
This paper proposes a new data assimilation method for recovering the high-fidelity turbulent mean flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion (POD-Inversion) data assimilation method. Aiming at flows including shock wave discontinuities or separation at high angles of attack, the proposed method can reconstruct the high-fidelity mean flow field combined with experimental force coefficients. We firstly perform the POD analysis to turbulent eddy viscosity fields computed by the SA model and obtain base POD modes. Then the POD coefficients are optimized by global optimization algorithm coupling with computational fluid dynamics (CFD) solver. The high-fidelity turbulent mean flow fields are recovered by several main modes, which can dramatically reduce dimensions of the system. The effectiveness of the method is verified by cases of transonic flow around the RAE2822 airfoil at high Reynolds numbers and the separated flow around S809 airfoil at high angles of attack. The results demonstrate that the proposed data assimilation method can recover turbulent flow fields which optimally match the experimental data, and can significantly reduce the error of aerodynamic coefficients. Furthermore, the proposed method can provide high-fidelity mean field data to establish turbulence models based on machine learning.
Reynolds-averaged Navier-Stokes (RANS) simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such a situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in a posterior iteration. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in a posterior iteration; while the mutual coupling mode can maintain good convergence and stability. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in a posterior iteration.
View Video Presentation: https://doi.org/10.2514/6.2022-1174.vid Details of the high speed form of the Spalart-Allmaras turbulence model and the Menter turbulence model incorporated into the Kestrel KCFD unstructured finite volume CFD solver and the SAMAir Cartesian CFD solver have been presented. These turbulence models include compressibility corrections, automatic wall functions, and RANS/LES (DDES) options. Example RANS applications of both models have been presented. The compressible SSTM turbulence model produced the best overall results for the set of test cases presented here.
View Video Presentation: https://doi.org/10.2514/6.2022-0222.vid The primary objective of this paper is to assess the ability of the general purpose CFD code, ANSYS Fluent, to predict ground vortex effects when an intake is placed near the ground and under crosswind conditions as defined by the 5th Propulsion Aerodynamics Workshop (PAW-05). Three crosswind speed configurations are studied. A hierarchy of workshop-supplied computational meshes is employed to perform mesh-independence studies. The anisotropic mesh adaptation module, ANSYS OptiGrid, is applied to precisely capture the ground and trailing vortices formed at the intake. The general-purpose k-ω Shear Stress Transport (SST) turbulence model is used to perform all simulations. Numerical predictions of total pressure recovery and distortion coefficient are compared against existing experimental data at a plane representative of the fan face at the engine intake, the Aerodynamic Interface Plane (AIP). In addition, incoming boundary layer profiles, surface static pressure plots, flow field contours and streamlines are used to study the complex physics generated by the presence of the intake in close proximity to the ground.
Bulb turbine units are widely used in run-of river or dam projects with relatively low head, and can also be used for tidal energy utilization. Some types of bulb turbines have excessive vibration and fatigue failure problems, which threats their fatigue life. The model analyzed in this paper is a prototype bulb turbine rotor which suffered cracks, probably due to erosion and welding defects. The dynamic stress characteristics are analyzed under not only the non-cracked shaft condition but also the cracked one, to find possible causes of the failure.
The computational fluid dynamics (CFD) simulation is performed to obtain reliable hydraulic load on the runner for performing the FEM analysis. The CFD results are verified by comparing with the site test for the prototype one. The linear elastic fracture mechanics theory combined with the fluid-structural interaction theory is applied to developing a cracked FEM model, to obtain the dynamic stress characteristics for the runner, shaft and rotor. The results reveal that the change in dynamic stress level on the shaft flange root significantly depends on the operating conditions, and the stress amplitude on the shaft mainly depends on the structural weight. The stress at the cracked zone could be up to 376.5 MPa in the best efficiency point, with only 1.5 years of fatigue life.
Based on the numerical calculations and site inspection, it could be concluded that the insufficient sealing could lead to leakage flows with specific flow rates in flange root, which resulted in the occurrence of erosion; in addition, the welding at the flange root probably generated tiny defects. These two factors are likely lead to fatigue cracks and major failure of the shaft. Suggestions for solutions for the problems of the shaft are also discussed. Results of this study helps to find the reasons of the shaft fatigue failure. Furthermore, the analysis method could be used for an accurate calculation of fatigue life and providing guidance in future designs and operations of bulb turbine units.
The present work aims to investigate the post-flutter aerothermoelastic behaviours of the hypersonic skin panels by using the integrated aerothermoelastic analysis framework developed in this paper. The aerodynamic loading and heating are computed simultaneously by solving Reynolds-averaged Navier-Stokes equations (RANS). The structural and thermal finite element models of a hypersonic skin panel are built and solved numerically to model the structural dynamics and thermal conduction. An implicit predictor-corrector scheme is employed to address the fluid-thermal-structural interactions. The aerothermoelastic characteristics of a two-dimensional hypersonic panel obtained using both one-way and two-way coupling strategies are systematically compared and discussed. The results show that: 1) The air viscosity delays the onset of flutter significantly, albeit aggravates thermal effect on the flutter instability; 2) The buckled panel can be similarly predicted by both the one-way and two-way coupling strategies. In contrast, the two-way coupling captures shockwave/boundary layer interactions leading to high local temperature; 3) The modal transition is predicted when structural displacement feeds back into the aerothermoelastic analysis. 4) The variation of temperature gradient along the panel thickness is analogous to the time-domain displacement response as revealed by two-way coupling strategy; 5) One-way coupling predicts lower maximum Von Mises stress as compared with the two-way coupling counterpart under the conditions employed in the present study.
In the present study, a variable stiffness method (VSM) is revisited for aeroelastic computations with/without thermal effects. Unlike the traditional CFD/CSM coupling method (TM), which predicts aeroelastic responses by varying freestream conditions (e.g. freestream density, velocity), the freestream conditions in VSM can be fixed. The VSM is first verified theoretically and adopted to predict nonlinear aeroelastic responses. For aeroelastic computations, the method is applied to predict flutter onset of Isogai wing section and limit cycle oscillation (LCO) of Goland+ wing at transonic conditions. The structural free-play nonlinearity is included in the Isogai wing section aeroelastic system to further demonstrate the method. The aeroelastic computation with thermal effects is considered as the flutter onset prediction of a simply supported panel in supersonic flow. It is shown that the VSM method can replicate the nonlinear aeroelastic responses predicted by its traditional CFD/CSM coupling method counterpart under the same flow similarity parameters (e.g. Mach number, Reynolds number), whereby the freestream conditions need to be adjusted. Limitations of the VSM are also pointed out and discussed. To further assess the VSM, an ARMA model is constructed under the framework of the VSM and demonstrated by flutter onset prediction of the Isogai wing section at transonic regime.
Results of investigations of the heat exchange in the turbulent flow of nitrogen tetroxide in a cylindrical channel are presented. The equilibrium stage of the dissociation reaction N2O4 ⇄ 2NO2 was considered. It was established that an increase in the temperature of the wall of the channel leads to an intensification of the chemical reaction proceeding in the N2O4 flow and causes the absorption of the heat, transferred from the channel wall, in this flow to increase, with the result that the temperature of the near-wall layers and the thickness of the thermal boundary layer in the chemically reactive gas flow decrease to a level lower than those of a chemically inert heat-transfer agent. It is shown that the use of a dissociating heat-transfer agent in a short channel is advantageous in the case where the rate of its flow is small, and, to increase the efficiency of heat exchange in a high-velocity flow of such an agent, it is necessary to increase the length of a heat exchanger. Approximation formulas for determining the criteria of heat exchange in flows of chemically inert and reactive gases have been obtained.
The mathematical model and results of a numerical study of swirling turbulent air flow characteristics in a semi-closed cylinder rotating around a symmetry axis are presented. A physical and mathematical model is used to describe aerodynamics of the stationary isothermal axisymmetric swirling flow, which includes the Navier-Stokes equations in cylindrical coordinates. The study of turbulence characteristics is carried out using the composite model Menter SST (Shear Stress Transport). The numerical solution is obtained using a chess grid. Nodes for axial and radial velocity components are located in the middle of the control volume faces for scalar quantities. Calculations are performed on a grid with 2000 and 1700 nodes in the axial and radial directions, respectively. The grid refinement is performed near the walls and in the areas with large velocity gradients. The calculated results show that the main grid refinement by 2 times in the axial and radial coordinates leads to a change in the values of the main variables by less than 1%. It is shown that the flow structure is determined by the rotational speed and cylinder height. Analyzing the calculated results, the ratio of the cylinder height to the angular velocity of the cylinder rotation is obtained, which ensures the formation of a quasi-solid rotation zone in the near-edge region.
Francis turbines within hydropower plants are required to operate under off-design conditions to meet the grid demand and ensure stability. In line with this, part-load conditions are generally accompanied with draft tube vortex rope appearance and associated pressure pulsations, which may cause structural vibrations and possible plant disruption for severe cases. Therefore, this study makes an attempt weaken the draft tube vortex rope and the associated pressure pulsations for a Francis turbine under part-load conditions (0.6Qopt.), through the modification of runner hub extension (RHE) design. Four RHE designs were numerically tested, namely Type A, B, C, and D. Experimental tests were carried out to explore real time vortex rope dynamics, which were replicated by numerical simulation method. The RHE design was found to considerably influence the draft tube pressure field characteristics through its filling effect to low pressure zones. The draft tube pressure pulsation analysis showed that all RHE designs exhibited the same pulsation frequency equivalent to 28% of the runner rotational frequency, with different amplitudes. With Type C design, the draft tube vortex rope energy was considerably weakened, leading to lowest pressure pulsation amplitude. Note that this design is a cylindrical RHE with a thickened tail.
The paper presents numerical predictions of various turbulent shear flows in which the structure of the viscous sublayer exerts appreciable influence on the flow. The model of turbulence employed is one where the turbulence energy and its dissipation rate are calculated by way of transport equations which are solved simultaneously with the conservation equations for the mean flow. The flows considered include isothermal low Reynolds number pipe flows, and wall boundary layers with streamwise pressure gradient and wall injection; the predictions span both natural transition and laminarisation. Although complete agreement with experiment is not yet achieved in every case, it is argued that only a turbulence model of (at least) this level of complexity will permit a universal modelling of the near-wall turbulence structures commonly found in thermal power equipment.
Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.
A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: (1) conventional κ-ε and κ-ω+2$/ formulations generally are inaccurate for boundary layers in adverse pressure gradient; (2) using 'wall functions' tends to mask the shortcomings of such models; and (3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows.
Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.
Hot-wire measurements have been made in the boundary layer, the separated region, and the near wake for flow past an NACA 4412 airfoil at maximum lift. The Reynolds number based on chord was about 1,500,000. Special care was taken to achieve a two-dimensional mean flow. The main instrumentation was a flying hot wire, i. e. , a hot-wire probe mounted on the end of a rotating arm. A digital computer was used to control synchronized sampling of hot-wire data at closely spaced points along the probe arc. Ensembles of data were obtained at several thousand locations in the flowfield. The data include intermittency, two components of mean velocity, and twelve mean values for double, triple, and quadruple products of two velocity fluctuations.
This paper deals with a survey of mean flow and fluctuating quantities in a turbulent boundary layer developing on a smooth wall in a pressure domain P(x), where both dP/dx and d2P/dx2 are positive (increasingly adverse). The two-dimensional nature of the flow field was checked by momentum balance, as well as velocity traverses either side of the working section centre-line. Using the integrated form of the momentum integral equation, it was found that the skinfriction term and the summed momentum and pressure terms differed by at most 19%; but for the majority of measuring points they differed by less than 14%. The off-centre-line velocity profiles were indistinguishable from those taken on the centre-line. The flow field was also surveyed for fluctuating components $(\overline{u^2_1})^{\frac{1}{2}}, (\overline{u^2_2})^{\frac{1}{2}}, (\overline{u^2_3})^{\frac{1}{2}}$, and $\overline{u_1u_2}$, as well as for u1 spectra. Wherever possible, the results were compared with existing models of boundary-layer development. These comparisons indicated that the only all-embracing model for boundary-layer development is the law of the wall.
The results of an experimental investigation of shock-induced stall and leading-edge stall on a 64A010 airfoil section are presented. Advanced nonintrusive techniques - laser velocimetry and holographic interferometry - were used in characterizing the inviscid and viscous flow regions. The measurements include Mach contours of the inviscid now regions, and mean velocity, flow direction, and Reynolds shear stress profiles in the separated regions. The experimental observations of this study are relevant to efforts to improve surface-pressure prediction methods for airfoils at or near stall.
15 Surface particle traces on upper surface of ONERA M6 wing at a=5.06', SST model Fig. 16 Surface particle traces on upper surface of ONERA M6 wing at a=4.56', SST model
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Fig.15 Surface particle traces on upper surface of ONERA M6 wing at a=5.06', SST model Fig. 16 Surface particle traces on upper surface of ONERA M6 wing at a=4.56', SST model
ExperiencewithTwo-LayerModels, Combiningthek-EmodelwithaOne-EquationModel v NeartheWall
- W Rodi
An ExperimentalInvestigationofasupercriticalAirfoilatTransonicSpeeds
- G G Seegmiller
- H L C Thomasj
- L A Hand
- J Andszodruch
Acquisitionand Application ofTransonicWingandFar-FieldTestData forThree-DimensionalComputationalMethodEvaluation
- B Hinson
- K Andburdges
An InvestigationofTransonicTurbulentBoundaryLayerSeparation Generatedonan AxisymmetricFlowModel
- W D Bachalo
- D Andjohnson
Pressure Distributionson theONERAM6WingatTransonicMach Numbers
- V Schmitt