Baldwin-Lomax Turbulence Model Research Articles

Numerical Flowfield Visualization Over Heat Shield Of Satellite Launch Vehicle at Mach 0.8 - 3.0

The paper presents a numerical flowfield visualization over a typical payload shroud of a satellite launch vehicle at Mach number range of 0.80 -3.0 and Reynolds number range of 33 x 106 - 46 x 106 /m. The numerical simulation over the bulbous heat shield is carried out by solving time-dependent compressible axisymmetric turbulent Reynolds-averaged NavierStokes equations. The closure of these equations is obtained employing the Baldwin-Lomax turbulence model. A three-stage Runge-Kutta time-stepping scheme has been used in conjunction with finite-volume discretization of the computational domain. The flowfield features over the bulbous heat shield have been analyzed from the velocity vector and the density contour plots. Flow separation on the payload shroud due to the normal shock wave is observed at Mach number 0.80 and 0.90. The normal shock movement on the heat shield is simulated for various transonic Mach number. A recirculation zone of flowfield is formed in the boat-tail region of the heat shield. The vorticity formation ahead of the heat shield moves close to the heat shield with the increasing transonic Mach number, which is observed in the density contours plots of the flowfield. Shock stand-off distance at the supersonic speed is calculated and compared with asymptotic formula of Frank and Zierep. They are found in good agreement.

Effect of surface radiation on the surface heat flux of two-dimensional hypersonic panel flow

This article investigates the effect of surface radiation on the surface heat flux of a two-dimensional hypersonic panel flow by comparing the surface heat fluxes of penetrating-radiative-equilibrium cases with those of constant-wall-temperature cases. A Du Fort–Frankel-type difference scheme is applied to cases with different external flow properties and is verified by comparing the results under a constant-wall-temperature boundary condition with self-similar solutions. Both laminar and turbulent flows are considered, and turbulence is modeled using a Baldwin–Lomax turbulence model with the assumption that full-scale turbulence is reached at the leading edge. The results show that the surface heat fluxes for laminar penetrating-radiative-equilibrium cases are greater by the order of 10% than those for constant-wall-temperature cases with the same temperature value at the corresponding points. Though turbulent instances are substantially more difficult, surface heat fluxes of penetrating-radiative-equilibrium cases are fairly similar to those of constant-wall-temperature cases. These results serve as the foundation for a brief discussion of how parameters affect the outcome and the proposal of a modified reference enthalpy method that can be used to predict heat flux when surface radiation causes a streamwise variation in wall temperature.

Modeling Laminar-to-Turbulent Transition in the Panel Test Facility Arcjet

A computational fluid dynamics (CFD) laminar-to-turbulence transition model was developed for the NASA Ames Research Center’s 20 MW Panel Test Facility (PTF). Surface pressure, heat flux to a water-cooled plate, and surface temperature on a tile plate coated with reaction-cured glass were measured across several conditions in the facility and compared with laminar and fully turbulent CFD simulations. The potential for bypass transition in the PTF nozzle was assessed via application of the Langtry–Menter four-equation transitional shear-stress transport (SST) model. Results from the transition model were inconsistent with measurements. Flow interaction with a boundary-conditioning plate feature inside the nozzle was also investigated as a potential source of laminar-to-turbulent transition, using two turbulence models with specified transition locations. The Baldwin–Lomax turbulence model was configured to simulate a transition at the upstream edge of the boundary conditioning plate and produced results consistent with the surface pressure measurements, but not the cold-wall heat flux. Finally, the SST turbulence model was calibrated to transition at the upstream edge of the boundary conditioning plate and produced results consistent with both the surface pressure and cold-wall heat flux measurements. The SST-based model demonstrated reasonable agreement with surface temperature measurements on the reaction-cured glass tile, albeit with some discrepancies.

High-resolution simulation and parametric research on helicopter rotor vortex flowfield with TAMI control in hover

In order to investigate the effect of active jet control on the rotor vortex flowfield in hover, a high-accuracy numerical method is presented in this paper, and a novel computer code is developed to calculate rotor flowfield with tip air mass injection. In the present computational fluid dynamics method, the Navier–Stokes equation is selected as the governing equation. For the sake of reducing numerical diffusion in calculation, the upwind Roe scheme with a fifth-order WENO scheme is employed to spatial discretization. A dual-time method is utilized in time marching and the high-efficiency implicit LU-SGS scheme is applied to every pseudo time step. The Baldwin–Lomax turbulence model is employed for eddy viscosity modeling. A surface boundary condition, which may effectively simulate the effect of tip air mass injection, is introduced into the current method. The overset grid method, which can veritably simulate the rotor blade motion, is adopted to exchange the flowfield information between the rotor blade and background grids. By the established method, the rotor flowfield with jet control of different jet angles is simulated. Furthermore, parametric analyses of jet velocity are carried out at different tip March numbers and collective pitches. It is demonstrated that tip air mass injection can make the tip vortex rolled up and generated in advance compared with the clean rotor, which can change the position and strength of the vortex core greatly. It is also shown that the rotor aerodynamic characteristics, such as blade surface pressure and radial lift distributions, are more sensitive to tip air mass injection control at the condition with a lower Mach number or a lower collective pitch.

Aerodynamic shape study of supersonic surface to surface missiles with continuous flexible nose

The aerodynamic characteristics of nine configurations of supersonic continuous deflectable nose guided missiles have been investigated. The optimized geometry was achieved based on the accuracy of confliction with constant target in ground to ground mission. The studied configurations consist of a spherical nose tip, a tangent ogive, one set of stabilizing tail fines and a cylindrical body whose midsection is flexible to form an arc of a circle. So the cylindrical body consists of a fixed part in the vicinity of the nose, middle flexible part and main body with stabilizers. The effects of fixed length (Fix = 0, 1.5, 3Cal) and flexible length (Flex = 1, 2.5, 5Cal) parameters on the aerodynamics and flight dynamics of guided missile have been studied. A code has been developed to solve full Navier-Stokes equations using finite volume and Runge-Kutta time stepping techniques and modified Baldwin-Lomax turbulence model. Multi-block technique was also used to solve the main body and fin parts flow fields. Further, a 3 degree of freedom code along with a pure pursuit guidance subroutine was developed to compare planar flight dynamics of missiles. It was found that although the missiles with bigger lengths for fixed and flex parts show more maneuverability, but this is not favorable for all missile missions as sometimes it decreases the confliction accuracy. Flight dynamic analysis shows that a change in initial launch angle may shift the favorite configuration. This means only the aerodynamic defined aim functions cannot completely supersede flight dynamic analysis in geometric optimization. Further, the thrust vector moment is an important portion of total control moment as it enhances the hitting accuracy and also decreases the importance of geometry.

Optimization for rotor blade-tip planform with low high-speed impulsive noise characteristics in forward flight

Rotor noise is one of the most important issues for helicopter designer, and high-speed impulsive noise is particularly intense among the various rotor noise sources due to compressibility. Based on Computational Fluid Dynamics/Ffowcs Williams and Hawkings equations with Penetrable Data Surface (CFD/FW-Hpds) methods and hybrid optimization technique, a new optimization design procedure for rotor blade planform with low high-speed impulsive noise characteristics is established. First, in order to accurately capture the unsteady aerodynamic characteristics of rotor, based on the moving-embedded grid methodology, a CFD simulation is developed by solving the compressible Reynolds-average Navier–Stokes equations with Baldwin–Lomax turbulence model. The low dissipation Roe-Monotone Upwind-centered Scheme for Conservation Laws (MUSCL) scheme and highly efficient implicit lower–upper symmetric Gauss–Seidel scheme are used for spatial and temporal discretization, respectively. Second, taking the CFD results as sound pressure information input, the high-speed impulsive noise characteristics generated by transonic rotor are analyzed through a robust numerical method based on FW-Hpds equations. Third, the genetic algorithm and surrogated model based on radial basis function are combined as a hybrid optimization technique; during the optimization process, the blade grids are generated by a highly efficient parameterized method. Aiming at the minimization of the sound pressure level of rotor in forward flight, the parametric effect analyses of blade-tip shapes on transonic noise have been conducted first. Then, optimization analyses based on the rotor blade with double-swept and tapered tip have been accomplished with the aerodynamic performance as constraints. Compared with the baseline blade, it shows that the sound pressure level of rotor with optimized blade-tip shape can be decreased obviously at the present calculating condition due to its weaker transonic delocalization phenomenon in the region of blade tip. In the rotor plane, absolute peak value of sound pressure produced by the optimized blade planform is reduced about 59.1% of that by the baseline one, and the reduced value in sound pressure level is up to 5.6 dB.

Periodic transonic flow simulation using fourier-based algorithm

The present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady Euler and Navier-Stokes equations, using time spectral method (TSM) and compares it with the traditional methods like BDF and explicit structured adaptive grid method. The TSM uses a Fourier representation in time and hence solves for the periodic state directly without resolving transients (which consume most of the resources in a time-accurate scheme). Mathematical tools used here are discrete Fourier transformations. The TSM has been validated with 2D external aerodynamics test cases. These test cases are NACA 64A010 (CT6) and NACA 0012 (CT1 and CT5) pitching airfoils. Because of turbulent nature of flow, Baldwin-Lomax turbulence model has been used in viscous flow analysis with large oscillation amplitude (CT5 type). The results presented by the TSM are compared with experimental data and the two other methods. By enforcing periodicity and using Fourier representation in time that has a spectral accuracy, tremendous reduction of computational cost has been obtained compared to the conventional time-accurate methods. Results verify the small number of time intervals per pitching cycle (just four time intervals) required to capture the flow physics with small oscillation amplitude (CT6) and large oscillation amplitude (CT5) as compared to the other two methods.

Comparison of Numerical Methods Evaluating Airfoil Aerodynamic Characteristics at Low Reynolds Number

The flowfields around the NACA 0012 airfoil at Reynolds numbers , , and are studied, and the predictability of aerodynamic characteristics derived from various numerical methods is examined. Two-dimensional laminar simulation, two-dimensional Reynolds-averaged Navier–Stokes simulation using the Baldwin–Lomax turbulence model, and three-dimensional implicit large-eddy simulation are employed in this study. The two-dimensional laminar and three-dimensional implicit large-eddy simulations accurately predict the separation point, and capture the characteristics of a separation bubble for each Reynolds number and each angle of attack. Nonlinearity in the lift curve is also captured in the results of the two-dimensional laminar and three-dimensional implicit large-eddy simulations. The two-dimensional Reynolds-averaged Navier–Stokes simulation using the Baldwin–Lomax turbulence model predicts the separation point nearer the trailing edge than does the two-dimensional laminar and three-dimensional implicit large-eddy simulations, and the separation bubble is not captured for any Reynolds number and angle of attack by this method. Nonlinearity of the lift curve does not appear in the results of the two-dimensional Reynolds-averaged Navier–Stokes simulation using the Baldwin–Lomax turbulence model. The two-dimensional laminar simulation can predict airfoil aerodynamic characteristics qualitatively, and it can be used as an appropriate numerical method at lower Reynolds numbers. The three-dimensional-implicit-large-eddy-simulation technique can be employed when more accurate qualitative characteristics are needed.

Development of a Numerical Based Correlation for Performance Losses due to Surface Roughness in Axial Turbines

AbstractIn the present work, a recently developed in-house 2D CFD code is used to study the effect of gas turbine stator blade roughness on various performance parameters of a two-dimensional blade cascade. The 2D CFD model is based on a high resolution flux difference splitting scheme of Roe (1981). The Reynolds Averaged Navier-Stokes (RANS) equations are closed using the zero-equation turbulence model of Baldwin-Lomax (1978) and two-equation Shear Stress Transport (SST) turbulence model. For the smooth blade, results are compared with experimental data to validate the model. Finally, a correlation between roughness Reynolds number and loss coefficient for both turbulence models is presented and tested for three other roughness heights. The results of 2D turbine blade cascades can be used for one-dimensional models such as mean line analysis or quasi-three-dimensional models e.g. streamline curvature method.

Improvement of Baldwin–Lomax turbulence model for supersonic complex flows

Entropy represents the dissipation rate of energy. Through direct numerical simulation (DNS) of supersonic compression ramp flow, we find the value of entropy is monotonously decreasing along the wall-normal direction no matter in the attached or the separated region. Based on this feature, a new version of Baldwin–Lomax turbulence model (BL-entropy) is proposed in this paper. The supersonic compression ramp and cavity-ramp flows in which the original Baldwin–Lomax model fails to get convergent solutions are chosen to evaluate the performance of this model. Results from one-equation Spalart–Allmaras model (SA) and two-equation Wilcox k–ω model are also included to compare with available experimental and DNS data. It is shown that BL-entropy could conquer the essential deficiency of the original version by providing a more physically meaningful length scale in the complex flows. Moreover, this method is simple, computationally efficient and general, making it applicable to other models related with the supersonic boundary layer.

Effect of wall conditions on DDT in hydrogen–oxygen mixtures

Detonation in ducts is usually studied assuming adiabatic walls because of the high kinetic energy due to the incoming flow being supersonic. In the present work, numerical simulations of deflagration-to-detonation transition (DDT) using a detailed chemical reaction model are performed under adiabatic and isothermal boundary conditions in a tube with no-slip walls. The results show a local explosion driving DDT, which occurs near the tube wall in the case of an adiabatic wall, but close to the flame front in the case of an isothermal wall. Furthermore, to examine the effects of a turbulent boundary layer, a simulation using the Baldwin–Lomax turbulence model is carried out. In the case of the isothermal wall, there is again a local explosion near the tube wall, which leads to detonation. In summary, the present study confirms that the boundary conditions affect the transition to detonation and that the boundary layer is a key component of DDT.

Influence of Geometrical Parameters of Heat Shield on Flow Characteristics at Transonic Mach

The numerical simulation over the bulbous heat shield is carried out by solving time-dependent compressible axisymmetric turbulent Reynolds-averaged Navier-Stokes equations. The solution of these equations is obtained employing the Baldwin-Lomax turbulence model. A three-stage Runge-Kutta time-stepping scheme has been used in conjunction with finite-volume discretization of the computational domain. The flowfield features over the bulbous payload shroud have been analyzed using the density contour plots and surface pressure distributions. Flow separation on the payload shroud due to the terminal shock wave is observed at transonic Mach numbers range. The normal shock movement on the heat shield is simulated for various transonic Mach numbers. The maximum diameter of the various heat shields is kept constant in order to evaluate the movement of terminal shock. A recirculation zone of the flowfield is formed in the boat-tail region of the payload shroud. The density increases ahead of the stagnation region of the heat shield moves close to the heat shield with the increasing transonic Mach number. It also depends on the cone angle of the heat shield as observed in the density contours plots of the flowfield.

Investigation on the effect of trailing edge ejection on a turbine cascade

This paper presents a detailed experimental and numerical investigation for a turbine cascade with different trailing edge ejection. The numerical simulation is based on Three-Dimensional Navier–Stokes equations coupled with an effective ejection model, where a high resolution non-oscillatory scheme, LU-SGS implicit algorithm and Baldwin-Lomax turbulence model are employed. The experiments presented in this paper focused on a transonic turbine cascade performance with different ejection to validate the numerical simulation results. The results show that the blowing ratio has a small effect on the Mach number distribution and exit flow angle with two slot types. However the energy loss coefficient increases initially, and subsequently has a decrease tendency with the increasing of blowing ratio. The ejection from the symmetry slot blows away the vortex at the blade trailing edge and strengthens the mixing between the wake and main flow. The ejection from the pressure side cutback only clears up the vortex near the slot surface, and has small effect on the flow field near the trailing edge.

Numerical Simulation of Air-He Shock Tube Flow with Equilibrium Air Model

In this study, a compressible multi-component Navier-Stokes flow solver with real gas effect is developed for studying the high-speed flow in an air-He shock tube. For compressible multi-component flow simulation, a reduced five-equation model in conjunction with HLLC approximate Riemann solver is employed. For the real gas effect, a curve-fitting approximation for equilibrium air constructed from Grabau-type transition functions is adopted. In addition, Baldwin-Lomax turbulence model is used for turbulent flow simulation. In this work, several typical test cases will be demonstrated first. Subsequently, air-He shock tube simulations with the real gas effect will be performed by using parallel computation. Based on the present results, the real gas effect shows significant influence on the temperature behind the reflected shock. In addition, the driver gas contamination and the development of shock bifurcation are presented by flow visualization.

Free surface flow around a ship model using an interface-capturing method

A free surface, turbulent flow code around ship hulls using the Slightly Compressible Flow formulation is used for simulating the flow around a Wigley hull. The code uses finite differences and the numerical scheme was marched in time using the 2nd order explicit Runge–Kutta method. Turbulent flows were simulated using the Baldwin–Lomax turbulence model. The grid is generated using an algebraic grid generator. The free surface treatment method is an interface-capturing one, on a fixed grid on which the kinematic free surface equation is solved. Several boundary conditions were implemented and their behavior was assessed. The flow conditions are the ones for which experimental and numerical results exist. The results show very good agreement with the experimental results.

Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric transitional/turbulent flows

An appropriate combination of the thin-layer Navier–Stokes (TLNS) and parabolized Navier–Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic transitional/turbulent flowfields of perfect gas and equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching technique. Both the TLNS and the PNS equations are numerically solved by using the implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting procedure is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. For turbulent flow simulations, both the Cebeci–Smith (CS) and the Baldwin–Lomax (BL) turbulence models are analyzed with the present technique for the case of long slender blunt bodies. The Baldwin–Lomax turbulence model, which does not need the determination of the edge of the boundary layer, is modified in the present work to include the effects of variable properties and damping factor to accurately calculate flowfield characteristics in turbulent regions. Detailed comparisons are made with other numerical and experimental results to assess the accuracy and efficiency of the present solution procedure for computing hypersonic transitional/turbulent flows over long slender blunt bodies. The results of these computations are found to be in good agreement with available data. The effects of real gas on the flowfield characteristics are also studied.

Unsteady compressible flow simulation around low-aspect-ratio rectangular flat wings

Unsteady compressible flow solutions around a sharp-edged rectangular flat wing of an aspect ratio of 1.0 are obtained using a parallel Reynolds-averaged Navier–Stokes algorithm. The simulated cases are obtained for Mach numbers of 0.42–0.87 and Reynolds numbers of the order of 200 000–300 000 in the transitional flow regime up to an angle of attack of 15°. A Degani–Schiff modification for the Baldwin–Lomax turbulence model is used to distinguish between the boundary layers and the primary and secondary vortices over the flat plate. Unsteady vortex shedding frequencies and Strouhal number variation with the angle of attack are obtained by using the fast Fourier transform. The flow around the low-aspect-ratio rectangular flat wing is strongly dominated by the leading- and side-edge vortices and flow separations. The numerical results are compared with the prior experimental data acquired at the von Karman Institute that shows a mix of laminar/transitional flow. In the simulations, top surface pressures of the rectangular flat wing are well predicted except in the leading-edge region. Time-mean averaged surface flow topologies are also found to be in good agreement with the experiment. Complex flow structures, including the primary and secondary separation bubbles and the footprints of the primary and secondary vortex cores, are well captured through the use of the modified algebraic turbulence model.

Redesign of a Low Speed Turbine Stage Using a New Viscous Inverse Design Method

The midspan section of a low speed subsonic turbine stage that is built and tested at DFVLR, Cologne, is redesigned using a new inverse blade design method, where the blade walls move with a virtual velocity distribution derived from the difference between the current and target pressure distributions on the blade surfaces. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time-accurate solution of the Reynolds-averaged Navier–Stokes equations. An algebraic Baldwin–Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and rotor regions. The computational fluid dynamics (CFD) analysis formulation is first assessed against the turbine stage experimental data. The inverse formulation that is implemented in the same CFD code is assessed for its robustness and merits. The inverse design method is then used to study the effect of the rotor pressure loading on the blade shape and stage performance. It is also used to simultaneously redesign both stator and rotor blades for improved stage performance. The results show that by carefully tailoring the target pressure loading on both blade rows, improvement can be achieved in the stage performance.

1405 火星探査航空機翼型の設計探査(OS8-1 近似最適化I)

In this research, modified PARSEC airfoil representations are developed and they are investigated by the design exploration of airfoils for the Mars airplane. The existent PARSEC airfoil representation method is useful for the aerodynamic optimization and the knowledge discovery, because the original PARSEC airfoil is parameterized based on the aerodynamic theory. In this method, designer can directly define airfoil's parameters, the leading edge radius, the maximum thickness, the maximum camber, and so on, However, the original PARSEC representation cannot use for not subsonic flow (supersonic flow, low Reynolds number flow), because it was parameterized in consideration of a subsonic wing. To solve the several airfoil design problem, modified representation method is constructed and its design performance is investigated by solving multi-objective design problem. This study employs Genetic Algorithm (GA) for exploration of the multi-objective problem. Flowfield is solved by the structured Navier-Stokes solver with Baldwin-Lomax turbulent model. According to these results, the modified airfoil representation method can solve the design problem under the Martian atmosphere better than the original method.

Turbulence modeling for two-dimensional water hammer simulations in the low Reynolds number range

Modeling turbulence in two-dimensional water hammer simulations is considered in the present study. The Baldwin–Lomax turbulence model is implemented, both in quasi-steady and frozen forms. Numerical simulations using both forms agree well with experimental data for lower Reynolds numbers (Re = 5600) and the attenuation of the transient is adequately captured. However, for higher Reynolds numbers (Re = 15,800), the frozen form overpredicts the attenuation of the transient. Moreover, it is shown that switching the turbulence model off altogether and applying a quasi-laminar approximation results in good agreement with experimental data for the lower Reynolds number case (Re = 5600) while underpredicting the attenuation of the transient for the higher Reynolds number case (Re = 15,800).