Baldwin-Lomax Model Research Articles

Comparison of Eddy-Viscosity Turbulence Models in Flows with Adverse Pressure Gradient

Results of computations of aerodynamic flows with attached and separated boundary layers with adverse pressure gradients are presented. The objective is to compare the predictive accuracy of 11 eddy-viscosity turbulence models frequently employed for computing aeronautical flows. The turbulence models considered are the algebraic model of Baldwin and Lomax; the one-equation model of Spalart and Allmaras along with two additional variants of it; six different k, w models; and the nonlinear eddy-viscosity model of Wallin and Johansson. Starting with a boundary-layer flow with a nominally zero pressure gradient, flows with a successively increased adverse pressure gradient are investigated. Computational results are compared with each other and to experimental data. It is found that the agreement between computational and experimental results varies between the turbulence models also for the simpler flow cases. Predictive accuracy obtained with a given model for a given flow case varies between the different flow variables evaluated. The best turbulence model changes from flow case to flow case. Models using transport equations for the eddy viscosity (or a related quantity) typically show better response to a pressure gradient than the algebraic Baldwin-Lomax model. However, no general conclusion on which model to use for adverse-pressure-gradient flows is drawn.

Finite element computation of turbulent flow past a multi-element airfoil

Flow past multi-element airfoil is studied via two-dimensional numerical simulations. The incompressible Reynolds averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite element formulation. The Spalart–Allmaras and Baldwin–Lomax models are employed for turbulence closure. The implementation of the Spalart–Allmaras model is verified by computing flow over a flat plate with a specified trip location. Good agreement is seen between the results obtained with the two models for flow past a NACA 0012 airfoil at 5° angle of attack. Results for the multi-element airfoil, with the two turbulence models, are compared with experiments for various angles of attack. In general, the pressure distribution, from both the models matches quite well with the experimental results. However, at larger angles of attack, the computational results overpredict the suction peak on the slat. The velocity profiles from the Baldwin–Lomax model are, in general, more diffused compared to those from the Spalart–Allmaras model. The agreement between the computed and experimental results is not too good in the flap region for large angles of attack. Both the models are unable to predict the stall; the flow remains attached even for relatively large angles of attack. Consequently, the lift coefficient is over predicted at large α by the computations. Overall, compared to the Baldwin–Lomax model, the predictions from the Spalart–Allmaras model are closer to experimental measurements.

An inverse blade design method for subsonic and transonic viscous flow in compressors and turbines

An inverse blade design method applicable to two- and three-dimensional inviscid and viscous flow in turbomachinery cascades is presented and is applied to design cascades in two-dimensional viscous flow. The pressure distribution along the blade surfaces is prescribed and is reached by modifying the initial guess of the blade geometry. The geometry modification is computed from a virtual velocity distribution derived from the difference between the current and the target pressure along the blade surfaces. The inverse method is implemented into and is consistent with the unsteady Reynolds-averaged Navier-Stokes (RANS) equations where an arbitrary Lagrangian–Eulerian (ALE) formulation on a moving and deforming grid is used. The grid velocities are determined from the space conservation law (SCL), which ensures a fully conservative computational procedure. The unsteady RANS equations are discretized using a cell-vertex finite volume method and the time accuracy is achieved using a dual time stepping scheme. An algebraic Baldwin–Lomax model is used for turbulence closure. The design method is first validated, and then its robustness, flexibility and usefulness are demonstrated on the redesign of recent compressor and turbine blade geometries used in modern gas turbine engines.

Vortex induced loads on marine risers

The Vortex-Induced Vibration on a circular cylinder is investigated as basis for applications on dynamics of risers used in offshore oil and gas industry. The numerical solution of the two-dimensional Reynolds Averaged Navier–Stokes equations is obtained for a circular cylinder laterally supported by a spring and a damper and free to oscillate in the transversal direction. The Beam and Warming implicit factorization scheme is used to solve the governing equations and the Baldwin–Lomax model is used to simulate the turbulent flow in the wake of the cylinder. The proposed numerical solution was able to provide a good picture of the real physics of the phenomenon including the Kármán vortex street effects on the lift and drag coefficients. The numerical results for the transversal oscillation amplitude are compared to experimental data showing a fairly precise agreement even at the difficult to simulate regime of the lock-in phenomenon.

Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.

Effect of leading edge cut on the aerodynamics of ram‐air parachutes

AbstractThe effect of the configuration of leading edge cut on the aerodynamic performance of ram‐air parachutes is studied via two‐dimensional flow simulations. The incompressible Reynolds‐averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite‐element formulation. The Baldwin–Lomax model is employed for turbulence closure. Flow past an LS(1) 0417 airfoil is investigated for various configurations of the leading edge cut and results are compared with those from a Clark‐Y airfoil section. It is found that the configuration of the leading edge cut affects the lift‐to‐drag ratio (L/D) of the parachute very significantly. The L/D value has strong implications on the flight performance of the parachute. One particular configuration results in a L/D value that is in excess of 25 at 7.5° angle of attack. Results are presented for other angles of attack for this configuration. Copyright © 2004 John Wiley & Sons, Ltd.

Numerical investigation of a high-speed centrifugal compressor with hub vane diffusers

Hub vane diffusers can obtain higher pressure recovery and efficiency compared with the vaneless diffuser and a wider operating range compared with the vane diffuser. To improve the performance of high pressure ratio centrifugal compressors it is necessary to understand the flow phenomena in the hub vane diffusers. Although some research work on hub vane diffuser flow has been published, many unknown flow physics and disputed questions still remain. A computational analysis of the flowfield in a high-speed centrifugal compressor with a backswept unshrouded impeller and wedge vane channel diffuser is presented. In order to obtain the optimum hub vane height, the pressure and velocity fields were numerically simulated for eight kinds of hub vane, which are varied as follows: h/b = 0 (vaneless), 0.2, 0.3, 0.4, 0.5, 0.6, 0.8 and 1 (vane). The advanced Navier-Stokes solver EURANUS/TURBO is applied with a Baldwin-Lomax model for closure. The calculations are performed with a central space discretization scheme, with second- and fourth-order artificial dissipation terms. The numerical procedure applied a four-stage explicit Runge-Kutta scheme, coupled to local time stepping. The good agreement of the computed stage performance and the experimental data of the stage with the vane diffuser shows that the solver is effective and reasonable. Numerical results show that the maximum flowrate attained by the stage with the vane diffuser is about 12.5 per cent less than with the hub vane diffusers. The stage efficiency reaches its maximum value for the hub vane diffuser with an h/b ratio of 0.5 at lower flowrate and for the hub vane diffuser with an h/b ratio of 0.4 at higher flowrate. The hub vane diffusers have a wider operating range than the vane diffuser. The hub vane diffuser with an h/b ratio of 0.3 shows a higher mass-averaged static pressure coefficient up to a flow coefficient φ = 0.16. The hub vane diffuser with an h/b ratio of 0.4 shows a slightly higher mass-averaged static pressure coefficient over an operating range of φ = 0.18–0.28, but it falls beyond φ = 0.3 below that of the vaneless diffuser. The performance of the centrifugal compressor with the shroud vane diffuser is better than that with the hub vane diffuser for the same height of the vane.

Computation of turbulent free‐surface flows around modern ships

AbstractThis paper presents the calculated results for three classes of typical modern ships in modelling of ship‐generated waves. Simulations of turbulent free‐surface flows around ships are performed in a numerical water tank, based on the FINFLO‐RANS SHIP solver developed at Helsinki University of Technology. The Reynolds‐averaged Navier–Stokes (RANS) equations with the artificial compressibility and the non‐linear free‐surface boundary conditions are discretized by means of a cell‐centred finite‐volume scheme. The convergence performance is improved with the multigrid method. A free surface is tracked using a moving mesh technology, in which the non‐linear free‐surface boundary conditions are given on the actual location of the free surface. Test cases recommended are a container ship, a US Navy combatant and a tanker. The calculated results are compared with the experimental data available in the literature in terms of the wave profiles, wave pattern, and turbulent flow fields for two turbulence models, Chien's low Reynolds number k–εmodel and Baldwin–Lomax's model. Furthermore, the convergence performance, the grid refinement study and the effect of turbulence models on the waves have been investigated. Additionally, comparison of two types of the dynamic free‐surface boundary conditions is made. Copyright © 2003 John Wiley& Sons, Ltd.

Passive control of condensation shock wave in Prandtl-Meyer expansion flow

In this paper, the effects of the passive technique by using the slotted wall on the characteristics of a condensation shock wave generated in a Prandtl-Meyer flow were investigated experimentally. Furthermore, in order to clarify the variation of condensation properties in the flow field, Navier-Stokes equations were solved numerically using a 3rd-order MUSCL type TVD finite-difference scheme with a second-order fractional-step for time integration. Baldwin-Lomax model was used as a turbulence model in the computations. From experimental results, it was found that the shock strength on the slotted wall became weak in comparison with no passive case (solid wall), and the present passive technique was the most effective when a foot of the condensation shock wave was located at the middle of slotted wall. Furthermore, it was confirmed numerically that the passive technique was also effective for the unsteady condensation shock wave.

821 高レイノルズ数 Base 流れ解析における LES/RANS hybrid 手法の信頼性検証

LES/RANS hybrid, LES and MILES simulations are applied to an axi-symmetric base flow for the supersonic flows at high Reynolds number. The idea of LES/RANS hybrid methodology is that RANS model is used in the boundary layer because of its low computational costs than LES, and LES is used in massively separated regions where unsteady flow structures are correctly captured. The subgrid-scale stresses are computed using the compressible form of Smagorinsky's model. Baldwin-Lomax model is applied to the RANS region. The LES/RANS hybrid simulations accurately capture the physics of turbulent flows. The reverse flow behind the base shows satisfactory agreement with the experimental data. The base pressure distributions, which is the primary parameter from the engineering interest, is in good agreement with the experimental results.

습공기 유동에서 발생하는 충격파와 경계층 간섭의 피동제어에 관한 연구

본 연구는 다공벽과 공동을 사용한 피동제어법을 천음속 습공기 유동에서 발생하는 충격파와 경계층 간섭에 적응하였다. 지배방정식은 액적성장 방정식과 완전히 결합된 2차원, 비정상, 압축성 Navier-Stokes 방정식이며, 3차 오더 MUSCL 타입의 TVD 기법을 사용하였다. 또 난류모델로는 Baldwin-Lomax 모델을 적용하였다. 본 연구에서 적용한 제어법의 유용성을 조사하기 위해 유동의 전압손실과 충격파 변위의 시간의존성 거동을 해석하였다. 수치계산 결과로부터 본 연구의 피동제어기법을 통해 천음속 습공기 유동에서 발생하는 충격파/경계층 간섭으로 인한 전압손실이 상당히 감소하였고, 익에서 충격파 운동을 억제하는 것으로 나타났다. 또 다공영역의 위치가 본 연구의 제어법의 효과에 상당한 영향을 준다는 것이 발견하였다. In the present study, a passive control method, using a porous wall and cavity system, is applied to the shock wave/boundary layer interactions in transonic moist air flow. The two-dimensional, unsteady, compressible, Navier-Stokes equations, which are fully coupled with a droplet growth equation, are solved by the third-order MUSCL type TVD finite difference scheme. Baldwin-Lomax model is employed to close the governing equations. In order to investigate the effectiveness of the present control method, the total pressure loss of the flow and the time-dependent behaviour of shock motions are analyzed in detail. The computed results show that the present passive control method considerably reduces the total pressure losses due to the shock wave/boundary layer interaction in transonic moist air flow and suppresses the unsteady shock wave motions over the airfoil as well. It is also found that the location of the porous ventilation significantly affects the control effectiveness.

Modeling the aeroacoustics of axial fans from CFD calculations

The main source of aeroacoustic noise in axial fans is the distribution of the fluctuating, unsteady, aerodynamic forces on the blades. Numerical simulations were carried out with the CFD code (NUMECA), first with steady flow conditions to validate the aerolic performances (pressure drop as a function of flow rate) of the simulated six-bladed axial fans. Simulations were then made with unsteady flows to compute the fluctuating force distributions on the blades. The turbulence was modeled either with the Baldwin–Lomax model or with the K-epsilon model (extended wall function). The numerical results were satisfactory both in terms of numerical convergence and in terms of the physical characteristic of the forces acting on the blades. The numerical results were then coupled into an in-house aeroacoustics code that computes the farfield radiated noise spectrum and directivity, based on the Ffowcs-Williams Hawkings formulation, or alternatively, on the simpler Lowson model. Results compared favorably with data obtained under nonanechoic conditions, based upon ISO 5801 and ISO 5136 standards.

Hysteresis in flow past a NACA 0012 airfoil

Computations for two-dimensional flow past a stationary NACA 0012 airfoil are carried out with progressively increasing and decreasing angles of attack. The incompressible, Reynolds averaged Navier–Stokes equations in conjunction with the Baldwin–Lomax model, for turbulence closure, are solved using stabilized finite element formulations. Beyond a certain angle of attack the flow stalls with a sudden loss of lift and increase in drag. Hysteresis in the aerodynamic coefficients is observed for a small range of angles of attack close to the stall angle. This is caused by the difference in the location of the separation point of the flow on the upper surface of the airfoil during the increasing and decreasing angles of attack. With the increasing angle, the separation point moves gradually towards the leading edge. With the decreasing angle, the movement of the separation point away from the leading edge is abrupt.

Models of steam force and torque of a rotor subjected to the leakage of tip clearance

The topic of this paper is focused on the models of steam force and torque of a rotor subjected to the leakage of tip clearance. The unsteady three-dimensional Navier-Stokes solver is used to simulate the flow field for a rotating blade row with a tip clearance. The basic algorithm time marches the fully three-dimensional unsteady equations of motion expressed in a finite volume form. The Baldwin-Lomax model is used as turbulence model. By simulating the complex flow field including oscillating tip clearance with rotor vibration, the instantaneous asymmetry and oscillatory pressures acting on the surfaces of the blade row can be acquired, and the instantaneous steam force and torque acting on the rotor can be calculated. A new nonlinear model of steam force is created in this paper, and a model of steam torque excited by leakage is also reported.

Shape optimization of two turbine stages using the deformed polyhedron method and a three-dimensional RANS solver

A combination of the Nelder-Mead deformed polyhedron method with a three-dimensional RANS solver is used in the paper for the constrained optimization of the shape of two selected turbine stages. The objective function is the total stage loss, with the exit kinetic energy also considered a loss. There are constraints imposed on the mass flowrate, exit angle, average reaction and reaction at tip and root. The exit angle and reactions are not allowed to assume values beyond prescribed ranges, whereas a penalty function is imposed on the mass flowrate if it falls outside the required interval. Among the optimized parameters are stator and rotor stagger and twist angles and stator sweep and lean, both straight and compound. The computations of the flowfield are compressible, viscous and three-dimensional. Turbulence effects are taken into account using the modified Baldwin-Lomax model. The process of optimization gives new designs with improved calculated efficiency. Part of the improvementis due to optimization of the stagger angles and blade numbers, as in classical one-dimensional optimization, and part of it is due to the fact that the blades assume new three-dimensional stacking lines.

Analysis of transitional flow and heat transfer over turbine blades: algebraic versus low-Reynolds-number turbulence model

AbstractThe numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation (k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.

Analysis of transitional flow and heat transfer over turbine blades: Algebraic versus low-Reynolds-number turbulence model

The numerical simulation of flow and heat transfer over turbine blades involving laminar-turbulent transition is presented. The predicted results are compared with the experimental surface heat transfer and pressure distributions for two transonic turbine blades over a wide range of flow conditions. The time-dependent, mass-averaged Navier-Stokes equations are solved by an explicit four-stage Runge-Kutta scheme in the finite volume formulation. Local time stepping, variable-coefficient implicit residual smoothing and a full multigrid method have been implemented to accelerate the steady state calculation. The turbulence is simulated by the algebraic Baldwin-Lomax model together with an explicitly imposed model for transition. For comparison, the low-Reynolds-number version of the two-equation ( k-∊) model of Chien is also used. The modified Baldwin-Lomax model performs well in predicting the onset of laminar-turbulent transition, whereas the Chien model shows a tendency to mimic the transition early and over a shorter distance.

An improved Navier-Stokes flow computation of AGARD case-10 flow over RAE2822 airfoil using Baldwin-Lomax model

Transonic flow over the RAE2822 airfoil has been solved for flow coditions corresponding to the AGARD test case 10. An extensively tested steady Navier-Stokes flow solver based on the finitevolume cell-centered explicit Runge-Kutta time stepping scheme has been used to simulate the flow. The experiment has shown a zone of separated flow after the foot of the shock. Under the conditions of considerable shock-boundary layer interaction, the Baldwin-Lomax eddy viscosity model has been found to produce unsatisfactory results. But, at the same time, efforts using different schemes and the turbulence/eddy viscosity models do not seem to lead to any significantly improved simulation of this flow even when computations have been made with marginally adjusted mach number and/or angle of attack. Interestingly, when the present code was used to study the above case, significantly improved result has been obtained (with marginally adjustedM ∞ and α) that is as good as and even better than the computations seen in the literature using various improved turbulence models. This computation appears to be the first of its kind where Baldwin-Lomax model has been used to produce such good quality result for this flow. This may even point towards a need to have another look at the wind tunnel interference correction used in AGARD test.

Film cooling on a turbine guide vane: A numerical analysis with a multigrid technique

The flow and heat transfer due to film cooling over a turbine nozzle guide vane, which was also cooled by internal convection, were numerically analysed under engine conditions. The time-dependent, two-dimensional, mass-averaged, Navier-Stokes (N-S) equations are solved in the physical plane based on the four-stage Runge-Kutta algorithm in the finite volume formulation. Local time stepping, variable coefficient implicit residual smoothing and a full multigrid technique have been implemented to accelerate the steady state calculations. Turbulence was simulated by the algebraic Baldwin-Lomax (B-L) model. The computed heat transfer distributions with film cooling in conjunction was successful in describing the coolant behavior over the curved suction and pressure surfaces of a turbine blade for varying blowing and temperature ratios.

Computation of two-dimensional flows past ram-air parachutes

Computational results for flow past a two-dimensional model of a ram-air parachute with leading edge cut are presented. Both laminar (Re=104) and turbulent (Re=106) flows are computed. A well-proven stabilized finite element method (FEM), which has been applied to various flow problems earlier, is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. The Baldwin-Lomax model is employed for turbulence closure. Turbulent flow computations past a Clarck-Y airfoil without a leading edge cut, for α=7.5°, result in an attached flow. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift-to-drag ratio obtained with the present computations is in good agreement with those reported in the literature. The effect of the size and location of the leading edge cut is studied. It is found that the flow on the upper surface of the parafoil is fairly insensitive to the configuration of the cut. However, the flow quality on the lower surface improves as the leading edge cut becomes smaller. The lift-to-drag ratio for various configurations of the leading edge cut varies between 3.4 and 5.8. It is observed that even though the time histories of the aerodynamic coefficients from the laminar and turbulent flow computations are quite different, their time-averaged values are quite similar.