Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k–ε Turbulence Model

1992 ◽  
Vol 114 (3) ◽  
pp. 627-642 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe ◽  
Time Step

An explicit, three-dimensional, coupled Navier–Stokes/k–ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows, have been extended to three dimensions, including a low Reynolds number compressible form of the k–ε turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure, which eliminates the finite difference metric singularity at leading and trailing edges on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity, and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data are available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire, and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near-wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

Three-Dimensional Navier-Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k-ε Turbulence Model

1991 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Three Dimensions ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe

An explicit, three-dimensional, coupled Navier-Stokes/k-ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows have been extended to three-dimensions, including a low Reynolds number compressible form of the k-ε turbulence model, local timestep specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure which eliminates the finite difference metric singularity, at leading and trailing edges, on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data is available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

Computation of Compressible Flow and Heat Transfer in a Rotating Duct With Inclined Ribs and a 180-Degree Bend

1997 ◽  
Author(s):  
M. A. Stephens ◽  
T. I-P. Shih
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Sections ◽  
Three Dimensional ◽  
Side Wall ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Outer Side ◽  
Flow And Heat Transfer ◽  
Density Ratios

Computations were performed to study the three-dimensional flow and heat transfer in a U-shaped duct of square cross section with and without ribs under rotating and staggered inclined ribs of rounded cross sections on the leading and trailing walls. Parameters investigated include: two rotation numbers (0, 0.24), two density ratios (0.13, 0.22), and smooth versus ribbed walls at a Reynolds number of 25,000 and an inlet Mach number of 0.05. For the conditions of the present study, rib-induced secondary flows were found to dominate over those induced by the Coriolis force in terms of flow pattern. This shifted tendency for flow separation induced by centrifugal buoyancy from the leading wall to the outer-side wall for radially outward flow. The secondary flows induced by the 180-degree bend were found to be comparable to that induced by the ribs, creating very complex interactions in flow and surface heat transfer characteristics. The computations are based on the ensemble-averaged conservation equations of mass, momentum (compressible Navier-Stokes), and energy closed by a low Reynolds number k-ω model of turbulence. Solutions were generated by using a cell-centered finite-volume method based on flux-difference splitting and a diagonalized alternating-direction implicit scheme with multigrid.

Three-Dimensional Steady Flow Through A Bifurcation

1990 ◽  
Vol 112 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Chain-Nan Yung ◽  
Kenneth J. De Witt ◽  
Theo G. Keith
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Steady Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Simple Algorithm ◽  
Outer Wall ◽  
Navier Stokes

Steady flow of an incompressible, Newtonian fluid through a symmetric bifurcated rigid channel was numerically analyzed by solving the three-dimensional Navier-Stokes equations. The upstream Reynolds number ranged from 100 to 1500. The bifurcation was symmetrical with a branch angle of 60 deg and the area ratio of the daughter to the mother vessel was 2.0. The numerical procedure utilized a coordinate transformation and a control volume approach to discretize the equations to finite difference form and incorporated the SIMPLE algorithm in performing the calculation. The predicted velocity pattern was in qualitative agreement with experimental measurements available in the literature. The results also showed the effect of secondary flow which can not be predicted using previous two-dimensional simulations. A region of reversed flow was observed near the outer wall of the branch except for the case of the lowest Reynolds number. Particle trajectory was examined and it was found that no fluid particles remained within the recirculation zone. The shear stress was calculated on both the inner and the outer wall of the branch. The largest wall shear stress, located in the vicinity of the apex of the branch, was of the same order of magnitude as the level that can cause damage to the vessel wall as reported in a recent study.

Prediction of Three-Dimensional Developing Turbulent Flow in a Square Duct With an Anisotropic Low-Reynolds-Number k-ε Model

1991 ◽  
Vol 113 (4) ◽  
pp. 608-615 ◽  
Author(s):  
Hyon Kook Myong ◽  
Toshio Kobayashi
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Reynolds Shear Stress ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Complex Flow ◽  
Square Duct ◽  
Low Reynolds

Three-dimensional developing turbulent flow in a square duct involving turbulence-driven secondary motion is numerically predicted with an anisotropic low-Reynolds-number k-ε turbulence model. Special attention has been given to both regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, the no-slip boundary condition at the wall is directly used in place of the common wall function approach. The resulting set of equations simplified only by the boundary layer assumption are first compared with previous algebraic stress models, and solved with a forward marching numerical procedure for three-dimensional shear layers. Typical predicted quantities such as mean axial and secondary velocities, friction coefficients, turbulent kinetic energy, and Reynolds shear stress are compared with available experimental data. These results indicate that the present anisotropic k-ε turbulence model performs quite well for this complex flow field.

scholarly journals Incidence Angle and Pitch-Chord Effects on Secondary Flows Downstream of a Turbine Cascade

1992 ◽  
Author(s):  
A. Perdichizzi ◽  
V. Dossena
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Turbine Cascade ◽  
Oil Flow ◽  
Secondary Velocity ◽  
Secondary Flow Field

This paper describes the results of an experimental investigation of the three-dimensional flow downstream of a linear turbine cascade at off-design conditions. The tests have been carried out for five incidence angles from −60 to +35 degrees, and for three pitch-chord ratios: s/c = 0.58,0.73,0.87. Data include blade pressure distributions, oil flow visualizations, and pressure probe measurements. The secondary flow field has been obtained by traversing a miniature five hole probe in a plane located at 50% of an axial chord downstream of the trailing edge. The distributions of local energy loss coefficients, together with vorticity and secondary velocity plots show in detail how much the secondary flow field is modified both by incidence and cascade solidity variations. The level of secondary vorticity and the intensity of the crossflow at the endwall have been found to be strictly related to the blade loading occurring in the blade entrance region. Heavy changes occur in the spanwise distributions of the pitch averaged loss and of the deviation angle, when incidence or pitch-chord ratio is varied.

Three Dimensional Clocking Effects in a One and a Half Stage Transonic Turbine

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
O. Schennach ◽  
J. Woisetschläger ◽  
B. Paradiso ◽  
G. Persico ◽  
P. Gaetani
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Fast Response ◽  
Secondary Flows ◽  
Pressure Probe ◽  
Time Resolved ◽  
Flow Angle ◽  
Aerodynamic Pressure ◽  
Velocity Flow ◽  
Transonic Turbine

This paper presents an experimental investigation of the flow field in a high-pressure transonic turbine with a downstream vane row (1.5 stage machine) concerning the airfoil indexing. The objective is a detailed analysis of the three-dimensional aerodynamics of the second vane for different clocking positions. To give an overview of the time-averaged flow field, five-hole probe measurements were performed upstream and downstream of the second stator. Furthermore in these planes additional unsteady measurements were carried out with laser Doppler velocimetry in order to record rotor phase-resolved velocity, flow angle, and turbulence distributions at two different clocking positions. In the planes upstream of the second vane, the time-resolved pressure field has been measured by means of a fast response aerodynamic pressure probe. This paper shows that the secondary flows of the second vane are significantly modified by the different clocking positions, in connection with the first vane modulation of the rotor secondary flows. An analysis of the performance of the second vane is also carried out, and a 0.6% variation in the second vane loss coefficient has been recorded among the different clocking positions.

scholarly journals Numerical simulation of complex 3D compressible viscous flows through rotating blade passage

2003 ◽  
pp. 55-82
Author(s):  
M. Despotovic ◽  
Milun Babic ◽  
D. Milovanovic ◽  
Vanja Sustersic
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Convergence Acceleration ◽  
Design Tool ◽  
Navier Stokes ◽  
Internal Flows ◽  
Navier Stokes Equations ◽  
Rotating Blade ◽  
Compressible Viscous Flows

This paper describes a three-dimensional compressible Navier-Stokes code, which has been developed for analysis of turbocompressor blade rows and other internal flows. Despite numerous numerical techniques and statement that Computational Fluid Dynamics has reached state of the art, issues related to successful simulations represent valuable database of how particular tech?nique behave for a specifie problem. This paper deals with rapid numerical method accurate enough to be used as a design tool. The mathematical model is based on System of Favre averaged Navier-Stokes equations that are written in relative frame of reference, which rotates with constant angular velocity around axis of rotation. The governing equations are solved using finite vol?ume method applied on structured grids. The numerical procedure is based on the explicit multistage Runge-Kutta scheme that is coupled with modem numerical procedures for convergence acceleration. To demonstrate the accuracy of the described numer?ical method developed software is applied to numerical analysis of flow through impeller of axial turbocompressor, and obtained results are compared with available experimental data.

scholarly journals Computed Eccentricity Effects on Turbine Rim Seals at Engine Conditions With a Mainstream

1994 ◽  
Author(s):  
Zhou Guo ◽  
David L. Rhode ◽  
Fred M. Davis
Keyword(s):  
Reynolds Number ◽  
Temperature Rise ◽  
Three Dimensional ◽  
Computer Code ◽  
Interaction Effects ◽  
Navier Stokes ◽  
Radial Clearance ◽  
Turbine Wheel ◽  
Blade Root

A previously verified axisymmetric Navier-Stokes computer code was extended for three-dimensional computation of eccentric rim seals of almost any configuration. All compressibility and thermal/momentum interaction effects are completely, included, and the temperature, pressure and Reynolds number of the mainstream, coolant stream and turbine wheel are fixed at actual engine conditions. Regardless of the seal eccentricity, both ingress and egress are found between θ = −30° and 100°. which encompasses the location of maximum radial clearance at θ = 0°. All other θ locations within the rim seal show only egress, as does the concentric basecase for all circumferential locations. Further, the maximum ingress occurs near θ = 30° for all eccentricities. This is found to produce a blade root/retainer temperature rise from the concentric case of 390 percent at 50 percent eccentricity and a 77 percent rise at 7.5 percent eccentricity. In addition, the nature of an increased eccentricity causing a decreased seal effectiveness is examined, along with the corresponding increase of cavity-averaged temperature.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

A Calculation Scheme for Three-Dimensional Viscous Incompressible Flows

1987 ◽  
Vol 109 (4) ◽  
pp. 345-352 ◽  
Author(s):  
M. Reggio ◽  
R. Camarero
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Data ◽  
Momentum Balance ◽  
Navier Stokes ◽  
Test Cases ◽  
Pressure Gradients ◽  
Navier Stokes Equations

A numerical procedure to solve three-dimensional incompressible flows in arbitrary shapes is presented. The conservative form of the primitive-variable formulation of the time-dependent Navier-Stokes equations written for a general curvilinear coordiante system is adopted. The numerical scheme is based on an overlapping grid combined with opposed differencing for mass and pressure gradients. The pressure and the velocity components are stored at the same location: the center of the computational cell which is used for both mass and the momentum balance. The resulting scheme is stable and no oscillations in the velocity or pressure fields are detected. The method is applied to test cases of ducting and the results are compared with experimental and numerical data.

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