B. Lakshminarayana

Low-Reynolds-number k-epsilon model for unsteady turbulent boundary-layer flows

An assessment of the near-wall and low-Reynolds-number functions used in low-Reynolds-number k-epsilon models suggests that they are not suitable for the near-wall region of unsteady turbulent boundary layers, where the flow is characterized by rapid changes in phase. An improved low-Reynolds-number k-epsilon model is developed in this paper. The near-wall and low-Reynolds-number functions in this model are formulated as functions of the local turbulent Reynolds numbers instead of the inner variable y(+). The present model also has the correct asymptotic behavior in the near-wall region. The turbulence model has been incorporated in an unsteady boundary-layer code and validated for unsteady turbulent boundary layers with and without adverse pressure gradients. The predictions agree well with the experimental data and the theoretical analysis. For the cases tested, the present model correctly predicts the unsteady near-wall flow and the unsteady shin friction at various frequencies.

The Structure of Tip Clearance Flow in Axial Flow Compressors

Detailed measurements of the flow field in the tip region of an axial flow compressor rotor were carried out using a rotating five-hole probe. The axial, tangential, and radial components of relative velocity, as well as the static and stagnation pressures, were obtained at two axial locations, one at the rotor trailing edge, the other downstream of the rotor. The measurements were taken up to about 26 percent of the blade span from the blade tip. The data are interpreted to understand the complex nature of the flow in the tip region, which involves the interaction of the tip leakage flow, the annulus wall boundary layer and the blade wake. The experimental data show that the leakage jet does not roll up into a vortex. The leakage jet exiting from the tip gap is of high velocity and mixes quickly with the mainstream, producing intense shearing and flow separation. There are substantial differences in the structure of tip clearance observed in cascades and rotors.

Tip clearance effects in a turbine rotor : Part I : Pressure field and loss

This paper presents an experimental investigation of the effects of the tip clearance flow in an axial turbine rotor. The effects investigated include the distribution and the development of the pressure, the loss, the velocity, and the turbulence fields. Theseflow fields were measured using the techniques of static pressure taps, rapid response pressure probes, rotating five-hole probes, and Laser Doppler Velocimeter. Part I of this paper covers the loss development through the passage, and the pressure distribution within the passage, on the blade surfaces, on the blade tip, and on the casing wall. Regions with both the lowest pressure and the highest loss indicate the inception and the trace of the tip leakage vortex. The suction effect of the vortex slightly increases the blade loading near the tip clearance region. The relative motion between the turbine blades and the casing wall results in a complicated pressure field in the tip region. The fluid near the casing wall experiences a considerable pressure difference across the tip. The highest total pressure drop and the highest total pressure loss were both observed in the region of the tip leakage vortex, where the loss is nearly twice as high as that near the passage vortex region. However, the passage vortex produces more losses than the tip leakage vortex in total. The development of the loss in turbine rotor is similar to that observed in cascades. Part II of this paper covers the velocity and the turbulence fields.

Unsteady Flow Field Due to Nozzle Wake Interaction With the Rotor in an Axial Flow Turbine: Part I—Rotor Passage Flow Field

The two-dimensional steady and unsteady flow field at midspan in a turbine rotor has been investigated experimentally using an LDV with an emphasis on the interaction of the nozzle wake with the rotor flow field. The velocity measurements are decomposed into a time-averaged velocity, a periodic velocity component, and an unresolved velocity component. The results in the rotor passage were presented in Part 1. The flow field downstream of the rotor is presented in this paper. The rotor wake profiles and their decay characteristics were analyzed. Correlations are presented that match the decay of the various wake properties. The rotor wake velocity defect decays rapidly in the trailing edge region, becoming less rapid in the near and far wake regions. The rotor wake semi-wake width increases rapidly in the trailing edge region and then grows more gradually in the near and far wake regions. The decay of the maximum unresolved unsteadiness and maximum unresolved velocity cross correlations is very rapid in the trailing edge region and this trend slows in the far wake region. In the trailing edge region, the maximum periodic velocity correlations are much larger than the maximum unresolved velocity correlations. But the periodic velocity correlations decay much faster than the unresolved velocity correlations. The interactions of the nozzle and rotor wakes are also studied. While the interaction of the nozzle wake with the rotor wake does not influence the decay rate of the various wake properties, it does change the magnitude of the properties. These and other results are presented in this paper.

Tip Clearance Effects in a Turbine Rotor: Part II—Velocity Field and Flow Physics

A comprehensive experimental investigation was undertaken to explore the flow field in the tip clearance region of a turbine rotor to understand the physics of tip leakage flow. Specifically the paper looks at its origin, nature, development, interaction with the secondary flow, and its effects on performance. The experimental study was based on data obtained using a rotating five-hole probe, Laser Doppler Velocimeter, high-response pressure probes on the casing, and static pressure taps on the rotor blade surfaces. The first part of the paper deals with the pressure field and losses. Part II presents and interprets the vorticity, velocity, and turbulence fields at several axial locations. The data provided here indicates that the tip leakage vortex originates in the last half chord. The leakage vortex is confined close to the suction surface corner near the blade tip by the relative motion of the blade and the casing, and by the secondary flow in the tip region. The tip leakage flow clings to the blade suction surface until midchord then lifts off of the suction surface to form a vortex in the last 20 percent of the blade chord. The relative motion between blades and casing leads to the development of a scraping vortex that, along with the secondary flow, reduces the propagation of the tip leakage flow into the mainflow. The rotational effects and coriolis forces modify the turbulence structure in the tip leakage flow and secondary flow as compared to cascades.

Explicit Navier-Stokes computation of cascade flows using the k-epsilon turbulence model

A fully explicit two-dimensional flow solver, based on a four-stage Runge-Kutta scheme, has been developed and used to predict two-dimensional viscous flow through turbomachinery cascades for which experimental data are available. The formulation is applied to the density-weighted time-averaged Navier-Stokes equations. Several features of the technique improve the ability of the code to predict high Reynolds number flows on highly stretched grids. These include a low Reynolds number compressible form of the A-e turbulence model, anisotropic scaling of artificial dissipation terms, and locally varying timestep evaluation based on hyperbolic and parabolic stability considerations. Comparisons between computation and experiment are presented for both a supersonic and a low-subsonic compressor cascade. These results indicate that the code is capable of predicting steady two-dimensional viscous cascade flows over a wide range of Mach numbers in reasonable computation times.

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

An explicit, three-dimensional, coupled Navier-Stokes/k-∈ 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-∈ turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators

Stability of explicit navier-stokes procedures using k-ε and k - ε/algebraic reynolds stress turbulence models

Abstract A three-dimensional explicit Navier-Stokes procedure has been developed for application to compressible turbulent flows, including rotation effects. In the present work, a numerical stability analysis of the discrete, coupled system of seven governing equations is presented. Order of magnitude arguments are presented for flow and geometric properties typical of internal flows, including turbomachinery applications, to ascertain the relative importance of grid stretching, rotation and turbulence source terms, and effective diffusivity on the stability of the scheme. It is demonstrated through both analysis and corroborative numerical experiments that: (1 ) It is quite feasible to incorporate, efficiently, a two-equation k - ϵ turbulence model in an explicit time marching scheme, provided certain numerical stability constraints are enforced. (2) The role of source terms due to system rotation on the stability of the numerical scheme is not significant when appropriate grids are used and realistic rotor angular velocities are specified. (3) The direct role of source terms in the turbulence transport equations on the stability of the numerical scheme is not significant when appropriate grids are used and realistic freestream turbulence quantities are specified, except in the earliest stages of iteration (a result which is contrary to that generally perceived). (4) There is no advantage to numerically coupling the two-equation model system to the mean flow equation system, in regard to convergence or accuracy. (5) For some flow configurations, including turbomachinery blade rows, it is useful to incorporate the influence of artificial dissipation in the prescription of a local timestep. (6) Explicit implementation of an algebraic Reynolds stress model (ARSM) is intrinsically stable provided that the discrete two-equation transport model which provides the necessary values of k and ϵ is itself stable.

Numerical Simulation of Tip Clearance Effects in Turbomachinery

The numerical formulation developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The value of this artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure oftip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities as leakage mass flow, vortex strength, losses, dominant leakage flow regions, and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately.

A space-marching method for viscous incompressible internal flows

Abstract This paper deals with the development of a space-marching method for steady incompressible flows. The method solves the continuity and the momentum equations as a coupled system at each streamwise station. The character of the system of equations is changed from elliptic to hyperbolic/parabolic in order to enable the equations to be marched in space. The present method has two main advantages compared to the existing parabolic or spacemarching methods for an incompressible flow: (i) It avoids the solution of Poisson equations, and (ii) conserves the mass flow without employing any iterative procedure. The present method can capture strong secondary velocities and strong transverse pressure gradients. Predictions of the flow through straight and strongly curved ducts are in good agreement with the analytical and the experimental results.