Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines

1990 ◽  
Vol 112 (3) ◽  
pp. 391-398
Author(s):  
S. Abdallah ◽  
C. F. Smith
Keyword(s):  
Experimental Data ◽  
Poisson Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Type Equation ◽  
Neumann Boundary ◽  
Momentum Equation ◽  
Rotor Blades ◽  
Pressure Poisson Equation

A primitive variable formulation is used for the solution of the incompressible Euler equation. In particular, the pressure Poisson equation approach using a nonstaggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a nonstaggered grid. Numerical solutions of the momentum equations are obtained using the second-order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive overrelaxation method. Three turbo-machinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.

Three-Dimensional Solutions for Inviscid Incompressible Flow in Turbomachines

1989 ◽  
Author(s):  
S. Abdallah ◽  
C. F. Smith
Keyword(s):  
Experimental Data ◽  
Poisson Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Type Equation ◽  
Neumann Boundary ◽  
Relaxation Method ◽  
Staggered Grid ◽  
Pressure Poisson Equation

A primitive variable formulation is used for the solution of the incompressible Euler’s equation. In particular, the pressure Poisson equation approach using a non-staggered grid is considered. In this approach, the velocity field is calculated from the unsteady momentum equation by marching in time. The continuity equation is replaced by a Poisson-type equation for the pressure with Neumann boundary conditions. A consistent finite-difference method, which insures the satisfaction of a compatibility condition necessary for convergence, is used in the solution of the pressure equation on a non-staggered grid. Numerical solutions of the momentum equations are obtained using the second order upwind differencing scheme, while the pressure Poisson equation is solved using the line successive over-relaxation method. Three turbomachinery rotors are tested to validate the numerical procedure. The three rotor blades have been designed to have similar loading distributions but different amounts of dihedral. Numerical solutions are obtained and compared with experimental data in terms of the velocity components and exit swirl angles. The computed results are in good agreement with the experimental data.

Computation of Inviscid Incompressible Flow Using the Primitive Variable Formulation

1986 ◽  
Vol 108 (1) ◽  
pp. 68-75 ◽  
Author(s):  
S. Abdallah ◽  
H. G. Smith
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Type Equation ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Fine Grid ◽  
Navier Stokes Equations ◽  
Pressure Poisson Equation ◽  
Fine Mesh

The primitive variable formulation originally developed for the incompressible Navier–Stokes equations is applied for the solution of the incompressible Euler equations. The unsteady momentum equation is solved for the velocity field and the continuity equation is satisfied indirectly in a Poisson-type equation for the pressure (divergence of the momentum equation). Solutions for the pressure Poisson equation with derivative boundary conditions exist only if a compatibility condition is satisfied (Green’s theorem). This condition is not automatically satisfied on nonstaggered grids. A new method for the solution of the pressure equation with derivative boundary conditions on a nonstaggered grid [25] is used here for the calculation of the pressure. Three-dimensional solutions for the inviscid rotational flow in a 90 deg curved duct are obtained on a very fine mesh (17 × 17 × 29). The use of a fine grid mesh allows for the accurate prediction of the development of the secondary flow. The computed results are in good agreement with the experimental data of Joy [15].

Effects of Tip Clearance on Hot Streak Migration in a High-Subsonic Single-Stage Turbine

2000 ◽  
Author(s):  
Daniel J. Dorney ◽  
Douglas L. Sondak
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Single Stage ◽  
Rotor Blades ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Radial Spreading ◽  
Rotor Surface ◽  
Hot Streak ◽  
Turbine Airfoils

Experimental data have shown that combustor temperature non-uniformities can lead to the excessive heating of first-stage rotor blades in turbines. This heating of the rotor blades can lead to thermal fatigue and degrade turbine performance. The results of recent studies have shown that variations in the circumferential location, or clocking, of the first-stage vane airfoils can be used to minimize the adverse effects of the hot streaks due to the hot fluid mixing with the cooler fluid contained in the vane wake. In addition, the effects of the hot streak/airfoil count ratio on the heating patterns of turbine airfoils have been quantified. In the present investigation, three-dimensional unsteady Navier-Stokes simulations have been performed for a single-stage high-pressure turbine geometry operating in high subsonic flow to study the effects of tip clearance on hot streak migration. Baseline simulations were initially performed without hot streaks to compare with the experimental data. Two simulations were then performed with a superimposed combustor hot streak; in the first the tip clearance was set at the experimental value, while in the second the rotor was allowed to scrape along the outer case (i.e., the limit as the tip clearance goes to zero). The predicted results for the baseline simulations show good agreement with the available experimental data. The simulations with the hot streak indicate that the tip clearance increases the radial spreading of the hot fluid, and increases the integrated rotor surface temperature compared to the case without tip clearance.

Secondary Flow Development In A Cascade Like Passage Of A Turbomachine

1983 ◽  
pp. 11-23
Author(s):  
Amer Nordin Darus
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Rotational Flow ◽  
Simultaneous Solution ◽  
Analytical Formulation ◽  
Curved Duct ◽  
Flow Development ◽  
Vorticity Equations

Makalah ini memaparkan formulasi analitik dan penyelesaian numerik aliran dimensi tiga yang rotasional di dalam sebuah saluran yang melengkung. Formulasi ini berdasarkan perhitungan halaju aliran dan komponen vortisiti selari axis saluran tersebut. Halaju sekunder ditentukan melalui penyelesaian serentak persamaan-persamaan ke terusan dan vortisiti melalui penggunaan fungsi seperti fungsi arus. Hasil-hasil numerik diberikan dan dibandingkan dengan data-data eksperimen yang ada. This article presents the analytical formulation and numerical solution of the three-dimensional rotational flow in curved duct. The formulation is based on calculating the flow - wise velocity and vorticity. components from the momentum equation. The secondary velocities are determined from the simultaneous solution of the continuity and vorticity equations through the use of a streamlike function. The results presented arc compared with the existing experimental data.

Determination of the Pressure Field Using Three-Dimensional, Volumetric Velocity Measurements

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Hansheng Pan ◽  
Sheila H. Williams ◽  
Paul S. Krueger
Keyword(s):  
Poisson Equation ◽  
Temporal Resolution ◽  
Pressure Field ◽  
Three Dimensional ◽  
Vortical Flow ◽  
Flow Conditions ◽  
Velocity Measurements ◽  
Pressure Poisson Equation ◽  
Computational Fluid Dynamics Cfd

Methods to determine the pressure field of vortical flow from three-dimensional (3D) volumetric velocity measurements (e.g., from a TSI V3VTM system) are discussed. The boundary pressure was determined where necessary using the unsteady Bernoulli equation for both line integration and pressure Poisson equation methods. Error analysis using computational fluid dynamics (CFD) data was conducted to investigate the effects of spatial resolution, temporal resolution, and velocity error levels. The line integration method was more sensitive to temporal resolution, while the pressure Poisson equation method was more sensitive to boundary flow conditions. The latter was generally more suitable for V3VTM velocity measurements.

scholarly journals Effects of Hot Streak Shape on Rotor Heating in a High-Subsonic Single-Stage Turbine

2000 ◽  
Author(s):  
Daniel J. Dorney ◽  
Karen L. Gundy-Burlet
Keyword(s):  
Experimental Data ◽  
Surface Area ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Single Stage ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Strong Function ◽  
Hot Streak ◽  
Turbine Airfoils

Experimental data have shown that combustor temperature non-uniformities can lead to the excessive heating of first-stage rotor blades in turbines. This heating of the rotor blades can lead to thermal fatigue and degrade turbine performance. The results of recent studies have shown that variations in the circumferential location (clocking) of the hot streak relative to the first-stage vane airfoils can be used to minimize the adverse effects of the hot streak. The effects of the hot streak/airfoil count ratio on the heating patterns of turbine airfoils have also been evaluated. In the present investigation, three-dimensional unsteady Navier-Stokes simulations have been performed for a single-stage high-pressure turbine operating in high subsonic flow. In addition to a simulation of the baseline turbine, simulations have been performed for circular and elliptical hot streaks of varying sizes in an effort to represent different combustor designs. The predicted results for the baseline simulation show good agreement with the available experimental data. The results of the hot streak simulations indicate: that a) elliptical hot streaks mix more rapidly than circular hot streaks, b) for small hot streak surface area the average rotor temperature is not a strong function of hot streak temperature ratio or shape, and c) hot streaks with larger surface area interact with the secondary flows at the rotor hub endwall, generating an additional high temperature region.

Calculation of turbulence-driven secondary motion in non-circular ducts

1984 ◽  
Vol 140 ◽  
pp. 189-222 ◽  
Author(s):  
A. O. Demuren ◽  
W. Rodi
Keyword(s):  
Eddy Viscosity ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Momentum Equation ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Calculation Methods ◽  
Mean Flow ◽  
Square Duct ◽  
Secondary Motion

Experiments on and calculation methods for flow in straight non-circular ducts involving turbulence-driven secondary motion are reviewed. The origin of the secondary motion and the shortcomings of existing calculation methods are discussed. A more refined model is introduced, in which algebraic expressions are derived for the Reynolds stresses in the momentum equations for the secondary motion by simplifying the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975), while a simple eddy-viscosity model is used for the shear stresses in the axial momentum equation. The kinetic energy k and the dissipation rate ε of the turbulent motion which appear in the algebraic and the eddy-viscosity expressions are determined from transport equations. The resulting set of equations is solved with a forward-marching numerical procedure for three-dimensional shear layers. The model, as well as a version proposed by Naot & Rodi (1982), is tested by application to developing flow in a square duct and to developed flow in a partially roughened rectangular duct investigated experimentally by Hinze (1973). In both cases, the main features of the mean-flow and the turbulence quantities are simulated realistically by both models, but the present model underpredicts the secondary velocity while the Naot-Rodi model tends to overpredict it.

Numerical Study on Added Resistance Computations in Short Waves

2016 ◽  
Author(s):  
Xinshu Zhang ◽  
Kang Tian ◽  
Yunxiang You
Keyword(s):  
Experimental Data ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Three Dimensional ◽  
Added Resistance ◽  
Rankine Panel Method ◽  
Short Waves ◽  
Global Performance ◽  
Different Types ◽  
Wigley Hull

Evaluation of added resistance in short waves is critical to the assessment of the global performance of a ship traveling in a seaway. In this paper, three methods of added resistance evaluation in short waves are briefly reviewed, including those proposed by Fujii & Takahashi [1], Faltinsen et al. [2], and Kuroda et al. [3]. Based on the experimental data collected by Kuroda et al., a new method is developed for the estimation of added resistance in short waves. The proposed method is validated by comparing the obtained numerical results with experimental data and other numerical solutions for different types of hulls, including the Wigley hull I, KVLCC2 hull, Series 60 hull with CB = 0.7, and the S-175 hull. The present study confirms that the developed method can well predict the added resistance in short waves and complement the three-dimensional Rankine panel method developed in a previous study focusing on intermediate and long waves.

Heat Transfer Committee Best 1994 Paper Award: Experimental and Theoretical Investigations of Heat Transfer in Closed Gas-Filled Rotating Annuli II

1996 ◽  
Vol 118 (1) ◽  
pp. 11-19 ◽  
Author(s):  
D. Bohn ◽  
R. Emunds ◽  
V. Gorzelitz ◽  
U. Kru¨ger
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Flux ◽  
Gas Turbine ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Code ◽  
Convection Flow ◽  
Wide Range

Increasing the thermal efficiency by higher turbine inlet temperatures is one of the most important aims in the area of gas turbine development. Because of the high temperatures, the turbine vanes and blades have to be cooled, and also knowledge of the mechanically and thermally stressed parts in the hottest zones of the rotor is of great interest. The prediction of the temperature distribution in a gas turbine rotor containing closed, gas-filled cavities, for example, in between two disks, has to account for the heat transfer conditions encountered in these cavities. In an entirely closed annulus, forced convection is not present, but a strong natural convection flow exists, induced by a nonuniform density distribution in the centrifugal force field. In Bohn et al. (1994), experimental and numerical investigations on rotating cavities with pure centripetal heat flux had been carried out. The present paper deals with investigations on a pure axially directed heat flux. An experimental setup was designed to realize a wide range of Ra numbers (2·108< Ra < 5·1010) usually encountered in cavities of gas turbine rotors. Parallel to the experiments, numerical calculations have been conducted. The numerical results are compared with the experimental data. The numerical scheme is also used to account for the influence of Re on heat transfer without changing Ra. This influence could not be pointed out by experiments, because a variation of the Re–Ra characteristic of the employed annuli was not possible. It was found that the numerical and experimental data are in quite good agreement, with exception of high Ra, where the numerical scheme predicts higher heat transfer than the experiments show. One reason may be that in the experiments the inner and outer cylindrical walls were not really adiabatic, an assumption used in the numerical procedure. Moreover, the assumption of a two-dimensional flow pattern may become invalid for high Ra. The influence of three-dimensional effects was studied with the three-dimensional version of the numerical code. In contrast to the radial directed heat transfer, it was found that Nu is much smaller and depends strongly on Re, whereas the radial heat transfer is only weakly influenced by Re.

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