Computation of Off-Design Flows in a Transonic Compressor Rotor

1986 ◽  
Vol 108 (1) ◽  
pp. 144-150 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Stokes Equations ◽  
Current Paper ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Interactive Method ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Supersonic Inlet ◽  
Maximum Benefit

Recent years have seen increasing efforts to develop efficient solvers for the compressible Navier–Stokes equations. For maximum benefit to be derived from this effort, these Navier–Stokes solvers must be capable of dealing with off-design flows as readily and accurately as the on-design cases. The current paper outlines an efficient implicit algorithm developed recently by the author for solving the compressible Navier–Stokes equations in turbomachinery blade-blade flows. The Navier–Stokes solver is applied to the study of a transonic compressor rotor with supersonic inlet velocities for three cases, one on-design and two off-design. The results are compared with experimental measurements and with the predictions of a viscous-inviscid interactive method.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

Расчетно-экспериментальное исследование влияния вдува/отсоса газа через перфорированную поверхность на пограничный слой при сверхзвуковом числе Маха

2021 ◽  
Vol 47 (21) ◽  
pp. 19
Author(s):  
П.А. Поливанов
Keyword(s):  
Boundary Layer ◽  
Experimental Study ◽  
Stokes Equations ◽  
Numerical Data ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Piv Method ◽  
Sst Turbulence Model ◽  
Method Analysis

In this paper a numerical and experimental study of the effect of blowing/suction through a perforated surface on a turbulent boundary layer at a Mach number M = 1.4 is carried out. Most of the calculations were performed by Reynolds-averaged Navier-Stokes equations with the k-w SST turbulence model. The calculated geometry completely repeated the experimental one including the perforated surface. The numerical data were compared with experimental measurements obtained by the PIV method. Analysis of the data made it possible to find the limits of applicability of the numerical method for this flow.

Supersonic inlet study using the Navier-Stokes equations

1986 ◽  
Vol 2 (2) ◽  
pp. 181-187 ◽  
Author(s):  
Louis G. Hunter ◽  
John M. Tripp ◽  
Douglas G. Howlett
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Supersonic Inlet

Simulating Periodic Unsteady Flows Using Cubic-Spline Based Time Collocation Method

2013 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time periodical unsteady flows are typical in turbomachinery. Simulating such flows using conventional time marching approach is most accurate but extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline based time collocation method is proposed. In this method, the time derivatives in the Navier-Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic-splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor-stator interactions and IGV-rotor interactions. The results show that the proposed cubic-spline based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, whilst the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that the better modeling of the flows can be expected.

The Role of Coulombic Forces in Quasi-Two Dimensional Electrochemical Deposition

1996 ◽  
Vol 451 ◽  
Author(s):  
G. Marshall ◽  
P. Mocskos ◽  
F. Molina ◽  
S. Dengra
Keyword(s):  
Numerical Modeling ◽  
Pattern Formation ◽  
Electrochemical Deposition ◽  
Growth Pattern ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Dimensionless Numbers ◽  
Navier Stokes Equations

ABSTRACTRecent work demonstrates the relevant influence of convection during growth pattern formation in thin-layer electrochemical deposition. Convection is driven mainly by coulombic forces due to local charges at the tip of the aggregation and by buoyancy forces due to concentration gradients. Here we study through physical experiments and numerical modeling the regime under which coulombic forces are important. In the experimental measurements fluid motion near the growing tips of the deposit is visualized with neutrally buoyant latex spheres and its speed measured with videomicroscope tracking techniques and image processing software. The numerical modeling consists in the solution of the 2D dimensionless Nernst-Planck equations for ion concentrations, the Poisson equation for the electric field and the Navier-Stokes equations for the fluid flow, and a stochastic growth rule for ion deposition. A new set of dimensionless numbers governing electroconvection dominated flows is introduced. Preliminary experimental measurements and numerical results indicate that in the electroconvection dominated regime coulombic forces increase with the applied voltage, and their influence over growth pattern formation can be assessed with the magnitude of the dimensionless electric Froude number. It is suggested that when this number decreases the deposit morphology changes from fractal to dense branching.

The Effect of Reynolds Number on Transonic Compressor Blade Rotor Section

2012 ◽  
Author(s):  
A. Shahrabi Farahani ◽  
H. Beheshti Amiri ◽  
H. Khazaei ◽  
A. Madadi ◽  
A. Fathi
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blade Passage ◽  
Axial Compressors ◽  
Choked Flow ◽  
Transonic Compressor ◽  
Boundary Layer Interaction

To achieve at a more precise designing procedure in axial-compressors as well as a higher pressure ratio value, a comprehensive understanding on the flow aerodynamics and the governing phenomena is required. Existence of these complicated phenomena e.g., simultaneous production of supersonic and subsonic flows, shock-boundary layer interaction, unique incidence phenomenon, etc, makes it difficult to analyze the flow in the transonic compressors. One of the methods which is useful in the modeling of the phenomena occur in the compressors is investigating the flow in the blade to blade passage. In this paper, employing the simultaneous solution of the full Navier-Stokes equations (using the Roe-FDS numerical method) and turbulence equations (using the K–w (SST) model) the flow has been simulated in the blade to blade passage of a transonic compressor. In the following, in order to comparison the predicted results with experimental data, required adjustments and conditions have been taken into account. After passing through the first transonic compressor stages, the flow becomes remarkably compressed. In such conditions, the Reynolds number considerably changes compared to the inflow Reynolds number. In the present work, it is intended to numerically investigate the effects of the inflow Reynolds number on the unique incidence, flow losses, deviation angle, and also shock position changes, in three different important states of “Minimum loss” and “Choked flow” in started conditions and “Stall operation” in unstarted conditions.

IGV-Rotor Interaction Analysis in a Transonic Compressor Using the Navier-Stokes Equations

1996 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Inlet Guide Vane ◽  
Operating Characteristics ◽  
Navier Stokes Equations ◽  
Transonic Compressor ◽  
Mass Flow Rates

A recently developed, time-accurate multigrid viscous solver has been extended to handle quasi-three-dimensional effects and applied to the first stage of a modern transonic compressor. Interest is focused on the inlet guide vane (IGV):rotor interaction where strong sources of unsteadiness are to be expected. Several calculations have been performed to predict the stage operating characteristics. Flow structures at various mass flow rates, from choke to near stall, are presented and discussed. Comparisons between unsteady and steady pitch-averaged results are also included in order to obtain indications about the capabilities of steady, multi-row analyses.

scholarly journals Navier-Stokes Solutions of Unsteady Flow in a Compressor Rotor

1986 ◽  
Author(s):  
James N. Scott ◽  
Wilbur L. Hankey
Keyword(s):  
Unsteady Flow ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Suction Surface ◽  
Blade Passage ◽  
Radial Location ◽  
Transonic Compressor ◽  
Compressor Rotor

In order to achieve more accurate predictions of unsteady flow in a transonic compressor rotor an existing numerical approach has been modified by incorporating a turbulence model. The computations are performed by solving the complete time-dependent compressible Navier-Stokes equations using MacCormack’s explicit finite difference algorithm. These equations are solved for the flow through two adjacent rotor blades at a stream surface near the blade tip subjected to the wakes emitted from upstream stators. At this radial location the flow enters the blade passage at an absolute Mach number of 0.66. The high blade curvature at this radial location produces a large region of separated flow on the suction surface with laminar flow. To more accurately resolve the features of this flow separation the Baldwin-Lomax algebraic eddy-viscosity turbulence model is incorporated into the numerical procedure in regions, near the blade surface. The unsteady flow features are represented at the inflow boundary through the use of characteristic variables involving the upstream and downstream running Riemann invariants and the entropy variation expressed in terms of the total pressure profile. At the outflow boundary the concept of a “second throat” or choke point is implemented in conjunction with supersonic outflow conditions. The results are compared with numerical results obtained without the use of a turbulence model (laminar) for a single blade passage. Improved agreement with limited experimental data is also noted.

Simulating Periodic Unsteady Flows Using a Cubic-Spline-Based Time Collocation Method

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time-periodical unsteady flows are typical in turbomachinery. Simulating such flows using a conventional time marching approach is the most accurate but is extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline-based time collocation method is proposed. In this method, the time derivatives in the Navier–Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor–stator interactions, and IGV–rotor interactions. The results show that the proposed cubic-spline-based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, while the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of a time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that better modeling of the flows can be expected.

An inverse methodology for the rheology of a power-law non-Newtonian fluid

2008 ◽  
Vol 222 (5) ◽  
pp. 761-768 ◽  
Author(s):  
H C H Bandulasena ◽  
W B Zimmerman ◽  
J M Rees
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Stokes Equations ◽  
Current Paper ◽  
Navier Stokes ◽  
Single Experiment ◽  
Navier Stokes Equations ◽  
Flow Features ◽  
Dilute Aqueous Solutions ◽  
Constitutive Parameters

The current paper presents a novel methodology for calculating the rheological para-meters for dilute aqueous solutions of a power-law non-Newtonian fluid, xanthan gum (XG). Previous studies have verified the fidelity of finite-element modelling of the Navier—Stokes equations for reproducing the velocity fields of XG solutions in a microfluidic T-junction with experimental observations obtained using micron resolution particle image velocimetry (μ-PIV). As the pressure-driven fluid is forced to turn the corner of the T-junction, a range of shear rates, and therefore viscosities, are produced within the flow system. Thus, a setup that potentially establishes the rheological profile of XG from a single experiment is selected. An inverse method based on finding the mapping between the statistical moments of the velocity field and the constitutive parameters of the viscosity profile demonstrated that such a system could potentially be used for the design of an efficient microfluidic rheometer. However, μ-PIV technology is expensive and the equipment is bulky. The current paper investigates whether different flow features could be used to establish the rheological profile.

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