Nozzle Discharge Coefficients—Compressible Flow

1974 ◽  
Vol 96 (1) ◽  
pp. 21-24 ◽  
Author(s):  
A. T. Olson
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Compressible Flow ◽  
Approximation Method ◽  
Two Dimensional ◽  
Core Flow ◽  
Flow Discharge ◽  
One Dimensional ◽  
Power Test ◽  
Discharge Coefficients

Using Walz’s approximation method for boundary layer calculation, along with a one-dimensional treatment of the compressible inviscid core flow, discharge coefficients for small nozzle to pipe diameter ratios have been calculated. Discharge co-efficients calculated for the ASME long radius nozzle agree with those recommended by the ASME Power Test Code. In addition, experimental confirmation of an indicated Mach number effect has been achieved in a nozzle modified to minimize two-dimensional effects.

scholarly journals A Method for Calculating Turbulent Boundary Layers and Losses in the Flow Channels of Turbomachines

1987 ◽  
Author(s):  
Lawrence F. Schumann
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Streamwise Velocity ◽  
Quantitative Agreement ◽  
Stream Line ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Core Flow ◽  
One Dimensional ◽  
Special Cases

An interactive inviscid core flow-boundary layer method is presented for the calculation of turbomachine channel flows. For this method, a one-dimensional inviscid core flow is assumed. The end-wall and blade surface boundary layers are calculated using an integral entrainment method. The boundary layers are assumed to be collateral and thus are two-dimensional. The boundary layer equations are written in a stream-line coordinate system. The streamwise velocity profiles are approximated by power law profiles. Compressibility is accounted for in the streamwise direction but not in the normal direction. Equations are derived for the special cases of conical and two-dimensional rectangular diffusers. For these cases, the assumptions of a one-dimensional core flow and collateral boundary layers are valid. Results using the method are compared with experiment and good quantitative agreement is obtained.

scholarly journals Sound propagation in a lined nozzle with shear and bias flows

2018 ◽  
Vol 18 (1) ◽  
pp. 3-48
Author(s):  
LMBC Campos ◽  
C Legendre
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Boundary Layers ◽  
Lower Boundary ◽  
Cross Flow ◽  
Core Flow ◽  
The Core ◽  
Wide Range ◽  
Bias Flow ◽  
Number Formula

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

Numerical Investigation of the Compressible Flow Through a Turbine Center Frame Duct

2018 ◽  
Author(s):  
Li-Wei Chen ◽  
Christian Wakelam ◽  
Jonathan Ong ◽  
Andreas Peters ◽  
Andrea Milli ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Numerical Investigation ◽  
Compressible Flow ◽  
Flow Behavior ◽  
Computational Domain ◽  
Turbulent Structures ◽  
Curvature Effects ◽  
Eddy Simulation ◽  
Static Pressure Distribution

Numerical investigation of the compressible flow in the Turbine Center Frame (TCF) duct was carried out using a Reynolds-averaged Navier-Stokes (RANS) method, and a Hybrid RANS/Large Eddy Simulation (HLES) method, i.e. Stress-Blended Eddy Simulation (SBES). The reference Reynolds number based on the TCF inlet condition is 530,000, and the inlet Mach number is 0.41. It is found that the boundary layer flow behavior is very sensitive to the incoming turbulence characteristics, so the upstream grid used to generate turbulence in the experiment is also included in the computational domain. Results have been validated carefully against experimental data, in terms of static pressure distribution on hub and casing walls, total pressure and Mach number profiles on the TCF measurement planes, as well as over-all pressure loss coefficient. Further, various fundamental mechanisms dictating the intricate flow phenomena, including concave and convex curvature effects, interactions between inlet turbulent structures and boundary layer, and turbulent kinetic energy budget, have been studied systematically. The current study is to evaluate the performance of HLES method for TCF flows and develop a further understanding of unsteady flow physics in the TCF duct. The results obtained in this work provide physical insight into the mechanisms relevant to the turbine intercase or TCF duct flows subjected to complex inlet disturbances.

Lift and drag in two-dimensional steady viscous and compressible flow

2015 ◽  
Vol 784 ◽  
pp. 304-341 ◽  
Author(s):  
L. Q. Liu ◽  
J. Y. Zhu ◽  
J. Z. Wu
Keyword(s):  
Mach Number ◽  
Viscous Flow ◽  
Compressible Flow ◽  
Velocity Component ◽  
Transverse Velocity ◽  
The Body ◽  
Far Field ◽  
Two Dimensional ◽  
Wide Range ◽  
Lift And Drag

This paper studies the lift and drag experienced by a body in a two-dimensional, viscous, compressible and steady flow. By a rigorous linear far-field theory and the Helmholtz decomposition of the velocity field, we prove that the classic lift formula $L=-{\it\rho}_{0}U{\it\Gamma}_{{\it\phi}}$, originally derived by Joukowski in 1906 for inviscid potential flow, and the drag formula $D={\it\rho}_{0}UQ_{{\it\psi}}$, derived for incompressible viscous flow by Filon in 1926, are universally true for the whole field of viscous compressible flow in a wide range of Mach number, from subsonic to supersonic flows. Here, ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$ denote the circulation of the longitudinal velocity component and the inflow of the transverse velocity component, respectively. We call this result the Joukowski–Filon theorem (J–F theorem for short). Thus, the steady lift and drag are always exactly determined by the values of ${\it\Gamma}_{{\it\phi}}$ and $Q_{{\it\psi}}$, no matter how complicated the near-field viscous flow surrounding the body might be. However, velocity potentials are not directly observable either experimentally or computationally, and hence neither are the J–F formulae. Thus, a testable version of the J–F formulae is also derived, which holds only in the linear far field. Due to their linear dependence on the vorticity, these formulae are also valid for statistically stationary flow, including time-averaged turbulent flow. Thus, a careful RANS (Reynolds-averaged Navier–Stokes) simulation is performed to examine the testable version of the J–F formulae for a typical airfoil flow with Reynolds number $Re=6.5\times 10^{6}$ and free Mach number $M\in [0.1,2.0]$. The results strongly support and enrich the J–F theorem. The computed Mach-number dependence of $L$ and $D$ and its underlying physics, as well as the physical implications of the theorem, are also addressed.

Approximate Solution—One-Dimensional Energy Equation for Transient, Compressible, Low Mach Number Turbulent Boundary Layer Flows

1989 ◽  
Vol 111 (3) ◽  
pp. 619-624 ◽  
Author(s):  
J. Yang ◽  
J. K. Martin
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Internal Combustion Engines ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Empirical Relation ◽  
Approximate Solutions ◽  
Low Mach Number ◽  
One Dimensional

Unsteady surface heat-flux and temperature profiles in the transient, compressible, low Mach number, turbulent boundary layer typically found in internal combustion engines have been determined by numerically integrating a linearized form of the one-dimensional energy equation. An empirical relation for μt/μ has been used to consider turbulent conductivity. Approximate solutions have been acquired by multiparameter fits to the numerical solutions. Comparisons of the approximate solutions with motored engine experiments show good agreement.

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