Unsteady transonic nozzle flow of dense gases

1996 ◽  
Vol 310 ◽  
pp. 113-137 ◽  
Author(s):  
A. Kluwick ◽  
St. Scheichl
Keyword(s):  
Stokes Equations ◽  
Classical Equation ◽  
Transition Process ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Supersonic Expansion ◽  
Navier Stokes Equations ◽  
Specific Heats ◽  
Dense Gases ◽  
Theoretical Considerations

Vapours of retrograde fluids, i.e. media with large values of the specific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic expansion or compression. As a result, the acceleration of such a fluid through a converging-diverging Laval nozzle under steady flow conditions may lead to the occurrence of an expansion shock discontinuity. Theoretical considerations then suggest that nozzles with two throats should be designed to achieve a full shock-free subsonic-supersonic expansion.In this study the unsteady flow of a dense, retrograde gas through slender nozzles (with one and two throats) is considered. The combination of the Navier-Stokes equations supplemented with a non-classical equation of state for the fluid yields a generalized wave equation, with its validity restricted to flow conditions near the critical value M = 1. This equation is used to study the transition process which sets in if a steady subsonic solution is perturbed by lowering the pressure at the end of the nozzle.

Transonic nozzle flow of dense gases

1993 ◽  
Vol 247 ◽  
pp. 661-688 ◽  
Author(s):  
A. Kluwick
Keyword(s):  
Stokes Equations ◽  
Equations Of State ◽  
Weak Shock ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Perturbation Equation ◽  
Navier Stokes Equations ◽  
Sonic Point ◽  
Specific Heats ◽  
Dense Gases

The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Navier–Stokes equations supplemented with realistic equations of state for gases which have relatively large specific heats a novel form of the viscous transonic small-perturbation equation is derived. Evaluation of the inviscid limit of this equation shows that three sonic points rather than a single sonic point may occur during isentropic expansion of such media, in contrast to the case of perfect gases. As a consequence, a shock-free transition from subsonic to supersonic speeds cannot, in general, be achieved by means of a conventional converging–diverging nozzle. Nozzles leading to shock-free flow fields must have an unusual shape consisting of two throats and an intervening antithroat. Additional new results include the computation of the internal thermoviscous structure of weak shock waves and a phenomenon referred to as impending shock splitting. Finally, the relevance of these results to the description of external transonic flows is discussed briefly.

Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model

2005 ◽  
Vol 127 (3) ◽  
pp. 619-626 ◽  
Author(s):  
G. M. Laskowski ◽  
A. Vicharelli ◽  
G. Medic ◽  
C. J. Elkins ◽  
J. K. Eaton ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Design Procedure ◽  
Cascade Model ◽  
Inverse Design ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Flow Conditions ◽  
Navier Stokes Equations ◽  
Attached Flow ◽  
Transonic Turbine

A new transonic turbine cascade model that accurately produces infinite cascade flow conditions with minimal compressor requirements is presented. An inverse design procedure using the Favre-averaged Navier-Stokes equations and k‐ε turbulence model based on the method of steepest descent was applied to a geometry consisting of a single turbine blade in a passage. For a fixed blade geometry, the passage walls were designed such that the surface isentropic Mach number (SIMN) distribution on the blade in the passage matched the SIMN distribution on the blade in an infinite cascade, while maintaining attached flow along both passage walls. An experimental rig was built that produces realistic flow conditions, and also provides the extensive optical access needed to obtain detailed particle image velocimetry measurements around the blade. Excellent agreement was achieved between computational fluid dynamics (CFD) of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the measured SIMN.

The evolution of piston-driven pipe flow: thermal transpiration

2006 ◽  
Vol 463 (2079) ◽  
pp. 675-696
Author(s):  
A.M.J Davis
Keyword(s):  
Pipe Flow ◽  
State Transition ◽  
Stokes Equations ◽  
Solvability Condition ◽  
Navier Stokes ◽  
Entry And Exit ◽  
Flow Conditions ◽  
Additional Result ◽  
Navier Stokes Equations ◽  
Thermal Transpiration

The steady-state transition from and to the uniform entry and exit flow profiles is well described, at large aspect ratio, in terms of the stream function by the pipe eigenfunctions. But these latter are unsuited to oscillatory motion or the time evolution of the symmetric piston-driven pipe flow, for which an appropriate solution has a combination of a Fourier series along the finite pipe and a Fourier–Bessel series in the transverse direction. A non-uniqueness requires the identification of a solvability condition and care is needed in demonstrating its satisfaction. An additional result is that the solution must be constructed to satisfy the normal flow conditions identically. Application is made to thermal transpiration, recently explained by the revised Navier–Stokes equations and boundary conditions.

scholarly journals On the viscous hypersonic blunt body problem

1964 ◽  
Vol 20 (3) ◽  
pp. 353-367 ◽  
Author(s):  
William B. Bush
Keyword(s):  
Blunt Body ◽  
Free Stream ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Absolute Temperature ◽  
The Body ◽  
Navier Stokes ◽  
Nose Radius ◽  
Navier Stokes Equations ◽  
Specific Heats

The viscous hypersonic flow past an axisymmetric blunt body is analysed based upon the Navier-Stokes equations. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number, P, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach number, M, and the free-stream Reynolds number based on the body nose radius, R, go to infinity, and ε = (γ − 1)/(γ + 1), where γ is the ratio of the specific heats, and δ = 1/(γ − 1) M2 go to zero.

scholarly journals Large eddy simulations in 2030 and beyond

2014 ◽  
Vol 372 (2022) ◽  
pp. 20130320 ◽  
Author(s):  
U Piomelli
Keyword(s):  
Stokes Equations ◽  
Academic Community ◽  
Large Eddy Simulations ◽  
Navier Stokes ◽  
Academic Environment ◽  
Flow Conditions ◽  
Local Flow ◽  
Navier Stokes Equations ◽  
The Past ◽  
Large Eddy

Since its introduction, in the early 1970s, large eddy simulations (LES) have advanced considerably, and their application is transitioning from the academic environment to industry. Several landmark developments can be identified over the past 40 years, such as the wall-resolved simulations of wall-bounded flows, the development of advanced models for the unresolved scales that adapt to the local flow conditions and the hybridization of LES with the solution of the Reynolds-averaged Navier–Stokes equations. Thanks to these advancements, LES is now in widespread use in the academic community and is an option available in most commercial flow-solvers. This paper will try to predict what algorithmic and modelling advancements are needed to make it even more robust and inexpensive, and which areas show the most promise.

Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Giulio Croce ◽  
Olga Rovenskaya ◽  
Paola D'Agaro
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mach Number ◽  
Heat Sink ◽  
Conjugate Heat Transfer ◽  
Stokes Equations ◽  
Heat Transfer Analysis ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Navier Stokes Equations

A fully conjugate heat transfer analysis of gaseous flow in short microchannels is presented. Navier–Stokes equations, coupled with Maxwell and Smoluchowski slip and temperature jump boundary conditions, are used for numerical analysis. Results are presented in terms of Nusselt number, heat sink thermal resistance, and resulting wall temperature as well as Mach number profiles for different flow conditions. The comparative importance of wall conduction, rarefaction, and compressibility are discussed. It was found that compressibility plays a major role. Although a significant penalization in the Nusselt number, due to conjugate heat transfer effect, is observed even for a small value of solid conductivity, the performances in terms of heat sink efficiency are essentially a function only of the Mach number.

Thermal Details in a Rotor–Stator Cavity at Engine Conditions With a Mainstream

1992 ◽  
Vol 114 (2) ◽  
pp. 446-453 ◽  
Author(s):  
S. H. Ko ◽  
D. L. Rhode
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Flow Conditions ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Purge Flow ◽  
Compressible Turbulent Flow

This investigation involves a numerical study of enclosed Rotor–Stator cavities of gas turbine engines. The complete elliptic form of the 2-D, axisymmetric Navier–Stokes equations for compressible turbulent flow were solved. Included are the complete fluid and thermal effects of the hot mainstream gas interacting with the cooling cavity purge flow at actual engine flow conditions for generalized geometries. Additional flow conditions above and below those for engine nominal conditions are also considered. The relationships among the important flow parameters are investigated by examining the entire set of computations. The predictions reveal that a small recirculation zone in the stator shroud axial gap region is the primary mechanism for the considerable thermal transport from the mainstream to the turbine blade root/retainer region of the rotor.

The Effect of Midplane Guide Vanes in a Biplane Wells Turbine

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Tapas K. Das ◽  
Abdus Samad
Keyword(s):  
Stokes Equations ◽  
Guide Vane ◽  
Flow Analysis ◽  
Leading Edge ◽  
Navier Stokes ◽  
Flow Conditions ◽  
Wells Turbine ◽  
Navier Stokes Equations ◽  
Guide Vanes ◽  
Ansys Cfx

Guide vanes (GVs) improve the performance of a turbine in terms of efficiency, torque, or operating range. In this work, a concept of different orientations of GVs in between a two-row biplane wells turbine (BWT) was introduced and analyzed for the performance improvement. The fluid flow was simulated numerically with a commercial software ANSYS CFX 16.1. The Reynolds-averaged Navier–Stokes equations with the k-ω turbulence closure model were solved for different designs and flow conditions. For the base model, the results from simulation and experiments are in close agreement. Among the designs considered, the configuration, where the blades are in one line (zero circumferential angle between blades of two plane) and the midplane guide vane has concave side to the leading edge of the blade, performed relatively better. However, the performance was still less compared to the base model. The reason behind the reduction in performance from the base model is attributed to the blockage of flow and the change of flow path occurring due to the presence of the midplane GVs. The flow analysis of different cases and the comparison with the base model are presented in the current study.

On the suppression of shock-induced separation in Bethe–Zel'dovich–Thompson fluids

1999 ◽  
Vol 393 ◽  
pp. 1-21 ◽  
Author(s):  
M. S. CRAMER ◽  
S. PARK
Keyword(s):  
Boundary Layer ◽  
Single Phase ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dense Gas ◽  
Navier Stokes Equations ◽  
Compression Waves ◽  
Specific Heats ◽  
Bzt Fluids ◽  
Steady Laminar

We consider the reflection of oblique compression waves from a two-dimensional, steady, laminar boundary layer on a flat, adiabatic plate at free-stream pressures such that dense-gas effects are non-negligible. The full Navier–Stokes equations are solved through use of a dense-gas version of the Beam–Warming implicit scheme. The main fluids studied are Bethe–Zel'dovich–Thompson (BZT) fluids. These are ordinary gases which have specific heats large enough to cause the fundamental derivative of gasdynamics to be negative for a range of pressures and temperatures in the single-phase vapour regime. It is demonstrated that the unique dynamics of BZT fluids can result in a suppression of shock-induced separation. Numerical tests performed reveal that the physical mechanism leading to this suppression is directly related to the disintegration of any compression discontinuities originating in the flow. We also demonstrate numerically that the interaction of expansion shocks with the boundary layer produces no adverse effects.

scholarly journals Thermal Details in a Rotor-Stator Cavity at Engine Conditions With a Mainstream

1991 ◽  
Author(s):  
S. H. Ko ◽  
D. L. Rhode
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Flow Conditions ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Purge Flow ◽  
Compressible Turbulent Flow

This investigation involves a numerical study of enclosed rotor-stator cavities of gas turbine engines. The complete elliptic form of the 2-D, axisymmetric Navier-Stokes equations for compressible turbulent flow were solved. Included are the complete fluid and thermal effects of the hot mainstream gas interacting with the cooling cavity purge flow at actual engine flow conditions for generalized geometries. Additional flow conditions above and below that for engine nominal conditions are also considered. The relationships among the important flow parameters are investigated by examining the entire set of computations. The predictions reveal that a small recirculation zone in the stator shroud axial gap region is the primary mechanism for the considerable thermal transport from the mainstream to the turbine blade root/retainer region of the rotor.

Sign in / Sign up

Export Citation Format

Share Document